phase ordering from off critical quenches and the measurement of the dynamic exponent lambda the ordering dynamics of a system with a nonconserved order parameter is considered following a quench into the ordered phase from high temperature the correlation of the order parameter field with its initial condition or more generally the correlation between the fields at different times involves the dynamic exponent lambda a non trivial exponent associated with the t 0 fixed point that drives phase ordering it is shown that lambda can be determined from the growth of the mean order parameter m t in a system which has a small but non zero mean order parameter m0 at t 0 since m t approximately m0l t lambda where l t approximately t1 2 is the characteristic length scale at time t the role of a weak external field h is also considered for h not 0 the growth of m t involves two power law terms m t approximately h at3 btlambda 2 for m0 0 with x 1 2 or 1 for a scalar or vector order parameter respectively the results are illustrated by the exact solution of the o n model at large n for general values of m0 and h

dynamic correlations in domain growth a 1 n expansion the authors consider the dynamics of the n component ginzburg landau model with nonconserved order parameter model a following a quench from a high temperature equilibrium state to zero temperature the two time correlation function of the order parameter field is found in the 1 n expansion to have the asymptotic scaling form ck t t t d2 t t lambda 2 f k2t k2t for t t with f 0 0 constant the form of the new exponent lambda which is a non trivial function of n and d was given explicitly to o 1 n in a recent letter the purpose of this study is to present a more detailed account of the calculation leading to the o 1 n form for lambda they also examine the role of thermal fluctuations in the ordered phase and the effect of long range initial correlations on the ordering process

finite difference scheme for a fractional telegraph equation with generalized fractional derivative terms abstract in this paper a finite difference scheme is presented for the generalized time fractional telegraph equation gtfte defined using generalized fractional derivative gfd terms introduced recently the generalization of fractional derivatives is done by introducing scale and weight functions and for their particular choices gfd reduces to caputo and riemann liouville derivatives we present the solution behaviour of the gtfte by changing the weight and scale functions in gfd the convergence and the stability of the finite difference scheme fds are also presented and for the numerical simulation of the fds we consider examples which validate our numerical method

growth of order in vector spin systems scaling and universality the growth of order in vector spin systems with nonconserved order parameter model a is considered following an instantaneous quench from infinite to zero temperature the results of numerical simulations in spatial dimension d 2 and spin dimension 2n5 are presented for n4 a scaling regime where a characteristic length scale l t emerges is entered for sufficiently long times with l t t12 the autocorrelation function a t decays with time as a t t d lambda 2 and the exponent lambda n agrees well with the predictions of the 1 n expansion the cases n 2 and 3 are more complicated due to the non trivial role played by topological singularities i e vortices n 2 and polyakov solitons n 3 for n4 universal amplitudes and scaling functions characterizing the energy relaxation and the equal time correlation function are identified it is argued that for d3 where an ordered phase exists at low temperature such universal quantities characterize the entire ordered phase

time fractional telegraph equations and telegraph processes with brownian time we study the fundamental solutions to time fractional telegraph equations of order 2 we are able to obtain the fourier transform of the solutions for any and to give a representation of their inverse in terms of stable densities for the special case 1 2 we can show that the fundamental solution is the distribution of a telegraph process with brownian time in a special case this becomes the density of the iterated brownian motion which is therefore the fundamental solution to a fractional diffusion equation of order 1 2 with respect to time

analytical solution for the time fractional telegraph equation by the method of separating variables in this paper a method of separating variables is effectively implemented for solving a time fractional telegraph equation tfte we discuss and derive the analytical solution of the tfte with three kinds of nonhomogeneous boundary conditions namely dirichlet neumann and robin boundary conditions

on effective computation of fundamental units ii introduction in part i of this paper we described the theoretical improvements of our method of computing fundamental units in algebraic number fields which we achieved in the last few years those improvements were of considerable influence on the corresponding computer program since its first 1976 2 implementation it was completely rewritten and changed in so many details that a new presentation cannot be avoided in sections 1 and 2 of this paper we describe the applications of part i 6 to the algorithm for constructing fundamental units section 3 contains a complete list of numerical examples concerning algebraic number fields of small degree and small absolute discriminant besides the fundamental units the tables contain much information about fields of degree five and six which was so far unknown the determination of those fields and their subfields is described in 3 besides the fundamental units we also listed the order of the torsion subgroup tuf of the unit group u whenever it is different from 2 it was computed by the methods of section 2 of 5 all computations were carried out on the control data cyber 76 of the computer center of the university of cologne

