fractional levy stable motion can model subdiffusive dynamics we show in this paper that the sample time average mean squared displacement msd of the fractional levy stable motion behaves very differently from the corresponding ensemble average second moment while the ensemble average msd diverges for 2 the sample msd may exhibit either subdiffusion normal diffusion or superdiffusion thus h self similar levy stable processes can model either a subdiffusive diffusive or superdiffusive dynamics in the sense of sample msd we show that the character of the process is controlled by a sign of the memory parameter d h 1 we also introduce a sample p variation dynamics test which allows to distinguish between two models of subdiffusive dynamics finally we illustrate a subdiffusive behavior of the fractional levy stable motion on biological data describing the motion of individual fluorescently labeled mrna molecules inside live e coli cells but it may concern many other fields of contemporary experimental physics doi 10 1103 physreve 82 021130

asymptotic stability of solutions for 1 d compressible navier stokes cahn hilliard system abstract this paper is concerned with the evolution of the periodic boundary value problem and the mixed boundary value problem for a compressible mixture of binary fluids modeled by the navier stokes cahn hilliard system in one dimensional space the global existence and the large time behavior of the strong solutions for these two systems are studied the solutions are proved to be asymptotically stable even for the large initial disturbance of the density and the large velocity data we show that the average concentration difference for the two components of the initial state determines the long time behavior of the diffusive interface for the two phase flow

an l bound for solutions of the cahn hilliard equation in this paper we consider the equation partial t u varepsilon delta u varepsilon sum limits i j 1 n partial ij f ij u varepsilon x varepsilon 2 delta 2 u varepsilon with fij constant when u e is large and we obtain l bounds independent of 0

parameter estimation for infinite variance fractional arima consider the fractional arima time series with innovations that have infinite variance this is a finite parameter model which exhibits both long range dependence long memory and high variability we prove the consistency of an estimator of the unknown parameters which is based on the periodogram and derive its asymptotic distribution this shows that the results of mikosch gadrich kluppelberg and adler for arma time series remain valid for fractional arima with long range dependence we also extend the limit theorem for sample autocovariances of infinite variance moving averages developed in davis and resnick to moving averages whose coefficients are not absolutely summable

global existence and asymptotics of solutions of the cahn hilliard equation abstract this paper is concerned with the cauchy problem of the cahn hilliard equation u t u 2 u 0 x r n t 0 u t 0 u 0 x x r n first we construct a local smooth solution u t x to the above cauchy problem then by combining some a priori estimates sobolev s embedding theorem and the continuity argument the local smooth solution u t x is extended step by step to all t 0 provided that the smooth nonlinear function u satisfies a certain local growth condition at some fixed point u r and that u 0 x u l 1 r n is suitably small secondly we show that the global smooth solution u t x satisfies the following temporal decay estimates d k u t x u l p r n c 1 t k 4 n 4 1 1 p t 0 k 0 1 here p 1 c 0 is a constant depending on and 0 is any positive constant which can be chosen sufficiently small at last we show that under a strong assumption on the growth of the nonlinear function u at u u the asymptotics of solutions of the above cauchy problem is described by u 0 t n 4 g x t 4 here 0 r n u 0 x u d x g x r n exp 4 i x d

convergence of the cahn hilliard equation to the hele shaw model we prove that level surfaces of solutions to the cahn hilliard equation tend to solutions of the hele shaw problem under the assumption that classical solutions of the latter exist the method is based on a new matched asymptotic expansion for solutions a spectral analysis for linearizd operators and an estimate for the difference between the true solutions and certain approximate ones

