hyperbolic type transport equations abstract in recent years hyperbolic type transport equations have acquired a great deal of importance in problems ranging from theoretical physics to biology in spite of their greater mathematical difficulty as compared with their parabolic type analogs arising from the framework of linear irreversible thermodynamics they have in many ways superseded the latter ones although the use of this type of equations is well known since the last century through the telegraphist equation of electromagnetic theory their use in studying several problems in transport theory is hardly fifty years old in fact the first appearance of a hyperbolic type transport equation for the problem of heat conduction dates back to cattaneos work in 1948 three years later in 1951 s goldstein showed how in the theory of stochastic processes this type of an equation is obtained in the continuous limit of a one dimensional persistent random walk problem after that other phenomenological derivations have been offered for such equations the main purpose of this paper is to critically discuss a derivation of a hyperbolic type fokker planck equation recently presented using the same ideas as m s green did in 1952 to provide the stochastic foundations of irreversible statistical mechanics arguments are given to show that such an equation as well as transport equations derived from it by taking appropriate averages are at most approximate and that a much more detailed analysis is required before asserting their validity

first passage times for a generalized telegrapher s equation abstract all definitions and analyses of the one dimensional telegrapher s equation assume an underlying translational invariant space we here generalize this model to allow for non uniform spatial properties and derive the form of the backward equation and the associated boundary conditions in the presence of trapping points we show that moments of the first passage time till trapping can be calculated in closed form from a formalism based on the backward equation

the weak metric approximation property we introduce and investigate the weak metric approximation property of banach spaces which is strictly stronger than the approximation property and at least formally weaker than the metric approximation property among others we show that if a banach space has the approximation property and is 1 complemented in its bidual then it has the weak metric approximation property we also study the lifting of the weak metric approximation property from banach spaces to their dual spaces this enables us in particular to show that the subspace of c0 constructed by johnson and schechtman does not have the weak metric approximation property

the continuum limit of a two dimensional persistent random walk abstract we consider a two dimensional persistent random walk in which the motion consists of alternative steps along one of two vectors a and b it is shown that the continuum limit of the evolution equation is not a two but rather a one dimensional telegrapher s equation

a discrete formulation of the theory of sojourn times in a two state system abstract most theoretical analyses of single molecule spectroscopy sms are formulated in terms of a first order isomerization process the mathematical problem to which the analysis reduces requires one to find the probability density for the total residence time in one of the states at a given observation time t in this paper we develop a slightly more rigorous theory in which account is taken of the discrete pulsing of the laser it is shown how to pass to the continuum limit we develop analogous results to analyze experiments in which the quantum yield is less than 1

age representation of levy walks partial density waves relaxation and first passage time statistics l vy walks lws define a fundamental class of finite velocity stochastic processes that can be introduced as a special case of continuous time random walks alternatively there is a hyperbolic representation of them in terms of partial probability density waves using the latter framework we explore the impact of aging on lws which can be viewed as a specific initial preparation of the particle ensemble with respect to an age distribution we show that the hyperbolic age formulation is suitable for a simple integral representation in terms of linear volterra equations for any initial preparation on this basis relaxation properties i e the convergence towards equilibrium of a generic thermodynamic function dependent on the spatial particle distribution and first passage time statistics in bounded domains are studied by connecting the latter problem with solute release kinetics we find that even normal diffusive lws where the long term mean square displacement increases linearly with time may display anomalous relaxation properties such as stretched exponential decay we then discuss the impact of aging on the first passage time statistics of lws by developing the corresponding volterra integral representation as a further natural generalization the concept of lws with wearing is introduced to account for mobility losses

persistent random motion with maximally correlated fluctuations how often should a random walker change its direction of motion in order to maximize correlation in velocity fluctuations over a finite time interval we address this optimal diffusion problem in the context of the one dimensional persistent random walk where we evaluate the correlation and mutual information in velocity trajectories as a function of the persistence level and the observation time we find the optimal persistence level corresponds to the average number of direction reversals asymptotically scaling as the square root of the observation time this square root scaling law makes the relative growth between the average number of direction reversals and the persistence length invariant with respect to changes in the overall time duration of the random walk

a functional central limit theorem for the becker doring model we investigate the fluctuations of the stochastic becker d oring model of polymerization when the initial size of the system converges to infinity a functional central limit problem is proved for the vector of the number of polymers of a given size it is shown that the stochastic process associated to fluctuations is converging to the strong solution of an infinite dimensional stochastic differential equation sde in a hilbert space we also prove that at equilibrium the solution of this sde is a gaussian process the proofs are based on a specific representation of the evolution equations the introduction of a convenient hilbert space and several technical estimates to control the fluctuations especially of the first coordinate which interacts with all components of the infinite dimensional vector representing the state of the process

