Loris Ferrari
email: loris.ferrari@unibo.it

Chemical and structural disorder effects on the Curie temperature

Keywords: disordered systems, magnetic phase transition, ferromagnetism, ferroelectrics PACS: 75.50.Lk, 75.30.Kz, 75.10.-b, Curie temperature, Disorder effects, Mean field theory

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Chemical and Structural disorder effects on theCurie temperature

Introduction

The modifications induced by disorder on ferromagnetic and ferroelectric systems is a long standing question [START_REF] Luborsky | Amorphous Ferromagnets[END_REF][START_REF] Lines | [END_REF] that continues to stimulate a very active field of investigations, both theoretical and experimental. From the experimental viewpoint [3,4,5,6], the reported data seem to escape from any attempt to classify the disorder effects in a general and simple scheme. The increase or decrease of the Curie temperature T c , for instance, is still an open question. Data referring to pure mechanical treatments (for example, milling), tend to favor the decrease of T c with increasing disorder [6]. This agrees, qualitatively, with earliest theoretical results [7]. In random alloys, most of the measured data are concerned with the non monotonic behavior of T c , as a function of the average concentration of various magnetic or non magnetic components [8]. The disorder, resulting from the random fluctuations about those average values, is especially studied in connection to the changes of the magnetization [3,4], while the effects on T c itself are usually neglected. For ferroelectrics, recent experimental data and theoretical models [5,9,10] report about the increase of T c with increasing cationic disorder. The earliest theories predict no disorder effects on the T c of Ising-like systems [11], and a depression of T c in Heisenberg-like systems [7]. More recently, contrasting theoretical results have been reported for ferromagnetic Anderson-Hubbard models, some pointing to an increase of T c [12,13], others pointing to a decrease [14]. In the present work we study the simplest possible case of a direct interaction between localized spins, i.e. a lattice {r} of sites, each occupied by a spin s r , with interaction energy U (r, r ) s r s r . More elaborated dynamical models, involving the indirect coupling through itinerant electrons [15,16] and the Mott-Hubbard interaction [12,13,14], are ignored in what follows. Though we speak about "spins" for brevity, it is intended that the present approach can be extended to electric dipoles too. The basic elements entering the spin interactions can be split into two main classes: chemical and structural. The formers account for the on-site features (atomic orbitals, local electric dipoles or magnetic moments, etc.), while the latters account for the off-site feaures, typically the spin-spin relative positions. In order to study their distinct disorder effects, we assume a model interaction in which the chemical and structural features are factorized: U (r, r ) = -λ r λ r J (r -r ) .

(

) 1
The on site-parameters λ r 's, with probability distribution P λ , are statistically independent from the random positions {r}'s of the lattice sites. Hence, the off-site couplings J (r -r )'s are themselves random variables, with a probability distribution P J , independent from P λ . We call "average crystal", with Curie temperature T J,λ , the ordered system with interaction energy λ r λ r J (r -r ) , where and/or P J . In contrast, • • • will indicate a mean value including the thermal average too. Though T J,λ does not refer, in general, to any real crystal, it represents a convenient reference value, with respect to which one studies the enhancement or depression of T c with increasing chemicalstructural fluctuations. In view of studying the disorder effects to the lowest significant order, we shall refer to the so called disordered crystal model, i.e. a lattice {r} whose sites r = f + u f are slightly shifted with respect to a reference crystalline lattice {f }, by a random displacement u f (|u f | << first nearest neighbor distance). Taking advantage of the one-to-one correspondence between {r} and {f }, all the quantities can be expressed in terms of the reference crystal lattice. In particular, the coupling J (r -r ) reads, on setting

ρ f f = u f -u f : J (r -r ) = J f f = J(f -f ) + ∂J(f -f ) ∂f α ρ α f f + 1 2 ∂ 2 J(f -f ) ∂f α ∂f α ρ α f f ρ α f f + • • • , (2)
to second order in the displacements, where α numerates the spatial cartesian components and the summation over repeated indices is intended. In this case, the structural disorder is described by the probability distribution P ρ (ρ) of the random anti-symmetric variable ρ f f = -ρ f f . In Sections 2 and 3 it will be shown that the random fluctuations always enhance the Curie temperature, with the exception of the structural disorder in Heisenberg-like systems (see Table 1 for a qualitative summary). In this case the overall effect on T c turns out to be model-dependent. This is due to the existence of a negative contribution [7], that is argued to reflect the interplay between structural disorder and spin waves. In Section 4, the present results will be compared with those obtained in ref.s [7,11], in which the interaction energy U (r, r ) is assumed as an overall random variable, without distinction between structural and chemical disorder. In Section 5, the applications of the model interaction eq.n (1) to real systems are discussed. The model fits well with ferroelectric systems, since λ r , carrying the chemical disorder, can be related to the magnitude of the on-site dipole, and the coupling function J(r -r ) is influenced only by the structural disorder, through the relative position r -r . Experimental evidences supporting the results of Section 2 have been actually reported, in the context of ferroelectrics perovskites [5,9]. An alternative theory, specific for ferroelectrics, has been already formulated [10], with results quite consistent with those obtained in Section 2. The application of eq.n (1) to ferromagnets with exchange interactions is less immediate, due to the impossibility of an exact separation of chemical and structural components, when those are nested in an exchange integral. However, an approximate method is proposed for estimating the relative weight of chemical and structural disorder in this case too. It should be clear that eq.n (2) can be applied also to the thermal atomic displacements in an otherwise perfect crystal. The resulting modification of T c will be calculated in Section 5.

T c Chemical Structural Ising + + Heisenberg + ± model-dependent

Disorder effects on Ising-like systems

For Ising-like model we mean an array of N semi-classical spins s g , all oriented along the z-axis, and ranging over a set Λ of discrete or continuous values (for simplicity, we assume the same Λ for all the spins). In this static approximation, the set of magnetic energies E depends on a N -component vector s = s g1 , s g2 • • • , s g N . From eq.n (1) one has:

E (s) = - 1 2 g,f λ g λ f s g s f J gf , (3)
where the prime in the sum means g = f . For ferromagnetic systems, one can assume J > 0 and λ g > 0. According to the MF approximation, the energy E in eq.n (3) is replaced by a sum E mf = (1/2) g g of single-site energies [17,18]:

g (s g | ŝ) = -s g λ g f =g λ f ŝf J gf , (4)
in which ŝf is the thermal mean value of the spin variable s f . The self consistent equation, determining ŝg then reads: If Λ (the array of the spin values) is symmetric with respect to zero, i.e., each value of the spin is present with both signs, the function F in eq.n (5) has the following properties [START_REF]For discrete valued spins, F is a Brillouin function[END_REF]:

ŝg = s∈Λ e -β g (s| ŝ) s s∈Λ e -β g (s| ŝ) = F   βλ g f =g λ f ŝf J gf   . (5
F (2n) (0) = 0 for each n ; Ḟ (0) > 0 ; ... F (0) < 0 . (6)
One main point in eq.n (1), is the possibility of rescaling the s r 's and defining new interacting variables S r = λ r s r . While studying the S r 's or the s r 's is perfectly equivalent, in an exact calculation, this is not the case in a MF approach in which either S r or s r are assumed siteindependent. In both cases, the approximation involved is neglecting the statistical correlations between the interacting variables. In the latter case, however, one neglects also the correlations between the s r 's and the λ r 's. In fact, passing to the dressed spins S g , equation ( 5) reads:

Ŝg = λ g F   βλ g f =g Ŝf J gf   = Φ g λ g , Ŝ . (7)
Equation ( 7) contains the on-site disorder only through the parameter λ g . Therefore Ŝg is statistically independent from the other λ's, while ŝg is not (eq.n ( 5)). This shows that the correct procedure is calculating S , then, possibly, expressing s as λ -1 S .

The quantity of interest is the joint probability distribution P joint Ŝ of the dressed spin values. Neglecting the correlations of the Ŝg 's means assuming P joint Ŝ = g P S Ŝg . Setting x g = β Ŝg , the equation for the probability distribution P (x g ) becomes, from eq.n (7):

P (x g ) = dP λ f =g dx f P (x f ) dP ρ (ρ gf ) δ (βΦ g -x g ) , (8a)
where

Φ g (λ, x) = λF   λ f =g x f J gf   , (8b)
and dP λ = P λ dλ, dP ρ = P ρ dρ account for on-site and off-site disorder respectively (recall eq.n ( 2)). The mean value S = κT x and the standard deviation σ S = κT x 2 -x 2 of the dressed spins follow from the two coupled equations: according to eq.ns (8). On setting:

x = dxP (x)x = β λF ; x 2 = dxP (x)x 2 = β 2 λ 2 F 2 , (9)
ρ = 0 , λ = 1 + ∆λ , x = x + ∆x (10a) ∆λ = ∆x = 0 (10b) ρ 2 α = σ 2 ρ , ∆λ 2 = σ 2 λ , ∆x 2 = σ 2 x , (10c)
one defines the fluctuations of the random variables about their mean values and the corresponding square standard deviations. The first relation (10a) means that the reference crystal and the average crystal coincide. The second relation (10a) means that λ = 1, which can be assumed without loss of generality (possibly on rescaling J). The first relation (10c) refers to each of the cartesian components of ρ, that we assume to be independent from one another and identically distributed. The system of equations ( 9) is obtained by expanding the integrand in (8a) to the lowest significant order in the fluctuations ∆x, ∆λ and ρ. This results in the following expressions:

x β = F (θ) + Ḟ (θ) x σ 2 λ J 0 + σ 2 ρ J 2 + + F (θ) 2 x 2 σ 2 λ J 2 0 + x 2 σ 2 ρ w 2 1 + σ 2 x J 2 1 , (11a)
x 2 β 2 = 1 + σ 2 λ F 2 (θ) + + 2F (θ) x σ 2 ρ J 2 F (θ) Ḟ (θ) + 2σ 2 λ F (θ) J 0 + + Ḟ 2 (θ) + F (θ) F (θ) x 2 σ 2 λ J 2 0 + x 2 σ 2 ρ w 2 1 + σ 2 x J 2 1 (11b)
in which (recall eq.n (2)):

