a new code for electrostatic simulation by numerical integration of the vlasov and ampere equations using maccormack s method abstract we present a new simulation code for electrostatic waves in one dimension which uses the vlasov equation to integrate the distribution function and ampere s equation to integrate the electric field forward in time previous vlasov codes used the vlasov and poisson equations using ampere s equation has two advantages first boundary conditions do not have to be set on the electric field second it forms a logical basis for an electromagnetic code since the time integration of the electric and magnetic fields is treated in a similar way maccormack s method is used to integrate the vlasov equation which was found to be easy to implement and reliable a stability analysis is presented for the maccormack scheme applied to the vlasov equation conditions for stability are more stringent than the simple courant friedrich s lewy cfl conditions for the spatial and velocity grids we provide a simple linear function which when combined with the cfl conditions should ensure stability simulation results for landau damping are in excellent agreement with numerical solutions of the linear dispersion relation for a wide range of wavelengths the code is also able to retain phase memory as demonstrated by the recurrence effect and reproduce the effects of particle trapping the use of ampere s equation enables standing and traveling waves to be produced depending on whether the current is zero or non zero respectively in simulations where the initial current is non zero and maxwell s equations are satisfied initially additional standing waves may be set up which could be important when the coupling of wave fields from a transmitter to a plasma is considered

statistical mechanics of classical particles with logarithmic interactions the inhomogeneous mean field thermodynamic limit is constructed and evaluated for both the canonical thermodynamic functions and the states of systems of classical point particles with logarithmic interactions in two space dimensions the results apply to various physical models of translation invariant plasmas gravitating systems as well as to planar fluid vortex motion for attractive interactions a critical behavior occurs which can be classified as an extreme case of a second order phase transition to include in particular attractive interactions a new inequality for configurational integrals is derived from the arithmetic geometric mean inequality the method developed in this paper is easily seen to apply as well to systems with fairly general interactions in all space dimensions in addition it also provides us with a new proof of the trudinger moser inequality known from differential geometry in its sharp form

a piecewise time linearized method for the logistic differential equation a piecewise time linearized technique is employed to determine an approximate analytical solution to the logistic differential equation this technique yields a nonlinear map or difference equation which preserves the fixed points and linear stability of the logistic differential equation it is shown that this map is continuous and piecewise differentiable c coincides with that of the euler forward method for small time steps and differs from the predictor corrector method proposed by certaine and adomian s decomposition technique

singularly perturbed volterra integral equations ii a formal methodology is developed to obtain a uniformly valid asymptotic solution to a class of singularly perturbed volterra integral equations the methodology systematically determines the appropriate integral equations which govern the inner and outer solutions at each order of the perturbation analysis several examples are presented to illustrate the procedure

exponentially fitted one step methods for the numerical solution of the scalar ricatti equation abstract using stability analysis and information from the constant coefficient problem we motivate an explicit exponentially fitted one step method to approximate the solution of a scalar riccati equation y c x y 2 d x y e x 0 x x y 0 y 0 where 0 is a small parameter and the coefficients c d and e are assumed to be real valued and continuous an explicit euler type scheme is presented which when applied to the numerical integration of the continuous problem give solutions satisfying a uniform in error estimate with order one where suitable restrictions are imposed on the coefficients c d and e together with the choice of y 0 using a counterexample we show that for a particular class of problems the solutions of the fitted scheme do not converge uniformly in to the corresponding solutions of the continuous problems numerical results are presented which compare the fitted scheme with a number of implicit schemes when applied to the numerical integration of some sample problems

kinetic solvers with adaptive mesh in phase space an adaptive mesh in phase space amps methodology has been developed for solving multidimensional kinetic equations by the discrete velocity method a cartesian mesh for both configuration r and velocity v spaces is produced using a tree of trees tot data structure the r mesh is automatically generated around embedded boundaries and is dynamically adapted to local solution properties the v mesh is created on the fly in each r cell mappings between neighboring v space trees is implemented for the advection operator in r space we have developed algorithms for solving the full boltzmann and linear boltzmann equations with amps several recent innovations were used to calculate the discrete boltzmann collision integral with dynamically adaptive v mesh the importance sampling multipoint projection and variance reduction methods we have developed an efficient algorithm for calculating the linear boltzmann collision integral for elastic and inelastic collisions of hot light particles in a lorentz gas our amps technique has been demonstrated for simulations of hypersonic rarefied gas flows ion and electron kinetics in weakly ionized plasma radiation and light particle transport through thin films and electron streaming in semiconductors we have shown that amps allows minimizing the number of cells in phase space to reduce the computational cost and memory usage for solving challenging kinetic problems

