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Stars/Star fissions

Star fission is the splitting of a star at a critical angular momentum, or period in its history, with the consequence of zero-age contact in the resultant binary star. This splitting may have its highest probability of occurring during early star formation.

Stars
Def.

 * 1) any small luminous dot appearing in the cloudless portion of the night sky, especially with a fixed location relative to other such dots or
 * 2) a luminous celestial body, made up of plasma (particularly hydrogen and helium) and having a spherical shape

is called a star.

Stellar astronomy
When any effort to acquire a system of laws or knowledge focusing on a stellar astr, aster, or astro, that is, any natural star in the sky especially at night, succeeds even in its smallest measurement, stellar astronomy is the name of the effort and the result.

Stellar astrophysics
Def. "any object forming on a dynamical timescale, by gravitational instability", is called a star.

Instantaneous zero-age star formation is defined by the 0 Myr grids of the H II region emission line spectrum, specifically the ionizing spectral energy distribution (normalized to the flux at the Lyman limit).

Stars along the main sequence fall into zero-age mass ranges:

 * Stars below about 8 Mʘ (solar mass) do not explode as supernovae. This is obviously most stars;

 * Stars from about 8 to about 15 Mʘ explode as supernovae, but do not have a strong stellar wind, and so explode into the interstellar medium;

 * Stars from about 15 to 25 Mʘ have a substantial wind; the wind is enriched only in helium, where the chemical composition of the wind at the time of explosion is approximately 0.5 in He and 0.5 in H. The mass in the shell of wind-swept material is moderate;

 * Stars from about 25 Mʘ have a strong wind, enriched in heavy elements with little hydrogen left. The mass in the shell of wind-swept material is large.

The ‘zero-age’ for a star is when it first appears on the Hertzsprung-Russell diagram by burning hydrogen in its core through nuclear fusion reactions.

Planetary sciences
"The deficiency of some noble metals in the crust of the earth has been explained for many years as the result of leaching by a metallic phase (chiefly iron) which later formed the earth's core."

"A broadly similar deficiency also exists in the moon; but the moon has almost no core."

If "the moon was formed by fission of the earth (followed by intense volatilization) after the core of the earth had formed [...], then the earth must have existed for some time as a liquid mass, before dividing."

"A Maclaurin ellipsoid rotating near the upper limit of dynamical stability is, in principle, secularly unstable with respect to a transformation to a triaxial, Jacobi ellipsoid."

For "a loss of mechnical energy (by conversion to heat); [the transformation] will therefore proceed very slowly if the ellipsoid has low viscosity. Thus the core can form while the viscosity is low, and eventually, falling temperature and rising viscosity will result in fission, by way of an unstable Jacobi ellipsoid."

Colors
"The ancient and massive Koronis family now has four identified subfamilies (asteroid families made by the breakup of fragments of the ancient collision), with ages running from 5.7 to 290 My."

"Analysis of family members with accurate SDSS measurements shows a correlation of average subfamily color with age [...] The reddening trend with age remains even when comparing only asteroids of similar size, confirming the presence of space weathering phenomena."

The origin of the "bluer colors of small objects:
 * 1) those objects receive more jolts from random collisions capable of shaking the regolith and exposing fresh material beneath;
 * 2) those objects receive more jolts from the cycle of fission and recombination driven by YORP; and
 * 3) the lower gravity on those objects retains regolith less well."

"Since all families in Figure 2 are made from the same original material, we interpret the differences between them in terms of processes over time. The mechanism that caused the break in the old Koronis data, began after 6 My and was complete by 220 My (though the reddening continued beyond 220 My)."

"YORP torques lead many objects to fission and then reaccrete. The reaccretion event may be energetic enough to freshen the regolith. This effect works better for smaller objects as needed [Or,] proportionate collisions could have outcomes that differ with size due to varying surface gravity. It is easier to knock the weathered regolith clear of the asteroid altogether for small asteroids."

Minerals
"Piezonuclear reactions, which occur in inert and non-radioactive elements, are induced by high pressure and, in particular, by brittle fracture phenomena in solids under compression. These low-energy reactions generally take place in nuclei with an atomic weight that is lower or equal to that of iron (Fe)."

Pressure, "exerted on radioactive or inert media, can generate nuclear reactions and reproducible neutron emissions. In particular, low-energy nuclear reactions and heat generation have been verified in pressurised deuterium gas [...] and in radioactive deuterium-containing liquids during ultrasound and cavitation".

"Neutron emission measurements, by means of helium-3 neutron detectors, occurred during crushing failure [...] in particular regard neutron emissions from granite (gneiss) specimens [...] transforming heavier (Fe) into lighter (Mg, Al, Si) atoms."

The "neutron measurements obtained from two granite specimens under compressive loading condition have exceeded the neutron background by approximately one order of magnitude, in correspondence to their brittle failure [...] for the fracture experiments on green Luserna Granite specimens [...], analysis of the fracture surfaces, conducted by energy dispersive X-ray spectroscopy, has shown a considerable reduction in the iron content (25%) [...] This iron decrease is counterbalance by an increase in aluminium, silicon, and magnesium. In particular, the increase in aluminium content corresponds to the 85% of the iron decrease. Therefore, the piezonuclear fission reactions [are]:"

 * $$Fe^{56}_{26} \rightarrow 2 Al^{27}_{13} + 2 neutrons$$

 * $$Fe^{56}_{26} \rightarrow Mg^{24}_{12} + Si^{28}_{14} + 4 neutrons.$$

Granite "is predominantly constituted by quartz and feldspar minerals"."

"Neutron emissions measured near the Earth's surface exceeded the neutron background by about one order of magnitude in correspondence with seismic activity and more appreciable earthquakes [...] This relationship between the processes in the Earth's crust and neutron flux variations has allowed increasing tectonic activity to be detected and methods for short-term prediction and monitoring of earthquakes to be developed"."

Additional "piezonuclear fission reactions that could take place in correspondence with plate collision and subduction:"

 * $$Co^{59}_{27} \rightarrow Al^{27}_{13} + Si^{28}_{14} + 4 neutrons,$$

 * $$Ni^{59}_{28} \rightarrow 2 Si^{28}_{14} + 3 neutrons, and $$

 * $$Ni^{59}_{28} \rightarrow Na^{23}_{11} + Cl^{35}_{17} + 1 neutron.$$

Theoretical stellar astrophysics
The "star formation process happens very quickly and in regions of the Galaxy that are difficult to study observationally."

Theoretical star fissions
Nonaxisymmetric "magnetic instabilities can be readily produced from a toroidal magnetic field [...] in rotating spherical systems. [As can] the growth rate of the three-dimensional magnetic instabilities. [Magnetic] field and velocity perturbations with small radial and latitudinal scales can effectively extract energy from the basic toroidal field and grow. [The] most unstable mode of the instabilities is always three-dimensional and characterized by small radial and latitudinal scales."

A deep "strong toroidal magnetic field suppresses turbulent convection and dramatically reduces the α-effect [...] Other dynamo processes must replace the conventional turbulent dynamo in this situation."

In "an interface dynamo [...] turbulent convective motions in an upper region produce an α-effect generating a weak magnetic field that penetrates into the neighboring lower region."

Binary stars
Def. two stars that appear to be one when seen with the naked eye, either because they orbit one another (binary stars) or happen to be in the same line of sight even though they are separated by a great distance is called a double star.

Def. a star that appears as a double due to an optical illusion; in reality, the stars may be far apart from each other is called an optical double.

