mean first passage time of quantum transition processes abstract in this paper we consider the problem of mean first passage time mfpt in quantum mechanics the mfpt is the average time of the transition from a given initial state passing through some intermediate states to a given final state for the first time we apply the method developed in statistical mechanics for calculating the mfpt of random walks to calculate the mfpt of a transition process as applications we 1 calculate the mfpt for multiple state systems 2 discuss transition processes occurring in an environmental background 3 consider a roundabout transition in a hydrogen atom and 4 apply the approach to laser theory

free vibration of an axially loaded prestressed planar frame abstract the influence of some parameters on the natural vibration frequency of a non linear two member frame is studied the perturbation method is used for solving the problem which is formulated on the basis of hamilton s principle numerical results concerning the influence of prestress and axial force on the natural frequency are compared with those from an experiment additional numerical results show the effect of the distribution of both the flexural and axial rigidities as well as the mass per unit length between frame s members on the natural frequency of the sytem the amplitude frequency relation for different loadings is demonstrated also

on the failure of static stability analyses of nonconservative systems in regions of divergence instability abstract the stability of perfect bifurcational discrete dissipative systems under follower loads in regions of existence non existence of adjacent equilibria is thoroughly re examined in the light of recent progress in nonlinear dynamics a general theory for such nongradient systems described by autonomous ordinary differential equations is developed conditions for the existence of adjacent equilibria the stability of precritical critical and postcritical states as well as for different types of local bifurcations are established focusing attention on the interaction of geometric nonlinearities and vanishing damping new findings contradicting widely accepted results of the classical linear analysis are discovered in a small region of adjacent equilibria near a compound branching point which is explicitly determined an interaction of two consecutive postbuckling modes occurs related to the following phenomena in case of vanishing damping loss of stability may occur via a hopf dynamic bifurcation prior to static divergence buckling moreover the critical states of divergence instability may be associated with a double zero jacobian eigenvalue satisfying also the conditions of a hopf local bifurcation besides local dynamic bifurcations global bifurcations are also found an example is used to illustrate the qualitative findings

levy brownian motion on finite intervals mean first passage time analysis we present the analysis of the first passage time problem on a finite interval for the generalized wiener process that is driven by levy stable noises the complexity of the first passage time statistics mean first passage time cumulative first passage time distribution is elucidated together with a discussion of the proper setup of corresponding boundary conditions that correctly yield the statistics of first passages for these non gaussian noises the validity of the method is tested numerically and compared against analytical formulas when the stability index alpha approaches 2 recovering in this limit the standard results for the fokker planck dynamics driven by gaussian white noise

non linear analysis of elastic plane frames with crooked bars in this investigation the postbuckling response of plane frames consisting of a large number of crooked bars is achieved by means of an efficient method based on non linear kinematic stability analysis the entire formulation of the non linear equilibrium equations presented in matrix form is implemented by the computer program nlsrf non linear stability of rod frames critical loads and critical displacements are obtained through a direct computation by using the additional stability condition resulting from the vanishing of the stability determinant the efficacy of the method proposed herein is demonstrated by a three storey single span frame

divergence of a rotating shaft with an intermediate support and conservative axial loads abstract the dynamic behavior of a rotating shaft with an intermediate support and conservative axial loads is analyzed using euler beam theory and the assumed mode method the equations of motion are then transformed to the standard form of eigenvalue problems for determining the critical dimensionless rotational speeds and the critical axial loads corresponding to the divergence type instability of the shaft results of numerical simulations are presented for various combinations of support locations axial loads and rotational speeds

stability of a timoshenko beam resting on a winkler elastic foundation the influences of a winkler elastic foundation modulus slenderness ratio and elastically restrained boundary conditions on the critical load of a timoshenko beam subjected to an end follower force are investigated the characteristic equation for elastic stability is derived it is found that the critical flutter load for the cantilever timoshenko beam will first decrease as the elastic foundation modulus is increased and when the elastic foundation modulus is greater than the corresponding critical value which corresponds to the lowest critical load it will increase instead in particular if the elastic foundation modulus is large enough the critical flutter load for the cantilever timoshenko beam can be greater than that of the bernoulli euler beam for a clamped translational or clamped rotational elastic spring supported beam resting on an elastic foundation there exists a critical value of the spring constant for each beam at this critical point the critical load jumps and the type of instability mechanism changes the jump mechanisms for beams resting on elastic foundations of different modulus values are different

comparison and validation of multi phase closure models the purpose of this paper is to propose a simple one or two parameter multiphase flow model suitable for the description of rayleigh taylor and richtmyer meshkov mixing layers we justify model closure assumptions in this model by comparison to rayleigh taylor and richtmyer meshkov simulation data we show that the relative errors related to model closure terms are about 10 and are about two to four times smaller than related closure models of abgrall and saurel

static and dynamic local and global bifurcations in nonlinear autonomous structural systems discrete damped or undamped gradient systems described by nonlinear autonomous ordinary differential equations ode of motion are examined in detail emphasis is given to the relationship between static with possibly existing dynamic bifurcations criteria for dynamic bifurcations and stability of precritical critical and postcritical states associated with the nature of jacobian eigenvalues are also presented cases of discrepancies between local and global dynamic analysis regarding the stability of equilibriums are reported for the first time finally using a simple energy criterion exact dynamic buckling loads for vanishing but nonzero damping are readily obtained

