the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

the structure and analysis of spherical time dependent processes the class of all spherical processes is investigated irrespective of moments properties of these processes are studied including their structure representations and linear and nonlinear spaces a basic representation is x t a 1 2 y t t in t where ais nonnegative and y t is gaussian time series analysesnot requiring moments are set forth in both the time and frequency domains including spectral analysis solutions of forecasting problems are found to be linear when the process is spherical with the property that errors of the optimal forecasts are stochasticalay most concentrated about zero these developments apply to the alpha sub gaussian processes and are advanced for use with certain heavy tailed processes arising in economics engineering and the physical sciences

on similarity solutions of zabolotskaya khokhlov equation abstract the new closed form solutions of the 2 1 dimensional zabolotskaya khokhlov equation are constructed by using the similarity transformations method via lie group theory the zabolotskaya khokhlov equation has been reduced into a new partial differential equation with smaller number of independent variables further using the similarity transformations method the new partial differential equation is reduced into an ordinary differential equation the ordinary differential equation provides semi analytical solutions elastic behaviour of multisolitons and dromion annihilation of solutions are analyzed physically through their evolutional profiles

skew gaussian random field in this article we introduce the concept of skewness to the gaussian random field theory by defining a new two dimensional non gaussian random field called skew gaussian random field we derive the expected euler characteristic of its excursion set moreover an approximation to the size distribution of one connected component is derived as an illustration we present a simulation study to compare the approximation mechanism with the exact one

canonical detection in spherically invariant noise the paper deals with the detection of signals with unknown parameters in impulsive noise modeled as a spherically symmetric random process the proposed model subsumes several interesting families of noise amplitude distributions generalized cauchy generalized laplace generalized gaussian contaminated normal it also allows handling of the case of correlated noise by a whitening approach the generalized maximum likelihood decision strategy is adopted resulting in a canonical detector which is independent of the amplitude distribution of the noise a general method for performance evaluation is outlined and a comprehensive performance analysis is carried out for the case of m ary equal energy orthogonal signals under several distributional assumptions for the noise the performance is contrasted with that of the maximum likelihood receiver for completely known signals so as to assess the loss due to the a priori uncertainty as to the signal parameters

coloring non gaussian sequences we propose a novel method for generating random sequences matching both a target non gaussian distribution and a target autocorrelation in the proposed scheme samples matching the target distribution are drawn independently and then suitably rearranged to match the target autocorrelation our method overcomes the difficulties of the standard method in generating sequences with unknown inverse distribution many examples are included

finite element method for conserved phase fields stress mediated diffusional phase transformation phase field models with conserved phase field variables result in a 4th order evolution partial differential equation pde when coupled with the usual 2nd order thermo mechanics equations such problems require special treatment in the past the finite element method fem has been successfully applied to non conserved phase fields governed by a 2nd order pde for higher order equations the convergence of the standard galerkin fem requires that the interpolation functions belong to a higher continuity class we consider the cahn hilliard phase field model for diffusion controlled solid state phase transformation in binary alloys coupled with elasticity of the solid phases a galerkin finite element formulation is developed with mixed order interpolation c 0 interpolation functions for displacements and c 1 interpolation functions for the phase field variable to demonstrate convergence of the mixed interpolation scheme we first study a one dimensional problem nucleation and growth of the intermediate phase in a thin film diffusion couple with elasticity effects then we study the effects of completeness of c 1 interpolation on parabolic problems in two space dimensions by considering the growth of the intermediate phase in a binary system quadratic convergence expected for conforming elements is achieved for both one and two dimensional systems

an enhanced hybrid method for the simulation of highly skewed non gaussian stochastic fields abstract in this paper an enhanced hybrid method ehm is presented for the simulation of homogeneous non gaussian stochastic fields with prescribed target marginal distribution and spectral density function the presented methodology constitutes an efficient blending of the deodatis micaletti method with a neural network based function approximation precisely the function fitting ability of neural networks based on the resilient back propagation rprop learning algorithm is employed to approximate the unknown underlying gaussian spectrum the resulting algorithm can be successfully applied for simulating narrow banded fields with very large skewness at a fraction of the computing time required by the existing methods its computational efficiency is demonstrated in three numerical examples involving fields that follow the beta and lognormal distributions

