the broadwell model for initial values in l 1 _ bf r the cauchy problem for the broadwell model is shown to have a global mild solution for initial data inl 1 with smalll1 norm and a local solution for arbitrary initial data inl 1 for data which are small inl1 the asymptotic behaviour of the solutions ast is determined moreover it is shown that a global solution exists for all initial values inl 1 with finite entropy if theh theorem holds

analysis of an adaptive control scheme for a partially observed controlled markov chain the authors consider an adaptive finite state controlled markov chain with partial state information motivated by a class of replacement problems they present parameter estimation techniques based on the information available after actions that reset the state to a known value are taken it is proved that the parameter estimates converge w p 1 to the true unknown parameter under the feedback structure induced by a certainty equivalent adaptive policy it is shown that the adaptive policy is self optimizing in a long run average sense for any measurable sequence of parameter estimates converging w p 1 to the true parameter

singular perturbations of first order hyperbolic systems with stiff source terms abstract this work develops a singular perturbation theory for initial value problems of nonlinear first order hyperbolic systems with stiff source terms in several space variables it is observed that under reasonable assumptions many equations of classical physics of that type admit a structural stability condition this condition is equivalent to the well known subcharacteristic condition for one dimensional 2 2 systems and the well known time like condition for one dimensional scalar second order hyperbolic equations with a small positive parameter multiplying the highest derivatives under this stability condition we construct formal asymptotic approximations of the initial layer solution to the nonlinear problem furthermore assuming some regularity of the solutions to the limiting inner problem and the reduced problem we prove the existence of classical solutions in the uniform time interval where the reduced problem has a smooth solution and justify the validity of the formal approximations in any fixed compact subset of the uniform time interval the stability condition seems to be a key to problems of this kind and can be easily verified moreover this presentation unifies and improves earlier works for some specific equations

boundary layer behavior in the fluid dynamic limit for a nonlinear model boltzmann equation in this paper we study the fluid dynamic limit for the one dimensional broadwell model of the nonlinear boltzmann equation in the presence of boundaries we consider an analogue of maxwell s diffusive and reflective boundary conditions the boundary layers can be classified as either compressive or expansive in terms of the associated characteristic fields we show that both expansive and compressive boundary layers before detachment are nonlinearly stable and that the layer effects are localized so that the fluid dynamic approximation is valid away from the boundary we also show that the same conclusion holds for short time without the structural conditions on the boundary layers a rigorous estimate for the distance between the kinetic solution and the fluid dynamic solution in terms of the mean free path in thel norm is obtained provided that the interior fluid flow is smooth the rate of convergence is optimal

on a class of exact two dimensional stationary solutions for the broadwell model of the boltzmann equation potential flows in steady state conditions are studied in detail in the framework of the plane broadwell discrete velocity model 1964 of the boltzmann equation it is shown that explicit exact solutions with physical meaning can be obtained in terms of elementary or special functions previously discovered analytical incompressible rows are recovered as particular cases new solutions for compressible flows are classified and discussed

discretized maximum likelihood and almost optimal adaptive control of ergodic markov models three distinct controlled ergodic markov models are considered here the models are a discrete time controlled markov process with complete observations a controlled diffusion process with complete observations and a discrete time controlled markov process with partial observations the partial observations for the third model have the special form of complete observations in a fixed recurrent set and noisy observations in its complement for each of the models an almost self optimizing adaptive control is given these adaptive controls are constructed from a family of estimates that use a finite discretization of the parameter set and a finite family of almost optimal ergodic controls by a randomized certainty equivalence method a continuity property of the information of a model for one parameter value with respect to another is used to establish this almost optimality property

asymptotic behavior of one dimensional discrete velocity models in a slab we prove results on the asymptotic behavior of solutions to discrete velocity models of the boltzmann equation in the one dimensional slab 0 x 1 with general stochastic boundary conditions at x 0 and x 1 assuming that there is a constant wall maxwellian m mi compatible with the boundary conditions and under a technical assumption meaning strong thermalization at the boundaries we prove three types of results i if no velocity has x component 0 there are real valued functions 1 t and 2 t such that in a measure theoretic sense fi 0 t 1 t m i fi 1 t 2 t mi as t 1 and 2 are closely related and satisfy functional equations which suggest that 1 t 1 and 2 t 1 as t ii under the additional assumption that there is at least one non trivial collision term containing a product f k f l with k l where k denotes the x component of the velocity associated with f k we show that in a measure theoretic sense 1 t and 2 t converge to 1 as t this entails l1 convergence of the solution to the unique wall maxwellian for this result k l 0 is admissible iii in the absence of any collision terms but under the assumption that there is an irrational quotient i j l k here i l 0 and j k 0 renewal theory entails that the solution converges to the unique wall maxwellian in l

discretizations for the incompressible navier stokes equations based on the lattice boltzmann method a discrete velocity model with spatial and velocity discretization based on a lattice boltzmann method is considered in the low mach number limit a uniform numerical scheme for this model is investigated in the limit the scheme reduces to a finite difference scheme for the incompressible navier stokes equation which is a projection method with a second order spatial discretization on a regular grid the discretization is analyzed and the method is compared to chorin s original spatial discretization numerical results supporting the analytical statements are presented

