time periodic solutions of the compressible magnetohydrodynamic equations abstract the compressible magnetohydrodynamic equations with a time periodic external force in r n are studied in this paper we establish the existence uniqueness and time asymptotic stability of time periodic solutions when n 5 our proof is essentially based on a combination of the energy method and the time decay estimates of solutions to the linearized system

global well posedness of strong solutions to the magnetohydrodynamic equations of compressible flows abstract this paper is concerned with the global well posedness of strong solutions to the compressible mhd equations in a bounded domain r 3 we first establish the local existence and uniqueness of strong solutions with arbitrary initial data and external force field based on the local existence result and some a priori estimates the global existence and large time behavior of strong solutions are proved under the assumptions that the initial data and external force field are small enough furthermore the existence of the time periodic solution is also obtained when the external force field is time periodic

analysis of self organized criticality in ehrenfest s dog flea model the self organized criticality in ehrenfest s historical dog flea model is analyzed by simulating the underlying stochastic process the fluctuations around the thermal equilibrium in the model are treated as avalanches we show that the distributions for the fluctuation length differences at subsequent time steps are in the shape of a q gaussian the distribution which is obtained naturally in the context of nonextensive statistical mechanics if one avoids the finite size effects by increasing the system size we provide clear numerical evidence that the relation between the exponent ensuremath tau of avalanche size distribution obtained by maximum likelihood estimation and the q value of appropriate q gaussian obeys the analytical result recently introduced by caruso et al phys rev e 75 055101 r 2007 this allows us to determine the value of q parameter a priori from one of the well known exponents of such dynamical systems

option pricing formulas based on a non gaussian stock price model options are financial instruments that depend on the underlying stock we explain their non gaussian fluctuations using the nonextensive thermodynamics parameter q a generalized form of the black scholes bs partial differential equation and some closed form solutions are obtained the standard bs equation q 1 which is used by economists to calculate option prices requires multiple values of the stock volatility known as the volatility smile using q 1 5 which well models the empirical distribution of returns we get a good description of option prices using a single volatility

global solutions of nonlinear magnetohydrodynamics with large initial data a free boundary problem for nonlinear magnetohydrodynamics with general large initial data is investigated the existence uniqueness and regularity of global solutions are established with large initial data in h1 it is shown that neither shock waves nor vacuum and concentration in the solutions are developed in a finite time although there is a complex interaction between the hydrodynamic and magnetodynamic effects an existence theorem of global solutions with large discontinuous initial data is also established

boundedness vs unboundedness of a noise linked to tsallis q statistics the role of the overdamped approximation an apparently ideal way to generate continuous bounded stochastic processes is to consider the stochastically perturbed motion of a point of small mass in an infinite potential well under overdamped approximation here however we show that the aforementioned procedure can be fallacious and lead to incorrect results we indeed provide a counter example concerning one of the most employed bounded noises hereafter called tsallis stariolo borland tsb noise which admits the well known tsallis q statistics as stationary density in fact we show that for negative values of the tsallis parameter q corresponding to sufficiently large diffusion coefficient of the stochastic force the motion resulting from the overdamped approximation is unbounded we then investigate the cause of the failure of kramers first type approximation and we formally show that the solutions of the full newtonian non approximated model are bounded following the physical intuition finally we provide a new family of bounded noi

escort mean values and the characterization of power law decaying probability densities escort mean values or q moments constitute useful theoretical tools for describing basic features of some probability densities such as those which asymptotically decay like power laws they naturally appear in the study of many complex dynamical systems particularly those obeying nonextensive statistical mechanics a current generalization of the boltzmann gibbs theory they recover standard mean values or moments for q 1 here we discuss the characterization of a non negative probability density by a suitable set of all its escort mean values together with the set of all associated normalizing quantities provided that all of them converge this opens the door to a natural extension of the well known characterization for the q 1 instance of a distribution in terms of the standard moments provided that all of them have finite values this question would be specially relevant in connection with probability densities having divergent values for all nonvanishing standard moments higher than a give

on the superposition operator and integrable solutions of some functional equations on etudie les equations x t f t x t et x t f t x t dans l espace l 1 a b equipe de la topologie de la convergence faible on montre que ces equations ont des solutions integrables qui sont additionnellement des fonctions monotones p p