variational principles and lagrangian functions for stochastic processes and their dissipative statistical descriptions abstract a variational lagrangian formulation for stochastic processes and for the evolution equations of the associated probability density functions is developed particular attention is dedicated to poisson kac processes possessing finite propagation velocity the variational formulation in terms of lagrangian and hamiltonian densities permits to address different forms of reversibility characterizing these processes with respect to processes driven by nowhere differentiable wiener fluctuations and associated with the concepts of dynamic and statistical reversibility the latter property i e the statistical reversibility implies that the extended markov operator associated with poisson kac and generalized poisson kac processes forms a group continuously parametrized with respect to time

three dimensional telegrapher s equation and its fractional generalization we derive the three dimensional telegrapher s equation out of a random walk model the model is a three dimensional version of the multistate random walk where the number of different states form a continuum representing the spatial directions that the walker can take we set the general equations and solve them for isotropic and uniform walks which finally allows us to obtain the telegrapher s equation in three dimensions we generalize the isotropic model and the telegrapher s equation to include fractional anomalous transport in three dimensions

long range correlations in the electric signals that precede rupture further investigations the correlations within the time series of the seismic electric signal ses activities have been studied in a previous paper p varotsos n sarlis and e skordas phys rev e 66 011902 2002 here we analyze the time series of successive high and low level states durations the existence of correlation between the states is investigated by means of hurst and detrended fluctuation analysis dfa the multifractal dfa mf dfa is also employed the results point to a stronger correlation and hence longer memory in the series of the high level states furthermore an analysis in the natural time domain reveals that certain power spectrum characteristics seem to distinguish ses activities from artificial man made electric noises more precisely for natural frequencies 0 f 0 5 the curves of the ses activities and artificial noises lie above and below respectively that of the uniform distribution ud a classification of these two types of electric signals ses activities artificial noises cannot be achieved on the basis of the values of the power law exponents alone if the hurst analysis dfa and mf dfa are applied to the original time series the latter two methods however seem to allow a distinction between the ses activities and artificial noises when treating them not in conventional the time frame but in the natural time domain to further test the techniques a time series produced by another system was examined we chose a signal of ion current fluctuations in membrane channels icfmcs the following conclusions among others have been obtained first the power spectrum analysis in the natural time domain shows that the icfmc curve almost coincides in the range 0 f 0 5 with that of the ud and hence icfmc lies just in the boundary between the ses activities and artificial noises second mf dfa indicates monofractality for the icfmcs with a generalized hurst exponent h 50 8460 03 in the range 7 70 ms

diffusion coefficients for multi step persistent random walks on lattices we calculate the diffusion coefficients of persistent random walks on lattices where the direction of a walker at a given step depends on the memory of a certain number of previous steps in particular we describe a simple method which enables us to obtain explicit expressions for the diffusion coefficients of walks with a two step memory on different classes of one two and higher dimensional lattices

when the telegrapher s equation furnishes a better approximation to the transport equation than the diffusion approximation it has been suggested that a solution to the transport equation which includes anisotropic scattering can be approximated by the solution to a telegrapher s equation a j ishimaru appl opt 28 2210 1989 we show that in one dimension the telegrapher s equation furnishes an exact solution to the transport equation in two dimensions we show that since the solution can become negative the telegrapher s equation will not furnish a usable approximation a comparison between simulated data in three dimensions indicates that the solution to the telegrapher s equation is a good approximation to that of the full transport equation at the times at which the diffusion equation furnishes an equally good approximation s1063 651x 97 04205 0

random walk with persistence the exact analytic result is obtained for the fourier transform of the generating functionf r s 0 s n p r n wherep r n is the probability density for the end to end distancer inn steps of a random walk with persistence the moments r 2 n r 4 n and r 6 n are calculated and approximate results forp r n and r 1 n are given

generalized cattaneo telegrapher s equations in modeling anomalous diffusion phenomena we study generalized cattaneo telegrapher s equations involving memory effects introduced by smearing the time derivatives consistency conditions where the smearing functions obey restrict freedom in their choice but the proposed scheme goes beyond the approach based on using fractional derivatives we find conditions under which solutions of the equations considered so far can be recognized as probability distributions i e are normalizable and nonnegative on their domains nonnegativity of solutions is demonstrated by methods of positive definite and completely monotonic functions with the bernstein theorem being the cornerstone of the ongoing proofs analysis of exactly solvable examples and relevant mean squared displacements enables us to classify diffusion processes described by such got solutions and to identify them with either ordinary or anomalous diffusion which character may change over time to complete the present research we compare our results with those obtained using the continuous time random walk and the continuous time persistent random walk approaches

