some explicit examples of hamiltonian minimal lagrangian submanifolds in complex space forms abstract in this paper we find some new explicit examples of hamiltonian minimal lagrangian submanifolds among the lagrangian isometric immersions of a real space form in a complex space form

adaptive artificial boundary condition for the two level schrodinger equation with conical crossings in this paper we present an adaptive approach to design the artificial boundary conditions for the two level schrodinger equation with conical crossings on the unbounded domain we use the windowed fourier transform to obtain the local wave number information in the vicinity of artificial boundaries and adopt the operator splitting method to obtain an adaptive local artificial boundary condition then reduce the original problem into an initial boundary value problem on the bounded computational domain which can be solved by the finite difference method by this numerical method we observe the surface hopping phenomena of the two level schrodinger equation with conical crossings several numerical examples are provided to show the accuracy and convergence of the proposed method

an improved domain decomposition method for the 3d helmholtz equation the efficiency of a non overlapping domain decomposition method is strictly related to the transmission operator acting at the interfaces between subdomains a new operator arising from the non reflecting boundary conditions theory and a new iteration scheme lead to a dramatic improvement of the performances of the scheme which was originally proposed by bruno despres and which is recalled in the first part of this paper the convergence of the new method is proved and some numerical results show the comparison of the performances

second variation and stabilities of minimal lagrangian submanifolds in kahler manifolds first we derive a new second variation formula which holds for any minimal lagrangian submanifold in k ihler manifolds using this we prove that any minimal lagrangian submanifold in kfihler manifolds with nonpositive chern class is stable we also prove that in kfihler manifolds with positive chern class any stable minimal lagrangian submanifold l satisfies that h l 0 next we introduce the notion of hamiltonian stability either local or global of minimal lagrangian submanifolds in einstein kfihler manifolds using our second variation formula we find a general criterion for the local hamiltonian stability for minimal lagrangian submanifolds in einstein k ihler manifolds this criterion is satisfied for all real forms which are einstein of irreducible hermitian symmetric spaces e g the cannonical rp c cp it is also satisfied by the clifford torus t c cp

asymptotic boundary conditions for dissipative waves general theory an outstanding issue in the computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges employing the method of steepest descents dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators the existence of a small number of dominant wave groups may be expected for systems with dissipation estimates of the error as a function of domain size are derived under general hypotheses leading to convergence results some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed

weak ill posedness of spatial discretizations of absorbing boundary conditions for schrodinger type equations when we wish to solve numerically a differential problem defined on an infinite domain it is necessary to consider a finite subdomain and to use artificial boundary conditions in such a way that the solutions in the finite subdomain approximate the original solution these boundary conditions are called absorbing when small reflections to the interior domain are allowed in this paper we develop a general class of absorbing boundary conditions for schrodinger type equations by using rational approximations to the transparent boundary conditions with this approach previous absorbing boundary conditions in the literature are included in this class we use the method of lines for the discretization of the initial boundary value problems obtained this way we show that the ordinary differential systems that arise after the spatial discretization are weakly ill posed explaining a previous conjecture of fevens and jiang the time discretization is carried out with a stable runge kutta methods where the high order ones may be used to compensate for the possible troubles present in the problems semidiscretized in space

elicitation strategies for soft constraint problems with missing preferences properties algorithms and experimental studies we consider soft constraint problems where some of the preferences may be unspecified this models for example settings where agents are distributed and have privacy issues or where there is an ongoing preference elicitation process in this context we study how to find an optimal solution without having to wait for all the preferences in particular we define algorithms that interleave search and preference elicitation to find a solution which is necessarily optimal that is optimal no matter what the missing data will be with the aim to ask the user to reveal as few preferences as possible we define a combined solving and preference elicitation scheme with a large number of different instantiations each corresponding to a concrete algorithm which we compare experimentally we compute both the number of elicited preferences and the user effort which may be larger as it contains all the preference values the user has to compute to be able to respond to the elicitation requests while the number of elicited preferences is important when the concern is to communicate as little information as possible the user effort measures also the hidden work the user has to do to be able to communicate the elicited preferences our experimental results on classical fuzzy weighted and temporal incomplete csps show that some of our algorithms are very good at finding a necessarily optimal solution while asking the user for only a very small fraction of the missing preferences the user effort is also very small for the best algorithms

efficient thermal field computation in phase field models we solve the phase field equations in two dimensions to simulate crystal growth in the low undercooling regime the novelty is the use of a fast solver for the free space heat equation to compute the thermal field this solver is based on the efficient direct evaluation of the integral representation of the solution to the constant coefficient free space heat equation with a smooth source term the computational cost and memory requirements of the new solver are reasonable and no artificial boundary conditions are needed this allows one to solve for the thermal field in a computational domain whose size depends only on the size of the growing crystal and not on the extent of the thermal field which can result in significant computational savings in the low undercooling regime

