The unusual re-entrant phenomenon is observed in the anisotropic three-state Potts model on a generalized kagome lattice. By employing the linearized tensor renormalization group method, we find that the re-entrance can appear in the region not only under a partially ordered phase that is commonly known but also a phase without a local order parameter, which is found to fall into the universality class of Kosterlitz-Thouless (KT). The region of the re-entrance depends strongly on the ratios of the next-nearest-neighbor couplings $\alpha =J_2/\left|J_1\right|$ and $\beta =J_3/\left|J_1\right|$. The phase diagrams in the plane of temperature versus $\beta$ for different $\alpha$ are obtained. Through massive calculations, it is also disclosed that the quasientanglement entropy can be applied to accurately determine the KT transition temperature.

We study the role of scale-free structure and noise in collective dynamics of neuronal networks. For this purpose, we simulate and study analytically a cortical circuit model with stochastic neurons. We compare collective neuronal activity of networks with different topologies: classical random graphs and scale-free networks. We show that, in scale-free networks with divergent second moment of degree distribution, an influence of noise on neuronal activity is strongly enhanced in comparison with networks with a finite second moment. A very small noise level can stimulate spontaneous activity of a finite fraction of neurons and sustained network oscillations. We demonstrate tolerance of collective dynamics of the scale-free networks to random damage in a broad range of the number of randomly removed excitatory and inhibitory neurons. A random removal of neurons leads to gradual decrease of frequency of network oscillations similar to the slowing of the alpha rhythm in Alzheimer's disease. However, the networks are vulnerable to targeted attacks. A removal of a few excitatory or inhibitory hubs can impair sustained network oscillations.

Most sensory cells use transmembrane chemoreceptors to detect chemical signals in the environment. The biochemical properties and spatial organization of chemoreceptors play important roles in achieving and maintaining sensitivity and accuracy of chemical sensing. Here we investigate the effects of receptor cooperativity and adaptation on the physical limits for sensing a chemical gradient. We study a single cell with aggregated chemoreceptor arrays on the cell surface and derive a general formula to the limits for gradient sensing from the uncertainty of instantaneous receptor activity. In comparison to independent receptors, we find that cooperativity by nonadaptive receptors could significantly lower the sensing limits in a chemical concentration range determined by the biochemical properties of ligand-receptor binding and ligand-induced receptor activity. Cooperativity by adaptive receptors is beneficial to gradient sensing within a broad range of background concentrations. Our results also show that the isotropic receptor aggregate layout on the cell surface represents an optimal configuration for gradient sensing.

A methodology to compute azimuthal waves, appearing in thermal convection of a pure fluid contained in a rotating spherical shell, and to study their stability is presented. It is based on continuation, Newton-Krylov, and Arnoldi methods. An application to the study of a double-Hopf bifurcation of the basic state is shown for Ekman and Prandtl numbers $E={10}^{-4}$ and $\sigma =0.1$, respectively, radius ratios $\eta \in [0.32,0.35]$, Rayleigh numbers $R\in [1.8\times {10}^5,6\times {10}^5]$, and nonslip and perfectly conducting boundary conditions. The knowledge of the bifurcation diagrams, including the unstable solutions, allows one to understand the coexistence of stable thermal Rossby waves of different azimuthal wave numbers at some parameter regions, and the origin of some new intermittent solutions found, as trajectories close to heteroclinic chains. Moreover, the structure of the eigenfunctions at the secondary bifurcations explains the existence of the amplitude and shape modulated waves.

In order to better understand the interplay of partnership and competition in population dynamics, we study a family of generalized May-Leonard models with $N$ species. These models have a very rich structure, characterized by different types of space-time patterns. Interesting partnership formations emerge following the maxim that “the enemy of my enemy is my friend”. In specific cases cyclic dominance within coarsening clusters yields a peculiar coarsening behavior with intriguing pattern formation. We classify the different types of dynamics through the analysis of the square of the adjacency matrix. The dependence of the population densities on emerging pattern and propagating wave fronts is elucidated through a Fourier analysis. Finally, after having identified collaborating teams, we study interface fluctuations where we initially populate different parts of the system with different teams.

