correlation structure of fractional pearson diffusions the stochastic solution to a diffusion equations with polynomial coefficients is called a pearson diffusion if the first time derivative is replaced by a caputo fractional derivative of order less than one the stochastic solution is called a fractional pearson diffusion this paper develops an explicit formula for the covariance function of a fractional pearson diffusion in steady state in terms of mittag leffler functions that formula shows that fractional pearson diffusions are long range dependent with a correlation that falls off like a power law whose exponent equals the order of the fractional derivative

mixed boundary value problems for the stationary navier stokes system in polyhedral domains the authors consider boundary value problems for the navier stokes system in a polyhedral domain where different boundary conditions in particular dirichlet neumann slip conditions are arbitrarily combined on the faces of the polyhedron they prove existence and regularity theorems for weak solutions in weighted and nonweighted l p sobolev and holder spaces with sharp integrability and smoothness parameters

zero relaxation limit to centered rarefaction waves for a rate type viscoelastic system abstract we study a rate type viscoelastic system proposed by i suliciu 1990 internat j engrg sci 28 827 841 which is a 3 3 hyperbolic system with relaxation as the relaxation time tends to zero this system convergences to the well known p system formally in the case where the initial data are the riemann data such that the corresponding solutions of the p system are centered rarefaction waves we show that if the wave strength is suitably small then the solution for the relaxation system exists globally in time and converges to the solution of the corresponding rarefaction waves uniformly as the relaxation time goes to zero except for an initial layer the jump discontinuities in the solutions are decaying exponentially fast as time tends to infinity

nonlinear stability of rarefaction waves for compressible navier stokes equations it is shown that expansion waves for the compressible navier stokes equations are nonlinearly stable the expansion waves are constructed for the compressible euler equations based on the inviscid burgers equation our result shows that navier stokes equations and euler equations are time asymptotically equivalent on the level of expansion waves the result is proved using the energy method making essential use of the expansion of the underlining nonlinear waves and the specific form of the constitutive eqution for a polytropic gas

solving the fractional nonlinear bloch system using the multi step generalized differential transform method in this paper the multi step differential transform method is employed for the first time to solve a time fractional nonlinear bloch system the nonlinear bloch equation is known to govern the dynamics of an ensemble of spins controlling the basic process of nuclear magnetic resonance nmr this nonlinear bloch equation is formed from a system of nonlinear ordinary differential equations of fractional order the fractional derivatives are described in the caputo sense the results obtained are in good agreement with the ones in the open literature and it is shown that the technique introduced here is robust efficient and easy to implement

discrete direct methods in the fractional calculus of variations finite differences as a subclass of direct methods in the calculus of variations consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem this article generalizes the same idea for fractional variational problems we consider a minimization problem with a lagrangian that depends on the left riemann liouville fractional derivative using the grunwald letnikov definition we approximate the objective functional in an equispaced grid as a multi variable function of the values of the unknown function on mesh points the problem is then transformed to an ordinary static optimization problem the solution to the latter problem gives an approximation to the original fractional problem on mesh points

on the weak solutions to steady navier stokes equations with mixed boundary conditions in this paper for the navier stokes equations in a bounded connected polygon or polyhedron omega subset r d d 2 3 with a homogenous stress type mixed boundary condition we establish an a priori estimate for the weak solutions and the existence result without small data and or large viscosity restriction and a global uniqueness result is obvious based on the a priori estimate obtained

modeling and numerical analysis of fractional order bloch equations this paper deals with the bloch equations which are a set of macroscopic equations that are used for modeling of nuclear magnetization as a function of time these equations were introduced by felix bloch in 1946 and they are used for a description of the nuclear magnetic resonance nmr this physical phenomenon is used in medicine chemistry physics and engineering to study complex material fractional order generalization of the bloch equations was presented by richard magin et al in 2008 as an opportunity to extend their use to describe a wider range of experimental situations involving heterogeneous porous or composite materials in this paper we describe numerical and simulation models created for matlab simulink of the classical and the fractional order bloch equations the behaviour and stability analysis of the bloch equations are presented as well

fractional bloch equation with delay in this paper we investigate a fractional generalization of the bloch equation that includes both fractional derivatives and time delays the appearance of the fractional derivative on the left side of the bloch equation encodes a degree of system memory in the dynamic model for magnetization the introduction of a time delay on the right side of the equation balances the equation by also adding a degree of system memory on the right side of the equation the analysis of this system shows different stability behavior for the t 1 and the t 2 relaxation processes the t 1 decay is stable for the range of delays tested 1 100 ms while the t 2 relaxation in this model exhibited a critical delay typically 6 ms above which the system was unstable delays are expected to appear in nmr systems in both the system model and in the signal excitation and detection processes therefore by including both the fractional derivative and finite time delays in the bloch equation we believe that we have established a more complete and more realistic model for nmr resonance and relaxation

superconvergence of the local discontinuous galerkin method for elliptic problems on cartesian grids in this paper we present a superconvergence result for the local discontinuous galerkin ldg method for a model elliptic problem on cartesian grids we identify a special numerical flux for which the l2 norm of the gradient and the l2 norm of the potential are of orders k 1 2 and k 1 respectively when tensor product polynomials of degree at most k are used for arbitrary meshes this special ldg method gives only the orders of convergence of k and k 1 2 respectively we present a series of numerical examples which establish the sharpness of our theoretical results

