Simple expressions are presented for the equations of state of a correlated electrolyte solution, calculated straightforwardly within a full nonlinear Debye-Hückel approach in terms of the mean potential at contact, that predict quantitatively different phase behavior from the popular Debye-Hückel limiting law. The theory includes pair correlations accurately and may provide a basis for a quantitative theoretical study of organic or multivalent ionic solutions. As an example, cohesive effects are addressed of strong couplings between ions on the effective interactions between nanoparticles.

Motivated by recent experimental progress to readout quantum bits implemented in superconducting circuits via the phenomenon of dynamical bifurcation, transitions between steady orbits in a driven anharmonic oscillator, the Duffing oscillator, are analyzed. In the regime of weak dissipation a consistent diffusion equation in the semiclassical limit is derived to capture the intimate relation between finite tunneling and reflection and bath induced quantum fluctuations. From the corresponding steady-state distribution an analytical expression for the switching probability is obtained. It is shown that a reduction of the transition rate due to finite reflection at the phase-space barrier is overcompensated by an increase due to environmental quantum fluctuations that are specific for diffusion processes over dynamical barriers. The scaling behavior of the rate is discussed and it is revealed that close to the bifurcation threshold the escape dynamics enters an overdamped domain such that the quantum-mechanical energy scale associated with friction even exceeds the thermal energy scale.

We present a molecular-dynamics study of discharges in a granular pile evincing a catastrophic regime depending on the outlet size. The avalanche size distribution function suggests a phase transition where the height of the remaining pile is taken as the order parameter. Our results indicate that there is a critical outlet size beyond which discharges become catastrophic and the initial pile is split in two minor piles. As the system size increases, finite-size analysis indicates that the critical orifice width converges to a finite value.

The diffusion of fractal aggregates constructed with the method by Thouy and Jullien [J. Phys. A 27, 2953 (1994)] comprised of $N_p$ spherical primary particles was studied as a function of the aggregate mass and fractal dimension using molecular dynamics simulations. It is shown that finite-size effects have a strong impact on the apparent value of the diffusion coefficient $\left(D\right)$, but these can be corrected by carrying out simulations using different simulation box sizes. Specifically, the diffusion coefficient is inversely proportional to the length of a cubic simulation box, and the constant of proportionality appears to be independent of the aggregate mass and fractal dimension. Using this result, it is possible to compute infinite dilution diffusion coefficients $\left(D_o\right)$ for aggregates of arbitrary size and fractal dimension, and it was found that $D_o\propto N_p^{-1/d_f}$, as is often assumed by investigators simulating Brownian aggregation of fractal aggregates. The ratio of hydrodynamic radius to radius of gyration is computed and shown to be independent of mass for aggregates of fixed fractal dimension, thus enabling an estimate of the diffusion coefficient for a fractal aggregate based on its radius of gyration.

In this paper, we investigate the non-Markovian dynamics of a model to mimic the excitation energy transfer (EET) between chromophores in photosynthesis systems. The numerical path integral method is used. This method includes the non-Markovian effects of the environmental affects, and it does not need the perturbation approximation in solving the dynamics of systems of interest. It implies that the coherence helps the EET between chromophores through lasting the transfer time rather than enhancing the transfer rate of the EET. In particular, the non-Markovian environment greatly increases the efficiency of the EET in the photosynthesis systems.

Based on a fiber bundle model we substantially extend the phase-transition analogy of thermally activated breakdown of homogeneous materials. We show that the competition of breaking due to stress enhancement and due to thermal fluctuations leads to an astonishing complexity of the phase space of the system: varying the load and the temperature a phase boundary emerges, separating a Griffith-type regime of abrupt failure analogous to first-order phase transitions from disorder dominated fracture where a spanning cluster of cracks emerges. We demonstrate that the phase boundary is the Kertész line of the system along which thermally activated fracture appears as a continuous phase transition analogous to percolation. The Kertész line has technological relevance setting the boundary of safe operation for construction components under high thermal loads.

The work studies the spatiotemporal activity propagation in a two-dimensional spatial system involving a finite transmission speed. We derive a numerical scheme in detail to integrate the corresponding evolution equation and validate the derived algorithm by a study of a spatially periodic system. Finally, the work demonstrates numerically transmission delay-induced breathers subjected to anisotropic external input.

Spectral dimensions have been widely used to understand transport properties on regular and fractal lattices. However, they have received little attention with regard to complex networks such as scale-free and small-world networks. Here, we study the spectral dimension and the return-to-origin probability of random walks on hierarchical scale-free networks, which can be either fractal or nonfractal depending on the weight of the shortcuts. Applying the renormalization-group (RG) approach to a Gaussian model, we obtain the exact spectral dimension. While the spectral dimension varies between 1 and 2 for the fractal case, it remains at 2, independent of the variation in the network structure, for the nonfractal case. The crossover behavior between the two cases is studied by carrying out the RG flow analysis. The analytical results are confirmed by simulation results and their implications for the architecture of complex systems are discussed.