J 0 = D =0 J(D) , J 2 1 = D =0 J 2 (D) (12a) J 2 = 1 2 D =0 ∇ 2 D J , J 2 3 = D =0 (∇ D J) 2 (
In order to calculate the Curie temperature T c , one looks for the solutions of the equation system (11) by an appropriate expansion of the functions F , Ḟ and F in θ or x (eq.n (12c)), up to x 3 . Recalling eq.ns (6), one gets, for the non trivial solutions ( x = 0):

x 2 = κT ρ,λ A 1 + σ 2 λ + σ 2 ρ J 2 -σ 2 x J 2 1 | ... F (0)| 2 Ḟ (0) - T T ρ,λ ≥ 0 (13a)
and

σ 2 x = x 2 -x 2 = x 2 4 σ 2 λ + σ 2 ρ J 2 /J 0 + σ 2 ρ J 2 3 /J 2 0 T /T ρ,λ 2 -J 2 1 /J 2 0 ≥ 0 , (13b)
in which

κT ρ,λ = Ḟ (0)J 0 (14a)
defines the Curie temperature of the reference (or average) crystal, and

A = | ... F (0)| 6 J 3 0 1 + 6σ 2 λ + 3σ 2 ρ J 2 3 /J 2 0 (14b)
is a positive constant. On substituting eq.n (13b) in eq.n (13a), it is immediately seen that x ∝ 1 -T /T c for T < T c , where

T c = T ρ,λ 1 + σ 2 λ + σ 2 ρ J 2 (15)
is the Curie temperature including the disordered effects to lowest order. It is seen that T c increases with increasing chemical disorder. If J 2 (eq.n (12a)) is positive, which is the standard case, for J(D) positive and decreasing with |D|, the structural disorder does enhance T c in turn. It is intended that equations ( 13) apply for T close to T c , which is, in turn, close to T ρ,λ . This ensures that σ 2

x (eq.n (13b)) is positive. In fact J 2 0 /J 2 1 (eq.ns (12a)) is certainly larger than 1, since it represents an effective number of first nearest neighbors (the exact number, actually, if J is a constant, coupling only the first nearest neighbors).

If one were to follow the same procedure adopted above, to calculate s according to eq.n (5), it is not difficult to see that the result would be simply T c = T ρ,λ 1 + σ 2 ρ J 2 , i.e. the absence of any chemical disorder effect on the Curie temperature. In fact, in eq.n (5) the random variables λ's refer to different sites, so that all the bilinear terms ∆λ g ∆λ f vanish in average. In contrast, Φ g in eq.n (7) depends only on λ g . This yields the term

β Ḟ (θ) x σ 2 λ J 0 (16)
(eq.n (11a)), that is responsible for the relative increment σ 2 λ of the Curie temperature in eq.n (15). As mentioned above, assuming s g siteindependent introduces an additional error with respect to the same assumptions on S g . Setting x g = βŝ g , an estimate of this error is given by the correlation term

c hg = λ h x g -λ h x g = = -β f dP λ (λ f ) ∆λ h f =g dP (x f ) dP ρ (ρ gf ) × × F   λ g f =g λ f x f J gf  
(recall eq.n ( 5)). On expanding F to first order in the ∆λ g,f 's and in the ρ gf 's, the preceding equation yields

c hg = βσ 2 λ x J(g -h) Ḟ ( x J 0 ) .

Recalling the definition (12c), the sum

h c hg = β x σ 2 λ J 0 Ḟ (θ) (17)
gives the total error, that coincides exactly with the term eq.n (16). Hence, the absence of chemical disorder effects in the Curie temperature T c = T ρ,λ 1 + σ 2 ρ J 2 , calculated under the assumption s f siteindependent, results from neglecting the statistical correlations between the λ h 's and the ŝg 's. This error is exactly compensated by the increase of the Curie temperature, calculated for the dressed spins S g = λ g s g .

Disorder effects on Heisenberg-like systems

The simplest example of Heisenberg ferromagnet is an array of Pauli spins s l , interacting through the coupling energy eq.n (1). This leads to the following Hamiltonian:

8 F o r P e e r R e v i e w O n l y H = - 1 2 l,h J lh λ l λ h s l s h = (18a) = 1 2 l,h J lh λ l λ h n l -b † l b h -n l n h , (18b)
in which, passing from (18a) to (18b), the spin components

s x g = b g + b † g , s y g = i b † g -b g , s z g = 1 -2 b † g b g (19)
have been expressed in terms of the creation-annihilation operators b † g , b g . Those obey Bosonic and Fermionic commutation rules for f = g and f = g, respectively [START_REF] Bogolyubov | [END_REF]. In particular:

b f , b † g = δ f g (1 -2 n g ) , n f = b f b † f . ( 20
)
Following the same procedure as in Section 2, we define the dressed spins S f = λ f s f and the corresponding operators

B † f = λ f b † f , B f = λ f b f such that, from (20): B f , B † g = δ f g λ 2 f -2 N f , S z f = λ f -2 N f λ f , N f = B f B † f . (21)
The Hamiltonian (18a) then becomes:

H = 2 l,h J lh λ l λ h N l -B † l B h - N l N h λ l λ h . ( 22
)
Following the seminal work of Zubarev [21] and the development by Montgomery et al [7], one defines the time dependent two-site Green function G gf (t -t ) = B g (t) ; B † f (t ) T , whith motion equation:

i dG gf (t -t ) dt = δ (t -t ) B g (t) , B † f (t) T + + [B g (t), H] ; B † f (t ) T . (23)
Note that in the present section the thermal average is indicated as

• • • T , instead of • • •. On time-Fourier transforming G gf (t -t ) = ∞ -∞ dω e -iω(t-t ) G gf (ω) ,
δ gf = 2π l ω λ g S -2 h J hg δ lg + 2J lg G lf (ω) (24)
under the following approximations:

N l (t)B g (t); B † f (t ) T = N l (t) T B g (t); B † f (t ) T (25a) λ g -2 N g T /λ g = S z g T = S independent from g . (25b)
Equation (25a) corresponds to decoupling the hierarchy of the higher order Green functions to the lowest possible level. Equation (25b) is equivalent to the assumption in Section 2 that the thermal averaged z-components of the dressed spins are statistically independent. Equation ( 24) is equivalent to eq.n (9a) of ref. [7], once noticed that λ g S = λ 2 g -2 N g T represents, in terms of the dressed spins, the same quantity 1 -2n = σ used therein (recall the second definition ( 21)). The self consistent equation determining S follows from calculating the mean value N g = λ 2

g -λ g S z T /2 and reads (see eq.n (8) in ref. [7] and eq.ns (10)):

1 + σ 2 λ -S 2 = 1 N dωTr Im G (ω, S) e βω -1 -1 , (26)
N being the total number of spins, β = 1/κT and h = 1. G (ω, S) represents the matrix of elements G gf (ω, S), whose "imaginary" part is defined as [21]:

Im G (ω, S) = lim →0 + i G (ω + i , S) -G (ω -i , S) , (27)
in the sense of the distribution theory. For simplicity, let us split the problem into two parts: on-site disorder without off-site disorder and vice versa. The resulting Curie temperatures will be indicated as T on c and T of f c respectively. Due to the assumed reciprocal independence and to the lowest-order approximation adopted, the two effects can be simply summed up to yield the total effect on T c . First, we deal with the on-site disorder only. In this case, recalling eq.n (12a), equation (32a) can be put in the form A G = I, where the matrix elements of A read, on account of eq.ns (10a):

A gl = A 0 gl 2π ω S -2J 0 δ lg + 2J (l -g) - -2π ω S δ lg ∆λ g -∆λ 2 g + • • • ∆A gl . ( 28a
)
The "unperturbed" matrix A 0 is easily diagonalized on the basis of eigenvectors |q with g-representation g | q = e i(g q) / √ N and eigenvalues:

a 0 (q) = 2π ω S -2 J 0 -J(q) ; J(q) = f J(f )e i(f q) . ( 28b
)
The eigenvalue perturbation is easily found to first order, from the definition (28a):

∆a 1 = q|∆A| q = -2π ω S g ∆λ g N - g ∆λ 2 g N + • • • = = 2π ω S g ∆λ 2 g N + • • • , (29)
in which the final expression is obtained from the central limit theorem in the thermodynamic limit. Equation (29) shows that the perturbation is quadratic in the ∆λ's, which leads to include the second order perturbation too, for self consistency. We anticipate that this does not change the final result, though the proof is a little bit complicated. The second order perturbation reads, in fact:

∆a 2 = q =q q|∆A| q q |∆A| q a 0 (q) -a 0 (q ) = = 2π ω 2 S 2 N 2 g,g ∆λ g ∆λ g q =q e i(q-q )(g -g) 2 J(q ) -J(q) . ( 30
)
Following ref. [7], we take the average a(q) , that reads, from eq.ns (29) and (30):

a(q) = a 0 (q) + 2πσ 2 λ ω S + ω S 2 ∆ 2 (q) , (31a)
∆ 2 (q) = 1 2N q =q J(q ) -J(q) -1 , (31b)
At the lowest significant order one sets A = q | q ; 1 1; q |/ a(q) , where | q ; 1 is the first-order perturbed eigenvector (not explicitly written here, for brevity). Hence the Green function turns out to be:

G = A -1 = 1 2π (1 + σ 2 λ ) q | q ; 1 1; q | ω/S -j 0 (q) + (ω/S) 2 ∆ 2 (q) = = 1 2π (1 + σ 2 λ ) q | q ; 1 1; q | [ω/S -j 0 (q)] [ω/S -x -(q)] ∆ 2 (q) (32a) with j 0 (q) = 2 J 0 -J(q) 1 + σ 2 λ , x -(q) = - 1 + j 0 ∆ 2 (q) ∆ 2 (q) . (32b)
The lower line in eq.n (32a) is obtained by expressing a (the denominator of the upper line) in terms of its zeroes x + = j 0 and x -(second eq.n (32b)), calculated to the lowest order in ∆ 2 . Having expressed G as a sum of (double) first order poles in ω/S, equation (27) readily yields

