the milne and kramers problems for the boltzmann equation of a hard sphere gas existence uniqueness and properties of asymptotic behavior are proved for solutions of the milne and kramers problems for the linearized boltzmann equation for a gas of hard spheres the proof uses energy like estimates and follows the analysis of bardos santos and sentis for the equations of neutron transport

a numerical model for the boltzmann equation with applications to micro flows given an integer lattice email protected r d we define g as the orthogonal group leaving l invariant starting from a basic kinetic model on g we construct a collision operator on l which keeps all the essential features of the classical boltzmann collision operator for a particular 3d lattice we demonstrate the suitability of this discrete model for the numerical simulation of rarefied flows for several examples e g in the context of micro flows we find a good qualitative and quantitative agreement of our simulation results with test data

construction of binary four and five point non stationary subdivision schemes from hyperbolic b splines binary non stationary four and five point subdivision schemes have been developed using hyperbolic b spline basis functions the proposed subdivision schemes generate pleasing curves near the control polygon as compared to the existing non stationary subdivision schemes developed using trigonometric b splines basis functions the main speciality of the hyperbolic subdivision schemes is that they can regenerate hyperbolas and parabolas quite efficiently

a family of non stationary subdivision schemes reproducing exponential polynomials we present a family of non stationary subdivision schemes taking the exponential quasi spline as the basic limit function reaching up to interpolatory refinable functions the exponential quasi spline generalizes the exponential b spline the associated non stationary subdivision scheme can reproduce the desired number of exponential polynomials due to the built in parameter permitting a wide range of tension control our scheme can avoid the undesirable artifact generated by usual non stationary interpolatory schemes on the irregularly spaced region of control points under a natural condition on the rate of convergence of the shape parameters all the subdivision schemes in the family have the same smoothness and approximation order as those of the asymptotically equivalent stationary schemes we present numerical examples to verify that our subdivision schemes have high flexibility and versatility in design

reproduction of exponential polynomials by multivariate non stationary subdivision schemes with a general dilation matrix we study scalar multivariate non stationary subdivision schemes with a general integer dilation matrix we characterize the capability of such schemes to reproduce exponential polynomials in terms of simple algebraic conditions on their symbols these algebraic conditions provide a useful theoretical tool for checking the reproduction properties of existing schemes and for constructing new schemes with desired reproduction capabilities and other enhanced properties we illustrate our results with several examples

generation of fractal curves and surfaces using ternary 4 point interpolatory subdivision scheme in this paper the generation of fractal curves and surfaces along with their properties using ternary 4 point interpolatory subdivision scheme with one parameter are analyzed the relationship between the tension parameter and the fractal behavior of the limiting curve is demonstrated through different examples the specific range of the tension parameter has also been depicted which provides a clear way to generate fractal curves since the fractal scheme introduces in the paper have more number of control points therefore it gives more degree of freedom to control the shape of the fractal curve

the weighted particle method for convection diffusion equations ii the anisotropic case on etend la methode particulaire utilisee dans la partie i pour les equations de convection diffusion aux operateurs de diffusion anisotrope des conditions plus complexes que dans le cas isotrope sont exigees pour les fonctions de cutoff une analyse d erreur detaillee est effectuee

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

a family of non uniform subdivision schemes with variable parameters for curve design in this paper we present non uniform subdivision schemes with variable parameter sequences a locally different tension parameter is set at each edge of the initial control polygon to control locally the shape of the resulting curve such that the scheme becomes non uniform due to the variable parameters the scheme can reproduce locally different analytic curves such as conics lissajous trigonometric and catenary curves hence blending curves including such analytic components can be successfully generated we discuss the convergence and smoothness of the proposed non uniform schemes and present some numerical results to demonstrate their advantages in geometric modeling furthermore as an application we propose a chamfering algorithm which can be used in designing automobile and mechanical products

algebraic conditions on non stationary subdivision symbols for exponential polynomial reproduction we present an accurate investigation of the algebraic conditions that the symbols of a non singular univariate binary non stationary subdivision scheme should fulfill in order to reproduce spaces of exponential polynomials a subdivision scheme is said to possess the property of reproducing exponential polynomials if for any initial data uniformly sampled from some exponential polynomial function the scheme yields the same function in the limit the importance of this property is due to the fact that several curves obtained by combinations of exponential polynomials such as conic sections spirals or special trigonometric and hyperbolic functions are considered of interest in geometric modeling since the space of exponential polynomials trivially includes standard polynomials this work extends the theory on polynomial reproduction to the non stationary context a significant application of the derived algebraic conditions on the subdivision symbols is the construction of new non stationary subdivision schemes with specific reproduction properties