exact evaluation of the collapse phase boundary for two dimensional directed polymers the phase boundary of the collapsed phase for a directed polymer on a square lattice in the presence of an attractive wall and monomer monomer interactions is calculated exactly using transfer matrix techniques the position of the multicritical point is also identified

minimal co volume hyperbolic lattices ii simple torsion in a kleinian group this paper represents the nal step in solving the problem posed by siegel in 1945 of determining the minimal co volume lattices of hyperbolic 3 space h also problem 3 60 f in the kirby problem list from 1993 here we identify the two smallest co volume lattices both these groups are two generator arithmetic lattices generated by two elements of nite orders 2 and 3 their co volumes are 0 0390 and 0 0408 the precise values are given in terms of the dedekind zeta function of a number eld via a formula of borel our earlier work dealt with the cases when there is a nite spherical subgroup or high order torsion in the lattice thus here we are concerned with the study of simple torsion of low order and the geometric structure of klein 4 subgroups of a kleinian group we also identify certain universal geometric constraints imposed by discreteness on kleinian groups which are of independent interest to obtain these results we use a range of geometric and arithmetic criteria to obtain information on the structure of the singular set of the associated orbifold and then co volume bounds by studying equivariant neighbourhoods of xed point sets together with a rigorous computer search of certain parameter spaces for two generator kleinian groups

transfer matrix study of the adsorption of a flexible self avoiding polymer chain in two dimensions the authors model the polymer as a self avoiding walk on a semi infinite square lattice with an energy contribution in from each step along the lattice boundary the critical adsorption temperature ta and the ordinary and special surface exponents of the walk above and at the adsorption temperature respectively are estimated with transfer matrix finite size scaling methods for the adsorption temperature they obtain exp in kta 2 041 or 0 002 and for the crossover and susceptibility exponents of the special transition phi sp 0 501 or 0 003 and gamma 1sp 1 454 or 0 004

the accuracy and stability of an implicit solution method for the fractional diffusion equation we have investigated the accuracy and stability of an implicit numerical scheme for solving the fractional diffusion equation this model equation governs the evolution for the probability density function that describes anomalously diffusing particles anomalous diffusion is ubiquitous in physical and biological systems where trapping and binding of particles can occur the implicit numerical scheme that we have investigated is based on finite difference approximations and is straightforward to implement the accuracy of the scheme is o dx 2 in the spatial grid size and o dt 1 c in the fractional time step where 0 email protected 1 is the order of the fractional derivative and c 1 is standard diffusion we have provided algebraic and numerical evidence that the scheme is unconditionally stable for 0 c 1

phase ordering dynamics of a vector order parameter mazenko s theory of phase ordering dynamics is generalized to an n component nonconserved vector order parameter the scaling functions for the equal time and two time correlation functions are calculated as well as the exponent characterizing the decay of autocorrelations the equal time correlation function is numerically quite close to that recently calculated by bray and puri 1991 and by toyoki 1991 and exhibits the same power law tail in its fourier transform the time dependent structure factor

domain growth properties of a two dimensional kinetic ising model the domain growth properties of the two dimensional single spin flip kinetic ising model with a metropolis type transition function and checkerboard updating are investigated numerically with quenches from the high temperature phase to temperatures in the ordered phase and to tc measuring the structure factor s 0 t varies as t2x and the autocorrelation function a t varies as t lambda x as a function of time the effect of deterministic dynamics at t 0 with x 1 0 is followed throughout the ordered phase at t tc tnot approximately tc crossover from x 1 0 to x 0 5 is shown to occur with increasing time and even at t tc the scaling exponents are still discernibly dependent on time lambda however is found to be unaffected in the whole temperature range