Tr Im G = 1 (1 + σ 2 λ ) q δ (ω/S -j 0 ) 1 + 2j 0 ∆ 2 + δ (ω/S -x -) (x --j 0 ) ∆ 2 q . ( 33
)
Substituting (33) in eq.n (26), one gets:

1 + σ 2 λ -S 2 = S N (1 + σ 2 λ ) q 1 e βS j0(q) -1 [1 + 2j 0 (q)] + + 1 ∆ 2 (q) e βS x-(q) -1 [x -(q) -j 0 (q)] , (34)
whose limit S → 0 gives the equation for T on c . From eq.ns (32b), and expanding all terms to the lowest order in ∆ 2 , equation (34) yields:

1 + σ 2 λ 2 = κT on c N (1 + σ 2 λ ) q 1 j 0 (q) -∆ 2 (q) = = κT on c N (1 + σ 2 λ ) q 1 j 0 (q) , (35)
since q ∆ 2 (q) = 0 for symmetry (eq.n (31b)). As anticipated above, the second-order perturbation term ∆ 2 has no influence on the final result eq.n (35). In the absence of on-site disorder, equations ( 35) and (32b) yield:

T -1 ρ,λ = κ N q J 0 -J(q) -1 (36)
for the Curie temperature of the average crystal. Then equations ( 35) and (36) show that the on-site disorder leads to the same increasing factor T on c /T ρ,λ = 1+σ 2 λ for the Curie temperature of a Heisenberg ferromagnet, as for the semi-classical, Ising-like model. The effects of the pure off-site disorder can be studied with the same procedure adopted above. The matrix elements A gh now read:

A gh = A 0 gh -4π δ gh l ∂J(g -l) ∂g α ρ α gl - ∂J(g -h) ∂g α ρ α gh - -2π δ gh l ∂ 2 J(g -l) ∂g α ∂g α ρ α gl ρ α gl - ∂ 2 J(g -h) ∂g α ∂g α ρ α gh ρ α gh , (37)
where the unperturbed matrix elements A 0 gh are the same as in eq.n (28a) and the sum over repeated α-indices is intended. The first order correction to the unperturbed eigenvalue a 0 (q) (eq.n (28b)) is

∆a 1 (q) = 1 N gh e iq(h-g) A gh -A 0 gh ∆A gh = -4πσ 2 ρ J 2 -J 2 (q) , (38a)
where

J 2 (q) = 1 2 f ∇ 2 D J(D)e iq D , J 2 = J 2 (0) . ( 38b
)
The second order correction is:

13

F o r P e e r R e v i e w O n l y ∆a 2 (q) = 1 N 2
q =q g,h,g h e iq(h -g)+iq (h-g ) a 0 (q) -a 0 (q ) ∆A gh ∆A g h

From eq.n (37) and from the relation ρ α gh ρ α g h = σ 2 ρ δ αα (δ gg δ hh -δ gh δ hg ), one gets:

∆a 2 (q) = 32π 2 σ 2 ρ N q =q c(q,q ) J 2 3 + J 2 3 (q + q ) -J 2 3 (q) -J 2 3 (q ) a 0 (q) -a 0 (q ) , (39a)
with

J 2 3 (q) = D [∇ D J(D)] 2 e iq D , J 2 3 = J 2 3 (0) . ( 39b
)
The time-transformed Green function G = q |q ; 1 1; q| a 0 (q) + ∆a 1 (q) + ∆a 2 (q) is now expressed as a sum of single poles in ω/s. The equation for T c readily follows from eq.ns (38), ( 39) and (28b). At the lowest order in σ 2 ρ one finally gets:

T of f c = T ρ,λ 1 + σ 2 ρ (C + -C -) , (40a)
with the two constants C ± given by:

C + = 1 q J 0 -J(q) -1 q J 2 -J 2 (q) J 0 -J(q) 2 , (40b)
C -= 1
N q J 0 -J(q)
-1 q,q c(q, q ) 2J 0 -J(q) -J(q

) J 0 -J(q) 2 J 0 -J(q ) 2 . ( 40c
)
The positivity of the two terms C ± is not "universal". However, from the definition of c(q, q ) in eq.n (39a), it follows that C ± > 0 if J(q) and J 2 3 (q) are positive and decreasing with increasing argument, which is the standard case in the ferromagnetic regime. In conclusion, the Curie temperature of a Heisenberg ferromagnet, including both chemical and structural disorder, turns out to be:

T c = T ρ,λ 1 + σ 2 λ + σ 2 ρ (C + -C -) , (41)
to the lowest significant order in the random fluctuations. The overall sign of C + -C -depends on the coupling function J(r-r ) in a complicated way, and cannot be determined by simple arguments. For Heisenberg-like systems, the enhancement or depression of T c due to the structural disorder is, thereby, model-dependent.

Comparison with other MF theories

A comparison of the preceding results can be made with the MF theories developed in ref.s [11,7], that assume the interaction energy U (r, r ) as an overall random variable. In this representation, the disorder effects are those produced by the energy fluctuations about the mean value U that determines the average crystal and, accordingly, the reference Curie temperature T U . Since there is no rescaling of the interacting variables, one is left with the calculation of the mean value s of the "naked" spins. Let us first consider the Ising-like systems. In this case it is easy to see from ref. [11] that T c = T U , and the disorder effects simply result in a depression of the magnetization, in the close proximity of the Curie temperature:

s ∝ 1 - T T U 1 -δ 2 , ( 42
)
where δ is proportional to the fluctuations of the interaction energy. In the present model, one has s = λ -1 S = 1 + σ 2 λ S , according to eq.ns (10) (the lowest order approximation is intended), and σ 2

x ∝ (1 -T /T c ) (eq.ns ( 13)). Hence, setting T = T ρ,λ in eq.n (14b) and after a suitable rearrangement of terms in eq.ns ( 13), (14b), one gets:

s ∝ 1 - T T c 1 -δ 2 , (43a)
δ 2 = 2σ 2 λ 1 + 2J 2 1 /J 2 0 1 -J 2 1 /J 2 0 + 3 2 σ 2 ρ J 2 3 /J 2 0 1 -J 2 1 /J 2 0 . (43b)
As can be seen, the random fluctuations of the coupling energy U , resulting from σ 2 λ and σ 2 ρ , tend to depress s close to the Curie temperature, as in eq.n (42). At this stage, it is instructive expressing T U (eq.n (42)) in terms of the present model. First, we calculate the mean value and the standard deviation of the interaction energy according to eq.ns (1) end ( 2

U (r, r ) = dP ρ dP λ U (r, r ) = -J(f -f ) - σ 2 ρ 2 ∇ 2 f J(f -f ), (44a)
σ 2 U = σ 2 ρ [∇ f J(f -f )] 2 + 2σ 2 λ J(f -f ) . (44b)
Since T U is the Curie temperature corresponding to the average crystal with interaction energy eq.n (44a), one easily gets:

T U = T ρ,λ 1 + J 2 σ 2 ρ T c = T U + σ 2 λ T ρ,λ    (Ising) (45)
in which T ρ,λ (eq.n (14a)) is the reference Curie temperature in the chemical-structural disorder representation, and the lower line follows from eq.n (15). It is not difficult to perform the same calculation for the Heisenberglike systems too. From eq.ns (44) and (41), it follows that

T U = T ρ,λ 1 + σ 2 ρ C + T c = T U -σ 2 ρ C -T ρ,λ + σ 2 λ T ρ,λ    (Heisenberg) . (46)
In the absence of chemical disorder (σ 2 λ = 0), equations ( 45) and (46) recover the results of ref.s [11,7] that the Curie temperature is not affected by the random fluctuations of the interaction energy about its mean value, in Ising-like systems (eq.n (45)), and decreases linearly with σ 2 U in Heisenberg-like systems (eq.n (46)). In fact, the term J 2 σ 2 ρ comes from eq.n (44a), and the term -σ 2 ρ C -T ρ,λ comes from eq.n (44b), i.e. right from σ U (eq.n (40c)). The main point of the preceding arguments is that, passing from the chemical-structural representation to the one adopted in ref.s [7,11] (in which the unique random variable is U itself), the positive terms J 2 σ 2 ρ and T ρ,λ σ 2 ρ C + , due to the structural disorder, seemingly disappear, since they are incorporated in T U (i.e. in a different average crystal). In contrast, the increasing effect of the chemical disorder on T c cannot be removed by a redefinition of the average crystal, i.e. by replacing T ρ,λ with T U . This shows that the model interaction eq.n (1) and the one adopted in ref.s [7,11] cannot be mapped one into another, except in the absence of chemical disorder. At this stage, it should be clear that speaking about a Curie temperature increasing (or decreasing) with increasing disorder is misleading, unless one defines exactly which representation of the disorder has been adopted. As mentioned in Section 1, the model interaction eq.n ( 1) is an ideal expression in which the spin-spin coupling can be exactly factorized in a part J(r -r ), depending only on the positions of the spins (structural disorder), and a part λ r λ r , accounting for the characteristic of the spins themselves (chemical disorder). The simplest application is certainly on ferroelectric systems. In this case the "spins" are actually atomic scale displacements of charges, generating electric dipoles, whose intensity is determined by the Born effective charge Z * r , that can be related, after suitable rescaling, to the on-site parameter λ r . The dipole-dipole coupling J(r -r ) is usually split into a nearest-neighbor contribute, strongly dependent on the local symmetries, plus a long-range term ∝ |r -r | -3 [22]. Of course, the present model applies to magnetic dipoles too, whose interaction energy is usually small, compared to the exchange interaction. However, there are cases in which this is not true [23]. A theoretical model for perovskite ferroelectrics, leading to an increase of T c has been formulated by Bokov [10], by calculating the total polarization as the sum of single-cell contributions, each characterized by a local T c , whose fluctuations reflect the different cationic content of the cell. An experimental support to the validity of eq.n (15) has been obtained right for ferroelectric perovskites, by Sinclair and Attfield [5]. The measured T c of ATiO 3 -systems (with A a cation) is shown to increase linearly with the square standard deviation σ 2 A of the Aradius size, whose random fluctuations are obtained by the binary cationic mixture A = Ba 1-x Mg x , and the changes of σ 2

