A theoretical analysis about the influence of the hertz elastic contact on a three body chain...

when two balls are dropped together , both vertically aligned and hitting the ground at the same time , an interesting rebound effect is obtained . if the smaller ball is above , it may rise surprisingly high into the air . this effect may still be enhanced if one drops a chain of balls , ordered by their relative weight , the lightest ball at the top . this system was already discussed in pedagogical articles more than 30 years ago , assuming perfect and independent elastic collisions between each pair of balls . it was considered an attractive and ideal system to study elastic collisions . however , if the balls are dropped together , all collisions will happen at the same time . because they are not instantaneous , the final velocity distribution of the balls will be dependent on the particular interactions between them , even in those cases where the interactions are elastic , _ i.e. _ , with no loss of energy . in their beautiful article , the class of w. g. harter considered at some point non - instantaneous collisions . to study them , they introduced a simple quasi - linear model , which could be valid if we think not of spheres but of uni - dimensional springs . the dynamical differential equations were solved using an analog computer program . however , they concluded that the quasi - linear model did not agree with their experimental results , and they proposed a phenomenological non linear model . the interaction field was then obtained directly from empirical data , by dropping a ball onto a painted flat metal surface from varying heights . in this way the interaction could be plotted as a function of the spot size , and eventually as a function of the depression of the ball . although the strategy to obtain the non linear interaction was remarkable , the discussion that followed was not sufficiently developed . in fact , from the theoretical point of view and as a first approximation , the analysis of the non - instantaneous multiple collisions effect

We study the non - instantaneous multiple collisions effect in a system of two balls dropped together. The non linear model is a simple quasi - linear model, which can be valid if we think not of spheres but of uni - dimensional springs. We also investigate the nonlinear interaction field by dropping a ball onto a painted flat metal surface from varying heights, and then as a function of the depression of the ball.

a theoretical analysis about the influence of the hertz elastic contact on a three body chain collision is presented . in spite of the elastic character of the collision , the final velocity of each particles depends on the particular interaction between them . a system involving two elastic spheres falling together one in top of the other under the action of gravity , and colliding with an horizontal hard wall is studied in detail . the effect of the hertz contact interaction can be easily put


In ion traps , entangling gate operations can be realized by a bichromatic pair of laser beams that...

the processing of information based on the laws of quantum physics has become a very active field of research during the last decade . for the experimental demonstration of fundamental key results of quantum information theory , ion - trap based systems have played a major role . the success of ion trap experiments can be attributed to the fact that encoding quantum information in either hyperfine ground or meta - stable excited atomic states provides well - defined quantum bits ( qubits ) with long coherence times . the use of lasers for manipulating the qubit state allows for precisely switchable interactions with low decoherence rates . the fundamental operations of qubit initialization , arbitrary single qubit manipulation and quantum state - detection have already been used in atomic clocks with single ions for many years . contrary to other realizations of quantum information processing , the most demanding operation in ion traps consists in the realization of an entangling gate operation . because of the repulsive coulomb force , the inter - ion distance is orders of magnitude bigger than the characteristic length scale of any state - dependent interaction between ions in ground or low - lying excited states . in all current experiments creating entangled ions , gate operations rely on interactions that are mediated by the vibrational degrees of freedom of the ion string . these gate operations fall into two categories : 1 . quantum gates induced by a laser beam that interacts with a single ion at a time as originally proposed in the seminal paper by i. cirac and p. zoller and later realized by the innsbruck ion trapping group . in these gates , a single ion is entangled with a vibrational mode of the ion string and the entanglement is subsequently transferred from the vibrational mode to the internal state of a second ion . 2 . quantum gates induced by a bichromatic laser that collectively interacts with two or more ions . here , a vibrational mode becomes t

We present a new method for the realization of quantum gates in ion traps. This method is based on the entangling gate operation, which is a key feature of the current experiments with single ions. The resulting gate operation is characterized by the interaction between two or more ions and the vibrational modes of the ionic string.

in ion traps , entangling gate operations can be realized by a bichromatic pair of laser beams that collectively interact with the ions . in this paper , a new method of modelling the laser - ion interaction is introduced that turns out to be superior to standard techniques for the description of gate operations on optical qubits . the treatment allows for a comparison of the performance of gates based on and interactions on optical transitions where the bichromatic laser field can be realized b


We use the hb13 stellar population synthesis models to study the rle of interacting binary pairs as...

the spectral energy distribution of many early type galaxies ( etgs ) and spiral galaxy bulges increases to shorter wavelengths in the range from 1200 to 2000 . this phenomenon is called uvx or uv upturn ( cf . figure [ fig : dcc ] ) . observational evidence shows that uvx increases with stellar metallicity . found that etgs with bluer 1550-v colour have larger stellar velocity dispersion and higher absorption line index . giant elliptical galaxies with large values have [ mg / fe ] index higher than most metal rich stars in the solar neighbourhood . the work of and reinforces the conclusion of that metallicity is a fundamental parameter , and that the stronger cases of uvx occur in massive metal rich ( ) etgs . the launch of the galaxy evolution explorer ( _ galex _ ) satellite revolutionised the study of the uv emission of galaxies . combined _ galex _ and sloan digital sky survey ( _ sdss _ , ) observations have revealed that a substantial fraction ( 30% ) of etgs exhibit strong nuv and fuv emission , consistent with residual star formation , and that only a small percentage ( 5% ) of etgs shows the classical uvx . using galex colours combined with sauron spectroscopy , and rejecting galaxies with recent star formation , found that galaxies with bluer fuv - v colour have stronger mg__b _ _ and lower absorption . this result suggests that galaxies with bluer fuv - v are older or have higher metallicity , or both . a similar conclusion was reached by studying a sample of 150 red and passive coma cluster galaxies with spectroscopic age and estimated element abundances determinations . they also found a strong correlation of fuv - nuv colour with age and metallicity . nowadays , the favoured candidate sources for the uvx are extreme horizontal branch ( ehb ) stars and their descendants . ehb stars are low - luminosity core he - burning stars with temperatures reaching up to 23000 k and lifetime yr . hence , they are difficult to observe , but they contribute consider

We present a new study of the uvx emission of galaxies with bluer fuv - v colour. Using _ galex _ and sloan digital sky survey ( _ sdss _ ( ), we find that a significant fraction ( 30% ) of early type galaxias exhibit strong nuv and fuv emission, consistent with residual star formation. This result suggests that galaxii have older or higher metallicity, or both.

we use the hb13 stellar population synthesis models to study the rle of interacting binary pairs as progenitors of ehb stars . we assemble a sample of 3417 early type galaxies observed both in the optical ( _ sdss_-dr8 ) and the uv ( _ galex_-gr6 ) . the galaxies in our sample can be classified according to their position in the colour - colour diagram as uv weak or red sequence galaxies ( ) , uv strong or uvx galaxies ( ) , and recent star forming galaxies ( ) . analysing this sample using the


The phase diagram of nuclear matter is quite rich - it shows such phenomena as phase - transitions...

let us consider asymmetric nuclear matter ( anm ) characterized by a proton and a neutron densities , . these densities can be transformed in a set of 2 mutually commuting charges , where is the density of baryons , and the asymmetry density . in infinite matter , the extensivity of the free energy implies that it can be reduced to a free energy density : the system is stable against separation into two phases if the free energy of a single phase is lower than the free energy in all two - phases configurations . this stability criterium implies that the free energy density is a convex function of the densities . a local necessary condition is the positivity of the curvature matrix : =  [ }{  _ { i}  _ { j}}|_{t} ]   [ }{  _ { j}}|_{t} ] \ ] ] where we have introduced the chemical potentials . we represent in fig . [ fig1 ] the energy surface as a function of and , deduced from sly230a skyrme interaction . in the symmetric case ( ) , one can see the negative curvature of the energy which defines the spinodal area , whereas in pure neutron matter ( ) , no negative curvature and so no spinodal instability are predicted . we can also notice that the isovector density dependence is almost parabolic illustrating the positivity of . and for the sly230a interaction . the contour delimitate the spinodal area . ] we show in fig . [ fig2 ] several aspects of the spinodal contour defined as the region where the matrix $ ] is negative . in the left part is plotted the spinodal contour in anm for several forces . it exhibits important differences . in the case of sly230a force ( as well as sgii , d1p ) , the total density at which spinodal instability appears decreases when the asymmetry increases whereas for siii ( as well as d1 , d1s ) it increases up to large asymmetry and finally decreases . we observe that all forces which fulfill the global requirement that they reproduce symmetric nuclear matter ( snm ) equation of state as well as the pure neutron matter calculations , le

We consider asymmetric nuclear matter ( anm ) with a proton and neutron densities. The free energy density is a convex function of the density, which can be reduced to a free energy. In the symmetric case, the spinodal area is defined as the region where the matrix $ ] is negative. For the sgii force ( as well as syii ( aswell as d1p ), it exhibits important differences.

the phase diagram of nuclear matter is quite rich - it shows such phenomena as phase - transitions , formation of condensates , clustering , etc . from the analysis of the spinodal instability , one can learn about the region of liquid - gas coexistence in nuclear matter at low densities and finite isospin asymmetries . in a recent paper , we have shown that asymmetric nuclear matter at sub - nuclear densities should undergo only one type of instability . the associated order parameter is domina


We study the light -even neutral higgs boson production in association with an electron and a jet...

