Spiral wave propagation in period-2 excitable media is accompanied by line defects, the locus of points with period-1 oscillations. Here we investigate spiral line defects in cardiac tissue where period-2 behavior has a known arrhythmogenic role. We find that the number of line defects, which is constrained to be an odd integer, is 3 for a freely rotating spiral, with and without meander, but 1 for a spiral anchored around a fixed heterogeneity. We interpret this finding analytically using a simple theory where spiral wave unstable modes with different numbers of line defects correspond to quantized solutions of a Helmholtz equation. Furthermore, the slow inward rotation of spiral line defects is described in different regimes.

In this paper we study a fully relativistic model of a two-dimensional hard-disk gas. This model avoids the general problems associated with relativistic particle collisions and is therefore an ideal system to study relativistic effects in statistical thermodynamics. We study this model using molecular-dynamics simulation, concentrating on the velocity distribution functions. We obtain results for $x$ and $y$ components of velocity in the rest frame $\left(\Gamma \right)$ as well as the moving frame $\left({\Gamma }^{\prime }\right)$. Our results confirm that Jüttner distribution is the correct generalization of Maxwell-Boltzmann distribution. We obtain the same “temperature” parameter $\beta$ for both frames consistent with a recent study of a limited one-dimensional model. We also address the controversial topic of temperature transformation. We show that while local thermal equilibrium holds in the moving frame, relying on statistical methods such as distribution functions or equipartition theorem are ultimately inconclusive in deciding on a correct temperature transformation law (if any).

We present a theoretical study of a system with competing short-range ferromagnetic attraction and a long-range antiferromagnetic repulsion, in the presence of a uniform external magnetic field. The interplay between these interactions, at sufficiently low temperature, leads to the self-tuning of the magnetization to a value which triggers phase coexistence, even in the presence of the external field. The investigation of this phenomenon is performed using a Ginzburg-Landau functional in the limit of an infinite number of order parameter components (large $N$ model). The scalar version of the model is expected to describe the phase separation taking place on a cell surface when this is immersed in a uniform concentration of chemical stimulant. A phase diagram is obtained as a function of the external field and the intensity of the long-range repulsion. The time evolution of the order parameter and of the structure factor in a relaxation process is studied in different regions of the phase diagram.

We present an analysis of the power fluctuations in the statistical steady state of a passively mode-locked laser. We use statistical light-mode theory to map this problem to that of fluctuations in a reference equilibrium statistical physics problem and, in this way, study the fluctuations nonperturbatively. The power fluctuations, being noncritical, are Gaussian and proportional in amplitude to the inverse square root of the number of degrees of freedom. We calculate explicit analytic expressions for the covariance matrix of the overall pulse and cw power variables, providing complete information on the single-time power distribution in the laser, and derive a set of fluctuation-dissipation relations between them and the susceptibilities of the steady-state quantities.

We experimentally study the electrical transport in partially water-saturated pore network. The porous medium under investigation is a Fontainebleau sandstone, characterized by x-ray tomography. We show the existence of two electrical conductivity regimes. At high water saturation, the electric resistivity follows a well-known Archie law. Below a water saturation $S_w\sim 0.2$, a strong negative deviation from this Archie law is observed. We attribute this transition to the existence of “a thick liquid film,” assuring the ionic conduction in the low saturation regime. A numerical simulation is proposed to confirm this scenario. Two possible protocols are used to distribute the brine phase in the pore network of a three-dimensional microtomography image. The first one is based on a minimization of the interfacial energy. The second takes into account a quasistatic capillary displacement. The classical random-walk algorithm is used to compute the electric conductivity at various water saturations. Without the “thick film,” both of the two fluid-placing protocols show a disconnectedness transition of the brine phase when $S_w<0.2$. Adding this “film” to solid surface, the electrical continuity is maintained. The bending down trend is correctly reproduced, showing that in this range, the electric response cannot be described by a power law as usual.

A theoretical approach to the description of the Soret effect in binary nonpolar liquids is proposed. The temperature gradient of the partial pressure is determined as the driving force of thermal diffusion. The hard-sphere fluid is chosen as a reference system and an explicit relation for the Soret coefficient is found. Two additive contributions owing to steric repulsions and attractive interactions form the so-called chemical contribution to $S_T$ [C. Debuschewitz and W. Köhler, Phys. Rev. Lett. 87, 055901 (2001)]. The parameters of interparticle interactions are defined with the help of the solvation theory. In particular, the van der Waals constant of cross interactions is expressed via the excess volume of mixture. The proposed theory is applied to the benzene-cyclohexane system. A reasonable agreement of theoretical and experimental results is revealed for the Soret coefficient and its temperature dependence.