a remark on possible violations of the pauli principle recently ignatiev and kuzmin 1988 developed a theoretical model to implement small violations of the pauli principle the authors remark that the pauli principle is unique among discrete symmetries and that in consequence any apparent violation actually signals new physical degrees of freedom with no violation of the pauli principle they construct an algebraic model which incorporates the algebra of ignatiev and kuzmin and leads to the same apparent violations yet preserves the pauli principle their algebra is that of a jordan pair an algebraic concept which provides a natural framework for structures that do not assume bilinear commutation relations

minimal co volume hyperbolic lattices i the spherical points of a kleinian group we identify the two minimal co volume lattices of the isometry group of hyperbolic 3 space that contain a finite spherical triangle group these two groups are arithmetic and are in fact the two minimal co volume lattices our results here represent the key step in establishing this fact thereby solving a problem posed by siegel in 1945 as a consequence we obtain sharp bounds on the order of the symmetry group of a hyperbolic 3 manifold in terms of its volume analogous to the hurwitz 84g 84 theorem of 1892 the finite spherical subgroups of a kleinian group give rise to the vertices of the singular graph in the quotient orbifold we identify the small values of the discrete spectrum of hyperbolic distances between these vertices and show these small values give rise to arithmetic lattices once vertices are sufficiently separated one obtains volume bounds by studying equivariant sets

new exponent for dynamic correlations in domain growth the dynamics of the n component ginzburg landau model with non conserved order parameter model a are considered following a quench to zero temperature the correlation function of the order parameter field is found in the 1 n expansion to have the asymptotic scaling form ck t t t d2 t t lambda 2 f k2t k2t for t t with f 0 0 constant the new exponent lambda is calculated to o 1 n for general space dimension d and has a non trivial dependence on n and d

the embedding e0 and the spectrum dependent r matrix for q f4 the explicit embedding forms of e0 for the minimal representations of the quantum f4 e6 and e7 are obtained in this paper in terms of jimbo s method the spectrum dependent r matrices both trigonometric and rational for those representations are computed

arithmeticity discreteness and volume we give an arithmetic criterion which is sufficient to imply the discreteness of various two generator subgroups of p sl 2 c we then examine certain two generator groups which arise as extremals in various geometric problems in the theory of kleinian groups in particular those encountered in efforts to determine the smallest co volume the margulis constant and the minimal distance between elliptic axes we establish the discreteness and arithmeticity of a number of these extremal groups the associated minimal volume arithmetic group in the commensurability class and we study whether or not the axis of a generator is simple

comparative study of three numerical schemes for fractional integro differential equations this paper presents a comparative study of three numerical schemes such as linear quadratic and quadratic linear scheme for the fractional integro differential equations defined in terms of the caputo fractional derivatives the error estimates of the respective approximations are also established numerical tests of the discussed schemes show that all schemes work well and when the number of terms approximating the solution is increased the desired solution is achieved the accuracy of the numerical schemes with respect to the step size h is analysed and illustrated through various tables finally comparative performances of the schemes are discussed comparative study of three schemes such as linear quadratic and quadratic linear schemes is presented for the fractional integro differential equations the convergences of the schemes are also established the performances of the schemes are compared through the test examples

dynamic correlations in phase ordering the 1 n expansion reconsidered the ordering dynamics of a system with a non conserved order parameter is considered following a quench into the ordered phase from high temperature newman and bray 1990 have set up an expansion in powers of 1 n for the o n model to obtain correlation functions and the two time exponent lambda but their calculation contains a simplifying assumption which is incorrect tight upper and lower bounds for lambda are obtained as a function of the space dimension d these bounds exclude the result of newman and bray although the dependence of lambda on d is qualitatively very similar comparison with simulations shows that the first order 1 n calculation does not agree with numerical results as well as previously thought

response of non equilibrium systems with long range initial correlations the long time dynamics of the d dimensional spherical model with a non conserved order parameter and quenched from an initial state with long range correlations is studied through the exact calculation of the two time autocorrelation and autoresponse functions in the ageing regime these are given in terms of non trivial universal scaling functions of both time variables at criticality five distinct types of ageing are found depending on the form of the initial correlations while at low temperatures only a single type of ageing exists the autocorrelation and autoresponse exponents are shown to be generically different and to depend on the initial conditions the scaling form of the two time response functions agrees with a recent prediction coming from conformal invariance