on the influence of reflective boundary conditions on the statistics of poisson kac diffusion processes abstract we analyze the influence of reflective boundary conditions on the statistics of poisson kac diffusion processes and specifically how they modify the poissonian switching time statistics after addressing simple cases such as diffusion in a channel and the switching statistics in the presence of a polarization potential we thoroughly study poisson kac diffusion in fractal domains diffusion in fractal spaces highlights neatly how the modification in the switching time statistics associated with reflections against a complex and fractal boundary induces new emergent features of poisson kac diffusion leading to a transition from a regular behavior at shorter timescales to emerging anomalous diffusion properties controlled by walk dimensionality of the fractal set

unraveling the structure of treelike networks from first passage times of lazy random walkers we study the problem of random search in finite networks with a tree topology where it is expected that the distribution of the first passage time f t decays exponentially we show that the slope of the exponential tail is independent of the initial conditions of entering the tree in general and scales exponentially or as a power law with the extent of the tree l depending on the tendency p to jump toward the target node it is unfeasible to uniquely determine l and p from measuring the tail slope or the mean first passage time mfpt of an ordinary diffusion along the tree to unravel the structure we consider lazy random walkers that take steps with probability m when jumping on the nodes and return with probability q from the leaves by deriving an exact analytical expression for the mfpt of the intermittent random walk we verify that the structural information of the tree can be uniquely extracted by measuring the mfpt for two randomly chosen types of tracer particles with distinct experimental parameters m and q we also address the applicability of our approach in the presence of disorder in the structure of the tree or statistical uncertainty in the experimental parameters

continued fraction solution for the radiative transfer equation in three dimensions starting from the radiative transfer equation we obtain an analytical solution for both the free propagator along one of the axes and an arbitrary phase function in the fourier laplace domain we also find the effective absorption parameter which turns out to be very different from the one provided by the diffusion approximation we finally present an analytical approximation procedure and obtain a differential equation that accurately reproduces the transport process we test our approximations by means of simulations that use the henyeygreenstein phase function with very satisfactory results

some applications of persistent random walks and the telegrapher s equation abstract a persistent random walk can be regarded as a multidimensional markov process the bias free telegraphers equation is 2 p t 2 1 t p t v 2 2 p it can be regarded as interpolating between the wave equation t and the diffusion equation t 0 previously it has found application in thermodynamics cf the review in rev mod phys 61 1989 41 62 1990 375 more recent applications are reviewed in the present article

collision statistics for random flights with anisotropic scattering and absorption for a broad class of random walks with anisotropic scattering kernels and absorption we derive explicit formulas that allow expressing the moments of the collision number n v performed in a volume v as a function of the particle equilibrium distribution our results apply to arbitrary domains v and boundary conditions and allow assessing the hitting statistics for systems where the typical displacements are comparable to the domain size so that the diffusion limit is possibly not attained an example is discussed for one dimensional random flights with exponential displacements where analytical calculations can be carried out

memory based persistence in a counting random walk process this paper considers a memory based persistent counting random walk based on a markov memory of the last event this persistent model is a different than the weiss persistent random walk model however leading thereby to different results we point out to some preliminary result in particular we provide an explicit expression for the mean and the variance both nonlinear in time of the underlying memory based persistent process and discuss the usefulness to some problems in insurance finance and risk analysis the motivation for the paper arose from the counting of events whether rare or not in insurance that presume that events are time independent and therefore based on the poisson distribution for counting these events

two dimensional telegraphic processes and their fractional generalizations we study the planar motion of telegraphic processes we derive the two dimensional telegrapher s equation for isotropic and uniform motions starting from a random walk model which is the two dimensional version of the multistate random walk with a continuum number of states representing the spatial directions we generalize the isotropic model and the telegrapher s equation to include planar fractional motions earlier we worked with the one dimensional version masoliver phys rev e 93 052107 2016 prehbm2470 004510 1103 physreve 93 052107 and derived the three dimensional version masoliver phys rev e 96 022101 2017 prehbm2470 004510 1103 physreve 96 022101 an important lesson is that we cannot obtain the two dimensional version from the three dimensional or the one dimensional one from the two dimensional result each dimension must be approached starting from an appropriate random walk model for that dimension