stiff well posedness and asymptotic convergence for a class of linear relaxation systems in a quarter plane abstract in this paper we study the asymptotic equivalence of a general linear system of 1 dimensional conservation laws and the corresponding relaxation model proposed by s jin and z xin 1995 comm pure appl math 48 235 277 in the limit of small relaxation rate the main interest is this asymptotic equivalence in the presence of physical boundaries we identify and rigorously justify a necessary and sufficient condition which we call the stiff kreiss condition or skc in short on the boundary condition to guarantee the uniform well posedness of the initial boundary value problem for the relaxation system independent of the rate of relaxation the skc is derived and simplified by using a normal mode analysis and a conformal mapping theorem the asymptotic convergence and boundary layer behavior are studied by the laplace transform and a matched asymptotic analysis an optimal rate of convergence is obtained

broadwell model and conservative supersonic boundary in this paper we consider an initial boundary value problem for the broadwell model with a supersonic physical boundary here we pose a conservative boundary condition which preserves the total number of particles we show that the solution converges pointwise to a boundary layer exponentially when the perturbations of the initial data to the equilibrium state are sufficiently small by using green s function as established in lan et al netw heterog media 1 167 183 2006 weighted energy estimates and by constructing a pair of anti derivatives to convert the conservative boundary condition into a dissipative boundary condition with conservation laws together with an a priori chosen boundary layer

reaction advection random motions in inhomogeneous media abstract a probabilistic approach to reaction advection systems with a finite propagation speed is developed the convergence to traveling wave solutions in inhomogeneous media is studied the results are heavily based on the author s previous paper branching random motions nonlinear hyperbolic systems and travelling waves preprint of simon bolivar university caracas venezuela 2003 32 pp submitted for publication

secant lines in a preliminary study of phonetic reduction of ɪ and e two subjects from the x ray microbeam speech production database were examined in their production of the vowels i and epsilon in alveolar and dental consonant contexts secant lines or first order splines between the three most anterior pellets were examined at vowel critical times these critical times were zero crossings in the tangential acceleration of the midpoints of the secant lines we expected and found in general that vowel reduction occurred as a function of vowel duration in measures of the secant line midpoint to palate distance and secant line orientation at vowel critical times the shorter the vowel the smaller the distance of the secant line midpoints to the palate and the less downward the orientation of the secant lines at the vowel critical times phonetic reduction was also apparent in the formant frequencies there were differences between the speakers in terms of the range of vowel duration and degree of reduction the subjects differed in the functional parts of the tongue spanned by the secant lines and the shape of their palates these differences were factors in the observed relations between formant frequencies and the articulatory secant line measures for each subject

relaxation limit for piecewise smooth solutions to systems of conservation laws abstract in this paper we study the asymptotic equivalence of a general system of 1 d conservation laws and the corresponding relaxation model proposed by s jin and z xin 1995 comm pure appl math 48 235 277 in the limit of small relaxation rate it is shown that if the relaxation system satisfies the subcharacteristic condition and the solution of the hyperbolic conservation laws is piecewise smooth with a finite number of noninteracting shocks satisfying the entropy condition then there exist solutions of the relaxation systems that converge to the solution of the original conservation laws equilibrium system at a rate of order e as the rate of relaxation e goes to zero the proof uses a matched asymptotic analysis and an energy estimate related to the nonlinear stability theory for viscous shock profiles

a new contribution to nonlinear stability of a discrete velocity model for a class of discrete velocity models of kinetic theory we prove exponential nonlinear conditional stability of the constant basic state in the slab 0 1

the discrete boltzmann equation with multiple collisions global existence and stability for the initial value problem this paper deals with the analysis of the initial value problem in all space rd d 2 for the discrete boltzmann equation with multiple collisions after a preliminary analysis of the mathematical modeling of the evolution equations global existence and asymptotic behavior are proven using suitable stability criteria some applications verify the analysis for specific models

self similar fluid dynamic limits for the broadwell system this report discusses a new approach for the resolution of the fluid dynamic limit for the broadwell system of the kinetic theory of gases appropriate in the case of riemann maxwellian data since the formal limiting system is expected to have self similar solutions we are motivated to replace the knudsen number in the broadwell model so that the resulting model admits self similar solutions x t and then let go to zero the limiting procedure is justified and the resulting limit is a solution of the riemann problem for the fluid dynamic limit equations a class of riemann data for which this program can be carried out is exhibited furthermore it is shown that for the carleman model the complete program can be done successfully for arbitrary riemann data

planar x z mixtures discrete boltzmann equations with species either in odd or even x z values we present large size physical discrete boltzmann equations or discrete velocity models results for binary mixtures of gas light mass 1 and heavy mass m in a half plane coordinates x z interface at z 0 without velocities except the rest particle where the sums x z are either odd or even for heavy or light species the models fill all integer coordinates z 0 of the plane with only a z spatial dependence densities with x z are equal here to previous results we generalize with new mathematical tools to any binary mixture with m ratio of any even to odd values m 2p 2q 1 and ratio of odd to odd values m 2p 1 2q 1 p q arbitrary integers with only binary collisions we construct large size physical discrete models only mass energy and momentum along the z axis invariants without other invariants which are called spurious we prove the existence of a physical square diagonals along the x and z axes grid where for the first component all x z a sufficient value functio

