We present studies for an individual based model of three interacting populations whose individuals are mobile in a two-dimensional lattice. We focus on the pattern formation in the spatial distributions of the populations. Also relevant is the relationship between pattern formation and features of the populations’ time series. Our model displays both traveling wave solutions, clustering and uniform distributions, both related to the parameter values. We also observed that the regeneration rate, the parameter associated to the primary level of trophic chain, the plant, regulated the presence of predators, as well as the type of spatial configuration. This result corroborates the theory that the enrichment of prey can stabilize the predator-prey dynamic in more realistic models.

The dynamics of fluctuations of a family of macroscopic quantities in one-dimensional systems (which includes the roughness and the total length of an interface, and the end-to-end distance of a filament) are analyzed. At thermodynamic equilibrium, the time-correlation function of these quantities can be expressed in terms of time-correlation functions of local quantities. In some cases, macroscopic quantities exhibit a universal diffusive behavior, which is not reached by local quantities.

We study the dynamics of parallel tempering simulations, also known as the replica exchange technique, which has become the method of choice for simulation of proteins and other complex systems. Recent results for the optimal choice of the control parameter discretization allow a treatment independent of the system in question. By analyzing mean first passage times across the control parameter space, we find an expression for the optimal number of replicas in simulations covering a given temperature range. Our results suggest a particular protocol to optimize the number of replicas in actual simulations.

The dynamics of a chemical pulse at the interface of excitable media having different diffusion properties is presented experimentally using the Belousov-Zhabotinsky reaction system. When a chemical pulse propagates from a larger diffusion region to a smaller diffusion region, it stops and forms a steady excitation band at the interface. Furthermore, a pulse train stimulated by this band appears subsequently. A simple one-dimensional model with discontinuous diffusion is proposed, and a numerical simulation is performed that shows good agreement with the experiment. Unidirectional pulse propagation across the interface is strongly suggested on the basis of the proposed model.

We investigate the growth of a pattern of liquid crests emerging in a layer of magnetic liquid when subjected to a magnetic field oriented normally to the fluid surface. After a steplike increase of the magnetic field, the temporal evolution of the pattern amplitude is measured by means of a Hall-sensor array. The extracted growth rate is compared with predictions from linear stability analysis by taking into account the proper nonlinear magnetization curve $M\left(H\right)$. The remaining discrepancy can be resolved by numerical calculations via the finite-element method. By starting with a finite surface perturbation, it can reproduce the temporal evolution of the pattern amplitude and the growth rate. The investigations are performed for two magnetic liquids, one with low and one with high viscosity.

We study the temperature-dependent structural behavior of self-avoiding walks (SAWs) on two-dimensional Sierpinski carpets as a simple model of polymers adsorbed on a disordered surface. Thereby, the Sierpinski carpet defines two types of sites with energy 0 and $ϵ>0$, respectively, yielding a deterministic fractal energy landscape. In the limiting cases of temperature $T\to 0$ and $T\to \infty$, the known behaviors of SAWs on Sierpinski carpets and on regular square lattices, respectively, are recovered. For finite temperatures, the structural behavior is found to be intermediate between the two limiting cases; the characteristic exponents, however, display a nontrivial dependence on temperature.

A model for the supercooled liquid is considered by taking into account its solidlike properties. We focus on how the long time dynamics is affected due to the coupling between the slowly decaying density fluctuations and the local displacement variables in the frozen liquid. Results from our model agree with the recent observation of Novikov and Sokolov [Nature (London) 431, 961 (2004)] that the fragility index $m$ of a glass forming material is linearly related to the corresponding ratio $K∕G$ of the bulk and the shear moduli.

In this paper, we address the question of whether aging in the nonequilibrium glassy state is controlled by the equilibrium $\alpha$-relaxation process, which occurs at temperatures above $T_g$. Recently, Lunkenheimer et al. [Phys. Rev. Lett. 95, 055702 (2005)] proposed a model for the glassy aging data of dielectric relaxation using a modified Kohlrausch-Williams-Watts form $\text{exp}\left[-{\left(t_{\text{age}}/{\tau }_{\text{age}}\right)}^{{\beta }_{\text{age}}}\right]$. The aging time $t_{\text{age}}$ dependence of the relaxation time ${\tau }_{\text{age}}$ is defined by these authors through a functional relation involving the corresponding frequency $\nu \left(t_{\text{age}}\right)=1/\left(2\pi {\tau }_{\text{age}}\right)$, but the stretching exponent ${\beta }_{\text{age}}$ is the same as ${\beta }_{\alpha }$, the $\alpha$-relaxation stretching exponent. We present here an alternative functional form for ${\tau }_{\text{age}}\left(t_{\text{age}}\right)$ directly involving the relaxation time itself. The proposed model fits the data of Lunkenheimer et al. perfectly with a stretching exponent ${\beta }_{\text{age}}$ different from ${\beta }_{\alpha }$.

We propose a method for approximating the adhesion parameters in the Shan and Chen multicomponent, multiphase lattice Boltzmann model that leads to the desired fluid-solid contact angle. The method is a straightforward application of Young’s equation with substitution of the Shan and Chen cohesion parameter and a density factor for the fluid-fluid interfacial tension, and the adhesion parameters for the corresponding fluid-solid interfacial tensions.

Liu et al. [Phys. Rev. E 74, 056302 (2006)] have presented a WKB analysis of the helical magnetorotational instability (HMRI), and claim that it does not exist for Keplerian rotation profiles. We show that, if radial boundary conditions are included, the HMRI can exist even for rotation profiles as flat as Keplerian, provided only that at least one of the boundaries is sufficiently conducting.