random matrix ensembles from nonextensive entropy the classical gaussian ensembles of random matrices can be constructed by maximizing boltzmann gibbs shannon s entropy s text bgs ensuremath ensuremath int d mathbf h p mathbf h mathrm ln p mathbf h with suitable constraints here we construct and analyze random matrix ensembles arising from the generalized entropy s q 1 ensuremath ensuremath int d mathbf h p mathbf h q q ensuremath 1 thus s 1 s text bgs the resulting ensembles are characterized by a parameter q measuring the degree of nonextensivity of the entropic form making q ensuremath rightarrow 1 recovers the gaussian ensembles if q ensuremath ne 1 the joint probability distributions p mathbf h cannot be factorized i e the matrix elements of mathbf h are correlated in the limit of large matrices two different regimes are observed when ql1 p mathbf h has compact support and the fluctuations tend asymptotically to those of the gaussian ensembles anomalies appear for qg1 both p mathbf h and the marginal distributions p h ij show power law tails numerical analyses reveal that the nearest neighbor spacing distribution is also long tailed not wigner dyson and after proper scaling very close to the result for the 2 ifmmode times else texttimes fi 2 case char22 a generalization of wigner s surmise we discuss connections of these nonextensive ensembles with other non gaussian ones such as the so called l evy ensembles and those arising from soft confinement

a nonlinear operator functional equation of volterra type in this work we establish the existence of a solution of a nonlinear equation of volterra type in the class of monotonic functions on the interval r 0 our technique rely on the concept of measure of noncompactness and its associated darboux fixed point theorem

nonextensive foundation of levy distributions a deep connection between the ubiquity of l evy distributions in nature and the nonextensive thermal statistics introduced a decade ago has been established recently tsallis et al phys rev lett 75 3589 1995 by using unnormalized q expectation values it has just been argued on physical grounds that normalized q expectation values should be used instead we revisit within this more appropriate scheme the l evy problem and verify that the relevant analytic results become sensibly simplified whereas the basic physics remains unchanged

global existence for the magnetohydrodynamic system in critical spaces in this article we show that the magnetohydrodynamic system in mathbb r n with variable density variable viscosity and variable conductivity has a local weak solution in the besov space dot b n p 1 p 1 1 mathbb r n times dot b n p 2 1 p 2 1 mathbb r n times dot b n p 2 1 p 2 1 mathbb r n for all 1 and some 1 if the initial density approaches a positive constant moreover this solution is unique if we impose the restrictive condition 1 we also prove that the constructed solution exists globally in time if the initial data are small in particular this allows us to work in the framework of besov space with negative regularity indices and this fact is particularly important when the initial data are strongly oscillating

what should a statistical mechanics satisfy to reflect nature there is no compelling reason imposing that the methods of statistical mechanics should be restricted to the dynamical systems which follow the usual boltzmann gibbs prescriptions more specifically ubiquitous natural and artificial systems exhibit generic stationary states which are not ergodic nor close to it in any geometrically simple subset of the a priori allowed phase space in any even extended trivial sense a vast class of such systems appears nevertheless to be tractable within thermostatistical methods completely analogous to the usual ones the question posed in the title arises then naturally some answer to this complex question is advanced in the present review of nonextensive statistical mechanics and its recent connections

law of error in tsallis statistics in order to theoretically explain the ubiquitous existence of power law behavior such as chaos and fractals in nature tsallis entropy has been successfully applied to the generalization of the traditional boltzmann gibbs statistics the fundamental information measure of which is shannon entropy tsallis entropy s sub q is a one parameter generalization of shannon entropy s sub 1 in the sense that lim sub q spl rarr 1 s sub q s sub 1 the generalized statistics using tsallis entropy are referred to as tsallis statistics in order to present the law of error in tsallis statistics as a generalization of gauss law of error and prove it mathematically we apply the new multiplication operation determined by q logarithm and q exponential the fundamental functions in tsallis statistics to the definition of the likelihood function in gauss law of error the present maximum likelihood principle mlp leads us to determine the so called q gaussian distribution which coincides with one of the tsallis distributions derived from the maximum entropy principle for tsallis entropy under the second moment constraint

time periodic solutions of compressible navier stokes equations abstract in this paper we study the navier stokes equations with a time periodic external force in r n we show that a time periodic solution exists when the space dimension n 5 under some smallness assumption the main idea is to combine the energy method and the spectral analysis for the optimal decay estimates on the linearized solution operator with the optimal decay estimates we prove the existence and uniqueness of time periodic solution in some suitable function space by the contraction mapping theorem in addition we also study the time asymptotic stability of the time periodic solution

