wigner function for the radial equation of the coulomb problem in langer space in this paper a theoretical study of the coulomb problem in quantum phase space is reported the langer coordinate transformation is used to map the coulomb problem into a one dimensional morse oscillator as a result the wigner distribution functions for the morse oscillator are obtained the form of these functions is presented for a few principal quantum number n and the angular momentum quantum number l the results obtained correspond to the solution of the coulomb problem in the spherical coordinate system

the morphology of nodal lines random waves versus percolation in this paper we investigate the properties of nodal structures in random wave fields and in particular we scrutinize their recently proposed connection with short range percolation models we propose a measure which shows the difference between monochromatic random waves which are characterized by long range correlations and gaussian fields with short range correlations which are naturally assumed to be better modelled by percolation theory we also study the relevance of the quantities which we compute to the probability that nodal lines are in the vicinity of a given reference line

clouds fibres and echoes a new approach to studying random walks on fractals up to now the general approach of constructing evolution differential equations to describe random walks on fractals has not succeeded is this because the true probability density function is inherently fractal when plotted in the appropriate similarity variable we find a cloud which is not too smooth further investigation shows that this cloud has a structure that might be overlooked if one is looking for the usual single valued probability density function the cloud is composed of an infinite family of smooth fibres each of which describes the behaviour of the walk on an infinite echo point class the fibres are individually smooth and so are naturally amenable to analysis with differential equations

the finite volume element method for diffusion equations on general triangulations this paper develops discretization error estimates for the finite volume element method on general triangulations of a polygonal domain in mathcal r 2 using a special type of control volume the theory applies to diffusion equations of the form begin gathered nabla a nabla u f quad text in omega hfill u 0 quad text on partial omega hfill end gathered under fairly general conditions the theory establishes o h estimates of the error in a discrete mathcal h 1 seminorm under an additional assumption concerning local uniformity of the triangulation the estimate is improved to o h 2

resonance and web structure in discrete soliton systems the two dimensional toda lattice and its fully discrete and ultra discrete analogues we present a class of solutions of the two dimensional toda lattice equation its fully discrete analogue and its ultra discrete limit these solutions demonstrate the existence of soliton resonance and web like structure in discrete integrable systems such as differential difference equations difference equations and cellular automata ultra discrete equations

some errors estimates for the box method we define and analyze several variants of the box method for discretizing elliptic boundary value problems in the plane our estimates show the error to be comparable to a standard galerkin finite element method using piecewise linear polynomials

entropic sampling of simple polymer models within wang landau algorithm in this paper we apply a new simulation technique proposed in wang and landau wl 2001 phys rev lett 86 2050 to sampling of three dimensional lattice and continuous models of polymer chains distributions obtained by homogeneous unconditional random walks are compared with results of entropic sampling es within the wl algorithm while homogeneous sampling gives reliable results typically in the range of 4 5 orders of magnitude the wl entropic sampling yields them in the range of 20 30 orders and even larger with comparable computer effort a combination of homogeneous and wl sampling provides reliable data for events with probabilities down to 10 35 for the lattice model we consider both the athermal case self avoiding walks saws and the thermal case when an energy is attributed to each contact between nonbonded monomers in a self avoiding walk for short chains the simulation results are checked by comparison with the exact data in wl calculations for chain lengths up to n 300 scaling relations for saws are well reproduced in the thermal case distribution over the number of contacts is obtained in the n range up to n 100 and the canonical averages internal energy heat capacity excess canonical entropy mean square end to end distance are calculated as a result in a wide temperature range the continuous model is studied in the athermal case by sorting conformations of a continuous phantom freely joined n bonded chain with a unit bond length over a stochastic variable the minimum distance between nonbonded beads we determine the probability distribution for the n bonded chain with hard sphere monomer units over its diameter a in the complete diameter range 0 a 2 within a single es run this distribution provides us with excess specific entropy for a set of diameters a in this range calculations were made for chain lengths up to n 100 and results were extrapolated to n for a in the range 0 a 1 25

numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures finite element and finite difference methods are combined with the method of characteristics to treat a parabolic problem of the form cu t bu x au x x f optimal order error estimates in l 2 and w 1 2 are derived for the finite element procedure various error estimates are presented for a variety of finite difference methods the estimates show that for convection dominated problems b gg a these schemes have much smaller time truncation errors than those of standard methods extensions to n space variables and time dependent or nonlinear coefficients are indicated along with applications of the concepts to certain problems described by systems of differential equations