collapsing and adsorbing polygons the adsorption transition in the phase diagram of a self interacting lattice polygon is examined the polygon has a nearest neighbour contact fugacity and the interaction between the polygon and an impenetrable wall is modelled by a visit fugacity which is conjugate to the number of vertices of the polygon incident with the wall the partition function of this model is z c y z d p v cp c v c y v z c where p c v c is the number of polygons with c nearest neighbour contacts v visits to the wall and n edges and counted up to translations parallel to the wall the limiting free energy of this model is f c y z d limn 1 1 logz c y z and it is known to be a non analytic function of y for each z 1 for all z2 0 1

axial distances in discrete mobius groups abstract we describe here new lower bounds for the trace of the commutator of a discrete two generator group of mobius transformations these results lead to sharp estimates for the distance between the axes of elliptics in a discrete group and hence to new bounds for the volume of hyperbolic manifolds and orbifolds that will be discussed elsewhere

numerical and analytical solutions of new generalized fractional diffusion equation our current paper is devoted to studying the numerical and analytical solutions for a class of generalized fractional diffusion equations gfdes with new generalized time fractional derivative gtfd the gtfd we propose here is defined in the caputo sense we consider the gfdes on a bounded domain the numerical solutions are obtained by using the finite difference method fdm of full discretization the stability of fdm is discussed and the order of convergence is evaluated numerically numerical experiments are given which illustrate that the fdm is simple and effective for solving the gfdes with different coefficients and source functions an interesting phenomenon is that we can observe the period like solution in gfdes with a particular positive periodic weight function using the method of separation of variables we convert the homogeneous gfde into two ordinary differential equations and solve them via the help of solutions of the initial value problem with caputo derivative in the analytical solution we observe that the weight function in the denominator and scale function mapping the response domain differently since the derivative considered in this article is new many existing results of fdes are generalized

a new spectral galerkin method for solving the two dimensional hyperbolic telegraph equation abstract telegraph equation is more suitable than ordinary diffusion equation in modeling reaction diffusion for several branches of sciences and engineering in this paper a new numerical technique is proposed for solving the second order two dimensional hyperbolic telegraph equation subject to initial and dirichlet boundary conditions firstly a time discrete scheme based on the finite difference method is obtained unconditional stability and convergence of this semi discrete scheme are established secondly a fully discrete scheme is obtained by the sinc galerkin method and the problem is converted into a sylvester matrix equation especially when a symmetric sinc galerkin method is used the resulting matrix equation is a discrete adi model problem then the alternating direction sinc galerkin adsg method is applied for solving this matrix equation also the exponential convergence rate of sinc galerkin method is proved finally some examples are given to illustrate the accuracy and efficiency of proposed method for solving such types of differential equations compared to some other well known methods

small isospectral and nonisometric orbifolds of dimension 2 and 3 revisiting a construction due to vigneras we exhibit small pairs of orbifolds and manifolds of dimension 2 and 3 arising from arithmetic fuchsian and kleinian groups that are laplace isospectral in fact representation equivalent but nonisometric

finite difference spectral approximations for the time fractional diffusion equation in this paper we consider the numerical resolution of a time fractional diffusion equation which is obtained from the standard diffusion equation by replacing the first order time derivative with a fractional derivative of order a with 0 a 1 the main purpose of this work is to construct and analyze stable and high order scheme to efficiently solve the time fractional diffusion equation the proposed method is based on a finite difference scheme in time and legendre spectral methods in space stability and convergence of the method are rigourously established we prove that the full discretization is unconditionally stable and the numerical solution converges to the exact one with order o dt 2 a n m where dt n and m are the time step size polynomial degree and regularity of the exact solution respectively numerical experiments are carried out to support the theoretical claims