fractional brownian motion versus the continuous time random walk a simple test for subdiffusive dynamics fractional brownian motion with hurst index less then 1 2 and continuous time random walk with heavy tailed waiting times and the corresponding fractional fokker planck equation are two different processes that lead to a subdiffusive behavior widespread in complex systems we propose a simple test based on the analysis of the so called p variations which allows distinguishing between the two models on the basis of one realization of the unknown process we apply the test to the data of golding and cox phys rev lett 96 098102 2006 describing the motion of individual fluorescently labeled mrna molecules inside live e coli cells it is found that the data does not follow heavy tailed continuous time random walk the test shows that it is likely that fractional brownian motion is the underlying process

the stability test for symmetric alpha stable distributions symmetric alpha stable distributions are a popular statistical model for heavy tailed phenomena encountered in communications radar biomedicine and econometrics the use of the symmetric alpha stable model is often supported by empirical evidence where qualitative criteria are used to judge the fit leading to subjective decisions objective decisions can only be made through quantitative statistical tests here a goodness of fit hypothesis test for symmetric alpha stable distributions is developed based on their unique stability property critical values for the test are found using both asymptotic theory and from bootstrap estimates experiments show that the stability test using bootstrap estimates of the critical values is better able to discriminate between symmetric alpha stable distributions and other heavy tailed distributions than classical tests such as the kolmogorov smirnov test

stability and lack of memory of the returns of the hang seng index abstract in this paper we show that the logarithmic returns of the hang seng index from january 2 1987 to november 14 2005 statistically resemble a sequence of independent identically distributed levy stable random variables this is in stark contrast to xiu and jin 2007 39 where long memory farima processes with gaussian noise were suggested as well fitted to the data the lack of memory is checked by using lo s modified r s statistic and a new method of estimation of the memory parameter d which applies the notion of empirical mean squared displacement in order to test stability of the data we employ several statistical tests based on the empirical distribution function finally we also show that the returns possess no conditional heteroscedasticity property thus excluding the arch garch family of processes as possible underlying models

a gradient stable scheme for a phase field model for the moving contact line problem in this paper an efficient numerical scheme is designed for a phase field model for the moving contact line problem which consists of a coupled system of the cahn hilliard and navier stokes equations with the generalized navier boundary condition 1 2 4 the nonlinear version of the scheme is semi implicit in time and is based on a convex splitting of the cahn hilliard free energy including the boundary energy together with a projection method for the navier stokes equations we show under certain conditions the scheme has the total energy decaying property and is unconditionally stable the linearized scheme is easy to implement and introduces only mild cfl time constraint numerical tests are carried out to verify the accuracy and stability of the scheme the behavior of the solution near the contact line is examined it is verified that when the interface intersects with the boundary the consistent splitting scheme 21 22 for the navier stokes equations has the better accuracy for pressure

convergence of the cahn hilliard equation to the mullins sekerka problem in spherical symmetry abstract we show that as e 0 the solution of the cahn hilliard equation formula converges to a solution of the mullins sekerka problem formula where denotes a normal v the normal velocity and k the sum of principal curvatures of the interface provided the solutions are radially symmetric we use energy type estimates to show that the solution of the cahn hilliard equation can be approximated by the well known stationary wave solution that corresponds to the potential w

approximate solutions of the cahn hilliard equation via corrections to the mullins sekerka motion we develop an alternative method to matched asymptotic expansions for the construction of approximate solutions of the cahn hilliard equation suitable for the study of its sharp interface limit the method is based on the hilbert expansion used in kinetic theory besides its relative simplicity it leads to calculable higher order corrections to the interface motion