We study the quantum Jarzynski relation for driven quantum models embedded in various environments. We do so by generalizing a proof presented by Mukamel [Phys. Rev. Lett. 90, 170604 (2003)] for closed quantum systems. In this way, we are able to prove that the Jarzynski relation also holds for a bipartite system with microcanonical coupling. Furthermore, we show that, under the assumption that the interaction energy remains constant during the whole process, the relation is valid even for canonical coupling. The same follows for open quantum systems at high initial temperatures up to third order of the inverse temperature. Our analytical study is complemented by a numerical investigation of a special model system.

We demonstrate the effect of the depletion force in experiments and simulations of vertically vibrated mixtures of large and small steel spheres. The system exhibits size segregation and a large increase in the pair correlation function of the large spheres for short distances that can be accurately described using a combination of the depletion potential derived for equilibrium colloidal systems and a Boltzmann factor. The Boltzmann factor defines an effective temperature for the system, which we compare to other measures of temperature.

We present the measurements of the proton spin-lattice relaxation time $T_1$ of liquid crystal 4-$n$-octyl-$4^{\prime }$-cyanobiphenyl (8CB) confined into randomly oriented $\sim 15\mathrm{nm}$ pores of untreated porous glass. In the low kilohertz range the spin-lattice relaxation rate in the nanoconfined 8CB is about ten times larger than in the bulk. We show that the increase is mainly due to molecular reorientations mediated by translational displacements (RMTD). In the paranematic phase the power law describing the RMTD dispersion, ${\left(T_1^{-1}\right)}_{\mathit{RMTD}}\propto {\omega }^{-p}$, is well characterized by the exponent $p=0.5\pm 0.06$ and suggests an equipartition of diffusion modes with different wavelengths. The largest distance related to the decay of the orientational correlation function is about twice the diameter of the cavity. The situation is different in the nematic phase, where the orientational correlation is eventually lost at $\sim 60\mathrm{nm}$ in the direction along the pore, a distance corresponding roughly to the length of a pore segment in the glassy matrix. The exponent $p$ is between 0.65 and 0.9, depending on the temperature, which implies that in the nematic phase long wavelength modes are relatively more important—a consequence of the uniform director field along the pore. These observations are in agreement with the model of mutually independent pores with nematic director parallel to the pore axis in each segment. We point out that in strongly confined liquid crystals the proton NMR relaxometry does not provide the evidence of director fluctuations correlated over micrometer distances as was suggested earlier. The local translational diffusion of molecules within the cavities is found about as fast as in bulk.

We report on quantitative comparisons between simulation results of a bead-spring model and mode-coupling theory calculations for the structural and conformational dynamics of a supercooled, unentangled polymer melt. We find semiquantitative agreement between simulation and theory, except for processes that occur on intermediate length scales between the compressibility plateau and the amorphous halo of the static structure factor. Our results suggest that the onset of slow relaxation in a glass-forming melt can be described in terms of monomer caging supplemented by chain connectivity. Furthermore, a unified atomistic description of glassy arrest and of conformational fluctuations that (asymptotically) follow the Rouse model emerges from our theory.

We study a spatial cyclic predator-prey model with an even number of species (for $n=4$, 6, and 8) that allows the formation of two defensive alliances consisting of the even and odd label species. The species are distributed on the sites of a square lattice. The evolution of spatial distribution is governed by iteration of two elementary processes on neighboring sites chosen randomly: if the sites are occupied by a predator-prey pair then the predator invades the prey’s site; otherwise the species exchange their sites with a probability $X$. For low $X$ values, a self-organizing pattern is maintained by cyclic invasions. If $X$ exceeds a threshold value, then two types of domain grow up that are formed by the odd and even label species, respectively. Monte Carlo simulations indicate the blocking of this segregation process within a range of $X$ for $n=8$.

The electrophoretic transport of three chemically reacting species, two of which can bind reversibly to form the third, is analyzed mathematically. The species are assumed to move horizontally through a long channel with different electrophoretic mobilities and diffusion coefficients. By considering small perturbations of the system about equilibrium or when one of the two binding species is much more abundant than the other, the governing advection-reaction-diffusion equations can be linearized and studied via the method of moments. The result is a set of coupled ordinary differential equations for the moments that can be solved analytically. Analysis of the long-time evolution of the moments yields mean velocities and dispersion coefficients for each species. The results provide a method for measuring the rate and equilibrium constants of binding reactions using capillary electrophoresis.

Pattern formations in populations of “pulsating particles” which can autonomously vary their volumes were investigated. It was found that clusters of pulsating particles whose pulsation frequencies depend on the number of other particles in the vicinity form the following dynamical network structures: (i) void type networks exhibiting large voids, and (ii) branching type networks consisting of individual branches. Such global structures are formed through the annihilation and creation of local structures in the particle populations induced by tug-of-war-like interactions among them.

Interfacial dynamical blebbing of an oil droplet on an aqueous solution is reported. The oil droplet and the aqueous solution contain a fatty acid and a cationic surfactant, respectively. When the oil droplet was placed on an aqueous surface, the oil-water interface formed blebs, spherical extrusions on the oil-water interface and circular ones on the edge of the oil droplet. With increase of the concentration of the surfactant and/or the fatty acid, the generated blebs become smaller. Based on the experimental observations together with theoretical considerations, we conclude that the bleb formation is induced through generation and destruction of a gel-like intermediate phase.

We propose an approach for properly analyzing stochastic time series by mapping the dynamics of time series fluctuations onto a suitable nonequilibrium surface-growth problem. In this framework, the fluctuation sampling time interval plays the role of time variable, whereas the physical time is treated as the analog of spatial variable. In this way we found that the fluctuations of many real-world time series satisfy the analog of the Family-Viscek dynamic scaling ansatz. This finding permits us to use the powerful tools of kinetic roughening theory to classify, model, and forecast the fluctuations of real-world time series.