Stefan Mehedinteanu
email: s.mehedinteanu@yahoo.com

Electrons Ejected Due of Light Irradiation of Hydrogen/Deuterons Layer on Metals -A New Source of Instant Electrical Energy

Keywords: numbers: 52.25.-b, 31.15.-p, 32.70.-n

Based on the previously author works about models on nucleons structure and on the bias current inside valence nucleons during decay   ) decayed to  W pairs during Spacetime fabric along Universe Evolution Epochs, to the boundaries (CFT) giving the first geodesic (object dimension). This necessary energy-QET in the nucleon to create  W pairs is always here as explain the free nucleons decay. This advanced ions screening, that permit the neighborhood ions to fall-in the Einstein Ring due of lost of the kinematic equilibrium of the electron on the orbit , that enhancement of the packing into a nucleus (nucleosynthesis).

The state of art

[Kr] 4d 10 5s 2 5p 6 per shell 2, 8, 18, 18, 8 135 Xe syn 9.14 h β - 1.16MeV Cs 135 Fort_22.inp for Xe 54.00 9 2 8 0.00 : z nc nv iexc rnlc 1 0 2.00 : n l f 2 0 2.00 2 1 6.00 3 0 2.00 3 1 6.00 3 2 10.00 4 0 2.00 4 1 6.00 4 2 10.00 5 0 2.00 5 1 6.00 2 h : lmax s_pp_def An atom's nth electron shell can accommodate 2n 2 electrons,

Core charge can also be calculated as 'atomic number' minus 'all electrons except those in the outer shell'. For example: Chlorine (element 17), with electron configuration 1s 2 2s 2 2p 6 3s 2 3p 5 , has 17 protons and 10 inner shell electrons (2 in the first shell, and 8 in the second) so:

Core charge = 17 -10 = +7

A subshell is the set of states defined by a common azimuthal quantum number, ℓ, within a shell. The values ℓ = 0, 1, 2, 3 correspond to the s, p, d, and f labels, respectively. The maximum number of electrons that can be placed in a subshell is given by 2(2ℓ + 1). This gives two electrons in an s subshell, six electrons in a p subshell, ten electrons in a d subshell and fourteen electrons in an f subshell.

In [4a], about the interaction of hydrogen with palladium surfaces, although bulk palladium can absorb large amounts of hydrogen, the most favorable position for hydrogen is on the surface, not in the bulk. Here, the adsorption energy of atomic H on Pd(100) in the fourfold hollow ~ 0.45 eV and in the bridge position ~0.15 eV that are near constant as a function of the coverage (0.25÷1), that were determined by density functional theory calculations within the local density approximation (LDA) using the FP-LMTO method and by DFT calculations employing the generalized gradient approximation (GGA) for the exchange-correlation functional and using ultrasoft



stimulation by a laser, in the present one is analyzed the feasibility of these experiments. Thus, by using QM&MD programme: fhi98md is confirmed the apparition of high Hydrogen (Deuterium) coverage (at ~pm distances) of the surface of Pd lattice, mainly due of the Hydrogen or Deuterium screening by Pd valence electrons, the same for the graphene case, just near nucleons' Einstein Ring. Also is proved the author's model of vortex assisted photon beta decay, when a laser photon makes this process much more probable by creating a spot (melt) in nucleon with suppressed order parameter that lowering the energy barrier for vortex crossing together with an heavy electron (bias current  e ) as resulting from the decay of the permanent rate of bosons pairs as produced inside nucleons by a Schwinger effect of the nucleon's inner Electro-Magnetic (EM) field. Then, if is used lasers of modest power it can appears a net gain of ~20. At this high coverage fraction, the H(D) ions at a deep screening near ground state is followed by an electron expulsion, and of proton charge neutralized (like a neutron). In the following, is definitively elucidated the physical basis of the Einstein ring, as due of a QCD operation in case of bulk nucleons when is itself infused a quantum energy teleported (QET) that corresponds to stress-energy tensor as discretized into  n sheeted Riemann surfaces glued, through quantum vacuum bosonic fields alias the remnant gravitons of the Quantum existing primordial micro-black (white) halls ( Hs W B ) (

Based on the previously author works about models on nucleons structure and on the bias current inside valence nucleons during decay   stimulation by a laser, in the present one is analyzed the feasibility of some experiments to prove this theoretical finding [1].

The adsorption and absorption of hydrogen on palladium are described in [2a], when the binding energies of about 22, 25, and 35 kcal/mole were observed, and the saturation coverage at 300 °K was 0.39 H/Pd and at 200 °K this value was increased to 0.95 H/Pd.

In [2b], the neutron diffraction studies have shown that hydrogen atoms randomly occupy the octahedral interstices in the metal lattice (in a fcc lattice there is one octahedral hole per metal atom). The limit of absorption at normal pressures is PdH 0.7 , indicating that approximately 70% of the octahedral holes are occupied. The absorption of hydrogen is reversible, and hydrogen rapidly diffuses through the metal lattice.

The process of surface absorption of hydrogen has been shown by scanning tunneling to require aggregates of at least three vacancies on the surface of the crystal to promote the dissociation of the hydrogen molecule [START_REF] Mitsui | Dissociative hydrogen adsorption on palladium requires aggregates of three or more vacancies[END_REF].

Since the structure of the atoms is:

Pd: [Kr] 4d 10 2, 8, 18, 18; Kr: [Ar] 3d 10 4s 2 4p 6 2, 8, 18, 8

Ar: [Ne] 3s 2 3p 6 2, 8 ,8 Ne: [He] 2s 2 2p 6 He: 1s 2 2 , in order to obtain the inputs fort.11 and fort.12 together with start.inp for fhi98start and fhi98md we use for fhiPP the input:

fort_22.inp for Pd 46.00 8 3 8 0.00 : z nc nv iexc rnlc 1 0 2.00 : n l f 2 0 2.00 2 1

6.00 3 0 2.00 3 1 6.00 3 2 10.00 4 0 2.00 4 1 6.00 4 2 9.00 5 0

1.00 5 1 0.00 2 h : lmax type Xenon pseudotentials (US-PP). The coverage is defined as the number of hydrogen atoms per primitive surface unit cell. Adsorption in the fourfold hollow position is much more favorable than at the bridge position. This is a general trend for hydrogen adsorption on low-index Pd surfaces: hydrogen generally prefers to adsorb at the highly coordinated sites.

In [4b], they report on the ability of freestanding single layer graphene to provide tens of electrons for charge neutralization of a slow highly charged ion within a few femtoseconds. The amount of charge transferred to the highly charged ions (HCI) can be estimated by measuring the distribution of exit charge states out q and the energy of highly and velocities below 0.5 nmfs -1 were used. Ions are transmitted through SLG under normal incidence and analyzed with respect to their charge state and kinetic energy by an electrostatic analyzer .

   4 . 3 h
is the width of the graphene layer. In this case, the elastic collisions (nuclear stopping) may cause direct knockout of carbon atoms, but less than one carbon atom is sputtered on average by a 10-100 keV Xe ions. Even if point defects are produced, they will likely disappear due to dissociation of ubiquitous hydrocarbon molecules. The absence of any traces of largescale lattice deformations thus confirms the intrinsic ability of suspended SLG to locally sustain exceptionally high current densities, even though it cannot efficiently diffuse heat to a substrate.

The HCI starts capturing electrons from graphene already at 9Ȧ. The strong attractive potential accelerates electrons towards the HCI and, approximately, half of them end up captured by it along the incoming path before penetration into the graphene sheet. The induced electronic charge density as the HCI approaches the graphene layer has two components : one is formed by the convoy electrons around the HCI position, forming an asymmetric wake potential that slows down the ion, and the other one is located at the graphene layer due to the target polarization. Both components merge as the HCI gets closer to the target and forward electron emission starts. Finally, after crossing the layer the projectile is nearly neutralized and the corresponding induced electronic charge is centred around the HCI along its outgoing path. The actual HCI is probably not fully relaxed at the instant of crossing the graphene layer and, therefore, it still suffers a number of autoionization processes and subsequent de-excitation without a significant energy loss.

The Einstein Ring around nucleons

In quantum gravity, a virtual black hole is a black hole that exists temporarily as a result of a quantum fluctuation of spacetime [START_REF] Mitsui | Dissociative hydrogen adsorption on palladium requires aggregates of three or more vacancies[END_REF] cited in [START_REF] Mehedinteanu | A New Mechanism: AdS/QCD(QET)/CFT/GW to Fabric of Spacetime[END_REF]. Theoretical arguments suggest that virtual black holes should have mass and the lifetime on the order of the Planck particles. Therefore, we consider the Micro-black-holes pairs, that occur with a number density of approximately one per Quantum bubble[3a]cited in [START_REF] Mehedinteanu | A New Mechanism: AdS/QCD(QET)/CFT/GW to Fabric of Spacetime[END_REF], that means one per quantum bubble volume , the age of the Universe.

Considerations on The Fabric of Spacetime Around Objects

These are obtained by using well-known Inflation models [16a-d] cited in [START_REF] Mehedinteanu | A New Mechanism: AdS/QCD(QET)/CFT/GW to Fabric of Spacetime[END_REF], where the scale leaving the horizon at a given epoch is directly related to the number

 dN k d  
, and therefore

) ( ) ln(  N k k end  , or, ] [m ke k N end 
, where end k is the scale leaving the horizon at the end of slow-roll inflation, or usually ] [

1 1 m k k end    , the correct equation being ] [ 1   m e k k N end .
During Universe evolution, the horizon leave is when

a a G a   3 4 2 3 2   2 2 2 8 c p c G a a             ] [ 3 m kg  ; energy density 2 c p   
If we divide with 2 a we obtain for outside (low density) the object as a pushing GW wave (BH, planets, stars etc.)

] [ ] [ 2 2 3 4 3 4 3 2 3 2 2 2 2            m n a c G a c GE a c G a GM s H a a g merging at   ; (3)
, where:

g g E n   ;   g P g merging at n n     ;   3 4 3 a M  ; 2 Mc E  ; BH BH m n M    ; the scalar curvature is 2 2 6H R 
. For inside of the objects as given by equation (v) from [START_REF] Mehedinteanu | A New Mechanism: AdS/QCD(QET)/CFT/GW to Fabric of Spacetime[END_REF]:

] [ 3 8 2 2   s H n G 
; n -the number of boundary points (v)

During Universe evolution at Electroweak epoch [START_REF] Mehedinteanu | A New Mechanism: AdS/QCD(QET)/CFT/GW to Fabric of Spacetime[END_REF] when, with the gravitons released from the nucleon's horizon as a quantized mass, , that of an energy

        . Now, from
J a c EW g 26 10 2       (when it born !) ; and when 1   leave leave leave H k a , of  W mass kg M W U 25 _ 10    inside the nucleon; 2 _ c m c W BH C     ;
In the following, by a QCD operation in case of bulk nucleons is self infused a quantum energy teleported (QET) that corresponds to stress-energy tensor as discretized into  n sheeted Riemann surfaces glued, through quantum vacuum bosonic fields alias the remnant gravitons of the Quantum existing Hs W B ) (  decayed to  W pairs during Spacetime fabric along Universe Evolution Epochs, to the boundaries (CFT) giving the first geodesic (object dimension) [START_REF] Mehedinteanu | A New Mechanism: AdS/QCD(QET)/CFT/GW to Fabric of Spacetime[END_REF]. This necessary energy-QET in the nucleon to

          w BH g merging at n n  
, which is a very small interaction gravitons fraction of  W transferred as QET (see below) to the horizon where is generated as gravitational wave (GW) that deforms the space it creating the Einstein Ring, or the curvature radius givens by eq. ( 2) from [START_REF] Mehedinteanu | A New Mechanism: AdS/QCD(QET)/CFT/GW to Fabric of Spacetime[END_REF], ]

[ 10 3 . 1 10 m R   
. If the electrons screening of nearer nucleons is sufficiently to attain this dimension, the breakup of theirs kinematic equilibrium (centrifugal force and Spining) it means theirs fall in this curvature radius (Einstei Ring) that producing a packing like in nucleonsynthesis.