quasi incompressible cahn hilliard fluids and topological transitions one of the fundamental problems in simulating the motion of sharp interfaces between immiscible fluids is a description of the transition that occurs when the interfaces merge and reconnect it is well known that classical methods involving sharp interfaces fail to describe this type of phenomena following some previous work in this area we suggest a physically motivated regularization of the euler equations which allows topological transitions to occur smoothly in this model the sharp interface is replaced by a narrow transition layer across which the fluids may mix the model describes a flow of a binary mixture and the internal structure of the interface is determined by both diffusion and motion an advantage of our regularization is that it automatically yields a continuous description of surface tension which can play an important role in topological transitions an additional scalar field is introduced to describe the concentration of one of the fluid components and the resulting system of equations couples the euler or navier stokes and the cahn hilliard equations the model takes into account weak non locality dispersion associated with an internal length scale and localized dissipation due to mixing the non locality introduces a dimensional surface energy dissipation is added to handle the loss of regularity of solutions to the sharp interface equations and to provide a mechanism for topological changes in particular we study a non trivial limit when both components are incompressible the pressure is kinematic but the velocity field is non solenoidal quasi incompressibility to demonstrate the effects of quasi incompressibility we analyse the linear stage of spinodal decomposition in one dimension we show that when the densities of the fluids are not perfectly matched the evolution of the concentration field causes fluid motion even if the fluids are inviscid in the limit of infinitely thin and well separated interfacial layers an appropriately scaled quasi incompressible euler cahn hilliard system converges to the classical sharp interface model in order to investigate the behaviour of the model outside the range of parameters where the sharp interface approximation is sufficient we consider a simple example of a change of topology and show that the model permits the transition to occur without an associated singularity

relaxation limit of interacting shock waves for non isentropic gas dynamics abstract in this paper we study the relaxation limit of interacting shock waves for non isentropic gas dynamics such a model is introduced by jin and xin for numerical analysis and named as jin xin relaxation system given any entropy solution of non isentropic gas dynamics which consists of two different families of shocks interacting at some positive time we show that such solution is the relaxation limit for a family of smooth global solutions of the jin xin relaxation system we remark that after the interacting time not only shocks but also contact discontinuity is generated

long term memory in stock market prices a test for long term memory that is robust to short range dependence is developed it is a modification of the r s statistic and the relevant asymptotic sampling theory is derived via functional central limit theory contrary to previous findings when applied to daily and monthly stock returns indexes over several time periods this test yields no evidence of long range dependence once short range dependence is accounted for monte carlo experiments show that the modified r s test has power against at least two specific models of long term memory suggesting that models with short range dependence may adequately capture the behavior of historical stock returns copyright 1991 by the econometric society

stability of contact discontinuities for the 1 d compressible navier stokes equations in this paper we study the large time asymptotic behavior of solutions of the one dimensional compressible navier stokes system toward a contact discontinuity which is one of the basic wave patterns for the compressible euler equations it is proved that such a weak contact discontinuity is a metastable wave pattern in the sense introduced in 24 for the 1 d compressible navier stokes system for polytropic fluid by showing that a viscous contact wave which approximates the contact discontinuity on any finite time interval for small heat conduction and then runs away from it for large time is nonlinearly stable with a uniform convergence rate provided that the initial excess mass is zero this result is proved by an elaborate combination of elementary energy estimates with a weighted characteristic energy estimate which makes full use of the underlying structure of the viscous contact wave

wavelet based estimators of scaling behavior various wavelet based estimators of self similarity or long range dependence scaling exponent are studied extensively these estimators mainly include the bi orthogonal wavelet estimators and the wavelet transform modulus maxima wtmm estimator this study focuses both on short and long time series in the framework of fractional autoregressive integrated moving average farima processes we advocate the use of approximately adapted wavelet estimators for these ideal processes the scaling behavior actually extends down to the smallest scale i e the sampling period of the time series if an adapted decomposition is used but in practical situations there generally exists a cutoff scale below which the scaling behavior no longer holds we test the robustness of the set of wavelet based estimators with respect to that cutoff scale as well as to the specific density of the underlying law of the process in all situations the wtmm estimator is shown to be the best or among the best estimators in terms of the mean squared error mse we also compare the wavelet estimators with the detrended fluctuation analysis dfa estimator which was previously proved to be among the best estimators which are not wavelet based estimators the wtmm estimator turns out to be a very competitive estimator which can be further generalized to characterize multiscaling behavior