one of the most significant tasks for high - energy experiments is to search for scalar higgs particles . although the standard model ( sm) has achieved impressive experimental success , the higgs boson , which is predicted by the sm for spontaneous electroweak symmetry breaking , remains a mystery . moreover , there exists the problem of the quadratically divergent contributions to the corrections to the higgs boson mass , which is the so - called naturalness problem . alternative conceptional difficulties , such as the hierarchy problem , the necessity of the tuning and the nonoccurrence of gauge coupling unification at high energies , suggest that the sm is probably the low - energy limit of a more fundamental theory . as the most hopeful extensions of the sm , the supersymmetric ( susy ) models can solve such problems mentioned above . the minimal supersymmetric standard model ( mssm) is the simplest one among all the susy extensions of the sm . in this model , two higgs doublets and give masses to up- and down - type fermions . the higgs sector consists of three neutral higgs bosons , one -odd particle ( ) , two -even particles ( and ) , and a pair of charged higgs bosons ( ) . however , these higgs bosons have not been directly explored experimentally until now . the lep experiments provided lower mass bounds as : for the sm higgs boson ( at c.l . ) , and for the mssm bosons and for ( at c.l.) . recently , a possible high - energy collider in - collision mode at the lhc , the large hadron - electron collider ( lhec ) , has been sketched . there will exist a rich physics program . the lhec can be used to accurately determine the parton dynamics and the momentum distributions of quarks and gluons in the proton , and furthermore it may play a significant role in the discovery and interpretation of new physics . the incoming proton beam at the lhec has an energy and the energy of incoming electron is considered as according to several scenarios , with the center -

We present a new method for the search of scalar higgs particles in the minimal supersymmetric standard model ( mssm ). This method is based on the lhec - based, large hadron - electron collider ( lhc ) experiment at the sm and m. The physics program is derived from the lep experiments.

we study the light -even neutral higgs boson production in association with an electron and a jet at the possible cern large hadron - electron collider within the minimal supersymmetric standard model . we investigate the possible supersymmetric effects on this process and compare our standard model numerical results with those in previous work . we present the leading - order and qcd next - to - leading - order corrected total cross sections and the distributions of the transverse momenta of th


In magnetic materials a variety of non - collinear ground state configurations may emerge as a...

* analytical model . * detailed theoretical study of nonlinear magnetization dynamics is rarely to be accomplished in closed analytical form , however before we present the results of our numerical simulations we elaborate a simple toy model which allows us to include all relevant interactions and make predictions which will be shown to be qualitatively correct . we examine the behaviour of a quasi - one - dimensional ferromagnet with lack of inversion symmetry located along axis placed in the transverse magnetic field : the hamiltonian ( per a unit volume ) of such a system is known to incorporate the terms due to exchange , dzyaloshinskii - moriya , and zeeman interaction . we have also included , a component which stands for easy - plane ( plane ) anisotropy in the expression ( [ magnen ] ) . in the following we assume the magnetisation is determined by a vector field , so that , while and are coordinates of space and time ; the parameters , , and represent exchange and dm couplings , and magnetic anisotropy respectively . in the absence of an external field dm favours the formation of a spiral structure along the axis , which is incommensurate with the underlying crystalline structure , whereas the magnetic field , applied in the direction , tends to align the spins in this direction . the delicate interplay between these two interactions may lead to the formation of elongated domains of width ( see below in the text ) in which magnetisation is uniform . there exists a critical field , where as long as the system is collinear , ferromagnetic . the vector field allows a parametrisation with polar and azimuthal angles : . there are many magnetic materials where the magnetic anisotropy is very high , so that . for such systems one can use , where . if this is the case , the landau - lifshitz equation , combined with the hamiltonian in eqn.[magnen ] , leads to the following equations for the leading order terms for : where is the gyromagnetic ratio . note that subst

We present a simple toy model for the magnetisation of quasi - one - dimensional ferromagnets with lack of inversion symmetry located along axis placed in the transverse magnetic field. The model is based on the landau -lifshitz equation and the hamiltonian, which are both integrals of the eqn.[magnen ] equation. We also consider the behaviour of a quasi - two - dimension ferromet with absence of inverted symmetry.

in magnetic materials a variety of non - collinear ground state configurations may emerge as a result of competition among exchange , anisotropy , and dipole - dipole interaction , yielding magnetic states far more complex than those of homogenous ferromagnets . of particular interest in this study are particle - like configurations . these particle - like states , e.g. , magnetic solitons , skyrmions , or domain walls , form a spatially localised clot of magnetic energy . in this paper we addre


A strongly coupled quark - gluon plasma ( qgp ) of heavy constituent quasiparticles is studied by a...

investigation of properties of the quark - gluon plasma ( qgp ) is one of the main challenges of strong - interaction physics , both theoretically and experimentally . many features of this matter were experimentally discovered at the relativistic heavy ion collider ( rhic ) at brookhaven . the most striking result , obtained from analysis of these experimental data , is that the deconfined quark - gluon matter behaves as an almost perfect fluid rather than a perfect gas , as it could be expected from the asymptotic freedom . there are various approaches to studying qgp . each approach has its advantages and disadvantages . the most fundamental way to compute properties of the strongly interacting matter is provided by the lattice qcd . interpretation of these very complicated computations requires application of various qcd motivated , albeit schematic , models simulating various aspects of the full theory . moreover , such models are needed in cases when the lattice qcd fails , e.g. at large baryon chemical potentials and out of equilibrium . a semi - classical approximation , based on a point like quasi - particle picture has been introduced in . it is expected that the main features of non - abelian plasmas can be understood in simple semi - classical terms without the difficulties inherent to a full quantum field theoretical analysis . independently the same ideas were implemented in terms of molecular dynamics ( md ) . recently this md approach was further developed in a series of works . the md allowed one to treat soft processes in the qgp which are not accessible by perturbative means . a strongly correlated behavior of the qgp is expected to show up in long - ranged spatial correlations of quarks and gluons which , in fact , may give rise to liquid - like and , possibly , solid - like structures . this expectation is based on a very similar behavior observed in electrodynamic plasmas . this similarity was exploited to formulate a classical non - relativist

We study the properties of the quark - gluon plasma ( qgp ) in terms of molecular dynamics ( md ). The main features of the qcd are studied in terms, namely, the asymptotic freedom and the lattice qd. We show that the mcd is a simple semi - classical approximation for the scalar - like behavior of the matter.

a strongly coupled quark - gluon plasma ( qgp ) of heavy constituent quasiparticles is studied by a path - integral monte - carlo method , which improves the corresponding classical simulations by extending them to the quantum regime . it is shown that this method is able to reproduce the lattice equation of state and also yields valuable insight into the internal structure of the qgp . the results indicate that the qgp reveals liquid - like rather than gas - like properties . at temperatures ju


We consider deflection of polarizable molecules by inhomogeneous optical fields , and analyze the...

optical dipole forces acting on molecules in nonresonant laser fields is a hot subject of many recent experimental studies . by controlling molecular translational degrees of freedom with laser fields , novel elements of molecular optics can be realized , including molecular lens and molecular prism . the mechanism of molecular interaction with a nonuniform laser field is rather clear : the field induces molecular polarization , interacts with it , and deflects the molecules along the intensity gradient . as most molecules have anisotropic polarizability , the deflecting force depends on the molecular orientation with respect to the deflecting field . previous studies on optical molecular deflection have mostly considered randomly oriented molecules , for which the deflection angle is somehow dispersed around the mean value determined by the orientation - averaged polarizability . the latter becomes intensity - dependent for strong enough fields due to the field - induced modification of the molecular angular motion . this adds a new ingredient for controlling molecular trajectories , which is important , but somehow limited because of using the same fields for the deflection process and orientation control . in this work , we show that the deflection process can be significantly affected and controlled by _ preshaping _ molecular angular distribution _ before _ the molecules enter the interaction zone . this can be done with the help of numerous recent techniques for laser molecular alignment , which use single or multiple short laser pulses ( transform - limited , or shaped ) to align molecular axes along certain directions . short laser pulses excite rotational wavepackets , which results in a considerable transient molecular alignment after the laser pulse is over , i.e. at field - free conditions ( for reviews on field - free alignment , see , e.g. ) . field - free alignment was observed both for small diatomic molecules as well as for more complex molecules ,

We present a new method for controlling optical dipole forces acting on molecules in nonresonant laser fields. The technique is based on preshaping molecular angular distribution before the molecules enter the interaction zone. This allows to control the deflection process and orientation control by pres shaping the moleculaire angulation.

we consider deflection of polarizable molecules by inhomogeneous optical fields , and analyze the role of molecular orientation and rotation in the scattering process . it is shown that molecular rotation induces spectacular rainbow - like features in the distribution of the scattering angle . moreover , by preshaping molecular angular distribution with the help of short and strong femtosecond laser pulses , one may efficiently control the scattering process , manipulate the average deflection a


It is well known that the strong subadditivity theorem is hold for classical system , but it is...

entropy is an important concept not only for physics but also for information science . from the definition of entropy , we can get some simple properties of it , such as concavity , continuity property , additivity and subadditivity . but some other properties is not so obvious , such as the strong subadditivity theorem ( ssa ) . among all of the properties of entropy , the most famous one is the ssa , and it is very difficult to prove this theorem for quantum system . the content of this theorem can be expressed as the following : two overlapping subsystem and , the entropy of their union ( ) plus the entropy of their intersection ( ) does not exceed the sum of the entropies of the subsystems ( and ) , that is where it is well known that this theorem is true for classical information theory , but to prove this theorem is true for quantum system is very difficult . this theorem is first conjectured to be true for the quantum system by lanford and robibson . the first proof of this conjecture is given by lieb _ _ several years later . this proof is based on the concave of the function in . another proof based on the same fact was proposed by uhlmann . recently , quantum information theory attracts more and more attentions for its misterious properties and its potential applications in science and technology . the ssa plays an important role in this new field too . the fundamental scource in quantum information is entanglement between many particles which can be viewed as the relations between the partial particles . so distinguish whether a set of the partial particles come from a single state ( -representability problem) and further to obtain its entanglement property are important in quantum information while ssa gives a strong constraint on the partial particles and the whole system . the convenience of the ssa is that it has explicit physical and manipulating meaning . so it is a convenient necessary criterion for the -representability problem . recently , we us

