distributional limit theorems in infinite ergodic theory we present a unified approach to the darling kac theorem and the arcsine laws for occupation times and waiting times for ergodic transformations preserving an infinite measure our method is based on control of the transfer operator up to the first entrance to a suitable reference set rather than on the full asymptotics of the operator we illustrate our abstract results by showing that they easily apply to a significant class of infinite measure preserving interval maps we also show that some of the tools introduced here are useful in the setup of pointwise dual ergodic transformations

process dependent persistence in precipitation records abstract whether long term persistence ltp exists in precipitation process has been studied for several decades and it is still an open question in this study the precipitation records of hourly and daily resolutions are applied to estimate the persistence of precipitation over a wider range of scales mainly by means of detrended fluctuation analysis dfa the results show that precipitation persistence can be described as a varying rather than a universal scaling behavior two distinct scaling regimes are determined by their associated power law behavior f s s f s is the fluctuation function s is the time scale is the scaling exponent and they are process dependent a regime of frontal systems with stronger ltp s is less than around 200 h 0 74 and a regime of random nature of weather system and climate variability with weaker ltp s is larger than around 200 h 0 54 this result indicates that when we simulate the precipitation process it is necessary to take the different persistent properties over the corresponding scale range into account to select the appropriate model

indication of multiscaling in the volatility return intervals of stock markets a certain trend with the mean interval we generate surrogate records using the schreiber method and find that their cumulative distributions almost collapse to a single curve and moments are almost constant for most ranges of those substantial differences suggest that nonlinear correlations in the original volatility sequence account for the deviations from a single scaling law we also find that the original and surrogate records exhibit slight tendencies for short and long due to the discreteness and finite size effects of the records respectively to avoid as possible those effects for testing the multiscaling behavior we investigate the moments in the range 10100 and find that the exponent from the power law fitting m has a narrow distribution around 0 which depends on m for the 500 stocks the distribution of for the surrogate records are very narrow and centered around 0 this suggests that the return interval distribution exhibits multiscaling behavior due to the nonlinear correlations in the original volatility

long term memory in extreme returns of financial time series abstract it is well known that while daily price returns of financial markets are uncorrelated their absolute values volatility are long term correlated here we provide evidence that certain subsequences of the returns themselves also exhibit long term memory these subsequences consist of maxima or minima of returns in consecutive time windows of r days our analysis shows that for both stocks and currency exchange rates long term correlations are significant for r 4 we argue that this long term memory which is similar to that observed in volatility clustering sheds further insight on price dynamics that might be used for risk estimation

on optimal node spacing for immersed boundary lattice boltzmann method in 2d and 3d abstract a computational study on optimal spacing of lagrangian nodes discretizing a rigid and immobile immersed body boundary in 2d and 3d is presented in order to show how the density of the lagrangian points affects the numerical results of the immersed boundary lattice boltzmann method ib lbm the study is based on the implicit velocity correction based ib lbm proposed by wu and shu 2009 2010 that allows computing the fluid body interaction force however the original method fails for densely spaced lagrangian points due to ill conditioned or even singular linear systems that arise from the derivation of the method we propose a modification that improves the solvability of the linear systems and compare the performance of both methods using several benchmark problems the results show how the spacing of the lagrangian points affects the numerical results mainly the permeability of the discretized body boundary in applications to fluid flows over rigid obstacles and blood flows in arteries in 2d and 3d

smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics this paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mecanics we adopt a new point of view which has emerged progressively in recent years and which takes seriously into account the chaotic character of the microscopic time evolution the emphasis is on nonequilibrium steady states rather than the traditional approach to equilibrium point of view of boltzmann the nonequilibrium steady states in presence of a gaussian thermostat are described by srb measures in terms of these one can prove the gallavotti cohen fluctuation theorem one can also prove a general linear response formula and study its consequences which are not restricted to near equilibrium situations at equilibrium one recovers in particular the onsager reciprocity relations under suitable conditions the nonequilibrium steady states satisfy the pairing theorem of dettmann and morriss the results just mentioned hold so far only for classical systems they do not involve large size i e they hold without a thermodynamic limit

discrete lattice effects on the forcing term in the lattice boltzmann method we show that discrete lattice effects must be considered in the introduction of a force into the lattice boltzmann equation a representation of the forcing term is then proposed with the representation the navier stokes equation is derived from the lattice boltzmann equation through the chapman enskog expansion several other existing force treatments are also examined