a variety of exact travelling wave solutions for the 2 1 dimensional boiti leon pempinelli equation abstract in this paper the 2 1 dimensional boiti leon pempinelli blp equation will be studied the tanh coth method will be used to obtain exact travelling wave solutions for this equation the exp function method will also be applied to the blp equation to derive a new variety of travelling wave solutions with distinct physical structures

group classification for isothermal drift flux model of two phase flows in this paper a full symmetry group classification for isothermal multiphase drift flux model is presented all invariant functions are developed for the lie algebra which play a vital role in construction of optimal systems further with the help of one dimensional optimal classification group invariant solutions are obtained which describe the asymptotic behavior of general solution

exact solutions and conservation laws of 2 1 dimensional boiti leon pempinelli equation in this paper we obtain the symmetry group theorem by using the modified ck s direct method and some new exact solutions of 2 1 dimensional blp equation also we derive the corresponding lie algebra and the conservation laws of blp equation

stochastic differential equations an approach to the generation of continuous non gaussian processes the generation of continuous random processes with jointly specified probability density and covariation functions is considered the proposed approach is based on the interpretation of the simulated process as a stationary output of a nonlinear dynamic system excited by white gaussian noise and described by a system of a first order stochastic differential equations sde the authors explore how the statistical characteristics of the equation s solution depends on the form of its operator and on the intensity of the input noise some aspects of the approximate synthesis of stochastic differential equations and examples of their application to the generation of non gaussian continuous processes are considered the approach should be useful in signal processing when it is necessary to translate the available a priori information on the real random process into the language of its markov model as well as in simulation of continuous correlated processes with the known probability density function

comment on solitons backlund transformation and lax pair for the 2 1 dimensional boiti leon pempinelli equation for the water waves j math phys 51 093519 2010 recent studies on the water waves have been impressive of current interest in fluid physics jiang et al j math phys 51 093519 2010 have reported certain soliton interactions along with binary bell polynomial type backlund transformation and lax pair for the 2 1 dimensional boiti leon pempinelli system for water waves however the story introduced by that paper can be made more complete since in fluid physics and other fields the variable coefficient models can describe many physical processes more realistically than their constant coefficient counterparts hereby on a 2 1 dimensional variable coefficient boiti leon pempinelli generalization water wave symbolic computation is performed for the horizontal velocity of the water wave as well as the wave elevation variable coefficient dependent auto backlund transformation is constructed out along with some variable coefficient dependent shock wave type solutions relevant variable coefficient constraints are also given with respect to water waves

multichannel detection for correlated non gaussian random processes based on innovations the paper addresses the problem of multichannel signal detection in additive correlated non gaussian noise using the innovations approach although this problem has been addressed extensively for the case of additive gaussian noise the corresponding problem for the non gaussian case has received limited attention this is due to the fact that there is no unique specification for the joint probability density function pdf of n correlated non gaussian random variables the authors overcome this problem by using the theory of spherically invariant random processes sirps and derive the innovations based detector it is found that the optimal estimators for obtaining the innovations processes are linear and that the resulting detector is canonical for the class of pdfs arising from sirps the authors also present a performance analysis of the innovations based detector for the case of a k distributed sirp

on closed form solutions of 2 1 breaking soliton system by similarity transformations method abstract in the present research similarity transformation method via lie group theory is proposed to seek some more exact closed form solutions of the 2 1 dimensional breaking soliton system the system describes the interactions of the riemann wave along y axis and long wave along x axis some explicit solutions of breaking soliton system are attained with appropriate choices of the arbitrary functions and making use of arbitrary constants involved in the infinitesimals in order to obtain physically meaningful solutions numerical simulation is performed on the basis of graphical representation the physical analysis of solutions reveals into multi solitons periodic quadratic asymptotic and stationary profiles

spherically invariant vector random fields in space and time this paper is concerned with spherically invariant or elliptically contoured vector random fields in space and or time which are formulated as scale mixtures of vector gaussian random fields while a spherically invariant vector random field may or may not have second order moments a spherically invariant second order vector random field is determined by its mean and covariance matrix functions just like the gaussian one this paper explores basic properties of spherically invariant second order vector random fields and proposes an efficient approach to develop covariance matrix functions for such vector random fields

