classical to critical crossovers from field theory we extend our previous determinations of nonasymptotic critical behavior of phys rev b 32 7209 1985 and 35 3585 1987 to accurate expressions of the complete classical to critical crossover in three dimensional field theory in terms of the temperaturelike scaling field i e along the critical isochore for 1 the correlation length the susceptibility and the specific heat in the homogeneous phase for the n vector model n 1 to 3 and 2 the spontaneous magnetization coexistence curve the susceptibility and the specific heat in the inhomogeneous phase for the ising model n 1 the present calculations include the seventh loop order of murray and nickel and closely account for the up to date estimates of universal asymptotic critical quantities exponents and amplitude combinations provided by guida and zinn justin j phys a 31 8103 1998

decreasing and fast solutions for a second order difference equation related to fisher kolmogorov s equation abstract we prove the existence of so called fast solutions of a second order difference equation related to traveling wave solutions of fisher kolmogorov s equation variational approach is used and the fast solutions are obtained as minimizers of an energy functional on a weighted hilbert space numerical experiments are presented

master crossover functions for one component fluids by introducing three well defined dimensionless numbers we establish the link between the scale dilatation method able to estimate master i e unique singular behaviors of the one component fluid subclass and the universal crossover functions recently estimated garrabos and bervillier phys rev e 74 021113 2006 from the bounded results of the massive renormalization scheme applied to the ensuremath phi d 4 n model of scalar order parameter n 1 and three dimensions d 3 representative of the ising like universality class the master i e rescaled crossover functions are then able to fit the singular behaviors of any one component fluid without adjustable parameter using only one critical energy scale factor one critical length scale factor and two dimensionless asymptotic scale factors which characterize the fluid critical interaction cell at its liquid gas critical point an additional adjustable parameter accounts for quantum effects in light fluids at the critical temperature the effective extension of the thermal field range along the critical isochore where the master crossover functions seems to be valid corresponds to a correlation length greater than three times the effective range of the microscopic short range molecular interaction

reaction diffusion equations in one dimension particular solutions and relaxation abstract reaction diffusion equations for the concentration of one species in one spatial dimension are considered where the diffusion coefficient as well as creation and annihilation terms are monomials when the exponent of the annihilation term is smaller than the one of the creation term unstable equilibrium solutions may exist in the opposite case travelling wave solutions are found in phase space yielding the value of speed even when the wave form cannot be written in closed form the stability of some solutions is studied numerically showing their robustness in the case of nonlinear diffusion it is found that localized initial conditions evolve to the stable steady state via the travelling waves the invasion of the stable state into the unstable one is via a travelling front with the largest possible gradient this front can be interpreted as the final result of the growth of the most unstable mode the exact solutions allow a modulation approach to study the problem with slowly varying coefficients it is shown that when the creation term is of compact support in space equilibria of compact support are also obtained

te tm scheme for computation of electromagnetic fields in accelerators we propose a new two level economical conservative scheme for short range wake field calculation in three dimensions the scheme does not have dispersion in the longitudinal direction and is staircase free second order convergent unlike the finite difference time domain method fdtd it is based on a te tm like splitting of the field components in time additionally it uses an enhanced alternating direction splitting of the transverse space operator that makes the scheme computationally as effective as the conventional fdtd method unlike the fdtd adi and low order strang methods the splitting error in our scheme is only of fourth order as numerical examples show the new scheme is much more accurate on the long time scale than the conventional fdtd approach

a 3 d enlarged cell technique ect for the conformal fdtd method in this paper we present an enlarged cell technique ect to avoid the time step reduction encountered in the conformal finite difference time domain cfdtd method due to small irregular cells truncated by metallic boundaries we focus our efforts on the discussion of the accuracy and stability of the ect and its comparison with other conformal methods especially the one called the uniformly stable conformal usc method we also provide a simplified ect which is much easier to implement in the ect a stability criterion is first constructed to identify instable irregular cells i e those having so small an area to cause instability those instable cells are then enlarged into their adjacent cells to obtain a large stable area careful treatment is performed on the communication between the intruding and intruded cells in terms of electromotive force by keeping the total electromotive force conservative this technique is verified by several 3 d numerical experiments results show that the ect is second order accurate and numerically stable at the regular courant time step limit