determining anisotropic real analytic conductivities by boundary measurements if an electrical potential is applied to the surface of a solid body the current flux across the surface depends on the conductivity in the interior of the body we want to consider the inverse problem of determining the conductivity by these boundary measurements

warped product decompositions of real space forms and hamiltonian stationary lagrangian submanifolds abstract a lagrangian submanifold of a kaehler manifold is said to be hamiltonian stationary or h stationary for short if it is a critical point of the area functional restricted to compactly supported hamiltonian variations in this article we present some simple relationship between warped product decompositions of real space forms and hamiltonian stationary lagrangian submanifolds we completely classify h stationary lagrangian submanifolds in complex space forms arisen from warped product decompositions more precisely we prove that there exist two such families of h stationary lagrangian submanifolds in c n two families in c p n and twenty one families in c h n as immediate by product we obtain many new families of hamiltonian stationary lagrangian submanifolds in complex space forms

perfectly matched layers for the heat and advection diffusion equations we design a perfectly matched layer for the advection diffusion equation we show that the reflection coefficient is exponentially small with respect to the damping parameter and the width of the pml and this independently of the advection and of the viscosity numerical tests assess the efficiency of the approach

hamiltonian stationary tori in the complex projective plane hamiltonian stationary lagrangian surfaces are lagrangian surfaces in a four dimensional kahler manifold which are critical points of the area functional for hamiltonian infinitesimal deformations in this paper we analyze these surfaces in the complex projective plane in a previous work we showed that they correspond locally to solutions to an integrable system formulated as a zero curvature on a twisted loop group here we give an alternative formulation using non twisted loop groups and as an application we show in detail why hamiltonian stationary lagrangian tori are finite type solutions and eventually describe the simplest of them the homogeneous ones

artificial boundary conditions for the linear advection diffusion equation a family of artificial boundary conditions for the linear advection diffusion equation with small viscosity is developed well posedness for the associated initial boundary value problem is analyzed the error produced by truncating the domain is estimated numerical results are presented 1 introduction when computing the solution of a partial differential equation in an unbounded domain one often introduces artificial boundaries in order to limit the computational cost these boundaries must be chosen not too far from the domain of interest therefore the boundary conditions must be good approxima tions to the so called transparent i boundary condition i e such ithat the solution of the problem in the bounded domain is equal to the solution in the original domain the transparent boundary condition is usually an integral relation in time and space between u and its normal derivative on the boundary which makes it impractical from a numerical point of view one must approximate this relation to get local boundary conditions they are often called absorbing or artificial boundary conditions this question is of crucial interest in such different areas as geophysics plasma physics fluid dynamics 1 2 3 and the use of such conditions is now classical in geophysics our interest for the linear advection diffusion equation comes from the navier stokes equation but it arises also in other fields as for example meteorology 6 the incompressible navier stokes equation can be written as

artificial boundary conditions for diffusion equations numerical study abstract recently in 3 a new method has been presented providing a family of artificial boundary conditions for parabolic equations which are local in time and stable this method applies to variable coefficients and curved boundaries but unfortunately there are no error estimates as an alternative we present in this paper numerical simulations showing the efficiency of the method the construction of the artificial boundary conditions depends on the number and values of points at which z 1 2 is interpolated by rational fractions in the complex plane particular attention is paid to the choice of those points

on the numerical solution of the heat equation i we describe a fast solver for the inhomogeneous heat equation in free space following the time evolution of the solution in the fourier domain it relies on a recently developed spectral approximation of the free space heat kernel coupled with the non uniform fast fourier transform unlike finite difference and finite element techniques there is no need for artificial boundary conditions on a finite computational domain the method is explicit unconditionally stable and requires an amount of work of the order o nm log n where n is the number of discretization points in physical space and m is the number of time steps we refer to the approach as the fast recursive marching frm method

absorbing boundary conditions for relativistic quantum mechanics equations this paper is devoted to the derivation of absorbing boundary conditions for the klein gordon and dirac equations modeling quantum and relativistic particles subject to classical electromagnetic fields microlocal analysis is the main ingredient in the derivation of these boundary conditions which are obtained in the form of pseudo differential equations basic numerical schemes are derived and analyzed to illustrate the accuracy of the derived boundary conditions