We study the strong subadditivity theorem ( ssa ) for quantum system. We prove this theoretic by using the concave of the function in. The result is obtained for the -representability problem and its entanglement property.

it is well known that the strong subadditivity theorem is hold for classical system , but it is very difficult to prove that it is hold for quantum system . the first proof of this theorem is due to lieb by using the lieb s theorem . here we use the conditions obtained in our previous work of matrix analysis method _ _ to give a new proof of this famous theorem . this new proof is very elementary , it only needs to carefully analyse the minimal value of a function . this proof also shows that th


The search for novel spintronic devices brings about new ways to control switching in magnetic thin...

and optimizing the switching of thin magnetic films in a variety of spintronic devices has been of great interest since the discovery of giant magnetoresistance ( gmr ) - . many ways of control have been demonstrated such as spin - torque , toggle and heat assisted switching to mention a few . today , the search for new applications has pushed the need even further . in thermally assisted mram the information is stored by exchange coupling between an antiferromagnetic ( afm ) and a ferromagnetic ( fm ) film . switching of the fm film is controlled by heating the two films above the nel temperature of the afm and then cooling down in the presence of an external magnetic field . recently a new device based on a novel way to control switching was proposed . by exchange coupling two fm films through a weakly fm alloy the coupling is controlled by changes in temperature . at room temperature the alloy is weakly fm and the two films are exchange coupled through the alloy . at a temperature higher than the curie temperature the alloy is paramagnetic and the two strongly fm films decouple . provided the films have separate switching fields their moments can then be aligned either parallel or antiparallel . either external or internal heating can be used . by using a weakly fm alloy of ni and cu , we demonstrate this new way to thermally control the switching of a magnetic film and how it can be used with a gmr read out layer . the complete device structure is shown in fig 1 . all films were deposited on thermally oxidized si substrates using magnetron sputtering at a base pressure better than torr . the bottom nife ( nife ) film was used as an underlayer to promote the growth of afm irmn ( irmn ) . the irmn was used to exchange bias a cofe ( cofe ) reference layer in a cofe / cu / nife gmr read out layer . a ni - cu alloy was cosputtered from ni and cu targets such that the curie temperature of the alloy was just above room temperature . on top of the alloy an exchange bias

We present a new way to control the switching of thin magnetic films in a variety of spintronic devices. By using a weakly fm alloy of ni and cu, we demonstrate that the switching is controlled by changes in temperature. At room temperature the two films are exchange coupled through the alloy and the two strongly fM films decouple. The two strong fmm films can then be aligned either parallel or antiparallel.

the search for novel spintronic devices brings about new ways to control switching in magnetic thin - films . in this work we experimentally demonstrate a device based on thermoelectrically controlled exchange coupling . the read out signal from a giant magnetoresistance element is controlled by exchange coupling through a weakly ferromagnetic ni - cu alloy . this exchange coupling is shown to vary strongly with changes in temperature , and both internal joule heating and external heating is use


We present numerical simulations that include 1-d eulerian multi - group radiation - hydrodynamics...

since the original identification of interacting supernovae ( sne ; ; ) and the creation of the sn iin class , the sample of such peculiar type ii sne has grown from a few to a few tens of events . it has also revealed an intriguing diversity , spanning a range of luminosities , duration , line profile morphology , with events like sne 1988z , 1994w , 2006gy , and the enigmatic sn2009ip . the origin of type iin sne is associated with the interaction of fast material with previously - expelled slowly - expanding material . the resulting shock leads to deceleration of the inner shell , acceleration of the outer shell , and conversion of kinetic energy into internal and radiative energy . because ( standard ) non - interacting sne radiate merely 1% of their total energy ( the rest being kinetic ) , interacting sne can easily reach extraordinary luminosities by tapping this abundant reservoir of kinetic energy . for example , an interaction extracting 30% of a ejecta could produce a sn iin with a luminosity of 10 for 3 months . super luminous interacting sne require both a high kinetic energy in the inner shell and a large mass reservoir in the outer shell ( see , e.g. , ) . two good examples of such sne iin are sn2006gy and more recently sn2010jl . the latter has extensive photometric and spectroscopic observations and also has spectropolarimetric data . how stars produce the outer shell is unclear it may be material ejected by the pair - production instability or it may be material ejected via a super - eddington wind . here , we simply consider the interaction between a fast moving inner shell and a slowly - moving massive outer shell , and leave aside speculations concerning their origin . numerical simulations of interacting sne are generally undertaken with radiation hydrodynamics , hydrodynamics combined with a parameterised cooling function , or pure hydrodynamics ( by assuming adiabaticity ; see , e.g. , ) . when studying super - luminous sne iin , radiation hy

We present a numerical simulation of the interaction between a fast moving inner shell and a slowly - moving massive outer shell in the presence of a supernova. We consider the interaction with a slow - expanding material, which is a type iin, and show that it can be explained by the interaction of kinetic energy with kinetic energies. The resulting shock leads to deceleration of the inner shell, acceleration of the outer shell.

we present numerical simulations that include 1-d eulerian multi - group radiation - hydrodynamics , 1-d non - local - thermodynamic - equilibrium ( non - lte ) radiative transfer , and 2-d polarised radiative transfer for super - luminous interacting supernovae ( sne ) . our reference model is a inner shell with ramming into a cold outer shell ( the circumstellar - medium , or csm ) that extends from 10 to 2 cm and moves at 100 . we discuss the light curve evolution , which can not be captured


Let be the unique nonassociative finite simple moufang loop constructed over

let be a finite - dimensional vector space over a field , equipped with a quadratic form and a multiplicative operation . following , we say that is a _ composition algebra _ if is a _ nonassociative _ ring with identity element , is nondegenerate , and is satisfied for every , . the bilinear form associated with will also be denoted by . recall /that is defined by . write if , and set . the standard -dimensional real cayley algebra constructed by the _ cayley - dickson process _ ( or _ doubling _ ) is the best known nonassociative composition algebra . there is a remarkably compact way of constructing that avoids the iterative cayley - dickson process . as in , let , , , be a basis whose vectors are multiplied according to for , , . ( alternatively , see . ) the norm of a vector is given by . importantly , all the _ structural constants _ , defined by , are equal to , and therefore the construction can be imitated over any field . for of odd characteristic , let us denote the ensuing algebra by . when is even , the above construction does not yield a composition algebra . the following facts about composition algebras can be found in . every non - trivial composition algebra has dimension , or , and we speak of a _ complex _ , _ quaternion _ or _ octonion _ algebra , respectively . we say that is a _ division algebra _ if it has no zero divisors , else is called _ split_. there can be many non - isomorphic octonion algebras over a given field . exactly one of them is guaranteed to be split . moreover , when is finite , all octonion algebras over are isomorphic ( and thus split ) . let be the unique octonion algebra constructed over . all composition algebras satisfy the so - called _ moufang identities _ these identities are the essence of moufang loops , undoubtedly the most investigated variety of nonassociative loops . more precisely , a quasigroup is a _ moufang loop _ if it possesses a neutral element and satisfies one ( and hence all ) of the moufang identiti

We consider a non - trivial composition algebra over a finite field. The quaternion or octonion algebras are, and, complex. In this paper, we discuss the structure of the oblique - odyll - cayley algebra.

let be the unique nonassociative finite simple moufang loop constructed over . we prove that is the chevalley group , by extending multiplicative automorphism of into linear automorphisms of the unique split octonion algebra over . many of our auxiliary results apply in the general case . in the course of the proof we show that every element of a split octonion algebra can be written as a sum of two elements of norm one .