dynamic stability of a tapered cantilever beam on an elastic foundation subjected to a follower force the equation of motion in matrix form of a tapered cantilever euler beam subjected to a follower force at the free end is formulated based on the lagrangian approach and the assumed mode method the beam is resting on a winkler type elastic foundation the effects of the presence of viscous damping in the foundation which makes the foundation viscoelastic and the presence of internal damping in the beam on the critical flutter loads are examined separately to evaluate their relative importance as expected internal damping of the beam tends to drastically reduce the critical flutter loads for a beam of uniform cross section for tapered beams the effects are however dependent on the taper ratio of the beam as well as the modulus of the elastic foundation the critical flutter loads of both tapered beams and beams of uniform cross section are found to be unaffected by the presence of viscous damping in the elastic foundation the effect of varying the modulus of the elastic foundation on the critical flutter loads is also discussed in the paper

fluctuations in multiplicative systems with jumps fluctuation properties of the langevin equation including a multiplicative power law noise and a quadratic potential are discussed the noise has the l evy stable distribution if this distribution is truncated the covariance can be derived in the limit of large time it falls exponentially covariance in the stable case studied for the cauchy distribution exhibits a weakly stretched exponential shape and can be approximated by the simple exponential the dependence of that function on system parameters is determined then we consider a dynamics which involves the above process and obeys the generalized langevin equation the same as for the gaussian case the resulting distributions possess power law tails which fall similarly to those for the driving noise whereas central parts can assume the gaussian shape moreover a process with the covariance 1 t at large time is constructed and the corresponding dynamical equation is solved diffusion properties of systems for both covariances are discussed

energy based dynamic buckling estimates for autonomous dissipative systems the dynamic buckling global response of a nonlinear 3 degree of freedom dissipative model under a step loading of infinite duration is thoroughly discussed geometrically imperfect models with symmetric or antisymmetric imperfections losing their static stability through a limit point and an asymmetric bifurcation point respectively are considered emphasis is given to the combined effect of nonlinearities geometric and or material and damping exact approximate and lower upper bound estimates based on energy criteria for establishing the dynamic buckling response of such autonomous models without solving the highly nonlinear initial value problem are assessed the reliability and efficiency of the proposed readily obtained estimates is illustrated via numerical simulation the accuracy of which is checked using energy balance considerations certain interesting byproducts associated with a postlimit point bifurcation and breakdown of the symmetry of deformation are also revealed

elastic stability of non uniform columns abstract a simple and efficient method is proposed to investigate the elastic stability of three different tapered columns subjected to uniformly distributed follower forces the influences of the boundary conditions and taper ratio on critical buckling loads are investigated the critical buckling loads of columns of rectangular cross section with constant depth and linearly varied width t 1 constant width and linearly varied depth t 2 and double taper t 3 are investigated among the three different non uniform columns considered taper ratio has the greatest influence on the critical buckling load of column t 3 and the lowest influence on that of column t 1 the types of instability mechanisms for hinged hinged and cantilever non uniform columns are divergence and flutter respectively however for clamped hinged and clamped clamped non uniform columns the type of instability mechanism for column t 1 is divergence while that for columns t 2 and t 3 is divergence only when the taper ratio of the columns is greater than certain critical values and flutter for the rest value of taper ratio when the type of instability mechanism changes from divergence to flutter there is a finite jump for the critical buckling load the influence of taper ratio on the elastic stability of cantilever column t 3 is very sensitive for small values of the taper ratio and there also exist some discontinieties in the critical buckling loads of flutter instability for a hinged hinged non uniform column t 2 or t 3 with a rotational spring at the left end of the column when the taper ratio is less than the critical value the instability mechanism changes from divergence to flutter as the rotational spring constant is increased for a clamped elastically supported non uniform column when the taper ratio is greater than the critical value the instability mechanism changes from flutter to divergence as the translational spring constant is increased

fractional model equation for anomalous diffusion abstract in recent years the phenomenon of anomalous diffusion has attracted more and more attention one of the main impulses was initiated by de gennes idea of the ant in the labyrinth several authors presented asymptotic probability density functions for the location of a random walker on a fractal object as this density function and the time dependence of its second moment are now well established a modified diffusion equation providing the correct result is formulated the parameters of this fractional partial differential equation are uniquely determined by the fractal hausdorff dimension of the underlying object and the anomalous diffusion exponent the presented equation reduces exactly to the ordinary isotropic diffusion equation by appropriate choice of the parameters a closed form solution is given in terms of fox s h function in the asymptotic case a halved diffusion equation can be established furthermore the differences to equations considered previously are discussed

postbuckling behavior of a clamped elastically supported planar structure under follower force the behavior of a geometrically nonlinear planar two member structure clamped at one end and elastically supported at the other under follower force is studied the characteristics of forces in the members of the structure during loading vs the rigidity of the supporting spring are discussed the changes of bending moment at which the system elements interact the lateral displacement and tangent slope angle vs loading force are presented the critical instability divergence mechanism of a double bar column is compared with the corresponding single column