A are controlled by the relative concentration x. In this case, it is reasonable to think of a direct influence of the cationic disorder on the Born effective charge, or on other local quantities determining the dipole intensity. This would result in what we call the chemical disorder, whose enhancing effect on T c is common to Ising-like and Heisenberg-like systems. The application of eq.n (1) to the exchange magnetic interactions is less immediate. As a typical example, let us deal with a substitutional random alloy, each site of which can be occupied by an orbital ψ α , with probability p α . In this case the true exchange energy between two spins with relative position D = r -r reads:

U true (r, r ) = -e 2 dr 1 dr 2 |r 1 -r 2 | × × ψ αr (r 1 ) ψ * α r (r 1 -D) ψ α r (r 2 -D) ψ * αr (r 2 ) = = U true (α r , α r ; D) . (47)
Since the on-site features are displayed by the two orbitals ψ αr , ψ α r , it is clear that no exact factorization is possible. However, in view of a qualitative account of the on-site vs off-site disorder effects, one can replace U true with a form like eq.n (1), for an appropriate choice of J(D) and λ r . In particular, the quantities

J(D) = - α,α p α p α U true (α, α ; D) (48a) λ r = α p α U true (α r , α ; D) dD J(D)dD = = α p α U true (α , α r ; D) dD J(D)dD (48b)
define, respectively, the mean dependence of the exchange energy on the relative position, and on the on-site orbital (note that λ r = 1). In this case, U (r, r ) = -λ r λ r J(D) reproduces the statistical properties of U true modulo the coupling of the random variables' fluctuations. Hence, the use of eq.ns (48) is especially suitable in a MF approximation, aiming to achieve a guess of the relative importance of the chemical and structural disorder. Recent theoretical works have stressed the importance of the thermal disorder for a correct interpretation of the magnetic properties. In ref. [15,16], the coupling between thermal fluctuations and itinerant electrons is argued to yield a crucial contribute to the magnetization, especially in the transition between ballistic and diffusive regime. In ref. [24] the effects of the thermal expansivity on the magnetization are shown to be non negligible in some cases. It is worthwhile mentioning that the disordered crystal model and eq.n (2) have a staightforward application to the thermal disorder effects in an otherwise perfect ferromagnetic crystal. In this case, in fact, the fluctuations of the distance |r -r |, described by the random variable ρ, are of pure thermal origin. For high enough temperature T , the probability distribution P ρ is Gaussian with square standard deviation σ 2 ρ = κT /M Ω 2 D , where M is the atomic mass (for monoatomic systems), and Ω D is comparable to the Debye frequency. In the reasonable hypothesis that the spin variables are fast enough to allow for the application of the Born-Oppenheimer approximation, equation (40a) can be used to calculate the resulting (structural) disorder effect on the Curie temperature:

T of f c = T ρ 1 + κT ρ M Ω 2 D (C + -C -) , (49)
T ρ being the Curie temperature of the rigid crystal. In the present work the disorder effects on the Curie temperature, due to the chemical and structural disorder, have been studied separately, by assuming a suitably factorized form of the spin interactions (eq.n (1)). It is shown that the chemical (on site) disorder leads to distinguish between spins s g and "dressed" spins S g = λ g s g . In the realm of the mean field approximation, it has been argued that the better approximation is assuming S g site-independent, and calculating the dressed magnetization ∝ S . If necessary, one may set s = λ -1 S . Following this line, it has been shown in Sections 2 , 3 that the chemical disorder enhances T c , by a term proportional to the square standard deviation σ 2 λ , both in Ising-like and in Heisenberg-like systems. The structural (off-site) disorder enhances in turn the T c of the Ising-like systems, but contributes two terms ±σ 2 ρ C ± , with opposite sign, to the T c of the Heisenberg-like systems. The overall effect, enhancement or depression, is model-dependent. Since -σ 2 ρ C -is specific of the Heisenberg-like systems with structural disorder, one may argue that the delocalization driven by the spin waves is the unique responsible of the negative sign. Special emphasis is given (Section 4) to the representation of the disorder, by comparing the present model with other MF theories [11,7], in which the random variable is the interaction energy U (r, r ) itself. It is shown that the structural disorder provides a representation equivalent to the one in ref.s [11,7], while the chemical disorder does not. This argument calls attention on the necessity of specifying the disorder representation adopted, in order that the enhancement or depression of the Curie temperature is defined unambiguously. Supports to the results in Sections 2 , 3 have been found in experimental data and other theoretical models referring to perovskite ferroelectrics [5,9,10], to which the factorization (1) applies directly. In ferromagnets, a comparison with experiments is less immediate and, at present, not significant, for two related reasons. First, most of the experimental works on ferromagnets are concerned on the modifications of T c induced by changes of some controlled average parameters (pressure, alloy/defect concentration, etc.). The effects of the random fluctuations about those average values (what we mean for "disorder effects") are indeed more difficult to be observed. Second, the current theoretical approaches usually deal with the interaction energy U (r, r ) as with an overall random variable and no clear separation is made between structural and chemical part [11,7]. Indeed, the factorization (1) is not exactly feasible, if the chemical-structural features are nested in an exchange integral, as it is the case of ferromagnets. However, the approximate method suggested in Section 5 for factorizing the two contributions in the exchange interactions too, could be of some

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of disorder (chemical and structural) on Tc of Ising and Heisenberg-like systems. + and -indicate enhancement and depression respectively

http://mc.manuscriptcentral.com/pm-pml Philosophical Magazine & Philosophical Magazine Letters

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J Cottyn

H Van Landeghem

K Stockman

S Derammelaere

A Method to Align a Manufacturing Execution System With Lean Objectives

Keywords: manufacturing, execution system, lean, ISA 95, continuous improvement, value stream map

The application of IT and Lean principles have long been seen as mutually exclusive, but both approaches are more and more claimed to be interdependent and complimentary. Real-time production information is crucial to make important business decisions. A Manufacturing Execution System (MES) can provide the necessary support during the Lean journey. MES can trigger, feed or validate the Lean decision making process by providing useful information. In addition, MES can maintain the process improvements by enforcing the standardized way of working. However, this is only possible when MES is aligned and is kept aligned to the Lean objectives. The MES processes must be included in the continuous improvement cycle to prevent them of becoming obsolete. In this work a method is proposed to analyze this alignment between Lean and MES. The Manufacturing Operations Management (MOM) framework provided by ISA 95 is believed to deliver the necessary components to identify and structure this alignment. Mapping MES and Lean activities onto the same framework brings valuable insights about their dependency. The analysis is explored through a case example. Preventing the system of becoming obsolete, by proposing standard model changes, is an important direction for further research.

Introduction

Today's economic environment drives the adoption of strategic initiatives. In order to survive, companies need to get the most and the best out of the available resources. It is a continuous struggle to eliminate unnecessary production costs; improve manufacturing, process and business performance; increase throughput; reduce cycle times; maintain quality; etc. (Epicor 2008a). One of the strategic initiatives that helps manufacturers to remain competitive is Lean Manufacturing. Lean is a philosophy carrying the motto 'Doing more, with less!'. The concept of 'Lean' was first introduced by [START_REF] Womack | The machine that changed the world[END_REF] in order to describe the working philosophy and practices of the Japanese vehicle manufacturers and in particular the Toyota Production System (TPS). The essence of Lean thinking is specifying value and -by doing so -simultaneously uncovering waste. The initial concept of Lean was extended to five key principles by [START_REF] Womack | Lean Thinking[END_REF]: Specify value; identify value streams; make value flow; let the customer pull value and pursue perfection. The ultimate goal is a production process without any of the seven deadly wastes: overproduction, waiting, transport, extra processing, inventory, motion and defects.

However, as that situation is impossible to reach, Lean manufacturing is a continuous process towards perfection.

Lean thinking has evolved over time and has expanded beyond its origins in the automotive industry and its narrow definition around shop floor improvement (Hines et al. 2004). Lean is a philosophy and not a tool itself. Numerous tools and techniques -such as Single Minute Exchange of Dies (SMED), Six Sigma, Kanban, Value Stream Mapping (VSM), 5S, Total Quality Management (TQM), Theory of Constraints (TOC), Total Productive Maintenance (TPM), Business Process Management (BPM), Visual Management, etc. -can support the Lean transformation in order to identify, measure and remove waste, variability and overburden and deliver improvements in specific areas. SMED reduces waiting and overproduction by creating shorter machine setup times. VSM draws the actual material (and information) flow through the manufacturing resources and can reveal important areas for improvement. VSM can be considered as the starting point for any Lean transformation and its applicability is well documented in literature [START_REF] Rother | Learning to See: Value Stream Mapping to Add Value and Eliminate Muda[END_REF][START_REF] Braglia | A new value stream mapping approach for complex production systems[END_REF], Abdulmalek et al. 2007, Nash and Mazur and Chen 2008, [START_REF] Serrano | Evaluation of value stream mapping in manufacturing system redesign[END_REF]. Kanban reduces inventory by introducing a consumer pulled production system. The thoughtful application of the various approaches to exploit full Lean potential has had its share of attention (Shah andWard 2003, Lasa et al. 2009). In order to avoid the misapplication of Lean manufacturing tools and metrics, Pavnaskar et al. (2003) introduce a classification scheme. With the classification scheme, manufacturing problems can be linked to the appropriate Lean manufacturing tools that will solve the problem.