non equilibrium dynamics of the ising model for t less than equal totc the growth of order in ising models with nonconserved order parameter is considered for quenches to final temperatures tf 0 and tf tc the results of numerical simulations in spatial dimension d 2 are presented in all cases a scaling regime is entered for sufficiently long times where the characteristic length scale is the domain size l t approximately t12 for tf 0 and the nonequilibrium correlation length xi t approximately t1z for tf tc the equal time correlation function has the expected scaling forms f r l t and r d 2 eta fc r xi t for tf 0 and tc respectively the scaling function fc x has interesting short distance behaviour which is elucidated using scaling arguments and by in and 1 n expansions the t 0 scaling function f x depends on whether the spin correlations present in the initial conditions are of long or short range as does the exponent which describes the decay of the autocorrelation function a t si t si o approximately l t results for a quench from the equilibrium critical state to tf 0 are consistent with theoretical predictions

universality class for domain growth in random magnets a 2d ising model with random ferromagnetic bonds is studied by monte carlo simulation following a quench from t infinity to t tc the domain size grows as l t approximately in t to x at late times the data are consistent with the theoretical prediction chi 4 the exponent defined by si 0 si t approximately l t and the scaling functions for the spatial correlations are very close to those of the pure system suggesting that pure and random systems belong to the same universality class

geodesic intersections in arithmetic hyperbolic 3 manifolds it was shown by chinburg and reid that there exist closed hyperbolic 3 manifolds in which all closed geodesics are simple subsequently basmajian and wolpert showed that almost all quasi fuchsian 3 manifolds have all closed geodesics simple and disjoint the natural conjecture arose that the chinburg reid examples also had disjoint geodesics here we show that this conjecture is both almost true they have no geodesics that intersect except at right angles and spectacularly false any pair of closed geodesics admits infinitely many closed geodesics which intersects both geodesics of the pair perpendicularly the latter statement is shown to be true for all closed arithmetic hyperbolic 3 manifolds section 0 introduction by a hyperbolic n manifold we shall mean a complete orientable n dimensional riemannian manifold all of whose sectional curvatures are 1 if m is a hyperbolic 3 manifold the universal cover of m can be identified with h the upper half space model of hyperbolic 3 space andm is realized ash for some a discrete torsionfree subgroup of isom h3 now isom h3 can be identified with psl 2 c which in turn is isomorphic to pgl 2 c and is called a kleinian group in the sequel we will only be interested in the case when m is closed in which case is referred to as cocompact of interest to us is the structure of the set of closed geodesics in closed hyperbolic 3 manifolds the motivation comes from the following a closed geodesic in a closed hyperbolic n manifold is simple if it has no self intersections and nonsimple otherwise in dimension 2 every closed hyperbolic manifold has a non simple closed geodesic however in dimension 3 the situation is much more complex many closed hyperbolic 3 manifolds contain immersions of totally geodesic surfaces and so there are non simple closed geodesics in jr examples were given of closed hyperbolic 3 manifolds containing a non simple closed geodesic but having no immersed totally geodesic surface however it was shown in cr that there exist closed hyperbolic 3 manifolds in which all closed geodesics are simple subsequently basmajian and wolpert bw showed that almost all 3 manifolds arising as the quotient of h 1991 mathematics subject classification primary 57m50 secondary 30f40

theory of phase ordering kinetics the theory of phase ordering dynamics that is the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken symmetry phase is reviewed with the emphasis on recent developments interest will focus on the scaling regime that develops at long times after the quench how can one determine the growth laws that describe the time dependence of characteristic length scales and what can be said about the form of the associated scaling functions particular attention will be paid to systems described by more complicated order parameters than the simple scalars usually considered for example vector and tensor elds the latter are needed for example to describe phase ordering in nematic liquid crystals on which there have been a number of recent experiments the study of topological defects domain walls vortices strings and monopoles provides a unifying framework for discussing coarsening in these dia erent systems

computational aspects of fem approximation of fractional advection dispersion equations on bounded domains in r 2 in this paper we investigate the numerical approximation of the variational solution to the fractional advection dispersion equation fade on bounded domains in r2 more specifically we investigate the computational aspects of the galerkin approximation using continuous piecewise polynomial basis functions on a regular triangulation of the domain the computational challenges of approximating the solution to fractional differential equations using the finite element method stem from the fact that a fractional differential operator is a non local operator several numerical examples are given which demonstrate approximations to fades