complete analysis of phase transitions and ensemble equivalence for the curie weiss potts model using the theory of large deviations we analyze the phase transition structure of the curie weiss potts spin model which is a mean field approximation to the nearest neighbor potts model it is equivalent to the potts model on the complete graph on n vertices the analysis is carried out both for the canonical ensemble and the microcanonical ensemble besides giving explicit formulas for the microcanonical entropy and for the equilibrium macrostates with respect to the two ensembles we analyze ensemble equivalence and nonequivalence at the level of equilibrium macrostates relating these to concavity and support properties of the microcanonical entropy the curie weiss potts model is the first statistical mechanical model for which such a detailed and rigorous analysis has been carried out

conservative numerical schemes for the vlasov equation abstract a new scheme for solving the vlasov equation using a phase space grid is proposed the algorithm is based on the conservation of the flux of particles and the distribution function is reconstructed using various techniques that allow control of spurious oscillations or preservation of the positivity several numerical results are presented in two and four dimensional phase space and the scheme is compared with the semilagrangian method this method is almost as accurate as the semilagrangian one and the local reconstruction technique is well suited for parallel computation

linearized methods for ordinary differential equations the conservation properties singularities and nonlinear dynamics of both time linearized methods which provide piecewise analytical solutions and keep the independent variable continuous and implicit linearized techniques which are based on discretization and linearization are analyzed in this paper it is shown that both methods are implicit and provide explicit maps but they do not preserve the energy in conservative systems it is also shown that time linearized methods preserve both the fixed points and the linear stability of the original ordinary differential equation whereas linearized techniques do preserve the fixed points and the linear stability of attractors but the stability of the repellers depends on the time step and the implicitness parameter the results clearly indicate that the linearized techniques which more faithfully reproduce the nonlinear dynamics of the original ordinary differential equation are second order accurate in time

multidimensional upwind methods for hyperbolic conservation laws abstract we present a class of second order conservative finite difference algorithms for solving numerically time dependent problems for hyperbolic conservation laws in several space variables these methods are upwind and multidimensional in that the numerical fluxes are obtained by solving the characteristic form of the full multidimensional equations at the zone edge and that all fluxes are evaluated and differenced at the same time in particular operator splitting is not used correct behavior at discontinuities is obtained by the use of solutions to the riemann problem and by limiting some of the second order terms numerical results are presented which show that the methods described here yield the same high resolution as the corresponding operator split methods

asymptotic solutions to some two dimensional singularly perturbed fredholm integral equations the leading order term in the asymptotic solution is developed to a class of two dimensional singularly perturbed fredholm integral equations of the first kind as an application of the results the scattering of plane waves by flat acoustically soft obstacles is considered to leading order the field is expressed as a line integral about the edge of the obstacle

gibbs non gibbs transitions via large deviations computable examples we give new and explicitly computable examples of gibbs non gibbs transitions of mean field type using the large deviation approach introduced in van enter et al in mosc math j 10 687 711 2010 these examples include brownian motion with small variance and related diffusion processes such as the ornstein uhlenbeck process as well as birth and death processes we show for a large class of initial measures and diffusive dynamics both short time conservation of gibbsianness and dynamical gibbs non gibbs transitions

variational description of gibbs non gibbs dynamical transitions for spin flip systems with a kac type interaction we continue our study of gibbs non gibbs dynamical transitions in the present paper we consider a system of ising spins on a large discrete torus with a kac type interaction subject to an independent spin flip dynamics infinite temperature glauber dynamics we show that in accordance with the program outlined in van enter et al moscow math j 10 687 711 2010 in the thermodynamic limit gibbs non gibbs dynamical transitions are equivalent to bifurcations in the set of global minima of the large deviation rate function for the trajectories of the empirical density conditional on their endpoint more precisely the time evolved measure is non gibbs if and only if this set is not a singleton for some value of the endpoint a partial description of the possible scenarios of bifurcation is given leading to a characterization of passages from gibbs to non gibbs and vice versa with sharp transition times our analysis provides a conceptual step up from our earlier work on gibbs non gibbs dynamical transitions for the curie weiss model where the mean field interaction allowed us to focus on trajectories of the empirical magnetization rather than the empirical density