from ornstein uhlenbeck dynamics to long memory processes and fractional brownian motion this article establishes a natural physical path leading from regular ornstein uhlenbeck dynamics to anomalous long memory processes and thereafter to fractional brownian motion considering a system composed of n different parts each part conducting its own ornstein uhlenbeck dynamics and all parts being perturbed by a common external l evy noise we show that the collective system dynamics in the limit n ensuremath rightarrow ensuremath infty converges to a temporal moving average of the driving noise the limiting moving average process in turn can posses a long memory in which case when observed over large time scales further yields fractional brownian motion the temporal correlation structure of the limiting moving average process turns out to be determined by the structural statistical variability of the system s composing parts thus the emergence of a long memory is a consequence of the intrinsic quenched disorder present at the system s formation epoch rather than the consequence of the external annealed disorder carried in continuously by the driving noise

criteria for occurrence of flutter instability before buckling the occurrence of utter instability through a hopf bifurcation before static buckling in regions of divergence in nonconservative nonself adjoint dissipative systems is thoroughly discussed using a qualitative analysis this region where both ziegler s and static criterion may fail to predict the actual critical load is de ned via two values bounds of the nonconservativenessloadingparameter the upperboundcorresponds to 0 5 being invariant with respect to all other parameters whereas the lower bound corresponds to a double critical divergence point beyond which there are no adjacent equilibria the location of the last point lying always between 0 and 0 5 depends on a stiffness parameter it is also found that the region of nonexistence of adjacent equilibria becomes maximum minimum when the double critical point corresponds to 0 5 0 the interaction of vanishing damping with various parameters leads to new phenomena related to point and periodic attractors as well as to a new type of dynamic bifurcation

power law correlated processes with asymmetric distributions motivated by the fact that many physical systems display sid power law correlations together with siid an asymmetry in the probability distribution we propose a stochastic process that can model both properties the process depends on only two parameters where one controls the scaling exponent of the power law correlations and the other controls the degree of asymmetry in the distributions leaving the correlations unaffected we apply the process to air humidity data and find that the statistical properties of the process are in a good agreement with those observed in the data

fractional diffusion exact representations of spectral functions for all the relevant transformed spaces i e fourier laplace and fourier laplace we present exact solutions of a fractional diffusion equation describing random transport on fractals the potential importance of such spectral representations lies in their applications to interpreting experimental measurements of anomalous diffusion processes in contrast to the well known asymptotic results the exact representations provide a much broader basis for comparison with data

diffusion equations for a markovian jumping process we consider a markovian jumping process which is defined in terms of the jump size distribution and the waiting time distribution with a position dependent frequency in the diffusion limit we assume the power law form for the frequency for small steps we derive the fokker planck equation and show the presence of the normal diffusion subdiffusion and superdiffusion for the l evy distribution of the step size we construct a fractional equation which possesses a variable coefficient and solve it in the diffusion limit then we calculate fractional moments and define the fractional diffusion coefficient as a natural extension to the cases with the divergent variance we also solve the master equation numerically and demonstrate that there are deviations from the l evy stable distribution for large wave numbers

anomalous diffusion in systems driven by the stable levy noise with a finite noise relaxation time and inertia dynamical systems driven by a general levy stable noise are considered the inertia is included and the noise represented by a generalized ornstein uhlenbeck process has a finite relaxation time a general linear problem the additive noise is solved the resulting distribution converges with time to the distribution for the white noise massless case moreover a multiplicative noise is discussed it can make the distribution steeper and the variance which is finite depends sublinearly on time subdiffusion for a small mass a white noise limit corresponds to the stratonovich interpretation on the other hand the distribution tails agree with the ito interpretation if the inertia is very large an escape time from the potential well is calculated

verification and validation for turbulent mixing abstract verification and validation constitute a relatively new requirement for numerical analysis it is one which results from the growing practical use of computation as a basis for engineering decisions while a number of procedures have been proposed for these tasks their application to the more difficult cases remains a research issue here we explain methods developed by ourselves and collaborators for verification and validation of simulations for chaotic multiscale flows specifically for turbulent mixing simulations

general criterion for harmonicity citation proesmans k vandebroek h van den broeck c 2017 general criterion for harmonicity physical review letters 119 14 1 5 doi 10 1103 physrevlett 119 147803

a front tracking algorithm for limited mass diffusion the advantage of front tracking over capturing methods for the numerical simulation of discontinuity surfaces in fluid flow is to eliminate the numerical diffusion of mass across a fluid interface for accurate modeling of an interface between miscible fluids however physical mass diffusion may be significant and must be added to the calculation the main purpose of this paper is to introduce a new front tracking algorithm in which the physical diffusion of mass across a tracked interface is included the accuracy and convergence properties of this algorithm are discussed the new algorithm is a subgrid algorithm in the sense that the asymptotic fine grid behavior is identical to conventional untracked capturing methods while the coarse grid behavior is improved it is thus most suitable for modeling small values of physical mass diffusion for which adequate numerical resolution is computationally demanding the mixing rates for the 3d rayleigh taylor instability of miscible fluids based on this algorithm agree with experimental values

boundary layer turbulence as a kangaroo process a nonlocal mixing length theory of turbulence transport by finite size eddies is developed by means of a novel evaluation of the reynolds stress the analysis involves the contruct of a sample path space and a stochastic closure hypothesis the simplifying property of exhange strong eddies is satisfied by an analytical sampling rate model a nonlinear scaling relation maps the path space onto the semi infinite boundary layer the underlying near wall behavior of fluctuating velocities perfectly agrees with recent direct numerical simulations the resulting integro differential equation for the mixing of scalar densities represents fully developed boundary layer turbulence as a nondiffusive kubo anderson or kangaroo type of stochastic process the model involves a scaling exponent with in the diffusion limit for the partly analytical solution for the mean velocity profile excellent agreement with the experimental data yields 0 58 1995 the american physical society