scaling relationships for anisotropic random walks aspects of transport in a highly multiple scattering environment are investigated by examining random walkers moving in media having anisotropic angular scattering cross sections turn angle distributions a general expression is obtained for the mean square displacement x2 of a random walker executing ann step walk in an infinite homogeneous material and results are used to predict scaling relations for the probability that a walker returns to the planar surface of a semi infinite medium at a distance from the point of its insertion

the strong approximation property we introduce and investigate the strong approximation property of banach spaces which is strictly stronger than the approximation property and at least formally weaker than the weak bounded approximation property among others we show that the weak bounded approximation property is equivalent to a quantitative strengthening of the strong approximation property some recent results on the approximation property of banach spaces and their dual spaces are improved

the weak metric approximation property and ideals of operators abstract we study the weak metric approximation property introduced by lima and oja we show that a banach space x has the weak metric approximation property if and only if f y x the space of finite rank operators is an ideal in w y x the space of weakly compact operators for all banach spaces y

first passage probabilities and mean number of sites visited by a persistent random walker in one and two dimensional lattices we study the first passage probability and mean number of sites visited by a discrete persistent random walker on a lattice in one and two dimensions this is performed by using the multistate formulation of the process we obtain explicit expressions for the generating functions of these quantities to evaluate these expressions we study the system in the strongly persistent limit in the one dimensional case we recover the behavior of the continuous one dimensional persistent random walk telegrapher process in two dimensions we obtain an explicit expression for the probability distribution in the strongly persistent limit however the laplace transforms required to evaluate the first passage processes could only be evaluated in the asymptotic limit corresponding to long times in which regime we recover the behavior of normal two dimensional diffusion

a continuous time generalization of the persistent random walk abstract we develop the formalism for a continuous time generalization of the persistent random walk by allowing the sojourn time to deviate from the exponential form found in standard discussions of this subject this generalization leads to evolution equations in the time domain that differ and are of higher order than the telegrapher s equation which is found in the case of the markovian persistent random walk

on the time fractional cattaneo equation of distributed order abstract the present work revisits the time fractional cattaneo equation tfce by considering a generic class of time fractional derivatives of distributed order 0 1 at first we shed light on two main forms of tfce one natural generalization uses the caputo fractional derivative and the other compte metzler generalization is defined in the riemann liouville sense and the equivalence condition between their solutions is provided some special cases of these two forms are addressed hence different versions of distributed order tfce are proposed the fundamental solution of the two general forms of distributed order tfce are derived using integral transform technique the non negativity of solutions of tfce and its distributed order versions is examined using the special type functions technique gorenflo luchko and stojanovic 2013 two classes of order distribution are considered discrete order and continuous order distributions and some random choices of non negative order densities affirm graphically the non negativity of the general forms of distributed order tfce the double order as an example on the discrete order and exponentially exp and sinusoidally sin distributed order as an example on the continuous order are chosen finally connections between some models of distributed order tfce and continuous time random walk theory are established and the corresponding mean squared displacements are discussed

universal properties of a run and tumble particle in arbitrary dimension we consider an active run and tumble particle rtp in d dimensions starting from the origin and evolving over a time interval 0 t we examine three different models for the dynamics of the rtp the standard rtp model with instantaneous tumblings a variant with instantaneous runs and a general model in which both the tumblings and the runs are noninstantaneous for each of these models we use the sparre andersen theorem for discrete time random walks to compute exactly the probability that the x component does not change sign up to time t showing that it does not depend on d as a consequence of this result we compute exactly other x component properties namely the distribution of the time of the maximum and the record statistics showing that they are universal i e they do not depend on d moreover we show that these universal results hold also if the speed v of the particle after each tumbling is random drawn from a generic probability distribution our findings are confirmed by numerical simulations some of these results have been announced in a recent letter phys rev lett 124 090603 2020 10 1103 physrevlett 124 090603

on random time and on the relation between wave and telegraph equations kac s conjecture relating the solution of wave and telegraph equations in higher dimensions through a poisson process driven random time is established through the concepts of stochastic calculus new expression is derived for the probability density function of the random time we demonstrate how the relationship between the solution of a lossy wave and that of a lossless wave equation can be exploited to derive some statistical identities relevance of the results presented to the study of pulse propagation in a dispersive medium characterized by a lorentz or drude model is discussed and new evolution equations for 2 d maxwell s equations are presented for the drude medium it is shown that the computational time required for updating the electric field using the stochastic technique is expected to go up as o t