The crab nebula and the pulsar have been pointed several times by the bepposax satellite

it is well known since early x - ray observations that the spectral energy distribution of the crab pulsar ( psr b0531 + 21 ) is changing along with its double peak pulse profile . the intensity ratio of the second to the first peak increases from the soft x - rays up to the mev region where it reaches the highest value ( see the data archive of massaro , feroci & matt 1997 ) . the origin of this effect is not understood up to now . pulse shapes have been computed for different accelerator sites : polar caps ( sturner & dermer 1994 , daugherty & harding 1996 , miyazaki & takahara 1997 ) , outer gaps ( chiang & romani 1994 , romani & yadigaroglu 1995 ) and closed magnetosphere ( eastlund , miller & michel 1997 ) . these theoretical profiles , in some cases symmetric , do not match the energy dependence of the peak intensity ratio and can not explain the spectral changes across the pulse profile . a first phase resolved x - ray spectroscopy of the crab pulsar was performed by pravdo & serlemitsos ( 1981 ) who used the data of one day long observation of oso 8 . more recent data , with a much finer phase resolution , were presented by pravdo , angelini & harding ( 1997 , hereafter pah ) who analysed the rossixte data between 5 and 250 kev . the italian - dutch satellite bepposax observed the crab nebula and pulsar in 1996 during the science verification phase ( mineo et al . 1997 ) . from that epoch to the end of 1998 this source was pointed several times because it is used for a calibration check of the narrow field instruments ( hereafter nfi ; for a detailed description of the scientific payload of bepposax see boella et al . all these observations , when summed together , provide a high statistics data set which can be used for a very accurate phase resolved spectroscopy of the pulsed emission over an energy range wider than two orders of magnitude , from about 0.1 up to 300 kev . in this paper we present the results of an accurate spectral analysis that shows in d

We present a phase resolved x - ray spectroscopy of the crab pulsar ( psr b0531 + 21 ). The spectral energy distribution of the second to the first peak is determined by the double peak pulse profile, which is symmetric. We find that the spectra of the two pulses are different from those of the first and second peak profiles.

the crab nebula and the pulsar have been pointed several times by the bepposax satellite . we analysed all these observations , summed together , to study the main spectral properties with a good phase resolution . a new accurate estimate of the hydrogen column density in the crab direction =3.23 is given as derived from the analysis of the off - pulse emission at low energies . we studied the changes of the spectral index with the pulse phase and showed that in the interpeak region it is system


We report quantum monte carlo ( qmc ) , plane - wave density - functional theory ( dft ) , and...

one of the most important goals of _ ab initio _ computational electronic - structure theory is the development of accurate methods for describing interatomic bonding . quantum monte carlo ( qmc ) techniques are useful in this regard as they can provide a highly accurate description of electron correlation effects . although qmc methods are computationally expensive , they can be applied to systems which are large enough to model condensed matter . in this study we have considered solid neon , in which the bonding arises from the competition between short - range repulsion and the van der waals attraction between the atoms . high - quality experimental measurements of the equation of state ( eos ) exist , which can be used as reference data . furthermore , various neon pair potentials have been developed using experimental and theoretical data , which can also be used for comparison purposes . solid neon is therefore an ideal system in which to test the descriptions of van der waals bonding and short - range repulsion offered by various theoretical methods . we have calculated theoretical eos s for crystalline neon using the qmc and density - functional theory ( dft ) _ ab initio _ electronic - structure methods as well as various interatomic pair potentials . standard dft methods do not describe van der waals bonding accurately , but they might be expected to work quite well at high densities , where the short - range repulsion dominates . the high - pressure properties of neon are of some experimental interest , because neon is often used as a pressure - conducting medium in diamond - anvil - cell experiments. we have therefore extended the range of our qmc eos for neon to very high pressures ( about 400 gpa ) . the zero - point energy ( zpe ) of the lattice - vibration modes makes a small but important contribution to the total energy of solid neon . we have therefore studied the lattice dynamics of solid neon within the quasiharmonic - phonon approximation and w

We have calculated the equation of state ( eos ) for solid neon using the qmc and density - functional theory ( dft ) _ ab initio _ electronic - structure methods. The eeo is a measure of the energy of the lattice - vibration modes in the quasiharmonic - phonon approximation. We also calculate the zero - point energy of lattics in the w - wave approximilation.

we report quantum monte carlo ( qmc ) , plane - wave density - functional theory ( dft ) , and interatomic pair - potential calculations of the zero - temperature equation of state ( eos ) of solid neon . we find that the dft eos depends strongly on the choice of exchange - correlation functional , whereas the qmc eos is extremely close to both the experimental eos and the eos obtained using the best semiempirical pair potential in the literature . this suggests that qmc is able to give an accur


The two - point angular correlation function is a standard analysis tool used to study angular...

the two - point angular correlation function ( tpacf ) , denoted as , is the frequency distribution of angular separations between celestial objects in the interval . the tpacf is normalized to zero when integrated over all separation angles . a positive value of indicates that objects are often found with these separations , zero indicates no correlation , and a negative value indicates anti - correlation . the tpacf was developed for studying galaxy clustering , but has since been applied to gamma - ray burst angular distributions . it has been used extensively in this field , primarily for studying repetition and clustering . the technique has been found to be superior in repetition testing to nearest neighbor analysis , although it has not been compared directly to detailed multipole analysis . the tpacf has also been used in burst distance scale studies as an m31 test . angular sky exposure is important to the modeling of burst angular distributions . the gamma - ray burst angular distribution detected by batse is highly isotropic . however , batse s sky exposure is slightly anisotropic , and has been specified via a sky exposure map . this anisotropy is due primarily to earth blockage . it causes a small systematic deviation from isotropy that could show up in the gamma - ray burst angular distribution . in this study , we identify the form of the tpacf taken by batse sky exposure in the case of a large ( infinite ) number of detected bursts . we also search the batse 3b and 4b catalogs to determine to what extent this effect is present . two methods have been used to calculate the tpacf while including sky exposure effects : ( a ) monte carlo simulations of random burst catalogs are performed using sky exposure as a mask , and ( b ) summation of isotropic sampled points with the declination - dependent sky exposure are performed . the first technique requires simulation of gamma - ray burst catalogs , using an assumed isotropic gamma - ray burst angular distr

We present a method for calculating the two - point angular correlation function ( tpacf ) in the case of large ( infinite ) detected bursts. The method is based on monte carlo simulations of random burstic catalogs with declination - dependent sky exposure. We find that the tPACF is taken by batse sky exposure in the cases of a large number of detected burstings, and that the effect is not significant.

the two - point angular correlation function is a standard analysis tool used to study angular anisotropies . since batse s sky exposure ( the angular sampling of gamma - ray bursts ) is anisotropic , the tpacf should at some point identify anisotropies in batse burst catalogs due to sky exposure . the effects of batse sky exposure are thus explored here for batse 3b and 4b catalogs . sky - exposure effects are found to be small .


The chaperonin groel - groes , a machine which helps some proteins to fold , cycles through a...

* rationale for using the self - organized polymer ( sop ) model for allosteric transitions : * several studies have shown that the gross features of protein folding , mechanical unfolding of proteins and rna and the complicated global motions of large systems can be captured using native structure - based models . more recently , such native structure - based methods have also been used to probe transitions between two given end - point structures and to ascertain the nature of robust modes that mediate the allosteric transitions . in order to realistically simulate transitions between distinct allosteric states , it is necessary to use simple coarse - grained models that can be used to capture , at least qualitatively , the inherent dynamics connecting two or more states . although simple elastic network models have given insights into the nature of low frequency dynamics of a number of systems , the inherent linearity of the model limits their scope when dealing with potential non - linear motions that must be involved in the allosteric transitions . we have recently introduced a novel class of versatile structure - based models that incorporates the fundamental polymeric aspects of proteins and rna . the sop model , which is easily adopted for use in very large systems , has already proven to be successful in obtaining a number of totally unanticipated results for forced - unfolding and force - quench refolding of rna and proteins . building on the successful application to single molecule force spectroscopy of biomolecules we used a variant of the sop model to probe the complex allosteric transitions in a prototypical biological nanomachine , namely , the _ e. coli . _ chaperonin groel . structures of groel ( , , and ) , that are populated in the reaction cycle , have been determined ( see fig . s1 for a side view ) . given the two allosteric states ( say and of groel ) we induce transitions between the two states by switching the energy function representing o

We present a novel class of versatile structure - based models that incorporates the fundamental polymeric aspects of proteins and rna. These models are used to probe the complex allosteric transitions in a prototypical biological nanomachine, namely _ e. Coli. _ chaperonin groel. The model is based on a self - organized polymer ( sop ) model that includes the basic polymeric features of proteins, and a non - linear dynamical function that can be used to simulate the.

the chaperonin groel - groes , a machine which helps some proteins to fold , cycles through a number of allosteric states , the state , with high affinity for substrate proteins ( sps ) , the atp - bound state , and the ( ) complex . structures are known for each of these states . here , we use a self - organized polymer ( sop ) model for the groel allosteric states and a general structure - based technique to simulate the dynamics of allosteric transitions in two subunits of groel and the hepta


The general features of baryon form factors calculated with point form kinematics are derived

the calculation of hadronic form factors within the framework of poincar covariant quantum mechanics involves the following two separate ingredients : ( 1 ) bound - state wave functions , which represent vectors in the representation space of the little group of the poincar group , and ( 2 ) current operators that are covariant under a kinematic subgroup . covariant conserved currents are generated from these ingredients by the dynamics , while the choice of the kinematic subgroup specifies the form of kinematics . spectator currents , by definition , commute with quark spectator momenta , the definition of which depends on the choice of a form of kinematics . with instant and front form kinematics spectator currents provide an impulse approximation , in which the spatial structure of the bound - state wave function determines the quantitative features of the form factors . when the spatial extent of the bound - state wave function is scaled unitarily to zero both instant and front form kinematics yield form factors , which are independent of momentum transfer . point - form kinematics employs the full lorentz group as the kinematic subgroup . in this case the lorentz covariant spectator currents probe the velocity structure specified by the bound - state wave function . when the extent of the wave function is scaled unitarily to zero , point - form kinematics yields a nontrivial scaling limit for the form factors , which depends on the shape of the wave function . at high values of momentum transfer the scaled form factors decrease with an inverse power of the momentum transfer . the power is determined by the current operator and is independent of the shape of the wave function . a derivation of these features is presented in sections 2 and 3 below . the purpose here is to illuminate the unfamiliar qualitative features of relativistic quantum mechanics with point form kinematics . relations to quantum field theory are beyond the scope of this article . recently po

We present a new method for the calculation of hadronic form factors in the framework of poincar covariant quantum mechanics. The method is based on the kinematic subgroup, which is a kinetic subgroup that is covarient under a quark spectator momenta. It is shown that the lorentz currents are covariants under the full lorENTz group. This technique allows to calculate the form factors with an impulse approximation.