vowel posture normalization a simple normalization procedure was applied to point parametrized articulatory data to yield quantitative speaker general descriptions of average vowel postures articulatory data from 20 english and 8 japanese speakers drawn from existing x ray microbeam database corpora were included in the analysis the purpose of the normalization procedure was to minimize the effects of differences in vocal tract size and shape on average postures derived from the raw data the procedure resulted in a general reduction of cross speaker variance in the y dimension of the normalized space within both language groups this result can be traced to a systematic source of variance in the y dimension of the raw data i e palatal height successfully removed from the normalized data the procedure did not result in a comparable general reduction in cross speaker variance in the x dimension this negative result can be traced partly to the new observation that some speakers within the english sample habitually placed their tongues in a fronted position for all vowels whereas other speakers habitually placed their tongues in a rearward position methods for evaluating articulatory normalization schemes and possible sources of interspeaker variability in vowel postures are discussed

convergence of a splitting scheme applied to the ruijgrok wu model of the boltzmann equation this paper deals with upwind splitting schemes for the ruijgrok wu model physica a 113 1982 401 416 of the kinetic theory of rare7ed gases in the 8uid dynamic scaling we prove the stability and the convergence for these schemes the relaxation limit is also investigated and the limit equation is proved to be a 7rst order quasi linear conservation law the loss of quasi monotonicity of the present model makes it necessary to give a more careful analysis of its structure we also obtain global error estimates in the spaces w s p for 16s61 p 16p6 and pointwise error estimates for the approximate solution the proof naturally uses the framework introduced by nessyahu and tadmor siam j numer anal 29 1992 1505 1519 due to the convexity of the 8ux function c

construction of discrete kinetic models with given invariants we consider the general problem of the construction of discrete kinetic models dkms with given conservation laws this problem was first stated by gatignol in connection with discrete models of the boltzmann equation be and it has been addressed in the last decade by several authors even though a practical criterion for the non existence of spurious conservation laws has been devised and a method for enlarging existing physical models by new velocity points without adding non physical invariants has been proposed a general algorithm for the construction of all normal physical discrete models with assigned conservation laws in any dimension and for any number of points is still lacking in the literature we introduce the most general class of discrete kinetic models and obtain a general method for the construction and classification of normal dkms in particular it is proved that for any given dimension d 2 and for any sufficiently large number n of velocities for example n 6 for the planar case d 2 there exists just a finite number of distinct classes of dkms we apply the general method in the particular cases of discrete velocity models dvms of the inelastic be and elastic be using our general approach to dkms and our results on normal dvms for a single gas we develop a method for the construction of the most natural from physical point of view subclass of normal dvms for binary gas mixtures we call such models supernormal models snms they have the property that by isolating the velocities of single gases involved in the mixture we also obtain normal dvms

a random discrete velocity model and approximation of the boltzmann equation an approximation procedure for the boltzmann equation based on random choices of collision pairs from a fixed velocity set and on discrete velocity models is designed in a suitable limit the procedure is shown to converge to the time discretized and spatially homogeneous boltzmann equation

certainty equivalence control with forcing revisited abstract certainty equivalence control with forcing has been shown to be optimal for several stochastic adaptive control problems with the average cost per unit time criterion recently researchers have started looking at stochastic adaptive control problems with a view to minimizing the rate of increase of the learning loss this criterion is stronger than the average cost per unit time criterion certainty equivalence control with forcing does not usually suffice for the learning loss criterion and one has to develop fairly complicated schemes in order to achieve optimality the objective of this paper is to see how well one might be able to do with a certainty equivalence control with forcing type of scheme in particular we construct a class of such schemes whose learning loss is o log n 1 for 0 whereas optimal schemes typically have a o log n learning loss

stability of planar shock fronts for multidimensional systems of relaxation equations abstract we investigate stability of multidimensional planar shock profiles of a general hyperbolic relaxation system whose equilibrium model is a system under the necessary assumption of spectral stability and a standard set of structural conditions that are known to hold for many physical systems our main result generalizing the work of kwon and zumbrun in the scalar relaxation case is to establish the bounds on the green s function for the linearized equation and obtain nonlinear l 2 asymptotic behavior sharp decay rate of perturbed weak shock profiles to establish green s function bounds we use the semigroup approach in the low frequency regime and use the energy method for the high frequency bounds separately for the system equilibrium case the analysis of the linearized equation is complicated due to glancing phenomena we treat this difficulty similarly as in the inviscid and viscous systems under the constant multiplicity condition

l 1 stability of multi dimensional discrete velocity boltzmann equations we study the l 1 stability of multi dimensional discrete velocity boltzmann equations under suitable smallness assumption on initial data we show that bounded mild solutions are l 1 stable for a stability estimate we employ bony s multi dimensional analysis for total interactions over characteristic planes

a discrete boltzmann equation based on a cub octahedron in mathbb r 3 in this article we introduce a discrete boltzmann equation in mathbb r 3 velocity space based on a cub octahedron we present a layer wise construction of a regular collision model in a bounded grid of the sphere packing problem the paper contains the analytical results about the basic kinetic features of the regular collision model we analyze the computational complexity report the efficiency of the model and perform numerical experiments based on the discrete model boltzmann equation for some standard test problem

