The information-theoretic observables entropy (a measure of disorder), excess entropy (a measure of complexity), and multi-information are used to analyze ground-state spin configurations for disordered and frustrated model systems in two and three dimensions. For both model systems, ground-state spin configurations can be obtained in polynomial time via exact combinatorial optimization algorithms, which allowed us to study large systems with high numerical accuracy. Both model systems exhibit a continuous transition from an ordered to a disordered ground state as a model parameter is varied. By using the above information-theoretic observables it is possible to detect changes in the spatial structure of the ground states as the critical point is approached. It is further possible to quantify the scaling behavior of the information-theoretic observables in the vicinity of the critical point. For both model systems considered, the estimates of critical properties for the ground-state phase transitions are in good agreement with existing results reported in the literature.

In this paper we investigate the spin currents and the von Neumann entropy (vNE) of a Heisenberg $XXZ$ chain in contact with twisted $XY$-boundary magnetic reservoirs by means of the Lindblad master equation. Exact solutions for the stationary reduced density matrix are explicitly constructed for chains of small sizes by using a quantum symmetry operation of the system. These solutions are then used to investigate the optimal transport in the chain in terms of the vNE. As a result we show that the maximal spin current always occurs in the proximity of minima of the vNE and for particular choices of parameters (coupling with reservoirs and anisotropy) it can exactly coincide with them. As the coupling is increased, current reversals may occur and in the limit of strong coupling we show that minima of the vNE tend to zero, meaning that the maximal transport is achieved in this case with states that are very close to pure states.

Granular flows down inclined channels with smooth boundaries are common in nature and industry. Nevertheless, flat boundaries have been much less investigated than bumpy ones, which are used by most experimental and numerical studies to avoid sliding effects. Using numerical simulations of each grain and of the side walls we recover quantitatively experimental results. At larger angles we predict a rich behavior, including granular convection and inverted density profiles suggesting a Rayleigh-Bénard type of instability. In many aspects flows on a flat base can be seen as flows over an effective bumpy base made of the basal rolling layer, giving Bagnold-type profiles in the overburden. We have tested a simple viscoplastic rheological model [Nature (London) 441, 727 (2006)] in average form. The transition between the unidirectional and the convective flows is then clearly apparent as a discontinuity in the constitutive relation.

We study the influence of a terahertz field on thermal properties of DNA molecules. A Peyrard-Bishop-Dauxois model with the inclusion of a solvent interaction term is considered. The terahertz field is included as a sinusoidal driven force in the equation of motion. We show how under certain field and system parameters, the melting transition and bubble formation are modified.

In information-transport and biological systems, sometimes there is more than one pathway between two nodes, so that there is a backup in case one pathway becomes defective. The size of such biconnected nodes can be an important measure of the robustness of a system. The giant biconnected components of diverse real-world networks suggest the importance of scale-free topology in biconnectivity. Thus, here, we consider the critical behavior of the largest biconnected component (BC) as links are added and form a random scale-free network. The critical exponents ${\beta }_{\left(\mathrm{BC}\right)}$ and ${\beta }_{\left(\mathrm{SC}\right)}$ associated with the order parameter of the percolation transition of the biconnected component and the single-connected component (SC), respectively, are compared. We obtain a ratio ${\beta }_{\left(\mathrm{BC}\right)}/{\beta }_{\left(\mathrm{SC}\right)}=\lambda -1$ for $2<\lambda <3$ and 2 for $\lambda >3$, where $\lambda$ is the exponent of the degree distribution in scale-free networks. We also determine the finite-size scaling behavior of the order parameter analytically and numerically.

Spatial pattern formation is a key feature of many natural systems in physics, chemistry, and biology. The essential theoretical issue in understanding pattern formation is to explain how a spatially homogeneous initial state can undergo spontaneous symmetry breaking leading to a stable spatial pattern. This problem is most commonly studied using partial differential equations to model a reaction-diffusion system of the type introduced by Turing. We report here on a much simpler and more robust model of spatial pattern formation, which is formulated as a novel type of coupled map lattice. In our model, the local site dynamics are coupled through a competitive, rather than diffusive, interaction. Depending only on the strength of the interaction, this competitive coupling results in spontaneous symmetry breaking of a homogeneous initial configuration and the formation of stable spatial patterns. This mechanism is very robust and produces stable pattern formation for a wide variety of spatial geometries, even when the local site dynamics is trivial.

Polymer solution flow is studied numerically in a periodic, hexagonal array of cylinders as a model for a porous medium. We use a lattice Boltzmann method supplemented by a polymer stress, where the polymers are modeled as finitely extensible, nonlinear, elastic dumbbells. The simulated, nonmonotonic behavior of the effective viscosity ${\mu }^{\text{eff}}$ as a function of the Weissenberg number We is in qualitative agreement with experiments in the literature. An analytical model, which replaces the flexible polymers by rods and that replaces the flow field in the porous medium by a superposition of shear and elongation, correctly reproduces the simulated ${\mu }^{\text{eff}}$ as a function of the polymer extensibility parameter $b$ in the limit of large We.