the general features of baryon form factors calculated with point form kinematics are derived . with point form kinematics and spectator currents hadronic form factors are functions of and , over a range of values , are insensitive to unitary scale transformations of the model wave functions when the extent of the wave function is small compared to the scale defined by the constituent mass , . the form factors are sensitive to the shape of such compact wave functions . simple 3-quark proton wave


We present an efficient method for the calculation of free energy landscapes

the characteristics and the behaviour of physical systems can be understood and predicted by the investigation of the underlying free energy landscape . the knowledge of this often complex surface allows one to determine reaction pathways for chemical reactions as well as stable configurations for proteins and glass - forming systems . a successful tool for these studies are computer simulations which help to explore the characteristics of the system in detail . naturally , during the last years a lot of effort has been spent to develop novel efficient and time - saving methods . + specifically in protein sciences , the free energy approach is promising for the investigation of unknown folding mechanisms . to achieve a proper description of the dynamical behaviour , the trajectories may be projected onto a set of well chosen collective variables which allow to define an effective energy landscape . these variables can be interpreted as effective reaction coordinates spanning the phase space respectively the free energy space of the system . well known collective variables are the number of native contacts , dihedral angles and the essential eigenvectors or principal components of the protein . thus a set of well suited reaction coordinates offers the opportunity to describe the folding or unfolding of a protein adequately without too much loss of information . + however , it has to be mentioned that in some cases suitable collective variables are hard to determine . the investigation of the underlying dynamics of the system can then be performed by computational methods like discrete path sampling and transition path sampling to overcome this problem . these techniques represent computational algorithms which are not dependent on the usage of collective variables . + experiments and computer simulations have shown that naturally occuring proteins often have free energy landscapes with global funneling properties . nevertheless local minima can occur which represent

We present a computational method for the investigation of the free energy landscape of proteins in the presence of a set of well chosen collective variables. This technique is used to describe the dynamical behaviour of the system and to study the dynamics of the systems. It is shown that the free energies are derived from the interaction between the two components of the protein.

we present an efficient method for the calculation of free energy landscapes . our approach involves a history dependent bias potential which is evaluated on a grid . the corresponding free energy landscape is constructed via a histogram reweighting procedure a posteriori . due to the presence of the bias potential , it can be also used to accelerate rare events . in addition , the calculated free energy landscape is not restricted to the actual choice of collective variables and can in principl


I give an introduction to the problem of isospin violation and add some comments to the various...

isospin symmetry was introduced in the thirties by heisenberg in his studies of the atomic nucleus . since then , many particles have been found to appear in iso multiplets , like the nucleons , the pions , the delta isobars , a.s.o . with the advent of qcd , a deeper understanding of isospin symmetry has emerged . in the limit of equal up and down current quark masses and in the absence of electroweak interactions , isospin is an exact symmetry of qcd . the intra multiplet mass splittings allow to quantify the breaking of this symmetry , which is caused by different mechanisms ( for a detailed review , see ref. ) . first , the light quark masses are everything but equal ( still , their absolute masses are much smaller than any other qcd scale and thus this breaking can be treated as a perturbation ) . second , the light quarks have different charges and thus react differently to the electromagnetic ( em ) interactions . the em effects are also small since they are proportional to the fine structure constant . in the case of the pions , the mass splitting is almost entirely of em origin . this can be traced back to the absence of d like couplings in su(2 ) , thus promoting the quark mass difference to a second order effect . for the nucleons , matters are different , strong and em effects are of similar size but different signs . the fact that the neutron is heavier than the proton leads to the conclusion that , consistent with the analysis of the kaon masses . since we know that isospin is broken - so why bother ? first , the picture that has emerged from the hadron masses can not be considered complete , there is still on going discussion about the size of the violation of dashen s theorem , the possibility of a vanishing up quark mass to solve the strong cp problem and `` strange '' results from lattice gauge theory . also , the analysis of the quark mass dependence of the baryon masses remains to be improved ( for a classic , see ref. and a recent study , see re

We present a new analysis of the quark mass dependence of the baryons in the presence of a vanishing up quark masses. The results are presented in terms of the qcd and the kaon masses, as well as the em effects.

i give an introduction to the problem of isospin violation and add some comments to the various topics addressed in the working group .


We have used observations taken under the _ fuse _ s405/s505 channel realignment program to explore...

the diffuse background from the ultraviolet ( uv ) to the infrared ( ir ) is an important tracer of the interstellar dust and most of our knowledge of the large scale distribution of the dust has come from missions such as _ iras _ and _ cobe _ ( see , for example , * ? ? ? scattering in the uv is complementary to the ir emission and the combination of the two can lead to a unique determination of the interstellar dust parameters . unfortunately , there have been few observations of the diffuse uv radiation field and those have been , to a large degree , controversial as indicated by the conflicting reviews by and . in the far - ultraviolet ( fuv - below 1200 ) band , which we address in this paper , the only significant body of observations comes from . they used the ultraviolet spectrographs ( uvs ) aboard the two _ voyager _ spacecraft finding that the fuv sky was very patchy with both dark and bright regions . in this work , we have used serendipitous observations from the _ far ultraviolet spectrographic explorer _ ( _ fuse _ ) under the s405/505 program to further probe the diffuse fuv sky . although _ fuse _ can not match the sensitivity of the _ voyager _ uvs for observations of diffuse sources because of its relatively small field of view , we have , nevertheless , found many locations that do indeed have a strong enough signal to be detected by _ fuse_. we concentrate here on presenting the overall results from our study and will discuss individual locations in detail in subsequent papers . the _ fuse _ spacecraft and mission has been described by and by . the instrument consists of four coaligned optical channels , two of which are coated with silicon carbide ( sic ) and two with lithium fluoride ( lif ) over aluminum providing coverage over the spectral range from 905 1187 . observations may be made through any of 3 apertures : the lwrs ( ) aperture ; the mdrs ( ) aperture ; and the hirs ( ) aperture . in principle , extended radiation will be visible in

We present a new study of the far ultraviolet ( fuv - below 1200 ) spectrum from the _ far ultraviolet spectrographic explorer _ ( _ fuse _ ) spacecraft under the s405/505 program. The results are presented in terms of the sensitivity of the two _ voyager _ spacecraft to the uv and the spectral range of the diffuse background.

we have used observations taken under the _ fuse _ s405/s505 channel realignment program to explore the diffuse fuv ( 1000 - 1200 ) radiation field . of the 71 independent locations in that program , we have observed a diffuse signal in 32 , ranging in brightness from 1600 photons sr s to a maximum of photons sr s in orion . the _ fuse _ data confirm that the diffuse fuv sky is patchy with regions of intense emission , usually near bright stars , but also with dark regions , even at low galactic


A systematic study of the temperature dependence of the shapes and pairing gaps of some isotopes in...

heating can have a profound effect on nuclear shapes , causing a variety of shape transitions . experimentally , such responses to the thermal excitations have been studied from the shapes of the giant dipole resonances(gdr ) built on excited states . theoretically , they have been studied earlier in a finite temperature non - relativistic microscopic hartree - fock and hartree - fock bogoliubov ( hfb ) framework with a pairing plus quadrupole ( p+q ) interaction . for the nuclei studied , it has been found that while the superfluid nuclear phase has transition to the normal phase typically at t mev , the deformed shapes have transition to the spherical ones at a higher temperature , mostly between t to 1.8 mev for rare - earth nuclei . these calculations , however , have some limitations ; they employ a simplistic model hamiltonian in a limited model space , an inert core is assumed , moreover , the coulomb interaction has not been taken into account realistically . the understanding of the universal pattern of the mean field shape evolution with temperature has also been tried in a macroscopic approach commonly referred to as the landau theory of phase transition . a quantitative estimate of the persistence of the ground state deformation with temperature is however seen to be missing in some cases . recently , we have undertaken a study of the thermal evolution of nuclear properties , particularly the phase transition in the nuclear shape and the superfluidity in the relativistic mean field ( rmf ) theory . the pairing effects have been included in the bcs approximation . the rmf theory has proved to be an extremely powerful tool in explaining the gross properties of nuclei over the entire periodic table . in contrast to the non - relativistic models , this theory employs a single set of parameters to explain all these properties . moreover , in such calculations , the model space used is sufficiently large and all the nucleons are treated on equal footing . the

We study the thermal evolution of nuclear shapes in a finite temperature non - relativistic microscopic hartree - fock and hartreen - focalk bogoliubov ( hfb ) framework with a pairing plus quadrupole interaction. The model space is sufficiently large and all the nucleons are treated on equal footing. We find that the phase transition in the nuclear shape and the superfluidity in the relativistic mean field theory are consistent with the observed behavior of the ground state deformation.

a systematic study of the temperature dependence of the shapes and pairing gaps of some isotopes in the rare - earth region is made in the relativistic hartree - bcs theory . thermal response to these nuclei is always found to lead to a phase transition from the superfluid to the normal phase at a temperature mev and a shape transition from prolate to spherical shapes at mev . these shape transition temperatures are appreciably higher than the corresponding ones calculated in the non - relativis


We study the large reduced model of -dimensional yang - mills theory with special attention to the...