sufficient conditions for uniformly second order convergent schemes for stiff initial value problems abstract we present a convergence analysis for a class of one step exponentially fitted finite difference schemes for stiff initial value problems such schemes when applied to the numerical integration of the linear scalar problem y a x y f x x 0 x with y 0 given and where 0 is a small parameter give solutions satisfying a uniform in error estimate in this paper a set of sufficient conditions for uniform second order convergence is derived the findings differ from those reported in 1 3 and are complemented by the results of numerical experiments which illustrate the effectiveness of the proposed approach

on secondary bifurcations for some nonlinear convolution equations etude de quelques equations de convolution non lineaires sur le tore a d dimensions conditions d existence de bifurcations secondaires

surface tension in ising systems with kac potentials we consider an ising spin system with kac potentials in a torus of d d 2 and fix the temperature below its lebowitz penrose critical value we prove that when the kac scaling parameter vanishes the log of the probability of an interface becomes proportional to its area and the surface tension related to the proportionality constant converges to the van der waals surface tension the results are based on the analysis of the rate functionals for gibbsian large deviations and on the proof that they converge to the perimeter functional of geometric measure theory which extends the notion of area our considerations include nonsmooth interfaces proving that the gibbsian probability of an interface depends only on its area and not on its regularity

a new conservative unsplit method for the solution of the vlasov equation we have developed a new conservative method for solving the vlasov equation without using any splitting technique our goal is to maintain the positivity of the distribution function and to avoid un physical oscillations which might lead to numerical instabilities based on a finite volume conservative discretization of the conservative form of the vlasov equation we implemented a highly accurate second order upwind scheme in order to avoid un physical oscillations and their possible numerical instability we apply a flux limiter in the second order we validate our new vlasov solver by considering standard cases of one dimensional current driven ion acoustic instabilities solving a vlasov ampere set of equations

low temperature dynamics of the curie weiss model periodic orbits multiple histories and loss of gibbsianness we consider the curie weiss model at initial temperature 0 1 in vanishing external field evolving under a glauber spin flip dynamics with temperature 0 1 we study the limiting conditional probabilities and their continuity properties and discuss their set of points of discontinuity bad points we provide a complete analysis of the transition between gibbsian and non gibbsian behavior as a function of time extending earlier work for the case of independent spin flip dynamics

asymptotic properties of eigenvalues of integral equations the eigenvalue problem is considered for the integral equation int 0 a k x y varphi y dy lambda varphi x the eigenvalues and eigenfunctions are studied as functions of the upper limit a for small values of a with k smooth expansions of the solutions in powers of a are obtained and it is shown that lambda n a o a 2n 1 for real symmetric kernels it is shown that lambda n a is an increasing function of a for all values of a for large values of a with additional conditions on k expansions of the solutions in powers or fractional powers of a 1 are obtained

numerical solutions of integral and integro differential equations using chebyshev polynomials of the third kind abstract our purpose in this study is to construct an algorithm based on the use of a finite expansion in chebyshev polynomials of the third kind to solve singularly perturbed volterra integral equations first order integro differential equations of volterra type arising in fluid dynamics and volterra delay integro differential equations the convergence of the method is investigated finally some numerical experiments which confirm the theoretical results are shown and comparisons with other methods in literature are given

linearization techniques for singularly perturbed initial value problems of ordinary differential equations linearization methods for singularly perturbed initial value problems in ordinary differential equations based on taylor series expansions and piecewise analytical solutions are presented if only the linear terms are retained it is shown that exponentially fitted techniques are obtained whereas if quadratic terms are kept then riccati s equations result both linear and quadratic linearization methods are shown to be nonuniformly convergent in the small perturbation parameter and the former are more accurate than the latter in equally spaced grids linearization methods are also used with three different adaptive mesh refinement methods that account for the magnitude of the jacobian the variation of the solution and the resolution of the initial layer and it is shown that mesh refinement methods based on the variation of the solution can provide very accurate solutions although they may yield large errors at the outer edge of the initial layer if the grid spacing increases rapidly it is also shown that for values of the perturbation parameter on the order of unity quadratic linearization methods are more accurate than linearization methods and can account for the presence of internal layers it is also shown that linearization methods on grids whose spacing obeys a geometric progression are not robust and may suffer from a loss in the order of convergence compared with adaptive methods that resolve the boundary layer or adapt the grid according to the numerical solution