non conserved ordering kinetics abstract attempts are made to understand the relationship between the two analytic approaches to non conserved ordering kinetics one approach originates from the use of singular perturbation with respect to nonlinearity of the governing field equation another one focuses on the dynamics of topological defects recent progress in analytical and numerical investigations are briefly reviewed and the origin of complications found in some models of the vector order parameter is tentatively attributed to the interplay between phase and defect dynamics

kinetics of phase ordering in the o n model with a conserved order parameter we study the phase ordering dynamics of the o n model with a conserved order parameter for systems with topological defects we present results from both cell dynamical simulations and predictions of a gaussian auxiliary field gaf approximation for the xy n 2 model in two and three dimensions and the heisenberg n 3 model in three dimensions we describe the results for the structure factor s q and growth law l t from simulations the growth laws obtained are consistent with theoretical predictions based on energy scaling arguments the structure factor shows good dynamical scaling using a length extracted from its first moment the simulations are compared with the theoretical predictions of the gaf for the scaling functions our results show that the gaf gives a good qualitative description of most features of the structure factor however it overestimates the amplitude of the porod tail in the large q limit moreover for small q the structure factor exhibits a q2 behaviour instead of the expected generalized yeung result of q4

fractional differential models for anomalous diffusion abstract in this study we investigate three kinds of fractional differential models distributed order model variable order model and random order model for characterization of anomalous diffusion the characteristics physical advantages and potential applications of each model are highlighted the numerical simulations also validate our analytical and comparison results furthermore a generalized distributed variable order model and a more generalized distributed variable random order model are proposed to combine the advantages of distributed order model variable order model and random order model

phase separation by directional quenching and morphological transition abstract with the help of a two dimensional numerical simulation the time evolution of the phase separation of a mixture is studied for various types of quenching firstly the usual homogeneous types of quenching is briefly reviewed secondly the spatiotemporal inhomogeneous type of quenching is studied by setting the quench boundary which is the boundary between the stable phase and the unstable phase and shifting it with a constant velocity the time evolution of the domain morphologies are examined numerically three different types of domain morphologies are found one is irregular and is essentially equivalent to that produced by the homogeneous quench the other two are regular and are characteristic of the inhomogeneous quenching process one of the regular domain morphologies is parallel to the quench boundary on the average whereas the other regular one is perpendicular to the quench boundary the transition between the two regular morphologies is sharp

conservative dynamics phase ordering and stretched exponential decays the authors discuss the dynamics of an observable field related to a locally conserved field they show that for a model of phase ordering dynamics and for a variation of model c critical dynamics that the two time momentum space correlation function decays asymptotically as a stretched exponential they show that under some conditions the asymptotic behaviour is experimentally observable and argue that the non exponential behaviour is not a feature specific to these models but should rather apply for any observable coupled to a locally conserved field

a fourth order method of the convection diffusion equations with neumann boundary conditions abstract in this paper we have developed a fourth order compact finite difference scheme for solving the convection diffusion equation with neumann boundary conditions firstly we apply the compact finite difference scheme of fourth order to discrete spatial derivatives at the interior points then we present a new compact finite difference scheme for the boundary points which is also fourth order accurate finally we use a pade approximation method for the resulting linear system of ordinary differential equations the presented scheme has fifth order accuracy in the time direction and fourth order accuracy in the space direction it is shown through analysis that the scheme is unconditionally stable numerical results show that the compact finite difference scheme gives an efficient method for solving the convection diffusion equations with neumann boundary conditions

fitted reproducing kernel hilbert space method for the solutions of some certain classes of time fractional partial differential equations subject to initial and neumann boundary conditions latterly many problems arising in different fields of science and engineering can be reduced by applying some appropriate discretization to a series of time fractional partial differential equations unlike the normal case derivative the differential order in such equations is with a fractional order which will lead to new challenges for numerical simulation the purpose of this analysis is to introduce the reproducing kernel hilbert space method for treating classes of time fractional partial differential equations subject to neumann boundary conditions with parameters derivative arising in fluid mechanics chemical reactions elasticity anomalous diffusion and population growth models the method provides appropriate representation of the solutions in convergent series formula with accurately computable components numerical experiments with different order derivatives degree are performed to support the theoretical analyses which are acquired by interrupting the n term of the exact solutions finally the obtained outcomes showed that the proposed method is competitive in terms of the quality of the solutions found and is very valid for solving such time fractional neumann problems