We present a simple stochastic, one-dimensional model for heat transfer in weakly collisional media as fusion plasmas. Energies of plasma particles are treated as lattice random variables interacting with a rate inversely proportional to their energy schematizing a screened Coulomb interaction. We consider both the equilibrium (microcanonical) and nonequilibrium case in which the system is in contact with heat baths at different temperatures. The model exhibits a characteristic length of thermalization that can be associated with an interaction mean free path and one observes a transition from ballistic to diffusive regime depending on the average energy of the system. A mean-field expression for heat flux is deduced from system heat transport properties. Finally, it is shown that the nonequilibrium steady state is characterized by long-range correlations.

We present a loop cluster algorithm Monte Carlo method for calculating the local $Z_2$ Berry phase of the quantum spin models. The Berry connection, which is given as the inner product of two ground states with different local twist angles, is expressed as a Monte Carlo average on the worldlines with fixed spin configurations at the imaginary-time boundaries. The “complex weight problem” caused by the local twist is solved by adopting the meron cluster algorithm. We present the results of simulation on the antiferromagnetic Heisenberg model on an out-of-phase bond-alternating ladder to demonstrate that our method successfully detects the change in the valence bond pattern at the quantum phase transition point. We also propose that the gauge-fixed local Berry connection can be an effective tool to estimate precisely the quantum critical point.

The aggregation of binary colloids of the same size and balanced charges is studied by Brownian dynamics simulations for dilute suspensions. It is shown that, under appropriate conditions, the formation of colloidal crystals is dominated by kinetic effects leading to the growth of well-ordered crystallites of the sodium-chloride (NaCl) bulk phase. These crystallites form with very high probability even when the cesium-chloride (CsCl) phase is more stable thermodynamically. Global optimization searches show that this result is not related to the most favorable structures of small clusters, which are either amorphous or of the CsCl structure. The formation of the NaCl phase is related to the specific kinetics of the crystallization process, which takes place by a two-step mechanism. In this mechanism, dense fluid aggregates form at first and then crystallization follows. It is shown that the type of short-range order in these dense fluid aggregates determines which phase is finally formed in the crystallites. The role of hydrodynamic effects in the aggregation process is analyzed by stochastic rotation dynamics - molecular dynamics simulations, and we find that these effects do not play a major role in the formation of the crystallites.

In this paper, we analyze the charge dynamics of ionic polymer-metal composites (IPMCs) in response to voltage inputs composed of a large dc bias and a small superimposed time-varying voltage. The IPMC chemoelectrical behavior is described through the modified Poisson-Nernst-Planck framework, in which steric effects are taken into consideration. The physics of charge build-up and mass transfer in the proximity of the high surface electrodes is modeled by schematizing the IPMC as the stacked sequence of five layers, in which the ionomeric membrane is separated from the metal electrodes by two composite layers. The method of matched asymptotic expansions is used to derive a semianalytical solution for the concentration of mobile counterions and the electric potential in the IPMC, which is, in turn, used to establish an equivalent circuit model for the IPMC electrical response. The circuit model consists of the series connection of a resistor and two complex elements, each constituted by the parallel connection of a capacitor and a Warburg impedance. The resistor is associated with ion transport in the ionomeric membrane and is independent of the dc bias. The capacitors and the Warburg impedance idealize charge build-up and mass transfer in the vicinity of the electrodes and their value is controlled by the dc bias. The proposed approach is validated against experimental results on in-house fabricated IPMCs and the accuracy of the equivalent circuit is assessed through comparison with finite element results.

In this paper we focus on diversity-induced resonance, which was recently found in bistable, excitable, and other physical systems. We study the appearance of this phenomenon in a purely economic model of cooperating and defecting agents. An agent's contribution to a public good is seen as a social norm, so defecting agents face a social pressure, which decreases if free riding becomes widespread. In this model, diversity among agents naturally appears because of the different sensitivities towards the social norm. We study the evolution of cooperation as a response to the social norm (i) for the replicator dynamics and (ii) for the logit dynamics by means of numerical simulations. Diversity-induced resonance is observed as a maximum in the response of agents to changes in the social norm as a function of the degree of heterogeneity in the population. We provide an analytical, mean-field approach for the logit dynamics and find very good agreement with the simulations. From a socioeconomic perspective, our results show that, counterintuitively, diversity in the individual sensitivity to social norms may result in a society that better follows such norms as a whole, even if part of the population is less prone to follow them.

We show that in a source-free subwavelength region of microwave fields, there can exist field structures with a local coupling between the time-varying electric and magnetic fields differing from the electric-magnetic coupling in regular-propagating free-space electromagnetic waves. To distinguish such field structures from regular electromagnetic (EM) field structures, we term them as magnetoelectric (ME) fields. We study a structure and conservation laws of microwave ME near fields. We show that there exist sources of microwave ME near fields—the ME particles. These particles are represented by small quasi-two-dimensional ferrite disks with magnetic-dipolar-oscillation spectra. The near fields originating from such particles are characterized by topologically distinctive power-flow vortices, nonzero helicity, and a torsion degree of freedom. The paper consists of two main parts. In the first one, we give a theoretical background of properties of the electric and magnetic fields inside and outside of a ferrite particle with magnetic-dipolar-oscillation spectra resulting in the appearance of microwave ME near fields. In the second main part, we represent numerical and experimental studies of the microwave ME near fields and their interactions with matter. Based on the obtained properties of the ME near fields, we discuss possibilities for effective microwave sensing of natural and artificial chiral structures.