As various tools and techniques exist to work towards the Lean goal, it is necessary to carefully plan and keep track of the Lean efforts. Value stream mapping results in the construction of a Lean roadmap. This work plan is a sequence of Lean practices that will be performed in order to evolve from the current (AS-IS) to the future (TO-BE) situation. A Lean planning system can document as well the progress as the impact of each step on carefully selected Lean metrics. This assessment tool structures the Lean journey by continuously updating the performance and the work plan. Lean metrics are a set of performance measures for Lean manufacturing.

Examples are process throughput, total manufacturing lead time, labour productivity, Overall Equipment Effectiveness (OEE), etc. Many studies define their own metrics by performing some sort of statistical analysis on survey data. [START_REF] Shah | Defining and Developing Measures of Lean Production[END_REF] use a feature extraction method to determine adequate measures of Lean production. Ray et al. (2006) developed a Lean index for the wood products industry. The study demonstrates that the statistical methodology of factor analysis can be used to develop a quantitative definition and assessment of the concept of 'leanness' for any wood processing company. The impact of typical Lean activities on the features of a Lean environment and the Lean performance metrics are presented by [START_REF] Duque | Lean manufacturing measurement: The relationship between Lean activities and Lean metrics[END_REF].

Mejabi (2003) proposes a framework for a Lean planning system that can be used to monitor and quantify the continuous improvement efforts.

To be able to pinpoint improvement opportunities and assess the progress, (historical and real-time) information must be available (Aberdeen 2005). That is why manufacturers see a greater need to adopt, upgrade or expand their business IT solutions. For example, Enterprise Resource Planning (ERP) software maintains important business data and supports the administrative processes. Product Lifecycle Management (PLM) software guides the product through the different stages of its Carefully designed windows on the data can extract useful information, that is not visible at first sight. This Business Intelligence (BI) can expose the necessary opportunities to steer the business decision-making process.

Figure 1 shows how this idea can be extended to the manufacturing level. In this work the necessary alignment between strategic objectives and operational support is described. In particular, the role of manufacturing operations management (MOM) during the Lean journey is emphasized. Both approaches pursue the same objectives and -if properly combined -are seen as mutually supportive. MOM can trigger, feed or validate the Lean decision making process by providing useful information. In addition, MOM can maintain the process improvements by enforcing the standardized way of working. On the other hand, MOM processes most be included in the continuous improvement cycle to prevent them of becoming obsolete. Section 2 provides a general overview of the combination of the Lean philosophy and the use of Information Technology (IT). The MOM framework provided by the ISA 95 standard is believed to deliver the necessary components to structure the alignment between MES and Lean. Section 3 describes the method for this alignment, in as well green-as brownfield projects. The proposed method is explored by a case example in section 4. Section 5 concludes and mentions further research.

Continuous Improvement & IT

The application of IT and Lean principles have long been seen as mutually exclusive.

Lean advocates have the idea of putting in place a simplified information management system (Houy 2005). They consider that organizations based on continuous flow should limit information needs to local communication between upstream and downstream production units. In their view, it is preferable for employees to search for the information they need, as and when they need it, rather than configuring software to provide them with information that is repeated at predetermined times.

Womack gives the following idea about information management: "Piling up information in a large inventory is as bad -maybe worse -than piling up large inventories of products." Information must be sent in small batches at a high frequency instead of large batches infrequently. System failures must be made immediately visible, so that they can be treated directly. Manual systems -such as the labelling system (Kanban), the andon cord and others -are more suitable because they are harder to ignore and force immediate action. Hicks (2007) describes the application of the Lean philosophy on IT systems in more detail. Within the proposed context of Lean Information Management, the seven deadly wastes are projected on the use of IT systems.

However, both approaches are more and more claimed to be interdependent and complimentary (Epicor 2008b, Riezebos et al. 2009). A Lean approach to high product mix, shared production assets and volatile demand scenario's are far from ideal. Kanban cards and heijunka boards become unmanageable. Calculating raw material, work in process, finished goods inventories, etc. can no longer be based on simple rules of thumb and experimental design. Here is where IT comes in handy.

Complex issues can easily be dealt with in real-time. For example, [START_REF] Wan | Web-based Kanban system for job dispatching, tracking, and performance monitoring[END_REF] describe a web-based Kanban system for job dispatching, tracking and performance monitoring. Lean IT solutions can also connect with suppliers, for example to include them in Kanban loops. The legal provisions in regulated industries (ex. food, pharmaceutical) require tracing functionality to link each finished product to its raw materials and processing steps. Without IT support, this task would be impossible to achieve. The human factor plays a crucial role when it comes to process improvements. But it is also very important to maintain those accomplished improvements. IT is seen as an enabler of the implemented improvements. [START_REF] Bell | Lean Enterprise Systems: Using IT for Continuous Improvement[END_REF] and Rio (2005) describe IT as the ideal solution to enforce standard work procedures. [START_REF] Ward | Impact of Information Technology Integration and Lean/Just-In-Time Practices on Lead-Time Performance[END_REF] concluded that IT integration facilitates the implementation and the use of effective Lean/JIT practices. Efforts rarely exceed the use of spreadsheets or stand-alone software tools that require intensive human interaction. In fact, methods such as VSM are generally believed to be manual processes [START_REF] Biddle | The Lean Benchmark Report[END_REF]

Continuous improvement -the role of MES

MES -the role of continuous improvement

The main reason why the use of IT is feared by Lean practitioners is its tendency to become obsolete. [START_REF] Bell | Lean Enterprise Systems: Using IT for Continuous Improvement[END_REF] discusses the use of IT to maintain continuous improvement initiatives by also adapting the Enterprise IT system itself. From the point of view of the whole Lean Enterprise, Bell focuses on Enterprise Resource Planning (ERP) software. However, when considering Lean production, the combination with a Manufacturing Execution System (MES) seems more appropriate.

A MES is located closer to production and is fine-tuned to the specific company needs. The usability of MES highly depends on its ability to reflect the current

Alignment method for MES and Lean

Before implementing a MES, all processes -as well from the material as the information flow -must be critically reviewed to ensure an optimal workflow. Otherwise you just end up 'automating a mess'. That is why a thorough analysis is needed before selecting and configuring the software. By modeling the AS-IS situation, everyone is forced to question the current way of working. Problems get discovered and inefficiencies revealed, resulting in a TO-BE situation. Lean practitioners strongly suggest a manual Lean transformation before IT adoption (Masson and Jacobson 2007). But at which point can you switch from manual to IT? When your processes are perfect and won't change anymore? Lean is a continuous improvement process, so that situation will never occur. In addition, even early Lean efforts can benefit from IT support, in particular for data collection and analysis. As stated in section 2, some functionalities even require the support of IT, because they are too complex (ex. controlling WIP with high product mix and volatile demand) or simply enforced by legal provisions (ex. tracking & tracing). So why not take both Lean and MES into account during the first analysis and take the best of both (Gifford 2002)? This approach could also have a positive impact on the Return On Investment (ROI) calculation, as the intangible benefits of IT are quite difficult to quantify (Nagalingam and Li 1997[START_REF] Nasarwanji | The Impact of Manufacturing Execution Systems on Labor Overheads[END_REF], Fraser 2009). The quick wins of the Lean transformation could help justify the initial investment cost of MES.

Manufacturing Operations Management (MOM) analysis

Manufacturing operations management gives a detailed overview of all the activities that support manufacturing in the area of production, inventory, maintenance and quality. As well MES as Lean activities can be classified within this framework.

MES activities

Saenz et al. ( 2009) describe the traditional internal structure of most MES solutions.

They are designed on a modular basis, so each system can be configured and integrated as desired. As a consequence, the complexity of analyzing the manufacturing operations support needed for each manufacturing case is high and far from trivial. The contribution of the ISA 95 standard is only discussed briefly by [START_REF] Saenz De Ugarte | Manufacturing execution system -a literature review[END_REF] as the formalization of the exchange around the manufacturing system to other areas of the company. It's use is presented as the design of information flows between shop floor level applications and those of a higher level. In addition ISA 95 is stated to deliver a consistent terminology. Although these are in fact the main contributions, it's practical benefits reach a lot further and deserve some extra attention. ISA 95 part 1, 2 & 3 (ISA 2000) provide a number object models and terminology that serves as a common model of integration, a standard terminology to define system requirements and integration between different software systems. By mapping the existing manufacturing systems and tools on the models (AS-IS situation), filling the blanks with new systems, checking the integration needs and considering the different information flows, ISA 95 can be the roadmap for a well structured analysis. Based on the ISA 95 models, a blueprint of the TO-BE situation can be constructed. [START_REF] Scholten | The road to integration: A guide to applying the ISA-95 standard in manufacturing[END_REF] describes the procedure to construct a User Requirements Specification (URS) document. This document is used by consultants to clearly specify the requirements of the manufacturing company within the manufacturing operations domain. The result can be used in the selection procedure of the MES solution that best fits all needs. Figure 2

Lean activities

The MOM definition is part of the ISA 95 standard and was mainly introduced to create a common ground to classify and compare existing MES software systems or integrate different components to seamlessly one solution. However, MOM provides a framework to classify all manufacturing operations, disregarded the fact whether they are performed manually or automated. Therefore, the framework can also be used to classify the support for Lean practices and as consequence check the possible alignment between MES components and Lean practices [START_REF] Cottyn | The Complementarity of Lean Thinking and the ISA 95 standard[END_REF][START_REF] Cottyn | The combined adoption of production IT and strategic initiatives: Initial considerations for a Lean MES analysis[END_REF]. This is the foundation of the proposed alignment within this paper. Figure 3 illustrates how the Lean practices can be marked onto the MOM framework. A nonrestrictive amount of examples is given.

Alignment method

The MES functionalities and Lean practices can be mapped onto the same MOM framework for a specific company situation. This makes it possible to check the necessary information flow (support) in between all components during the MOM analysis. By zooming into a certain functionality, the required information flows can be identified in more detail. All information flows consist of standard object models, as defined by ISA 95 part 1, 2 & 3 (ISA 2000). Figure 4 shows the alignment method for a brown-and greenfield project. A brownfield project has historical information at the start, while a greenfield project hasn't. The available information is standardized to ISA 95 object models to enable a generic MOM analysis. The result of the complete exercise is an alignment between MES and the selected Lean practices in the work plan. In a greenfield project, the support is incorporated in the requirements analysis. A change management approach is necessary within a brownfield project.