fractal behavior of ternary 4 point interpolatory subdivision scheme with tension parameter in this paper the fractal curves and surfaces of ternary 4 point interpolatory subdivision scheme are developed and analyzed the fractal range of the tension parameter has also been determined the behavior of fractal curves and surfaces corresponding to different values of parameter has been depicted through six examples which offers direct means for an effective generation of subdivision fractals the real life applications of the proposed fractal subdivision scheme has also been demonstrated

shape controlled interpolatory ternary subdivision ternary subdivision schemes compare favorably with their binary analogues because they are able to generate limit functions with the same or higher smoothness but smaller support in this work we consider the two issues of local tension control and conics reproduction in univariate interpolating ternary refinements we show that both these features can be included in a unique interpolating 4 point subdivision method by means of non stationary insertion rules that do not affect the improved smoothness and locality of ternary schemes this is realized by exploiting local shape parameters associated with the initial polyline edges

convergence of nonstationary cascade algorithms a nonstationary multiresolution of l 2 mathbb r s is generated by a sequence of scaling functions phi k in l 2 mathbb r s k in mathbb z we consider phi k that is the solution of the nonstationary refinement equations phi k m sum j h k 1 j phi k 1 m cdot j k in mathbb z where h k is finitely supported for each k and m is a dilation matrix we study various forms of convergence in l 2 mathbb r s of the corresponding nonstationary cascade algorithm phi k n m sum j h k 1 j phi k 1 n 1 m cdot j as k or n tends to infty it is assumed that there is a stationary refinement equation at infty with filter sequence h and that sum k h k j h j infty the results show that the convergence of the nonstationary cascade algorithm is determined by the spectral properties of the transition operator associated with h

hyperbolic forms of ternary non stationary subdivision schemes originated from hyperbolic b splines in this work ternary non stationary subdivision schemes based on hyperbolic b spline basis functions have been presented the proposed hyperbolic ternary three point and four point subdivision schemes give pleasing as well as consistent curves with the control polygons as compared to the existing non stationary subdivision schemes obtained from trigonometric b splines the main speciality of the hyperbolic schemes is that they can reproduce hyperbolas and parabolas quite efficiently which has been demonstrated with the help of curvature plots

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

discrete model collision operators of boltzmann type in the present paper we develop a new kind of discrete velocity models to discretize the boltzmann collision operator the chosen approach is situated between the macroscopic ansatz of the bgk model and the microscopic ansatz of usual discrete velocity models beside questions of the solvability and the form of the solutions of the arising optimization problems the weak convergence of the discrete collision operators to the original operator is proved

a non stationary binary three point approximating subdivision scheme in this paper we present a non stationary binary three point approximating subdivision scheme which can generate a wide variety of c3 continuous limit curves with different initial control parameter 0 the continuity of the scheme is proved by using the conclusion in dyn and levin 1995 5 the advantage of the scheme is illustrated by a number of examples

scale induced closure for approximations of kinetic equations the order of magnitude method proposed by struchtrup phys fluids 16 11 3921 3934 2004 is a new closure procedure for the infinite moment hierarchy in kinetic theory of gases taking into account the scaling of the moments the scaling parameter is the knudsen number kn which is the mean free path of a particle divided by the system size

understanding propagation failure as a slow capture near a limit point this paper investigates the phenomenon of propagation failure in spatially discrete reaction diffusion systems with excitable kinetics excitable kinetics are modeled by the fitzhugh nagumo equations in the limit of weak coupling strength a traveling pulse propagating in a chain of cells is constructed the asymptotic solution for the first three cells is studied in detail a single riccati equation describes propagation through each cell from this equation a first approximation for the critical coupling strength below which the pulse is blocked is obtained near this critical coupling strength propagation or failure results from a slow passage near a limit point leading either to a successful jump propagation or to capture by a slowly varying steady state failure the analysis of the behavior of the first three cells suggests an algorithmic method to analyze propagation through an arbitrary number of coupled cells failure may appear at any cell in the chain but is described by the same riccati e