resonant triads for two bidirectional equations in 1 1 dimensions the two soliton solution of the kdv equation is known not to degenerate into a solution describing resonant triads of solitons in 1 1 dimensions however we show that two integrable coupled kdv systems of the drinfeld sokolov class possess solutions which may degenerate into resonant triads these solutions are associated with a resonance relation which generalizes the usual one previously considered by hirota and ito

sufficient conditions for the anti zeno effect the ideal anti zeno effect means that a perpetual observation leads to an immediate disappearance of the unstable system we present a straightforward way to derive sufficient conditions under which such a situation occurs expressed in terms of the decaying states and spectral properties of the hamiltonian they show in particular that the gap between zeno and anti zeno effects is in fact very narrow

simple strong glass forming models mean field solution with activation we introduce simple models inspired by previous models for froths and covalent glasses with trivial equilibrium properties but dynamical behaviour characteristic of strong glass forming systems these models are also a generalization of backgammon or urn models to a non constant number of particles where entropic barriers are replaced by energy barriers allowing for the existence of activated processes we formulate a mean field version of the models which keeps most of the features of the finite dimensional ones and solve analytically the out of equilibrium dynamics in the low temperature regime where activation plays an essential role

on the initial value problem of a periodic box ball system we show that the initial value problem of a periodic box ball system can be solved in an elementary way using simple combinatorial methods

extending bauer s corollary to fractional derivatives we comment on the method of dreisigmeyer and young j phys a math gen 368297 to model nonconservative systems with fractional derivatives it was previously hoped that using fractional derivatives in an action would allow us to derive a single retarded equation of motion using a variational principle it is proven that under certain reasonable assumptions the method of dreisigmeyer and young fails

variational problems with fractional derivatives euler lagrange equations we generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integral that is minimized also for the standard case when these two bounds coincide we derive a new form of euler lagrange equations we use approximations for fractional derivatives in the lagrangian and obtain the euler lagrange equations which approximate the initial euler lagrange equations in a weak sense

combinatorial aspects of the conserved quantities of the tropical periodic toda lattice the tropical periodic toda lattice trop p toda is a dynamical system attracting attention in the area of the interplay of integrable systems and tropical geometry we show that the young diagrams associated with trop p toda given by two very different definitions are identical the first definition is given via a lax representation of the discrete periodic toda lattice and the second one is associated with a generalization of the kerov kirillov reshetikhin bijection in the combinatorics of the bethe ansatz by means of this identification it is shown for the first time that the young diagrams given by the latter definition are preserved under time evolution this result is regarded as an important first step in clarifying the iso level set structure of this dynamical system in general cases i e not restricted to generic cases

screening of charged singularities of random fields many types of point singularity have a topological index or charge associated with them for example the phase of a complex field depending on two variables can either increase or decrease on making a clockwise circuit around a simple zero enabling the zeros to be assigned charges of 1 in random fields we can define a correlation function for the charge weighted density of singularities for many types of topologically charged singularity this correlation function satisfies an identity which shows that the singularities screen each other perfectly a positive singularity is surrounded by an excess of concentration of negatives which exactly cancel its charge and vice versa this paper gives a simple and widely applicable derivation of this result a counterexample where screening is incomplete is also exhibited

the spin contribution to the form factor of quantum graphs following the quantization of a graph with the dirac operator spin 1 2 we explain how additional weights in the spectral form factor k due to spin propagation around orbits produce higher order terms in the small asymptotics in agreement with symplectic random matrix ensembles we determine conditions on the group of spin rotations sufficient to generate cse statistics

edwards measures for powders and glasses can one construct a thermodynamics for compact slowly moving powders and grains a few years ago edwards proposed a possible step in this direction raising the fascinating perspective that such systems have a statistical mechanics of their own different from that of maxwell boltzmann and gibbs allowing us to have some information while still ignoring dynamic details recent developments in the theory of glasses have come to confirm these ideas within mean field in order to go beyond we explicitly generate edwards measure in a 3d model comparison of the results with the irreversible compaction data shows very good agreement the present framework immediately suggests new experimental checks