zero relaxation limit for piecewise smooth solutions to a rate type viscoelastic system in the presence of shocks abstract we study a rate type viscoelastic system proposed in i suliciu int j engng sci 28 1990 827 841 which is a 3 3 hyperbolic system with relaxation as the relaxation time tends to zero this system converges to the well known p system formally in the case that the solutions of the p system are piecewise smooth including finitely many noninteracting shock waves we show that there exist smooth solutions for suliciu s model which converge to those of the p system strongly as the relaxation time goes to zero the method used here is the so called matched asymptotic analysis suggested in j goodman and z p xin arch ration mech anal 121 1992 235 265 which includes two parts the matched asymptotic expansion and stability analysis

kinetic limits for a class of interacting particle systems we study one dimensional particle systems in which particles travel as independent random walks and collide stochastically the collision rates are chosen so that each particle experiences finitely many collisions per unit time we establish the kinetic limit and derive the discrete boltzmann equation for the macroscopic particle density

approximation of the boltzmann equation by discrete velocity models two convergence results related to the approximation of the boltzmann equation by discrete velocity models are presented first we construct a sequence of deterministic discrete velocity models and prove convergence as the number of discrete velocities tends to infinity of their solutions to the solution of a spatially homogeneous boltzmann equation second we introduce a sequence of markov jump processes interpreted as random discrete velocity models and prove convergence as the intensity of jumps tends to infinity of these processes to the solution of a deterministic discrete velocity model

contact discontinuity with general perturbations for gas motions the contact discontinuity is one of the basic wave patterns in gas motions the stability of contact discontinuities with general perturbations for the navier stokes equations and the boltzmann equation is a long standing open problem general perturbations of a contact discontinuity may generate diffusion waves which evolve and interact with the contact wave to cause analytic difficulties in this paper we succeed in obtaining the large time asymptotic stability of a contact wave pattern with a convergence rate for the navier stokes equations and the boltzmann equation in a uniform way one of the key observations is that even though the energy norm of the deviation of the solution from the contact wave may grow at the rate it can be compensated by the decay in the energy norm of the derivatives of the deviation which is of the order of thus this reciprocal order of decay rates for the time evolution of the perturbation is essential to close the a priori estimate containing the uniform bounds of the l8 norm on the lower order estimate and then it gives the decay of the solution to the contact wave pattern

hyperbolic conservation laws with stiff relaxation terms and entropy we study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms reduced systems inviscid and viscous local conservation laws and weakly nonlinear limits are derived through asymptotic expansions an entropy condition is introduced for n n systems that ensures the hyperbolicity of the reduced inviscid system the resulting characteristic speeds are shown to be interlaced with those of the original system moreover the first correction to the reduced system is shown to be dissipative a partial converse is proved for 2 2 systems this structure is then applied to study the convergence to the reduced dynamics for the 2 2 case 1994 john wiley sons inc

2d and 3d exact shock wave solutions with specular reflection to the discrete boltzmann models the authors construct exact solutions which are 2d two spatial coordinates for the four velocity planar model 3d for the cubic broadwell models and p dimensional for the p dimensional hypercubic discrete boltzmann model these solutions are shock waves which satisfy a specular reflection boundary condition at a wall

stability relaxation and oscillation of biodegradation fronts we study the stability and oscillation of travelingfronts in a three component advection reaction biodegradation model the three components are pollutant nutrient and bac teria concentrations under an explicit condition on the biomass growth and decay coefficients we derive reduced two component semilinear hyperbolic models through a relaxation procedure duringwhich biomass is slaved to pollutant and nutrient concentration variables the reduced two component models resemble the broadwell model of the discrete velocity gas the traveling fronts of the reduced system are explicit and are expressed in terms of hyperbolic tangent function in the nutrient deficient regime we perform energy estimates to prove the asymptotic stability of these fronts under explicit conditions on the coefficients in the system in the small dampinglimit we carry out wentzel kramers brillouin wkb analysis on front perturbations and show that fronts are always stable in the two component models we extend the wkb analysis to derive amplitude equations for front perturbations in the original three component model because of the bacteria kinetics we find two asymptotic regimes where perturbation amplitudes grow or oscillate in time we perform numerical simulations to illustrate the predictions of the wkb theory

discrete velocity models of the boltzmann equation a survey on the mathematical aspects of the theory discrete velocity models of the boltzmann equation are of considerable conceptual interest in the kinetic theory of gases and at the same time a fascinating mathematical subject the last decade has seen a lot of work on this subject which is reviewed here we put an emphasis on mathematical aspects in particular the global existence question qualitative properties of solutions explicit solutions and the fluid dynamical limit the mechanical background is discussed more concisely in part i numerous contributions concerning other questions are outlined we try to give a complete reference list up to and including 1985

uniform global existence and parabolic limit for partially dissipative hyperbolic systems abstract this work concerns smooth solutions to the cauchy problem for first order partially dissipative hyperbolic systems with a small parameter the systems are written in non conservative form in several space variables we introduce algebraic conditions on the structure of the systems under these conditions together with a partial dissipation condition and the shizuta kawashima stability condition we prove three main results around constant equilibrium states these results are uniform global existence with respect to the parameter global in time convergence of the systems to second order nonlinear parabolic systems in a slow time variable and global existence when the parameter is fixed we also give examples of physical models to which the above results can be applied