Def. two stars which form a stellar system, such that they orbit the point of equilibrium of their gravitational fields is called a double star.

Def. a stellar system that has two stars orbiting around each other is called a binary star.

A binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star, ... or secondary. Many visual binaries have long orbital periods of several centuries or millennia and therefore have orbits which are uncertain or poorly known.

Def. a binary star whose components can be visually resolved is called a visual binary.

"The overall frequency of occurrence of binary stars among the [pre-main sequence] PMS population is at least as large as has been documented for main-sequence stars (Duquennoy & Mayor 1991), that is, certainly greater than 50%."

"Young, stellar-mass binary systems have been found with semimajor axes ranging from 0.02 to 103 AU (orbital periods ranging from a couple of days to 104 years), with a binary frequency distribution as a function of semimajor axis that is qualitatively consistent with the log-normal–like distribution found for main-sequence stars. With this evidence in hand, Mathieu (1994) concluded that “binary formation is the primary branch of the star-formation process.”"

Contact binaries
A contact binary is a binary star system whose component stars are so close that they touch each other or have merged to share their gaseous envelopes. ... Almost all known contact binary systems are eclipsing binaries; eclipsing contact binaries are known as W Ursae Majoris variables, after their type star, W Ursae Majoris.

Zero-age contacts
“Zero-age contact must be a consequence of star fission under critical angular momentum.” When the angular momentum is too large, the star breaks into a detached binary. When the angular momentum is too small, the star remains as a single star. BH Centauri and V1010 Ophiuchi have zero-age radii and are zero-age contact systems. BH Centauri is an overcontact system.

Common envelope binaries
[A] common envelope (CE) refers to a short-lived (months to years) phase in the evolution of a binary star in which the largest of the two stars (the donor star) has initiated unstable mass transfer to its companion star. Breach of the common envelope crosses the Lagrange Point L1 with the donor-star mass beyond the Roche Lobe acting as the third dynamic point in a formerly binary system. Mass transfer is unstable when the radius of the donor star expands more rapidly or shrinks less rapidly than does the binary orbit. Hence, the donor will start mass transfer when it overfills its Roche lobe and as a consequence the orbit may shrink while the star expands, causing it to overflow the Roche lobe even more, which accerelates the mass transfer, causing the orbit to shrink faster and the donor to expand faster, etcetera. This leads to the run-away process of dynamically unstable mass transfer. The result will be the fast expansion of the donor's stellar envelope, which will then engulf the companion star. Hence the name common envelope.

The diagram on the right suggests a reverse common envelope process for binary star formation. At some point in star formation, two cores, one for a main-sequence star (yellow) and the other for a red giant (gray) form within a common envelope. As mass transfer continues or decelerates, the red giant transfers to at or below its Roche lobe (dashed black line) and a partially stable binary is formed.

Overcontact systems
When stars share an envelope the pair may be called an overcontact binary.

BH Centauri is a zero-age overcontact binary system with primary and secondary masses equal to (9.4±5.4) and (7.9±5.4) Mʘ. With later analysis including more recent data, "the mass ratio went from 0.97 to 0.84, and the degree of overcontact went from 21% to 48%."

V1010 Ophiuchi and V701 Scorpii are both overcontact systems. For V1010 Ophiuchi "the masses are 2 and 1 M⊙ while the radii are 2.1 and 1.5 R⊙. The location in the HR diagram suggests that they are zero-age stars, as do the radii".

At the right is a computer generated picture of the overcontact system V701 Scorpii. The overcontact in V701 Scorpii appears to be almost twice as much as in V1010 Ophiuchi.

"Most people would agree that fission is the most probable way to form binary systems, especially the close systems. The angular momentum must be the deciding factor as to whether a gas cloud becomes a single star or a binary system."

Dynamos
"[M]otions resulting from [a linear magnetohydrodynamic] instability act as a dynamo to sustain the magnetic field." "Supersonic flows are initially generated by the Balbus-Hawley magnetic shear instability."

A plasma with local magnetohydrodynamic instabilities creates mechanical turbulence, motion, or shear (a dynamo) which in turn generates or sustains the local magnetic field.

When this magnetohydrodynamic dynamo occurs between or within radiative layers, a radiative dynamo is operating.

There are three requisites for a dynamo to occur and subsequently operate:

 * An electrically conductive fluid medium such as a plasma or liquid iron
 * local magnetohydrodynamic instabilities
 * An energy source to create the local magnetohydrodynamic instabilities and to drive mechanical turbulence, motion, or shear within the fluid.

Def. any conversion of mechanical energy into electrical energy and associated magnetic fields is called a dynamo.

Def. "a dynamo taking place in the radiative layers" of a star, or other astronomical object, is called a radiative dynamo, or stellar radiative dynamo.

Interstellar magnetic fields
The "interstellar magnetic field significantly influences the onset of gravitational collapse in molecular clouds, the general consensus is that the field will largely decouple from a contracting cloud at number densities ≳1010 cm−3 because, at such high densities, the fractional ionization of the gas becomes extraordinarily small."

The "processes likely to be responsible for transforming single gas clouds into binary protostellar systems largely operate at densities higher than this limit".

Binary star formations
Binary and multi-star systems consist of two or more stars that are gravitationally bound, and generally move around each other in stable orbits. When two such stars have a relatively close orbit, their gravitational interaction can have a significant impact on their evolution. The masses of stars are determined from computation of the orbital elements.

Large lengths, such as the radius of a giant star or the semi-major axis of a binary star system, are often expressed in terms of the astronomical unit (AU)—approximately the mean distance between the Earth and the Sun (150 million km or 93 million miles).

The most common multi-star system is a binary star, but systems of three or more stars are also found. For reasons of orbital stability, such multi-star systems are often organized into hierarchical sets of co-orbiting binary stars. Larger groups called star clusters also exist. These range from loose stellar associations with only a few stars, up to enormous globular clusters with hundreds of thousands of stars.

If components in binary star systems are close enough they can gravitationally distort their mutual outer stellar atmospheres. In some cases, these close binary systems can exchange mass, which may bring their evolution to stages that single stars cannot attain. Examples of binaries are Sirius and Cygnus X-1 (of which one member is probably a black hole). Binary stars are also common as the nuclei of many planetary nebulae, and are the progenitors of both novae and type Ia supernovae.

The observation of binaries consisting of pre-main sequence stars, supports the theory that binaries are already formed during star formation.

"The question of binary star formation is now regarded as a central unsolved issue in star formation, given the observational evidence that the majority of stars are in binary systems both during the main sequence ... and pre-main sequence stages". "[T]he 'theory gap' currently separating theoretical models from the observations they purport to describe is the major unsolved problem in this area."

Bifurcations
Def. a division into two is called bifurcation.

Bifurcation means the splitting of a main body into two parts. Bifurcation theory is the study of bifurcation in dynamical systems.. The forking of a river into its tributaries is referred to as river bifurcation. A bifurcation can be a false dilemma in which two alternative statements are held to be the only possible options when there are more options. In cybernetics, a bifurcation is when a system switches from one stable state to another, where minor fluctuations may play a crucial role in deciding the outcome.

“About a century ago, Liapounov and Poincaré found that the sequence of Jacobi’s ellipsoids branches towards pear-shaped configurations for sufficiently high rotation.”

Equatorial break-up and instability occur at the point of bifurcation.

“Bifurcation of protostars can occur because of excessive angular momentum either during hydrodynamic collapse (‘fragmentation’), or else after the star has arrived on the HR diagram as a visible, slowly contracting star (‘fission’).”