an analysis of schwarz waveform relaxation domain decomposition methods for the imaginary time linear schrodinger and gross pitaevskii equations the aim of this paper is to derive and numerically validate some asymptotic estimates of the convergence rate of classical and quasi optimal schwarz waveform relaxation swr domain decomposition methods applied to the computation of the stationary states of the one dimensional linear and nonlinear schrodinger equations with a space dependent potential although swr methods are currently used for efficiently solving high dimensional partial differential equations their convergence analysis and most particularly obtaining expressions of their convergence rate remains largely open even in one dimension except in simple cases in this work we tackle this problem for linear and nonlinear one dimensional schrodinger equations by developing techniques which can be extended to higher dimensional problems and other types of pdes the approach combines the method developed in gander and halpern siam j num anal 45 2 666 697 2007 for the linear advection reaction diffusion equation and the theory of inhomogeneous pseudodifferential operators in conjunction with the associated symbolic asymptotic expansions for computing the stationary states we consider the imaginary time formulation of the schrodinger equation based on the normalized gradient flow ngf method and use a semi implicit euler scheme for the discretization some numerical results in the one dimensional case illustrate the analysis for both the linear schrodinger and gross pitaevskii equations

hamiltonian stationary lagrangian surfaces of constant curvature e in complex space form m2 4e abstract a lagrangian surface in a kaehler manifold is called hamiltonian stationary if it is a critical point of the area functional restricted to compactly supported hamiltonian variations in the first part of this article we study the traveling wave solutions of an over determined pde system arising from a study of hamiltonian stationary lagrangian surfaces of constant curvature e in a complex space form m 2 4 e then by applying the traveling wave solutions we construct families of type ii hamiltonian stationary lagrangian surfaces of constant curvature e in complex space forms m 2 4 e via an effective method of b y chen f dillen l verstraelen and l vrancken lagrangian isometric immersions of a real space form m n c into a complex space form m n 4 c math proc cambridge philo soc 124 1998 107 125 in the second part we are able to completely solve the over determined pde system for the case e 0 and to determine their corresponding hamiltonian stationary lagrangian surfaces as an immediate by product some interesting new families of hamiltonian stationary lagrangian surfaces of constant curvature are obtained

artificial conditions for the linear elasticity equations in this paper we consider the equations of linear elasticity in an exterior domain we exhibit artificial boundary conditions on a circle which lead to a non coercive second order boundary value problem in the particular case of an axisymmetric geometry explicit computations can be performed in fourier series proving the well posedness except for a countable set of parameters a perturbation argument allows to consider near circular domains we complete the analysis by some numerical simulations

absorbing boundary conditions for diffusion equations summary we construct and analyse a family of absorbing boundary conditions for diffusion equations with variable coefficients curved artifical boundary and arbitrary convection it relies on the geometric identification of the dirichlet to neumann map and rational interpolation of z 1 2 in the complex plane the boundary conditions are stable accurate and practical for computations

frozen gaussian approximation based domain decomposition methods for the linear schrodinger equation beyond the semi classical regime the paper is devoted to develop efficient domain decomposition methods for the linear schrodinger equation beyond the semiclassical regime which does not carry a small enough rescaled planck constant for asymptotic methods e g geometric optics to produce a good accuracy but which is too computationally expensive if direct methods e g finite difference are applied this belongs to the category of computing middle frequency wave propagation where neither asymptotic nor direct methods can be directly used with both efficiency and accuracy motivated by recent works of the authors on absorbing boundary conditions antoine et al 2014 13 and yang and zhang 2014 43 we introduce semiclassical schwarz waveform relaxation methods sswr which are seamless integrations of semiclassical approximation to schwarz waveform relaxation methods two versions are proposed respectively based on herman kluk propagation and geometric optics and we prove the convergence and provide numerical evidence of efficiency and accuracy of these methods

classification of hamiltonian stationary lagrangian submanifolds of constant curvature in cp3 with positive relative nullity abstract a lagrangian submanifold in a kaehler manifold is said to be hamiltonian stationary if it is a critical point of the area functional restricted to compactly supported hamiltonian variations in this paper we classify hamiltonian stationary lagrangian submanifolds of constant curvature in cp 3 with positive relative nullity as an immediate by product several explicit new families of hamiltonian stationary lagrangian submanifolds in cp 3 are obtained

dirichlet to neumann map for domains with corners and approximate boundary conditions we present in this paper the dirichlet to neumann operator for the wave equation on a straight wedge in r 2 using fourier integral operators as a consequence we recover the classical approximate boundary conditions of orders 1 and 2

adaptive absorbing boundary conditions for schrodinger type equations application to nonlinear and multi dimensional problems we propose an adaptive approach in picking the wave number parameter of absorbing boundary conditions for schrodinger type equations based on the gabor transform which captures local frequency information in the vicinity of artificial boundaries the parameter is determined by an energy weighted method and yields a quasi optimal absorbing boundary conditions it is shown that this approach can minimize reflected waves even when the wave function is composed of waves with different group velocities we also extend the split local absorbing boundary slab method z xu h han phys rev e 74 2006 037704 to problems in multi dimensional nonlinear cases by coupling the adaptive approach numerical examples of nonlinear schrodinger equations in one and two dimensions are presented to demonstrate the properties of the discussed absorbing boundary conditions