pulse propagation in discrete systems of coupled excitable cells propagation of pulses in myelinated fibers may be described by appropriate solutions of spatially discrete fitzhugh nagumo systems in these systems propagation failure may occur if either the coupling between nodes is not strong enough or the recovery is too fast we give an asymptotic construction of pulses for spatially discrete fitzhugh nagumo systems which agrees well with numerical simulations and discuss the evolution of initial data into pulses and pulse generation at a boundary formulas for the speed and length of pulses are also obtained

from approximating subdivision schemes for exponential splines to high performance interpolating algorithms in this work we construct three novel families of approximating subdivision schemes that generate piecewise exponential polynomials and we show how to convert these into interpolating schemes of great interest in curve design for their ability to reproduce important analytical shapes and to provide highly smooth limit curves with a controllable tension in particular throughout this paper we will focus on the derivation of 6 point interpolating schemes that turn out to be unique in combining vital ingredients like c 2 continuity simplicity of definition ease of implementation user independency tension control and ability to reproduce salient trigonometric and transcendental curves

a convergence proof for nanbu s simulation method for the full boltzmann equation it is shown that the discrete measures given by the nanbu simulation method converge with respect to the weak topology of measures to solutions of the boltzmann equation the main conditions for this result are that the cauchy problem for the boltzmann equation has a sufficiently smooth solution and that the discretization parameters cell size timestep and test particle number satisfy suitable constraints

convexity preservation of five point binary subdivision scheme with a parameter a five point binary subdivision scheme with a parameter u is presented the generating polynomial method and the holder exponent are used to investigate the uniform convergence and c k continuity of this subdivision scheme where k depends on the choice of the parameter u moreover the conditions on the initial points are discussed for the given limit curve to be convexity preserving and an example is given to illustrate our conclusion

non uniform interpolatory subdivision surface abstract this paper presents an interpolatory subdivision scheme with non uniform parametrization for arbitrary polygon meshes with arbitrary manifold topology this is the first attempt to generalize the non uniform four point interpolatory curve subdivision to surface with extraordinary points the scheme is constructed from the inspiration of the relation between the non uniform four point interpolatory subdivision scheme and the non uniform b spline refinement rule numerical examples and comparisons with the uniform interpolatory subdivision schemes indicate that the quality of the limit surface can be improved by using non uniform parameter values for non uniform initial data

on four point penalized lagrange subdivision schemes this paper is devoted to the definition and analysis of new subdivision schemes called penalized lagrange their construction is based on an original reformulation for the construction of the coefficients of the mask associated to the classical 4 points lagrange interpolatory subdivision scheme these coefficients can be formally interpreted as the solution of a linear system similar to the one resulting from the constrained minimization problem in kriging theory which is commonly used for reconstruction in geostatistical studies in such a framework the introduction in the formulation of a so called error variance can be viewed as a penalization of the oscillations of the coefficients following this idea we propose to penalize the 4 points lagrange system this penalization transforms the interpolatory schemes into approximating ones with specific properties suitable for the subdivision of locally noisy or strongly oscillating data according to a so called penalization vector a family of schemes can be generated a full theoretical study is first performed to analyze this new type of non stationary subdivision schemes then in the framework of position dependant penalization vector several numerical tests are provided to point out the efficiency of these schemes compared to standard approaches

a consistency result for a discrete velocity model of the boltzmann equation in this paper we study the link between a certain class of discrete velocity models dvms and the boltzmann equation those models possess an infinite number of velocities laying on a regular grid of step h in r3 our aim is to prove that it is possible to construct models consistent with the boltzmann equation i e such that the discrete collision term can be seen as an approximation of the collision integral of the boltzmann equation