critical crossover functions for simple fluids non analytical scaling determination of the ising like crossover parameter a non analytical scaling determination of the ising like crossover parameter is proposed considering the critical isochore of a simple fluid at finite distance from its critical temperature the mean crossover functions estimated from the bounded results of the massive renormalization scheme in field theory applied to the left phi 2 right d 2 left n right model in three dimensions d 3 and scalar order parameter n 1 are used to formulate the corresponding scaling equations valid in two well defined temperature ranges from the critical temperature the validity range and the ising like nature of the corresponding crossover description are discussed in terms of a single ising like scale factor characterizing the critical isochore the asymptotic value of this scale factor can be predicted within the ising like preasymptotic domain unfortunately the absence of precise experimental data in such a close vicinity of the critical point leads the direct testing impossible a contrario from our scaling equations and the use of precise measurements performed at finite distance from the critical point its local value can be estimated beyond the ising like preasymptotic domain this non analytical scaling determination only needs to make reference to the universal features estimated from the mean crossover functions and to introduce a single master dimensionless length common to all the simple fluids this latter parameter guaranties the uniqueness of the physical length unit used for the theoretical crossover functions and the fluid singular properties when the generalized critical coordinates of the vapor liquid critical point of each fluid are known xenon case along its critical isochore is considered as a typical example to demonstrate the singleness of the ising like crossover parameter with the measurements at finite temperature range of the effective singular behaviors of the isothermal compressibility in the homogeneous domain and the vapor liquid coexisting densities in the non homogeneous domain our scaling equations provide the local estimate of this crossover parameter as a function of the temperature distance from the critical temperature our results compare favorably with the single asymptotic value calculated only using four critical coordinates of xenon

locally conformal fdtd for anisotropic conductive interfaces locally conformal discretizations have been developed for the finite difference time domain fdtd method to mitigate staircasing errors that arise in the modeling of arbitrary e g curved slanted interfaces by regular orthogonal grids in particular locally conformal algorithms based on the computation of effective material parameters in partially filled fdtd cells are attractive because they are simple to implement and maintain the basic conditional stability of fdtd with only minor changes on the courant limit in this paper we propose a new locally conformal implementation for fdtd tailored for anisotropic conductive interfaces instead of employing arithmetic or geometrical averages we invoke the quasi static relationship between the current density and the electric field to derive the effective conductivities of partially filled fdtd cells

existence and convergence to a propagating terrace in one dimensional reaction diffusion equations we consider one dimensional reaction diffusion equations for a large class of spatially periodic nonlinearities including multistable ones and study the asymptotic behavior of solutions with heaviside type initial data our analysis reveals some new dynamics where the profile of the propagation is not characterized by a single front but by a layer of several fronts which we call a terrace existence and convergence to such a terrace is proven by using an intersection number argument without much relying on standard linear analysis hence on top of the peculiar phenomenon of propagation that our work highlights several corollaries will follow on the existence and convergence to pulsating traveling fronts even for highly degenerate nonlinearities that have not been treated before

development of a novel fdtd 2 4 compatible conformal scheme for electromagnetic computations of complex curved pec objects we present a modified fourth order finite difference time domain fdtd 2 4 conformal scheme for accurately computing electromagnetic characteristics of some complex three dimensional 3d perfectly conducting pec objects it has higher accuracy and efficiency than those of conventional fdtd and fdtd 2 4 methods as coarse meshes are employed with staircase errors reduced effectively during its implementation two integration loops of the faraday s law are used for updating magnetic field components while the updating equations of electric field ones are the same as those in the normal fdtd method a rigorous analysis of its global stability based on the conventional high order fdtd stability criterion and the fourier method is also performed in order to obtain stable and accurate numerical results a user defined geometric precision technique which gives a criterion for determining the time step is employed for our computations it is numerically demonstrated that using our proposed fdtd 2 4 compatible conformal scheme high accuracy and low dispersion errors can be achieved for fast predicting radar cross sections as well as induced current distribution of some complex 3 d structures