We study spin squeezing, negative correlations, and concurrence in the quantum kicked top model. We prove that the spin squeezing and negative correlations are equivalent for spin systems with only symmetric Dicke states populated. We numerically analyze spin squeezing parameters and concurrence in this model and find that the maximal spin squeezing direction, which refers to the minimal pairwise correlation direction, is strongly influenced by quantum chaos. Entanglement (spin squeezing) sudden death and sudden birth occur alternatively for the periodic and quasiperiodic cases, while only entanglement (spin squeezing) sudden death is found for the chaotic case.

The “edge” of the Antarctic polar vortex is known to behave as a barrier to the meridional (poleward) transport of ozone during the austral winter. This chemical isolation of the polar vortex from the middle and low latitudes produces an ozone minimum in the vortex region, intensifying the ozone hole relative to that which would be produced by photochemical processes alone. Observational determination of the vortex edge remains an active field of research. In this paper, we obtain objective estimates of the structure of the polar vortex by introducing a technique based on transfer operators that aims to find regions with minimal external transport. Applying this technique to European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-40 three-dimensional velocity data, we produce an improved three-dimensional estimate of the vortex location in the upper stratosphere where the vortex is most pronounced. This computational approach has wide potential application in detecting and analyzing mixing structures in a variety of atmospheric, oceanographic, and general fluid dynamical settings.

We use the Cahn-Hilliard approach to model the slow dissolution dynamics of binary mixtures. An important peculiarity of the Cahn-Hilliard-Navier-Stokes equations is the necessity to use the full continuity equation even for a binary mixture of two incompressible liquids due to dependence of mixture density on concentration. The quasicompressibility of the governing equations brings a short time-scale (quasiacoustic) process that may not affect the slow dynamics but may significantly complicate the numerical treatment. Using the multiple-scale method we separate the physical processes occurring on different time scales and, ultimately, derive the equations with the filtered-out quasiacoustics. The derived equations represent the Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations. This approximation can be further employed as a universal theoretical model for an analysis of slow thermodynamic and hydrodynamic evolution of the multiphase systems with strongly evolving and diffusing interfacial boundaries, i.e., for the processes involving dissolution/nucleation, evaporation/condensation, solidification/melting, polymerization, etc.

Plasma-based seeded soft-x-ray lasers have the potential to generate high energy and highly coherent short pulse beams. Due to their high density, plasmas created by the interaction of an intense laser with a solid target should store the highest amount of energy density among all plasma amplifiers. Our previous numerical work with a two-dimensional (2D) adaptive mesh refinement hydrodynamic code demonstrated that careful tailoring of plasma shapes leads to a dramatic enhancement of both soft-x-ray laser output energy and pumping efficiency. Benchmarking of our 2D hydrodynamic code in previous experiments demonstrated a high level of confidence, allowing us to perform a full study with the aim of the way for $10–100\mu \text{J}$ seeded soft-x-ray lasers. In this paper, we describe in detail the mechanisms that drive the hydrodynamics of plasma columns. We observed transitions between narrow plasmas, where very strong bidimensional flow prevents them from storing energy, to large plasmas that store a high amount of energy. Millimeter-sized plasmas are outstanding amplifiers, but they have the limitation of transverse lasing. In this paper, we provide a preliminary solution to this problem.

Exact solutions for the generalized nonlinear Schrödinger equation with inhomogeneous complex linear and nonlinear potentials are found. We have found localized and periodic solutions for a wide class of localized and periodic modulations in the space of complex potentials and nonlinearity coefficients. Examples of stable and unstable solutions are given. We also demonstrated numerically the existence of stable dissipative breathers in the presence of an additional parabolic trap.

In this paper we present analytical breather solutions of the three-dimensional nonlinear generalized Gross-Pitaevskii equation. We use an Ansatz to reduce the three-dimensional equation with space- and time-dependent coefficients into a one-dimensional equation with constant coefficients. The key point is to show that both the space- and time-dependent coefficients of the nonlinear equation can contribute to modulate the breather excitations. We briefly discuss the experimental feasibility of the results in Bose-Einstein condensates.

We link the appearance of universal kernels in random matrix ensembles to the phenomenon of shock formation in some fluid dynamical equations. Such equations are derived from Dyson’s random walks after a proper rescaling of the time. In the case of the Gaussian unitary ensemble, on which we focus in this paper, we show that the characteristics polynomials and their inverse evolve according to a viscid Burgers equation with an effective “spectral viscosity” ${\nu }_s=1/2N$, where $N$ is the size of the matrices. We relate the edge of the spectrum of eigenvalues to the shock that naturally appears in the Burgers equation for appropriate initial conditions, thereby suggesting a connection between the well-known microscopic universality of random matrix theory and the universal properties of the solution of the Burgers equation in the vicinity of a shock.