Spectral types B2-B5 and F3-G2 binaries with orbital periods shorter than 10 or 100 yr may result from the bifurcation of rapidly rotating protostars.

Binary formation by ... bifurcation is difficult to achieve theoretically for compressible viscous gases and may not occur frequently or ever.

Systems of spectroscopic binaries of periods less than 3.6 days "involve separations that are less than 2.5 times the sum of the radii of the components."

These systems "probably have already exchanged mass and no longer have their original mass ratios."

For these systems, we are unable to give their mecahnisms of origin.

Provisionally, "most or all binaries [are] formed in capture processes (including initial star formation in bound systems) and that bifurcation or fission need not have occurred frequently."

For the inclusion of compressibility and viscosity in theoretical calculations, "it is very difficult to produce binaries by fission and only under special circumstances."

“In view of the high frequency of spectroscopic binaries, the formation mechanism must be a frequent one, not a rare occurrence."

For most binaries to result from fission of a star into at least two stars, the expanding separation between the binaries must result in capture rather than expulsion from the system.

Fissions
Def. the process of splitting into smaller particles is called fission.

"Binary formation by fission or bifurcation of a contracting rotating protostar" is difficult to achieve theoretically for compressible viscous gases and may not occur frequently or ever.

Generally, fission is the splitting of something into two parts. In anthropology, fission is the process whereby a nation-state divides and becomes multiple states. In biology, fission is the subdivision of a cell or a multi-cellular body into two or more parts and the regeneration of each of the parts into a complete individual. In physics, nuclear fission is a nuclear reaction in which an atomic nucleus "splits into smaller parts (lighter nuclei), often producing free neutrons and photons (in the form of gamma rays), and releasing a tremendous amount of energy A large atomic nucleus such as uranium (236U) is split into two smaller particles (141Ba and 92Kr). Most nuclear fissions are binary fissions, but occasionally (2 to 4 times per 1000 events), three positively-charged fragments are produced in a ternary fission.

"Most people would agree that fission is the most probable way to form binary systems, especially the close systems."

"[F]ission is now commonly considered to be the most likely explanation for the existence of close binaries". But, "the hypothesis cannot be regarded as proved until the evolution of a rotating protostar has been followed from an initial state as a single star to a final state as a detached binary system." "[T]he high frequency of close binaries over a wide mass range surely implies that no special characteristics of the properties of stellar matter are essential to binary formation". "[T]he initial departure from axial symmetry is due to the onset of dynamical overstability for a mode of low order". "[G]ravitational torques between the debris and the main component (i.e., before fission) significantly influence the latter’s evolution." "[G]eneral trends emerge ... :

 * 1) [f]ollowing the appearance of departures from axial symmetry, a substantial fraction of mass is nearly always lost as debris,
 * 2) [e]volution into a bar-shaped structure is common ... ,
 * 3) [when] fission [occurs], it leads to a binary of small mass ratio, typically towards the lower end of the range 0.1-0.5."

With "significant mass exchange ... during [the] contact phase ..., the mass ratio immediately following fission may have little relevance to observed mass ratios."

"[F]ission [can] occur only in stars whose interior state at least approximates to incompressibility. With even the lowest degree of central condensation which [may] occur in a purely gaseous star, fission [is] an impossibility, [as] any excess of angular momentum [relieves] itself by equatorial ejection of matter" as debris. "About one-third of the stars observed ... are binaries which have almost certainly been formed by fission, so that these, at least, must have been in something approximating to the liquid [or fluid] state when fission took place." "At different temperatures the atoms [are] of different sizes through being ionized down to different levels."

"The idea of fission in rapidly rotating stars [is] not a return to the classical fission theory of Darwin and Jeans." “If fission occurs at all, it is probably catastrophic in character and has little resemblance to rotational breakup.” "[M]any close binaries are now in effect single objects possessing two massive nuclei, and a single envelope surrounding them." When such as object "tends to shed its envelope, exposing the separate nuclei as a normal double star, we [shall] call this process fission." When "the trend is in the opposite direction, we should probably speak of fusion."

Fragmentations
Def.
 * 1) a part broken off
 * 2) a small, detached portion
 * 3) an imperfect part

is called a fragment.

Def. the act or process of producing a fragment is called fragmentation.

Fragmentation of the molecular cloud during the formation of protostars is an acceptable explanation for the formation of a binary or multiple star system.

With respect to low-mass star formation, "fragmentation to form a binary star [may be] most simply achieved if collapse is initiated by an external impulse." "On its own, [the] process under which a dense molecular cloud core can collapse to form a binary, or multiple, star system would produce wide binaries". "[C]lose binaries [may be] formed because of mutual interactions between the protostellar discs surrounding the various fragments." "[T]he most likely collision which has an effect on the core is the one for which [the velocity change imparted by the impulse,] Δv ~ cs [(the internal sound speed),] induced by a clump of mass ~0.1M⊙." "[T]he impulsive collapse of the cloud cores [requires] that they are not primarily magnetically supported in their central regions."

"The sources are separated by 17", or 4200 AU. Binary separations of this order are consistent with early fragmentation in a relatively dense cloud ("prompt initial fragmentation," e.g., Pringle 1989; Looney et al. 2000), in which case the individual sources would have distinct protostellar envelopes."

"In a binary formed via gravitational fragmentation, we would expect the separation to correspond to the local Jeans length (Jeans 1928):"

 * $$\lambda_J = ( { \pi c^2_s \over G\mu_p m_H n } )^{1/2},$$

"where cs is the local sound speed, and μp = 2.33 and n are the mean molecular weight and mean particle density, respectively. A Jeans length of 4200 AU would require a relatively high density (n ~ 6 x 105 cm−3, assuming cs = 0.2 km s−1). The mean density of the Per-Bolo 102 core, measured within an aperture of 104 AU, is 4 x 105 cm−3, close to the required value."

Fissions by fusions
A binary star system that includes a nearby white dwarf can produce certain types of spectacular stellar explosions, including the nova and a Type 1a supernova. The explosion is created when the white dwarf accretes hydrogen from the companion star, building up mass until the hydrogen undergoes fusion.

Gravitational captures
While it is not impossible that some binaries might be created through gravitational capture between two single stars, given the very low likelihood of such an event (three objects are actually required, as conservation of energy rules out a single gravitating body capturing another) and the high number of binaries, this cannot be the primary formation process.

KIC 9832227 in 2013 " the speed of the orbit was gradually getting faster and faster, implying the stars are getting closer together. The pair is so close, in fact, they share an atmosphere [...] V1309 Scorpii, which also had a merged atmosphere, was spinning up faster and faster, and exploded unexpectedly in 2008."

The "pair will explode as a “red nova”—an explosion caused by a binary merging—in about 5 years’ time."

Supernova remnants
The image at right is an X-ray astronomy image of "the supernova remnant SNR MSH 11-16A, located about 30,000 light years away [in the constellation Carina]. The purple glow is [a coloration] from X-rays emitted by the gas superheated to millions of degrees by the explosion."

The second image at right is an enlargement of the Chandra X-ray Observatory image (in green) of the first image. "The Chandra image reveals a comet-shaped X-ray source well outside the boundary of the supernova remnant. This source consists of a point-like object with a long tail trailing behind it for about 3 light years."