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

asymptotic stability of combination of viscous contact wave with rarefaction waves for one dimensional compressible navier stokes system we are concerned with the large time behavior of solutions of the cauchy problem to the one dimensional compressible navier stokes system for ideal polytropic fluids where the far field states are prescribed when the corresponding riemann problem for the compressible euler system admits the solution consisting of contact discontinuity and rarefaction waves it is proved that for the one dimensional compressible navier stokes system the combination wave of a viscous contact wave which corresponds to the contact discontinuity with rarefaction waves is asymptotically stable provided the strength of the combination wave is suitably small this result is proved by using elementary energy methods

stability of a composite wave of two viscous shock waves for the full compressible navier stokes equation in this paper we investigate the asymptotic stability of a composite wave consisting of two viscous shock waves for the full compressible navier stokes equation by introducing a new linear diffusion wave special to this case we successfully prove that if the strengths of the viscous shock waves are suitably small with same order and also the initial perturbations which are not necessarily of zero integral are suitably small the unique global solution in time to the full compressible navier stokes equation exists and asymptotically tends toward the corresponding composite wave whose shifts in space of two viscous shock waves are uniquely determined by the initial perturbations we then apply the idea to study a half space problem for the full compressible navier stokes equation and obtain a similar result

a least squares finite element method for the numerical solution of the navier stokes cahn hilliard system modeling the motion of the contact line in this article we discuss the numerical solution of the navier stokes cahn hilliard system modeling the motion of the contact line separating two immiscible incompressible viscous fluids near a solid wall the method we employ combines a finite element space approximation with a time discretization by operator splitting to solve the cahn hilliard part of the problem we use a least squares conjugate gradient method we also show that the scheme has the total energy decaying in time property under certain conditions our numerical experiments indicate that the method discussed here is accurate stable and efficient

unipotent groups and curves of genus two in this paper we study unipotent groups associated to degenerations of smooth curves in particular we obtain results on the exponent of these groups and use these to get an almost complete description of the structure of unipotent groups associated to curves of genus two

front migration in the nonlinear cahn hilliard equation the method of matched asymptotic expansions is used to describe solutions of the nonlinear cahn hilliard equation for phase separation in n 1 space dimensions the expansion is formally valid when the thickness of internal transition layers is small compared with the distance separating layers and with their radii of curvature on the dominant slowest timescale the interface velocity is determined by the mean curvature of the interface by a non local relation which is identical to that in a well known quasi static model of solidification which exhibits a shape instability discovered by mullins sekerka j appl phys 34 323 329 1963 on a faster timescale the cahn hilliard equation regularizes a classic two phase stefan problem similarity solutions of the two phase stefan problem should describe boundary layers existence and uniqueness of such similarity solutions which admit metastable states is proved rigorously in an appendix

parameter estimation for arma models with infinite variance innovations abstract we consider a standard arma process of the form phi b xt theta b zt where the innovations zt belong to the domain of attraction of a stable law so that neither the zt nor the xt have a finite variance our aim is to estimate the coefficients of phi and theta since maximum likelihood estimation is not a viable possibility due to the unknown form of the marginal density of the innovation sequence we adopt the so called whittle estimator based on the sample periodogram of the x sequence despite the fact that the periodogram does not a priori seem like a logical object to study in this non l situation we show that our estimators are consistent obtain their asymptotic distributions and show that they converge to the true values faster than in the usual l2 case

efficient energy stable numerical schemes for a phase field moving contact line model in this paper we present two efficient energy stable schemes to solve a phase field model incorporating moving contact line the model is a coupled system that consists of incompressible navier stokes equations with a generalized navier boundary condition and cahn hilliard equation in conserved form in both schemes the projection method is used to deal with the navier stokes equations and stabilization approach is used for the non convex ginzburg landau bulk potential by some subtle explicit implicit treatments we obtain a linear coupled energy stable scheme for systems with dynamic contact line conditions and a linear decoupled energy stable scheme for systems with static contact line conditions an efficient spectral galerkin spatial discretization method is implemented to verify the accuracy and efficiency of proposed schemes numerical results show that the proposed schemes are very efficient and accurate we proposed two linear energy stable numerical schemes for a phase field moving contact line model discrete energy laws that are consistent to the continuous ones are proved the efficiency and fast convergence of the proposed schemes with spectral spatial approximations are numerically verified