The effect of an interstitial fluid on the mixing of sedimenting grains is studied numerically in a closed rectangular Hele-Shaw cell. We investigate the impact of the fluid compressibility and fluid viscosity on the dynamics and structures of the granular Rayleigh-Taylor instability. First we discuss the effect of the fluid compressibility on the initial fluid pressure evolution and on the dynamics of the particles. Here, the emerging patterns do not seem highly affected by the compressibility change studied. To characterize the patterns and motion the combined length of the particle trajectories in relation to the movement of the center of mass is analyzed, and the separation of particle pairs is measured as a function of the fluid viscosity.

The continuous nematic to smectic-$A$ $\left(N\text{-Sm}A\right)$ phase transition has been studied by high-resolution ac-calorimetry in binary mixtures of the liquid crystal octylcyanobiphenyl (8CB) and a nonmesogenic, low-molecular weight, solvent n-hexane (hex) as a function of temperature and solvent concentration. Heating and cooling scans about the $N\text{-Sm}A$ transition temperature were repeatedly performed on pure and six $8\text{CB}+\text{hex}$ samples having hexane molar concentration ranging from $x_{hex}=0.02$ to 0.12. All $8\text{CB}+\text{hex}$ samples in this range of $x_{hex}$ remain macroscopically miscible and exhibit an $N\text{-Sm}A$ heat capacity peak that shifts nonmonotonically to lower temperature and evolves in shape, with a reproducible hysteresis, as $x_{hex}$ increases. The imaginary part of heat capacity remains zero up to $x_{hex}^{TCP}\simeq 0.07$ above which the distinct peak is observed, corresponding to a jump in both the real and imaginary enthalpy, indicating the onset of first-order behavior. A simple power-law analysis reveals an effective exponent that increases smoothly from 0.30 to 0.50 with an amplitude ratio $A^{-}/A^{+}\to 1$ as $x_{hex}\to x_{hex}^{TCP}$. This observed crossover of the $N\text{-Sm}A$ toward a tricritical point driven by solvent concentration is consistent with previous results and can be understood as a solvent softening of the liquid crystal and concument promoting of nematic fluctuations.

We present a Monte Carlo algorithm that provides efficient and unbiased sampling of polymer melts consisting of two chains of equal length that jointly visit all the sites of a cubic lattice with rod geometry $L\times L\times rL$ and nonperiodic (hard wall) boundary conditions. Using this algorithm for chains of length up to 40 000 monomers and aspect ratios $1\le r\le 10$, we show that in the limit of a large lattice the two chains phase separate. This demixing phenomenon is present already for $r=1$ and becomes more pronounced, albeit not perfect, as $r$ is increased.

Plasmids are extrachromosomal DNA molecules which code for their own replication. We previously reported a setup using genes coding for fluorescent proteins of two colors that allowed us, using a simple model, to extract the plasmid-copy-number noise in a monoclonal population of bacteria [J. Wong Ng et al., Phys. Rev. E 81, 011909 (2010)]. Here we present a detailed calculation relating this noise to the measured levels of fluorescence, taking into account all sources of fluorescence fluctuations: not only the fluctuation of gene expression as in the simple model but also the growth and division of bacteria, the nonuniform distribution of their ages, the random partition of proteins at divisions, and the replication and partition of plasmids and chromosome. We show how to use the chromosome as a reference, which helps extracting the plasmid-copy-number noise in a self-consistent manner.

Statistical methods, including block entropy based approaches, have already been used in the study of long-range features of genomic sequences seen as symbol series, either considering the full alphabet of the four nucleotides or the binary purine or pyrimidine character set. Here we explore the alternation of short protein-coding segments with long noncoding spacers in entire chromosomes, focusing on the scaling properties of block entropy. In previous studies, it has been shown that the sizes of noncoding spacers follow power-law-like distributions in most chromosomes of eukaryotic organisms from distant taxa. We have developed a simple evolutionary model based on well-known molecular events (segmental duplications followed by elimination of most of the duplicated genes) which reproduces the observed linearity in log-log plots. The scaling properties of block entropy $H\left(n\right)$ have been studied in several works. Their findings suggest that linearity in semilogarithmic scale characterizes symbol sequences which exhibit fractal properties and long-range order, while this linearity has been shown in the case of the logistic map at the Feigenbaum accumulation point. The present work starts with the observation that the block entropy of the Cantor-like binary symbol series scales in a similar way. Then, we perform the same analysis for the full set of human chromosomes and for several chromosomes of other eukaryotes. A similar but less extended linearity in semilogarithmic scale, indicating fractality, is observed, while randomly formed surrogate sequences clearly lack this type of scaling. Genomic sequences always present entropy values much lower than their random surrogates. Symbol sequences produced by the aforementioned evolutionary model follow the scaling found in genomic sequences, thus corroborating the conjecture that “segmental duplication-gene elimination” dynamics may have contributed to the observed long rangeness in the coding or noncoding alternation in genomes.