product integration for volterra integral equations of the second kind with weakly singular kernels we introduce a new numerical approach for solving volterra integral equations of the second kind when the kernel contains a mild singularity we give a convergence result we also present numerical examples which show the performance and efficiency of our method

singularly perturbed integral equations with endpoint boundary layers a methodology is developed for certain singularly perturbed integral equations whose solution exhibits a boundary layer at either one or both endpoints of its domain the scheme indicates how the width and magnitude of the boundary layer s are determined and gives a construction of an asymptotic solution as well application to both linear and nonlinear equations is discussed and illustrated with examples

an algorithm for approximate solutions to weakly filtered synchronous control systems and nonlinear renewal processes a multi time perturbation algorithm is derived to study certain synchronous control systems and nonlinear renewal processes the new methods presented here study singular perturbation problems for nonlinear volterra integro differential equations whose kernels are close to the dirac delta function the algorithm provides useful approximate solutions to weakly filtered phase locked loop circuits and to nonlinear renewal equations describing certain population dynamics

singular perturbation solutions of a class of systems of singular integral equations a new class of systems of strongly singular integrodifferential equations is examined which emerges in the study of the bridged interface crack growth e g in fiber stitched layered composites this work generalizes the asymptotic analysis of strongly singular integral equations by willis and nemat nasser quart appl math 48 1990 pp 741 753 singular perturbation solutions up to the first order in a small paramter are presented for a general case which corresponds to the elasticity problem of bridged interface cracks in general anisotropic bimaterials in particular detailed solutions are described for a special case which includes the problem of bridged interface cracks in isotropic bimaterials methods are illustrated by solving particular examples

a performance comparison of semi lagrangian discontinuous galerkin and spline based vlasov solvers in four dimensions abstract the purpose of the present paper is to compare two semi lagrangian methods in the context of the four dimensional vlasov poisson equation more specifically our goal is to compare the performance of the more recently developed semi lagrangian discontinuous galerkin scheme to cubic spline interpolation which is widely used in eulerian vlasov simulation to that end we perform simulations for nonlinear landau damping and a two stream instability and provide benchmarks for the selalib and sldg codes both on a workstation and using mpi on a cluster in addition we will present results for the graphic processing unit gpu implementation contained in sldg we find that the semi lagrangian discontinuous galerkin scheme shows a moderate improvement in run time for nonlinear landau damping and a substantial improvement for the two stream instability it should be emphasized that these results are markedly different from results obtained in the asymptotic regime which favor spline interpolation thus we conclude that the traditional approach of evaluating numerical methods is misleading even for short time simulations in addition the absence of any global communication in the semi lagrangian discontinuous galerkin method gives it a decisive advantage for scaling to more than 256 cores

spatializing random measures doubly indexed processes and the large deviation principle the main theorem is the large deviation principle for the doubly indexed sequence of random measures w r q dx dy dx 1 dr k x l q k dy k 1 here is a probability measure on a polish space x d r k k 1 2 r is a dyadic partition of x hence the use of 2 r summands satisfying d r k 1 2 r and l q 1 l q 2 l q 2 r is an independent identically distributed sequence of random probability measures on a polish space y such that l q k q n satisfies the large deviation principle with a convex rate function a number of related asymptotic results are also derived the random measures w have important applications to the statistical mechanics of turbulence in a companion paper the large deviation principle presented here is used to give a rigorous derivation of maximum entropy principles arising in the well known miller robert theory of two dimensional turbulence as well as in a modification of that theory recently proposed by turkington