estimation of farima parameters in the case of negative memory and stable noise in this paper we extend a method of estimation of parameters of the fractional autoregressive integrated moving average farima process with stable noise to the case of negative memory parameter d we construct an estimator that is a modification of that of kokoszka and taqqu and prove its consistency for 1 2 we show that the estimator is accurate and possesses a low variance for farima time series with both light and heavy tailed noises it is illustrated by means of monte carlo simulations finally we compare the introduced method of estimation of d with classical methods like the r s modified r s and variance the results show that the proposed estimator is vastly superior to them

a finite element method for the numerical solution of the coupled cahn hilliard and navier stokes system for moving contact line problems in this paper a semi implicit finite element method is presented for the coupled cahn hilliard and navier stokes equations with the generalized navier boundary condition for the moving contact line problems in our method the system is solved in a decoupled way for the cahn hilliard equations a convex splitting scheme is used along with a p1 p1 finite element discretization the scheme is unconditionally stable a linearized semi implicit p2 p0 mixed finite element method is employed to solve the navier stokes equations with our method the generalized navier boundary condition is extended to handle the moving contact line problems with complex boundary in a very natural way the efficiency and capacity of the present method are well demonstrated with several numerical examples

signal modeling with self similar spl alpha stable processes the fractional levy stable motion model the purpose of the correspondence is the introduction of fractional levy stable motion flsm as a model for signals with long memory and high variability commonly encountered in natural processes we present a concise description of this model from a signal processing viewpoint and its successful application to real world infrared signals for the purpose of resolution enhancement via stochastic interpolation

postfiltering versus prefiltering for signal recovery from noisy samples we consider the extension of the whittaker shannon ws reconstruction formula to the case of signals sampled in the presence of noise and which are not necessarily band limited observing that in this situation the classical sampling expansion yields inconsistent reconstruction we introduce a class of signal recovery methods with a smooth correction of the interpolation series two alternative data smoothing methods are examined based either on a global postfiltering or a local data presmoothing we assess the accuracy of the methods by the global l sub 2 error both band limited and non band limited signals are considered a general class of correlated noise processes is taken into account the weak and strong rates of convergence of the algorithms are established and their relative efficiency is discussed the influence of noise memory and its moment structure on the accuracy is thoroughly examined

unipotent groups associated to reduced curves let x be a curve defined over an algebraically closed field k with char k p 0 assume that x k is reduced in this paper we study the unipotent part u of the jacobian jx k in particular we prove that if p is large in terms of the dimension of u then u is isomorphic to a product of additive groups ga

estimating heavy tail exponents through max self similarity in this paper a novel approach to the problem of estimating the heavy tail exponent 0 of a distribution is proposed it is based on the fact that block maxima of size m scale at a rate m1 for independent as well as for a number of dependent data this scaling rate can be captured well by the max spectrum plot of the data that leads to regression based estimators for consistency and asymptotic normality of these estimators is established for independent data under mild conditions on the behavior of the tail of the distribution the proposed estimators have an important computational advantage over existing methods namely they can be calculated and updated sequentially in an on line fashion without having to store the entire data set practical issues on the automatic selection of tuning parameters for the estimators and corresponding confidence intervals are also addressed extensive numerical simulations show that the proposed method is competitive for both small and large sample sizes robust to contaminants and continues to work under the presence of substantial amount of dependence the proposed estimators are used to illustrate the close connection between long range dependence and heavy tails over an internet traffic trace