infinitely many symmetries of the davey stewartson equation using a formal series symmetry method for the davey stewartson equation dse we find that there exist two sets of infinitely many formal series symmetries of the dse however different from the kadomtsev petviashvili equation kpe we failed to get infinitely many truncated symmetries only six truncated symmetries can be obtained simply from the formal series symmetries

phenomenological renormalisation of the self avoiding walk in two dimensions phenomenological renormalisation is used to calculate the exponent v and the connective constant of the self avoiding walk problem on a square lattice a transfer matrix technique is developed for the polymer problem the results indicate that flory s value v 0 75 is true in two dimensions to extremely high accuracy

a finite difference finite element technique with error estimate for space fractional tempered diffusion wave equation abstract an efficient numerical technique is proposed to solve one and two dimensional space fractional tempered fractional diffusion wave equations the space fractional is based on the riemann liouville fractional derivative at first the temporal direction is discretized using a second order accurate difference scheme then a classic galerkin finite element is employed to obtain a full discrete scheme furthermore for the time discrete and the full discrete schemes error estimate has been presented to show the unconditional stability and convergence of the developed numerical method finally two test problems have been illustrated to verify the efficiency and simplicity of the proposed technique

a soluble model of domain growth in one dimensional disordered systems we introduce a new algorithm for domain growth in disordered systems at low temperatures based on the tendency for such a system to freeze into metastable states we apply the algorithm to the d 1 random bond ising model for a variety of bond distributions the analytical forms we obtain for the two point correlation function and autocorrelation function agree well with numerical simulations of the model these forms are not the same as those of the pure ising model with glauber dynamics

on quantum deformations of the simplest lie parasuperalgebra quantum deformations of the simplest lie parasuperalgebra psqm 2 are constructed by taking advantage of the well known representations of suq 2 c as a particular result the authors show that the fundamental witten superalgebra sqm 2 cannot be deformed

self consistent screening approximation for critical dynamics we generalize bray s self consistent screening approximation to describe the critical dynamics of the theory in order to obtain the dynamical exponent z we have to make an ansatz for the form of the scaling functions which fortunately can be restricted by general arguments numerical values of z for d 3 and n 1 10 are obtained using two different ansatz and differ by a very small amount in particular the value of obtained for the three dimensional ising model agrees well with recent monte carlo simulations

the monge metric on the sphere and geometry of quantum states topological and geometrical properties of the set of mixed quantum states in the n dimensional hilbert space are analysed assuming that the corresponding classical dynamics takes place on the sphere we use the vector su 2 coherent states and the generalized husimi distributions to define the monge distance between two arbitrary density matrices the monge metric has a simple semiclassical interpretation and induces a non trivial geometry among all pure states the distance from the maximally mixed state proportional to the identity matrix admits the largest value for the coherent states while the delocalized chaotic states are close to this contrasts the geometry induced by the standard trace hilbert schmidt or bures metrics for which the distance from is the same for all pure states we discuss possible physical consequences including unitary time evolution and the process of decoherence we introduce also a simplified monge metric defined in the space of pure quantum states and more suitable for numerical computation

high order unconditionally stable difference schemes for the riesz space fractional telegraph equation in this paper a class of unconditionally stable difference schemes based on the pade approximation is presented for the riesz space fractional telegraph equation firstly we introduce a new variable to transform the original differential equation to an equivalent differential equation system then we apply a second order fractional central difference scheme to discretize the riesz space fractional operator finally we use 1 1 2 2 and 3 3 pade approximations to give a fully discrete difference scheme for the resulting linear system of ordinary differential equations matrix analysis is used to show the unconditional stability of the proposed algorithms two examples with known exact solutions are chosen to assess the proposed difference schemes numerical results demonstrate that these schemes provide accurate and efficient methods for solving a space fractional hyperbolic equation