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

fractal properties of the generalized chaikin corner cutting subdivision scheme in this paper we analyze the fractal properties of the generalized chaikin corner cutting subdivision scheme with two arbitrary parameters on the basis of the discussion of limit points on the limit curve the fractal range of the scheme is obtained and illustrated the results obtained suggest a clear direction for generating fractal curves by using this scheme two fractal examples and their complexity evaluation results obtained by using the box dimension are given

generalized daubechies wavelet families we present a generalization of the orthonormal daubechies wavelets and of their related biorthogonal flavors cohen daubechies feauveau 9 7 our fundamental constraint is that the scaling functions should reproduce a predefined set of exponential polynomials this allows one to tune the corresponding wavelet transform to a specific class of signals thereby ensuring good approximation and sparsity properties the main difference with the classical construction of daubechies is that the multiresolution spaces are derived from scale dependent generating functions however from an algorithmic standpoint mallat s fast wavelet transform algorithm can still be applied the only adaptation consists in using scale dependent filter banks finite support ensures the same computational efficiency as in the classical case we characterize the scaling and wavelet filters construct them and show several examples of the associated functions we prove that these functions are square integrable and that they converge to their classical counterparts of the corresponding order

a family of ternary subdivision schemes for curves a family of ternary 3 point subdivision schemes is introduced and has a degree of smoothness c1 continuity a family of ternary 4 point subdivision schemes is derived and has degrees of smoothness c1 and c2 continuities also a ternary 4 point approximating subdivision scheme is proposed that generates the limiting curve of c3 continuity the eigenvalue analysis and generating function formalism are used to analyze the continuity properties of these subdivision schemes also these subdivision schemes are compared with the established subdivision schemes

binary 3 point and 4 point non stationary subdivision schemes using hyperbolic function in this paper binary 3 point and 4 point non stationary subdivision schemes are presented using hyperbolic function as basis function asymptotic equivalence method is used to investigate the continuity of the proposed schemes comparison between the proposed schemes their stationary counterparts and some existing non stationary schemes has been depicted through examples it can be observed that the proposed schemes have the capability to reproduce conics particularly parabola

on a boundary layer problem for the nonlinear boltzmann equation this article deals with a boundary layer problem arising in the kinetic theory of gases when the mean free path of molecules tends to zero the model considered here is the stationary nonlinear boltzmann equation in one dimension with a slightly perturbed reflection boundary condition we restrict our attention to the case of hard spheres collisions with grad s cutoff assumption existence uniqueness and asymptotic behavior are derived by means of energy estimates

a non stationary combined subdivision scheme generating exponential polynomials abstract in this paper a non stationary combined subdivision scheme is presented which can unify several existing non stationary approximating and interpolatory subdivision schemes this scheme is obtained by generalizing the connection between the approximating and interpolatory schemes in the stationary case first formalized by maillot stam using a push back operator to the non stationary case for such a combined scheme we investigate its c l convergence and exponential polynomial generation reproduction property and get that it can reach c 4 degree of smoothness and generate reproduce certain exponential polynomials with suitable choices of the parameters besides we give a more generalized combined scheme for the purpose of generating and reproducing more general exponential polynomials the performance of our new schemes is illustrated by several numerical examples

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

improved binary four point subdivision scheme and new corner cutting scheme a binary 4 point approximating subdivision scheme presented by siddiqi and ahmad 2006 9 has been improved by introducing a global tension parameter an improved form of the scheme generates a family of c n n 1 2 3 4 limiting curves for certain range of global tension parameter and a c 5 limiting curve for a fixed value also a new corner cutting subdivision scheme has been proposed which generates a limiting curve of c 1 continuity the laurent polynomial method has been used to investigate the order of the derivative continuity of both subdivision schemes the performance of the subdivision schemes has been exposed by considering examples and compared with the existing schemes

a combined approximating and interpolating ternary 4 point subdivision scheme abstract in this paper a new combined approximating and interpolating ternary 4 point subdivision scheme with multiple parameters is proposed a set of nice properties such as support continuity and polynomial generation are briefly discussed the new combined scheme not only contains a lot of classical ternary schemes as special cases but also generates brand new ternary schemes compared to other approximating subdivision schemes limit curves generated by the new scheme are more consistent with the corresponding control polygons and keep detail features better examples are given to show the effectiveness of the scheme furthermore fractal property is analyzed and fractal curves are also given