solution of the nonlinear theory and tests of earthquake recurrence times we develop an efficient numerical scheme to solve accurately the set of nonlinear integral equations derived previously in a saichev and d sornette j geophys res 112 b04313 2007 which describes the distribution of interevent times in the framework of a general model of earthquake clustering with long memory detailed comparisons between the linear and nonlinear versions of the theory and direct synthetic catalogs show that the nonlinear theory provides an excellent fit to the synthetic catalogs while there are significant biases resulting from the use of the linear approximation we then address the suggestions proposed by some authors to use the empirical distribution of interevent times to obtain a better determination of the so called clustering parameter our theory and tests against synthetic and empirical catalogs find a rather dramatic lack of power for the distribution of interevent times to distinguish between quite different sets of parameters casting doubt on the usefulness of this statistic for the specific purpose of identifying the clustering parameter

dimensional estimates for singular sets in geometric variational problems with free boundaries we show that singular sets of free boundaries arising in codimension one anisotropic geometric variational problems are hn 3 negligible where n is the ambient space dimension in particular our results apply to capillarity type problems and establish everywhere regularity in the three dimensional case

memory in the occurrence of earthquakes we study the statistics of the recurrence times ensuremath tau between earthquakes above a certain magnitude m in six one global and five regional earthquake catalogs we find that the distribution of the recurrence times strongly depends on the previous recurrence time ensuremath tau 0 such that small and large recurrence times tend to cluster in time this dependence on the past is reflected in both the conditional mean recurrence time and the conditional mean residual time until the next earthquake which increase monotonically with ensuremath tau 0 as a consequence the risk of encountering the next event within a certain time span after the last event depends significantly on the past an effect that has to be taken into account in any effective earthquake prognosis

multiscale multifractal detrended fluctuation analysis of earthquake magnitude series of southern california abstract the multifractal characteristics of magnitude time series of earthquakes that occurred in southern california from 1990 to 2010 are studied in this work a method for the scale division of the magnitude of these earthquakes based on empirical mode decomposition emd and multifractal analysis is proposed this method gains a new insight into measuring multifractal properties of the magnitude time series at multiple scales and it reveals further information about the dynamic seismic behavior by using emd a time series can be decomposed into mode time series that represent different time frequency components we find that time frequency components show long range correlation with different hurst exponents by using r s analysis based on the different fractal structures of components we consider three different scale series micro mid and macro scale subsequences which are superposed and reconstructed by the components the multifractal properties of the three scale subsequences are analyzed by using multifractal detrended fluctuation analysis mf dfa the results show that the three different scale subsequences have various shapes of multifractal spectra and corresponding distinct properties the micro scale subsequence singularity spectrum shows left skewed indicating a relative dominance of the lower hurst exponent the mid scale subsequence has a right skewed singularity spectrum the macro scale subsequence exhibits the most significant persistence and shows the strongest multifractality

adaptation reduces variability of the neuronal population code sequences of events in noise driven excitable systems with slow variables often show serial correlations among their intervals of events here we employ a master equation for generalized non renewal processes to calculate the interval and count statistics of superimposed processes governed by a slow adaptation variable for an ensemble of neurons with spike frequency adaptation this results in the regularization of the population activity and an enhanced postsynaptic signal decoding we confirm our theoretical results in a population of cortical neurons recorded in vivo

near mean field behavior in the generalized burridge knopoff earthquake model with variable range stress transfer simple models of earthquake faults are important for understanding the mechanisms for their observed behavior in nature such as gutenberg richter scaling because of the importance of long range interactions in an elastic medium we generalize the burridge knopoff slider block model to include variable range stress transfer we find that the burridge knopoff model with long range stress transfer exhibits qualitatively different behavior than the corresponding long range cellular automata models and the usual burridge knopoff model with nearest neighbor stress transfer depending on how quickly the friction force weakens with increasing velocity extensive simulations of quasiperiodic characteristic events mode switching phenomena ergodicity and waiting time distributions are also discussed our results are consistent with the existence of a mean field critical point and have important implications for our understanding of earthquakes and other driven dissipative systems