transient chaos in fractional bloch equations the bloch equation provides the fundamental description of nuclear magnetic resonance nmr and relaxation t 1 and t 2 this equation is the basis for both nmr spectroscopy and magnetic resonance imaging mri the fractional order bloch equation is a generalization of the integer order equation that interrelates the precession of the x y and z components of magnetization with time and space dependent relaxation in this paper we examine transient chaos in a non linear version of the bloch equation that includes both fractional derivatives and a model of radiation damping recent studies of spin turbulence in the integer order bloch equation suggest that perturbations of the magnetization may involve a fading power law form of system memory which is concisely embedded in the order of the fractional derivative numerical analysis of this system shows different patterns in the stability behavior for a near 1 00 in general when a is near 1 00 the system is chaotic while for 0 98 a 0 94 the system shows transient chaos as the value of a decreases further the duration of the transient chaos diminishes and periodic sinusoidal oscillations emerge these results are consistent with studies of the stability of both the integer and the fractional order bloch equation they provide a more complete model of the dynamic behavior of the nmr system when non linear feedback of magnetization via radiation damping is present

an a priori error analysis of the local discontinuous galerkin method for elliptic problems in this paper we present the first a priori error analysis for the local discontinuous galerkin ldg method for a model elliptic problem for arbitrary meshes with hanging nodes and elements of various shapes we show that for stabilization parameters of order one the l2 norm of the gradient and the l2 norm of the potential are of order k and k 1 2 respectively when polynomials of total degree at least k are used if stabilization parameters of order h 1 are taken the order of convergence of the potential increases to k 1 the optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains

chaotic attractors in incommensurate fractional order systems in this paper based on the stability theorems in fractional differential equations a necessary condition is given to check the existence of 1 scroll 2 scroll or multi scroll chaotic attractors in a fractional order system this condition is proposed for incommensurate order systems in general but in the special case it converts to the condition given in the previous works for the commensurate fractional order systems though the presented condition is only a necessary and not sufficient condition for the existence of chaos it can be used as a powerful tool to distinguish for what parameters and orders of a given fractional order system chaotic attractors can not be observed and for what parameters and orders the system may generate chaos it can also be used as a tool to confirm or reject results of a numerical simulation some of the numerical results reported in the previous literature are confirmed by this tool

global stability of strong rarefaction waves for the generalized kdv burgers equation this paper is concerned with the global stability of strong rarefaction waves for the generalized kdv burgers equation in contrast to former results obtained by z a wang and c j zhu stability of the rarefaction wave for the generalized kdv burgers equation acta math sci 22b 3 2002 319 328 ours do not require the strength of the rarefaction waves to be small and the initial disturbance can also be chosen large c 2006 elsevier ltd all rights reserved

global existence and optimal temporal decay estimates for systems of parabolic conservation laws ii the multidimensional case this paper is a continuation of our previous paper it is concerned with the global existence and the optimal temporal decay estimates for the cauchy problem of the following multidimensional parabolic conservation laws

sustaining stable dynamics of a fractional order chaotic financial system by parameter switching in this paper a simple parameter switching ps methodology is proposed for sustaining the stable dynamics of a fractional order chaotic financial system this is achieved by switching a controllable parameter of the system within a chosen set of values and for relatively short periods of time the effectiveness of the method is confirmed from a computer aided approach and its applications to chaos control and anti control are demonstrated in order to obtain a numerical solution of the fractional order financial system a variant of the grunwald letnikov scheme is used extensive simulation results show that the resulting chaotic attractor well represents a numerical approximation of the underlying chaotic attractor which is obtained by applying the average of the switched values moreover it is illustrated that this approach is also applicable to the integer order financial system

rarefactions and large time behavior for parabolic equations and monotone schemes we consider the large time behavior of monotone semigroups associated with degenerate parabolic equations and monotone difference schemes for an appropriate class of initial data the solution is shown to converge to rarefaction waves at a determined asymptotic rate

dg approximation of coupled navier stokes and darcy equations by beaver joseph saffman interface condition in this work we couple the incompressible steady navier stokes equations with the darcy equations by means of the beaver joseph saffman s condition on the interface under suitable smallness conditions on the data we prove existence of a weak solution as well as some a priori estimates we establish local uniqueness when the data satisfy additional smallness restrictions then we propose a discontinuous galerkin scheme for discretizing the equations and do its numerical analysis

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

a case study of global stability of strong rarefaction waves for 2 2 hyperbolic conservation laws with artificial viscosity this paper is concerned with the global stability of strong rarefaction waves for a class of 2 x 2 hyperbolic conservation laws with artificial viscosity i e the p system with artificial viscosity

chaos in fractional ordered liu system abstract present paper deals with fractional version of a dynamical system introduced by c liu l liu and t liu c liu l liu t liu a novel three dimensional autonomous chaos system chaos solitons fractals 39 4 2009 1950 1958 numerical investigations on the dynamics of this system have been carried out properties of the system have been analyzed by means of lyapunov exponents furthermore the minimum effective dimensions have been identified for chaos to exist in commensurate and incommensurate orders it is noteworthy that the results obtained are consistent with the analytical conditions given in the literature