the fluid dynamic limit of the broadwell model of the nonlinear boltzmann equation in the presence of shocks this paper studies the asymptotic equivalence of the broadwell model of the nonlinear boltzmann equation to its corresponding euler equation of compressible gas dynamics in the limit of small mean free path e it is shown that the fluid dynamical approximation is valid even if there are shocks in the fluid flow although there are thin shock layers in which the convergence does not hold more precisely by assuming that the fluid solution is piecewise smooth with a finite number of noninteracting shocks and suitably small oscillations we can show that there exist solutions to the broadwell equations such that the broadwell solutions converge to the fluid dynamical solutions away from the shocks at a rate of order e as the mean free path e goes to zero for the proof we first construct a formal solution for the broadwell equation by matching the truncated hilbert expansion and shock layer expansion then the existence of broadwell solutions and its convergence to the fluid dynamic solution is reduced to the stability analysis for the approximate solution we use an energy method which makes full use of the inner structure of time dependent shock profiles for the broadwell equations

a discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws abstract we present a new relaxation approximation to scalar conservation laws in several space variables by means of semilinear hyperbolic systems of equations with a finite number of velocities under a suitable multidimensional generalization of the whitham relaxation subcharacteristic condition we show the convergence of the approximated solutions to the unique entropy solution of the equilibrium cauchy problem

normal high order discrete velocity models of the boltzmann equation abstract this paper aims at approximations of the collision operator in the boltzmann equation the developed framework guarantees the normality of the approximation which means correct collision invariants h theorem and equilibrium solutions it fits into the discrete velocity model framework is given in such a way that it is understandable with undergraduate level mathematics and can be used to construct approximations with arbitrary high convergence orders at last we give an example alongside a numerical verification here the convergence orders range up to 3 2 and the time complexity is given by 3 1 2 4 2 3 in 2 3 dimensions

interaction between duration context and speaking style in english stressed vowels acoustic observations are reported for english front vowels embedded in a w l frame and carrying constant main stress the vowels were produced by five speakers in clear and citation form styles at varying durations but at a constant speaking rate the acoustic analyses revealed i that formant patterns were systematically displaced in the direction of the frequencies of the consonants of the adjacent pseudosymmetrical context ii that those displacements depended in a lawful manner on vowel duration iii that this context and duration dependence was more limited for clear than for citation form speech and that the smaller formant shifts of clear speech tended to be achieved by increases in the rate of formant frequency change the findings are compatible with a revised and biomechanically motivated version of the vowel undershoot model lindblom j acoust soc am 35 1773 1781 1963 that derives formant patterns from numerical information on three variables the locus target distance vowel duration and rate of formant frequency change the results further indicate that the clear samples were not merely louder but involved a systematic undershoot compensating reorganization of the acoustic patterns

galerkin petrov approach for the boltzmann equation abstract in this work we propose a new galerkin petrov method for the numerical solution of the classical spatially homogeneous boltzmann equation this method is based on an approximation of the distribution function by associated laguerre polynomials and spherical harmonics and test in a variational manner with globally defined three dimensional polynomials a numerical realisation of the algorithm is presented the algorithmic developments are illustrated with the help of several numerical tests

a completely solvable model of the nonlinear boltzmann equation abstract in one space and one time dimension a model of the nonlinear boltzmann equation is presented that is exactly solvable for all initial conditions furthermore this model has the following desirable properties i conservation of the number of particles ii energy conservation iii nonlinearity iv positivity of distribution functions and v unique equilibrium state for any given density which is approached as t for most physically interesting initial conditions some of the simple properties of this model are studied

nonlinear functionals of multi d discrete velocity boltzmann equations in this paper we study nonlinear functionals measuring potential interactions and l1 distance between two mild solutions for the multi dimensional discrete velocity boltzmann equations when the initial data are a small perturbation of a vacuum we employ bony s dispersion estimates to show that these functionals satisfy lyapunov type estimates which are useful for the study of time asymptotics and l1 stability of mild solutions

discrete kinetic schemes for multidimensional systems of conservation laws we present here some numerical schemes for general multidimensional systems of conservation laws based on a class of discrete kinetic approximations which includes the relaxation schemes by s jin and z xin these schemes have a simple formulation even in the multidimensional case and do not need the solution of the local riemann problems for these approximations we give a suitable multidimensional generalization of the whitham s stability subcharacteristic condition in the scalar multidimensional case we establish the rigorous convergence of the approximated solutions to the unique entropy solution of the equilibrium cauchy problem

asymptotic stability of traveling wave solutions of systems for one dimensional gas motion the asymptotic stability of traveling wave solutions with shock profile is investigated for several systems in gas dynamics 1 the solution of a scalar conservation law with viscosity approaches the traveling wave solution at the ratet for some 0 ast provided that the initial disturbance is small and of integral zero and in addition decays at an algebraic rate for x 2 the traveling wave solution with nishida and smoller s condition of the system of a viscous heat conductive ideal gas is asymptotically stable provided the initial disturbance is small and of integral zero 3 the traveling wave solution with weak shock profile of the broadwell model system of the boltzmann equation is asymptotically stable provided the initial disturbance is small and its hydrodynamical moments are of integral zero each proof is given by applying an elementary energy method to the integrated system of the conservation form of the original one the property of integral zero of the initial disturbance plays a crucial role in this procedure