stretched gaussian asymptotics of the truncated levy flights for the diffusion in nonhomogeneous media abstract the levy jumping process defined in terms of the jumping size distribution and the waiting time distribution is considered the jumping rate depends on the process value the fractional diffusion equation which contains the variable diffusion coefficient is solved in the diffusion limit that solution resolves itself to the stretched gaussian when the order parameter 2 the truncation of the levy flights in the exponential and power law form is introduced and the corresponding random walk process is simulated by the monte carlo method the stretched gaussian tails are found in both cases the time which is needed to reach the limiting distribution strongly depends on the jumping rate parameter when the cutoff function falls slowly the tail of the distribution appears to be algebraic

nonlinear dynamic buckling of discrete structural systems under impact loading abstract nonlinear dynamic buckling of discrete dissipative or nondissipative nonlinearly elastic structural systems geometrically perfect or imperfect under impact loading is thoroughly examined applying the law of impulse momentum one can determine analytically the initial conditions valid immediately after impact thereafter the response of the system is governed by a set of autonomous highly nonlinear ordinary differential equations using an efficient and qualitative analysis exact and lower upper bound dynamic buckling estimates very useful for structural design purposes are established without integrating the aforementioned nonlinear initial value problem the analysis is supplemented by a variety of numerical results of a two degrees of freedom dissipative model from these results it is clearly shown how the point attractor response of the system is changed after a sudden jump to dynamic buckling occurring through a global dynamic bifurcation

hydrodynamics of confined colloidal fluids in two dimensions we apply a hybrid molecular dynamics and mesoscopic simulation technique to study the dynamics of two dimensional colloidal disks in confined geometries we calculate the velocity autocorrelation functions and observe the predicted t 1 long time hydrodynamic tail that characterizes unconfined fluids as well as more complex oscillating behavior and negative tails for strongly confined geometries because the t 1 tail of the velocity autocorrelation function is cut off for longer times in finite systems the related diffusion coefficient does not diverge but instead depends logarithmically on the overall size of the system the langevin equation gives a poor approximation to the velocity autocorrelation function at both short and long times

a cumulative entropy method for distribution recognition of model error abstract this paper develops a cumulative entropy method cem to recognize the most suitable distribution for model error in terms of the cem the levy stable distribution is employed to capture the statistical properties of model error the strategies are tested on 250 experiments of axially loaded cft steel stub columns in conjunction with the four national building codes of japan aij 1997 china dl t 1999 the eurocode 4 eu4 2004 and united states aisc 2005 the cumulative entropy method is validated as more computationally efficient than the shannon entropy method compared with the kolmogorov smirnov test and root mean square deviation the cem provides alternative and powerful model selection criterion to recognize the most suitable distribution for the model error

anomalous diffusion for a correlated process with long jumps abstract we discuss diffusion properties of a dynamical system which is characterised by long tail distributions and finite correlations the particle velocity has the stable levy distribution it is assumed as a jumping process the kangaroo process with a variable jumping rate both the exponential and the algebraic form of the covariance defined for the truncated distribution are considered it is demonstrated by numerical calculations that the stationary solution of the master equation for the case of power law correlations decays with time but a simple modification of the process makes the tails stable the main result of the paper is a finding that in contrast to the velocity fluctuations the position variance may be finite it rises with time faster than linearly the diffusion is anomalously enhanced on the other hand a process which follows from a superposition of the ornstein uhlenbeck levy processes always leads to position distributions with a divergent variance which means accelerated diffusion

dynamic stability criteria of nonlinear elastic damped undamped systems under step loading the nonlinear dynamic stability of simple nonlinearly elastic systems with or without viscous damping under step loading of infinite or finite duration is discussed the analysis refers to discrete structural systems with one or two degrees of freedom which under the action of the same loading applied statically lose their stability by snapping considering the stability of motion in the large in the sense of lagrange conditions for a bounded or an unbounded motion and thereby dynamic buckling criteria are properly established for one degree of freedom systems it is found that regardless of the length of time of loading application as well as regardless of whether or not damping is included the motion ceases to be bounded when the phase point velocity vanishes using this criterion exact or approximate lower bound dynamic buckling loads for damped or undamped systems under step loading of infinite or finite duration can be obtained without solving the strongly nonlinear differential equation of motion

integral equation formulation and analysis of the dynamic stability of damped beams subjected to subtangential follower forces abstract this paper presents a mathematical model based on integral equations for numerical investigations of stability analyses of damped beams subjected to subtangential follower forces a mathematical formulation based on euler bernoulli beam theory is presented for beams with variable cross sections on a viscoelastic foundation and subjected to lateral excitation conservative and non conservative axial loads using the boundary element method and radial basis functions the equation of motion is reduced to an algebro differential system related to internal and boundary unknowns generalized formulations for the deflection the slope the moment and the shear force are presented the free vibration of loaded beams is formulated in a compact matrix form and all necessary matrices are explicitly given the load frequency dependence is extensively investigated for various parameters of non conservative loads of internal and viscous dampings and for various positions of the concentrated foundation for an undamped beam a dynamic stability analysis is illustrated numerically based on the coalescence criterion the flutter load and instability regions with respect to various parameters are identified the effects of internal and viscous dampings on the critical flutter load are examined separately and relative effects are evaluated the dynamic responses before near and after the flutter are investigated a simple and quite general methodological approach is presented comprehensive numerical tests for flutter analysis are reported and discussed