But what happen in case of solid compact objects (with nucleonic structure)? We know, that the penetration of gluons magnetic B flux inside of an nucleon [START_REF] Mehedinteanu | On the Acceleration of Beta Nuclides Decay by the Photonuclear Reaction[END_REF] , [START_REF] Suganuma | Lattice QCD Study for Confinement in Hadrons[END_REF], see figure 4

., is ] [ . . . 2 / 1 2 2 0 m e n c m s            , m-gluons mass, s n -number of gluons per 3 ] [m , C Js Tm e e usually e c       ] [ 15 07 . 2 2 0    
, where from [START_REF] Mehedinteanu | The Numerical Analysis of Beta Decay Stimulation by the High Thermal Spike of Photon Incidence to Valence nucleons[END_REF] we have

x x B    2 log 2 2 ) ( 2 0   ,   x , where 78 . 1   C e  ( C is Euler's constant),
         2 2 2 0 2 2 Am J e B  



In the case of a homogeneous potential directed along the z-axis [START_REF] Grasso | Potential s in the Early Universe[END_REF], the Einstein stressenergy tensor is:

   8 2 2 0 33 22 11 00 B c T T T T B       ; 0 0  i T
, where ] [ Here, the Hubble constant is defined as

4 3 4 2 ) ( 3 8 c c GV H    in ] [ 2  m , (v') at Compton length mc l C  
that result the electric field:

3 0 2 ) ( ) (   e C V E   , The energy is ] [ 8 2 2 0 J V V B c V vol B vol        ; 3 8 ) 4 ( 2 C C c C vol V       ,
We can rewrite eq. (v') as: with

c M U C    ] [ 3 8 ) ( 3 8 ) ( 3 8 2 4 3 4 3 2 3 4 4 3 4 2     m c n nV G c c M GV c c GV H C U C       Or, 2 2 3 2 2 2 3 8 3 8 nc G c n GM H a a C U        
; where the total mass is

2 c V n M U  ; 2 c U M U  ; R GM U 2  -the gravitational potential, or 3 C U nl M   ; object U M M  Thus, we obtain the expression ] [ 3 4 3 4 ] [ 3 4 ] [ 2 2 2 3 2 2 3 3 2 2 2 2          m c l n M G c G s a a G s H a a C merging at U       (2) 1 
 H R Also, the deformation could be done as (author' approach based on the eq. ( 12) from [START_REF] Jacobson | Horizon Entropy[END_REF]:

end ab k T   1   ;
where

G c   8 2 
as Newton constant, and the stress-energy tensor arrived in CFT layer

(horizon) is   3 28 2 _ 10 43 . 1 m kg V c n T layer GW g horizon g ab          ; where 3 _ _ C merging at g layer GW n V     ,



. To note that this deformation is the same as in case of the lensing of Earth [START_REF] Mehedinteanu | A New Mechanism: AdS/QCD(QET)/CFT/GW to Fabric of Spacetime[END_REF] A such GW can deforms the space around the nucleons, that any incoming outwards nucleon fall-in, that facilitates the eventually theirs fusion if is screened the Coulomb repulsion, like above, when the Xe lost theirs electrons.

Casimir effect a proof of gravitons existence

The Casimir energy is .

How the stress-energy tensor is effectively teleported to CFT-boundary?

The ground-state energy is called the zero-point energy. This simple example exposes that zero-point fluctuation is capable of carrying nonzero energy. And it is not only the harmonic oscillator but also other general interacting many-body systems that have zeropoint fluctuation with nonvanishing energy in the ground state, like bosonic field etc. Each subsystem is fluctuating with nonzero energy density in the ground state.

In the ground state of an ordinary many-body system, like for a quantum field, there exists a quantum correlation called entanglement [START_REF] Grasso | Potential s in the Early Universe[END_REF] among zero-point fluctuations of the subsystems. Zero-point fluctuations of the vacuum in regions A and B are correlated due to the kinetic term of its Hamiltonian ref.

[22] cited in [START_REF] Mehedinteanu | What Is Gravity and How Is Embedded in Mater Particles giving them mass (not the Higgs _eld)?[END_REF]. By virtue of the existence of entanglement, when local zero-point fluctuation is measured at a position, the measurement result includes information about quantum fluctuation at a distant position. This vacuum-state entanglement is at the heart of the quantum energy teleportation (QET) protocol with quantum fields, see [START_REF] Mehedinteanu | What Is Gravity and How Is Embedded in Mater Particles giving them mass (not the Higgs _eld)?[END_REF]. This QET mechanism can be summarized using an analogy as follows. The zero-point energy, which will become the output energy , 20 and 40 capture ~9, ~17 and ~34 electrons during the passage through the graphene layer, respectively.

B E  of QET,
In the following, we can say that these experimental results legitimate more our previously works [7a] and the present one, when we substitute the ruly pseudo-potential ( QM-code input) for hydrogenlike atoms (including alpha) with the screened Coulomb potential as deduced from the well-known Gamow alpha decay theory [7a].

Potential energy (chemisorptions) of a H atom over a fcc hollow site of a Pd(111) surface as a function of the distance from the surface for a frozen substrate , have been determined by DFT-GGA calculations as of ~-0.23÷0.3÷0.2eV for distances ~-1÷0÷1 Å, for a coverage of θ= 1, and of θ= 1/3.

In present work we done a similar calculation with the program fhi98md [START_REF] Bockstedte | Density-functional theory calculations for polyatomic systems: Electronic structure, static and elastic properties and Abinitio molecular dynamics[END_REF], [6]. In the following being calculated the electrical current as resulting from laser irradiation of these H(D) Pd coverage.

The gravitational charge quantization

Now, to remember from author's work [START_REF] Mehedinteanu | What Is Gravity and How Is Embedded in Mater Particles giving them mass (not the Higgs _eld)?[END_REF],

P m G
is the gravitational charge defined by L. Motz as resulting from:

2 2 1 r m G m G F G 
, where it can say that the gravitational charge

1 m G q  is the source of gravitational field 2 1 r m G
at the distance r , and that this field is coupled to the gravitational charge 2 m G at the position r (relative to the source of the field ) via the product of the field strength and the charge. L. Motz derived the quantization condition on gravitational charge in a similar manner by noting that moving particle with velocity V  and with gravitational charge

P m G
is coupled not only to the Newtonian gravitational fields of all other particles (the gravielectric field ) in the usual way, but also to the Coriolis field v m   divided by gravitational charge P m G , due of the inertial Coriolis force, see figure 2 (defined as

r mv v m F P C 2 2       ), by means of the cross product     G c c V m G P    2 
, see below.

The gravimagnetic field, in GEM equations, we have:

  B v E q F e   
, or equivalently ) 4 (

g g B v E m F    ; rmv L  ; the electrical field 2 0 4 r q E   ; the gravitelectric field ] [ ] [ 4 1 2         s B ms B v m F g E g g g



; the mass with the charge and the mass density with the charge density, so, the gravimagnetic field is

G c m G F q F E P C C g     .
This cross product term give rice to an angular momentum is proportional to moment of inertia I and angular speed  ,

 I L  . Because m r I 2 
for a single particle and r v   for circular motion, angular momentum can be expanded as rmv L 

, or,

v rm L P 
the component in the motion of the particle which is of the order of

 2 2 r m L P 
and is parallel to the field   .

Therefore, it is obtained the quantization condition as:

 2 2 2    r m L P .
Since it was interested in the quantization of fundamental gravitational charge, it is found a value for r and  that must be associated with such charge. To do this, L.Motz considered the Universe to two such charges in gravitational equilibrium and resolving about each other in the first Bohr orbit. The radius of this orbit is just 3 2 P Gm r   , which it was taken as to be r . In this case (unlike the standard Coriolis force), the force is not fictional, but is due to frame dragging induced by the rotating body when , and introducing into Coriolis force expression This will be so only if

G C F r G m v r c m GL v m F    
c r v   
is of the order of c since the centrifugal force (being

charge times field) is just     G c m G  2 
. Introducing these two relationships into the above quantization equation, is obtained

 2 2   cr m L P
, or, substituting for r as Bohr orbit when the electron is held in a circular orbit by electrostatic attraction, after some manipulations:

; This it was demonstrated by using a code package fhi98md which is an efficient code to perform density-functional theory (DFT) total-energy calculations for materials ranging insulators to transition metals [START_REF] Bockstedte | Density-functional theory calculations for polyatomic systems: Electronic structure, static and elastic properties and Abinitio molecular dynamics[END_REF], [6], [START_REF] Mehedinteanu | ON THE NUMERICAL ANALYSIS OF DECAY RATE ENHANCEMENT IN METALLIC ENVIRONMENT[END_REF]. The package employs first-principles pseudopotentials, and a plane-wave basis-set, and is used to done a special calculus for some metals (Pd) where are depozided on the surface and implanted interstitially 1;2;3 H ions. The package fhi98md is an efficient code to perform density-functional theory totalenergy calculations for materials ranging insulators to transition metals. The package employs first-principles pseudopotentials, and a plane-wave basis-set. For exchange and correlation both the local density and generalized gradient approximations are implemented.

P m m  , 0 4 1   e k ; with  n mvr  ,   2 2   mvr ; 1  n ; m e k
In Polly-atomic systems as for example molecules, crystals, defects in crystals, surfaces, it is highly desirable to perform accurate electronic structure calculations, without introducing uncontrollable approximations. The emergency functional the key variable in DFT is the electron density n (r). Consequently, the complementary tool from the all package FHIPP it was used to obtain the pseudo-potentials of H(D), Pd. Thus, is suficiently to substitute the ruly pseudopotential ( QM-code input) for hydrogenlike atoms (including alpha) with the screened Coulomb potential as deduced from the well-known Gamow alpha decay theory.