"The point-like X-ray source was discovered by the International Gamma-Ray Astrophysics Laboratory, or INTEGRAL, and is called IGR J11014-6103 (or IGR J11014 for short). The elongated emission is pointing towards the center of MSH 11-61A where the pulsar would have been formed. Another interesting feature of the Chandra image, also seen with XMM-Newton, is the faint X-ray tail extending to the top-right. The cause of this feature is unknown, but similar tails have been seen from other pulsars that also do not line up with the pulsar's direction of motion."

"Based on earlier observations, astronomers estimate that the age of MSH 11-61A, as it appears in the image, is approximately 15,000 years, and it lies at a distance of about 30,000 light years away from Earth. Combining these values with the distance that the pulsar has appeared to have traveled from the center of the MSH 11-61A, astronomers estimate that IGR J11014 is moving at a speed between 5.4 million and 6.5 million miles per hour."

Entities
"While many stars form in binary systems, binary formation is still not well understood. This is particularly true for close binary systems with orbital periods of a few days. If the orbital characteristics of these systems would not have changed since pre-main-sequence then the stars would have formed from one entity, as during the pre-main-sequence phase their sizes were bigger. As fission seems unlikely (Tohline 2002), the orbit probably shrunk and therefore the angular momentum of these systems must have undergone a complex history. One part of the angular momentum distribution which is seldom probed is the stellar spin."

There are spin "aligned systems and [...] spinorbit misalignment. [Stellar] obliquity seems not to be a simple function of orbital distance or eccentricity."

In "the DI Herculis system [...] rotation is strongly misaligned with the orbital spin".

Neutrons
"The feasibility of thermal neutron fission and fast neutron fission in planetary and protostellar matter [may be] calculated from nuclear reactor theory. Means for concentrating actinide elements and for separating actinide elements from reactor poisons [exist]. [I]ntermittent or interrupted planetaryscale nuclear fission breeder reactors [may occur] in connection with observed changes in the giant outer planets and changes in the geomagnetic field. [T]hermonuclear fusion reactions in stars are ignited by nuclear fission energy [...] dark matter, inferred to exist in the Universe, might be accounted for, at least in part, by the presence of dark stars (not necessarily brown dwarfs) whose protostellar nuclear fission reactors failed to ignite thermonuclear fusion reactions."

Opticals
"For a few special cases, rotational velocities for protostars have been obtained directly from observations of the outer optically thin regions. In the case of B335, [...] Ω = 1.4 x 10-14 s-1, uniform out to a radius of 0.22 pc, from velocity gradients in 13CO and C18O. A univorm-density sphere of that radius would have j = 2.6 x 1021 cm2 s-1, consistent with the lower end of the observed range. Rotation is not important in determining the force balance in the outer regions, and [...] this object is in fact undergoing gravitational collapse."

Submillimeters
"Interferometry at 870 µm [...] has been used to resolve the compact inner dust disks in the sources HL Tau and L1551 IRS 5; the disk radii are 60 and 80 AU, respectively, and the disk planes are apparently perpendicular to the bipolar flows."

Radios
Millimeter "interferometry [has been used] to infer the presence of a 45 AU disk in L1551 IRS 5."

In "the system IRAS 16293 - 2422 [observations] at cm, mm and submillimeter wavelengths indicate that this source is a binary system, with a separation 800 AU and with two associated bipolar outflows. The orbitl j = 4.5 x 1020 cm2 s-1, assuming each component has a mass of 1 M⊙. Surrounding the binary pair is a circumbinary disk with an outer radius of 2000 AU and projected rotational velocity of ≈ 0.75 km s-1. [...] the j at its outer edge can be estimated to be 2.25 x 1021 cm2 s-1. These angular momenta are quite consistent with those in the cores of molecular clouds; the binary could have fragmented out of the inner portions of the core (which have lower angular momentum than average), while the circumbinary disk could have formed from the outer regions. Thus this system [...] well illustrates the commonly accepted picture that the angular momenta of cloud cores are transformed during the collapse phase into the orbital motion of disks and binary systems."

Sun
Def. the star which the Earth revolves around and from which it receives light and warmth. is called the sun.

Depending on context and the definition of a star, the sun may or may not be included.

The mass of the coronal ejection in the image at right is many times that of the Earth. As the Sun itself remains, the ejection may be a fragmentation.

Mira
A red giant is a luminous giant star. The outer atmosphere is inflated and tenuous, making the radius immense and the surface temperature low, somewhere from 5,000 K and lower. The appearance of the red giant is from yellow orange to red, including the spectral types K and M, but also class S stars and most carbon stars. The most common red giants are the so-called red giant branch stars (RGB stars). Another case of red giants is the asymptotic giant branch stars (AGB). To the AGB stars belong the carbon stars of type C-N and late C-R. The stellar limb of a red giant is not sharply-defined, as depicted in many illustrations. Instead, due to the very low mass density of the envelope, such stars lack a well-defined photosphere. The body of the star gradually transitions into a 'corona' with increasing radii.

At right "is a NASA Hubble Space Telescope image of the cool red giant star Mira A (right), officially called Omicron Ceti in the constellation Cetus, and its nearby hot companion (left) taken on December 11, 1995 in visible light using the European Space Agency's Faint Object Camera (FOC). The stars in this false-color picture are separated by an angular size of only 0.6 arcseconds (equal to 70 times the distance between Earth and the Sun), but clearly resolved by the FOC. Image reconstruction techniques have been used to further enhance the details in the Mira images."

The Hubble Space Telescope (HST) ultraviolet images and later X-ray images by the Chandra space telescope show a spiral of gas rising off Mira in the direction of Mira B. The companion's orbital period around Mira is approximately 400 years.

Mira B, also known as VZ Ceti, is the companion star to the variable star Mira. Its orbit around Mira is poorly known; the most recent estimate listed in the Sixth Orbit Catalog of Visual Binary Stars gives an orbital period of roughly 500 years, with a periastron around the year 2285. Assuming the distance in the Hipparcos catalog and orbit are correct, Mira A and B are separated by an average of 100 AU.

Long-known to be erratically variable itself, its fluctuations seem to be related to its accretion of matter from Mira's stellar wind, which makes it a symbiotic star.

The new data suggest that Mira B is a normal main sequence star of spectral type K and roughly 0.7 solar masses, rather than a white dwarf as first envisioned.

Even more recently (2010) analysis of rapid optical brightness variations has indicated that Mira B is in fact a white dwarf.

Betelgeuse
"The yellow/red "image" or "photo" of Betelgeuse usually seen is actually not a picture of the red giant but rather a mathematically generated image based on the photograph. The photograph was actually of much lower resolution: The entire Betelgeuse image fit entirely within a 10x10 pixel area on the Hubble Space Telescopes Faint Object Camera. The actual images were oversampled by a factor of 5 with bicubic spline interpolation, then deconvolved."

The image at the right is "of the supergiant star Betelgeuse obtained with the NACO adaptive optics instrument on ESO’s Very Large Telescope. The use of NACO combined with a so-called “lucky imaging” technique, allows the astronomers to obtain the sharpest ever image of Betelgeuse, even with Earth’s turbulent, image-distorting atmosphere in the way. The resolution is as fine as 37 milliarcseconds, which is roughly the size of a tennis ball on the International Space Station (ISS), as seen from the ground. The image is based on data obtained in the near-infrared, through different filters. The field of view is about half an arcsecond wide, North is up, East is left."