We study the transient synchronization dynamics of locally coupled phase oscillators moving on a one-dimensional lattice. Analysis of spatial phase correlation shows that mobility speeds up relaxation of spatial modes and leads to faster synchronization. We show that when mobility becomes sufficiently high, it does not allow spatial modes to form and the population of oscillators behaves like a mean-field system. Estimating the relaxation timescale of the longest spatial mode and comparing it with systems with long-range coupling, we reveal how mobility effectively extends the interaction range.

The effect of shear on the development of Rayleigh-Taylor instability (RTI) is studied at an Atwood number of 0.035 using the gas tunnel at Texas A&M University. Two types of diagnostics, imaging and simultaneous hot wire and cold wire anemometry, are used to measure mix widths, pointwise instantaneous velocities, and density. Image analysis has shown that the superposition of shear on RTI development increases the mixing width and growth rate at early times ($\tau =\frac{x}{U}\sqrt{\frac{A_{t}g}{H}}\ll 1$). In particular, the mixing region shows distinct characteristics of shear (Kelvin-Helmholtz instability) and buoyancy (RTI). The Kelvin-Helmholtz (KHI) instability is observed to be dominant at early times, and the RTI at late times ($\tau >1$). In the late-time self-similar regime ($\tau >1$), the mix width growth rate coefficient obtained using digital image analysis converges to a value between 0.06 and 0.07 for the compound buoyancy and shear (KH+RT) driven flows. Vertical velocity fluctuation rms values at the mixing layer centerline are measured using a hot-wire technique. These rms values are correlated to the centerline mixing width growth rate, and this growth rate coefficient is found to lie between 0.06 and 0.07 at $\tau >1$ for the KH+RT flows. The transition in flow dominance from shear instability to RTI is observed to correspond with Richardson numbers ($\mathrm{Ri}=\frac{-2hg\Delta \rho }{\rho \Delta U^2}$) of −1.5 to −2.5. Molecular mixing between the fluids is examined by looking at the probability density function distribution of the density fluctuations. A different type of mixing behavior is observed over time for the compound cases compared with the transient development of Rayleigh-Taylor driven mixing.

We consider the relativistic generalization of the harmonic oscillator problem by addressing different questions regarding its classical aspects. We treat the problem using the formalism of Hamiltonian mechanics. A Lie algebraic technique is used to solve the associated Liouville equations, yielding the phase-space evolution of an ensemble of relativistic particles, subject to a “harmonic” potential. The nonharmonic distortion of the spatial and momentum distributions due to the intrinsic nonlinear nature of the relativistic contributions is discussed. We analyze the relativistic dynamics induced by two types of Hamiltonian, which can be ascribed to those of harmonic oscillator type. Finally, we briefly discuss the quantum aspects of the problem by considering possible strategies for the solution of the associated Salpeter equation.

In a recent paper, Bonitz, Pehlke, and Schoof [Phys. Rev. E 87, 033105 (2013)], hereafter referred to as BPS, have raised some points against the Shukla-Eliasson attractive potential [P. K. Shukla and B. Eliasson, Phys. Rev. Lett. 108, 165007 (2012); P. K. Shukla and B. Eliasson, Phys. Rev. Lett. 108, 219902(E) (2012); P. K. Shukla and B. Eliasson, Phys. Rev. Lett. 109, 019901(E) (2012)], hereafter referred to as SEAP, around a stationary test charge in a quantum plasma. Our objective here is to discuss the insufficiency of the BPS reasoning concerning the applicability of the linearized quantum hydrodynamic theory, as well as to point out the shortcomings in BPS’s arguments and to suggest how to salvage BPS’s density functional theory and simulations, which have failed to produce results that correctly match with that of Shukla and Eliasson.