All that our suggest to use for hydrogen-like atoms (for other atoms are kept the original formulations) the pseudo-potential form, so neglecting the non-local contributions at the level of atom itself, respectively:

  R r for r e Z Z D o   2 4 1  
In [1] cited in [START_REF] Mehedinteanu | ON THE NUMERICAL ANALYSIS OF DECAY RATE ENHANCEMENT IN METALLIC ENVIRONMENT[END_REF] , an explanation of the large screening was suggested by the Debye plasma model applied to the quasi-free metallic electrons. In this approach, they combined the Drude model of metals (with a kinetic energy 0.5 kT for the quasi-free valence electrons) with the Debye model of plasma: the Drude-Debye model, in short Debye model. The electron Debye radius around the deuterons in the lattice is given by

  2 / 1 2 / 1 2 0 ) / ( 69 / a eff a eff D n T n e kT R     
(m), with the temperature T of the quasi-free electrons in units K, n eff the number of thesis electrons per metallic atom and the atomic density  a in units of atoms m -3 . For T = 293 K ,  a = 6 x 10 28 m -3 , and n eff = 1, is obtained a radius R D , which is about a factor 10 smaller than the Bohr radius of a hydrogen atom, therefore, we have The input is obtained with fhi98start applied to files start.inp and inp.mod, that obtaining inp.ini as an input to fhi98md plus the pseudopontetials fort for each species [START_REF] Mehedinteanu | ON THE NUMERICAL ANALYSIS OF DECAY RATE ENHANCEMENT IN METALLIC ENVIRONMENT[END_REF]. In figure 1

 stimulation by a thermal spike of a photon

In order to accelerate the decay   by a single photon reaction, a new model it was proposed in [START_REF] Mehedinteanu | ON THE NUMERICAL ANALYSIS OF DECAY RATE ENHANCEMENT IN METALLIC ENVIRONMENT[END_REF], [8], [START_REF] Bulaevskii | [END_REF] to calculate a direct reaction of single photon with one of nucleon of the valence n-n; p-p; n-p pairs (see IBM model [30,31]cited in [START_REF] Mehedinteanu | ON THE NUMERICAL ANALYSIS OF DECAY RATE ENHANCEMENT IN METALLIC ENVIRONMENT[END_REF]) of the nucleus, that being in the unstable state ( a decay   nuclide), they are the most susceptible to react with the photon, see some of model's results from [START_REF] Mehedinteanu | ON THE NUMERICAL ANALYSIS OF DECAY RATE ENHANCEMENT IN METALLIC ENVIRONMENT[END_REF], figures

4 1  , respectively.
The interaction between a photon of high energy and of low band width

3 10    E E
and of nucleon into state of excitation has been characterized by the beta decay energy  Q from the nuclei, that is viewed as a direct reaction, without the formation of a compound nucleus. Essentially, the general picture of this model described in details in [8], [START_REF] Mehedinteanu | The Numerical Analysis of Beta Decay Stimulation by the High Thermal Spike of Photon Incidence to Valence nucleons[END_REF], [10a], [10b] is that the vortex (boson W , figure 3.) crossing may trigger the n s  transition. A photon makes this process much more probable by creating a spot (melt) with suppressed order parameter and thus with lower energy barrier for vortex crossing. A sketch of the strip and of the belt across are shown in Figure 4, the induced vortex crossing together with an electron (travel current  e ), which turns superconducting hot belt into the normal state resulting in a vortex assisted photon beta decay. As a consequence of the Lorentz force acting on a vortex crossing a thin and narrow current-biased strip the energy c I 0  is released, which for currents I > 0.6Ic suffices to create a normal belt across the entire width w of the strip (extending to a few correlation lengths ξ along the strip). Therefore, by using the same nucleon model we can account for a vortex (W boson) assisted photon count rate, as in The effective ohmic resistance is R eff = R s R/( R s + 2π(ξ/w) 2 R ).

[8], [9a], [9b]:   ) exp( 1    h pc R R ,where: 1 2 1 2 0 2 4 ) , (                  h ch h eff B h I I w TR k I R            I I I I R ch ch h GL h ln 1 1 0 1             The current being   2 3 0 0   h c ch I I    ] [ 10 2 8
We can suppose than along the hot belt induced by the incident photon , the charge

   W e creates a bias current(   e e I h 2 ] 3 ) ( 1 [ 3 2 2 3 0     
, see below, who circulates due of the potential difference between the vortex and the rest of isotope.

At the first sight, the ohmic resistance of this ad-hoc electrical circuit created by the bias current is given as:

2 1 1 vortex GL V U R    
,where the vortex potential is

 0 H V vortex  , 0
H -an "external" electro-magnetic field of a dipole created by the pair u u (the chromoelectrical field) , but here is used as

         C N e
       2 0 Am J H B 
, and the characteristic distance    , the coherence length, and the power is

    ) (   W vortex U , with ] [ 24 5 . 1 ) 8 ( s e T k c B GL       -the Ginzburg-
         ;    143 1 R ;  1000 s R ;  141 eff R , fm w 1  . With ] [ 10 2 2 15 0 Tm     ; fm 117 . 0   ;   x , it results ] / [ 10 6 . 3 2 7 0 fm A I c   , I c0W =I c0 .W rate =3.6x10 7 .10 -8 =0.36[A/fm 2 ] 9 . 6 / 10 5 11 _ 11 11 _ 0 11 _      prag prag h h E E   , 9 . 6 / 10 6 . 9 9 _ 14 9 _ 9 _ 0 9 _      prag prag h h E E   ; that results 1 18 10 7 . 3    s R  The total
           , 2 1fm area  ; the production rate of W ± =10 -8 , ] [ 7 V I R U eff   ; 138 . 0 0  c I I
as obtained by trials (figure 5), and where h 0  is obtained by using the lower critical field , with the incident of single photons rate of

                  
s counts R ph / 10 5 13   , 1  h pc R R
, for all beta-decay isotopes, i.e. these rates are not dependent of the nuclide type, the photons energy needs to be above a threshold energy value of very precise value inside the nucleon (see section 3.2 below), which can decay into heavyelectrons (muons) but more sure into electrons, and also is released the remnant graviton of the inside nucleon primordial BHs  pair as a QET, as to be later extracted as GW that generates the curvature radius (Einstein Ring). In the second case of Nd:YAG laser when



, for an absorption coverage area of Pd/H~1; 1 Bohr=5.29x10 -11 [m], or about ~2x10 9 /10 8 =20 than the power used to produce a such laser spot. These values are in case of ELI-laser when: the power is ~2Pw, the flux ~10 13 ph/s; flux~10 24 w/m 2 , or the extracted power is lower~ 1.4x10 8 /2x10 15 =0.7x10 -7 times that used by the laser, or without any energy gain. But we can obtain a net energy gain if use, example, a smaller laser Nd:YAG when the flux ~10 13 ph/s, or

K T 9 10 
, but not smaller than this lower limit value, since the current through the "hot belt" is the same i.e. ~ ) at 532 nm and normally 10 Hz repetition rate , of 0.2 J pulses with 5 ns pulse length ejects ions with energies in the MeV range. The nsresolved signal to a collector can be observed directly on an oscilloscope, showing ions arriving with energies in the range 2-14 MeV/u at flight times 12-100 ns, mainly protons from p n  transformation , and deuterons ejected by proton collisions. An expected signal at several mA peak current corresponds to 1×10 13 particles released per laser shot and to an energy release > 1 J assuming isotropic formation and average particle energy of 3MeV as observed, or ) by the laser stimulated beta decay, so there is "not any fusion", see below. If an experiment it will be done, that it will be for the first time when the findings confirm author's models [START_REF] Mehedinteanu | ON THE NUMERICAL ANALYSIS OF DECAY RATE ENHANCEMENT IN METALLIC ENVIRONMENT[END_REF], [8], [START_REF] Bulaevskii | [END_REF], the most important are, the particles energy in MeV range, and the electrical current of ~few mA, remaining to be confirmed the number of particles, respectively of ~10 10 per laser shot. This vortex-assisted mechanism may be verified by application of magnetic fields, which effectively enhance ch I along with the vortex crossing rates but do not affect the creation of hot spots by photons.

The free neutron decay calculation

In the following, we will use some results of section

C N E e c m E c         ; ] [ 10 7 . 3 19 T c E B    .
From the section (4.1b) of [8], are used the bosons  W pairs generated inside the nucleons as due of one quark u u u  as a resultant of 3  flux tubes vortex potential , see figure (1.b)

of [8], respectively

GeV mc 81 2    -which after the release of an electron that it getting the final beta energy as been equally to the out of barrier turning point after the tunneling, and accounting for the valence nucleons interactions (shellenergy levels). The number of assaults of the barrier, like in Gamow theory [START_REF] Mehedinteanu | On the Acceleration of Beta Nuclides Decay by the Photonuclear Reaction[END_REF][START_REF] Suganuma | Lattice QCD Study for Confinement in Hadrons[END_REF] cited in [6] .

In case of WKB [START_REF] Mehedinteanu | On the Acceleration of Beta Nuclides Decay by the Photonuclear Reaction[END_REF] cited in [6], the transmission coefficient is

r Q V m T     2 2 ,
and the decay constant

T a e n    .
For the thick barrier the transmission coefficient is

b mQ v Qb T   2 2 2     ;
, where, the kinetic energy of the particle after the barrier at b

                            E E E
) ( 3 g q q vortex u u   of GeV V 80  , results as a vol n s V V R s R      1 18 10 3 . 2 , where ] 1 [ 10 2 3 71 s m V R   and the volume is b C vol V m V      ] [ 10
W V V R R Compton      8 10
. Thus, it results a main conclusion of this investigation, namely, that the "interacting" potentials inside the nucleons are that were already established in [ for beta-decay. In our understanding, the created electron takes the energy at the turning point out of the barrier equally with the electron itself for unbounded neutrons, or that of the binding energy of nucleon in isotope nucleus, when it passes the barrier of gluon condensate characterized by an quantum tunneling suppression given as: W is the same as to be the necessarily energy to traverse the gluonic barrier, when it decays into  e at the end. The free neutron decay Consequently, for the   decay process, the energy combines well with the existing one, that releasing an electron which penetrates barrier: In case of   decay, it can only happen inside nuclei when the daughter nucleus has a greater binding energy (and therefore a lower total energy) than the mother nucleus. The difference between these energies goes into the reaction of converting a proton into a neutron, a positron and a neutrino and into the kinetic energy of these particles. Thus, an opposite process to the above negative beta decay,   decay of nuclei (only bounded proton) when , like at LHC when the gluonic "cover" of protons it was "melted (at least 2 gluons)", and the resulted difference ) 125 100 225 ( GeV    being just that of the Higgs boson (a quanta of energy!) which it was, in this spectacular way "released" [START_REF] Bulaevskii | [END_REF] as  2 2  g . In the process of electron capture, one of the orbital electrons, usually from K or L electron shell, is captured by a proton in the nucleus, forming a neutron and an electron neutrino.