recently the large reduced models have been revived in the context of nonperturbative formulations of string theory . the iib matrix model , which is the reduced model of ten - dimensional supersymmetric yang - mills theory , is expected to be a nonperturbative formulation of superstring theory . in this article , we study the large reduced model of yang - mills theory , which we refer to as the `` bosonic model '' in what follows . it is nothing but the bosonic part of the iib matrix model . the action is given by ^ 2),\ ] ] where are traceless hermitian matrices . we investigate the dynamical aspects of the model related to the eigenvalues of , which correspond to the space - time coordinates in the iib matrix model . one of the most important quantities is the extent of the space time defined by . we also define a quantity which represents the uncertainty of the space - time coordinates and an order parameter for the ssb of the lorentz invariance . we determine these values for the bosonic model by monte carlo simulation . for 2 with sufficiently large , the integral of is convergent without any cutoff because of an attractive potential between the eigenvalues of . this enables us to absorb by rescaling , which means that is nothing but a scale parameter . the large behavior of is , therefore , parametrized as , since is proportional to on dimensional grounds . in the iib matrix model , plays an important role to deduce the space - time dimension , which is to be determined dynamically from the eigenvalue distibution of . we determine for the bosonic model . the observables we measure are the following . where $ ] . here , we have normalized the above quantities so that they are dimensionless , and hence they are independent of . we note that can be obtained analytically as . in the fig . [ fig : d4ulog ] , we show our results of monte carlo simulation for 4 with 4 , 8 , 16 , 32 , 64 , 128 , 256 . one can see that are constant for . in fig . [ fig : d10ulog ] , w

We study the large reduced model of yang - mills theory by monte carlo simulation. The eigenvalues of are given by, which correspond to the space time coordinates in the iib matrix model. We determine these values for the bosonic model by monteinstein simulation, and show that they are dimensionless.

we study the large reduced model of -dimensional yang - mills theory with special attention to the dynamical aspects related to the eigenvalues of the matrices , which correspond to the space - time coordinates in the iib matrix model . we define a quantity which represents the uncertainty of the space - time coordinates and show that it is of the same order as the extent of the space time , which means that the classical space - time picture is maximally broken . the absence of the ssb of the l


Adiabatic invariants foliate phase space , and impart a macro - scale hierarchy by separating...

the process of self - organization of a structure may appear to be an antithesis of the maximum entropy _ ansatz _ , yet various nonlinear systems display what may be viewed as the simultaneous existence of order and disorder . this co - existence begins to make sense if the self - organization processes and the entropy principle were to manifest on different scales ; disorder can still develop at a microscopic scale while an ordered structure emerges on some appropriate macroscopic scale . writing a theory of self - organization , then , will be an exercise in delineating and understanding the characteristic _ scale hierarchy _ of the physical system . a biological body is a typical example in which an evident hierarchical structure is preprogrammed enabling effective consumption of energy and materials as well as emission of entropy and waste . a physical macro - system a collective system of simple elements ( a gravitational system , a plasma , etc.) is anchored on a different framework . an automatic emergence of scale hierarchy is not programmed ; yet the controlling nonlinear dynamics can mimic a fundamental process of _ creation_. in this paper we develop a new framework to expose the creation process in action . the ordering principle is generally epitomized in a constraint a possible conservation law that , by restricting the class of motions available to the system , limits its ability to degenerate into general disorder . the _ effective _ phase space ( ensemble ) limited by such a constraint is the relevant _ macro - hierarchy _ on which nontrivial structures emerge . by invoking the geometrical notion of hamiltonian mechanics , we formulate a macro - hierarchy as a _ casimir leaf _ of foliated phase space , i.e. , the level - set of a _ _ casimir invariant__ . the connection between the notion of scale hierarchy and a casimir invariant ( an _ a priori _ geometrical structure of the phase space ) is built by identifying a casimir invariant as an _ adiaba

We study the emergence of scale hierarchy in a nontrivial macro - system. We show that the level - set of a casimir invariant is an _ adiaba _ of foliated phase space, i. E., the level set of an adiabata.

adiabatic invariants foliate phase space , and impart a macro - scale hierarchy by separating microscopic variables . on a macroscopic leaf , long - scale ordered structures are created while maximizing entropy . a plasma confined in a magnetosphere is invoked to unveil the organizing principle in the vicinity of a magnetic dipole , the plasma self - organizes to a state with a steep density gradient . the resulting nontrivial structure has maximum entropy in an appropriate , constrained phase s


We present a new model for the x - ray properties of the intracluster medium that explicitly...

one of the fundamental puzzles of the x - ray universe concerns the relation between the x - ray luminosity and gas temperature of clusters of galaxies . a simple scaling analysis ( kaiser 1986 ) suggests that the temperature and luminosity should be related by . temperatures have now been measured for the diffuse x - ray emission for an extensive range of groups and clusters ( david et al . 1993 ; ponman et al . 1996 ; allen & fabian 1998 ; markevitch 1998 ; mulchaey & zabludoff 1998 ; arnaud & evrard 1999 ; helsdon & ponman 2000 ) . in contrast to the theoretical prediction , the observations show a much shallower trend , approximately . a closely related problem is the evolution of the cluster x - ray luminosity function . kaiser s ( 1986 ) analysis of the evolution of the x - ray properties of clusters suggested that dense , x - ray luminous associations of galaxies should be more numerous in the intermediate and high redshift universe . this possibility was soon ruled out by the initial results of the emss cluster survey ( gioia et al . 1990 ; henry et al . 1992 ) , which quickly established that clusters in the distant universe have a comparable space density to those of the local universe . this has been confirmed in more recent rosat surveys ( eg . , jones et al . 2000 ) . initially , one might have hoped that including radiative cooling of the gas ( omitted from kaiser s analysis ) might resolve this discrepancy . unfortunately , it is extremely difficult to obtain numerically convergent results from simulations once gas cooling is included . the difficulty is inherent to the problem . because the universe is dense at early times , cooling is initially very efficient . this leads to an unrealistically large fraction of the halo baryon content cooling at high redshifts to form very small galaxies . as white & rees ( 1978 ) , white & frenk ( 1991 ) , cole ( 1991 ) , suginohara & ostriker ( 1998 ) and pearce et al . ( 2000 ) amongst others have shown , some fo

We present a numerical simulation of the evolution of clusters in the x - ray universe with a gas cooling function. The results are presented as a result of a simple scaling analysis of the cluster x.

we present a new model for the x - ray properties of the intracluster medium that explicitly includes heating of the gas by the energy released during the evolution of cluster galaxies . we calculate the evolution of clusters by combining the semi - analytic model of galaxy formation of cole et al . with a simple model for the radial profile of the intracluster gas . we focus on the cluster x - ray luminosity function and on the relation between x - ray temperature and luminosity ( the t - l rel


We produce ultracold dense trapped samples of rbcs molecules in their rovibrational ground state ,...

in contrast to the case of homonuclear alkali dimers , whose excited states have a resonant dipole - dipole van der waals interaction , in heteronuclear dimers the excited and ground states both have van der waals interactions , where is the internuclear distance . this makes it more likely that a suitable excited state exists that simultaneously has good franck - condon overlap with the feshbach and ground states , making four - photon transfer schemes unnecessary . we initially chose laser wavelengths to address states of the strongly coupled system but found the ground - state transfer efficiency to be extremely poor , even though the predicted and measured laser couplings were strong . a transition to the , state worked much better and the results using this intermediate state are presented in this work . we attribute the low transfer efficiency to the fact that zeeman and hyperfine splittings in states are much smaller than our one - photon stirap linewidth ( , where and are the peak pump and dump rabi frequencies and is the stirap - pulse overlap time ) . in this case , multiple intermediate states are addressed simultaneously , which causes loss . while this can often be remedied by detuning far from all intermediate states , large rabi frequencies are often required . in stirap of cs , where the magnetic field is low enough that the total angular momentum is nearly a good quantum number , a fixed ratio between the dump and pump rabi frequencies of the multiple intermediate states exists and the losses are ameliorated . decomposing the feshbach state into its hund s case ( a ) nuclear - spin decoupled basis states reveals it to be a superposition of , 2 and 3 with only the component coupling to due to the selection rules and . here is the total molecular angular momentum excluding nuclear spin and is the projection of the total electron spin onto the internuclear axis . the intermediate state is actually not expected to allow coupling to the ground state due

We present a new method for decomposing the feshbach state into its hund s case ( a ) nuclear - spin decoupled basis states. This is a simple and efficient way to address multiple intermediate states in the strong coupled system. The two - photon transfer scheme is used to solve the problem of a single -photon coupling to the ground state.

we produce ultracold dense trapped samples of rbcs molecules in their rovibrational ground state , with full nuclear hyperfine state control , by stimulated raman adiabatic passage ( stirap ) with efficiencies of . we observe the onset of hyperfine - changing collisions when the magnetic field is ramped so that the molecules are no longer in the hyperfine ground state . a strong quadratic shift of the transition frequencies as a function of applied electric field shows the strongly dipolar chara


We numerically study the spin polarization of the fractional quantum hall state at filling factor

the most striking feature of the laughlin state describing the fractional quantum hall ( fqh ) effect at filling fraction is the appearance of quasi - particle excitations with fractional charge and fractional statistics . the idea of particles that do not behave as fermions or bosons , something that can occur in two spatial dimensions , is still a reason for wonder , and a motivation for seeking phases of matter with exotic excitations in low dimensions . the laughlin wavefunction served as a foundation to explain all the odd - denominator incompressible fqh states . however , it does not include the possibility of an even - denominator state . therefore , the quantum hall plateau observed at poses a special challenge . while various theories have been proposed for this state , much of the excitement has been generated by the possibility that it is a non - abelian topological state . in ground - breaking work , moore and read proposed the pfaffian wavefunction as a description of electrons in an incompressible half - filled landau level . conjectured that this ground - state may be realized at . recently , it was noted that there is another possible state , the so - called anti - pfaffian , which would be degenerate in energy with the pfaffian state in the absence of landau level mixing . since excitations above both the pfaffian and anti - pfaffian ground - states are non - abelian anyons , it has been suggested that the plateau can be a platform for topological quantum computation . therefore , determining the nature of the state has gained additional urgency , beyond fqh physics . in order to set a context for the importance of our theoretical numerical study of the 5/2 spin polarization question , we first briefly describe the highly confusing experimental status of the subject . immediately following the original discovery of the 5/2 fqhe , eisenstein et al . found that the application of a modest in - plane magnetic field destroys the fqhe . this was interpr