This is the last of a series of three papers. In the first [Phys. Rev. E 87, 033105 (2013)], the same authors presented a critical analysis of the prediction of “novel attractive forces” between protons in dense hydrogen put forward by Shukla and Eliasson in a recent Letter [Phys. Rev. Lett. 108, 165007 (2012)]. Based on ab initio density functional theory (DFT) calculations and general considerations, it was shown that no such force exists. In the second of the three papers [Phys. Rev. E 87, 037101 (2013)], Shukla, Eliasson, and Akbari-Moghanjoughi (SEA) rejected this analysis. SEA did not discuss our arguments but claimed that the discrepancy between their quantum hydrodynamic model (QHD) and DFT is due to a failure of the latter. It is the purpose of the present Reply to demonstrate that this claim is incorrect because DFT is more accurate than QHD, by construction.

We study numerically the geometrical properties of minimally weighted paths that appear in the minimally weighted path (MWP) model on two-dimensional lattices assuming a combination of periodic and free boundary conditions (BCs). Each realization of the disorder consists of a random fraction $(1-\rho )$ of bonds with unit strength and a fraction $\rho$ of bond strengths drawn from a Gaussian distribution with zero mean and unit width. For each such sample, a path is forced to span the lattice along the direction with the free BCs. The path and a set of negatively weighted loops form a ground state. A ground state on such a lattice can be determined performing a nontrivial transformation of the original graph and applying sophisticated matching algorithms. Here we examine whether the geometrical properties of the paths are in accordance with the predictions of the Schramm-Loewner evolution (SLE). Measuring the fractal dimension, considering the winding angle statistics, and reviewing Schramm's left passage formula indicate that the paths cannot be described in terms of SLE.

The mapping of diffusion in a 2D channel with varying cross section $A\left(x\right)$ onto the longitudinal coordinate $x$ is revisited. We present an algorithm based on construction of a specific hierarchy of equations for the transverse moments of the 2D density. Elimination of all the moments but the zeroth one, the 1D density $p(x,t)$, results in the mapped equation. Our calculation validates the earlier mapping procedure [P. Kalinay and J. K. Percus, Phys. Rev. E 74, 041203 (2006); P. Kalinay and J. K. Percus, Phys. Rev. E 78, 021103 (2008)], presuming existence of the backward mapping operator, and it naturally arrives at the extended Fick-Jacobs equation [D. Reguera and J. M. Rubì, Phys. Rev. E 64, 061106 (2001)] in the stationary flow, without any phenomenological conjectures.

Anomalous transport is found to be ubiquitous in complex geological formations and it has a paramount impact on petroleum engineering and groundwater sciences. This process can be well described by the continuous time random walk (CTRW) model, in which the probability density function $w\left(t\right)$ of a particle's transition time $t$ follows a power law for large $t$: $w\left(t\right)\sim t^{-1-\alpha }$ ($0<\alpha <2$). In this work, based on the CTRW theory, a semifractional advection-diffusion equation is proposed to model the anomalous transport for $1<\alpha <2$, which is, as evidenced by field and numerical experiments, possibly the typical situation for many complex geological porous media with weakly heterogeneous microstructures.

Using numerical simulations, we investigate the properties of the dynamic phase transition that is encountered in the three-dimensional Ising model subjected to a periodically oscillating magnetic field. The values of the critical exponents are determined through finite-size scaling. Our results show that the studied nonequilibrium phase transition belongs to the universality class of the equilibrium three-dimensional Ising model.

The notion of configuration temperature is extended to discontinuous systems by identifying the temperature as the nontrivial root of several integral equations regarding the distribution of the energy change upon configuration perturbations. The relations are generalized to pressure and a distribution mean force.