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

wave block in excitable media due to regions of depressed excitability we study propagation failure using the one dimensional scalar bistable equation with a passive gap region by applying comparison principles for this type of equation the problem of finding conditions for block is reduced to finding conditions for the existence of steady state solutions we present a geometrical method that allows one to easily compute the critical gap length above which a steady state solution and thus block first occurs the method also helps to uncover the general bifurcation structure of the problem including the stability of the steady state solutions in obtaining these results we characterize the relationship between the properties of the system and propagation failure the method can easily be extended to other gap dynamics we use it to show that block associated with any local inhomogeneity must be associated with a limit point bifurcation

analysis of asymptotically equivalent binary subdivision schemes non stationary uniform subdivision schemes are presented including some important examples as the up function and exponential splines the multivariate analysis of subdivision schemes is extended to a class of non stationary schemes which are asymptotically equivalent to converging stationary or non stationary schemes

a new non stationary binary 6 point subdivision scheme in this paper the hyperbolic form of binary 6 point interpolating non stationary subdivision scheme has been constructed using the hyperbolic function some of the important properties of the proposed scheme has been discussed the comparison of the proposed scheme with the trigonometric form of binary 6 point interpolatory non stationary scheme is depicted through examples which indicate that the proposed scheme not only accommodates and is more consistent with the control polygon but also generates pleasing curves corresponding to the larger parametric values in and outside the parametric interval as compared to the trigonometric form of binary 6 point scheme developed by daniel et al comparison with some other interpolating non stationary subdivision schemes has also been demonstrated

traveling waves in a spring block chain sliding down a slope travelling waves in a spring block chain sliding down an inclined plane are studied for a piecewise linear spinodal friction force we construct analytically front waves pulse waves are obtained as the matching of two travelling fronts with identical speeds explicit formulas are obtained for the wavespeed and the wave form in the anti continuum limit the link with propagating phenomena in the burridge knopoff model is briefly discussed

discretization and numerical schemes for steady kinetic model equations abstract there are still many open questions concerning the relationship between steady kinetic equations random particle games designed for these equations and transitions e g to fluid dynamics and turbulence phenomena the paper presents some first steps into the derivation of models which on one hand may be used for the design of efficient numerical schemes for steady gas kinetics and on the other hand allow to study the interplay between particle schemes and physical phenomena

an interpolating 6 point c2 non stationary subdivision scheme in this paper we consider a 6 point interpolating c 2 binary non stationary subdivision scheme and present some of its important properties we highlight some advantages of the scheme and demonstrate its performance by some examples

regularized boltzmann operators abstract in this paper we propose two regularization approaches for the boltzmann collision operator the constructed operators preserve the mass momentum and energy their equilibrium states are maxwellians and they satisfy the h theorem in the first approach the regularization consists in allowing microscopic collisions which do not exactly preserve energy and momentum however the limit of the mollified operator when the cut off parameter tends to 0 is not the usual boltzmann operator unless a certain condition on the distribution function is satisfied in the second approach the regularization relies on a smoothing of the masses of the particles and leads to a regularized operator which formally tends to the boltzmann operator for any arbitrary distribution function when the cut off parameter tends to zero

limits of level and parameter dependent subdivision schemes in this paper we present a new matrix approach for the analysis of subdivision schemes whose non stationarity is due to linear dependency on parameters whose values vary in a compact set indeed we show how to check the convergence in c r s and determine the holder regularity of such level and parameter dependent schemes efficiently via the joint spectral radius approach the efficiency of this method and the important role of the parameter dependency are demonstrated on several examples of subdivision schemes whose properties improve the properties of the corresponding stationary schemes

modified form of binary and ternary 3 point subdivision schemes binary 3 point scheme developed by hormann and sabin hormann k and sabin malcolm a 2008 a family of subdivision schemes with cubic precision computer aided geometric design 25 41 52 has been modified by introducing a tension parameter which generates a family of c 1 limiting curves for certain range of tension parameter ternary 3 point scheme introduced by siddiqi and rehan siddiqi shahid s and rehan k 2009 a ternary three point scheme for curve designing international journal of computer mathematics in press doi 10 1080 00207160802428220 has also been modified by introducing a tension parameter which generates family of c 1 and c 2 limiting curves for certain range of tension parameter laurent polynomial method is used to investigate the continuity of the subdivision schemes the performance of modified schemes has been demonstrated by considering different examples along with its comparison with the established subdivision schemes

oscillatory wave fronts in chains of coupled nonlinear oscillators wave front pinning and propagation in damped chains of coupled oscillators are studied there are two important thresholds for an applied constant stress f for f f cs static peierls stress there are only stable moving wave fronts for piecewise linear models extending an exact method of atkinson and cabrera s to chains with damped dynamics corroborates this description for smooth nonlinearities an approximate analytical description is found by means of the active point theory generically for small or zero damping stable wave front profiles are nonmonotone and become wavy oscillatory in one of their tails