anomalous fluctuation properties we complement and extend our work on fluctuations arising in nonequilibrium systems in steady states driven by l evy noise h touchette and e g d cohen phys rev e 76 020101 r 2007 as a concrete example we consider a particle subjected to a drag force and a l evy white noise with tail index ensuremath mu 0 2 and calculate the probability distribution of the work done on the particle by the drag force as well as the probability distribution of the work dissipated by the dragged particle in a nonequilibrium steady state for 0l ensuremath mu l2 both distributions satisfy what we call an anomalous fluctuation property characterized by positive and negative fluctuations that asymptotically have the same probability for ensuremath mu 2 by contrast the work and dissipated work distributions satisfy the known conventional and extended fluctuation relations respectively which are both characterized by positive fluctuations that are exponentially more probable than negative fluctuations the difference between these different fluctuation behaviors is discussed in the context of large deviation theory experiments that could probe or reveal an anomalous fluctuation property are also discussed

analytic approach to the problem of convergence of truncated levy flights towards the gaussian stochastic process an analytic expression for characteristic function defining a truncated l evy flight is derived it is shown that the characteristic function yields results in agreement with recent simulations of truncated l evy flights by mantegna and stanley phys rev lett 73 2946 1994 with the analytic expression for the characteristic function the convergence of the l evy process towards the gaussian is demonstrated without simulations in the calculation of first return probability the simulations are replaced by numerical integration using simple quadratures

instability of lightly damped linear nonconservative systems in computing the critical load for a linear nonconservative system one needs to construct the load frequency curve from the characteristic equation that contains asymmetric matrices based on the finite element formulation traditionally this requires repeated solution of complex eigenvalues from the characteristic equation at many load levels which is extremely time consuming in practice small damping of the rayleigh type is assumed a bieigenvalue curve is adopted to approximate the load frequency curve for the first few modes of interest such a curve can be uniquely determined once the derivatives of the frequency with respect to the load parameter have been calculated for a preset load level after the bieigenvalue curve is established the critical load can be computed by setting its first derivative equal to zero the effectiveness of the present method is demonstrated in the numerical study

stability analysis of stochastically parametered nonconservative columns nonconservatively loaded columns which have stochastically distributed material property values and stochastic loadings in space are considered young s modulus and mass density are treated to constitute random fields the support stiffness coefficient and tip follower load are considered to be random variables the fluctuations of external and distributed loadings are considered to constitute a random field the variational formulation is adopted to get the differential equation and boundary conditions the non self adjoint operators are used at the boundary of the regularity domain the statistics of vibration frequencies and modes are obtained using the standard perturbation method by treating the fluctuations to be stochastic perturbations linear dependence of vibration and stability parameters over property value fluctuations and loading fluctuations are assumed bounds for the statistics of vibration frequencies are obtained the critical load is first evaluated for the averaged problem and the corresponding eigenvalue statistics are sought then the frequency equation is employed to transform the eigenvalue statistics to critical load statistics specialization of the general procedure to beck leipholz and pfluger columns is carried out for pfluger column nonlinear transformations are avoided by directly expressing the critical load statistics in terms of input variable statistics

divergence and flutter of a cantilever rod with an intermediate spring support abstract the equation of motion in matrix form of a cantilever euler beam subject to a tipconcentrated follower force at the free end is formulated based on the lagrangian approach and the assumed mode method the non conservative nature of the system is identified by the non symmetric matrix in the equation of motion the beam is assumed to rest on an intermediate spring support jump phenomenon for the critical follower load is found to occur for both variations in the support location as well as the stiffness of the spring support detailed history of the changes in the load frequency diagram due to variation in the support location and the stiffness of the spring support is presented to explain the occurrence of the jump phenomenon an interesting finding is that the rod is found to be extremely unstable for a certain combination of spring stiffness and support location for a cantilever rod

correlation cascades of levy driven random processes abstract we explore the correlation structure of a large class of random processes driven by non gaussian levy noise sources with possibly infinite variances examples of such processes include levy motions levy driven ornstein uhlenbeck motions levy driven moving average processes fractional levy motions and fractional levy noises based on the fact that non gaussian levy noises are continuum superpositions of poisson noises we unveil an underlying cascade of levy correlation functions which characterize the process distribution and the correlation structure of the processes under consideration in the case where the driving levy noise sources are fractal the resulting cascade admits a unique scale free form

