Conditional Granger causality of diffusion processes

The statistical concept of Granger causality is defined by prediction improvement, i.e. the causing time series contains unique information about the future of the caused one. Recently we proposed extending this concept to bivariate diffusion processes by defining Granger causality for each point of the state space as the Granger causality of a process obtained by local linearisation. This provides a Granger causality map, well-defined at least in the vicinity of stable fixed points of the deterministic part of the dynamics. This extension has convenient properties, but carries several important limitations. In the current paper we show how the Granger causality of diffusion processes can be further generalized, incorporating in particular the concept of conditional causality. Moreover, we demonstrate the application potential to systems with a more complex attractor structure such as limit cycles or bistability of fixed points.     

No-go theorem for k-essence dark energy

We demonstrate that if k-essence can solve the coincidence problem and play the role of dark energy in the Universe, the fluctuations of the field have to propagate superluminally at some stage. We argue that this implies that successful k-essence models violate causality. It is not possible to define a time ordered succession of events in a Lorentz invariant way. Therefore, k-essence cannot arise as a low energy effective field theory of a causal, consistent high energy theory.     

Dynamic behavior of temperature field in a buoyancy-driven turbulent fire

We study the dynamic behavior of temperature field in a buoyancy-driven turbulent fire from the viewpoints of symbolic dynamics, complex networks, and statistical complexity. The permutation entropy and the horizontal visibility network entropy allow us to capture the subtle changes in temperature fluctuations. The possible existence of deterministic chaos in temperature fluctuations, as well as in streamwise flow velocity fluctuations [Takagi et al., Phys. Rev. E 96 (2017) 052223], is clearly verified using the multiscale complexity-entropy causality plane.     

Behavior of general one-dimensional diffusion processes

We develop simple rigorous techniques to estimate the behavior of general one-dimensional diffusion processes. Any one-dimensional diffusion process (with drift) can be mapped onto a symmetric diffusion through an explicit change of variable. For such processes we can estimate explicitly the diffusion exponent, the recurrence properties, and the large fluctuations. In a second part, we apply these results to different models (including the Sinaï random walk: diffusion in a random drift) and we show how the main features of the diffusion can be readily handled.     

Finite correlation time effects in nonequilibrium phase transitions: I. Dynamic equation and steady state properties

We determine an approximate renormalized equation of evolution for an arbitrary nonlinear single-degree-of-freedom system externally driven by Gaussian parametric fluctuations of finite correlation time. The renormalization scheme used here gives a second order equation with a time-and-state-dependent “diffusion coefficient”. We are able to calculate the diffusion coefficient in closed form. The steady-state distribution can easily be obtained from the evolution equation. We are thus able to determine the parameter dependence of the steady-state distribution and, in particular, the influence of a correlation time of the fluctuations, which does not vanish, on the steady-state distribution.     

Self-propelled particles with fluctuating speed and direction of motion in two dimensions

We study general aspects of active motion with fluctuations in the speed and the direction of motion in two dimensions. We consider the case in which fluctuations in the speed are not correlated to fluctuations in the direction of motion, and assume that both processes can be described by independent characteristic time scales. We show the occurrence of a complex transient that can exhibit a series of alternating regimes of motion, for two different angular dynamics which correspond to persistent and directed random walks. We also show additive corrections to the diffusion coefficient. The characteristic time scales are also exposed in the velocity autocorrelation, which is a sum of exponential forms.     

Universal behavior of nonequilibrium fluctuations in free diffusion processes

We show that giant nonequilibrium fluctuations are present during the free diffusive remixing occurring in ordinary liquid mixtures and in macromolecular solutions. The static structure factor of the fluctuations is measured by using a quantitative shadowgraph technique. We show that structure factors at different times and from different samples can be rescaled onto a single master curve without any adjustable parameter, thus giving strong evidence that nonequilibrium fluctuations are a universal feature of free diffusion processes.     

Description of critical fluctuations of a diffusion process by means of the most probable path

We show that the most probable oscillating paths of a diffusion process can be taken as representatives for critical fluctuations.     