master singular behavior for the sugden factor of one component fluids near their gas liquid critical point we present the master i e unique behavior of the squared capillary length the so called sugden factor as a function of the temperaturelike field along the critical isochore asymptotically close to the gas liquid critical point of about twenty one component fluids this master behavior is obtained using the scale dilatation of the relevant physical fields of the one component fluids the scale dilatation method introduces the fluid dependent scale factors in a manner analog to the linear relations between physical fields and scaling fields needed by the renormalization theory applied to any physical system belonging to the ising like universality class the master behavior for the sugden factor satisfies hyperscaling it can be asymptotically fitted by the leading terms of the theoretical crossover functions for the correlation length and the susceptibility in the homogeneous domain recently obtained from massive renormalization in field theory in the absence of corresponding estimation of the theoretical crossover functions for the interfacial tension we define the range of the temperaturelike field where the master leading power law can be practically used to predict the singular behavior of the sugden factor in conformity with the theoretical description provided by the massive renormalization scheme within the extended asymptotic domain of the one component fluid subclass

finite difference time domain modeling of curved surfaces em scattering the finite difference time domain fdtd method is generalized to include the accurate modeling of curved surfaces this generalization the contour path cp method accurately models the illumination of bodies with curved surfaces yet retains the ability to model corners and edges cp modeling of two dimensional electromagnetic wave scattering from objects of various shapes and compositions is presented

existence of traveling waves of invasion for ginzburg landau type problems in infinite cylinders we study a class of systems of reaction diffusion equations in infinite cylinders which arise within the context of ginzburg landau theories and describe the kinetics of phase transformation in second order or weakly first order phase transitions with non conserved order parameters we use a variational characterization to study the existence of a special class of traveling wave solutions which are characterized by a fast exponential decay in the direction of propagation our main result is a simple verifiable criterion for existence of these traveling waves under the very general assumptions of non linearities we also prove boundedness regularity and some other properties of the obtained solutions as well as several sufficient conditions for existence or non existence of such traveling waves and give rigorous upper and lower bounds for their speed in addition we prove that the speed of the obtained solutions gives a sharp upper bound for the propagation speed of a class of disturbances which are initially sufficiently localized we give a sample application of our results using a computer assisted approach

a fast multigrid based electromagnetic eigensolver for curved metal boundaries on the yee mesh for embedded boundary electromagnetics using the dey mittra dey and mittra 1997 1 algorithm a special grad div matrix constructed in this work allows use of multigrid methods for efficient inversion of maxwell s curl curl matrix efficient curl curl inversions are demonstrated within a shift and invert krylov subspace eigensolver open sourced at ofortt https github com bauerca maxwell cfortt on the spherical cavity and the 9 cell tesla superconducting accelerator cavity the accuracy of the dey mittra algorithm is also examined frequencies converge with second order error and surface fields are found to converge with nearly second order error in agreement with previous work nieter et al 2009 2 neglecting some boundary cut cell faces as is required in the time domain for numerical stability reduces frequency convergence to first order and surface field convergence to zeroth order i e surface fields do not converge additionally and importantly neglecting faces can reduce accuracy by an order of magnitude at low resolutions