eliminating finite size effects and detecting the amount of white noise in short records with long term memory long term memory is ubiquitous in nature and has important consequences for the occurrence of natural hazards but its detection often is complicated by the short length of the considered records and additive white noise in the data here we study synthetic gaussian distributed records x i of length n that consist of a long term correlated component 1 ensuremath a y i characterized by a correlation exponent ensuremath gamma 0l ensuremath gamma l1 and a white noise component a ensuremath eta i 0 ensuremath le a ensuremath le 1 we show that the autocorrelation function c n s has the general form c n s c ensuremath infty s ensuremath e a 1 ensuremath e a where c ensuremath infty 0 1 c ensuremath infty sg0 b a s ensuremath ensuremath gamma and e a 2 b a 2 ensuremath ensuremath gamma 1 ensuremath ensuremath gamma n ensuremath ensuremath gamma o n ensuremath 1 the finite size parameter e a also occurs in related quantities for example in the variance ensuremath delta n 2 s of the local mean in time windows of length s ensuremath delta n 2 s ensuremath delta ensuremath infty 2 s ensuremath e a 1 ensuremath e a for purely long term correlated data b 0 ensuremath cong 2 ensuremath ensuremath gamma 1 ensuremath ensuremath gamma 2 yielding e 0 ensuremath cong n ensuremath ensuremath gamma and thus c n s frac 2 ensuremath ensuremath gamma 1 ensuremath ensuremath gamma 2 s ensuremath ensuremath gamma ensuremath n ensuremath ensuremath gamma 1 ensuremath n ensuremath ensuremath gamma and ensuremath delta n 2 s s ensuremath ensuremath gamma ensuremath n ensuremath ensuremath gamma 1 ensuremath n ensuremath ensuremath gamma we show how to estimate e a and c ensuremath infty s from a given data set and thus how to obtain accurately the exponent ensuremath gamma and the amount of white noise a

algorithms for brownian dynamics computer simulations multivariable case several brownian numerical schemes for treating stochastic differential equations at the position langevin level are analyzed from the point of view of their algorithmic efficiency for large n systems the algorithms are tested using model colloidal fluids of particles interacting via the yukawa potential limitations in the conventional brownian dynamics algorithm are shown and it is demonstrated that much better accuracy for dynamical and static quantities can be achieved with an algorithm based on the stochastic expansion and second order stochastic runge kutta algorithms the importance of the various terms in the stochastic expansion is analyzed and the relative merits of second order algorithms are discussed

fractional diffusion and levy stable processes anomalous diffusion in which the mean square distance between diffusing quantities increases faster than linearly in time has been observed in all manner of physical and biological systems from macroscopic surface growth to dna sequences herein we relate the cause of this nondiffusive behavior to the statistical properties of an underlying process using an exact statistical model this model is a simple two state process with long time correlations and is shown to produce a random walk described by an exact fractional diffusion equation fractional diffusion equations describe anomalous transport and are shown to have exact solutions in terms of fox functions including l evy ensuremath alpha stable processes in the superdiffusive domain 1 21

simple jumping process with memory transport equation and diffusion we present a stochastic jumping process defined in terms of jump size probability density and jumping rate which is a generalization of the well known kangaroo process the definition takes into account two process values after and before the jump therefore the process is able to preserve memory about its previous values it possesses a simple stationary limit its master equation is interpreted as the kinetic equation with variable collision rate the process can be easily applied to model systems which relax to distributions other than maxwellian the case of a constant jumping rate corresponds to the diffusion process either normal or ballistic

from continuous time random walks to the fractional fokker planck equation we generalize the continuous time random walk ctrw to include the effect of space dependent jump probabilities when the mean waiting time diverges we derive a fractional fokker planck equation ffpe this equation describes anomalous diffusion in an external force field and close to thermal equilibrium we discuss the domain of validity of the fractional kinetic equation for the force free case we compare between the ctrw solution and that of the ffpe

fractional diffusion equation for a power law truncated levy process abstract truncated levy flights are stochastic processes which display a crossover from a heavy tailed levy behavior to a faster decaying probability distribution function pdf putting less weight on long flights overcomes the divergence of the levy distribution second moment we introduce a fractional generalization of the diffusion equation whose solution defines a process in which a levy flight of exponent is truncated by a power law of exponent 5 a closed form for the characteristic function of the process is derived the pdf of the displacement slowly converges to a gaussian in its central part showing however a power law far tail possible applications are discussed

continuous time random walk with generic waiting time and external force we derive an integrodifferential diffusion equation for decoupled continuous time random walk that is valid for a generic waiting time probability density function and external force using this equation we also study diffusion behaviors for a couple of specific waiting time probability density functions such as exponential a combination of power law and generalized mittag leffler function and a sum of exponentials under the influence of a harmonic trap we show that first two waiting time probability density functions can reproduce the results of the ordinary and fractional diffusion equations for all the time regions from small to large times but the third one shows a much more complicated pattern furthermore from the integrodifferential diffusion equation we show that the second einstein relation can hold for any waiting time probability density function

global stabilty analysis of a classical non conservative system under a follower load abstract the bifurcations critical conditions and global stability of the classical two degree of freedom ziegler s dissipative model under a partial follower load are thoroughly discussed with the aid of a complete non linear dynamic analysis attention is mainly focused on the range of values of the non conservativeness loading parameter for which adjacent equilibria do not exist various characteristic findings are established by studying the nature of the jacobian matrix eigenvalues associated with the above non linear autonomous dissipative system it is found that the system exhibits stable hopf bifurcations global stability for the entire region of non adjacent equilibria while the classical linear stability analysis leads to flutter instability local instability moreover in an explicit general form the significant effect of damping on the critical dynamic bifurcation load is established on the basis of the latter the critical loads for the case of vanishing damping are found to be completely different from those of the classical local stability analysis all findings of this analysis are checked against numerical solution of the equations of motion