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

periodic solutions to the compressible magnetohydrodynamic equations in a periodic domain abstract in this paper we study the compressible magnetohydrodynamic system with a time periodic external force in a periodic domain in r n based on the idea in 12 we obtain the existence of a time periodic solution under some smallness and symmetry assumptions on the external force and improve the result from 12 in the following sense we extend the space dimension from 3 to n n 1 the uniqueness of the small periodic solution is also obtained

global variational solutions to the compressible magnetohydrodynamic equations abstract we prove the existence of globally defined variational solutions to the compressible magnetohydrodynamic mhd equations with the coefficients depending on the temperature as a by product we give a simple proof for the nonexistence of nontrivial weak time periodic solutions by the entropy principle of clausius duhem and a new poincare type inequality

optimal decay estimates on the linearized boltzmann equation with time dependent force and their applications although the decay in time estimates of the semi group generated by the linearized boltzmann operator without forcing have been well established there is no corresponding result for the case with general external force this paper is mainly concerned with the optimal decay estimates on the solution operator in some weighted sobolev spaces for the linearized boltzmann equation with a time dependent external force no time decay assumption is made on the force the proof is based on both the energy method through the macro micro decomposition and the lp lq estimates from the spectral analysis the decay estimates thus obtained are applied to the study on the global existence of the cauchy problem to the nonlinear boltzmann equation with time dependent external force and source precisely for space dimension n 3 the global existence and decay rates of solutions to the cauchy problem are obtained under the condition that the force and source decay in time with some rates this time decay restriction can be removed for space dimension n 5 moreover the existence and asymptotic stability of the time periodic solution are given for space dimension n 5 when the force and source are time periodic with the same period

a generalization of the cumulant expansion application to a scale invariant probabilistic model as well known cumulant expansion is an alternative way to moment expansion to fully characterize probability distributions provided all the moments exist if this is not the case the so called escort mean values or q moments have been proposed to characterize probability densities with divergent moments c tsallis et al j math phys 50 043303 2009 we introduce here a new mathematical object namely the q cumulants which in analogy to the cumulants provide an alternative characterization to that of the q moments for the probability densities to illustrate the technical details of the procedure we apply this new scheme to further study a recently proposed family of scale invariant discrete probabilistic models a rodriguez et al j stat mech theory exp 2008 p09006 r hanel et al eur phys j b 72 263 2009 having q gaussians as limiting probability distributions

tsallis threshold analysis of digital speckle patterns generated by rough surfaces abstract in this work we report on a study of entropic threshold of digital speckle patterns images produced by rough surfaces using tsallis entropy the speckle pattern images were obtained in the diffraction plane at the normal direction and they are the outcome of the incidence of a laser beam in the rough metallic surfaces the speckle pattern images were segmented in order to verify the sensitivity of the optimal tsallis entropic threshold value as a function of the surface roughness we show that the surface roughness can be sensed and tuned by this method

incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions this paper is concerned with the incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions it is rigorously shown that the weak solutions of the compressible magnetohydrodynamic equations converge to the strong solution of the viscous or inviscid incompressible magnetohydrodynamic equations as long as the latter exists both for the well prepared initial data and general initial data furthermore the convergence rates are also obtained in the case of the well prepared initial data

global existence and convergence rates of smooth solutions for the compressible magnetohydrodynamic equations abstract in this paper we are concerned with the global existence and convergence rates of the smooth solutions for the compressible magnetohydrodynamic equations in r 3 we prove the global existence of the smooth solutions by the standard energy method under the condition that the initial data are close to the constant equilibrium state in h 3 framework moreover if additionally the initial data belong to l p with 1 p 6 5 the optimal convergence rates of the solutions in l q norm with 2 q 6 and its spatial derivatives in l 2 norm are obtained