The nonlinear propagation of electromagnetic waves in pair plasmas, in which the electrostatic potential plays a very important but subdominant role of a “binding glue” is investigated. Several mechanisms for structure formation are investigated, in particular, the “asymmetry” in the initial temperatures of the constituent species. It is shown that the temperature asymmetry leads to a (localizing) nonlinearity that is qualitatively different from the ones originating in ambient mass or density difference. The temperature-asymmetry-driven focusing-defocusing nonlinearity supports stable localized wave structures in 1–3 dimensions, which, for certain parameters, may have flat-top shapes.

We apply a recently proposed criterion for the existence of phase transitions, which is based on the properties of the saddles of the energy landscape, to a simplified model of a system with gravitational interactions referred to as the self-gravitating ring model. We show analytically that the criterion correctly singles out the phase transition between a homogeneous and a clustered phase and also suggests the presence of another phase transition not previously known. On the basis of the properties of the energy landscape we conjecture on the nature of the latter transition.

We revisit the statistical mechanics problem of coarse-graining a system that at a detailed level is described by an already coarse-grained dynamics. The dynamics at the more detailed level is described by a Fokker-Planck equation instead of the Liouville equation. The method generalizes Zwanzig theory of projection operators and produces a friction matrix in terms of a correlation function that is not manifestly an autocorrelation. Therefore, from this expression, it is not obvious that the friction matrix is definite positive. We show that the Green-Kubo transport matrix can be written in the Einstein-Helfand form, which is manifestly positive definite. We also discuss the role of time reversal and detailed balance in the coarse-grained dynamics.

Nonequilibrium molecular dynamics simulations have been performed to estimate, analyze, and correlate the thermal conductivity of a fluid composed of short Lennard-Jones chains (up to 16 segments) over a large range of thermodynamic conditions. It is shown that the dilute gas contribution to the thermal conductivity decreases when the chain length increases for a given temperature. In dense states, simulation results indicate that the residual thermal conductivity of the monomer increases strongly with density, but is weakly dependent on the temperature. Compared to the monomer value, it has been noted that the residual thermal conductivity of the chain was slightly decreasing with its length. Using these results, an empirical relation, including a contribution due to the critical enhancement, is proposed to provide an accurate estimation of the thermal conductivity of the Lennard-Jones chain fluid model (up to 16 segments) over the domain $0.8\le T^{\ast }\le 6$ and $0\le {\rho }^{\ast }\le 1$. Additionally, it has been noted that all reduced thermal conductivity values of the Lennard-Jones chain fluid model merge on the same “universal” curve when plotted as a function of the excess entropy. Furthermore, it is shown that the reduced configurational thermal conductivity of the Lennard-Jones chain fluid model is approximately proportional to the reduced excess entropy for all fluid states and all chain lengths.

We analyze the models that account the ionic contribution to the complex dielectric constant of a nematic liquid crystal. We compare the predictions of the model of [Sawada et al., Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 318, 225 (1998)] based on the assumption that the electric field in the liquid coincides with the applied one, with the model of Macdonald where the electric field in the sample is determined in self-consistent manner by solving the equation of Poisson. We show that the model of Sawada et al., widely used to determine the bulk density of ions and their diffusion coefficient in liquid crystal cells, predicts a thickness dependence of the real and imaginary parts of the dielectric constant different from that predicted by the model of Macdonald. On the contrary, the predictions of the two models coincide for what concerns the frequency dependencies of the two components of the dielectric constant. By considering a typical case, we show that the numerical values of the ionic properties derived by means of the model of Sawada et al. may differ even more than 1 order of magnitude by those predicted by the model of Macdonald. A rescaling procedure allowing to evaluate the bulk density of ions and the ionic diffusion coefficient determined by means of the model of Sawada et al. in agreement with the one of Macdonald is proposed.

The validity of the Stokes-Einstein (SE) relation for particle diffusion in the nano- and molecular scales has attracted much interest, but the results in the literature are controversial. In this work, it is shown that there exists a critical particle size where the SE relation breaks down by comparing particle transport in the macro- and molecular scales. Using molecular-dynamics simulations, we study the critical size and find that the van der Waals force plays an important role in particle diffusion as the particle size approaches molecular scale. Due to the limitations of computing facilities, we could not find exactly where the critical particle size is, but the simulation results qualitatively predict that this critical size is of a few nanometers.