analysis of non stationary hermite subdivision schemes reproducing exponential polynomials abstract the aim of this paper is to study the convergence and smoothness of non stationary hermite subdivision schemes of order 2 in conti et al 2017 provided sufficient conditions for the convergence of a non stationary hermite subdivision scheme that reproduces a set of functions including exponential polynomials the analysis has been focused on the non stationary hermite scheme with the order 3 but the case of 2 which is practically most useful is yet to be investigated in this regard the first goal of this paper is to fill the gap we analyze the convergence of non stationary hermite subdivision schemes of order 2 next we provide a tool which allows us to estimate the smoothness of a non stationary hermite scheme by developing a novel factorization framework of non stationary vector subdivision operators using the proposed non stationary factorization framework we estimate the smoothness of the non stationary hermite subdivision schemes the non stationary interpolatory hermite scheme proposed by conti et al 2015 and a new class of non stationary dual hermite subdivision schemes of de rham type

a ternary 4 point approximating subdivision scheme in the implementation of subdivision scheme three of the most important issues are smoothness size of support and approximation order our objective is to introduce an improved ternary 4 point approximating subdivision scheme derived from cubic polynomial interpolation which has smaller support and higher smoothness comparing to binary 4 point and 6 point schemes ternary 3 point and 4 point schemes see table 2 the method is easily generalized to ternary 2n 2 point approximating subdivision schemes we choose a ternary scheme because a way to get smaller support is to raise arity and we use polynomial reproduction to get higher approximation order easily 2007 elsevier inc all rights reserved

discrete kinetic models in the fluid dynamic limit we investigate discrete kinetic models in the fluid dynamic limit described by the euler system and the navier stokes correction obtained by the chapman enskog procedure we show why reliable small systems can be expected only for small mach numbers and derive a calculus for designing models for given prandtl numbers

smooth curve interpolation with generalized conics abstract efficient algorithms for shape preserving approximation to curves and surfaces are very important in shape design and modelling in cad cam systems in this paper a local algorithm using piecewise generalized conic segments is proposed for shape preserving curve interpolation it is proved that there exists a smooth piecewise generalized conic curve which not only interpolates the data points but also preserves the convexity of the data furthermore if the data is strictly convex then the interpolant could be a locally adjustable gc 2 curve provided the curvatures at the data points are well determined it is also shown that the best approximation order is o h 6 an efficient algorithm for the simultaneous computation of points on the curve is derived so that the curve can be easily computed and displayed the numerical complexity of the algorithm for computing n points on the curve is about 2 n multiplications and n additions finally some numerical examples with graphs are provided and comparisons with both quadratic and cubic spline interpolants are also given

regularity of non stationary subdivision a matrix approach in this paper we study scalar multivariate non stationary subdivision schemes with integer dilation matrix m and present a unifying general approach for checking their convergence and for determining their holder regularity latter in the case m mi m ge 2 m mi m 2 the combination of the concepts of asymptotic similarity and approximate sum rules allows us to link stationary and non stationary settings and to employ recent advances in methods for exact computation of the joint spectral radius as an application we prove a recent conjecture by dyn et al on the holder regularity of the generalized daubechies wavelets we illustrate our results with several examples

nonuniform cascade algorithms abstract for a sequence of bounded linear operators hk k 0 1 on a banach space s the algorithm k n hk k 1 n 1 generates a family of sequences k n n 0 k 0 1 from an initial family of vectors k 0 s k 0 1 we study the convergence of k n as n and give an application on the convergence of cascade algorithms for nonuniform splines when s is the space of all sequences i i z with norm sup i z i and i i z belong to the banach space x l 2 r

asymptotic construction of pulses in the discrete hodgkin huxley model for myelinated nerves a quantitative description of pulses and wave trains in the spatially discrete hodgkin huxley model for myelinated nerves is given predictions of the shape and speed of the waves and the thresholds for propagation failure are obtained our asymptotic predictions agree quite well with numerical solutions of the model and describe wave patterns generated by repeated firing at a boundary

unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement this paper describes a unified flow solver ufs for rarefied and continuum gas flows the ufs separates the rarefied and continuum flow domains and selects appropriate solvers to combine the efficiency of continuum models with the accuracy of kinetic models the direct numerical solution of the boltzmann transport equation is used in rarefied regions while kinetic schemes of continuum fluid dynamics are used elsewhere using similar computational techniques for the kinetic and continuum solvers and employing intelligent domain decomposition algorithms attain the efficiency and numerical stability of the ufs solutions of test problems are presented to illustrate the capabilities of the ufs for high and low speed flows it is shown that the ufs can dynamically adapt the computational mesh and automatically introduce and remove kinetic patches to provide significant savings by limiting molecular scale solutions only to the regions where they are needed

fractal generation using ternary 5 point interpolatory subdivision scheme this paper is devoted to explore the generation of fractal curves and surfaces using ternary 5 point interpolatory subdivision scheme the fractal behavior of the limiting curves and surfaces is analyzed with the help of tension parameter it may be noted that the proposed fractal scheme determines two intervals of range of shape control parameter the behavior of the shape control parameter for the generation of fractals has been visualized through five examples which provides faster rate of generation of fractals

the δ e method for the boltzmann equation a new numerical method is proposed to solve the boltzmann equation a frame is set up by using a discrete velocity approximation in the infinite velocity space but by considering only those distribution function points which are not too small the distribution function points may occur anywhere in the infinite discrete velocity space and are not constrained to a pre specified region a fourth order finite difference is used for the convection terms a monte carlo like method is applied to the discrete velocity model of the collision integral the effort of the method is proportional to the number of discrete points numerical examples are given for the full boltzmann equation and results for some benchmark problems are compared with analytical or prior solutions

models of unidirectional propagation in heterogeneous excitable media two differential equation models of excitable media threshold and recovery kinetics with solutions that exhibit unidirectional propagation are presented it is shown that unidirectional propagation in heterogeneous excitable media with non oscillatory kinetics can be initiated from homogeneous initial data simulations on a reaction diffusion model with fitzhugh nagumo kinetics and spatially heterogeneous parameters yields a rotating wave on a one dimensional circular spatial domain an ordinary differential equation model with four semi coupled excitable cells and heterogeneous parameters is analyzed to determine a critical parameter region over which unidirectional propagation may occur

improving smoothness and accuracy of modified butterfly subdivision scheme motivated by the increasing request of surface representation techniques suitable for biomedical imaging applications we construct a non stationary subdivision scheme for regular 3 directional grids which enjoys the following properties i interpolation ii affine invariance iii c2 smoothness iv approximation order 6 and v the capability of reproducing several trigonometric surfaces especially ellipsoids to study the smoothness properties of this new scheme via existing analysis tools we also construct an auxiliary stationary subdivision scheme enjoying properties i iv taking into account that when applied on regular 3 directional grids the modified butterfly scheme is c1 and has approximation order 4 the subdivision schemes derived in this paper can be considered improved variants of the modified butterfly scheme

discrete velocity models and numerical schemes for the boltzmann bgk equation in plane and axisymmetric geometries we present new numerical models for computing transitional or rarefied gas flows as described by the boltzmann bgk and bgk es equations we first propose a new discrete velocity model based on the entropy minimization principle this model satisfies the conservation laws and the entropy dissipation moreover the problem of conservation and entropy for axisymmetric flows is investigated we find algebraic relations that must be satisfied by the discretization of the velocity derivative appearing in the transport operator then we propose some models that satisfy these constraints owing to these properties we obtain numerical schemes that are economic in terms of discretization and robust in particular we develop a linearized implicit scheme for computing stationary solutions of the discrete velocity bgk and bgk es models this scheme is the basis of a code which can compute high altitude hypersonic flows in 2d plane and axisymmetric geometries our results are analyzed and compared to other methods

kinetic boundary layers on the adequate discretization of the boltzmann collision operator we develop criteria for the discretization of the boltzmann collision operator under which linearized kinetic boundary layers exhibit the same algebraic structure as their continuous counterparts these criteria are shown to be sufficient for the well posedness of kinetic boundary layers after the analysis of the discrete layer an example illustrates how to include models which lead to differential algebraic problems existence and uniqueness of nonlinear boundary layers adjacent to an equilibrium state are proven