numerical study of the two species vlasov ampere system in this paper we propose energy conserving eulerian solvers for the two species vlasov ampere va system and apply the methods to simulate current driven ion acoustic instability the two species va systems are of practical importance in applications and they conserve many physical quantities including the particle number of each species and the total energy that is comprised of kinetic energy for both species and the electric energy the main goal of this paper is to generalize our previous work for the single species va system 9 and vlasov maxwell vm system 8 to the two species case the methodologies proposed involve careful design of temporal discretization and the use of the discontinuous galerkin dg spatial discretizations we show that the energy conserving time discretizations for single species equations 9 8 can also work for the two species case if extended properly compared to other high order schemes we emphasize that our schemes can preserve the total particle number and total energy on the fully discrete level regardless of mesh size making them very attractive for long time simulations we benchmark our algorithms on a test example to check the one species limit and the current driven ion acoustic instability to simulate the current driven ion acoustic instability a slight modification for the implicit method is necessary to fully decouple the split equations this is achieved by a gauss seidel type iteration technique numerical results verified the conservation and performance of our methods finally we remark that the schemes in this paper can be readily extended to applications when the models take more general form such as the multi species vm equations

uniform and optimal schemes for stiff initial value problems abstract we formulate a class of difference schemes for stiff initial value problems with a small parameter multiplying the first derivative we derive necessary conditions for uniform convergence with respect to the small parameter that is the solution of the difference scheme uih satisfies u i h u x i ch where c is independent of h and we also derive sufficient conditions for uniform convergence and show that a subclass of schemes is also optimal in the sense that u i h u x i c min h finally we show that this class contains higher order schemes

variational description of gibbs non gibbs dynamical transitions for the curie weiss model we perform a detailed study of gibbs non gibbs transitions for the curie weiss model subject to independent spin flip dynamics infinite temperature dynamics we show that in this setup the program outlined in van enter fernandez den hollander and redig 3 can be fully completed namely that gibbs non gibbs transitions are equivalent to bifurcations in the set of global minima of the large deviation rate function for the trajectories of the magnetization conditioned on their endpoint as a consequence we show that the time evolved model is non gibbs if and only if this set is not a singleton for some value of the final magnetization a detailed description of the possible scenarios of bifurcation is given leading to a full characterization of passages from gibbs to non gibbs and vice versa with sharp transition times under the dynamics gibbsianness can be lost and can be recovered our analysis expands the work of ermolaev and kulske 7 who considered zero mag netic field and finite temperature spin flip dynamics we consider both zero and non zero magnetic field but restricted to infinite temperature spin flip dynamics our results re veal an interesting dependence on the interaction parameters including the presence of forbidden regions for the optimal trajectories and the possible occurrence of overshoots and undershoots in the optimal trajectories the numerical plots provided are obtained with the help of mathematica

uniform difference method for singularly perturbed volterra integro differential equations singularly perturbed volterra integro differential equations is considered an exponentially fitted difference scheme is constructed in a uniform mesh which gives first order uniform convergence in the discrete maximum norm numerical experiments support the theoretical results

tension spline collocation methods for singularly perturbed volterra integro differential and volterra integral equations we consider the numerical discretization of singularly perturbed volterra integro differential equations vide y t q1 t q2 t y t 0t k t s y s ds t i 0 t y 0 y0 and volterra integral equations vie y t g t 0t k t s y s ds t i by tension spline collocation methods in certain tension spline spaces where is a small parameter satisfying 0 1 and ql q2 g and k are functions sufficiently smooth on their domains to ensure that eqs and posses a unique solution we give an analysis of the global convergence properties of a new tension spline collocation solution for 0 1 for singularly perturbed vide and vie thus extending the existing theory for 1 to the singularly perturbed case

an efficient dynamical systems method for solving singularly perturbed integral equations with noise in this paper we apply the dynamical systems method dsm proposed by a g ramm and the variational regularization method vrm to obtain numerical solution to some singularly perturbed ill posed problems contaminated by noise the results obtained by these methods are compared to the exact solution for the model problems it is found that the dynamical systems method is preferable because it is easier to apply highly stable robust and it always converges to the solution even for large size models

hamiltonian and lagrangian for the trajectory of the empirical distribution and the empirical measure of markov processes we compute the hamiltonian and lagrangian associated to the large deviations of the trajectory of the empirical distribution for independent markov processes and of the empirical measure for translation invariant interacting markov processes we treat both the case of jump processes continuous time markov chains and interacting particle systems as well as diffusion processes for diffusion processes the lagrangian is a quadratic form of the deviation of the trajectory from the solution of the kolmogorov forward equation in all cases the lagrangian can be interpreted as a relative entropy or relative entropy density per unit time