Value stream mapping -a crucial Lean practice at the start of the Lean journey -is explored as an example. Until recently, VSM has generally been a manual process [START_REF] Biddle | The Lean Benchmark Report[END_REF]. It is based on five phases put into practice by a special team created for such a purpose [START_REF] Rother | Learning to See: Value Stream Mapping to Add Value and Eliminate Muda[END_REF] (5) Achieving the work plan. Similarities between product workflows are searched to define product families. The necessary data are collected by walking through the production process. The current state map is drawn with paper and pencil. After analysis, a future state map and a Lean transformation plan is created. Following up the Lean progress is done by continuously repeating the data collection and drawing steps. However, this approach has a number of limitations:

• It is time and labor consuming. It takes a while to walk through the whole process and collect all necessary data.

• The result is only a snapshot of the real value stream and can lead to poor decisions.

• The manual process is prone to different kinds of errors: process interpretation faults, wrong measurements, writing or reading errors, vague estimates, etc.

• The manual drawing of the current and future state can be sloppy and cause misinterpretation within the team.

• The operational threshold is very high. The data collection won't be done frequently due to the high time and labor intensity. That can cause an inefficient follow-up of the progress and -as a consequence -an inability to react to unforeseen circumstances. An insufficient follow-up makes it hard to sustain the continuous improvement initiatives.

The use of IT can increase the practical performance of VSM [START_REF] Serrano | Evaluation of value stream mapping in manufacturing system redesign[END_REF].

There are electronic tools available that allow a better representation of the maps, support the analysis and document and visualize the progress. They are called electronic value stream mapping (eVSM) tools and are mostly based on spreadsheets.

Another recent evolution is the combination of VSM with discrete event simulation to analyze and evaluate the current and future states (Lian and Van Landeghem 2007).

After a simulation run, the potential impact of the proposed modifications can be measured. This allows the team to make changes and observe the effects without disrupting the production process or causing downtime and costs. But the main effort, namely collecting the data, remains purely manual.

A good alignment with a MES -where a lot of data is already availablecould speed up this process. We are not suggesting a tool to automatically perform the construction and analysis of VSM. But MES can deliver meaningful information to generate an eVSM template to start from or to be used to validate the manual result. When the information from MES doesn't match the manual result, then something is wrong. As well a wrong manual exercise as information errors in MES are not acceptable and must be corrected somehow. Figure 5 shows part of the MOM framework that is useful in the case of VSM, which is contained within (or connected to) the performance analysis. Useful information for the construction (or validation) of the value stream map are the different incoming arrows. Possible input from MES can be:

• Identifying product families

• Creating part of the AS-IS process flow

• Creating part of the AS-IS information flow All information can be identified through standard ISA 95 object models. Activity definitions are described by process segment object models. The actual use of those processes is delivered by segment response object models. Based on that information, the different VSM atoms can be connected together to form the material and information value stream. The corresponding performance information can be added as KPI's on the map.

Case example: a furniture company

To illustrate the use of the alignment method, a case example is performed within a small (< 50 employees) furniture company. There is (limited) production support by software tools in the AS-IS situation, so the case is treated as a brownfield project.

Map the AS-IS situation

Information flow

The current manufacturing operations support is shown in Figure 6 Based on the scanning results, the theoretical production time of each step within ERP is regularly modified (manually). This is done to actualize cost calculation for the different models and can be used as starting value for a comparable production activity for new models.

Material flow

The available historical data (6 months of production) are mapped onto ISA 95 object models. To generate a starting template for eVSM, the same steps are performed as in the manual case. All end products have a similar production path (production definition), so they are combined to one product family. The map is drawn in opposite direction of the value stream itself. The last step of the VSM is the process segment of which the corresponding segment responses have the final product(s) of the product family as 'Material Produced Actual'. Then, for each 'Material Consumed Actual' of that segment response, the next process segment (with that material type as 'Material Produced Actual') is drawn in front of the previous one. These steps must be repeated until the beginning of the value stream, namely receiving the raw materials. The selected values to be added to the map are the number of employees and the mean cycle time of each activity (the duration is recorded by the barcode scanning). The time that each product stays in inventory is not exactly known, but is expressed in a mean number of days (date of next activity -date of previous activity). The eVSM template of figure 7 can be used as starting document for the manual effort or later on used for validation purposes.

Map the TO-BE situation

On one hand the company wants to upgrade and simplify their manufacturing operations (information flow). On the other hand, they want to optimize production performance by reducing the work in process (and by doing so, reducing the product lead time) and creating a higher manufacturing visibility. Figure 8 shows the desired software landscape. In a first phase all production support must be incorporated by a paperless MES system. The production manager gets the released orders from ERP and must be able to launch orders on the shop floor. Each work center has a touch panel with an overview of its waiting list of orders. Through simple screen actions, employees can indicate which order they start. They get electronic information about the required materials and actions. When finished they are guided through some quality checks and can forward the order to the next step. Based on this information, the monthly desired key performance indicators are calculated in real-time for the manager. In a second step, a small Warehouse Management System (WMS) will be implemented to control the stock of raw materials.

Create a Lean work plan

To start the Lean journey, 5S will be introduced on the shop floor. In addition a Visual Management screen will keep all employees informed about the production performance (ex. Seats/day, quality problems/week, etc.). In order to reduce the work in process, a CONWIP system will be initiated. The number of orders on the production floor will be limited. Each time an order is finished, the production manager can launch a new one. To optimize the production activities, each work center will prioritize its waiting orders.

• The cutting process will group the available orders based on the colour. That will minimize the changeover times. • The sticking process will group orders with similar actions, because employees prefer repetitive actions (and perform better this way). • The covering process will group orders according to the region of the customer. This approach must minimize the waiting times of the end products to be transported to the customer. This strategy will be initiated based on the historical data and later on fine-tuned depending on the performance. The different practices will be implemented in a phased approach (Figure 9).

Align MES with Lean

When considering the overlap of Lean and MES activities in the MOM framework, the MES system must be configured to support the Lean practices. A few examples:

• Each work center must have a user-friendly screen that enables the employees to easily assess the priority of each order. For example, at the cutting process, each order is listed (and marked) depending on its colour. The information at the covering process contains the region of the customer. At the stitching process a similarity percentage of each order can be given. • The CONWIP restriction must be enforced. However, the production manager must have the authority to fine-tune this value. • The manager must have access to a dashboard screen containing all KPI values and trends. Some values are displayed within the production hall to inform and stimulate the employees. • The time registration at each work center must reveal the value-adding time. A proper use of the system must be enforced by logical and fixed user screens.

The production manager must be informed of eventual abnormalities. • The performance information can be used at a later stage to redraw a basic eVSM document and re-analyze the situation.

Based on this requirements, the MES system must be configured. However, MES must follow process improvements and must be reconfigured to control the change.

Conclusion and Further Research

Different

  Real-time production information is crucial to the daily manufacturing operations. But additionally, Manufacturing Intelligence (MI) can provide the necessary visibility for the continuous improvement efforts within the production facility. Different kinds of software tools can analyze the real-time data and turn them into valuable knowledge to optimize manufacturing operations. Production departments have always favored the development of custom-made software applications for manufacturing operations support, due to a lack of attention paid by information system specialists to the shop floor. However, the difficulty of integrating multiple point systems has brought software providers to package multiple execution management components into single and integrated solutions (Saenz et al. 2009). These systems, commonly referred to as Manufacturing Execution System (MES), provide a common user interface and data management system. The emergence of functional (MESA 1997) and integration (ISA 2000) standards defined the role of those systems within Computer Integrated Manufacturing (CIM) more closely. That has proven to be an important step from custom-made to pseudo-standard (configured) MES solutions.

  Some research has already been done on the combination between the LeanProduction System and Enterprise Resource Planning (ERP)(Goddard 2003). New technologies -such as SOA -enable the development of software systems that are able to support the requirements of Lean information management(Pfadenhauer et al. 2006). These MES systems can be flexible enough to accommodate the continuous improvement philosophy of a Lean environment. The (near) real-time information flow of the MES looks like a better fit for Lean than the batch oriented ERP systems.No previous research on this topic has been found, but software vendors already anticipate the Lean MES story. Stand-alone applications are already developed to automate and support Lean practices, such as E-Kanban, Six Sigma programs, Visual Management screens, Key Performance Indicators generators (KPI), etc. More and more MES software vendors have some Lean support incorporated. Every product folder has some reference to the Lean philosophy(Siemens 2007, GE Fanuc 2009). It must be that there is need for a MES that supports the Lean philosophy. In its Plantto-Enterprise (P2E) model, the Manufacturing Enterprise Solution Association (MESA) shows how strategic initiatives are linked to the shop floor within the entire enterprise IT system(MESA 2008). The model depicts the generation of information at the most basic value adding process levels of the plant and how this information supports and is supported by enterprise business application processes and longer term strategic initiatives. The importance of a well established manufacturing operations layer to create the necessary real-time manufacturing visibility is emphasized. MESA published manufacturing guidebooks for each strategic initiative they defined. Lean manufacturing is one of them (MESA 2010). However, a study of and Jacobson 2007) shows a limited adoption of Lean IT so far. Ease of deployment and use remains a barrier to the adoption of Lean software on the shop floor. There is still room for innovators, for example to provide much-needed analytical workbenches on top of real-time data collection. A functionality that -in our opinion -is part of (or connected to) the presented MOM framework and can be aligned with MES software.The continuous improvement philosophy of Lean (kaizen) can be supported by the Manufacturing Intelligence (MI) incorporated in MES. DMAIC (Define-Measure-Analyze-Improve-Control) is a structured and disciplined approach to process improvement and is part of the Six Sigma methodology. Based on the DMAIC decision-making cycle, the role of MES in continuous improvement can be illustrated.The first steps are defining metrics and measuring them. A system that continually improves, relies on feedback. Due to its real-time data availability, MES is seen as the best tool to measure real-time performance indicators such as the use of materials, process times and machine breakdowns(Hwang 2006[START_REF] Saenz De Ugarte | Manufacturing execution system -a literature review[END_REF]. Typical operational Key Performance Indicators (KPI) reflect safety, customer service and cost factors such as overtime, inventory, utilization and quality[START_REF] Mesa | Metrics that matter: Uncovering KPIs that justify operational improvement[END_REF]. The analysis phase requires human expertise and additional tools such as operational research and analytical methods. Process metrics (ex. OEE for equipment performance), analysis (ex. Pareto charts for machine breakdown causes) and reporting has become somewhat standard functionality within MES software applications. But the current literature lacks sufficient attention on how to make MES (or even information technology in general) support this analysis[START_REF] Saenz De Ugarte | Manufacturing execution system -a literature review[END_REF]).