We present a numerical study of the quantum hall plateau at filling fraction. We show that the pfaffian wavefunction is a description of electrons in an incompressible half - filled landau level. The polarization of the state is determined by the application of a modest in - plane magnetic field.

we numerically study the spin polarization of the fractional quantum hall state at filling factor . by using both exact diagonalization and the density matrix renormalization group ( dmrg ) methods on the sphere , we are able to analyze more values of partial spin polarization ( in addition to fully - polarized and unpolarized ) than any previous studies . we find that for the coulomb interaction the exact finite - system ground - state is fully polarized , for shifts corresponding to both the m


We define a bounded cohomology class , called the _ median class _ , in the second bounded...

the goal of this paper is to define a cohomological invariant of some non - positively curved metric spaces for a non - elementary action of a group and to use this invariant to establish rigidity phenomena . the paradigm is that bounded cohomology with non - trivial coefficients is the appropriate framework to study negative curvature . the first instance of this fact is the gromov sela cocycle on the real hyperbolic -space ( in fact , on any simply connected space with pinched negative curvature ) with values into the differential one - forms on ( see and ( * ? ? ? * ) ) . more recently , the same philosophy has been promoted by monod , monod shalom and mineyev monod shalom . they prove that a non - elementary isometric action on a negatively curved space ( belonging to a very rich class ) yields the non - vanishing of second bounded cohomology with appropriately defined coefficients of a geometric nature . such negatively curved spaces include proper cat(-1 ) spaces , gromov hyperbolic graphs of bounded valency , gromov hyperbolic proper cocompact geodesic metric spaces , or simplicial trees . on the other hand , if is a simple lie group with rank at least two and is any unitary representation with no invariant vectors , then , , thus showing that in non - positive curvature the situation can not be expected to be completely analogous . in this paper we move away from the negative curvature case and look at actions on cat(0 ) cube complexes . cat(0 ) cube complexes are simply connected combinatorial objects introduced by gromov in . they have been used is several important contexts , such as moussong s characterization of word hyperbolic coxeter groups in terms of their natural presentation , . a prominent use of cat(0 ) cube complexes was made by sageev in his thesis , : generalizing stalling s theorem on the equivalence between splittings of groups and actions on trees , , he proved an equivalence between the existence of an action of a group on a cat(0 ) cube

We study the rigidity phenomena of a non - elementary isometric action on a cat(0 ) cube complexes. We show that the non - trivial cohomology of bounded cohomological spaces with non _ trivial coefficients is not completely analogous to the non.

we define a bounded cohomology class , called the _ median class _ , in the second bounded cohomology with appropriate coefficients of the automorphism group of a finite dimensional cat(0 ) cube complex . the median class of behaves naturally with respect to taking products and appropriate subcomplexes and defines in turn the _ median class of an action _ by automorphisms of . we show that the median class of a non - elementary action by automorphisms does not vanish and we show to which extent


We study the stability of a bose - fermi system loaded into an array of coupled one - dimensional (...

the quest for lower temperatures in ultracold gases has lead to the development of many ingenious techniques to cool several atomic and molecular species . in particular , the explosion of activity concerning ultracold fermi gases has become possible largely owing to the success of sympathetic cooling , which allows to efficiently cool fermions by mixing them with bosons . at the same time , this procedure has stimulated the investigation , both experimental and theoretical , of bose - fermi mixtures . here , the possibility of tuning the inter - species interaction strength using feshbach resonances , has led to the exploration of many interesting phenomena such as collapse and phase separation , as well as boson - mediated cooper pairing . furthermore , feshbach resonances can also be used to generate heteronuclear molecules , which can exhibit large electric dipole moments . this opens the interesting possibility of studying dipole - dipole interactions in quantum degenerate gases . meanwhile , the advent of optical - lattice confinement has turned ultracold atomic gases into unique environments where to simulate and understand strongly correlated phenomena relevant to condensed matter systems . this has been made it possible , for example , by confining the atomic clouds in reduced dimensions , such as a one dimensional ( 1d ) array of two - dimensional ( 2d ) planes or a 2d array of 1d tubes . whereas the former has enabled the study of interesting phenomena occurring in two - dimensions , the latter has provided us with an amazingly tunable tool to explore the physics of interacting 1d quantum systems , of which it is much more difficult to find faithful realizations in a more conventional condensed matter context . array of one - dimensional ( 1d ) tubes of length . the fermions are light enough to hop between the tubes whereas bosons , which are assumed to be much heavier , are confined in the 1d tubes . the bosonic and fermionic wannier functions ( and , re

We study the physics of a one - dimensional array of two -dimensional ( 1d ) tubes in a single - dimension environment. We find that the bosonic and fermionic wannier functions ( and, re ) are confined in the 1d tubes, while the bosons are assumed to be much heavier. This allows us to study the dynamics of interacting 1d quantum systems.

we study the stability of a bose - fermi system loaded into an array of coupled one - dimensional ( 1d ) `` tubes '' , where bosons and fermions experience different dimensions : bosons are heavy and strongly localized in the 1d tubes , whereas fermions are light and can hop between the tubes . using the yb-li system as a reference , we obtain the equilibrium phase diagram . we find that , for both attractive and repulsive interspecies interaction , the exact treatment of 1d bosons via the bethe


If there is cpt violation , the nature of entanglement for neutral meson pairs produced in meson...

the operator where is the charge conjugation operator , is the parity operator and the time reversal operator is a symmetry of the s matrix for local , unitary and lorentz invariant field theories . if one of these assumptions is not valid then may cease to be a symmetry or be ill defined . we shall consider the situation where an otherwise relativistic theory is not unitary . the lack of unitarity at a fundamental level will be postulated as due to space - time foam . in the decoherence scenario the s - matrix of the effective low - energy field theory would then have to be replaced by a linear non - factorisable superscattering operator relating initial and final - state density matrices if this is correct then the usual formulation of quantum mechanics has to be modified ; from the theory of open systems ( see e.g. , ) we know that , on tracing over the environmental degrees of freedom , a system can be described by a master equation +  \ ] ] where is a liovillian superoperator . the foam can be regarded as an environment and so the open systems point of view is also a natural one . it should be pointed out that this suggestion may be invalid if there is _ holography _ in quantum gravity , such that any information on quantum numbers of matter , that at first sight appears to be lost into the horizon , is somehow reflected back from the horizon surface , thereby maintaining quantum coherence . this may happen , for instance , in some highly supersymmetric effective theories of strings , which however do not represent realistic low - energy theories of quantum gravity . supersymmetry breaking complicates the issue , thus spoiling complete holography . recently , s. hawking , inspired by the above recent ideas in string theory , has also argued against the loss of coherence in a _ euclidean _ quantum theory of gravity . in such a model , summation over trivial and non - trivial ( black - hole ) space - time topologies in the path over histories makes an asymptotic

We consider the _ euclidean _ quantum theory of gravity with a non - trivial ( black - hole ) space - time topology. In this model, the path over histories is a _ black _ hole, which is derived from the s - matrix of the effective low - energy field theory. The corresponding s matrix is based on a linear non - factorisable superscattering operator, and the resulting s matrix is compared to the ev.

if there is cpt violation , the nature of entanglement for neutral meson pairs produced in meson factories may , on general grounds , be affected . the new form of entanglement is the omega effect . gravitational decoherence , due to space - time foam , may be one route for deviations from cpt invariance . two models of space - time foam are considered . one , based on non - critical string theory , is able to produce the new correlations in a natural way . the other , based on the paradigm of t


Dynamical 2 + 1 flavour lattice qcd is used to calculate the splittings between the masses of...

hadrons containing a single bottom quark have received much attention recently . over the last decade , the bottom meson sector has been investigated in great detail at the factories ( belle and babar ) and using the tevatron at fermilab . with the recent d measurement of the baryon , we are rapidly approaching a complete picture of the ground - state bottom baryon sector as well . the start up of the large hadron collider ( lhc ) will dramatically increase our knowledge of physics ; both the dedicated physics experiment , lhcb , and the general purpose atlas and cms experiments expect to observe unprecedented numbers of pairs , many of which will hadronise to bottom mesons and baryons . in the bottom meson sector , many important observations have been made in the last decade , dramatically refining our knowledge of flavour physics . the ckm mechanism of the standard model currently provides a good description of current flavour - changing measurements of and mesons , bringing us into the precision era of flavour physics . the various lhc experiments aim to investigate the decays of bottom baryons with enough precision to further test the standard model . in particular , the fact that bottom baryon polarisation can be measured may uncover new right - handed couplings . to search for physics beyond the standard model in these systems , it is necessary to have accurate predictions from the standard model . typically , this requires non - perturbative evaluations of matrix elements from lattice qcd and thus an understanding of bottom hadrons in lattice qcd . the simplest properties of the bottom hadrons are their masses . before more complicated bottom observables can be predicted with any rigour , it is necessary to have reliable lattice calculations of the masses and mass splittings . there are many lattice studies of the mass of the mesons in the literature but fewer of the bottom baryons and , only recently , the first unquenched bottom baryon calculations have ap

