Derivation of the Langevin Equation from the Microcanonical Ensemble.

When writing down a Langevin equation for the time evolution of a "system" in contact with a thermal bath, one typically makes the implicit (and often tacit) assumption that the thermal environment is in equilibrium at all times. Here, we take this assumption as a starting point to formulate the problem of a system evolving in contact with a thermal bath from the perspective of the bath, which, since it is in equilibrium, can be described by the microcanonical ensemble. We show that the microcanonical ensemble of the bath, together with the Hamiltonian equations of motion for all the constituents of the bath and system together, give rise to a Langevin equation for the system evolution alone. The friction coefficient turns out to be given in terms of auto-correlation functions of the interaction forces between the bath particles and the system, and the Einstein relation is recovered. Moreover, the connection to the Fokker-Planck equation is established.

Evolution of dietary diversity and a starvation driven cross-diffusion system as its singular limit.

We rigorously prove the passage from a Lotka-Volterra reaction-diffusion system towards a cross-diffusion system at the fast reaction limit. The system models a competition of two species, where one species has a more diverse diet than the other. The resulting limit gives a cross-diffusion system of a starvation driven type. We investigate the linear stability of homogeneous equilibria of those systems and rule out the possibility of cross-diffusion induced instability (Turing instability). Numerical simulations are included which are compatible with the theoretical results.

On the interplay of harvesting and various diffusion strategies for spatially heterogeneous populations.

The paper explores the influence of harvesting (or culling) on the outcome of the competition of two species in a spatially heterogeneous environment. The harvesting effort is assumed to be proportional to the space-dependent intrinsic growth rate. The differences between the two populations are the diffusion strategy and the harvesting intensity. In the absence of harvesting, competing populations may either coexist, or one of them may bring the other to extinction. If the latter is the case, introduction of any level of harvesting to the successful species guarantees survival to its non-harvested competitor. In the former case, there is a strip of "close enough" to each other harvesting rates leading to preservation of the original coexistence. Some estimates are obtained for the relation of the harvesting levels providing either coexistence or competitive exclusion.

Intraguild predation with evolutionary dispersal in a spatially heterogeneous environment.

In many cases, the motility of species in a certain region can depend on the conditions of the local habitat, such as the availability of food and other resources for survival. For example, if resources are insufficient, the motility rate of a species is high, as they move in search of food. In this paper, we present intraguild predation (IGP) models with a nonuniform random dispersal, called starvation-driven diffusion, which is affected by the local conditions of habitats in heterogeneous environments. We consider a Lotka-Volterra-type model incorporating such dispersals, to understand how a nonuniform random dispersal affects the fitness of each species in a heterogeneous region. Our conclusion is that a nonuniform dispersal increases the fitness of species in a spatially heterogeneous environment. The results are obtained through an eigenvalue analysis of the semi-trivial steady state solutions for the linearized operator derived from the model with nonuniform random diffusion on IGPrey and IGPredator, respectively. Finally, a simulation and its biological interpretations are presented based on our results.

Fibonacci family of dynamical universality classes.

Universality is a well-established central concept of equilibrium physics. However, in systems far away from equilibrium, a deeper understanding of its underlying principles is still lacking. Up to now, a few classes have been identified. Besides the diffusive universality class with dynamical exponent [Formula: see text], another prominent example is the superdiffusive Kardar-Parisi-Zhang (KPZ) class with [Formula: see text]. It appears, e.g., in low-dimensional dynamical phenomena far from thermal equilibrium that exhibit some conservation law. Here we show that both classes are only part of an infinite discrete family of nonequilibrium universality classes. Remarkably, their dynamical exponents [Formula: see text] are given by ratios of neighboring Fibonacci numbers, starting with either [Formula: see text] (if a KPZ mode exist) or [Formula: see text] (if a diffusive mode is present). If neither a diffusive nor a KPZ mode is present, all dynamical modes have the Golden Mean [Formula: see text] as dynamical exponent. The universal scaling functions of these Fibonacci modes are asymmetric Lévy distributions that are completely fixed by the macroscopic current density relation and compressibility matrix of the system and hence accessible to experimental measurement.

Evolution of Dispersal with Starvation Measure and Coexistence.

Many biological species increase their dispersal rate if starvation starts. To model such a behavior, we need to understand how organisms measure starvation and response to it. In this paper, we compare three different ways of measuring starvation by applying them to starvation-driven diffusion. The evolutional selection and coexistence of such starvation measures are studied within the context of Lotka-Volterra-type competition model of two species. We will see that, if species have different starvation measures and different motility functions, both the coexistence and selection are possible.

Nondimensional analysis and application of gas desorption and diffusion driven by density gradient in coal particles.