regular article a new discrete velocity method for navier stokes equations the relation between the lattice boltzmann method which has recently become popular and the kinetic schemes which are routinely used in computational fluid dynamics is explored a new discrete velocity method for the numerical solution of navier stokes equations for incompressible fluid flow is presented by combining both the approaches the new scheme can be interpreted as a pseudo compressibility method and for a particular choice of parameters this interpretation carries over to the lattice boltzmann method

zero viscosity limit for analytic solutions of the navier stokes equation on a half space ii construction of the navier stokes solution this is the second of two papers on the zero viscosity limit for the incompressible navier stokes equations in a half space in either 2d or 3d under the assumption of analytic initial data we construct solutions of navier stokes for a short time which is independent of the viscosity the navier stokes solution is constructed through a composite asymptotic expansion involving the solutions of the euler and prandtl equations which were constructed in the first paper plus an error term this shows that the navier stokes solution goes to an euler solution outside a boundary layer and to a solution of the prandtl equations within the boundary layer the error term is written as a sum of first order euler and prandtl corrections plus a further error term the equation for the error term is weakly nonlinear its linear part is the time dependent stokes equation this error equation is solved by inversion of the stokes equation through expressing the solution as a regular euler like part plus a boundary layer prandtl like part the main technical tool in this analysis is the abstract cauchy kowalewski theorem

kinetic schemes in the case of low mach numbers originally kinetic schemes have been used as numerical methods to solve the system of compressible euler equations in gas dynamics the main idea in the approach is to construct the numerical flux function based on a microscopical description of the gas in this article the schemes are investigated in the case of isentropic euler equations and low mach numbers expanding the microscopical velocity distribution naturally leads to new kinetic schemes with strong resemblance to lattice boltzmann methods by adjusting the parameters of the kinetic scheme the numerical viscosity can be used to reproduce a given physical viscosity in this way a finite difference solver for the incompressible navier stokes equation is obtained its close relation to the lattice boltzmann approach is highlighted

fast algorithms for computing the boltzmann collision operator the development of accurate and fast numerical schemes for the five fold boltzmann collision integral represents a challenging problem in scientific computing for a particular class of interactions including the so called hard spheres model in dimension three we are able to derive spectral methods that can be evaluated through fast algorithms these algorithms are based on a suitable representation and approximation of the collision operator explicit expressions for the errors in the schemes are given and spectral accuracy is proved parallelization properties and adaptivity of the algorithms are also discussed

decay theorems for the broadwell equations in this note we establish boundedness and decay theorems for finitely supported solutions to the broadwell equations with four velocity components there is a vast literature on these and similar equations for details see the survey of platkowski illner and the references contained therein the particular variant of them we examine seems new though nonlinear they are homogeneous of degree one

towards an ultra efficient kinetic scheme part ii in a recent paper we presented a new ultra efficient numerical method for solving kinetic equations of the boltzmann type dimarco and loubere 2013 17 the key idea on which the method relies is to solve the collision part on a grid and then to solve exactly the transport part by following the characteristics backward in time on the contrary to classical semi lagrangian methods one does not need to reconstruct the distribution function at each time step this allows to tremendously reduce the computational cost and to perform efficient numerical simulations of kinetic equations up to the six dimensional case without parallelization however the main drawback of the method developed was the loss of spatial accuracy close to the fluid limit in the present work we modify the scheme in such a way that it is able to preserve the high order spatial accuracy for extremely rarefied and fluid regimes in particular in the fluid limit the method automatically degenerates into a high order method for the compressible euler equations numerical examples are presented which validate the method show the higher accuracy with respect to the previous approach and measure its efficiency with respect to well known schemes direct simulation monte carlo finite volume muscl weno

a discrete bgk approximation for strongly degenerate parabolic problems with boundary conditions abstract we consider a class of bgk systems with a finite number of velocities depending on a positive relaxation parameter that approximate strongly degenerate hyperbolic parabolic equations with initial boundary conditions we prove a priori estimates for the solutions of the systems showing that these functions converge towards the entropy solutions of strongly degenerate problems when the relaxation parameter goes to zero

space localization and well balanced schemes for discrete kinetic models in diffusive regimes we derive and study well balanced schemes for quasi monotone discrete kinetic models by means of a rigorous localization procedure we reformulate the collision terms as nonconservative products and solve the resulting riemann problem whose solution is self similar the construction of an asymptotic preserving ap godunov scheme is straightforward and various compactness properties are established within different scalings finally some computational results are supplied to show that this approach is realizable and efficient on concrete 2 2 models

the boltzmann equation global existence for a rare gas in an infinite vacuum solutions of the boltzmann equation are proved to exist globally in time under conditions that include the case of a finite volume of gas in an infinite vacuum when the mean free path of the gas is large enough it is also proved as might be expected in this case that the density of the gas at each point in space goes to zero as time goes to infinity