an adaptive version of the immersed boundary method a computational setting for the immersed boundary method employing an adaptive mesh refinement is presented enhanced accuracy for the method is attained locally by covering an immersed boundary vicinity with a sequence of nested progressively finer rectangular grid patches which dynamically follow the immersed boundary motion the set of equations describing the interaction between a non stationary viscous incompressible fluid and an immersed elastic boundary is solved by coupling a projection method specially designed for locally refined meshes to an implicit formulation of the immersed boundary method the main contributions of this work concern the formulation and the implementation of a multilevel self adaptive version of the immersed boundary method on locally refined meshes this approach is tested for a particular two dimensional model problem for which no significant difference is found between the solutions obtained on a mesh refined locally around the immersed boundary and on the associated uniform mesh built with the resolution of the finest level

statistics of return intervals in long term correlated records we consider long term correlated data with several distribution densities gaussian exponential power law and log normal and various correlation exponents ensuremath gamma 0l ensuremath gamma l1 and study the statistics of the return intervals r j between events above some threshold q we show that irrespective of the distribution the return intervals are long term correlated in the same way as the original record but with additional uncorrelated noise due to this noise the correlations are difficult to observe by the detrended fluctuation analysis which exhibits a crossover behavior but show up very clearly in the autocorrelation function the distribution p q r of the return intervals is characterized at large scales by a stretched exponential with exponent ensuremath gamma and at short scales by a power law with exponent ensuremath gamma ensuremath 1 we discuss in detail the occurrence of finite size effects for large threshold values for all considered distributions we show that finite size effects are most pronounced in exponentially distributed data sets where they can even mask the stretched exponential behavior in records of up to 10 6 data points finally in order to quantify the clustering of extreme events due to the long term correlations in the return intervals we study the conditional distribution function and the related moments we find that they show pronounced memory effects irrespective of the distribution of the original data

generalized lyapunov exponent as a unified characterization of dynamical instabilities the lyapunov exponent characterizes an exponential growth rate of the difference of nearby orbits a positive lyapunov exponent exponential dynamical instability is a manifestation of chaos here we propose the lyapunov pair which is based on the generalized lyapunov exponent as a unified characterization of nonexponential and exponential dynamical instabilities in one dimensional maps chaos is classified into three different types i e superexponential exponential and subexponential chaos using one dimensional maps we demonstrate superexponential and subexponential chaos and quantify the dynamical instabilities by the lyapunov pair in subexponential chaos we show superweak chaos which means that the growth of the difference of nearby orbits is slower than a stretched exponential growth the scaling of the growth is analytically studied by a recently developed theory of a continuous accumulation process which is related to infinite ergodic theory

interoccurrence time statistics in the two dimensional burridge knopoff earthquake model we have numerically investigated statistical properties of the so called interoccurrence time or the waiting time i e the time interval between successive earthquakes based on the two dimensional 2d spring block burridge knopoff model selecting the velocity weakening property as the constitutive friction law the statistical properties of frequency distribution and the cumulative distribution of the interoccurrence time are discussed by tuning the dynamical parameters namely a stiffness and frictional property of a fault we optimize these model parameters to reproduce the interoccurrence time statistics in nature the frequency and cumulative distribution can be described by the power law and zipf mandelbrot type power law respectively in an optimal case the b value of the gutenberg richter law and the ratio of wave propagation velocity are in agreement with those derived from real earthquakes as the threshold of magnitude is increased the interoccurrence time distribution tends to follow an exponential distribution hence it is suggested that a temporal sequence of earthquakes aside from small magnitude events is a poisson process which is observed in nature we found that the interoccurrence time statistics derived from the 2d bk original model can efficiently reproduce that of real earthquakes so that the model can be recognized as a realistic one in view of interoccurrence time statistics

application of a lattice boltzmann immersed boundary method for fluid filament dynamics and flow sensing complex fluid structure interactions between elastic filaments or cilia immersed in viscous flows are commonplace in nature and bear important roles some biological systems have evolved to interpret flow induced motion into signals for the purpose of feedback response given the challenges associated with extracting meaningful experimental data at this scale there has been particular focus on the numerical study of these effects porous models have proven useful where cilia arrangements are relatively dense but for more sparse configurations the dynamic interactions of individual structures play a greater role and direct modelling becomes increasingly necessary the present study reports efforts towards explicit modelling of regularly spaced wall mounted cilia using a lattice boltzmann immersed boundary method both steady and forced unsteady 2d channel flows at different reynolds numbers are investigated with and without the presence of a periodic array of elastic inextensible filaments it is demonstrated that the structure response depends significantly on reynolds number for low reynolds flow the recirculation vortex aft of successive filaments is small relative to the cilia spacing and does not fully bridge the gap in which case the structure lags the flow at higher reynolds number when this gap is fully bridged the structure and flow move in phase the trapping of vortices between cilia is associated with relatively lower wall shear stress at low to intermediate reynolds vortex bridging is incomplete and large deflection is still possible which is reflected in the tip dynamics and wall shear stress profiles