W Ursae Majoris
The W Ursae Majoris system consists of a pair of stars in a tight, circular orbit with a period of 0.3336 days, or eight hours and 23 seconds. During every orbital cycle, each star eclipses the other, resulting in a decrease in magnitude. The maximum magnitude of the pair is 7.75. During the eclipse of the primary, the net magnitude drops by 0.73, while the eclipse of the secondary causes a magnitude decrease of 0.68. Unlike normal eclipsing binaries, the contact nature makes it impossible to precisely tell when an eclipse of one component by the other starts or ends.

"The two stars in W Ursae Majoris are so close together that their outer envelopes are in direct contact. Hence they have the same stellar classification of F8Vp, which matches the spectrum of a main sequence star that is generating energy through the nuclear fusion of hydrogen. However, the primary component has a larger mass and radius than the secondary, with 1.19 times the Sun's mass and 1.08 times the Sun's radius. The secondary has 0.57 solar masses and 0.78 solar radii.

"The orbital period of the system has changed since 1903, which may be the result of mass transfer or the braking effects of magnetic fields. Star spots have been observed on the surface of the stars and strong X-ray emissions have been detected, indicating a high level of magnetic activity that is common to W Uma variables. This magnetic activity may play a role in regulating the timing and magnitude of mass transfer occurs.

V1010 Ophiuchi
Def. binaries "in which the stellar components are close enough that proximity effects are important but far enough apart that a large temperature differential may be maintained between the two stars" are called near-contact binaries.

"V1010 Oph ... is one of the brightest and best studied of the near-contact (P=0.66d) binaries." "The period of the binary is known to be decreasing ..., which can be understood in terms of conservative mass transfer (Shaw 1990)." "If this star is truly an evolved system, it may have been in contact previously. ... [I]t is not now in contact".

The temperatures of the two stars have been estimated spectrally as 8200 K and 5671 ± 30 K.

The first image at the right contains two light curves for V1010 Ophiuchi: the top is in yellow at 550.0 nm and the bottom is in blue at 435.0 nm.

The "eclipses are complete and the primary minimum is a transit [...] The system is in contact [shown in the second diagram at the right], with a surface potential near that of the inner contact surface [...] The temperature difference (2529 K) between the primary and secondary is quite large. This suggests that the temperature gradient at the interface must be very steep."

"The appreciable departure between the theoretical light curves and the observations [in the first figure at the right] at the ascending branch of the secondary minimum is due to [a large asymmetry from absorbing gaseous matter]."

"There are two likely ways to form contact systems:
 * 1) through star fission with critical angular momentum, i.e. the angular momentum is just right for the star to divide, but not large enough for it to be detached (zero-age contact);
 * 2) through mass exchange in which one or both components expand to fill the common envelope during the course of stellar evolution."

"V1010 Oph has essentially a ZAMS radius. Thus this system is likely to be essentially a zero-age contact system [formed through star fission]."

BH Centauri
"The eclipsing binary system BH Cen is a close (contact) binary in the extremely young galactic cluster Córdoba XXVI (NGC 2944)."

In 1928-30, "from ten light minima ... a (half) period P = 0.395790 7 [days is derived]." This half period estimate becomes the period P = 0.791 581 4 d, for the observations in 1928-30.

From more recent observations around 1977, P = 0.791 616 d. And, from 1979, P = 0.791 592 10 ± 0.000 14.

Beta Lyrae
Beta Lyrae is a semidetached binary system made up of a stellar class B7II primary star and a secondary that is probably also a B-type star. The brighter, less massive star (B7II) in the system was once the more massive member of the pair, which caused it to evolve away from the main sequence first and become a giant star. Because the pair are in a close orbit, as this star expanded into a giant it filled its Roche lobe and transferred most of its mass over to its companion. The secondary, now more massive star is surrounded by an accretion disk from this mass transfer, with bipolar, jet-like features projecting perpendicular to the disk. This accretion disk blocks our view of the secondary star, lowering its apparent luminosity and making it difficult for astronomers to pinpoint what its stellar type is. The amount of mass being transferred between the two stars is about 2 × 10–5 solar masses per year, or the equivalent of the Sun's mass every 50,000 years, which results in a increase in orbital period of about 19 seconds each year.

The orbital plane of this system is nearly aligned with the line of sight from the Earth, so the two stars periodically eclipse each other. This causes Beta Lyrae to regularly change its apparent magnitude from +3.4 to +4.6 over an orbital period of 12.9414 days. The two components are so close together that they cannot be resolved with optical telescopes, forming a spectroscopic binary. In 2008, the primary star and the accretion disk of the secondary star were resolved and imaged using the CHARA Array interferometer and the Michigan InfraRed Combiner (MIRC) in the near infrared H band (see video [at the right], allowing the orbital elements to be computed for the first time.

Plaskett's star
Plaskett's Star (HR 2422) is a spectroscopic binary at a distance of [5,245] light-years (1,608 pc). It is one of the most massive binary stars known, with components: A = 54 Mʘ and B = 56 Mʘ for a total mass of around [110 Mʘ]. The pair have a combined visual magnitude of 6.06, and is located in the constellation of Monoceros. The orbital period for the pair is 14.39625 ± 0.00095 days. The secondary is a rapid rotator with a projected rotational velocity of 300 km sec–1, giving it a pronounced equatorial bulge. Plaskett’s star is an example of fission.

Solar-like binaries
For a solar-like binary system, the primary has Teff ≲ 6000 K.

"TYC 4410-01037-1 [has] a mass of 1.07 ± 0.08 M⊙ and radius of 0.99 ± 0.18 R⊙. ... Teff = 5879 ± 29 K [and] [Fe/H] = -0.01 ± 0.05".

At right is a Keck adaptive optics image of TYC 4110-01037-1 in K′. A faint candidate tertiary companion (indicated by the arrow) with red colors is separated by 986 ± 4 mas from the primary star. If it is physically associated with the primary, it is most likely a dM3-dM4 star. The companion is designated MARVELS-3B.

Its "low-mass stellar companion [has a] small mass ratio [ q ≥ 0.087 ± 0.003] and short orbital period [78.994 ± 0.012 days, which] are atypical amongst solar-like ... binary systems. [The orbit has] an eccentricity of 0.1095 ± 0.0023, and a semi-amplitude of 4199 ± 11 m s-1. ... the minimum companion mass (if sin i = 1) [is] 97.7 ± 5.8 MJup."

"One possible way to create such a system would be if a triple-component stellar multiple broke up into a short period, low q binary during the cluster dispersal phase of its lifetime. A candidate tertiary body has been identified in the system via single-epoch, high contrast imagery. If this object is confirmed to be co-moving, ... it [may] be a dM4 star."

H I regions
The warm neutral medium (WNM) is 10-20 % of the ISM, ranges in size from 300-400 pc, temperature between 6000 and 10000 K, is composed of neutral atomic hydrogen, has a density of 0.2-0.5 atoms/cm3, and emits the hydrogen 21 cm line.

Also, within the H I regions is the warm ionized medium (WIM), constituting 20-50 % by volume of the ISM, with a size around 1000 pc, a temperature of 8000 K, an atom density of 0.2-0.5 atoms/cm3, of ionized hydrogen, emitting the hydrogen alpha line and exhibiting pulsar dispersion.

These regions are non-luminous, save for emission of the 21-cm (1,420 MHz) region spectral line. Mapping H I emissions with a radio telescope is a technique used for determining the structure of spiral galaxies.

Molecular clouds
A molecular cloud, sometimes called a stellar nursery if star formation is occurring within, is a type of interstellar cloud whose density and size permits the formation of molecules, most commonly molecular hydrogen (H2).