Conclusions

In the work by using QM&MD programmes: fhi96md is confirmed a high coverage H/Pd~1. Thus, there are used the prior author models of vortex assisted photon beta decay, when a laser photon makes this process much more probable by creating a spot (melt) in nucleon with suppressed order parameter that lowering the energy barrier for vortex crossing together with an heavy electron (bias current as produced inside nucleons by a Schwinger effect. The electrical power results as P w =2x10 9 w<<P laser =2Pw for a laser spot of size m  30 , that corresponds with ELI laser characteristics, or without a any net gain of energy. For the prior author's models validation it is necessarily to do laboratory experiments in the spirit of this work, namely based on the use of a Nd:YAG laser with pulse energy of < 0. ) at 532 nm and normally 10 Hz repetition rate. Thus in this case of much smaller power lasers when per photons is obtained ~10 -5 w x1ns(T=10 9 K)~10 -14 J of duration ~1ns and, respectively ~10 -14 J.10 13 ~0.1J~10 8 [w] for a pulse composed of ~10 13 ph/s. The net energy is much higher of 2x10 8 /10 8 =20. In such experiments is expected to obtain a particles energy in MeV range, a current of ~few mA, a voltage on the shunt 7[V], and the time-of-flight 10 -8 s. If these electrons are collected either in the metallic plate in serried into an electrical circuit, or into a spherical conductive cover , we can constitute a reliable source of direct electricity with the period equally that of laser pulse frequency. It is possible that the neutron of D do not transforms into proton, since the open hot belt created due of the laser photon incidence to close after electron passage, therefore it is not a consume of D. To obtain a D LAYER the author calculated that is necessary a thermal energy of 2-3eV to be deposited on the Pd plate in the vacuum chamber containing the D gas, this being in serried into an electrical circuit. If is used the co-deposition Pd/D technique, are obtained also cold fusions together with an electrical current, that due of electrons deep screening of deuterons in lattice, as explained by the author early. It is also found that as in case of other cosmic objects, the nucleons have an Einstein Ring around Bohr 1 radius, that if we realize a screening till this radius and futher, after that the neighborhood ion fall-in the Einstein Ring that enhances the packing into a atom's nucleus (nucleosynthesis).

  the dual gauge component of the total electrical field

  The equivalence between the Lorenz force energy which squeezes the electrical field  the interface between normal and superconducting phase we have

  distance between the two attractive metallic plates (fall-in), that corresponds with the results of our model when only one graviton release of  W as GW, we have GW energy of

  a spherical body the Coriolis field is the gravitomagnetic field g B near a rotating body can be derived from the GEM equations. It is exactly half of the Lense-

2 

 2 to Mach's principle, produces the centrifugal force c m . "A very general statement of Mach's principle is "Local physical laws are determined by the large-scale structure of the universe".

  , introducing in L we have:

Figure 2 . 2 .

 22 Figure 2. Coriolis field H

  (a,b,c,d) are presented the quart-octahedral holes in Pd lattice where are placed H(D) atoms. Thus, the main results of application are for: a),b),c) : respectively, simple quartoctahedral Pd4 we have : (non-eq) total energy = -78. a.u., for 1 D atom in the proximity of 1Pd (at 0.05Bohrs) of an internal energy at zero temperature =a.u., see fig. 1(b)

Fig. 1 . 3 . 3 . 1

 1331 Fig.1. The quart-octahedral hole of Pd-H coordinates.

5 .

 5 In our first case of muons born due of hot spot 68 -of-flight. In fact, this estimate coincides with the time it takes a vortex to cross the strip being pushed solely by the Lorentz force. With these it results R ν =1018 /s. The value of prag E is determined by trials in order to have 1 The model results show that in order to have instant rates(100% decay), or a beta decay rate of

  this case we don't have a net energy gain due of the small current ] rate of bosons as the source for further electrons (muons) production by Schwinger effect

  spike, but for an entirely laser wave (10 13 photons) when pass along a

  YAG laser with pulse energy of < 0.2 J is recommended to be used, with 5

  next section. The results from our calculation, in fact the proton it could be due of the transformation a neutron of deuteron into proton (

Fig. 3 .Fig. 4 .FIG. 5 .

 345 Fig.3. Abrikosov's triangular lattice for a nucleon (author's proposal [8], [9])

  constant electric field E the separation d must be sufficiently large 2 2mc eEd  Probability for separation d as a quantum fluctuation

  using the Schwinger effect as in section 2.1 of the companion author's paper [8] , the number of  W pairs produced inside the nucleon (more inside of the only one resultant flux tube , see figures 1.a; 1.b from [8]) due of the potential resultant

3 

 3  corresponds to the height of gluon condensate barrier, due of the phase slip with  sea quarks color flux tubes, see figures 1.a; 1.b. The value of the resulting flux tube it remains as in (4.2.a) of [8], respectively of GeV 4 . 0as the string strength. Thus, the probability (rate) to produce   e W, into a more simple way-without the external interactions of the neutron (free-not bounded), is given as: by emission of an electron and an electron antineutrino to become a proton understanding this occurs when one of the down quarks ) (d in the neutron ) (udd transforms into an up quark )(u due of interacting with the charge of  W boson of the pair  W , transforming the neutron into a proton ) (uud . In mean time the other part of this pair  W boson decays into an electron and an electron antineutrino

  decay an added energy it seems to be necessarily to reduce the barrier width

  About others calculations of beta decay processes of different isotopes, see the author's work[8].

e

  ) as resulting from the decay of the of bosons pairs rate

symmetry breaking-quarks epoch (QGP)

  ) (EW or Reheating due of the quantum fluctuations a huge number of the micro-black holes as Planck particles

	The number of gravitons that has been released following BHs 	merging is only
	  curvature radius of the object R .   26 _ 1 . 26 n 10     QGP BH g merging at n 		5 96 10 10 	10		26			9 . 7		10	74	P , and these generate the n are
	generated, In other words the contribution to the space-time deformation is due of P BH m m   ; the graviton energy being at horizon leave ;
	 n	a 9 . 7 c    QGP H	2 74 10  	J 4  26  10  P 2 n	; when 12 10  , for two  a	1 merging.  H , BHs  k	a		1	;	M		53 10 2  2 .	kg	;
		g										end																leave	leave	leave	end	U
	2 Thus, from the overall balance the number of gravitons which are consumed to push the c m c BH C     ; 62 61 3 1 10 1       P available BH n V H n  , space time is : 35 18 12 5 10 10 2 10 4 10 5        P BH n   , and the remnant number is
	First step
	 BH E U  remnat P  n  n P  g	70 10 10 J 16 5  	9 10 .		J		61 10	with		BH 	_	EW		10 19	a	end		EW		10 11	GeV		J 17	, it
	results with 2 . 9  10 k leave 1  [ 19  m   1 H ] k end The Confinement into nucleons [ 10 27 1 m ] leave    ; 2 . 8  by iteration for 7 10  EW end a ; 10 18 N 1 H    ] [ 10 5 . 6 20 m R    ; ] [ 10 5 . 1 27 m l l P C With a g qq end QGP BH g q q 3 4 _ _ _ 10 7 . 3 10 9 . 8    [ m 2 . 5 ] ; GeV ; in eq. (2); t 10 3 . 3  27   10 4 . 3 1 . 2  s 10 ;              ; Confinement, where GeV a QGP end EW BH QGP BH 4 _ _ _ 10 J 26 . 1 10 9 . 7  5 at J         	, and
	Second step or when immediately, when ] [ 4 . 0 1 m k end   , a  end  BH _ q with [ 10 27 1 1 m EW _ g q ] H k      by iteration for a EW 10 10 11 11   3 10 7 . 3   , with eq. (2) GeV 2  H . 16  N ; in eq. (2); J 17 at Reheating, that results ] [ 1500 1 m end   , ] [ 1447m R  ; [ 10 2 . 9 19  1  m k end end QGP laeve leae  s c H t 6 1 10 5      , and ] [ 10 7 1 1 1 m H k H        we found we found	]
	leave 1 H   The number of gravitons that has been released following leave ; 92 . 0  EW a ; ] [ 10 20 m  ; s t 29 10 3 . 3    ; 5 . 6 R   2 . 15  N .	end merging is only ] m ; BHs [ 10 20  
	] m 26 ; 10 [ 27  10  _ n  g q q g  7 . 1   gravitons potentially to escape (an inverse process of a black-hole ) from the micro-l l P C   92 . 0  EW a ; where 96 10    P g P g n n   as a "fix" number of    79 26 10 96 10 9 . 2 10 10 4 . 3 10        merging at n , and these generate the curvature radius of the object R . blacks holes during merging in order to generate particles. In both steps the number of gravitons that has been released following BHs  In other words the contribution to the space-time deformation is due of merging is only     68 26 96 26 _ 10 10 17 17 79 10 2 10 9 . 2     P g qq H n n , for two BHs  merging. 10 10       EW BH g merging at n n  , and these generate the curvature Thus, from the overall balance of BHs  the number of gravitons consumed (via  QCD QGP EW   ) to push the space time is
	radius of the object 5 10 12 R 4 10 5 8 1   10 d 17 H     	20 10  25 . 0   . 10 35 		n		35 10	.
	P In other words the contribution to the space-time deformation in this phase is due of only 5 In other words, at Confinement it remains at least few ( 4  ) gravitons, so 68 10 5 2 10    P EW H n n , for two BHs  merging. GeV J 6 . 0 10 10 4 10 26
	BH  Electroweak The particles decay to QGP; C nucleon	m		4 . 1		22  10	kg		9 . 7		4 10	GeV	, or
																														QGP
		BH 	_	QGP	BH   	_	EW				a	end	_	QGP		9 . 7	4 10 	GeV		5  10  26 . 1	J	,
		BH 	_	EW		10 19	a	end		EW		10 11	GeV		J 17	;	a	end	EW		7 10 8  2 .	;;	k	end 1 		9 . 7	10  14 	] m [	,
	a	end	_	QGP		6 10 1  27 .	,	C 		ee		3 . 2	10  21 	[	] m	, with eq. (2)	R		2 . 1		10	7 	m	, and
	H	1  	10 7 	[	] m	,				t					H	1 	c		3 . 3	16  10 	s	,	H	1 		k	1 		H	1 		10 20 	[	] m	we found
		end																end						end	leae	laeve	EW
	N		15	.	88

  is analogous to the energy In QET, we get information about a key to the safe, allowing us to extract the zero-point energy by a remote measurement at A via the vacuum-state entanglement. However, we must pay the quantum fluctuation at A for this extraction. The cost is energy

	These results are in range of the experimentally [4b] determined energy loss for ions with
	exit charge state	q	out		2	and	q	out		4	as a function of the incident charge state	in q ,
	around 3.2keV for	q		32	. The energy of the projectiles was kept constant for all	q at
						in							in
	E 40 	keV	. Here is calculated that HCIs with initial charge states		10
	int Therefore, a such infused energy (the cost pay) is due of QCD and is necessarily to po zero E  saved in the locked safe underground. A E , which is larger than the extracted zero-point energy ) ( int B po zero E   taken from the safe at B. E extract from quantum vacuum  W bosons pairs of the bulk of the object, and the energy extracted ) ( int B po zero E E 

 at CFT (object boundary-horizon) it results from the  W decay as gravitons release (GW).

in q

  Landau life time of 

																									W bosons.
	Numerically, with		T c	_	11		11 10 5	K	(ELI laser); and	T c	_	9		9 10	K	(Nd:YAG laser),
	E	prag	_	11		k	B	T c	_	11		MeV 43	;	E	prag	9 _ 	09 . 0	,	result
		0			W		k	B	c T		. 1 e		09	38 . 1 ( e		23	*	) 12 e . 2		2 . 36	, where	c T		12 10	K	at confinement,
	and										where				 results	from	eq.	(2)	from	[8]	as
																							W
		W			int	(	d				x			;	x		) 14 . 0	*	[ 117 . 0	] fm	. 1 e	[ 09	J	]

  is

				a n 	v	b	R	inner	; where the velocity is	v b	 2  	 m 1	2		9 . 2	8 10 	m	s	, where, the
	inner radius of the barrier is	R inner		b		5 . 3	] 17 m [  10 	, see below. For only one of the
	three vortex-flux tubes ( g q q ) we have:			eB 	m		4		10  9	[	J	]		GeV 25	, with the
	above ) (B which is obtained from eq.(1.a) from [8] with the resultant potential
	GeV V 81 	, that corresponds to	m q q		GeV 29	from 4.1a of [8], the energy of the
	particle for the first Landau level (as above), and we can see that it results to be equally
	with		1	3	rest mass of the  W , that resulting	n a		5 . 7	24 10 	s	1 