an unsplit 3d upwind method for hyperbolic conservation laws abstract an unsplit upwind method for solving hyperbolic conservation laws in three dimensions is developed this paper derives the algorithm by generalizing a two dimensional advection algorithm of van leer and colella to three dimensions and then making appropriate modifications the method is implemented using the equations of gas dynamics several test problems are computed to both verify and display the behavior of the method these test problems include a 1d blast wave a 2d shock reflection off a 30 ramp and a 3d astrophysical jet

coercive singular perturbations ii reduction and convergence general coercive singular perturbations are reduced to regular ones using an algebra of singularly perturbed wiener hopf type operators high order asymptotic formulae also for non smooth data are indicated and sharp error estimates are established

interfaces and typical gibbs configurations for one dimensional kac potentials we consider a one dimensional ising spin system with a ferromagnetic kac potential j r j having compact support we study the system in the limit 0 below the lebowitz penrose critical temperature where there are two distinct thermodynamic phases with different magnetizations we prove that the empirical spin average in blocks of size 1 for any positive converges as 0 to one of the two thermodynamic magnetizations uniformly in the intervals of size p for any given positivep 1 we then show that the intervals where the magnetization is approximately constant have lengths of the order of exp c 1 c 0 and that when normalized they converge to independent variables with exponential distribution we show this by proving large deviation estimates and applying the ventsel and friedlin methods to gibbs random fields finally if the temperature is low enough we characterize the interface namely the typical magnetization pattern in the region connecting the two phases

iterative and non iterative methods for non linear volterra integro differential equations iterative and non iterative methods for the solution of nonlinear volterra integro differential equations are presented and their local convergence is proved the iterative methods provide a sequence solution and make use of fixed point theory whereas the non iterative ones result in series solutions and also make use of fixed point principles by means of integration by parts and use of certain integral identities it is shown that the initial conditions that appear in the iterative methods presented here can be eliminated and the resulting iterative technique is identical to the variational iteration method which is derived here without making any use at all of lagrange multipliers and constrained variations it is also shown that the formulation presented here can be applied to initial value problems in ordinary differential volterra s integral and integro differential pantograph and nonlinear and linear algebraic equations a technique for improving accelerating the convergence of the iterative methods presented here is also presented and results in a lipschitz constant that may be varied as the iteration progresses it is shown that this acceleration technique is related to preconditioning methods for the solution of linear algebraic equations it is also argued that the non iterative methods presented in this paper may not competitive with iterative ones because of possible cancellation errors if implemented numerically an analytical continuation procedure based on dividing the interval of integration into disjoint subintervals is also presented and its limitations are discussed

piecewise quasilinearization techniques for singularly perturbed volterra integro differential equations abstract three families of iterative quasilinear methods for the numerical solution of singularly perturbed volterra integro differential equations are presented two of these methods are based on the piecewise integration of the differential equations and the use of quadrature rules while the third one employs a locally frozen approximation for the coefficients and right hand side of the differential equation it is shown that these quasilinear methods are first order accurate for step sizes equal to or larger than the initial layer thickness and are less accurate than exponentially fitted techniques whose coefficients are selected so that the finite difference equations have truncation errors of second and third order even though they exhibit only first order accuracy for initial layer thicknesses equal to or smaller than the step size it is also shown that the quasilinear methods presented in this paper are of exponential type and provide more accurate results than the backward euler and trapezoidal methods for step sizes larger than the initial layer thickness and the quasilinear frozen method is less accurate than quasilinear techniques that make use of an integrating factor and numerical quadratures

a critical comparison of eulerian grid based vlasov solvers a common problem with direct vlasov solvers is ensuring that the distribution function remains positive a related problem is to guarantee that the numerical scheme does not introduce false oscillations in velocity space in this paper we use a variety of schemes to assess the importance of these issues and to determine an optimal strategy for eulerian split approaches to vlasov solvers from these tests we conclude that maintaining positivity is less important than correctly dissipating the fine scale structure which arises naturally in the solution to many vlasov problems furthermore we show that there are distinct advantages to using high order schemes i e third order rather than second a natural choice which satisfies all of these requirements is the piecewise parabolic method ppm which is applied here to vlasov s equation for the first time