Molecular hydrogen is difficult to detect by infrared and radio observations, so the molecule most often used to determine the presence of H2 is CO (carbon monoxide). The ratio between CO luminosity and H2 mass is thought to be constant, although there are reasons to doubt this assumption in observations of some other galaxies.

Such clouds make up < 1% of the ISM, have temperatures of 10-20 K and high densities of 102 - 106 atoms/cm3. These clouds are astronomical radio and infrared sources with radio and infrared molecular emission and absorption lines.

Giant molecular clouds
A vast assemblage of molecular gas with a mass of approximately 103–107 times the mass of the Sun [See, e.g., Table 1 and the Appendix] is called a giant molecular cloud (GMC). GMCs are ≈15–600 light-years in diameter (5–200 parsecs). Whereas the average density in the solar vicinity is one particle per cubic centimetre, the average density of a GMC is 102–103 particles per cubic centimetre. Although the Sun is much denser than a GMC, the volume of a GMC is so great that it contains much more mass than the Sun. The substructure of a GMC is a complex pattern of filaments, sheets, bubbles, and irregular clumps.

The densest parts of the filaments and clumps are called "molecular cores", whilst the densest molecular cores are, unsurprisingly, called "dense molecular cores" and have densities in excess of 104–106 particles per cubic centimeter. Observationally molecular cores are traced with carbon monoxide and dense cores are traced with ammonia. The concentration of dust within molecular cores is normally sufficient to block light from background stars so that they appear in silhouette as dark nebulae.

GMCs are so large that "local" ones can cover a significant fraction of a constellation; thus they are often referred to by the name of that constellation, e.g. the Orion Molecular Cloud (OMC) or the Taurus Molecular Cloud (TMC). These local GMCs are arrayed in a ring in the neighborhood of the Sun coinciding with the Gould Belt. The most massive collection of molecular clouds in the galaxy forms an asymmetrical ring around the galactic center at a radius of 120 parsecs; the largest component of this ring is the Sagittarius B2 complex. The Sagittarius region is chemically rich and is often used as an exemplar by astronomers searching for new molecules in interstellar space.

H II regions
An H II region is a large, low-density cloud of partially ionized gas in which star formation has recently taken place.

At right is an image in three-color infrared of an H II region excited by a cluster of young, hot stars. The region is in Messier 17 (M 17). A large silhouette disc occurs to the southwest of the cluster center. This image is obtained with the ISAAC near-infrared instrument at the 8.2-m VLT ANTU telescope at Paranal.

At second right "is a near-infrared, colour-coded composite image of a sky field in the south-western part of the galactic star-forming region Messier 17. In this image, young and heavily obscured stars are recognized by their red colour. Bluer objects are either foreground stars or well-developed massive stars whose intense light ionizes the hydrogen in this region. The diffuse light that is visible nearly everywhere in the photo is due to emission from hydrogen atoms that have (re-)combined from protons and electrons. The dark areas are due to obscuration of the light from background objects by large amounts of dust — this effect also causes many of those stars to appear quite red. A cluster of young stars in the upper-left part of the photo, so deeply embedded in the nebula that it is invisible in optical light, is well visible in this infrared image. Technical information : The exposures were made through three filtres, J (at wavelength 1.25 µm; exposure time 5 min; here rendered as blue), H (1.65 µm; 5 min; green) and Ks (2.2 µm; 5 min; red); an additional 15 min was spent on separate sky frames. The seeing was 0.5 - 0.6 arcsec. The objects in the uppermost left corner area appear somewhat elongated because of a colour-dependent aberration introduced at the edge by the large-field optics. The sky field shown measures approx. 5 x 5 arcmin 2 (corresponding to about 3% of the full moon). North is up and East is left."

Hypotheses

 * 1) A star or protostar can fission into two or more parts subject to the separability of its interior.

title: Stars/Star fissions


text:
TAO/Persona Marianne

Persona description of Marianne, a volunteer instructor for new media courses for older people.

Personal characteristics
Marianne is a woman of 62 years old, who lives in a village close to Bern. Marianne has worked part-time in the administration of a company in Bern, but is retired since two years. She is married and has four adult children. At her former job, she has gained basic computer skills. However, it was only after her retirement that she got really interested in using the computer to process pictures. By reading books and internet-manuals, she taught herself how to use the program Photoshop and started showing her processed pictures via mail and online photography communities. After some time, friends and family members turned to her with their picture questions.

Marianne’s goals
Realizing how much she enjoyed not only processing her pictures, but also explaining others how to go about it, Marianne would like to help other older persons to get started with Photoshop and sharing pictures. She also misses the social contacts that she had when she still worked, so she would like to be involved with other people more.

Barriers regarding these goals
Marianne has never received any didactic training, so she does not know much about how to teach a group of people in an efficient yet pleasant way. Also, she finds it important to take good care of the household and to spend time with her husband, so she does not have much time to invest in the creation of courses. Above all, she does not want to have too many obligations towards the courses, as this reminds her of her working life. Now she wants to be in charge of her agenda.

Possible solutions to overcome these barriers
Marianne would like to get information about the didactic part of the courses. Also, she rather imagines herself giving courses developed by someone else, than having to create courses from scratch herself. A flexible working plan is a must for her.

Difficulties to expect
Marianne could be so absorbed be her own experiences with Photoshop, that it could be hard for her to distract the main lessons learned and to transfer these on an abstracted level to her course participants. Also, almost to prove that she knows enough about Photoshop (as an autodidact), she might be tempted to spend too much time on the ex-cathedra teaching, and not provide enough time for practicing. She never had any didactic courses herself, so maybe she does not know how to handle signs of boredom or questions from the participants.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: TAO/Persona Marianne


text:
MakerBot/Scanning An Object Using The Kinect: Full 360 Degree View

Purpose
To create a procedure to scan an object in 360 degrees for 3D printing

Procedure

 * 1. Install drivers from http://labs.manctl.com/rgbdemo/index.php/Main/Download.
 * The drivers must be installed in this order,

1)OpenNI 1.5.2.23.       2)SensorKinect 5.1.0.25. 3)Nite 1.5.2.21.
 * Visit the RGB-Demo website, go to the "Download" page and download the all in one driver package named "Zigfu"

 * 2. Install the Drivers manually by extracting the files from the .zip folder and going through the Control Panel > Device Manager > Kinect (Plug in/Disconnect the USB to the computer to find the right Com port if it is not recognized)> Properties > Hardware > Properties > Driver > Update Driver > Browse my computer... > Browse... > Find the extracted driver

 * 3. Download and extract the RGB-Demo software

 * 4a. For 360 degree views try using calibrate-kinect-ir.exe. I have not had success with this execution file, but this may be because I did not install the drivers manually. I just realized this as a possible solution after reading my partners tutorial for capturing a perspective view point cloud.

 * Calibrate the Kinect with the printed checkered board so that the Kinect can follow all the movements when an object is scanned in 360 degrees. After calibration, the image should look similar to this example.