We study the dynamics of a granular gas heated by a stochastic thermostat. From a Boltzmann description, we derive the hydrodynamic equations for small perturbations around the stationary state that is reached in the long time limit. Transport coefficients are identified as Green-Kubo formulas obtaining explicit expressions as a function of the inelasticity and the spatial dimension.

When solid surfaces are immersed in aqueous solutions, some of their charges can dissociate and leave behind charged patches on the surface. Although the charges are distributed heterogeneously on the surface, most of the theoretical models treat them as homogeneous. For overall non-neutral surfaces, the assumption of surface charge homogeneity is rather reasonable since the leading terms of two such interacting surfaces depend on the nonzero average charge. However, for overall neutral surfaces the nature of the surface charge distribution is crucial in determining the intersurface interaction. In the present work we study the interaction between two charged surfaces across an aqueous solution for several charge distributions. The analysis is preformed within the framework of the linearized Poisson-Boltzmann theory. For periodic charge distributions the interaction is found to be repulsive at small separations, unless the two surface distributions are completely out-of-phase with respect to each other. For quenched random charge distributions we find that due to the presence of the ionic solution in between the surfaces, the intersurface repulsion dominates over the attraction in the linear regime of the Poisson-Boltzmann theory. The effect of quenched charge heterogeneity is found to be particularly substantial in the case of large charged domains.

NF-$\kappa$B is a major transcription factor mediating inflammatory response. In response to a pro-inflammatory stimulus, it exhibits a characteristic response—a pulse followed by noisy oscillations in concentrations of considerably smaller amplitude. NF-$\kappa$B is an important mediator of cellular communication, as it is both activated by and upregulates production of cytokines, signals used by white blood cells to find the source of inflammation. While the oscillatory dynamics of NF-$\kappa$B has been extensively investigated both experimentally and theoretically, the role of the noise and the lower secondary amplitude has not been addressed. We use a cellular automaton model to address these issues in the context of spatially distributed communicating cells. We find that noisy secondary oscillations stabilize concentric wave patterns, thus improving signal quality. Furthermore, both lower secondary amplitude as well as noise in the oscillation period might be working against chronic inflammation, the state of self-sustained and stimulus-independent excitations. Our findings suggest that the characteristic irregular secondary oscillations of lower amplitude are not accidental. On the contrary, they might have evolved to increase robustness of the inflammatory response and the system's ability to return to a pre-stimulated state.

We examine the behavior of the Kolmogorov constants $C_2$, $C_k$, and $C_{k1}$, which are, respectively, the prefactors of the second-order longitudinal structure function and the three-dimensional and one-dimensional longitudinal energy spectrum in the inertial range. We show that their ratios, $C_2/C_{k1}$ and $C_k/C_{k1}$, exhibit clear dependence on the microscale Reynolds number $R_{\lambda }$, implying that they cannot all be independent of $R_{\lambda }$. In particular, it is found that $(C_{k1}/C_2-0.25)=1.95R_{\lambda }^{-0.68}$. The study further reveals that the widely used relation $C_2=4.02C_{k1}$ holds only asymptotically when $R_{\lambda }\gtrsim {10}^5$. It is also found that $C_2$ has much stronger $R_{\lambda }$ dependence than either $C_k$ or $C_{k1}$ if the latter indeed has a systematic dependence on $R_{\lambda }$. We further show that the varying dependence on $R_{\lambda }$ of these three numbers can be attributed to the difference of the inertial range in real- and wave-number space, with the inertial range in real-space known to be much shorter than that in wave-number space.

We introduce a variant of the banded random matrix ensemble and show, using detailed numerical analysis and theoretical arguments, that the phonon heat current in disordered quasi-one-dimensional lattices obeys a one-parameter scaling law. The resulting $\beta$ function indicates that an anomalous Fourier law is applicable in the diffusive regime, while in the localization regime the heat current decays exponentially with the sample size. Our approach opens a new way to investigate the effects of Anderson localization in heat conduction based on the powerful ideas of scaling theory.

We study the critical behavior of the random $q$-state Potts model in the large-$q$ limit on the diamond hierarchical lattice with an effective dimensionality $d_{\mathrm{eff}}>2$. By varying the temperature and the strength of the frustration the system has a phase transition line between the paramagnetic and the ferromagnetic phases which is controlled by four different fixed points. According to our renormalization group study the phase boundary in the vicinity of the multicritical point is self-similar; it is well represented by a logarithmic spiral. We expect an infinite number of reentrances in the thermodynamic limit; consequently one cannot define standard thermodynamic phases in this region.