ON EXTENSIONS OF SYMMETRIC OPERATORS

Keywords: 2010 Mathematics Subject Classification. 47A20, 47B25. Key words and phrases. symmetric operator, self-adjoint extension, generalized resolvent

There is a widely used linearization technique in the theory of Sturm-Liouville problems with boundary and/or discontinuity conditions polynomially dependent on the eigenvalue parameter. One considers a Hilbert (or Pontryagin) space of the form L 2 ⊕ C k and constructs a self-adjoint operator in this space such that the eigenvalue problem for this operator and the original boundary value problem become equivalent, in the sense that their eigenvalues coincide, the eigenfunctions of the latter problem are in one-to-one correspondence with the first components of the eigenvectors of the former problem, and so on (see, e.g., [START_REF] Bartels | Sturm-Liouville problems with transfer condition Herglotz dependent on the eigenparameter: Hilbert space formulation[END_REF], [START_REF] Behrndt | Finite rank perturbations in Pontryagin spaces and a Sturm-Liouville problem with λ-rational boundary conditions, Indefinite inner product spaces, Schur analysis, and differential equations[END_REF], [START_REF] Guliyev | Essentially isospectral transformations and their applications[END_REF], and the references therein). Fulton [START_REF] Fulton | Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions[END_REF]Remark 2.1] attributes this technique to Friedman [5, pp. 205-207]. The purpose of this short paper is to show that a straightforward generalization of this technique gives an explicit description of all minimal selfadjoint extensions of a densely defined, closed symmetric operator with deficiency indices (1, 1) (see below for definitions).

Let A be a densely defined, closed symmetric operator in a separable Hilbert space H with deficiency indices [START_REF] Bartels | Sturm-Liouville problems with transfer condition Herglotz dependent on the eigenparameter: Hilbert space formulation[END_REF][START_REF] Bartels | Sturm-Liouville problems with transfer condition Herglotz dependent on the eigenparameter: Hilbert space formulation[END_REF]. Let {C, Γ 0 , Γ 1 } be a boundary triplet for A * . This means that Γ 0 , Γ 1 : D(A * ) → C are two linear mappings such that abstract Green's identity

A * x, y H -x, A * y H = Γ 1 x • Γ 0 y -Γ 0 x • Γ 1 y, x, y ∈ D(A * )
holds and the mapping Γ : [START_REF] Schmüdgen | Unbounded self-adjoint operators on Hilbert space[END_REF]Chapter 14]. The domain of A then coincides with the kernel of Γ:

D(A * ) → C 2 , x → (Γ 0 x, Γ 1 x) is surjective [4],
D(A) = {x ∈ D(A * ) | Γ 0 x = Γ 1 x = 0}. ( 1
)
If A is a self-adjoint operator in a Hilbert space H ⊃ H such that A ⊂ A, then A is called a self-adjoint extension of A. A self-adjoint extension A is called minimal if no nontrivial subspace of H H is reducing for A [10, Section 4],
or equivalently [START_REF] Schmüdgen | Unbounded self-adjoint operators on Hilbert space[END_REF]Lemma 5.17]

H = span A -λI -1 x x ∈ H, λ ∈ C \ R ,
where span denotes the linear span.

A holomorphic operator-valued function R(λ) on C \ R is called a generalized resolvent of A if R(λ) = P H A -λI -1

H

for some self-adjoint extension A, where P H is the orthogonal projection onto H. For every generalized resolvent there is a unique (up to unitary equivalence) minimal self-adjoint extension with this property (see [START_REF] Naimark | Spectral functions of a symmetric operator (Russian)[END_REF]Theorem 8]). On the other hand, there is a one-to-one correspondence between generalized resolvents R(λ) and functions ω(λ) holomorphic on the open upper half-plane C + with |ω(λ)| ≤ 1: for every x ∈ H the value y := R(λ)x satisfies the equation

A * y -λy = x
and the condition (ω(λ) -1) Γ 1 y -i (ω(λ) + 1) Γ 0 y = 0 (see [START_REF] Bruk | A certain class of boundary value problems with a spectral parameter in the boundary condition (Russian)[END_REF]). Denoting

f (λ) := iω(λ) + i 1 -ω(λ)
we obtain a one-to-one correspondence between generalized resolvents R(λ) and Herglotz-Nevanlinna functions f , i.e. functions holomorphic on C + with Im f (λ) ≥ 0 (cf. [13, Subsection 1.2]). The above condition then becomes

Γ 1 y + f (λ)Γ 0 y = 0. (2)
The "Dirichlet" condition Γ 0 y = 0 corresponds to f = ∞. We will denote the generalized resolvent corresponding to f by R f (λ). It should be noted that complete parameterizations of all generalized resolvents in terms of Herglotz-Nevanlinna functions were first obtained independently by Naimark [START_REF] Naimark | On spectral functions of a symmetric operator (Russian)[END_REF] and Krein [START_REF] Krein | On Hermitian operators with deficiency indices one (Russian)[END_REF].

We are now ready to construct our minimal self-adjoint extension corresponding to a Herglotz-Nevanlinna function f . This function has a unique representation of the form [12, Appendix F]

f (λ) = h 0 λ + h + +∞ -∞ 1 t -λ - t 1 + t 2 dσ(t),
where h 0 ≥ 0, h ∈ R, and

+∞ -∞ dσ(t) 1 + t 2 < ∞
(the reader may refer to [START_REF] Gesztesy | On matrix-valued Herglotz functions[END_REF]Appendix A] for some examples of such representations). If h 0 > 0 then we consider the Hilbert space H := H ⊕ L 2 (R; dσ) ⊕ C with inner product given by x, y

H := x 0 , y 0 H + +∞ -∞ x 1 (t)y 1 (t) dσ(t) + x 2 y 2 h 0 for x =   x 0 x 1 x 2   , y =   y 0 y 1 y 2   ∈ H,
and define the operator

A x :=    A * x 0 tx 1 (t) -Γ 0 x 0 Γ 1 x 0 + hΓ 0 x 0 + +∞ -∞ x 1 (t) -t 1+t 2 Γ 0 x 0 dσ(t)    with D( A) := { x ∈ H | x 0 ∈ D(A * ), tx 1 (t) -Γ 0 x 0 ∈ L 2 (R; dσ), x 2 = -h 0 Γ 0 x 0 }.
If h 0 = 0 then we set H := H ⊕ L 2 (R; dσ), and define A by

A x := A * x 0 tx 1 (t) -Γ 0 x 0 and D( A) := x ∈ H x 0 ∈ D(A * ), tx 1 (t) -Γ 0 x 0 ∈ L 2 (R; dσ), Γ 1 x 0 + hΓ 0 x 0 + +∞ -∞ x 1 (t) - t 1 + t 2 Γ 0 x 0 dσ(t) = 0 . The extension A is canonical (i.e. H = H) if and only if f is a real constant (or ∞).
Theorem. For each Herglotz-Nevanlinna function f the operator A defined above is a minimal self-adjoint extension of the operator A with the corresponding generalized resolvent R f (λ).

Proof. We will consider the case h 0 > 0; the other case can be proved similarly. To prove the self-adjointness, let y, z ∈ H be such that

A x, y H = x, z H (3)
for all x ∈ D( A). Taking into account (1) and setting x 1 (t) ≡ 0 = x 2 we obtain Ax 0 , y 0 H = x 0 , z 0 H , x 0 ∈ D(A).

Hence y 0 ∈ D(A * ) and z 0 = A * y 0 . By surjectivity of Γ, there exists x 0 ∈ D(A * ) with Γ 0 x 0 = 0 and Γ 1 x 0 = 1. Then for this x 0 and x 1 (t) ≡ 0 the equality (3) gives y 2 = -h 0 Γ 0 y 0 . Setting x 0 = 0 in (3) we get

+∞ -∞ x 1 (t)(ty 1 (t) -Γ 0 y 0 -z 1 (t)) dσ(t) = 0 for all x 1 (t) ∈ L 2 (R; dσ) with tx 1 (t) ∈ L 2 (R; dσ). Since such functions are dense in L 2 (R; dσ), we obtain ty 1 (t) -Γ 0 y 0 = z 1 (t) ∈ L 2 (R; dσ). Finally choosing x 0 ∈ D(A * ) with Γ 0 x 0 = 1, the equality (3) yields z 2 = Γ 1 y 0 + hΓ 0 y 0 + +∞ -∞ y 1 (t) - t 1 + t 2 Γ 0 y 0 dσ(t).
Thus y ∈ D( A) and A y = z.

To see that the generalized resolvent corresponding to A is R f (λ), it suffices to check that if

y =   y 0 y 1 y 2   = A -λI -1   x 0 0   then y 0 satisfies (2)
, and this is straightforward. Finally, to check the minimality, we need to verify that the linear span of all y of this form with all possible values of x ∈ H and λ ∈ C \ R is dense in H. To this end, let z ∈ H be orthogonal to all such y, i.e.

  z, y H = z 0 , y 0 H + +∞ -∞ z 1 (t) Γ 0 y 0 t -λ dσ(t) -z 2 Γ 0 y 0 = 0 for all y 0 ∈ D(A * ). Surjectivity of Γ implies z 0 = 0 and +∞ -∞ z 1 (t) t -λ dσ(t) = z 2 , λ ∈ C \ R.Now the Stieltjes-Perron inversion formula [12, Theorem F.2] applied to the regular complex Borel measure z 1 dσ yields z 1 (t) = 0 for dσ-a.e. t and consequently z 2 = 0.


Mert Gençtürk

Enver Evci

Arda Guney

Yildiray Kabak

Gokce Erturkmen

Gokce B Laleci Er- Turkmen

Achieving Semantic Interoperability in Emergency Management Domain

Keywords: Semantic Interoperability, Semantic Web, Ontology, Emergency Management

scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Common standard interfaces allow data communication among disparate systems. By complying with a standard interface, each system can exchange data with every other compliant system. Otherwise the interoperability of the systems can be quite challenging, technologically complex, time consuming and expensive. Emergency management is a multi-discipline domain where effective management of crises and disasters requires communication of different organizations in different domains such as government, health, media, and military. Although each of these domains has its own wellestablished standards, not all emergency responding parties conform to the same set of standards, which creates a crucial interoperability challenge. Furthermore, standards have many optional fields and different versions. Even if only one standard is used by two different systems, interoperability of them can still be problematic due to misinterpretation of optional fields or usage of different versions [START_REF] Chen | Framework for enterprise interoperability[END_REF].

Semantic Interoperability has been an active research and development area in various domains such as eHealth and eBusiness. There are several completed and ongoing work in these domains for the semantic interoperability of electronic documents. OASIS Semantic Support for Electronic Business Document Interoperability (SET) TC [START_REF]OASIS Semantic Support for Electronic Business Document Interoperability[END_REF] is one of them and its basic idea is to explicate the semantics of different but overlapping electronic business document standards as ontologies and then provide semantic mediation among these ontologies. OASIS SET TC approach has been proven to be useful and effective in several studies such as iSURF project, where a Semantic Interoperability Service Utility were developed by following this approach for the exchange of supply chain planning information documents [START_REF] Kabak | iSURF Semantic Interoperability Service Utility for Collaborative Planning, Forecasting and Replenishment[END_REF].