We present a new study of the bottom meson sector in the large hadron collider ( lhc ). The results are presented in terms of the mass and splittings of the mesons, as well as the masses and splitting of the top quarks. We also discuss the implications for the future of the lHc experiments.

dynamical 2 + 1 flavour lattice qcd is used to calculate the splittings between the masses of mesons and baryons containing a single static heavy quark and domain - wall light and strange quarks . our calculations are based on the dynamical domain - wall gauge field configurations generated by the rbc and ukqcd collaborations at a spatial volume of ( 2.7 fm) and a range of quark masses with a lightest value corresponding to a ( partially - quenched ) pion mass of mev . when extrapolated to the p


In this work , we explore the flavour changing decays in a general supersymmetric scenario

since the discovery of a scalar boson with mass gev , at the lhc in 2012 , the standard model ( sm ) picture may have been completed . indeed , if this scalar particle corresponds to the sm higgs boson , the sm could be the correct description of nature up to scales close to the planck mass . so far , all the experimental evidence seems to be pointing in the direction of confirming that it is really the missing piece of the sm puzzle . nevertheless the exploration of features of this particle is just beginning and further studies are needed to confirm its identity . from now on , our efforts to probe the sm and to search for physics beyond it may follow two complementary paths : i ) push the energy frontier in the search for new particles and interactions and ii ) increase the precision on the couplings of the first ( so far ) fundamental scalar ever discovered . indirect searches , which would include the latter path , searches of rare processes or higher order corrections to low energy couplings , have been very successful in the past and have led to the discovery of new particles such as the third generation quarks . they have also been instrumental in exploring the scale of new physics beyond the collider reach . in the case of the higgs boson , the study of its couplings can be the way to go . scrutinizing non - standard higgs couplings is a way to test the presence of additional scalar bosons even when their direct production is closed . in the models beyond the sm in which there exists more than one higgs doublet , as in a two higgs doublet model ( 2hdm) or the mssm , the couplings of the candidate for the discovered scalar boson may not be flavour diagonal and thus it can have flavour changing decays . furthermore , these flavour changing couplings are dimensionless and therefore the effects of additional heavy particles may not decouple even when the masses of such particles are taken to infinity , providing a unique opportunity to find an assuring indirect

We investigate the couplings of a scalar boson with mass gev in the standard model ( sm ) picture. We find that the couplements of the candidate for the discovered s Scalar bosons are flavour diagonal and thus they can have flavour changing decays. Furthermore, these flavour changing coupling - changing decay is dimensionless and therefore the effects of additional heavy particles may not decouple even when the masses of such particles are taken to infinity.

in this work , we explore the flavour changing decays in a general supersymmetric scenario . in these models , the flavour changing decays arise at loop - level but , originating from a dimension - four operator , do not decouple and may provide a first sign of new physics for heavy masses beyond collider reach . in the framework of the minimal supersymmetric extension of the standard model ( mssm ) , we find that the largest branching ratio of the lightest higgs ( ) is after imposing present ex


We extend the gross - perry - yaffe approach of hot flat space instability to minkowski space

the issue of stability with respect to quantum fluctuations in the path integral approach to quantum gravity is a fundamental problem as important as quantum gravity itself . due to the attractive nature of the gravitational field , we expect to find a lot of unstable physical configurations . therefore one might worry about the stability of the ground state of quantum gravity . one generally accepts to regard minkowski space as the ground state , or vacuum , of quantum gravity . classical small perturbations about this vacuum are stable . this is guaranteed by positivity theorems of schoen and yauand witten . however one might find that flat space is quantum mechanically unstable . this problem was investigated for the first time by gross , perry and yaffe ( gpy) in the euclidean path integral context . they discovered that hot flat space is unstable and the loss of stability was interpreted as a spontaneous nucleation of a black hole with an inverse temperature , where is the black hole mass and is the newton constant . in the semiclassical approximation to the euclidean path integral  ) , %\ ] ] the decay probability per unit volume and time is defined as  ) _{} ( -i_{g}^{ ( 2 ) }  [ h_{} ]  ) , %\ ] ] where the gravitational field has been separated into a background field and a quantum fluctuation is the prefactor coming from the saddle point evaluation of and is the classical part of the action . if a single negative eigenvalue appears in the prefactor , it means that the related bounce shifts the energy of the false ground state . in the schwarzschild case gpy discovered one single negative mode . allen reconsidered the effect of finite boundaries on the appearance of a negative mode showing that , if the box enclosing the black hole is little enough the instability disappears . since the pioneering paper of gross , perry and yaffe , many other spacetime configurations have been investigated in different contexts . in particular , the de sitter case involving

We study the stability of a flat space in the path integral approach to quantum gravity. We find that the ground state is unstable and the loss of stability is interpreted as a spontaneous nucleation of a black hole with an inverse temperature. The decay probability per unit volume and time is defined as ) _ _ ( -i_i_g ) ( 2 ) and, respectively,. If the box enclosing the black hole is little enough the instability disappears.

we extend the gross - perry - yaffe approach of hot flat space instability to minkowski space . this is done by a saddle point approximation of the partition function in a schwarzschild wormhole background which is coincident with an eternal black hole . the appearance of an instability in the whole manifold is here interpreted as a black hole pair creation .


In some special zones of the high - dimensional coordinate space of few - body systems with...

since various systems may be governed by the same fundamental law , universality exists in nature . the early indications of universality in quantum mechanic three - body systems was discovered before 1970. the first strong evidence was given by efimov in 1970 on three weakly bound identical bosons. he found that , when the scattering length is sufficiently long , a sequence of loosely bound states , the `` efimov states '' , will appear . the properties of these states are governed by a universal law , not depend on the dynamic details of the 3-boson systems . in this paper , another kind of universality that exists in tightly bound quantum mechanic few - body systems is revealed and confirmed numerically . the hamiltonian of identical particles is invariant under the operations of a set of symmetry groups , , ( including the permutation group). consequently , the eigenstates are classified according to the representations of these groups , where denotes a set of coordinates and is a serial number . let be an element of , be that of , and denotes a special zone in the high - dimensional coordinate space . when , the effects of and might be equivalent so that . for an example , when is the zone of the squares ( sq ) , is a rotation about the normal of the sq by , and is a cyclic permutation of particles , then and are equivalent in . making use of the representations of groups , the equivalence leads to a set of homogeneous linear equations  _ { i'}(x ) = 0 , \ \ \ ( x  ) , \ ] ] where are the matrix elements of the representation . when the matrix of this set of equations is non - degenerate , the set must be zero in . in this case , becomes a prohibited zone ( pz ) and the wave function appears as an inherent nodal surface ( ins). eq . ( [ e01_sum ] ) demonstrates that , for each pair of equivalent operations , a constraint will be imposed on the eigenstates . since the matrixes of representations are absolutely irrelevant to dynamics , the constraint is universal

We study the equivalence of the hamiltonian in tightly bound quantum mechanic few - body systems. The corresponding eigenstates are characterized by a set of homogeneous linear equations, where is a matrix element of, and is a serial number. For each pair of equivalent operations, a constraint will be a non - degenerate matrix element.

in some special zones of the high - dimensional coordinate space of few - body systems with identical particles , the operation of an element ( or a product of elements ) of the symmetry groups of the hamiltonian on a quantum state might be equivalent to the operation of another element . making use of the matrix representations of the groups , the equivalence leads to a set of homogeneous linear equations imposing on the wave functions . when the matrix of these equations is non - degenerate ,


We construct a generic , simple , and efficient scheduling policy for stochastic processing...

the past few decades have witnessed a surge in interest on the design and analysis of scheduling policies for stochastic networks , e.g. , . one of the key insights from this body of work is that natural scheduling policies can lead to instability even when each server is nominally underloaded . ( there are several notions of stability for stochastic networks , but they intuitively entail that , in some sense , the number of customers in the system does not grow without bounds . ) this insight stimulated a search for tools that can characterize the stability regions of scheduling policies , i.e. , the exact conditions on the arrival and service rates under which a network is stabilized by a policy . it is the objective of this paper to study a question of a different kind : is it possible to construct a generic , simple , and efficient scheduling policy for stochastic processing networks , which leads to a ( globally ) stable network if all servers are ( locally ) nominally underloaded in some sense ? to our knowledge , we are the first to answer this question within the setting of stochastic processing networks , which constitute a large class of stochastic networks capable of modeling a variety of networked systems for communication , manufacturing , and service systems ( e.g. , ) . to investigate this question , the key is to determine if and how jobs from different parts of the network should be treated differently when they share the same buffer . various existing scheduling policies are ` throughput optimal ' in the sense that they achieve the largest possible stability region , but these policies suffer from significant drawbacks . they typically obtain the desired stability by framing the contention resolution between buffers as an appropriate global optimization problem . this optimization problem requires central coordination between network entities , and it is computationally hard to solve if the network is large . the resulting policies , such as the ma

We study the stability of a stochastic processing network with a large number of servers. We find that the system is stable even when all servers are nominally underloaded, and that the network can be stabilized by a generic scheduling policy if all servers share the same buffer. This is a question that has been discussed in previous papers.

we construct a generic , simple , and efficient scheduling policy for stochastic processing networks , and provide a general framework to establish its stability . our policy is randomized and prioritized : with high probability it prioritizes jobs which have been least routed through the network . we show that the network is globally stable under this policy if there exists an appropriate quadratic ` local ' lyapunov function that provides a negative drift with respect to nominal loads at serve