The impact of thermal fluctuations on the translocation dynamics of a polymer chain driven through a narrow pore has been investigated theoretically and by means of extensive molecular dynamics (MD) simulation. The theoretical consideration is based on the so-called velocity Langevin (V-Langevin) equation which determines the progress of the translocation in terms of the number of polymer segments, $s\left(t\right)$, that have passed through the pore at time $t$ due to a driving force $f$. The formalism is based only on the assumption that, due to thermal fluctuations, the translocation velocity $v=\dot{s}\left(t\right)$ is a Gaussian random process as suggested by our MD data. With this in mind we have derived the corresponding Fokker-Planck equation (FPE) which has a nonlinear drift term and diffusion term with a time-dependent diffusion coefficient $D\left(t\right)$. Our MD simulation reveals that the driven translocation process follows a super diffusive law with a running diffusion coefficient $D\left(t\right)\propto t^{\gamma }$ where $\gamma <1$. This finding is then used in the numerical solution of the FPE which yields an important result: For comparatively small driving forces fluctuations facilitate the translocation dynamics. As a consequence, the exponent $\alpha$ which describes the scaling of the mean translocation time $\langle \tau \rangle$ with the length $N$ of the polymer, $\langle \tau \rangle \propto N^{\alpha }$ is found to diminish. Thus, taking thermal fluctuations into account, one can explain the systematic discrepancy between theoretically predicted duration of a driven translocation process, considered usually as a deterministic event, and measurements in computer simulations. In the nondriven case, $f=0$, the translocation is slightly subdiffusive and can be treated within the framework of fractional Brownian motion (fBm).

Phase transitions in finite systems are rounded and shifted and affected by boundary effects due to the surface of the system. This interplay of finite size and surface effects for fluids confined inside of a sphere of radius $R$ is studied by a phenomenological theory and Monte Carlo simulations of a model for colloid-polymer mixtures. For this system the phase separation in a colloid-rich phase and a polymer-rich phase has been previously studied extensively in the bulk. It is shown that spherical confinement can strongly enhance the miscibility of the mixture. Depending on the wall potentials at the confining surface, the wetting properties of the wall can be controlled, and this interplay between preferential adsorption of one species to the confining surface and bulk unmixing leads to very special shapes of the loops observed for the chemical potential of the colloids as a function of their packing fraction. We also discuss the extent to which concepts used for phase transitions in macroscopic systems, such as critical exponents of the order parameter distinguishing the phases, or the Kelvin equation describing the shift of the chemical potential at phase coexistence with the radius $R$, are applicable.

Patchy colloids with highly directional interactions are ideal building blocks to control the local arrangements resulting from their spontaneous self-organization. Here we propose their use, combined with substrates and nonequilibrium conditions, to obtain structures, different from those of equilibrium thermodynamic phases. Specifically, we investigate numerically the irreversible adhesion of three-patch colloids near attractive substrates, and analyze the fractal network of connected particles that is formed. The network density profile exhibits three distinct regimes, with different structural and scaling properties, which we characterize in detail. The adsorption of a mixture of three- and two-patch colloids is also considered. An optimal fraction of two-patch colloids is found where the total density of the film is maximized, in contrast to the equilibrium gel structures where a monotonic decrease of the density has been reported.

Pattern forming instabilities induced by ultralow frequency sinusoidal voltages were studied in a rodlike nematic liquid crystal by microscopic observations and simultaneous electric current measurements. Two pattern morphologies, electroconvection (EC) and flexodomains (FD), were distinguished, both appearing as time separated flashes within each half period of driving. A correlation was found between the time instants of the EC flashes and those of the nonlinear current response. The voltage dependence of the pattern contrast $C\left(U\right)$ for EC has a different character than that for the FD. The flattening of $C\left(U\right)$ at reducing the frequency was described in terms of an imperfect bifurcation model. Analyzing the threshold characteristics of FD, the temperature dependence of the difference $|e_1-e_3|$ of the flexoelectric coefficients was also determined by considering elastic anisotropy.