In order to solve the interoperability problem, in European Commission supported C2-SENSE project [START_REF]C2-SENSE Project -Interoperability Profiles for Command/Control Systems and Sensor Systems in Emergency Management[END_REF] which aims to develop a profile based Emergency Interoperability Framework by the use of existing standards and semantically enriched Web services, we take this engineering approach and apply it to the emergency management domain to implement semantic mediation mechanisms to be able to harmonize information conforming to different but overlapping emergency standards. In this regard, in this paper, we present a Semantic Interoperability Suite which enables the information exchange between emergency management domain applications through a central layer instead of one-to-one transformations between several different content models, by developing a common ontology. Common Data Elements (CDEs) that have been elicited within this study underpin the common ontology which can be considered as the semantic dictionary of the interoperating applications.

2

Technology Description

Standards

The Emergency Data Exchange Language (EDXL), developed by OASIS International Open Standards Consortium, is a suite of XML-based messaging standards that facilitate emergency information sharing between government entities and the full range of emergency-related organizations [START_REF]Emergency Data Exchange Language (EDXL)[END_REF]. EDXL standardizes messaging formats for communications between these parties. EDXL includes several individual standards, that are Common Alerting Protocol (EDXL-CAP), Distribution Element (EDXL-DE), Hospital AVailability Exchange (EDXL-HAVE), Resource Messaging (EDXL-RM), Reference Information Model (EDXL-RIM), Situation Reporting (EDXL-SitRep), Tracking Emergency Patients (EDXL-SitRep).

The Common Alerting Protocol [START_REF]EDXL Common Alerting Protocol (EDXL-CAP) Specification[END_REF] is an XML-based data format for exchanging public warnings and emergencies between alerting technologies. CAP allows a warning message to be disseminated simultaneously over many warning systems to many applications.

Distribution Element [START_REF]EDXL Distribution Element (EDXL-DE) Specification[END_REF] is used as a container that facilitate the routing of any properly formatted XML emergency message to recipients.

EDXL-HAVE [START_REF]EDXL Hospital AVailability Exchange (EDXL-HAVE) Specification[END_REF] is a document format for exchanging information on status of a hospital, its services, and its resources such as bed capacity, service availability etc.

Resource Messaging [START_REF]EDXL Resource Messaging (EDXL-RM) Specification[END_REF] defines specific message types supporting the major communication requirements for allocation of resources across the emergency incident lifecycle.

EDXL-SitRep [START_REF]EDXL Situation Reporting (EDXL-SitRep) Specification[END_REF] is an XML-based data format for transmitting timely available situation reports, incident or event information, and operational picture.

In much the same way that HTML and HTTP standards enable the exchange of any type of information on the Web, The Open Geospatial Consortium's (OGC) Sensor Web Enablement Initiative (SWE) [START_REF]OGC Sensor Web Enablement (SWE)[END_REF] is focused on developing standards to enable the discovery of sensors and corresponding observations, exchange, and processing of sensor observations, as well as the tasking of sensors and sensor systems.

ISO/IEC 11179, Semantic Metadata Registry and IHE Data Element Exchange

ISO/IEC 11179 is an international standard developed with the aim of providing a metadata-driven data exchange in heterogeneous environments. Combining principles of semantic theory and data modelling, the standard defines the representation of metadata in a metadata registry [START_REF]Information technology -Metadata registries (MDR) -Registry metamodel and basic attributes[END_REF].

In our study, we employ an ISO/IEC 11179 compliant Semantic Metadata Registry (MDR) to maintain metadata of data elements (e.g. location, alert, observation) and communicate with it via the IHE Data Element Exchange (DEX) profile, which we authored [START_REF]Research and Public Health Technical Framework Supplement Data Element Exchange (DEX)[END_REF]. DEX provides a standardized way of querying data element metadata, and allows dynamic mappings between data elements such as EDXL data elements to their OGC equivalents when complemented with extraction specifications (e.g. XPATH, SQL scripts) maintained in Semantic MDR.

Methodology & Implementation

During the implementation of Semantic Interoperability Suite, first information domain has been carefully analysed and following standards corresponding to emergency management have been identified as relevant [START_REF] Božić | Requirements Engineering for Semantic Sensors in Crisis and Disaster Management[END_REF]. The common ontology has been created based on the knowledge that was gained as a result of this analysis. In this regard, first a number of Common Data Elements (CDEs) which can be considered as ontology resources have been defined and stored in Semantic MDR. CDEs are the smallest meaningful data container in a context. They can be regarded as the semantic dictionary of the interoperating application.

Fig. 1 illustrates an example decomposition of a CDE which refers to birth date information of a person. As shown in the figure, the concept of the CDE and the representation are separate in the metamodel. In the given example, "Person" is the Object Class and "Date of Birth" is the property together which constitute the concept of "Person.DateOfBirth". This is the concept of the data element regardless of its representation. The other main concepts for which CDEs are defined can be listed as address, location, resource, report, alert, and observation (sensor measurement). After CDEs are defined, a common ontology in OWL (Web Ontology Language) format is generated by following the OASIS SET TC approach. C2-SENSE Semantic Interoperability Suite enables domain experts to define extraction specifications only once, then the conversion between content models is done au-tomatically according to these specifications. It is possible to define extraction specifications for any number of standard content models. There is no need to make an update on the system, when specifications for a new content model is going to be added.

Overall architecture of C2-SENSE Semantic Interoperability Suite is illustrated in Fig. 2. In Semantic Interoperability Suite, a Semantic MDR Tool is provided to users as a graphical user interface (GUI) to facilitate the definition of CDEs and extraction specifications. Semantic MDR Tool can be considered a web-based metadata management and data modelling tool to create and maintain CDEs collaboratively either based on imported standard content models or from scratch [START_REF]Semantic MDR Tool[END_REF]. Given a standard format, it is able to list the data elements included in it; given the data element list, it can also provide mappings of elements to a specified target standard format.

Fig. 2. Architecture of C2-SENSE Semantic Interoperability Suite

Semantic Mediator is the component in Semantic Interoperability Suite fulfilling the duty of converting data represented in one standard to a data represented in another standard. This functionality is satisfied thanks to Semantic MDR and IHE DEX profile. When the system receives a request of conversion, it fetches common ontology (in other words CDEs) and corresponding extractions specifications from Semantic MDR using DEX profile. If the source and target content models are available in the registry, e.g. EDXL-SitRep as the source and OGC-O&M as the target, conversion is done automatically by Semantic Mediator according to pre-defined extraction specifications. Semantic Mediator is provided to outside world through a RESTful API.

Example Usage

In C2-SENSE project, an Emergency Domain Interoperability Framework, which Semantic Interoperability Suite is part of, has been developed. This framework has been validated by a realistic flood scenario in Puglia region of Italy. In this section, we present an example usage of Semantic Interoperability Suite in this scenario.

It has been raining in Puglia region for several days and the sensors located near Fortore river measures the water level exceeding the threshold value. Therefore, Regional Functional Center of Puglia is alerted and emergency plan for flood situation is started to be applied. As part of this plan, people living near flood area is evacuated, houses, healthcare services and equipment are provided, some roads are blocked and volunteers are involved to follow the situation on field. Meanwhile, a car accident occurred at the 15 th km of "Strada Statale 100". Immediate intervention of Fire Brigade is required. Therefore, Innova Puglia, who is the technology provider of Civil Protection Service of Puglia Region, alerts Fire Brigade regarding the accident. Fire Brigade system uses the EDXL-CAP as the data format and Innova Puglia system is able to produce message in this format. Hence, the following XML message (for the sake of simplicity, namespaces have been removed in the XML messages) is generated by Innova Puglia and sent to Fire Brigade successfully with no additional effort. <?xml version="1.0" encoding="UTF-8" standalone="yes"?> <alert xmlns="urn:oasis:names:tc:emergency:cap:1. After Fire Brigade receives the the alert message, it needs to inform corresponding local authorities about the situation, and this message should be sent in EDXL-SitRep format. However, Fire Brigade system is only able to produce and retrieve messages in EDXL-CAP format. A solution to this problem could be updating the Fire Brigade system so that it can support exchanging documents in EDXL-SitRep format as well. However, this requires a lot of work and is impossible to do during the emergency situation. Instead of this, Fire Brigade uses the Semantic Interoperability Suite of C2-SENSE system to convert the EDXL-CAP message presented above to EDXL-SitRep message automatically. The result of this operation is the following XML.

<?xml version="1.0" encoding="UTF-8"?> <sitRep xmlns="urn:oasis:names:tc:emergency:EDXL:SitRep:1.0"> <messageID>20161206.

Conclusion

In order to manage crises effectively, interoperability of different systems using dispersed standards is crucial. One way to provide interoperability among these systems is to update the existing software so that one system can generate messages in all the desired formats. It is obvious that this requires a lot of work and should be done for every single system. In this regard, C2-SENSE Semantic Interoperability Suite is a powerful mechanism since it enables organizations to make such conversions between emergency domain standards automatically without making any updates on their own systems.

Currently, C2-SENSE Semantic Interoperability Suite is able to make conversion among EDXL-SitRep, EDXL-RM, EDXL-HAVE, EDXL-CAP, OGC SensorML and O&M standards. Feasibility and usability of the system is currently being tested in a realistic flood scenario in Puglia Region of Italy within the scope of C2-SENSE Project.

6

•

  EDXL-SitRep (Situation Reporting) • EDXL-RM (Resource Messaging) • EDXL-HAVE (Hospital Availability Exchange) • EDXL-TEP (Tracking of Patients) • EDXL-CAP (Common Alerting Protocol) • OGC SensorML (Sensor Modeling Language) • OGC O&M (Observations and Measurements)

Fig. 1 .

 1 Fig. 1. An example of decomposition of a Common Data Element: Person.DateOfBirth.Date

Table 1

 1 below presents three different extraction specifications of EDXL-SitRep, EDXL-CAP and OGC-O&M standards for "LocationByCoordinates.Latitude" data element.

Table 1 .

 1 Data Element and Extraction Specifications

		Data Element
	Property	LocationByCoordinates.Latitude
	Data Type	characterstring
	Definition	Measure of the latitude of the coordinate in degrees
		Extraction Specification
	EDXL-SitRep /element(*,ResourceDetailType)/reportToLocation/ct:EDXLGeo-
		PoliticalLocation/ct:geoCode/ct:value
	EDXL-CAP	/cap:alert/cap:info/cap:area/cap:circle
	OGC-O&M	/om:featureOfInterest/gml:AbstractFeature/gml:bound-
		edBy/gml:Envelope/gml:coordinates

Table 1 )

 1 In technical point of view, for instance, in CAP message, latitude and longitude information is provided in "/cap:alert/cap:info/cap:area/cap:circle" element (see . In order to present this information in SitRep message, Semantic Mediator of Semantic Interoperability Suite performs following actions: 1. Retrieve CDEs and extraction specifications from Semantic MDR. 2. Find the corresponding Common Data Element for the XPATH "/cap:alert/cap:info/cap:area/cap:circle", that is LocationByCoordinates.Latitude.characterstring 3. Find the corresponding XPATH definition of SitRep for this Common Data Element, that is "/element(*,ResourceDetailType)/reportToLocation/ct:EDXLGeoPolitical-Location/ct:geoCode/ct:value" 4. Place the information.