expected number of maxima in the envelope of a spherically invariant random process in many engineering applications specially in communication engineering one encounters a bandpass non gaussian random process with a slowly varying envelope among the available models for non gaussian random processes spherically invariant random processes sirps play an important role these processes are of interest mainly due to the fact that they allow one to relax the assumption of gaussianity while keeping many of its useful characteristics in this paper we have derived a simple and closed form formula for the expected number of maxima of a sirp envelope since gaussian random processes are special cases of sirps this formula holds for gaussian random processes as well in contrast with the available complicated expression for the expected number of maxima in the envelope of a gaussian random process our simple result holds for an arbitrary power spectrum the key idea in deriving this result is the application of the characteristic function rather than the probability density function for calculating the expected level crossing rate of a random process

soliton solutions of kd system using similarity transformations method abstract present article deals with some exact solutions of 2 1 dimensional system of coupled konopelchenko dubrovsky equations similarity transformations method is proposed to seek the solution of the system using lie group theory the lie group theory is a very strong tool by which complicated nonlinear partial differential equations under the group transformations remains invariant a brief review of lie symmetries of a system of partial differential equations has been described during the process method reduces the number of independent variables by one hence the system of partial equations reduces into a new system of ordinary differential equations in addition the infinitesimals after first reductions are more general than the previous established results by us kumar et al 2016 consequently solutions so derived are more general than previously known results we have obtained nine solutions in the explicit form some of them are more general and some are new for the best knowledge of us ultimately single solitons multi solitons and shocks behaviour is represented graphically through the numerical simulation for physical validation of the results

invariant solutions and conservation laws to nonconservative fp equation we generate conservation laws for the one dimensional nonconservative fokker planck fp equation also known as the kolmogorov forward equation which describes the time evolution of the probability density function of position and velocity of a particle and associate these where possible with lie symmetry group generators we determine the conserved vectors by a composite variational principle and then check if the condition for which symmetries associate with the conservation law is satisfied as the fokker planck equation is evolution type no recourse to a lagrangian formulation is made moreover we obtain invariant solutions for the fp equation via potential symmetries

efficient identification of non gaussian mixtures non gaussian mixtures are commonly used as parametric models for impulsive interference superimposed on a gaussian background in this study the problem of efficient batch and recursive estimation of the parameters of such mixtures via minimization of the kullback leibler distance is considered the maximum likelihood estimator mle provides the starting point for the development of these estimators first it is shown that the mle yields consistent estimates of the parameters despite the existence of multiple roots in the kullback leibler distance function since direct implementation of the mle is difficult an alternative estimator designed with the objective of maximizing the likelihood function is proposed a simulation study of the proposed estimator reveals that it performs very well in terms of attaining the cramer rao lower bound stochastic approximation is also considered in this study a complete data modification to the standard recursion is presented which greatly facilitates its implementation three initiating estimators are developed for these recursions an iterative likelihood based scheme a batch estimator that uses a histogram of the data and an iterative scheme that integrates the concept of complete data into the method of moments estimator upon initiating the modified stochastic approximation recursion with these estimators it is seen that excellent estimates of the parameters can be obtained

lie symmetry analysis backlund transformations and exact solutions of a 2 1 dimensional boiti leon pempinelli system in this paper the lie symmetry analysis method is employed to investigate the lie point symmetries and the one parameter transformation groups of a 2 1 dimensional boiti leon pempinelli system by using ibragimov s method the optimal system of one dimensional subalgebras of this system is constructed truncated painleve analysis is used for deriving the backlund transformation the method of constructing lump type solutions of integrable equations by means of backlund transformation is first presented meanwhile the lump type solutions of the 2 1 dimensional boiti leon pempinelli system are obtained the lump type wave is one kind of rogue wave the fusion type n solitary wave solutions are also constructed in addition this system is integrable in terms of the consistent riccati expansion method

stochastic model based processing for detection of small targets in non gaussian natural imagery stochastic background models incorporating spatial correlations can be used to enhance the detection of targets in natural terrain imagery but are generally difficult to apply when the statistics are non gaussian chapple and bertilone see opt commun vol 150 p 71 76 1998 proposed a simple stochastic model for images of natural backgrounds based on the pointwise nonlinear transformation of gaussian random fields and demonstrated its effectiveness and computational efficiency in modeling the textures found in natural terrain imagery acquired from airborne ir sensors in this paper we show how this model can be used to design algorithms that detect small targets up to several pixels in size in natural imagery by identifying anomalous regions of the image where the statistics differ significantly from the rest of the background all of the model based algorithms described here involve nonlinear spatial processing prior to the final decision threshold monte carlo testing reveals that the model based algorithms generally perform better than both the adaptive threshold filter and the generalized matched filter for detecting low contrast targets despite the fact that they do not require the target statistics needed for constructing the matched filter