 * 4b. Use the rgbd-viewer or rgbd-reconstructor to see a color image and a RGB (red-green-blue) image through the Kinect
 * Note: Use the execution files one at a time, otherwise they crash

 * 5a. After calibrating the Kinect, 3D scanning using rgbd-scan-markers should work to capture a 360 degree view point cloud.
 * Note: There are options for saving the model and they are saved in the same folder where the software is found by default (example images below).
 * 5b. Use the grab-mesh (automatically captures mesh) or rgbd-reconstructor (use start button) to capture a point cloud which is saved as a .ply (polygon) mesh in the RGB-Demo folder

 * 6. Download and install MeshLab (search google)
 * Note: Many other free software programs besides MeshLab are available for 3D modeling, such as Blender, AutoDesk Maya with free 3 year Student License, or Autodesk 123D

 * 7. Refer to our tutorial on Cleaning up Point Cloud Meshes in MeshLab to push your project towards 3D printing

 * On RGB-Demo's main page a demonstrational video shows an object being scanned on the calibration board.


text:
MakerBot/Cleaning Up Point Cloud Meshes in Meshlab For 3D Printing

Purpose
Cleaning up a point cloud mesh of an object in Meshlab so that it can be printed using a 3D printer.

Deleting Unwanted Background Points

 * 1. Open the file that was taken from the Kinect in MeshLab. SelectPoints.gif 1 Output mesh.png

 * 2. Select either the desired points or the unwanted points using the Select Vertices tool. Rotate the mesh to make selecting easier.

 * 3. If a selection is made around the points you want to keep, then invert the selection using Filter -> Render -> Invert Selection. Press ctrl + delete to delete unwanted points from the mesh.

 * 4. Use Export as... (.ply) to save progress. Saving it at this point provides a good backup point, and the image is zoomed and centered when re-opened from the new file.

Option "A"

 * 5a. Under the Filters tab in the navigation menu choose Sampling -> Poisson-disk Sampling. In the Number of Samples, pick between 60000 and 100000 sample points(sometimes the system crashes.) Remember to check the Base Mesh Subsampling box or you will get an error.

 * 6a. Once the sampling has completed, a new layer will be added. Open the layers window under View -> Open Layer Dialog and make sure the Poison-disk Samples layer is highlighted.

 * 7a. Next, go to Filters –> Normals, Curvatures and Orientation -> Compute normals for point sets. In the new window, put a number greater than 15 for the Number of Neighbors.

 * 8a. Click Apply and manually Close that menu.

 * 9a. Then, go to Filters —> Points —> Surface Reconstruction Poisson. This will create a new layer called Poisson Mesh. From there you can add surfaces to the Model.

 * 10a. Finally save the model in a .obj file format to be opened in Maya or Blender.

 * Note: Meshlab can export the mesh as a .stl file for 3D printing with the MakerBot. However, further 3D modeling is required to create a base, ground layer, or support platform for the object before a printable code can be generated by the Replicator-G software used by the MakerBot.

Option B

 * 5b. Distribute normals using Render -> Show Vertex Normals. This will create normals pointing backwards, so they will need to be recomputed so that the normals are facing forward.

 * 6b. Recompute normals using Filter > Point Set -> Compute normals for point sets, change number to 16 for the number of neighbors and also check the box for Flip Normals. Change the camera to -1000 so that the sampling program knows that the cloud point data was taken from a large distance, this would give it a better idea where the normals should go.

 * 7b. Turn on layers from the top menu bar View -> Open Layer Dialog.

 * 8b. Now create a subset of the point cloud, go to Filters > Sampling > Poisson -Disk sampling, change the Number of Samples to 5000 and check the box for Base Mesh Subsampling. This will create an even sampling distribution of the cloud points, and will give a general surface to work with.

 * 9b. Click the Poisson-disk Samples layer. Now go to Filters > Point Set > Surface Reconstruction: Poisson, set parameters, 12 for Octree Depth and 7 for Solver Divide, these numbers can be changed depending on the scale of the original point cloud mesh. Make the numbers bigger if the point cloud is big.

 * 10b. Turn on the Light found within the tool bar and also turn on Smoothing which is next to the light button.

 * 11b. Now approximate more normals using the point cloud to add more detail. This time distribute points by going to Filter > Re-meshing-simplification and reconstruction > Use sub-division algorithm called LS3 loop. This algorithm will add more detail to the mesh. Sub-sample it three times by setting Iterations = 3 Addmorevertices.png

 * 12b. Use File -> Export as... to save the final version of the mesh which can be printed using a 3d printer.TurnOnSmoothing.png


text:
User:Egm6322.s12.team1.zheng.zx/R12

Problem 4: Write a matlab program to compute the convergents for $$\sqrt 2$$
 Solved without assistance

Given:

 * {| style="width:100%" border="0" align="left"

\displaystyle \sqrt 2=1+\frac{1}{2+\frac{1}{2+\frac{1}{2+\frac{1}{2+\frac{1}{\ddots}}}}} $$
 * }
 * }
 * }
 * {| style="width:100%" border="0" align="left"

\displaystyle C_0:=1 $$
 * }
 * }
 * }
 * {| style="width:100%" border="0" align="left"

\displaystyle C_1:=1+\frac{1}{2}=\frac{3}{2} $$
 * }
 * }
 * }
 * {| style="width:100%" border="0" align="left"

\displaystyle C_2:=1+\frac{1}{2+\frac{1}{2}}=1+\frac{2}{5}=\frac{7}{5} $$
 * }
 * }
 * }
 * {| style="width:100%" border="0" align="left"

\displaystyle C_3:=1+\frac{1}{2+\frac{1}{2+\frac{1}{2}}}=1+\frac{1}{2+\frac{2}{5}}=1+\frac{5}{12}=\frac{17}{12} $$
 * }
 * }
 * }

Find:
Write a matlab program to compute the convergents $$C_i$$for i=0,1,...,10,and plot these convergents together with the line $$\sqrt 2$$to visualize the convergence
 * {| style="width:100%" border="0" align="left"

\displaystyle \lim_{i \to \infty}C_i=\sqrt 2 $$
 * }
 * }
 * }

Solution:
clear

n=10;

f=sqrt(2); f=sym(f); f=char(f); fplot(f,[-2 2],'r','o'); legend('sqrt(2)'); hold on

disp(['C' char(48) '=']) disp(1)

f=1; f=sym(f); f=char(f); fplot(f,[-2 2]);

for x=1:n; s=0; for i=1:x; s=1/(2+s); end s=1+s; s=vpa(s); disp(['C' char(sym(x)) '=']) disp(s)

f=s; f=sym(f); f=char(f); fplot(f,[-2 2]);

end axis([-2 2 1.39 1.51])

The results are as follows:

From the results above, we can see that with the increasing of fraction terms, the value will be convergent to the actual value: $$\sqrt 2=1.4142135623730950488016887242097$$.

title: User:Egm6322.s12.team1.zheng.zx/R12


text:
TAO/Developing problem based approaches

Goal of the module
Describe and document activities that lead to the development of problem based approaches to the TAO Handbook and the TAO Community of Practice, based on persona descriptions and use scenarios.

Target group
Members of the TAO Community of Practice

Step 1
Brainstorm (potential) use cases with regard to problems derived from existing persona descriptions or from your own experience and list them on the corresponding page:
 * Brainstorming Use Cases for staff members in a managing or co-ordinating function (managers)

Step 2
Describe (potential) use cases with regard to problems derived from existing persona descriptions or from your own experience and list them on the corresponding page:

 * Use cases for staff members in a managing or co-ordinating function
 * Use cases for instructors, moderators, or facilitators
 * Use cases for consultants

title: TAO/Developing problem based approaches


text:
TAO/Use Cases for Managers

This page contains (potential) use cases for the TAO Handbook and Community of Practice from the perspective of staff members in a managing or co-ordinating function (see the personas overview page for a detailed description and a list of corresponding personas).