	2.71.1</messageID>
	<preparedBy>
	<personDetails>
	<personName>
	<nameElement>mailaddress@mailaddress.com</nameEl-
	ement>
	</personName>
	<addresses>
	<address>
	<locality>
	<nameElement>it-IT</nameElement>
	</locality>
	</address>
	</addresses>
	</personDetails>
	<timeValue>2016-12-06T10:45:40+01:00</timeValue>
	</preparedBy>
	<authorizedBy>
	<personDetails>
	<personName>
	<nameElement>INNOVAPUGLIA</nameElement>

Acknowledgements

The work presented in this paper is achieved in the scope of C2-SENSE project [4] supported by the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement number 607729.


G Baayen

Maat

P J A Gijsbers
email: peter.gijsbers@deltares.nl

J H Baayen

G J Ter Maat

Quick Scan Tool for Water Allocation in the Netherlands

Keywords: Water allocation, Netherlands, Quick scan tool, Goal programming

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Freshwater Availability in the Netherlands

The Netherlands is rich in water. In the current situation there is hardly any water scarcity, i.e. a situation in which usual consumption rates exceed the average water availability. However, the country has to cope with droughts, the natural phenomena in which there is temporarily decrease in fresh water availability, as occurred during extreme dry historical years 1976 and 2003.

The majority of the water system allows controlled redirection of water where most regions can be supplied from the national water system during dry periods, using the Rhine River and Meuse River as the main sources. After the Rhine and Meuse enters the Netherlands the water is distributed over the branches Waal, Nederrijn, and IJssel by means of a weir by Driel. In general, 2/3 of the inflow goes to the Waal, and 1/3 to the Nederrijn and IJssel. The IJssel supplies the Ijsselmeer and Markermeer lakes with fresh water. From the rivers and lakes, water is distributed to other parts of the country through an extensive network of ditches and canals [START_REF] Haasnoot | Middelkoop Fit for purpose? Building and evaluating a fast, integrated model for exploring water policy pathways[END_REF].

Water is used for controlling levels, flushing and actual extractions (e.g. irrigation and drinking water). In the Netherlands there is no absolute shortage of water but a 'problem' of the right quality at the right time at the right place. Specific phenomena for the Netherlands as a low-lying country is the risk of salt water intrusion in the western part of the Netherlands; during low flow of rivers sea water enters the main water ways due to the lack of driving forces pressurizing the water supply of the western part of the Netherlands. As described above, in the north water can be stored in the IJsselmeer and Markermeer, a man-made lake (total 2000 ha), that was created in 1932 by building a large dike (the Afsluitdijk) and is fed by the River IJssel. The lake supplies the Northern provinces during summertime. Groundwater is the main water source in the elevated areas in the south and east, since these grounds cannot be reached by re-routed surface water from the rivers. Finally the islands and peninsulas in the south west have to deal with both saltwater intrusion and limited fresh water supply options due to their surrounding by salt water bodies.

Policy arrangements are in place and coordinated by the National Coordination Committee for Drought Conditions (LCW) to deal with reduced water availability conditions. Leading principle is the so-called Verdringingsreeks, a priority lists which puts infrastructure and nature integrity preservation purposes such as water level and water quality control (flushing) above extractions for drinking and industry water above irrigation for agriculture.

The Adaptation Challenge

Climate change scenarios provided by the Royal Netherlands Meteorological Institute [START_REF]KNMI'14: Climate Change scenarios for the 21st Century -A Netherlands perspective KNMI scientific report WR 2014-01[END_REF] indicate that the Netherlands should expect both an increase in the number and extent of high flow events as well as low flow periods. It is expected that global climate change demands that various measures will be taken to guarantee the control of water levels and a supply of freshwater for the long term (at least until 2100). Socio-economic developments could raise water demands even further, beyond just climate change impacts. A quantitative assessment of both problems and solutions in collaboration with stakeholders should indicate if this expectation could come true and if yes, underpin to what extend one should expect.

In the previous phase of the policy process, the Dutch Deltaprogamme Phase 1, which ended in 2015, an adaptive pathways plan was presented to cope with droughts and water scarcity on the short term (until 2021), midterm (2050) and long term (2100). Funds were allocated for measures and on different levels: for the main water system, regional water system and for water users, that are agreed upon as implementation of the preferred pathway. For the short term it was also agreed upon to make the current system more flexible and robust by 'smart' operational water management.

The Need to Support Screening of Alternative Strategies

In 2008-2009 various Dutch institutes conducting water management research started a collaboration to jointly develop a National Hydrological Model [START_REF] Lange | An operational, multi-scale, multi-model system for consensus-based, integrated water management and policy analysis: The Netherlands Hydrological Instrument[END_REF]. This National Hydrological Model is a detailed integrated surface-groundwater system of the Netherlands, combining a 250x250m grid model for groundwater (Modflow) and unsaturated zone (Metaswap) with a 8800 network elements based surface water balance and allocation model. This water allocation model uses a heuristic approach to allocate water to various prioritized purposes where the uses with high priority receive water before uses with lower priority. The National Hydrological Model is applied for policy analysis and for operational forecasting.

For the operational forecasting application, the National Hydrological Model is encapsulated in a Delft-FEWS based operational forecasting system call RWsOS-Waterbeheer [START_REF] Weerts | Operational Water Resources Forecasting System for The Netherlands[END_REF]. Rijkswaterstaat, the Dutch National Authority responsible for the national waterways and water bodies uses RWsOS-Waterbeheer on a daily basis to produce a real-time forecast with a 10 day horizon using the National Hydrological Model. This operational system provides useful information to the National Coordination Committee for Drought Conditions to analyze the current water availability situation in the Netherlands. The Committee has the authority to change the water allocation at a national level if the drought situation is sufficient severe. For this purpose, it wants to be able to conduct what-if analysis runs such that trade-offs between different regions and sectors can be assessed when allocation patterns are changed. Since the runtime of the detailed National Hydrological Model is substantial, a need arose for a so-called Quick Scan Tool to accommodate this screening purpose. This operational tool will be referenced as the LCW-Quick Scan Tool.

In the policy analysis domain the National Hydrological Model is encapsulated in a larger modeling system called the National Water Model. The model is used for detailed policy analysis under future climate scenarios and socio-economic developments. Simulations, conducted for a 30 -100 year time series targeted at a mid-term 21 st century outlook (2050), take days to weeks. This makes it hard to use the model for an initial screening of interventions to address the issues that arise in terms of water supply and saline intrusion within a dynamic multi-stakeholder policy process. Also for these studies a need arose for a Quick Scan Tool that could be applied to analyze potential interventions for current or future bottlenecks in the water supply system. This policy analysis tool will be referenced as the PA-Quick Scan Tool. Once interesting interventions have been identified, they could be implemented in the National Hydrological Model of the Netherlands to conduct a detailed analysis.

Quick Scan Tool Requirements

While the two tools have different end users, they have also many similarities. The end users for the LCW-Quick Scan Tool are civil servants, namely the core members of the LCW itself. These people intend to use the tool as a preparation to the Committee meetings to investigate alternative water allocation strategies when hydrological conditions are becoming dry. Their tool needs to be based on the most recent datasets provided by RWsOS-Waterbeheer. The LCW-Quick Scan Tool must be easy and quick to use and provide insight in the current situation as well as the regional tradeoff of water balance effects of alternative allocation strategies. The end users for the PA-Quick Scan Tool are Deltares experts conducting the policy analysis for different climate and socio-economic development scenarios. The input datasets for the PA-Quick Scan Tool will be 30 year time series of water demands and river discharge, provided by the National Water Model.

Both applications require a water balance model that can cope with priority based water management rules for extractions and management of lake levels. The challenge for the modeling the national Dutch water system, characterized by a highdensity network of waterways, is to design a model schematization that represents the national water system with the main water delivery routes and storages appropriately while regional detail should be neglected when the issues at stake do not ask for those details. This network model has to accommodate regional trade-off analysis as well as analysis of the issues at stake, while potential interventions should transparently be facilitate in the parameterization of the model. Possible interventions can vary from changing requests (water demands for extraction and in-stream uses) to manipulation of the operating rules for the storages and modification of maximum intake capacities. To enable quick turnaround times in the analysis, all above interventions should be facilitated via a Graphical User Interface. Changing the order of water use priorities was left out of scope as reduction of water demands could be applied to accommodate analysis of the same intervention in water shortage conditions.

Methods and Techniques

The model underlying the Quick Scan Tool is composed of a coarse network of the Dutch water system including the major water storages, water distribution points and delivery routes to the various uses. Requests for water abstractions (agriculture, industry, drinking water, regional water systems) and instream flows for flushing are prioritized and assigned to the nodes and links in the network.

In the present section we discuss the methods and techniques used to develop a model for solving our water allocation problem.

The central design tenet of our tool is separation of concerns, i.e., implementation of conceptually disjunct functionalities in separate modules. In our case, the physical system model is kept separate from the specification of the water allocation goals. In the subsequent sections, we will discuss the methodologies underpinning the implementation of these two modules.

Modeling the water system

The Dutch water system may be viewed as a network composed of elementary objects, such as

• storage nodes • channel reaches
• weirs and pumping stations Objects of the same type share the same parameterized equations governing their dynamics. Storage nodes, for instance, are governed by the mass balance equation:

I o dV Q Q dt = - (1)
with storage volume V, inflow QI and outflow Qo. This is a differential equation. Instantaneous routing in a channel reach is governed by algebraic equations of type

down up Q Q = (2)
with upstream inflow Qup and downstream outflow Qdown. Collecting the equations for all the network elements, results in a system of differential-algebraic equations (DAE). For the Quick Scan Tool a need was identified for a system to describe classes of model elements using DAE, and to combine instances of these classes into a network model. A modeling language that allows this is Modelica [START_REF] Elmqvist | Modelica -A unified object-oriented language for physical systems modeling[END_REF]. The Modelica objects used for the Quick Scan Tool are reaches with instantaneous routing with an extra term for a lateral flux (discharge/extraction), connection nodes for network confluences and diversions, and storage nodes.

Optimization with prioritized goals

The priority ordering of the control goals of the Dutch water system (the Verdringingsreeks) leads us to consider sequential optimization of the prioritized goals in order. In operations research, this technique is known as lexicographic goal programming (LGP) [START_REF] Collette | Multiobjective optimization: principles and case studies[END_REF][START_REF] Baayen | Control and multi-objective convex optimization of environmental flow networks under predictive uncertainty[END_REF]. The idea of LGP is to optimize the goal 1 functions ƒi in a given order, prioritizing earlier goals over later goals. The goals are ordered by assigning each a non-negative integer priority value pi. The goals are then solved in their priority order. Following the optimization of a goal ƒi, its attainment level is fixed and added as a constraint to the optimization problem. The optimization of all following goals, in this way, will not worsen the attainment of any preceding goal. At each stage of LGP, optimization takes place within the degrees of freedom left open by the fixation of the attainment levels of the previous goals.