polynomial chaos representation of spatio temporal random fields from experimental measurements two numerical techniques are proposed to construct a polynomial chaos pc representation of an arbitrary second order random vector in the first approach a pc representation is constructed by matching a target joint probability density function pdf based on sequential conditioning a sequence of conditional probability relations in conjunction with the rosenblatt transformation in the second approach the pc representation is obtained by having recourse to the rosenblatt transformation and simultaneously matching a set of target marginal pdfs and target spearman s rank correlation coefficient srcc matrix both techniques are applied to model an experimental spatio temporal data set exhibiting strong non stationary and non gaussian features the data consists of a set of oceanographic temperature records obtained from a shallow water acoustics transmission experiment 1 the measurement data observed over a finite denumerable subset of the indexing set of the random process is treated as a collection of observed samples of a second order random vector that can be treated as a finite dimensional approximation of the original random field a set of properly ordered conditional pdfs that uniquely characterizes the target joint pdf in the first approach and a set of target marginal pdfs and a target srcc matrix in the second approach are estimated from available experimental data digital realizations sampled from the constructed pc representations based on both schemes capture the observed statistical characteristics of the experimental data with sufficient accuracy the relative advantages and disadvantages of the two proposed techniques are also highlighted

chi 2 random fields in space and time this paper introduces some 2 random functions which are not homogeneous stationary in general but contain the stationary case as a special case and whose correlation structures are nonparametric and flexible so that many parametric forms can be specified the mean square differentiability of such 2 random function is discussed we also make the comparison of two 2 random functions through their finite dimensional laplace transforms

statistical analysis of the nonhomogeneity detector for non gaussian interference backgrounds we derive the nonhomogeneity detector nhd for non gaussian interference scenarios and present a statistical analysis of the method the non gaussian interference scenario is assumed to be modeled by a spherically invariant random process sirp we present a method for selecting representative homogeneous training data based on our statistical analysis of the nhd for finite sample support used in covariance estimation in particular an exact theoretical expression for the nhd test statistic probability density function pdf is derived performance analysis of the nhd is presented using both simulated data and measured data from the multichannel airborne radar measurement mcarm program a performance comparison with existing nhd approaches is also included

representation of nonlinear random transformations by non gaussian stochastic neural networks the learning capability of neural networks is equivalent to modeling physical events that occur in the real environment several early works have demonstrated that neural networks belonging to some classes are universal approximators of input output deterministic functions recent works extend the ability of neural networks in approximating random functions using a class of networks named stochastic neural networks snn in the language of system theory the approximation of both deterministic and stochastic functions falls within the identification of nonlinear no memory systems however all the results presented so far are restricted to the case of gaussian stochastic processes sps only or to linear transformations that guarantee this property this paper aims at investigating the ability of stochastic neural networks to approximate nonlinear input output random transformations thus widening the range of applicability of these networks to nonlinear systems with memory in particular this study shows that networks belonging to a class named non gaussian stochastic approximate identity neural networks sainns are capable of approximating the solutions of large classes of nonlinear random ordinary differential transformations the effectiveness of this approach is demonstrated and discussed by some application examples

optimum diversity detection over fading dispersive channels with non gaussian noise we consider the problem of m ary signal detection over a single input multiple output simo channel affected by frequency dispersive rayleigh distributed fading and corrupted by additive non gaussian noise modeled as a spherically invariant random process we derive both the optimum detection structure and a suboptimal reduced complexity receiver based on the low energy coherence approach interestingly both detection structures are canonical i e they are independent of the actual noise statistics we also carry out a performance analysis of both receivers with reference to the case that the channel is affected by a frequency selective fading and for a binary frequency shift keying signaling format the results obtained through both a chernoff bounding technique and monte carlo simulations reveal that the adoption of diversity also represents a suitable means to restore performance in the presence of dispersive fading and impulsive non gaussian noise interestingly it is also shown that the suboptimal receiver incurs a limited loss with respect to the optimum unrealizable receiving structure