It should be specified whether a use scenario primarily involves the TAO Handbook, the TAO Community of Practice or both. (N.B.: The TAO Handbook contains formalized knowledge and know-how that can easily be transmitted in written form whereas the TAO Community of Practice is about generating and sharing know-how by bringing the right people together and putting them in front of concrete practical problems, for example in exchange workshops, peer consulting, coaching, inter-vision settings or similar).

title: TAO/Use Cases for Managers


text:
Category:User bn-N

Users in this category indicate they have skill level N for language Bengali.

title: Category:User bn-N


text:
Category:User hi-3

Users in this category indicate they have skill level 3 for language Hindi.

title: Category:User hi-3


text:
User:Deepon

Deepon Saha is pursuing M.tech in VLSI from Jadavpur University. He became an active wikipedian in early 2011 and started contributing in English Wikipedia. He loves to watch movies & is an active blogger.

 * Along with his studies, he is a research team member for SMDP-II project, Jadavpur University.

 * He also takes classes in VLSI short-term course for undergraduates in IC CENTRE at Jadavpur University.

Education

 * Deepon completed his schooling from Patha Bhavan, Kolkata.
 * He completed B.Tech in Electronics & Communication Engineering from Meghnad Saha Institute of Technology.
 * He is currently pursuing M.tech in VLSI from Jadavpur University.

Activities

 * Apart from Engineering, Photography is his passion & he doesn't travel without his camera.
 * Most of his photographs are part of the Myshutterspace photography community.
 * Deepon designs websites in his leisure time, he designed the website for IEEE Student Branch at Jadavpur University.
 * He is the webmaster for the IEEE Student Branch and Nano Device Simulation Lab at jadavpur University.

title: User:Deepon


text:
TAO/Use Cases for Instructors

This page contains (potential) use cases for the TAO Handbook and Community of Practice from the perspective of (volunteer) instructors, moderators, or facilitators (see the personas overview page for a detailed description and a list of corresponding personas).

It should be specified whether a use scenario primarily involves the TAO Handbook, the TAO Community of Practice or both. (N.B.: The TAO Handbook contains formalized knowledge and know-how that can easily be transmitted in written form whereas the TAO Community of Practice is about generating and sharing know-how by bringing the right people together and putting them in front of concrete practical problems, for example in exchange workshops, peer consulting, coaching, inter-vision settings or similar).

title: TAO/Use Cases for Instructors


text:
TAO/Use Cases for Consultants

This page contains (potential) use cases for the TAO Handbook and Community of Practice from the perspective of consultants (see the personas overview page for a detailed description and a list of corresponding personas).

It should be specified whether a use scenario primarily involves the TAO Handbook, the TAO Community of Practice or both. (N.B.: The TAO Handbook contains formalized knowledge and know-how that can easily be transmitted in written form whereas the TAO Community of Practice is about generating and sharing know-how by bringing the right people together and putting them in front of concrete practical problems, for example in exchange workshops, peer consulting, coaching, inter-vision settings or similar).

title: TAO/Use Cases for Consultants


text:
TAO/Taking stock of the project TAO

Goal of the Module
Take stock of the project TAO's outputs with view of their documentation in form of the TAO Handbook.

Target group
Members of the project TAO.

Step 1: Get the big picture
Take the inventory of the TAO project's (expected) outputs that are supposed to find entry to the TAO Handbook: Inventory.

Step 3: Document existing project know-how
Guidelines for the production of handbook entries:

 * The documentation of project know-how needs to be tailored to the target groups' needs and preferences (see personas as well as the problem-based approaches). In order to reach this goal, the documentation should take place in an iterative process, where some draft handbook content is produced and then shown to target group representatives in order to gather feedback.

 * The handbook entries should as much as possible be evidence based. Similar referencing standards should be applied as for Wikipedia articles in order to make assertions in the handbook traceable to their source. One major difference being that results from original research are admitted; in this case publication in peer-reviewed journals should however be aimed for as well (thus producing solid references on the go).

 * The handbook entries shall be complementary to corresponding Wikipedia articles; there is no point in filling the handbook with information that may as well be the object of a Wikipedia article. In this case, contact with the Wikipedia community should be sought in order to develop the Wikipedia articles in question.

Step 4: Define research tasks to fill the gaps
Based on the problem-based approaches new research questions may be developed and tackled within the project TAO or beyond.

title: TAO/Taking stock of the project TAO


text:
User talk:Deepon

If you leave a message here, I'll answer it here. So check back later. If I left a message on your talk page, please reply there. I'll watch your page and reply as soon as I can... :)

Click here to leave a new message.

title: User talk:Deepon


text:
TAO/Inventory of the TAO project's outputs

This page contains the inventory of the TAO project's (expected) outputs that are expected to find entry to the TAO Handbook.

Definitions
List the terms and concepts that have been defined or are going to be defined within the project TAO and are likely to be used within various contexts within the TAO Handbook and the TAO Community of Practice.

 * Online Community / Online Social Network / Virtual Team (see BFH students' paper on online communities and 60plus; there are probably also ZAWiW sources)
 * Typology of Online Communities (see BFH students' paper on online communities and 60plus)
 * Usability (see preliminary study "60 plus" for a definition; check with Edi)
 * Accessibility (see preliminary study "60 plus" for a definition; check with Edi)
 * Sociability (check preliminary study "60 plus"; BFH student's work on communities of practice may also yield some input; there might be some definitions and references in the comparative study SenCH - SenNL as well)
 * E-Inclusion (there are definitions on the TAO Sharepoint; there may be definitions created within the SeniorsKS Learning Project, check with Rosmarie)
 * Onliners / Offliners / Nonliners
 * Glossary of E-Learning Terms (is planned to be elaborated as part of an activity within the SeniorsKS LP)

Outreach / Advocacy

 * Assessment of the pertinence and the usefulness of TAO-related actions for society, online communities, and seniors
 * Effectiveness and efficiency considerations; arguments for or against certain types of actions in particular contexts

Internet Use / Use of Online Communities and Online Social Networks
Guiding questions:
 * 1) What are important general considerations?
 * 2) What target group characteristics are most relevant with regard to effective approaches? (age, familiarity with computers and the Internet, disabilities, language skills, etc.)

Usability / Accessibility / Sociability
With regard to usability, accessibility, and sociability, we need to differentiate between the following levels:
 * Software (e.g. Drupal, MediaWiki distribution)
 * Instance of the Software (e.g. the Drupal implementation at seniorweb.ch, tailored to the specific needs of the Seniorweb community)
 * Contributor Behavior (e.g. with regard to providing meta data along with pictures, etc.)

User Education

 * Teaching methods
 * etc.

Volunteering
Guiding questions:
 * 1) What are important general considerations?
 * 2) What target group characteristics are most relevant with regard to effective approaches? (age, familiarity with computers and the Internet, disabilities, language skills, etc.)

Add different dimensions based on literature review and workshops

Actions
For each action (Overview of actions):
 * Concept
 * Implementation report(s) with timeline
 * Information regarding effectiveness, efficiency, and impact (indicators over time)
 * Information regarding sustainability/scalability: Business Model, Indicators, Multiplication Concept
 * Information regarding transfer and internationalization: context analysis (particularities of a given implementation); international comparisons of relevant socioeconomic data
 * Testimonials
 * "resource" persons that can give information and/or provide assistance in case of a transfer (they have know-how concerning existing implementations and/or the methodological know-how for an analysis of the target context) --> Community of practice

Planning Methods

 * Planning table
 * SMART goals

Creative Methods and Problem Solving Methods

 * Systemic impact analysis
 * Design Thinking Approach


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