the p stability of backward differentiation method for singularly perturbed volterra integral equations with delay argument backward differentiation formulas are used for numerical solution of singularly perturbed volterra integral equations with delay argument dsvies in particular the p stability analysis of method is considered

singularly perturbed integral equations we study singularly perturbed fredholm equations of the second kind we give sufficient conditions for existence and uniqueness of solutions and describe the asymptotic behavior of the solutions we examine the relationship between the solutions of the perturbed and unperturbed equations exhibiting the degeneration of the boundary layer to delta functions the results are applied to several examples including the volterra equations

on the gaussian fluctuations of the critical curie weiss model in statistical mechanics it has been known for some time that the fluctuations of the curie weiss mean field model of ferromagnetism are non gaussian at the critical temperature here we establish the presence of a substantial gaussian element in the critical model by showing that the internal fluctuations i e the fluctuations within the fluctuating field are gaussian we show for instance that as the number n of sites increases to infinity the system with the appropriate space and spin scalings behaves asymptotically as a brownian motion with randomised drift and that the distribution of the drift has the non gaussian form familiar in this theory with the more conventional space scaling 1 n it is known that the system degenerates asymptotically to a straight line with random slope we prove here that the error from the straight line when appropriately amplified converges in distribution to a brownian bridge

outflow boundary conditions for the fourier transformed three dimensional vlasov maxwell system a problem with the solution of the vlasov equation is its tendency to become filamented oscillatory in velocity space which in numerical simulations can give rise to unphysical oscillations and recurrence effects we present a three dimensional vlasov maxwell solver three spatial and velocity dimensions plus time in which the vlasov equation is fourier transformed in velocity space and the resulting equations solved numerically by designing absorbing outflow boundary conditions in the fourier transformed velocity space the highest fourier modes in velocity space are removed from the numerical solution this introduces a dissipative effect in velocity space and the numerical recurrence effect is strongly reduced the well posedness of the boundary conditions is proved analytically while the stability of the numerical implementation is assessed by long time numerical simulations well known wave modes in magnetized plasmas are shown to be reproduced by the numerical scheme

spin flip dynamics of the curie weiss model loss of gibbsianness with possibly broken symmetry we study the conditional probabilities of the curie weiss ising model in vanishing external field under a symmetric independent stochastic spin flip dynamics and discuss their set of points of discontinuity bad points we exhibit a complete analysis of the transition between gibbsian and non gibbsian behavior as a function of time extending the results for the corresponding lattice model where only partial answers can be obtained for initial temperature beta 1 geq 1 we prove that the time evolved measure is always gibbsian for frac 2 3 leq beta 1 1 the time evolved measure loses its gibbsian character at a sharp transition time for beta 1 frac 2 3 we observe the new phenomenon of symmetry breaking in the set of points of discontinuity bad points corresponding to non zero spin average appear at a sharp transition time and give rise to biased non gibbsianness of the time evolved measure these bad points become neutral at a later transition time while the measure stays non gibbs in our proof we give a detailed description of the phase diagram of a curie weiss random field ising model with possibly non symmetric random field distribution based on bifurcation analysis

quadratic approximation of solutions for boundary value problems with nonlocal boundary conditions in this paper using the quasilinearization method coupled with the method of upper and lower solutions we study a class of second order nonlinear boundary value problems with nonlocal boundary conditions we establish some sufficient conditions under which corresponding monotone sequences converge uniformly and quadratically to the unique solution of the problem an example is also included to illustrate the main result

solving volterra integro differential equations by variable stepsize block bs methods properties and implementation techniques in this article block bs methods are considered for the numerical solution of volterra integro differential equations vides convergence and stability properties are analyzed a new matlab code for the solution of vides called videbs is presented numerical results using a variable stepsize implementation show the effectiveness of the proposed code

large deviation estimates for a conditional probability distribution applications to random interaction gibbs measures let x i y i d be independent identically distributed random variables with arbitrary distribution we show that for almost every y i i the conditional law of the empirical field given y i i satisfies to large deviation inequalities this applies to the study of gibbs measures with random interaction in the case of some mean field models as well as of short range summable interaction we show that the pressure is nonrandom and is given by a variational formula these random gibbs measures have the same large deviation rate which does not depend on the particular realization of the interaction their local behaviour is described in terms of conditional probabilities given the interaction of solutions to the variational formula