The dynamics of loop formation by linear polymer chains has been a topic of several theoretical and experimental studies. Formation of loops and their opening are key processes in many important biological processes. Loop formation in flexible chains has been extensively studied by many groups. However, in the more realistic case of semiflexible polymers, not much results are available. In a recent study [K. P. Santo and K. L. Sebastian, Phys. Rev. E 73, 031923 (2006)], we investigated opening dynamics of semiflexible loops in the short chain limit and presented results for opening rates as a function of the length of the chain. We presented an approximate model for a semiflexible polymer in the rod limit based on a semiclassical expansion of the bending energy of the chain. The model provided an easy way to describe the dynamics. In this paper, using this model, we investigate the reverse process, i.e., the loop formation dynamics of a semiflexible polymer chain by describing the process as a diffusion-controlled reaction. We make use of the “closure approximation” of Wilemski and Fixman [G. Wilemski and M. Fixman, J. Chem. Phys. 60, 878 (1974)], in which a sink function is used to represent the reaction. We perform a detailed multidimensional analysis of the problem and calculate closing times for a semiflexible chain. We show that for short chains, the loop formation time $\tau$ decreases with the contour length of the polymer. But for longer chains, it increases with length obeying a power law and so it has a minimum at an intermediate length. In terms of dimensionless variables, the closing time is found to be given by $\tau \sim L^n\text{exp}\left(\text{const}/L\right)$, where $n=4.5–6$. The minimum loop formation time occurs at a length $L_m$ of about 2.2–2.4. These are, indeed, the results that are physically expected, but a multidimensional analysis leading to these results does not seem to exist in the literature so far.

Molecular-dynamics simulations of a normal DNA duplex show that breathing events typically occur on the microsecond time scale. This paper analyzes a 12 base pairs DNA duplex containing the “rogue” base difluorotoluene (F) in place of a thymine base (T), for which the breathing events occur on the nanosecond time scale. Starting from a nonlinear Klein-Gordon lattice model and adding noise and damping, we obtain a mesoscopic model of the DNA duplex close to that observed in experiments and all-atom molecular dynamics simulations. The mesoscopic model is calibrated to data from the all-atom molecular dynamics package AMBER for a variety of twist angles of the DNA duplex. Defects are considered in the interchain interactions as well as in the along-chain interactions. This paper also discusses the role of the fluctuation-dissipation relations in the derivation of reduced (mesoscopic) models, the differences between the potential of mean force and the potential energies used in Klein-Gordon lattices, and how breathing can be viewed as competition between the along-chain elastic energy and the interchain binding energy.

Stock prices are known to exhibit non-Gaussian dynamics, and there is much interest in understanding the origin of this behavior. Here, we present a model that explains the shape and scaling of the distribution of intraday stock price fluctuations (called intraday returns) and verify the model using a large database for several stocks traded on the London Stock Exchange. We provide evidence that the return distribution for these stocks is non-Gaussian and similar in shape and that the distribution appears stable over intraday time scales. We explain these results by assuming the volatility of returns is constant intraday but varies over longer periods such that its inverse square follows a gamma distribution. This produces returns that are Student distributed for intraday time scales. The predicted results show excellent agreement with the data for all stocks in our study and over all regions of the return distribution.

We investigate the behavior of localized spots in three spatial dimensions in a model two-variable system describing the Belousov-Zhabotinsky reaction in water-in-oil microemulsion. We find three types of instabilities: splitting of a single spot (i) into two spots, (ii) into a torus, and (iii) into an unstable shell that splits almost immediately to six or eight new spots.

A transition between Kelvin’s equilibrium states is investigated. Using nonlinear theory, we have shown that the transition of polygonal patterns of the hollow vortex core from mode $N=2$ through $N=4$ occurs in two steps: quasiperiodicity and frequency locking. We have also shown that this transition can be modeled by a one-dimensional circle map. We extrapolate the present result and hypothesize that the transition between Kelvin’s equilibria follows the same route and the ratios of locking frequencies form a Farey sum and staircase function against the control parameter, where the staircase corresponds to the rational frequency ratio, $\left(N-1\right)/N$.

The initial stage of interface instability upon radial displacement of a fluid in a Hele-Shaw cell is investigated. An air-silicone oil system is analyzed. The critical radii of stability relative to long-wave perturbations are determined. It is found that, in the investigated range of parameters, instability most often begins by a translational mechanism. It is ascertained that in the overwhelming majority of cases the critical radii of instability are smaller than the values predicted by the linear stability theory and external effects make this difference even greater. The obtained results are discussed and compared with the existing theories.

Flow around two circular cylinders in a side-by-side arrangement normal to the free stream with heat release from one of the cylinders is studied experimentally. This flow, with no heat release, is known to exhibit a range of flow regimes at different cylinder spacings. In particular, the wake exhibits well-known intermittently bistable behavior in the center-to-center spacing (normalized by cylinder diameter) range of 1.2–2.0. We present, for the first time, the effect of heat release from one of the cylinders on the near-wake structure of the two cylinder configuration. The experiments are performed at spacing ratios of 1.1, 1.7, and 3.0, Reynolds numbers of 250, 350, and 450 and Richardson number less than 0.14. The investigations are carried out in a water tunnel using hydrogen bubble technique for flow visualization and particle-image-velocimetry for quantitative measurements. The bistability of the wake at a spacing ratio of 1.7 is controlled with a threshold heat release from one of the cylinders resulting in a stable narrow wake behind the heated cylinder and a wider wake behind the unheated cylinder. The heat release resulted in deflection of the gap-bleeding flow toward the heated cylinder at spacing ratio of $S/D=1.1$ and did not produce any visual changes in the near-wake structure at spacing ratio of 3.0.