  . But the real-time data availability and user friendliness of a MES can speed up and guide the analysis efforts. During the improvement phase, MES is naturally not involved. Except for the necessary improvement of MES itself to control the improved situation. To control the change, MES can standardize the new way of working by imposing standard work on the shop floor.

  manufacturing situation. The continuous improvement of MES itself during the Lean journey is important to keep the system reliable. A MES should always present the data wished for by the user, at the right format, at the right time, at the right place. This application of the Lean philosophy to information technology is referred to as Lean Information Management (Hicks 2007). Recent literature acknowledges the need for a reconfigurable (Zhaohui et al. 2009) and adaptable (Gang et al. 2010) MES in order to follow manufacturing changes quickly and adequately. A MES should be flexible enough to follow the changes made as result of continuous improvement initiatives.

  illustrates the use of the MOM the manufacturing operations support in a specific company situation (AS-IS).

  and consists of: • MS Excel: The production manager creates a production schedule once a week. Internal quality problems are kept in another Excel file. • Barcode scanning: The start of each activity on an order by an employee is recorded through barcode scanning. • Paper based: Work orders and product definitions are distributed by the production manager based on the schedule. Once or twice a day the progress is measured by revisiting each work center. Quality checks are indicated on the work orders and results are written down by the employees. • MS Access: Customer complaints are logged into a custom application.• Custom ERP system: Accounting, procurement of raw materials, order processing, etc.

  Most of the above functionality was introduced in the past to be able to calculate some Key Performance Indicators (KPI). Each month the manager retrieves information from the different systems and calculates the KPI values with MS Excel. • Number of seats produced • Efficiency of employee or work center • Leather consumed • Number of internal reparations • Number of external complaints

Figure 1 .Figure 2 .Figure 3 .Figure 5 .

 1235 Figure 1. Creating business and manufacturing visibility to support the continuous improvement cycle Figure 2. Example of the use of the MOM framework to list the manufacturing operations support Figure 3. Example of the use of the MOM framework to list the Lean practices Figure 4. The alignment method between MES and Lean for brown-and greenfield projects Figure 5. Detail of the MOM framework in the case of Value Steam Mapping Figure 6. The MOM support in the AS-IS situation of the case example Figure 7. The automatically generated eVSM template of the case example Figure 8. The TO-BE situation of software landscape of the case example Figure 9. The phased approach of the Lean transformation of the case example

  lifecycle. Collecting, maintaining and updating the business data in support of the business processes, is important for daily operations. But additionally, in-depth business visibility can be created by adding an appropriate level of intelligence.

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	P
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	R
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  kinds of software tools can analyze real-time data and turn them into valuable knowledge to optimize manufacturing operations. However, the difficulty of integrating multiple point systems has brought software providers to package multiple management approach for MES that facilitates the model state changes as result of typical Lean transformations. The impact of the proposed alignment on the Return On Investment (ROI) calculations can also be worthwhile. Mazur, L.M. and Chen, S.-J. G., 2008. Understanding and Reducing the Medication Delivery Waste Via Systems Mapping and Analysis. Health Care Management Science, 11, 55-65. Mejabi, O.O., 2003. Framework for a Lean manufacturing planning system, Pavnaskar, S.J., Gershenson, J.K., Jambekar, A.B., 2003. Classification scheme for Lean manufacturing tools. International Journal of Production Research, 41 (13), 3075-3090. Pfadenhauer, K., Kittl, B., Dustdar, S., Levy, D. Shop Floor Information Management and SOA. BPM 2006 Workshops, LNCS 4103, 237-248. Ray, C. D., Zuo, X., Michael, J. H., and Wiedenbeck, J. K., 2006. The Lean Index: Operational "LEAN" Metrics for the Wood Products Industry. Wood and Fiber Science, 38 (2), 238-255. Riezebos, J., Klingenberg, W. and Hicks, C., 2009. Lean Production and information technology : Connection or contradiction?, Computers in Industry, 60 (4),

	Fraser, J., 2009. Plant-to-Enterprise Integration: Foundation for MES/MOM Payback Lian, Y.-H., Van Landeghem, H., 2007. Analyzing the effects of Lean manufacturing
	[online]. Cambashi. Available from: http://www.cambashi.com/content1278 using a value stream mapping-based simulation generator, International
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	Gang, H., Jinhang, L. and Xiaodong, Y., 2010. Developing an Adaptable Masson, C. and Jacobson, S., 2007. Lean Planning and Execution Software:
	Manufacturing Execution System Framework, In: Proceedings of the 6th Extending Lean Thinking Across the Enterprise [online]. AMR Research
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	execution management components into single and integrated solutions. These R R R November 2008]. Goddard, R.W., 2003. The Role of Information Technology in the Lean Enterprise. R Possibilities [online]. MESA International. Available from: R R R
	systems, commonly referred to as Manufacturing Execution System (MES), provide a e e e Hicks, B., 2007. Lean Information Management: Understanding and Eliminating e e e e
	common user interface and data management system. An alignment method between a Manufacturing Execution System (MES) and Lean objectives is introduced within this work. MES can provide the necessary support during the Lean journey. MES can trigger, feed or validate the Lean decision making process by providing useful v i e w v i e w v i e w Waste. International Journal of Information Management, 27, 233-249. Hines, P., Holweg, M., Rich, N., 2004. Learning to evolve: A review of contemporary v i e v i e v i e v i e lean thinking. International Journal of Operations & Production Management, 24 (10), 994-1011. w w w w
	information. In addition, MES can maintain the process improvements by enforcing the standardized way of working. However, this is only possible when MES is aligned and is kept aligned to the Lean objectives. By mapping the activities of both on the O n l O n l O n l Houy, T., 2005. ICT and Lean Management: Will They Ever Get Along? Communications & Strategies, 59, 53-75. Hwang, Y.-D., 2006. The practices of integrating manufacturing execution systems and Six Sigma methodology. International Journal of Advanced O n l O n l O n l O n l Manufacturing Operations Management (MOM) framework of ISA 95, a common ground can be identified. In brownfield projects, historical data are available to create y y y Manufacturing Technologies, 31, 145-154. y y y y
	a template to start or to validate a manual Value Stream Map (VSM). Greenfield ISA 95, 2000. Enterprise-control system integration, ANSI/ISA 95.00.01 part 1 :
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Gifford C. H., 2002. 'LEAN' or MES? To optimize, take best of both [online]. ISA.

http://mc.manuscriptcentral.com/tprs Email: ijpr@lboro.ac.ukInternational Journal of Production Research


Data management in the humanities

Laurent Romary

Inria DARIAH, Transitional phase Director -From the growing interest for digital methods in nearly all research domains in the humanities, reflected by the number of projects supported at national and European level, we need to understand the tenets of digitally based scholarship and how specific data management issues in the humanities are. To this end the ESFRI 1 roadmap on European infrastructures has been seminal in identifying the need for a coordinating e-infrastructure in the humanities, DARIAH 2 , whose data policy is reflected in this paper.

Scholarly data in the humanities is a heterogeneous notion. Data creation, seen as the transcription of a primary document, the annotation of existing sources or the compilation of observations across collections of objects, is inherent to the scholarly activity and thus makes it strongly dependant upon the actual hypotheses or theoretical backgrounds of the researcher. There is indeed hardly any notion of data centre in the humanities since data production and enrichment is anchored on the individuals performing research.

The long-term vision 3 of DARIAH is to create a sound and solid infrastructure to ensure the long-term stability of digital assets, as well as the development of a wide range of even unanticipated services to carry out research on these assets. This comprises both technical aspects (identification, preservation), editorial (curation, standards) and sociological (openness, scholarly recognition). Such a vision is articulated around the notion of digital surrogates, which are information structures intended to identify, document or represent a primary source used in a scholarly work. Surrogates can be metadata records, scanned image of a document, digital photographs, transcription of a textual source, or any kind of extract or transformation 4 on some existing data. Surrogates act as a stable reference for further scholarly work, in replacementor in complementto the original physical source it represents or describes. Moreover, a surrogate can act as a primary source for the creation of further surrogates, thus forming a network that reflects the various steps of the scholarly workflow where sources are combined and enriched before being further disseminated to a wider community. Such a unified data landscape for humanities research implies that a clear policy in the domain of standards and good practices be defined. Scholars should both benefit from strong initiatives such as the TEI 5 (Text Encoding Initiative) and stabilize their experience by participating to the development of standards, in collaboration with other communities of practice (publishers, cultural heritage institutions, libraries).

1 ec.europa.eu/research/esfri/ 2 www.dariah.eu/ 3 http://ec.europa.eu/information_society/newsroom/cf/itemlongdetail.cfm?item_id=6204 4 E.g. the spectral analysis of a recorded speech signal 5 www.tei-c.org

The vision also impacts on the technical priorities for DARIAH, namely:

 deploying a repository infrastructure where researchers can transparently and trustfully deposit their productions, comprising permanent identification and access, targeted dissemination (private, restricted and public) and rights management, possibly in a semi-centralized way allowing efficiency, reliability and evolution (cf. http://hal.archives-ouvertes.fr/hal-00399881);

 defining standardized interfaces for accessing data through such repositories, but also through third-party data sources, with facilities such as threading, searching, selecting, visualising and importing data;

 experimenting the agile development of virtual research spaces based on such services, integrating community based research workflows (see http://hal.inria.fr/inria-00593677).