some more similarity solutions of the 2 1 dimensional blp system some more similarity solutions of the coupled boiti leon pempinelli system have been obtained by using similarity transformations method via lie group theory the solutions are attained under the restrictions imposed on the functions involved in infinitesimals then solutions are investigated through the graphical representation in different cases the cases depend upon some suitable choice of arbitrary functions involved there i e in the solutions to get physically meaningful structures analytical solutions are supplemented by numerical simulations with appropriate choice of arbitrary functions and constants eventually profiles show single soliton elastic multisolitons quasi periodic parabolic and asymptotic nature of solutions

similarity solutions of the konopelchenko dubrovsky system using lie group theory this research deals with the similarity solutions of 2 1 dimensional konopelchenko dubrovsky kd system solutions so obtained are derived by using similarity transformations method based on lie group theory the method reduces the number of independent variables by one exploiting lie symmetries and using invariance property thus the kd system can further be reduced to a new system of ordinary differential equations under a suitable choice of functions and the arbitrary constants these new equations yield the explicit solutions of the kd system which are discussed in the similarity solutions section of the article moreover the physical analysis of the solutions is illustrated graphically in the analysis and discussions section based on numerical simulations in order to highlight the importance of the study

on the generation of the baseband and narrowband non gaussian processes one of the widely used classifications of random processes implies their separation from the baseband and narrowband ones exponent and exponentially decaying cosine waves represent the most popular approximations of the observed processes autocovariation functions acf we consider the generation of such processes with any specified marginal probability density function pdf the approach is based on the representation of the process considered to be a stationary solution of certain stochastic differential equations sde with the white gaussian noise in the right hand side it removes the known pearson restrictions on the kind of available process pdf and in the part related to the generation of the processes with strictly exponential acf is very close to that considered by haddad 1970 concerning the generation of the narrowband non gaussian processes with the exact exponential envelope of its acf synthesis of the corresponding sde may be considered to be principally novel several examples of nonlinear dynamical systems generating baseband and narrowband stationary continuous processes with the given pdf are considered some aspects of the sde numerical simulation are presented the generation method proposed may be useful in communication and signal processing applications where a proper interference simulation appears to be really important

continuous discontinuous finite element approximations of fourth order elliptic problems in structural and continuum mechanics with applications to thin beams and plates and strain gradient elasticity abstract a new finite element method for fourth order elliptic partial differential equations is presented and applied to thin bending theory problems in structural mechanics and to a strain gradient theory problem the method combines concepts from the continuous galerkin cg method the discontinuous galerkin dg method and stabilization techniques a brief review of the cg method the dg method and stabilization techniques highlights the advantages and disadvantages of these methods and suggests a new approach for the solution of fourth order elliptic problems a continuous discontinuous galerkin c dg method is proposed which uses c 0 continuous interpolation functions and is formulated in the primary variable only the advantage of this formulation over a more traditional mixed approach is that the introduction of additional unknowns and related difficulties can be avoided in the context of thin bending theory the c dg method leads to a formulation where displacements are the only degrees of freedom and no rotational degrees of freedom need to be considered the main feature of the c dg method is the weak enforcement of continuity of first and higher order derivatives through stabilizing terms on interior boundaries consistency stability and convergence of the method are shown analytically numerical experiments verify the theoretical results and applications are presented for bernoulli euler beam bending poisson kirchhoff plate bending and a shear layer problem using toupin mindlin strain gradient theory

localized excitations in 2 1 dimensional systems by means of a special variable separation approach a common formula with some arbitrary functions has been obtained for some suitable physical quantities of various 2 1 dimensional models such as the davey stewartson ds model the nizhnik novikov veselov nnv system asymmetric nnv equation asymmetric ds equation dispersive long wave equation broer kaup kupershmidt system long wave short wave interaction model maccari system and a general n m component ablowitz kaup newell segur akns system selecting the arbitrary functions appropriately one may obtain abundant stable localized interesting excitations such as the multidromions lumps ring soliton solutions breathers instantons etc it is shown that some types of lower dimensional chaotic patterns such as the chaotic chaotic patterns periodic chaotic patterns chaotic line soliton patterns chaotic dromion patterns fractal lump patterns and fractal dromion patterns may be found in higher dimensional soliton systems the interactions between the traveling ring type soliton solutions are completely elastic the traveling ring solitons pass through each other and preserve their shapes velocities and phases some types of localized weak solutions peakons are also discussed especially the interactions between two peakons are not completely elastic after the interactions the traveling peakons also pass through each other and preserve their velocities and phases however they completely exchange their shapes