mean crossover functions for uniaxial three dimensional ising like systems we give simple expressions for the mean of the max and min bounds of the critical to classical crossover functions previously calculated bagnuls and bervillier phys rev e 65 066132 2002 within the massive renormalization scheme of the phi d 4 n model in three dimensions d 3 and scalar order parameter n 1 of the ising like universality class the mean functions are determined relying on the properties of the theoretical functions in the two limiting three dimensional 3d ising like and mean field like descriptions close to the wilson fisher fixed point and to the gaussian fixed point respectively such descriptions correspond to the preasymptotic domains near each fixed point where a wegner expansion restricted to two terms leading and first confluent terms is valid the ising like preasymptotic domain description includes the correlations between parameters due to the error bar determination of the exponents and amplitude combinations very close to the wilson fisher fixed point adding the equivalent description of the mean field preasymptotic domain close to the gaussian fixed point leads to define each mean crossover function with three calculated parameters fixing a unique value of one parameter whatever the selected mean crossover function we use this parameter as a relative sensor to estimate the dominant nature either ising like critical or mean field like classical of the crossover behavior finally we obtain an explicit criterion to measure the extension of the ising like preasymptotic domain which can then permit to coherently account for measurements performed in systems where the asymptotical approach to the critical point remains finite using a well controlled number of system dependent parameters like in the subclass of one component fluids

fast solutions and asymptotic behavior in a reaction diffusion equation abstract in this paper we deal with the existence of traveling waves solutions t w s for the reaction diffusion equation u t u x x f u in a very general setting of reaction terms f with two distinguished stationary states say 0 and 1 we link the existence of some type of solutions of the second order ode u c u f u 0 with the existence of fast t w s by defining fast solutions for this ode we find a value c m 0 related to the existence of global fast solutions and determine c m through a variational formula our results allow us particularly to show that any solution u x t of the reaction diffusion equation with compactly supported initial data and 0 u x 0 1 x r satisfies lim t u x c t t 0 uniformly on compact sets for all c c c m finally we connect c m with the minimum speed of propagation of all t w s c

critical exponents of the n vector model recently the series for two renormalization group functions corresponding to the anomalous dimensions of the fields and of the three dimensional field theory have been extended to next order seven loops by murray and nickel we examine the influence of these additional terms on the estimates of critical exponents of the n vector model using some new ideas in the context of the borel summation techniques the estimates have slightly changed but remain within the errors of the previous evaluation exponents such as related to the field anomalous dimension which were poorly determined in the previous evaluation of le guillou zinn justin have seen their apparent errors significantly decrease more importantly perhaps summation errors are better determined the change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values finally because an error has been discovered in the last order of the published expansions order we have also re analysed the determination of exponents from the expansion the conclusion is that the general agreement between expansion and three dimensional series has improved with respect to le guillou zinn justin

conformal fdtd modeling of imperfect conductors at millimeter wave bands the dey mittra conformal finite difference time domain cfdtd algorithm for perfect electrical conductors is modified for the analysis of finite conductivity conductors at millimeter wave frequencies formulas are derived for cfdtd coefficients using voltage state variables and a constant surface impedance boundary condition sibc the approach permits a fast implementation suitable for cuda type gpu hardware accuracy and stability are investigated with respect to the stability constraints on intersection areas introduced by dey mittra and benkler as well as the distance stability constraints of zagorodnov that permits 100 courant temporal sampling a relaxation of the zagorodnov distance constraints permits increased accuracy with respect to all alternative area constraints analytic solutions are used to judge the performance of the proposed cfdtd modifications for millimeter wave band applications

critical crossover functions for simple fluids towards the crossover modelling uniqueness based on a single non universal temperature scaling factor present in a simple fluid case a detailed analysis of non universal parameters involved in different critical to classical crossover models is given for the infinite limit of the cutoff wave number a set of three scaling parameters is defined for each model such that it shows all the shapes of the theoretical crossover functions overlap on the mean crossover function shapes close to the non trivial fixed point the analysis of corresponding links between their fluid dependent parameters opens a route to define a parametric model of crossover equation of state closely satisfying the universal features calculated from the ising like limit in the massive renormalization scheme