Beyond the technical aspects, an adequate licensing policy must me defined to assert the legal conditions under which data assets can be disseminated. This should be a compromise between making all publicly financed scholarly productions available in open access and preventing the adoption of heterogeneous reuse constraints and/or licensing models. We contemplate encouraging the early dissemination of digital assets in the scholarly process and recommend, when applicable, the use of a Creative Commons CC-BY license, that supports systematic attribution (and thus citation) of the source.

From a political point of view, we need to see with potential data providers (cultural heritage entities, libraries or even private sector stakeholders such as Google) how to create a seamless data landscape where the following issues should be jointly tackled:

 General reuse agreements for scholars, comprising usage in publications, presentation on web sites, integration (or referencing) in digital editions, etc.;

 Definition of standardized formats and APIs that could make the access to one or the other data provider more transparent;

 Identification of scenarios by covering the archival of version of records as well as scholarly created enrichments. For example, TEI transcriptions made by scholars could be archived back in the library where the primary source is actually situated.

As a whole, DARIAH should contribute to excellence in research by being seminal in the establishment of a large coverage, coherent and accessible data space for the humanities.

Whether acting at the level of standards, education or core IT services, we should keep this vision in mind when putting priorities as to what will impact the sustainability of the future digital ecology of scholars.


Etienne Brunet, Ce qui compte -Ecrits choisis, tome II, Céline Poudat (Ed.), Paris:Champion, coll. Lettres Numeriques n°11, 2011. ISBN : 2745322257 -Ce qui compte‖ (‗what counts'), which should also be read as -ceux qui comptent‖ (‗those who count'), thus referring to statistical lexicographers, is the second volume of a compendium of papers by Etienne Brunet, a Professor at the University of Nice who spent the last third of the twentieth century developing methods and tools in lexicometry.

For those who have never heard of Etienne Brunet, who essentially published in French, he could be depicted as the most prominent scholar of the French school of (computational) textual statistics, following the seminal role played in this respect by [START_REF] Muller | Principes et méthodes de statistique lexicale[END_REF] at a time when computers were not so common in the scholarly landscape). With a background in literary studies, he discovered the possible usage of computers for identifying the stylistic characteristics of a text in the course of his doctoral work on Jean Giroudoux and thereafter spent all his academic life exploring further the application of statistical methods to the understanding of lexical phenomena in texts. Etienne Brunet entered the still to be explored field of textual statistics with a profound love for literary authors and their language. He appreciates each turn of language, knowing what is characteristic of the author; he can trace a phenomenon he observes within a weighted series of words down to the characteristics of a specific novel. You would hardly find a result which is not explained with reference to a general perspective on the author concerned (see his remarkable analyses on Hugo, Zola or Proust). If I had to give a name to the discipline within which he should be situated, -computational literary criticism‖ would definitely come to my mind. With his deep understanding of the tenets of literary works, Etienne Brunet has developed incomparable expertise in the design of corpora, regarded as the experimental setting for his statistical exploration. In one of my favourite papers from the book [START_REF] Brunet | Où l'on mesure la distance entre les distances‖[END_REF], actually situated in the context of a larger dispute on the authorship of plays attributed to Corneille and Molière, he gives a wonderful description of how he carved out a series of samples so that a colleague of his could carry out a blind experiment on the data. The fascinating analysis he makes of the criteria he chose and the impact of various possible sample combinations demonstrates how clearly he understood the effect of the corpus, his observable, on the results he could expect to observe. A second essential skill that Etienne Brunet developed over the years was a deep and precise understanding of the behaviour of statistical measures in a text analysis context and their potential usefulness for specific inquiries. Among the statistical tools he learned to master we should probably put to the fore all these having to do with the expression of contrasts within a corpus. One of the major aspects for which I will remember the work of Etienne Brunet is his contribution to the development of an indepth methodology for contrastive analysis. For many years his favourite method has been the use of standard deviation (-écart réduit‖) as a general tool to observe differences within a corpus. Such differences may occur at many levels of analyses. At a macroscopic level, they can indicate the vocabulary characteristic of an author or a genre with respect to an appropriately varied corpus. They can elicit, stylistic variations within an author's production across various periods of time for instance. This method allows one to analyse a given text in its general organization, looking for specific differences of expression within sub-sequences of the text. Among the most usual applications that Etienne Brunet makes of this analysis of difference is the observation of lexical development within a corpus subdivided ito time-based subsets, as made available in the resources delivered with his software THIEF. It is also a tremendous tool to observe (-sketch‖, in Adam Kilgarriff's terms) words or expressions in context by the precise analysis of variations within a set of concordances, pointing out for example the impact of a morphologic deference on a word (for instance a plural mark) form in the semantic distribution of its co-lexicon. Not only does Etienne Brunet like to observe the statistical behaviour of words, but he also takes a personal pleasure in observing the methodological effects of these tools on the legibility or reliability of his results. Moreover, he tends to be a purist in his defence of the simplicity of the Normal distribution, as opposed to the Poisson or the hyper-geometric distributions, in cases where the differences actually observed do not require use of more complex models. His arguments are not purely mathematical; they have to do with the characteristics in size and composition of his corpus and the nature of the feature he wants to observe. It is important to situate this trend in contrastive analysis within the larger scholarly context in the France of his day. Etienne Brunet's work has a particular resonance for the linguistic community working on differential semantics, which, starting with Bernard Pottier (1974) and more recently under the leadership of François [START_REF] Rastier | Sémantique interprétative[END_REF], has advocated a description of linguistic phenomena based on observed contextual variations. Over the years, it is clear that a real community of practice has developed, sharing essentially the same vision of linguistic fundamentals. In France, Etienne Brunet is also famous for producing software usually accompanied by -textbases‖ containing lexical data for one author or another. In 1989, he produced the first version of Hyperbase, a Windows based program that is distributed along with an enormous amount of lexical and full text data. The take-up of Hyperbase may have suffered from its proprietary implementation, as well as its absence from the OSS sphere 1 . As an illustration of this aspect of Etienne Brunet's production, I would encourage interested readers to have a look at and play with the online concordances and statistics he compiled concerning Balzac's -Comédie humaine‖ 2 . This is the kind of clear and simple presentation of lexicometric results that one would certainly show students wanting to understand the role of statistical methods in literary studies. Finally, it is impossible to understand the work of Etienne Brunet, without noticing thathe has been first and foremost a practitioner, who would systematically implement and experiment rather than develop new ideas on paper. Most of his writings reflect this: they are all essentially based upon graphic and other outputs produced by his own programs. Fully aware of this, he takes pride in his fondness for numbers at a period where most linguists regarded statistical methods with disdain: « Aux amateurs de grands espaces et de grands nombres s'ouvre l'aventure concrête et solitaire bien loin des théoriciens qui se bousculent en piétinant la même surface pelée comme les minimes devant la cage de but » Those who love wide open spaces and large numbers are confronted by a well-defined and lonely adventure, far from the theoreticians scrabbling about in the same wellworn ground in front of the goal posts. This citation provides me with an opportunity to comment on Brunet's style, which in itself can be an obstacle to a full understanding of his contributions. It is almost as if, being constantly in contact with literary work, he needs to show that he too has a 1 The software can be bought online from http://www.unice.fr/bcl/spip.php?rubrique38 2 See http://ancilla.unice.fr/~brunet/BALZAC/balzac.htm literary style of his own. His early work in particular is stylistically very creative3 ; if an article begins with a metaphor it will be drawn out as long as possible within the piece. At times, this can be really annoying (particularly for the non-native speaker) leading to impatience as the reader waits for the actual results of an analysis to appear . This is all the more unfortunate in that, when focusing simply on defending a point of view in the context of a scholarly dispute, he can actually write some of the most crystal-clear pages on statistical methodology available (-Où l'on mesure la distance entre les distances‖). Putting all his energy within his software, Etienne Brunet also reflects his time with the absence of interest he shows in the way his data, whether text corpus or lexical results, could actually be made widely accessible by adopting standardized formats and devising a dissemination policy for his datasets independent of the software within which they are embedded. In his defence, he actually lived in a period when the largest database of French electronic texts, Frantext, was a bunker that could only be entered by a THIEF: the name he actually gave to software designed to ingest and manipulate Frantext data. Fortunately, times have changed. It has now become a basic tenet of research in digital humanities to think of the corpus as an object that should be published at an early stage. Finally, the dated atmosphere that one can feel when reading the book is also reflected in the very existence of the volume itself. Written in French, this is a printed book, which only a few French-speaking university libraries will make available on their shelves. Is that really the best way to disseminate the work of Etienne Brunet to a new generation? Only a handful of these papers4 may be tracked down on the web, when for instance by happy accident they are part of the online proceedings of a conference. Would it not have been much more forward-thinking to compile an electronic edition of these papers taking advantage of the secure environment offered by a publication archive5 . Perhaps translating some of the texts could have been too much of a challengeespecially considering the stylistic specificities of the authorbut perhaps this may also be an important lesson for the young generation of French scholars. English is a tool that must be mastered if one is to make a long lasting contribution to the world of scholarship, just as much as statistical methodology.

At times even borderline: « La statistique raffole des grands nombres comme les femmes faciles adorent les grandes fortunes » Statistics is crazy about large numbers, in the same way that easy women love the well-endowed.

I would actually encourage those interested in the works of Etienne Brunet to start with these:[START_REF] Brunet | La base textuelle Batelier‖[END_REF]Brunet , 2004, 2006a&b , 2006a&b

There is such a national service in France with the HAL platform: http://hal.archives-ouvertes.fr/