local immobilization of particles in mass transfer described by a jeffreys type equation we consider the jeffreys type equation as the foundation in three different models of mass transfer namely the jeffreys type and two phase models and the d 1 approximation to the linear boltzmann equation we study two classic 1 1 dimensional problems in the framework of each model the first problem is the transfer of a substance initially confined at a point the second problem is the transfer of a substance from a stationary point source we calculate the mean square displacement msd for the solutions of the first problem the temporal behavior of the msd in the framework of the first and third models is found to be the same as that in the brownian motion described by the standard langevin equation in addition we find a remarkable phenomenon when a portion of the substance does not move

some two and three dimensional persistent random walks abstract we formulate non markovian versions of the persistent random walk in two and three dimensions and in continuous time these models can be regarded as being generalizations of the original pearson random walk and of the freely jointed chain which has been of some importance in polymer physics solutions for the probability density of the displacement of the random walker can be furnished for a restricted essentially markovian set of these models it is shown that in two dimensions the solution to one of these models is equivalent to the solution to an inhomogeneous telegrapher s equation it does not appear to be possible starting from a similar model in three dumensions to find any form of the telegrapher s equation that follows from our solution of the equations in the fourier laplace transform domains

absolutely summing operators on c 0 1 as a tree space and the bounded approximation property let x be a banach space for describing the space p c 0 1 x of absolutely summing operators from c 0 1 to x in terms of the space x itself we construct a tree space l1tree x on x it consists of special trees in x which we call two trunk trees we prove that p c 0 1 x is isometrically isomorphic to l1tree x as an application we characterize the bounded approximation property bap and the weak bap in terms of x valued sequence spaces

one dimensional hyperbolic transport positivity and admissible boundary conditions derived from the wave formulation abstract we consider the one dimensional cattaneo equation for transport of scalar fields such as solute concentration and temperature in mass and heat transport problems respectively although the cattaneo equation admits a stochastic interpretation at least in the one dimensional case negative concentration values can occur in boundary value problems on a finite interval this phenomenon stems from the probabilistic nature of this model the stochastic interpretation provides constraints on the admissible boundary conditions as can be deduced from the wave formulation here presented moreover as here shown energetic inequalities and the dissipative nature of the equation provide an alternative way to derive the same constraints on the boundary conditions derived by enforcing positivity the analysis reported is also extended to transport problems in the presence of a biasing velocity field several general conclusions are drawn from this analysis that could be extended to the higher dimensional case

delayed uncoupled continuous time random walks do not provide a model for the telegraph equation while the velocity of the motion of particles in the dctrws is infinite in this paper we investigate the accuracy of the approximations to the dctrws provided by the telegraph equation we show that the diffusion equation beingthecorrectlimitofthedctrws givesbetterapproximationsin l2 normtothedctrwsthanthetelegraph equation we conclude therefore that first the dctrws do not provide any correct microscopic interpretation of the one dimensional telegraph equation and second the kinetic exact model of the telegraph equation is different from the model based on the dctrws

random walker and the telegrapher s equation a paradigm of a generalized hydrodynamics the telegrapher s equation te is the continuum limit of a persisting random walker we find that the te reproduces the original spectrum almost exactly for all wavelengths far beyond the validity of the expansion this surprising property is used as a paradigm towards the derivation of a generalized hydrodynamics applications to other problems are explored

distribution of magnetization in the finite ising chain an isomorphism is shown to hold between the persistent random walk and the ising chain as well as between the biased persistent random walk and the closed ising chain in the presence of an external magnetic field the analytical expressions for the distributions of spontaneous and induced magnetization for the ising chain are derived using this isomorphism we show that this derivation is significantly more laborious using the partition function

different microscopic interpretations of the reaction telegrapher equation in this paper we provide some new insights into the microscopic interpretation of the telegrapher s and the reaction telegrapher equations we use the framework of continuous time random walks to derive the telegrapher s equation from two different perspectives reported before the kinetic derivation kd and the delayed random walk derivation drwd we analyze the similarities and the differences between both derivations paying special attention to the case when a reaction process is also present in the system as a result we are able to show that the equivalence between the kd and the drwd can break down when transport and reaction are coupled processes also this analysis allows us to elaborate on the specific role of relaxation effects in reaction diffusion processes

telegrapher s equations with variable propagation speeds all derivations of the one dimensional telegrapher s equation based on the persistent random walk model assume a constant speed of signal propagation we generalize here the model to allow for a variable propagation speed and study several limiting cases in detail we also show the connections of this model with anomalous diffusion behavior and with inertial dichotomous processes