Effect of diffusion and fluctuations in the nonequilibrium charge carrier density on the angular distribution of the output intensity for injection lasers based on an InAsSb/InAsSbP heterostructure

We have used numerical modeling to study the effect of diffusion and fluctuations in the nonequilibrium carrier density in the active layer of injection lasers based on an InAsSb/InAsSbP heterostructure on the angular distribution of the output intensity. We show that diffusion smoothes out the nonequilibrium carrier distribution in the active layer, and the fundamental lasing mode is stable over a much broader range of stripe contact widths. At the same time, diffusional processes can lead to formation of local regions with a jump in the density of nonequilibrium charge carriers, fluctuations in which can act as a source of instability for the fundamental lasing mode. Analysis of the numerical modeling results gives qualitative agreement with experimental data on the dependence of the angular distribution of the output radiation for different stripe contact widths.     

On the kinetic theory of Brownian motion

The influence of fluctuations on the kinetic processes of Brownian motion is investigated. We consider fluctuations for which the correlation time is comparable with the relaxation time of the distribution function. Taking such large scale fluctuations into account is shown to lead to a change of the diffusion coefficient and to the appearance of additional correlations in the motions of Brownian particles. An expression is obtained for the correlation function of a Langevin source in the diffusion equation taking into account the contribution of large scale fluctuations.     

Investigating directed cortical interactions in time-resolved fMRI data using vector autoregressive modeling and Granger causality mapping

We present a framework aimed to reveal directed interactions of activated brain areas using time-resolved fMRI and vector autoregressive (VAR) modeling in the context of Granger causality. After describing the underlying mathematical concepts, we present simulations helping to characterize the conditions under which VAR modeling and Granger causality can reveal directed interactions from fluctuations in BOLD-like signal time courses. We apply the proposed approach to a dynamic sensorimotor mapping paradigm. In an event-related fMRI experiment, subjects performed a visuomotor mapping task for which the mapping of two stimuli (“faces” vs “houses”) to two responses (“left” or “right”) alternated periodically between the two possible mappings. Besides expected activity in sensory and motor areas, a fronto-parietal network was found to be active during presentation of a cue indicating a change in the stimulus-response (S-R) mapping. The observed network includes the superior parietal lobule and premotor areas. These areas might be involved in setting up and maintaining stimulus-response associations. The Granger causality analysis revealed a directed influence exerted by the left lateral prefrontal cortex and premotor areas on the left posterior parietal cortex.     

Nuclear spin dynamics in the quantum regime of a single-molecule magnet

We show that the nuclear spin dynamics in the single-molecule magnet Mn12-ac below 1 K is governed by quantum tunneling fluctuations of the cluster spins, combined with intercluster nuclear spin diffusion. We also obtain the first experimental proof that-surprisingly-even deep in the quantum regime the nuclear spins remain in good thermal contact with the lattice phonons. We propose a simple model for how T-independent tunneling fluctuations can relax the nuclear polarization to the lattice that may serve as a framework for more sophisticated theories.     

Phase separation in binary systems with competing internal and external multiplicative noises

We have considered phase separation processes in binary stochastic systems with thermal diffusion and ballistic mixing representing irradiation influence. Introducing fluctuations of thermal flux and an external source of atom relocations due to ballistic diffusion into dynamics of a globally conserved field, we have shown that there are two competing mechanisms of phase transitions type of “order-disorder”: thermally assisted diffusion and irradiation induced atomic exchange. We have studied dynamics of the structure function at early stages of decomposition. In the framework of the mean field theory we have derived the effective Fokker-Planck equation to describe phase separation processes. It was shown that the ordering processes can be controlled by both regular and stochastic parts of external source influence. A reentrant behavior of a mean field order parameter versus the external noise intensity and fluctuations correlation radius is found.     