on the lingual organization of the german vowel system a hybrid parafac and principal component model of tongue configuration in vowel production is presented using a corpus of german vowels in multiple consonant contexts fleshpoint data for seven speakers at two speech rates from electromagnetic articulography the parafac approach is attractive for explicitly separating speaker independent and speaker dependent effects within a parsimonious linear model however it proved impossible to derive a parafac solution of the complete dataset estimated to require three factors due to complexities introduced by the consonant contexts accordingly the final model was derived in two stages first a two factor parafac model was extracted this succeeded the result was treated as the basic vowel model second the parafac model error was subjected to a separate principal component analysis for each subject this revealed a further articulatory component mainly involving tongue blade activity associated with the flanking consonants however the subject specific details of the mapping from raw fleshpoint coordinates to this component were too complex to be consistent with the parafac framework the final model explained over 90 of the variance and gave a succinct and physiologically plausible articulatory representation of the german vowel space

large time behavior of the broadwell model of a discrete velocity gas with specularly reflective boundary conditions this paper studies the behavior of the one dimensional broadwell model of a discrete three velocity gas on a bounded domain 0 x 1 with specularly reflective boundary condition at x 0 1 for smooth initial data we show that the initial boundary value problem possesses a unique smooth solution which tends as t to a free state consisting of traveling waves f 1e x ct f 2e x ct f 3e x where each f ie is 2 periodic the convergence is in the weak topology of an appropriate orlicz banach state space no smallness assumptions are made on the data

large time behavior of discrete velocity boltzmann equations we study the asymptotic behavior of equations representing one dimensional motions in a fictitious gas with a discrete set of velocities the solutions considered have finite mass but arbitrary amplitude with certain assumptions every solution approaches a state in which each component is a traveling wave without interaction the techniques are similar to those in an earlier treatment of the broadwell model 1

a methodology for modeling vowel formant contours in cvc context models for the formant frequency contours of vowels in cvc context are presented and illustrated with an american english database comprising isolated syllables with c c b d g and v i i q ae a c u u v w both established and reinterpreted regularities among context effects are cast in a series of successively elaborated mathematical models the first model model i in common with all its successors embodies the notion of the superposition of cv and vc transitions according to which a formant trajectory fcvc n is modeled as fcv n tv gvc n where n is duration normalized time tv is a vowel target and fcv n and gvc n are initial and final consonant transition functions the rms errors for f1 f2 and f3 30 89 and 111 hz against independent test data are near the minimum theoretical values 32 69 and 100 hz predicted from interrepetition variation and its contribution to uncertainty in the model elements subsequently the elements of the additive model are individually characte

1 1 dimensional hierarchies of multispeed discrete boltzmann model equations multispeed discrete boltzmann models in rd satisfying all conservation laws and leading to well defined temperatures are studied the 1 1 dimensional restriction of the system of partial differential equations pde satisfied by the densities of these models can be classified one class is characterized along a chosen coordinate by the number and location of the independent densities and by the number and physical meaning of the independent collision terms each class defines a hierarchy of pde that depends on the dimension d of a particular model in rd different classes associated either with two velocity speeds 1 and 1 d 1 2 and 2 and 2 d 1 2 or three velocity speeds 0 1 and 0 2 are obtained each class represents a d hierarchy of a well known discrete model the simplest exact solutions which are the similarity shock wave solutions are discussed and compared with the rankine hugoniot solutions

wave structure induced by fluid dynamic limits in the broadwell model consider the fluid dynamic limit problem for the broadwell system of the kinetic theory of gases for maxwellian riemann initial data the formal limit is the riemann problem for a pair of conservation laws and is invariant under dilations of coordinates the approach of self similar fluid dynamic limits consists in replacing the mean free path in the broadwell model so that the resulting problem preserves the invariance under dilations the limiting procedure was justified in st here we study the structure of the emerging solutions we show that they consist of two wave fans separated by a constant state each wave fan is associated with one of the characteristic fields and is either a rarefaction wave or a shock wave the shocks satisfy the lax shock conditions and have the internal structure of a broadwell shock profile

hyperbolic systems with supercharacteristic relaxations and roll waves we study a distinguished limit for general 2 2 hyperbolic systems with relaxation which is valid in both the subcharacteristic and supercharacteristic cases this is a weakly nonlinear limit which leads the underlying relaxation systems into a burgers equation with a source term the sign of the source term depends on the characteristic interleaving condition in the supercharacteristic case the problem admits a periodic solution known as the roll wave generated by a small perturbation around equilibrium constants such a limit is justified in the presence of artificial viscosity using the energy method

uniformly accurate schemes for hyperbolic systems with relaxation we develop high resolution shock capturing numerical schemes for hyperbolic systems with relaxation in such systems the relaxation time may vary from order 1 to much less than unity when the relaxation time is small the relaxation term becomes very strong and highly stiff and underresolved numerical schemes may produce spurious results usually one cannot decouple the problem into separate regimes and handle different regimes with different methods thus it is important to have a scheme that works uniformly with respect to the relaxation time using the broadwell model of the nonlinear boltzmann equation we develop a second order scheme that works effectively with a fixed spatial and temporal discretization for all ranges of the mean free path formal uniform consistency proof for a first order scheme and numerical convergence proof for the second order scheme are also presented we also make numerical comparisons of the new scheme with some other schemes this study is motivated by the reentry problem in hypersonic computations