a cubic hermite finite element continuation method for numerical solutions of the von karman equations abstract we study a cubic hermite finite element method for numerical solutions of the von karman equations defined in a rectangular domain with totally clamped boundary conditions a novel iterative method combined with a predictor corrector continuation algorithm is exploited to trace solution curves of the von karman equations the fourth order finite element approximations compute accurate numerical solutions for the deformation and the airy stress function as well as their first order partial derivatives and the mixed second order partial derivatives in this regard the classical predictor corrector continuation method is interpreted in a different way our numerical results show that the bifurcation scenario of the von karman equations with totally clamped boundary conditions is different from those with simply supported and partially clamped boundary conditions

a multigrid finite element solver for the cahn hilliard equation a multigrid finite element solver for the cahn hilliard equation is presented that has mesh independent convergence rates for any time step size including in the important limit e 0 which is examined via numerical examples numerics are performed for a number of test problems which show that the features of the cahn hilliard equation minimising interface measure lyapunov energy functional etc are preserved we also explore the use of this solver in conjunction with adaptive time stepping and adaptive mesh strategies

elliptically contoured random fields in space and time elliptically contoured random fields are natural extensions of the gaussian random field and may or may not have second order moments a second order elliptically contoured random field is determined by its mean and covariance functions just like the gaussian one this paper proposes a class of covariance functions for second order elliptically contoured random fields by using the nonnegative mixture method which possess the following properties nonseparable nonstationary but with the stationary case as a special case and allowing for both positive and negative correlation some long range dependent models are also derived

laminar flow and heat transfer in the boundary layer of non newtonian fluids over a stretching flat sheet a theoretical analysis of the laminar boundary layer flow and heat transfer of power law non newtonian fluids over a stretching sheet with the sheet velocity distribution of the form u w cx m and the wall temperature distribution of the form t w t ax c is presented where x denotes the distance from the slit from which the surface emerges and c and a are constants m and c denote the sheet velocity exponent and the temperature exponent respectively within the framework of the boundary layer approximations the nonlinear boundary layer momentum equation and the energy equation are reduced to a set of ordinary differential equations it is found that when the velocity exponent m 1 3 or the power law index n 1 the similarity solutions are in existence for both the momentum equation and the energy equation analytical approximations with high accuracy for the reduced velocity and temperature profiles are obtained using a new procedure based on the homotopy analysis method besides the effects of the parameters m n and the prandlt number pr on the flow are investigated

regular article calculation of two phase navier stokes flows using phase field modeling phase field models provide a way to model fluid interfaces as having finite thickness this can allow the computation of interface movement and deformation on fixed grids this paper applies phase field modeling to the computation of two phase incompressible navier stokes flows the navier stokes equations are modified by the addition of the continuum forcing email protected f where c is the composition variable and f is c s chemical potential the equation for interface advection is replaced by a continuum advective diffusion equation with diffusion driven by c s chemical potential gradients the paper discusses how solutions to these equations approach those of the original sharp interface navier stokes equations as the interface thickness e and the diffusivity both go to zero the basic flow physics of phase field interfaces is discussed straining flows can thin or thicken an interface and this must be resisted by a high enough diffusion on the other hand too large a diffusion will overly damp the flow these two constraints result in an upper bound for the diffusivity of o e and a lower bound of o e 2 within these two bounds the phase field navier stokes equations appear to generate an o e error relative to the exact sharp interface equations an o h 2 e 2 numerical method is introduced that is energy conserving in the sense that creation of interface energy by convection is always balanced by an equal decrease in kinetic energy caused by surface tension forcing an o h 4 e 4 compact scheme is introduced that takes advantage of the asymptotic comparatively smooth behavior of the chemical potential for o e accurate phase field models the optimum path to convergence for this scheme appears to be email protected 4 5 the asymptotic rate of convergence corresponding to this is o h 4 5 but results at practical resolutions show that the practical convergence of the method is generally considerably faster than linear extensive analysis and computations show that this scheme is very effective and accurate it allows the accurate calculation of two phase flows with interfaces only two cells wide computational results are given for linear capillary waves and for rayleigh taylor instabilities the first set of computations is compared to exact solutions of the diffuse interface equations and of the original sharp interface equations the rayleigh taylor computations test the ability of the method to compute highly deforming flows these flows include near singular phenomena such as interface coalescences and breakups contact line movement and the formation and breakup of thin wall films grid refinement studies are made and rapid convergence is found for macroscopic flow features such as instability growth rate and propagation speed wavelength and the general physical characteristics of the instability and mass transfer rates