multiplicative levy processes ito versus stratonovich interpretation langevin equation with a multiplicative stochastic force is considered that force is uncorrelated it has the levy distribution and the power law intensity the fokker planck equations which correspond both to the ito and stratonovich interpretation are presented they are solved for the case without drift and for the harmonic oscillator potential the variance is evaluated it is always infinite for the ito case whereas for the stratonovich one it can be finite and rise with time slower that linearly which indicates subdiffusion analytical results are compared with numerical simulations

vibration and stability of a cantilever column subject to a follower force passing through a fixed point abstract the paper describes the stability and natural vibration of column loaded by a force passing through a fixed point it is proved that the system is conservative and its loss of stability occurs via divergence on the other hand a change in modes occurring along the fundamental eigencurve which modifies its slope from positive to negative with the increasing load is found theoretically and confirmed by the modal analysis for that reason the system is proposed to be called the divergence pseudo flutter system experimental results concerning the natural vibration frequency agreed well with the numerical ones

free vibrations and the stability of a geometrically non linear column loaded by a follower force directed towards the positive pole abstract a slender system built as a geometrically non linear system and subjected to specific load by a follower force directed towards the positive pole is discussed the load is induced by heads composed of circular profile elements the problem of stability and free vibration was formulated on the basis of hamilton s principle and then owing to its non linearity solved using the straightforward expansion method this paper provides example results of numerical computations concerning the influence of selected parameters characterizing the considered column including pre stressing on the stability and free vibration the accuracy of the adopted mathematical model is also proved on the basis of experimental studies

the role of prestressing in establishing regions of instability for a compound column under conservative or non conservative load the influence of prestressing of a non linear two member column on its natural vibration and stability is studied the perturbation method is used for solving the problem regions of divergence and flutter instabilities for a column has been determined on the basis of courses of eigencurves in relation to prestress rate discontinuities of the critical force have been observed for the border value of the prestress leading to the instability of the column without the external load although each prestress lowers the critical force it can be used for passive vibration control

criteria for occurrence of flutter instability before buckling in nonconservative dissipative systems the occurrence of flutter instability through a hopf bifurcation before static buckling in regions of divergence in nonconservative nonself adjoint dissipative systems is thoroughly discussed using a qualitative analysis this region where both ziegler s and static criterion may fail to predict the actual critical load is defined via two values bounds of the nonconservativeness loading parameter the upper bound corresponds to 0 5 being invariant with respect to all other parameters whereas the lower bound corresponds to a double critical divergence point beyond which there are no adjacent equilibria the location of the last point lying always between 0 and 0 5 depends on a stiffness parameter it is also found that the region of nonexistence of adjacent equilibria becomes maximum minimum when the double critical point corresponds to 0 5 0 the interaction of vanishing damping with various parameters leads to new phenomena related to point and periodic attractors as well as to a new type of dynamic bifurcation

modeling of financial data comparison of the truncated levy flight and the arch 1 and garch 1 1 processes we compare our results on empirical analysis of nancia l data with simulations of two stochastic models of the dynamics of stock market prices the two models are i the truncated l evy igh t recently introduced by us and ii the arch 1 and garch 1 1 processes we n d that the tlf well describes the scaling and its breakdown observed in empirical data while it is not able to properly describe the uctuation s of volatility empirically detected the arch 1 and garch 1 1 models are able to describe the probability density function of price changes at a given time horizon but both fail to describe the scaling properties of the pdfs for short time horizons c 1998 elsevier science b v all rights reserved

exact solution of the fokker planck equation for a broad class of diffusion coefficients we consider the langevin equation with a multiplicative noise term that depends on time and space the corresponding fokker planck equation in the stratonovich approach is investigated its exact solution is obtained for an arbitrary multiplicative noise term given by g x t d x t t and the behaviors of probability distributions for some specific functions of d x are analyzed we show that the asymptotic shape of the random walk model and power law decay obtained from other approaches can be reproduced from our solutions by employing two simple functions for g x t in particular for d x approximately x theta 2 the physical solutions for the probability distribution in the ito stratonovich and postpoint discretization approaches can be obtained and analyzed

the influence of an intermediate support on the stability behaviour of cantilever beams subjected to follower forces abstract a non uniform undamped beam which is simply supported at one end resting on an elastically flexible support at an intermediate abscissa q is examined the beam is subjected to a generic set of follower forces along the axis so that beck leipholz and hauger problems can be easily recovered as particular cases in all these systems a location for the intermediate support exists which corresponds to passage from flutter to divergence

flutter and divergence instability of nonconservative beams and plates for a conservative system the only possible instability is of divergence type for a nonconservative system however instability can be of divergence flutter or both depending on the amount of nonconservativeness in this paper we study the instability of a cantilevered beam and a simply supported plate subjected to a combination of fixed and follower forces a nonconservative parameter is introduced to provide all possible combinations of these forces for the beam instability changes from divergence to flutter at a critical value of this parameter for values of the parameter above the critical value the flutter instability remains as the only instability pattern in contrast to implications in the literature for the plate the instability is governed by flutter for a certain range of the nonconservative parameter even though divergence instability still exists the range depends on the geometry aspect ratio and material property poisson s ratio of the plate