An in-depth understanding of gas diffusion characteristics in coal is of great value to coalbed methane (CBM) production planning and coal mine safety management. However, the mechanism and model of gas diffusion is still unclear, and some methods for determining diffusion coefficients are not accurate enough. Accordingly, a free gas density gradient (FGDG)-driven coal particle gas desorption and diffusion model was established in this work, and numerical solutions were performed via finite difference method (FDM) and dimensionless method. The variation rules of dimensionless gas pressure, gas content, desorption capacity, and desorption rate were obtained. Finally, the application of the dimensionless method in diffusion modeling and diffusion coefficient inversion was discussed. The results show that the dimensionless method can simplify mathematical equation processing and analyze the common phenomena of desorption and diffusion under different parameters. The gas desorption diffusion in coal particles is from the surface to the inside, and there is obvious desorption hysteresis effect. The larger the dimensionless radius or dimensionless time, the smaller the dimensionless gas pressure, gas content, and dimensionless desorption rate. The dimensionless cumulative gas desorption amount increased rapidly first and then tended to flat with dimensionless time. The simulated curve can be easily converted into the variation curves of several different measured parameters, and the diffusion coefficient can be calculated accurately. The prediction curve of the FGDG diffusion model is in good agreement with the experimentally measured data, which verifies its reasonableness. The research content aims to provide some ideas for modeling gas desorption and diffusion behavior.

Holographic Grating Enhancement Induced by a Dual-Photo-Initiator System in PMMA Substrate Polymers.

Polymer systems induced by the reaction between monomers and photo-initiators play a crucial role in the formation of volume-phase gratings. In this paper, we fabricated a dual-photo-initiator photopolymer by doping EY (Eosin Yellow) molecules into a TI (Titanocene, Irgacure 784@BASF) dispersed PMMA (poly-[methyl methacrylate]) substrate system, with the aim of promoting the diffusion and polymerization processes in volume holographic storage. The two-wave interference system is adopted to record a permanent grating structure in our materials. The temporal diffraction variations of photopolymerization (during the interference exposure) and dark diffusion (after the interference exposure) processes have been investigated and analyzed. Aiming to analyze the influence of EY doping ratios on holographic performances, some key parameters were examined in the experiment. We first measured the temporal evolution of diffraction efficiency, then an exponential fitting was adopted to obtain the response time. Finally, the angular selectivity was evaluated by the Bragg condition after holographic recording. Also, the temporal evolution of each component is described by the nonlocal polymerization-driven diffusion model with a dual-photo-initiator composition, theoretically. Furthermore, we experimentally achieved the holographic grating enhancement in both the dark diffusion and photopolymerization processes by doping appropriate EY concentrations, respectively. This work provides a foundation for the acceptability of TI&EY/PMMA polymers in further holographic storage research.

Fast Von Mises strain imaging on ultrasound carotid vessel wall by flow driven diffusion method.

The elasticity of the vessel wall is important for the clinical identification of rupture-risks. The Von Mises strain can be a potential index for the indication of carotid vessel pathologies. In this paper, a fast clinically applicable real-time algorithm from time-sequence of B-mode carotid images is developed. Due to the compression induced by the normal cardiac pulsation, tissue motion occurs radially and non-rigidly. To obtain an accurate motion field, we developed a variational functional integrating the optical flow equation and an anisotropic regularizer, and designed a diffusion tensor to encourage coherence diffusion. The motion field is smoothed along the desired motion flow orientation. A fast, additive operator splitting scheme, which is ten times faster than the conventional discrete method, is used for the numerical implementation. To demonstrate the efficiency of the proposed approach, finite element models are set up for normal and pathological carotid vessel walls. The results indicate that the proposed diffusion approach obtains an accurate smooth and continuous motion field and greatly improves the follow up strain estimation using a fast differential strain filter. Furthermore, our approach using the Von Mises strain imaging on clinical ultrasound images of the carotid artery is validated. Participants above 65-years in age suffering from different stages of atherosclerosis in their carotid artery are selected. The results are evaluated by an experienced physician. The evaluation results demonstrate that the Von Mises strain has a good correspondence to the presence of certain suspicious areas in the B-mode images. The proposed method is therefore clinically applicable for the real-time Von Mises strain imaging of carotid vessel walls, and can be of great value as a complementary method to B-mode image for the clinical identification of the risk of plaque vulnerability.

Competitive spatially distributed population dynamics models: Does diversity in diffusion strategies promote coexistence?

We study the interaction between different types of dispersal, intrinsic growth rates and carrying capacities of two competing species in a heterogeneous environment: one of them is subject to a regular diffusion while the other moves in the direction of most per capita available resources. If spatially heterogeneous carrying capacities coincide, and intrinsic growth rates are proportional then competitive exclusion of a regularly diffusing population is inevitable. However, the situation may change if intrinsic growth rates for the two populations have different spatial forms. We also consider the case when carrying capacities are different. If the carrying capacity of a regularly diffusing population is higher than for the other species, the two populations may coexist; as the difference between the two carrying capacities grows, competitive exclusion of the species with a lower carrying capacity occurs.