solitons backlund transformation and lax pair for the 2 1 dimensional boiti leon pempinelli equation for the water waves under investigation in this paper is the 2 1 dimensional boiti leon pempinelli blp equation for the water waves by virtue of the binary bell polynomials and symbolic computation the bilinear form for the blp equation is obtained furthermore soliton solutions are presented and soliton interaction properties including the elastic inelastic and elastic inelastic collisions are discussed by the graphical analysis besides the backlund transformation in the form of the binary bell polynomials is derived via the backlund transformation the shock wave solutions and lax pair are both constructed

application of lie groups to compressible model of two phase flows this paper presents some exact solutions for the drift flux model of two phase flows using lie group analysis the analysis involves an isentropic no slip conservation of mass for each phase and the conservation of momentum for the mixture the present analysis employs a complete lie algebra of infinitesimal symmetries subsequent to these theoretical analysis a symmetry group is established the symmetry generators are used for constructing similarity variables which reduce the model equations to a system of ordinary differential equations odes in particular a general framework is discussed for solving the model equations analytically as a consequence of this new classes of exact group invariant solutions are developed this provides new insights into the fundamental properties of weak discontinuities and helps one to understand better on existence of solutions

isoparametric hermite elements isoparametric hermite elements are created using bogner fox schmit rectangles on a reference domain and mapping these numerically onto the computational domain the difficulties involved in devising explicit c1 shape functions for isoparametric elements are thus avoided and the resulting elements have all the benefits of full c1 continuity the simplicity of the bogner fox schmit element and the geometrical flexibility expected from higher order isoparametric elements the numerical mapping consists in the finite element solution of a linear boundary value problem which is inexpensive and is carried out as a preprocessing operation the required derivatives of the mapping then being supplied to the main analysis as data some care is required in defining the differential boundary conditions and guidance on this is provided examples are given showing the success of the mapping procedure and the use of the resulting elements in the solution of some boundary value problems the numerical results confirm a convergence analysis provided for the new isoparametric hermite element

covariance structure maximum likelihood estimates in compound gaussian noise existence and algorithm analysis recently a new adaptive scheme conte 1995 gini 1997 has been introduced for covariance structure matrix estimation in the context of adaptive radar detection under non gaussian noise this latter has been modeled by compound gaussian noise which is the product c of the square root of a positive unknown variable tau deterministic or random and an independent gaussian vector x c radictaux because of the implicit algebraic structure of the equation to solve we called the corresponding solution the fixed point fp estimate when tau is assumed deterministic and unknown the fp is the exact maximum likelihood ml estimate of the noise covariance structure while when tau is a positive random variable the fp is an approximate maximum likelihood aml this estimate has been already used for its excellent statistical properties without proofs of its existence and uniqueness the major contribution of this paper is to fill these gaps our derivation is based on some likelihood functions general properties like homogeneity and can be easily adapted to other recursive contexts moreover the corresponding iterative algorithm used for the fp estimate practical determination is also analyzed and we show the convergence of this recursive scheme ensured whatever the initialization

soliton solutions of blmp equation by lie symmetry approach abstract shallow water wave equations are usually described by korteweg de vries kdv type equations in this paper we have used lie transformation group theory to solve 2 1 dimensional boiti leon manna pempinelli blmp equation we have obtained some exact solutions of blmp equation in the explicit form through similarity reduction all the reported results are expressed in closed form and analysed physically through their evolution profiles the physical analysis reveals that the nature of solutions is parabolic quasi periodic multisoliton and asymptotic

modeling and unsupervised classification of multivariate hidden markov chains with copulas parametric modeling and estimation of non gaussian multidimensional probability density function is a difficult problem whose solution is required by many applications in signal and image processing a lot of efforts have been devoted to escape the usual gaussian assumption by developing perturbed gaussian models such as spherically invariant random vectors sirvs in this work we introduce an alternative solution based on copulas that enables theoretically to represent any multivariate distribution estimation procedures are proposed for some mixtures of copula based densities and are compared in the hidden markov chain setting in order to perform statistical unsupervised classification of signals or images useful copulas and sirv for multivariate signal classification are particularly studied through experiments