Solving ordered goals

Application of LGP to a multi-objective optimization problem results in a series of optimization problems. Let k be the priority level under consideration, and let the overall problem be constrained by the equation g(x) ≤ 0. The k'th optimization problem is then 1 Within this paper, the term goal and objective are interchangeable. min ( ) subject to g(x) 0 ( )

k x i i i f x f x k ε ≤ = ∀ < (3)
with the attainment level of the ith goal , : ( )

i i opt i f x ε = (4)
and xopt,i being the optimal solution of the ith optimization problem.

LGP has been applied to decision support for the short-term operation of hydropower resources, e.g. [START_REF] Eschenbach | Goal Programming Decision Support System for Multiobjective Operation of Reservoir Sys-tems[END_REF], to surface water allocation, e.g. [START_REF] Mcgregor | An application of lexicographic goal programming to resolve the allocation of water from the Rakaia River (New Zealand)[END_REF] and to water quality management.

Inequality goals

In water systems, one often encounters the need to keep variables within a desired range. A channel reach is a typical case, where one aims to keep the water level within desired lower and upper bounds. It may not always be possible to keep the water level within the desired range, as in case of drought or flooding. Inequality, or range, goals are therefore an important ingredient in a multi-objective optimization framework.

Let hi be a goal function and let [mi,Mi] be its desired range, with

{ } i m ∈ ∪ -∞  , { } i M ∈ ∪ -∞ 
k k p x k k k k k k k k k k k k x h m x M h M g x δ δ δ δ δ δ ≥ + - ≤ + - ≥ ≤ ≤   (5)
with violation variable δk and goal function enclosure [START_REF] Wächter | On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming[END_REF] [ , ]

k k h h such that ( ) k k k h h x h ≤ ≤
for all feasible x. The order p ≥ 1 denotes the norm under consider- ation. One would select p = 1 for linear penalization, or p =2 to penalize large violations disproportionately more than small ones. The concept of violation variables is illustrated in Figure 1 (left). The goal function merely lies within its enclosure when δk = 1, whereas the goal is fully satisfied when δk = 0. Starting from a feasible seed value of δk = 1, the objective is to minimize the value of δk. In addition, for every i < k, the following constraint is added to fix the goal attainment level: ( ) ( ) ( )

i i i i i i i i i m h m h x M h M δ δ + - ≤ ≤ + - (6)
When applying an inequality goal for every discretized time instance along the prediction horizon, the effect of an inequality goal is best described as a soft constraint. First, the optimizer will try to find a state trajectory that lies within the desired range. All trajectories that lie within the range incur no penalty cost and are therefore equally preferable. If it is not possible to find a trajectory that fully lies within the desired range, the optimizer will select a trajectory that lies outside of it as little as possible. The desired range, relaxed just enough to accommodate the actual trajectory, is taken as a standard (hard) constraint for subsequent goals. This idea is illustrated in Figure 1 (right). LGP with inequality goals has been applied to decision support for the short-term operation of hydropower resources [START_REF] Eschenbach | Goal Programming Decision Support System for Multiobjective Operation of Reservoir Sys-tems[END_REF].

Multiple goals per priority level.

In the Quick Scan Tool, every priority level i may come with multiple goal func-

tions { } k i k f
, each covering a different element of the model. These goals are assumed to be equally important, hence allowing the respective goal functions to be summed into a single objective function ƒi:

k i i k f f = ∑ (7)

Optimization solver

The interior point solver IPOT [START_REF] Wächter | On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming[END_REF] is used to solve the scalar optimization problems resulting from the lexicographic optimization procedure. IPOPT solves nonlinear problems, which is required for goals with order p > 1.

Software suite

The techniques covered in the preceding sections are available as standard components in the environmental flow optimization software suite RTC-Tools 2.0 [START_REF] Baayen | Control and multi-objective convex optimization of environmental flow networks under predictive uncertainty[END_REF], which supports Modelica model formulations. RTC-Tools is available under a dual-licensing scheme. The open source version is available online under the terms of the GNU General Public License version 3 [START_REF]GNU General Public License[END_REF]. Precompiled binaries, source code, and documentation are available from the project website at: https://www.deltares.nl/en/software/rtc-tools/.

The Quick Scan Tool application

The Quick Scan Tool application is a combination of two software products. Delft-FEWS provides the Graphical User Interface, the database and general data processing capabilities. The model component uses an internal model based on the RTC-Tools 2 model engine [START_REF] Baayen | Control and multi-objective convex optimization of environmental flow networks under predictive uncertainty[END_REF].

The model schematization

The Quick Scan Tool holds an internal network model for the water balance. The model, built in Modelica, is composed of model element of type branches, connection nodes, demand nodes, storages as well as boundary nodes (inflow and terminal). Each Modelica element holds its own water balance where flow enters via the 'in'-port and leaves via the 'out'-port. Lateral flows (extractions of discharges) can be applied to branches, demand nodes and storages.

The final network model schematization (Figure 3) is the result of five collaborative design sessions with the end users. The challenge was to design a network which is as simple as possible while providing an appropriate representation of the main water system including the main water delivery routes. The network model should accommodate analysis of the issues at hand while potential interventions should be facilitated transparently in the parameterization. The result is a schematization where areas in the north-east and in the south-east are grossly simplified compared to the actual water system as there are only few relevant water inlets. More network detail has been introduced in the west as many water delivery routes need to be analyzed in relation to saline intrusion of the most westward inlets. Capacities and management rule have been derived from the NHM.

The work and dataflow of the application

The dataflow of the Quick Scan Tool is composed of the following steps:

1. acquire the input data sets (requests for extractions and flushing), river discharges and lake levels) from the National Hydrological Model 2. conduct a spatial assignment, using a coupling table, of all requests to a node or branch of the coarse network model 3. transform request by water use function to a request by priority 4. allocate the available water resources using the LGP method

The result is a water distribution over the network, with per element the inflow, the outflow and the lateral flux achieved. Since this lateral flux is the total flux for all extracting (and discharging) water uses functions, this flux need to be split 5. split the lateral flux into the portions allocated to each water use 6. aggregate the results by area for presentation purposes 7. compute a delivery rate percentage, broken up by water use, for presentation purposes.

Table 1 illustrates the order of priorities that is adopted in the PA-Quick Scan Tool. The first three priorities are critical, i.e. similar to 'hard' constraints, as they intend to force the solution within the physical bounds of the water system. The remaining goals are water uses with their order prescribed by law and policies. As can be noted, the operating rules for the storages are divided in multiple goals such that lake levels can drop to meet high priority water demands. Target storage levels should be attained if sufficient water is available within the system. The goal with the last priority intends to minimize the outflow in a selected set of branches such that the water remains in the main rivers and only enters the water inlets to meet local water demands. All canal outlets that do not conduct a water delivery function to downstream uses should be included in this selection.

For in-stream flow requests (e.g. flushing and navigation locks), each new goal is identified by taking the maximum of all in-stream water use flow requests up till the priority at stake. For the lateral fluxes the LGP approach intends to squeeze the solution space with each priority such that the end result is at the desired request if the system is not under water shortage. The equations in the Figure 4 indicate that the requested lateral fluxes for different water uses need to be stacked to obtain a series of goals that squeeze the solution space in the ordering of goals.

Once the LGP has completed its computation, the resulting flows need to be split according to the different water uses. For any in-stream flow request the request is fulfilled if the realized flow is larger than the request. For lateral flux requests, the delivery per water use needs to be based on the 'peeling off' the realized lateral flux by order of priority and allocating the remaining flux to a specific water use up to the request.

Validation of model results

The QST-model has been validated by comparison of the water allocation against the water allocation result computed in the detailed National Hydrological Model (NHM). Differences may partly be explained by the fact that the NHM uses a heuristic water allocation method. Important items checked are the distribution of the main river inflows, the behavior of the lakes, the flushing on the outlets and the main inlets for the in the west. Figure 5 illustrates the water shortage for the flushing goal at the driest moment in the 30 year historical series, flushing being the goal with the lowest priority. In general the QST model results in fewer shortages. During the driest period, the difference with the NHM model result is 2-6% at this location, while most other network elements show hardly any difference. Also lake levels follow the same pattern between the two models if the QST is to lower the volume in order to meet in-stream flow requests.

Discussion and conclusions

Within the Netherlands, a need arose at the national level to supplement the current high-resolution National Hydrological Model with a water allocation model to enable the screening of national water allocation decisions for their regional trade-offs. This paper illustrates how a so-called Quick Scan Tool has been developed for this purpose. The tool is composed of a water allocation model engine and a software component that offers a front end as well as pre and post-processing capabilities. The water allocation model is built with the RTC-Tools 2 software framework using a lexicographic goal programming approach to priority based water allocation rules. In the pilot version Excel was chosen as the front end offering pre and postprocessing capabilities. Data processing required extensive handling of lookup tables while conducting the necessary aggregations from detailed source data to coarse model input to aggregated output for presentation on areal scale. The prototype application showed that RTC-Tools 2 was meeting the model needs, while Excel was not the appropriate data processing platform. In the final version, the Delft-FEWS software framework was chosen as a data processing and visualization platform. This platform offered much more insight to debug the data flow from aggregating source data to model input data to the aggregation of results.

The resulting Quick Scan Tool has been validated against the detailed National Hydrological Model to confirm that the tool outcomes are sufficiently similar to this accepted model to support the policy process. The visualization capabilities Delft-FEWS, with its map based flow animations and graphs, were very beneficial while discussing model setup and validation results with the water management experts of Rijkswaterstaat, the governmental body who initiated the development of the tool.

At the time of writing, the first actual use of the tool is put in practice with preliminary analysis of a combination of additional flushing and water extraction requests under future conditions for the assessment years 2050 and 2085.

In the near term, functional extensions are foreseen using meta-relations to transform reduced river flows into impacts on salinity rates and navigation depths.

RTC-Tools 2 and Delft-FEWS are software platforms which initially were developed for near real-time water system operations. Based on this Quick Scan Tool, it can be concluded that the flexibility and customization capabilities of these platforms also allow development of decision support tools for strategic planning processes.

.

  Let k be the priority order level under consideration, and let the overall problem be constrained by the equation g(x) ≤ 0. The k'th optimization problem is then ,

Fig. 1 .

 1 Fig. 1. Variable violation concept (left) and Relaxation of state beyond the target range (right)

Fig. 2 .

 2 Fig. 2. QST network schematization of the main water delivery system in the Netherlands

Fig. 3 .

 3 Fig. 3. Solution space squeezing and associated goal stacking for lateral fluxes

Fig. 4 .

 4 Fig. 4. Comparison of shortage at sea outlet between NHM (NieuweWaterWeg) and QSTmodel (NieuweWaterWeg_uitlaat)

Table 1 .

 1 Ordering of goals as applied in the PA-Quick Scan Tool

	Prio-	Model	Lower bound	Upper bound
	rity	variable
	1	Lateral	Natural loss/contribution	Maximum extraction
	2	Inflow	Min. capacity (physical)	Max. capacity (physical)
	3	Level	Min. storage level (physical)	Max. storage level (physical)
	4	Outflow	Request water level preserva-
			tion
	5	Level	Min. storage (low priority)	Max. storage (low priority)
	6	Lateral		Request Utilities
	7	Outflow	Request navigation locks
	8	Level	Min. storage (middle priority) Max. storage (middle priority)
	9	Lateral		Request rural water system
	10	Level	Min. storage (high priority)	Max. storage (high priority)
	11	Outflow	Request network flushing
	12	Level	Target storage level	Target storage level
	13	Outflow

6

References