Sunlight scattering intensity fluctuations from asymmetric particles

We propose to use the sun as a bright incoherent light source to probe the rotational diffusion of asymmetric particles. Lateral (spatial) coherence of the sun can be adjusted by proper optics to be shorter than the interparticle distance. In contrast to laser light scattering, where translational diffusion contribution dominates the scattering fluctuations, this method may probe directly into the time course of particles rotation and internal motion.     

Spinodal decomposition in Monte Carlo simulations of a binary alloy

Recently Cahn's generalized diffusion equation theory of spinodal decomposition in binary alloys has been modified to include the effects of thermal fluctuations. This paper reports studies of a one-dimensional binary alloy system in which fluctuations can be observed on an atomic time scale. The system, a computer-simulated linear chain binary alloy which evolves from an initially random atomic arrangement through interchange of unlike nearest neighbors via the Monte Carlo technique, rapidly develops grains of two different concentrations and then slowly experiences coarsening. A numerical solution of the diffusion equation successfully predicts the development of grain structure, but only predicts coarsening to the extent present as fluctuations in the initial atomic arrangement. The simulated alloy coarsens further than the prediction of the diffusion equation because of thermal fluctuations which develop naturally during its evolution. This suggests that thermal fluctuations may play an important role in coarsening in real alloys.     

Steady state statistics of driven diffusions

We consider overdamped diffusion processes driven out of thermal equilibrium and we analyze their dynamical steady fluctuations. We discuss the thermodynamic interpretation of the joint fluctuations of occupation times and currents; they incorporate respectively the time-symmetric and the time-antisymmetric sector of the fluctuations. We highlight the canonical structure of the joint fluctuations. The novel concept of traffic complements the entropy production for the study of the occupation statistics. We explain how the occupation and current fluctuations get mutually coupled out of equilibrium. Their decoupling close-to-equilibrium explains the validity of entropy production principles.     

Quantum-Gravitational Diffusion and Stochastic Fluctuations in the Velocity of Light

We argue that quantum-gravitational fluctuations in the space-time background give the vacuum non-trivial optical properties that include diffusion and consequent uncertainties in the arrival times of photons, causing stochastic fluctuations in the velocity of light in vacuo. Our proposal is motivated within a Liouville string formulation of quantum gravity that also suggests a frequency-dependent refractive index of the particle vacuum. We construct an explicit realization by treating photon propagation through quantum excitations of D-brane fluctuations in the space-time foam. These are described by higher-genus string effects, that lead to stochastic fluctuations in couplings, and hence in the velocity of light. We discuss the possibilities of constraining or measuring photon diffusion in vacuo via -ray observations of distant astrophysical sources.     

Analysis of price fluctuations in futures exchange markets

We show that the fluctuations of the tick-by-tick logarithmic price in a futures market can be described in terms of the Fokker-Planck equation (FPE). We calculate the corresponding drift and diffusion coefficients and argue that these values can contain some information pertaining to the market state. It is particularly showed that the Korean treasury bond (KTB) futures is well described by a FPE and has a similar structure to turbulence.     

The super long-time decay of velocity fluctuations in a two-dimensional fluid

We have calculated the velocity autocorrelation function for a tracer particle in a model two-dimensional fluid. The fluid was represented by a lattice Boltzmann equation with imposed fluctuations. By choosing a low Boltzmann diffusion coefficient for the tracer, the diverging contribution to the diffusion coefficient can be made to exceed the Boltzmann value even at short times. We were thus able to find evidence for the renormalized, or ‘super long-time’, decay of the VACF in a two-dimensional fluid. We find quantitative evidence for the 1/t√ln(t) decay predicted by theory.     

研究随机有势场中扩散行为标度律的一种自洽方法

本文介绍了一种研究随机有势场中扩散问题标度律的自洽方法 ,并综述性介绍了该方法在计算聚合物的Flory指数、研究随机介质中无规行走在长时间下的渐近行为、研究均匀各向同性湍流场中粒子的相对扩散、研究Kuramoto Sivashinsky方程的奇异扩散行为以及研究微乳浊液中热脉动对化学反应的影响等方面的应用