the finite difference time domain fdtd and the finite volume time domain fvtd methods in solving maxwell s equations the finite difference time domain fdtd and its current generalizations have been demonstrated to be useful and powerful tools for the calculation of the radar cross section rcs of complicated objects the radiation of antennas in the presence of other structures and other applications the mathematical techniques for conformal fdtd have matured the primary impediments to its implementation are the complex geometries and material properties associated with the problem even under these circumstances fdtd is more flexible to implement because it is based on first principles instead of a clever mathematical trick this paper gives an account of some new results on conformal fdtd obtained by the authors and their associates at lockheed martin space company since 1988 the emphasis is on nonsmooth boundary condition simulation

the asymptotic critical wave speed in a family of scalar reaction diffusion equations abstract we study traveling wave solutions for the class of scalar reaction diffusion equations u t 2 u x 2 f m u where the family of potential functions f m is given by f m u 2 u m 1 u for each m 1 real there is a critical wave speed c crit m that separates waves of exponential structure from those which decay only algebraically we derive a rigorous asymptotic expansion for c crit m in the limit as m this expansion also seems to provide a useful approximation to c crit m over a wide range of m values moreover we prove that c crit m is c smooth as a function of m 1 our analysis relies on geometric singular perturbation theory as well as on the blow up technique and confirms the results obtained by means of asymptotic methods in d j needham a n barnes reaction diffusion and phase waves occurring in a class of scalar reaction diffusion equations nonlinearity 12 1 1999 41 58 t p witelski k ono t j kaper critical wave speeds for a family of scalar reaction diffusion equations appl math lett 14 1 2001 65 73

conformal fdtd methods to avoid time step reduction with and without cell enlargement during the last decades there have been considerable efforts to develop accurate and yet simple conformal methods for modelling curved boundaries within the finite difference time domain fdtd algorithm in an earlier publication we proposed the uniformly stable conformal usc approach as a general three dimensional extension of fdtd without the need to reduce the maximum stable time step the main idea of usc is the usage of virtually enlarged cells near to the boundary leading to an increased implementation effort in this paper we review the usc method and introduce a new simple and accurate conformal scheme which does not use such enlarged cells this simplified conformal sc scheme has the same number of operations and algorithmic logic as the standard staircase method and thus is easily realizable in existing fdtd codes like usc it leads to accurate results without time step reduction showing a nearly second order convergence in practice the method is verified and compared to other approaches by means of several numerical 2d and 3d examples

convergent cartesian grid methods for maxwell s equations in complex geometries a convergent second order cartesian grid finite difference scheme for the solution of maxwell s equations is presented the scheme employs a staggered grid in space and represents the physical location of the material and metallic boundaries correctly hence eliminating problems caused by staircasing and contrary to the popular yee scheme enforces the correct jump conditions on the field components across material interfaces a detailed analysis of the accuracy of the new embedding scheme is presented confirming its second order global accuracy furthermore the scheme is proven to be a bounded error scheme and thus convergent conditions for fully discrete stability is furthermore established this enables the derivation of bounds for fully discrete stability with cfl restrictions being almost identical to those of the much simpler yee scheme the analysis exposes that the effects of staircasing as well as a lack of properly enforced jump conditions on the field components have significant consequences for the global accuracy it is among other things shown that for cases in which a field component is discontinuous along a grid line as happens at general two and three dimensional material interfaces the yee scheme may exhibit local divergence and loss of global convergence to validate the analysis several one and two dimensional test cases are presented showing an improvement of typically 1 to 2 orders of accuracy at little or no additional computational cost over the yee scheme which in most cases exhibits first order accuracy c 2001 academic press

long time numerical computation of electromagnetic fields in the vicinity of a relativistic source we propose an implicit scheme for the calculation of electromagnetic fields in the vicinity of short electron bunches moving in a transversally bounded domain as it has place in particle accelerators the scheme is able to accurately model curved boundaries and does not suffer from dispersion in direction of motion it is based on splitting the discrete curl operator in its transversal and longitudinal parts unlike previous conformal schemes the new method has a second order convergence without the need to reduce the maximal stable time step of the conventional staircase approach this feature allows the usage of a moving mesh easily several numerical examples are presented and the algorithm is compared to other approaches