We consider a higher-order complex Ginzburg-Landau equation, with the fourth-order dispersion and cubic-quintic nonlinear terms, which can describe the propagation of an ultrashort subpicosecond or femtosecond optical pulse in an optical fiber system. We investigate the modulational instability (MI) of continuous wave solution of this equation. Several types of modulational instability gains are shown to exist in both the anomalous and normal dispersion regimes. We find that depending on the sign of the fourth-order dispersion coefficient, the MI appears for normal and anomalous dispersion regime. Simulations of the full system demonstrate that the development of the MI leads to establishment of a regular or chaotic array of pulses, a chain of well-separated peaks with continuously growing or decaying amplitudes depending on the sign of the loss/gain coefficient and higher-order dispersions terms. Comparison of the calculations with reported numerical results shows a satisfactory agreement.

We present an approach to investigate the long-time stochastic dynamics of multidimensional classical systems, in contact with a heat bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short- and long-time scales and both molecular dynamics or Monte Carlo (MC) simulations are generally inefficient. Using a field theoretic approach, we perform analytically the average over the short-time stochastic fluctuations. This way, we obtain an effective theory, which generates the same long-time dynamics of the original theory, but has a lower time-resolution power. Such an approach is used to develop an improved version of the MC algorithm, which is particularly suitable to investigate the dynamics of rare conformational transitions. In the specific case of molecular systems at room temperature, we show that elementary integration time steps used to simulate the effective theory can be chosen a factor $\sim 100$ larger than those used in the original theory. Our results are illustrated and tested on a simple system, characterized by a rugged energy landscape.

In this paper, we present a systematic approach for characterization and reconstruction of statistically optimal representative unit cells of polydisperse particulate composites. Microtomography is used to gather rich three-dimensional data of a packed glass bead system. First-, second-, and third-order probability functions are used to characterize the morphology of the material, and the parallel augmented simulated annealing algorithm is employed for reconstruction of the statistically equivalent medium. Both the fully resolved probability spectrum and the geometrically exact particle shapes are considered in this study, rendering the optimization problem multidimensional with a highly complex objective function. A ten-phase particulate composite composed of packed glass beads in a cylindrical specimen is investigated, and a unit cell is reconstructed on massively parallel computers. Further, rigorous error analysis of the statistical descriptors (probability functions) is presented and a detailed comparison between statistics of the voxel-derived pack and the representative cell is made.

The segregation of granular mixtures in rotating cylinders into axial bands is not well understood so far. Abnormal diffusion of the grains has been proposed to play an important role in that process. We measure axial diffusion in binary mixtures, completely embedded in water, by means of nuclear magnetic imaging (magnetic resonance imaging). It is found that the small size particles in a radially segregated structure undergo normal (Fickian) axial diffusion, whereas an initial pulse of the large species shows subdiffusive behavior. An interpretation within a model for the particle dynamics is given. The diffusion of small particles occurs in the axial kernel, whereas particles of the large species migrate on the free surface of the granular bed.

The mechanism of wound closure in epithelial tissues, i.e., cell monolayer sheets, is investigated through computer simulations. A wound means an area in which some cells have been removed from the normal tissue. The vertex dynamics cell model [T. Nagai and H. Honda, Philos. Mag. B 81, 699 (2001)], which describes morphogenesis of epithelial tissues using the concepts of statistical physics, is modified and applied to the closure of small wounds without mitosis. It is shown that cell–basal-lamina adhesion governs the wound closure competing with cell-cell adhesion and cell elasticity. The simulation results reproduce the actual wound closure process qualitatively and partly quantitatively. The closing proceeds with the translation of the edges of wound polygons toward the wound center and the intermittent reduction in the number of polygon edges. Over time, the process leads to an exponential decrease in the wound area. A shape factor is introduced to describe the wound shape quantitatively and is used to examine the time variation thereof. A method for determining model parameters by comparison with the experiments is given.

The protein-DNA interaction dynamics is studied by modeling the DNA bases as classical spins in a coupled spin system, which are bosonized and coupled to thermal phonons and longitudinal motion of the protein molecule in the nonviscous limit. The nonlinear dynamics of this protein-DNA complex molecular system is governed by the completely integrable nonlinear Schrödinger (NLS) equation which admits $N$-soliton solutions. The soliton excitations of the DNA bases in the two strands make localized base-pair opening and travel along the DNA chain in the form of a bubble. This may characterize the bubble generated during the transcription process, when an RNA polymerase binds to a promoter site in the DNA double helical chain. When the protein-DNA molecular system interacts with the surrounding viscous solvating water medium, the dynamics is governed by a perturbed NLS equation. This equation is solved using a multiple scale perturbation analysis, by treating the viscous effect as a weak perturbation, and the results show that the viscosity of the solvent medium damps out the soliton as time progresses.