on shock wave solutions in extended discrete kinetic theory exact traveling wave solutions joining asymptotic maxwellians in the frame of discrete velocity models of the boltzmann equation are investigated and discussed in an extended formulation which also allows for removal creation and scattering collisions with the particles of a given background it is shown that the classical broadwell shock wave structure does not carry over to any extended problem on the other hand families of exact shock wave solutions do exist for extended two velocity models for which such waves are lacking in the classical i e unextended case

convergence to rarefaction waves for the nonlinear boltzmann equation and compressible navier stokes equations abstract the main purpose of this paper is to study the asymptotic equivalence of the boltzmann equation for the hard sphere collision model to its corresponding euler equations of compressible gas dynamics in the limit of small mean free path when the fluid flow is a smooth rarefaction or centered rarefaction wave with finite strength the corresponding boltzmann solution exists globally in time and the solution converges to the rarefaction wave uniformly for all time or away from t 0 as 0 a decomposition of a boltzmann solution into its macroscopic fluid part and microscopic kinetic part is adopted to rewrite the boltzmann equation in a form of compressible navier stokes equations with source terms in this setting the same asymptotic equivalence of the full compressible navier stokes equations to its corresponding euler equations in the limit of small viscosity and heat conductivity depending on the viscosity is also obtained

l1nonlinear stability of traveling waves for a hyperbolic system with relaxation where x t r r the unknowns u v belong to r the function f f u is in c r and 0 is a fixed constant relaxation systems often arise in many physical situations let us recall for example gases not in thermodynamic equilibrium vk kinetic theory ce cip pi chromatography raa river flows traffic flows and more general waves wh more recently the study of a special class of hyperbolic systems with relaxation was developed in view of the numerical approximation of discontinuous solutions of conservation laws jx an the 2 2 relaxation hyperbolic systems of conservation laws were first analyzed by liu li2 who justified some nonlinear stability criteria for diffusion waves expansion waves and traveling waves article no 0180

an improved image denoising model based on the directed diffusion equation by substituting an anisotropic diffusion operator for the isotropic laplace operator in the directed diffusion equation adding two different coefficients in the two diffusion terms and choosing the image denoised by soft wavelet shrinkage as the initial approximate image an improved directed diffusion equation model is proposed experiments show that the new model can solve the problem that edges and details will be rapidly blurred during the diffusion process in the directed diffusion equation

fluid dynamic limit for the centered rarefaction wave of the broadwell equation abstract we study the asymptotic equivalence of the 1 d broadwell model of the nonlinear boltzmann equation to its corresponding euler equation of compressible gas dynamics in the limit of small mean free path we consider the case where the initial data are allowed to have jump discontinuities such that the corresponding solutions to the euler equation contain centered rarefaction waves in particular riemann data connected by rarefaction curves are included we show that as long as the initial data are a small perturbation of a non vacuum constant state the solution for the broadwell equation exists globally in time and converges in the small mean free path limit to the solution of the corresponding euler equation uniformly except for an initial layer whose width is essentially the order of the mean free path

large time behavior of solutions for hyperbolic balance laws we study the existence and the large time behavior of global solutions to the initial value problem for hyperbolic balance laws in n space dimensions with n 3 admitting an entropy and satisfying the stable condition we first construct global existence of the solutions to such a system around a steady state if the initial energy is small enough then we show that k order derivatives of these solutions approach a constant state in the lp norm at a rate o t 12 k n2 np with p 2 and 0 n2 provided that initially z0 b 2 where b 2 is a homogeneous besov space these decay results do not impose an additional smallness assumption on lp norm of the initial data and we thus improve the results in 3 19 we also show faster decay results in the sense that if pz0 b 2 i p z0 b 2 1 with n2 n 22 k order derivatives of the solutions approach a constant state in the lp norm at a rate o t 12 k 1 n2 np

a constructive approach to steady nonlinear kinetic equations abstract we study steady boundary value problems of nonlinear kinetic theory using a continuation argument based on the variation of the knudsen number we derive a method for the construction of steady solutions of discrete velocity models in a slab this method is readily transformed into a numerical code in a preliminary numerical test case the numerical scheme turns out to yield solutions even for knudsen numbers small enough to calculate with high precision the asymptotic flow field adjacent to a kinetic boundary layer thus we are able to numerically simulate in a simplified situation the transition from a mesoscopic kinetic boundary layer to the macroscopic far field

exact solutions of a hierarchy of mixing speeds models this paper presents several new aspects of discrete kinetic theory dkt first a hierarchy of d dimensional d 1 2 3 models is proposed with 2d 3 velocities and three moduli speeds 0 2 and a third one that can be arbitrary it is assumed that the particles at rest have an internal energy which for microscopic collisions supplies for the loss of the kinetic energy in a more general way than usual collisions are allowed that mix particles with different speeds second for the 1 1 dimensional restriction of the systems of pde for these models which have two independent quadratic collision terms we construct different exact solutions the usual types of exact solutions are studied periodic solutions and shock wave solutions obtained from the standard linearization of the scalar riccati equations called riccatian shock waves then other types of solutions of the coupled riccati equations are found called non riccatian shock waves and they are compared with the previous ones the main new result