the existence of regions of divergence instability for nonconservative systems under follower forces abstract in this investigation the existence of regions of divergence instability for an elastically restrained column under a follower compressive force at its end is discussed necessary and sufficient conditions for the existence of regions of divergence instability are established the boundary between flutter and divergence instability passes always through a double critical point where the first and second static buckling eigenmodes coincide the eigenvalues buckling loads of nonself adjoint problems of this type are positive and distinct for the entire region of divergence instability except at its boundary where the first and second eigenvalues coincide at this boundary where the buckling mechanism changes from divergence to flutter and vice versa a sudden increase in the critical load occurs with the flutter load always being higher than the corresponding divergence load

solving the chapman kolmogorov equation for a jumping process a general solution to the chapman kolmogorov equation for a jumping process called the kangaroo process is derived a special case of algebraic dependences is discussed in detail in particular simple asymptotic formulas for probability distribution are presented it is demonstrated that there are two different classes of limiting stationary distributions an expression for the covariance is also derived

bifurcations in a two degree of freedom elastic system with follower forces abstract the stability and bifurcations of a two degree of freedom elastic system subjected to follower forces are studied attention is mainly concentrated on local behavior small amplitude motions about a centre equilibrium for the parameter values in the neighborhood of some point on the stability boundaries by using centre manifold theory and some codimension two bifurcations it is shown that a number of distinct bifurcations may occur in such a system according to the ratio of two damping coefficients numerical integrations of the full equations of motion have been performed to confirm the analytical aspects of the local solutions as well as to understand some aspects of the global behavior of the solutions

point attractors and dynamic buckling of autonomous systems under step loading abstract in this study the dynamic response of autonomous mainly dissipative multi d o f systems under step loading is re examined based on the geometrical point of view of the theory of non linear dynamical systems and the rapidly developing theory of attractors the investigation focuses on limit point like systems with snapping as their salient feature it is found that dynamic buckling through a saddle or its neighborhood although leading to a large amplitude motion may be associated with a point attractor response on the pre buckling fixed point depending on the amount of damping considered in close conjunction with the motion channel geometry and the total potential characteristics of all stable and complementary equilibria for such systems only a straightforward fully non linear dynamic analysis can provide valid information on the global dynamic stability since the shape of the total potential hypersurface may become very complicated rendering energy aspects practically not applicable a 2 d o f model simulating an asymmetric suspended roof is comprehensively analyzed to capture the above findings and a parametric investigation is carried out revealing a variety of new dynamic response types and leading to a more accurate insight of the stability of motion in the large

intertime jump statistics of state dependent poisson processes a method to obtain the probability distribution of the interarrival times of jump occurrences in systems driven by state dependent poisson noise is proposed such a method uses the survivor function obtained by a modified version of the master equation associated to the stochastic process under analysis a model for the timing of human activities shows the capability of state dependent poisson noise to generate power law distributions the application of the method to a model for neuron dynamics and to a hydrological model accounting for land atmosphere interaction elucidates the origin of characteristic recurrence intervals and possible persistence in state dependent poisson models

finite element solution of the stability problem for nonlinear undamped and damped systems under nonconservative loading a nonlinear finite element analysis of elastic structures which can be studied by a 3d beam theory subjected to conservative as well as to nonconservative forces is presented the stability behaviour of the system is studied by means of an eigenvalue analysis the stiffness matrix of the eigenvalue problem is asymmetric i e non self adjoint system the flutter and divergence modes of instability as well as the values of the critical load are identified for a number of numerical examples belonging to the benchmark tests proposed by nafems 1990 the results demonstrate the reliability of this finite element formulation in particular the effect of damping on the stability behaviour of such structures is investigated and the destabilizing effect of small damping is underlined finally the need to define a number of benchmark tests for nonlinear nonconservative analyses in presence of damping is included

nonlinear stochastic equations with multiplicative levy noise the langevin equation with a multiplicative levy white noise is solved the noise amplitude and the drift coefficient have a power law form a validity of ordinary rules of the calculus for the stratonovich interpretation is discussed the solution has the algebraic asymptotic form and the variance may assume a finite value for the case of the stratonovich interpretation the problem of escaping from a potential well is analyzed numerically predictions of different interpretations of the stochastic integral are compared

bifurcations associated with a double zero and a pair of pure imaginary eigenvalues interactive static and dynamic bifurcations associated with a nonlinear autonomous system and the stability properties of various solutions are explored attention is focused on the vicinity of a compound critical point where the jacobian of the system exhibits a double zero eigenvalue of index one and a pair of pure imaginary eigenvalues the system under consideration has three independent parameters and depending on the route followed in the parameter space the system may exhibit static bifurcations hopf bifurcations secondary hopf bifurcations and bifurcations into two or three dimensional tori the general analysis is based on a perturbation method which combines an intrinsic harmonic balancing technique with a certain unification procedure this approach leads to bifurcation equations and simplified differential equations governing the local dynamics in the vicinity of the compound critical point a control system is analyzed for illustration

complex fractal dimension of the bronchial tree the architecture of the mammalian lung has been shown to be correctly described using a fractal model with a complex dimension related to a cantor set with random errors for four different species here we provide an interpretation of that model that has implications for biological evolution we argue that fractals are more error tolerant than other structures and therefore have an evolutionary advantage

uncertainty quantification for chaotic computational fluid dynamics we seek error models for simulations that model chaotic flow stable statistics for the solution and for the error are obtained after suitable averaging procedures