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

renewal sequences and intermittency in this paper we examine the generating function z of a renewal sequence arising from the distribution of return times in the turbulent region for a class of piecewise affine interval maps introduced by gaspard and wang and studied by several authors we prove that it admits a meromorphic continuation to the entire complex z plane with a branch cut along the ray 1 moreover we compute the asymptotic behavior of the coefficients of its taylor expansion at z 0 from this we obtain the exact polynomial asympotics for the rate of mixing when the invariant measure is finite and of the scaling rate when it is infinite

immersed boundary methods for general finite difference and finite volume navier stokes solvers we present an immersed boundary algorithm for incompressible flows with complex boundaries suitable for cartesian or curvilinear grid system the key stages of any immersed boundary technique are the interpolation of a velocity field given on a mesh onto a general boundary a line in 2d a surface in 3d and the spreading of a force field from the immersed boundary to the neighboring mesh points to enforce the desired boundary conditions on the immersed boundary points we propose a technique that uses the reproducing kernel particle method w k liu s jun y f zhang reproducing kernel particle methods int j numer methods fluids 20 8 1995 1081 1106 for the interpolation and spreading unlike other methods presented in the literature the one proposed here has the property that the integrals of the force field and of its moment on the grid are conserved independent of the grid topology uniform or non uniform cartesian or curvilinear the technique is easy to implement and is able to maintain the order of the original underlying spatial discretization applications to two and three dimensional flows in cartesian and non cartesian grid system with uniform and non uniform meshes are presented

simulation of flexible filaments in a uniform flow by the immersed boundary method an improved version of the immersed boundary ib method is developed for simulating flexible filaments in a uniform flow the proposed ib method is based on an efficient navier stokes solver adopting the fractional step method and a staggered cartesian grid system the fluid motion defined on an eulerian grid and the filament motion defined on a lagrangian grid are independently solved and their interaction force is explicitly calculated using a feedback law a direct numerical method is developed to calculate the filament motion under the constraint of inextensibility when applied to the case of a swinging filament analogous to a rope pendulum the proposed method gave results very similar to those of the analytical solution derived using the perturbation method for a flexible filament flapping in a uniform flow the mechanism by which small vortex processions are produced was investigated the bistable property of the system was observed by altering the filament length and the effects of the boundary condition at the fixed end simply supported or clamped were studied for two side by side filaments in a uniform flow both in phase flapping and out of phase flapping were reproduced in the present simulations a repulsive force was included in the formulation to handle collisions between the free ends of side by side filaments undergoing out of phase flapping

short ranged memory model with preferential growth in this work we introduce a variant of the yule simon model for preferential growth by incorporating a finite kernel to model the effects of bounded memory we characterize the properties of the model combining analytical arguments with extensive numerical simulations in particular we analyze the lifetime and popularity distributions by mapping the model dynamics to corresponding markov chains and branching processes respectively these distributions follow power laws with well defined exponents that are within the range of the empirical data reported in ecologies interestingly by varying the innovation rate this simple out of equilibrium model exhibits many of the characteristics of a continuous phase transition and around the critical point it generates time series with power law popularity lifetime and interevent time distributions and nontrivial temporal correlations such as a bursty dynamics in analogy with the activity of solar flares our results suggest that an appropriate balance between innovation and oblivion rates could provide an explanatory framework for many of the properties commonly observed in many complex systems

probability of large movements in financial markets abstract based on empirical financial time series we show that the silence breaking probability follows a super universal power law the probability of observing a large movement is inversely proportional to the length of the on going low variability period such a scaling law has been previously predicted theoretically r kitt j kalda physica a 353 2005 480 assuming that the length distribution of the low variability periods follows a multi scaling power law