monte carlo simulations of the violation of the fluctuation dissipation theorem in domain growth processes numerical simulations of various domain growth systems are reported in order to compute the parameter describing the violation of fluctuation dissipation theorem fdt in aging phenomena we compute two time correlation and response functions and find that as expected from the exact solution of a certain mean field model equivalent to the o n model in three dimensions in the limit of n going to infinity this parameter is equal to one no violation of fdt in the quasiequilibrium regime short separation of times and zero in the aging regime

error estimation of a quadratic finite volume method on right quadrangular prism grids in this paper we develop a finite volume element method with affine quadratic bases on right quadrangular prism meshes for three dimensional elliptic boundary value problems the optimal h 1 norm error estimate of second order accuracy is proved under certain assumptions about the meshes numerical results are presented to illustrate the theoretical analysis

on the accuracy of the finite volume element method for diffusion equations on composite grids this paper develops the finite volume element fve method which is similar to the so called control volume finite element method but tailored to composite grid applications fve is described for the general two dimensional diffusion equation in divergence form o h 3 2 discretization error estimates are then developed for the case of triangular elements these results are improved to o h 2 using a special modification involving rectilinear elements at the grid interface

lowest nonzero eigenvalue of the diffusion equation for a brownian particle in a symmetric double well with low friction in this work a particle undergoing brownian motion in a symmetric double well is considered in the limit of low frictional forces and small temperature it is assumed that the particle fluctuations over equilibrium are governed by a second order diffusion equation in which the drift velocity solves a hjy equation while the diffusion coefficient is determined from the stationary condition the excited state is constructed by imposing suitable boundary conditions at the saddle point by means of an integral equation which is solved to a first approximation by iteration in the limit of high barrier the result is a complex eigenvalue for the relaxation of the fluctuation which is interpreted as a damped stochastic resonance the relation to kramer s rate is discussed

a quantum exactly solvable nonlinear oscillator related to the isotonic oscillator a nonpolynomial one dimensional quantum potential representing an oscillator which can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator harmonic oscillator with a centripetal barrier is studied first the general case that depends on a parameter a is considered and then a particular case is studied with great detail it is proven that it is schr dinger solvable and then the wavefunctions n and the energies en of the bound states are explicitly obtained finally it is proven that the solutions determine a family of orthogonal polynomials related to the hermite polynomials and such that i every is a linear combination of three hermite polynomials and ii they are orthogonal with respect to a new measure obtained by modifying the classic hermite measure

glassy behaviour in a simple topological model in this paper we study a simple purely topological cellular model which is allowed to evolve through a glauber kawasaki process we find a non thermodynamic transition to a glassy phase in which the energy defined as the square of the local cell topological charge fails to reach the equilibrium value below a characteristic temperature which is dependent on the cooling rate we investigate a correlation function which exhibits ageing behaviour and follows a master curve in the stationary regime when time is rescaled by a factor of the relaxation time tr this master curve can be fitted by a von schweidler law in the late relaxation regime the relaxation times can be well fitted at all temperatures by an offset arrhenius law a power law can be fitted to an intermediate temperature regime the exponent of the power law and the von schweidler law roughly agree with the relationship predicted by mode coupling theory by defining a suitable response function we find that the fluctuation dissipation ratio is held until sometime later than the appearance of the plateaux non monotonicity of the response is observed after this ratio is broken a feature which has been observed in other models with dynamics involving activated processes

kovacs effect and fluctuation dissipation relations in 1d kinetically constrained models strong and fragile glass relaxation behaviours are obtained simply changing the constraints of the kinetically constrained ising chain from symmetric to purely asymmetric we study the out of equilibrium dynamics of these two models focusing on the kovacs effect and the fluctuation dissipation fd relations the kovacs or memory effect commonly observed in structural glasses is present for both constraints but enhanced with the asymmetric ones most surprisingly the related fd relations satisfy the fd theorem in both cases this result strongly differs from the simple quenching procedure where the asymmetric model presents strong deviations from the fd theorem

the upwind finite volume element method based on straight triangular prism partition for nonlinear convection diffusion problem the upwind finite volume element method based on straight triangular prism partition is put forward for the nonlinear convection diffusion problems some techniques such as calculus of variations commutating operator and prior estimates are adopted optimal order error estimate in l 2 is derived to determine the error in approximate solution numerical experiment shows that the method is effective for avoiding numerical diffusion and nonphysical oscillations and reducing work time