preservation of long range temporal correlations under extreme random dilution abstract many natural time series exhibit long range temporal correlations that may be characterized by power law scaling exponents however in many cases the time series have uneven time intervals due to for example missing data points noisy data and outliers here we study the effect of randomly missing data points on the power law scaling exponents of time series that are long range temporally correlated the fourier transform and detrended fluctuation analysis dfa techniques are used for scaling exponent estimation we find that even under extreme dilution of more than 50 the value of the scaling exponent remains almost unaffected random dilution is also applied on heart interbeat interval time series it is found that dilution of 70 80 of the data points leads to a reduction of only 8 in the scaling exponent it is also found that it is possible to discriminate between healthy and heart failure subjects even under extreme dilution of more than 90

the weibull log weibull distribution for interoccurrence times of earthquakes abstract by analyzing the japan meteorological agency jma seismic catalog for different tectonic settings we have found that the probability distributions of time intervals between successive earthquakes interoccurrence times can be described by the superposition of the weibull distribution and the log weibull distribution in particular the distribution of large earthquakes obeys the weibull distribution with the exponent 1 1 indicating the fact that the sequence of large earthquakes is not a poisson process it is found that the ratio of the weibull distribution to the probability distribution of the interoccurrence time gradually increases with increase in the threshold of magnitude our results infer that weibull statistics and log weibull statistics coexist in the interoccurrence time statistics and that the change of the distribution is considered as the change of the dominant distribution in this case the dominant distribution changes from the log weibull distribution to the weibull distribution allowing us to reinforce the view that the interoccurrence time exhibits the transition from the weibull regime to the log weibull regime

missing data in aftershock sequences explaining the deviations from scaling laws in this paper we extend the branching aftershock sequence model to study the role of missing data at short times and small amplitudes after a mainshock we apply this model which contains three parameters characterizing the missing data to the magnitude and temporal statistics of four aftershock sequences in california we find that the observed time dependent deviations of the frequency magnitude scaling from the gutenberg richter power law dependency can be described quantitatively by the model we also show that for the same set of parameters the model is able to explain quantitatively the observed magnitude dependent deviations of the temporal decay of aftershocks from omori s law in addition we show that the same sets of data can also reproduce quite well the various functional forms of the probability density functions of the return times between consecutive events with magnitudes above a prescribed threshold as well as the violation of scaling at short and intermediate time scales

aging generates regular motions in weakly chaotic systems using intermittent maps with infinite invariant measures we investigate the universality of time averaged observables under aging conditions according to aaronson s darling kac theorem in non aged dynamical systems with infinite invariant measures the distribution of the normalized time averages of integrable functions converges to the mittag leffler distribution this well known theorem holds when the start of observations coincides with the start of the dynamical processes introducing a concept of the aging limit where the aging time t a and the total measurement time t goes to infinity while the aging ratio t a t is kept constant we obtain a novel distributional limit theorem of time averaged observables integrable with respect to the infinite invariant density applying the theorem to the lyapunov exponent in intermittent maps we find that regular motions and a weakly chaotic behavior coexist in the aging limit this mixed type of dynamics is controlled by the aging ratio and hence is very different from the usual scenario of regular and chaotic motions in hamiltonian systems the probability of finding regular motions in non aged processes is zero while in the aging regime it is finite and it increases when system ages

the weibull log weibull transition of the interoccurrence time statistics in the two dimensional burridge knopoff earthquake model abstract in analyzing synthetic earthquake catalogs created by a two dimensional burridge knopoff model we have found that a probability distribution of the interoccurrence times the time intervals between successive events can be described clearly by the superposition of the weibull distribution and the log weibull distribution in addition the interoccurrence time statistics depend on frictional properties and stiffness of a fault and exhibit the weibull log weibull transition which states that the distribution function changes from the log weibull regime to the weibull regime when the threshold of magnitude is increased we reinforce a new insight into this model the model can be recognized as a mechanical model providing a framework of the weibull log weibull transition

nonextensivity and natural time the case of seismicity nonextensive statistical mechanics pioneered by tsallis has recently achieved a generalization of the gutenberg richter law for earthquakes this remarkable generalization is combined here with natural time analysis which enables the distinction of two origins of self similarity i e the process memory and the process increments infinite variance by using also detrended fluctuation analysis for the detection of long range temporal correlations we demonstrate the existence of both temporal and magnitude correlations in real seismic data of california and japan natural time analysis reveals that the nonextensivity parameter q in contrast to some published claims cannot be considered as a measure of temporal organization but the tsallis formulation does achieve a satisfactory description of real seismic data for japan for q 1 66 when supplemented by long range temporal correlations