The interlink between particle-scale properties and macroscopic behavior of three-dimensional granular media subjected to mechanical loading is studied intensively by scientists and engineers, but not yet well understood. Here we study the role of key particle-scale properties, such as interparticle friction and particle elastic modulus, in the functioning of dual contact force networks, viz., strong and weak contacts, in mobilizing shear strength in dense granular media subjected to quasistatic shearing. The study is based on three-dimensional discrete element method in which particle-scale constitutive relations are based on well-established nonlinear theories of contact mechanics. The underlying distinctive contributions of these force networks to the macroscopic stress tensor of sheared granular media are examined here in detail to find out how particle-scale friction and particle-scale elasticity (or particle-scale stiffness) affect the mechanism of mobilization of macroscopic shear strength and other related properties. We reveal that interparticle friction mobilizes shear strength through bimodal contribution, i.e., through both major and minor principal stresses. However, against expectation, the contribution of particle-scale elasticity is mostly unimodal, i.e., through the minor principal stress component, but hardly by the major principal stress. The packing fraction and the geometric stability of the assemblies (expressed by the mechanical coordination number) increase for decrease in interparticle friction and elasticity of particles. Although peak shear strength increases with interparticle friction, the deviator strain level at which granular systems attain peak shear strength is mostly independent of interparticle friction. Granular assemblies attain peak shear strength (and maximum fabric anisotropy of strong contacts) when a critical value of the mechanical coordination number is attained. Irrespective of the interparticle friction and elasticity of the particles, the packing fraction and volumetric strain are constant during steady state. Volumetric strain in sheared granular media increases with interparticle friction and elasticity of the particles. We show that the elasticity of the particles does not enhance dilation in frictionless granular media. The results presented here provide additional understanding of the role of particle-scale properties on the collective behavior of three-dimensional granular media subjected to shearing.

Impact phenomena of nanoclusters subject to thermal fluctuations are numerically investigated. From the molecular dynamics simulation for colliding two identical clusters, it is found that the restitution coefficient for head-on collisions has a peak at a colliding speed due to the competition between the cohesive interaction and the repulsive interaction of colliding clusters. Some aspects of the collisions can be understood by the theory of Brilliantov et al. [Phys. Rev. E 76, 051302 (2007)], but many aspects are found from the simulation. In particular, we find that there are some anomalous rebounds in which the restitution coefficient is larger than unity. The phase diagrams of rebound processes against impact speed and the cohesive parameter can be understood by a simple phenomenology.

We report the influence of the polymer network density formed in short-pitch ferroelectric liquid crystal (FLC) on the soft and the Goldstone dielectric relaxation modes. The experimental results of the pure FLC and the FLC stabilized by a polymer network with various densities are presented and compared. These results reveal that in the $\text{Sm}{C}^{\ast }$ phase, when the polymer concentration increases, the Goldstone dielectric strength gradually decreases and the relaxation frequency is shifted to higher values. In the $\text{Sm}{A}^{\ast }$ phase, the results show that close to the $\text{Sm}{C}^{\ast }\text{-Sm}{A}^{\ast }$ transition temperature, $T_c$, the soft relaxation mode is largely influenced by the polymer network: a sharp decrease in the dielectric strength and an increase in the relaxation frequency when the polymer density increases were observed. The soft mode is relatively weakly affected by the network for higher temperatures $\left(T\ge T_c+0.5°\text{C}\right)$. This indicates that the behavior of the soft mode for this temperature domain is dominated rather by thermal effects than by the network. A simple phenomenological approach was proposed to explain the behavior of the soft-mode dielectric strength versus polymer concentration. This model takes into account the anisotropic interaction between the polymer network and the liquid crystal, and the elastic interaction resulting from the anchoring of the liquid crystal molecules at the polymer surfaces. The experimental results are in agreement with the proposed model.

Cardiac mechanoelectric feedback can play an important role in different heart pathologies. In this paper, we show that mechanoelectric models which describe both the electric propagation and the mechanic contraction of cardiac tissue naturally lead to close systems of equations with global coupling among the variables. This point is exemplified using the Nash-Panfilov model, which reduces to a FitzHugh-Nagumo-type equation with global coupling in the linear elastic regime. We explain the appearance of self-oscillatory regimes in terms of the system nullclines and describe the different dynamical attractors. Finally, we study their basin of attraction in terms of the system size and the strength of the stretch-induced currents.

Heat-induced diffusion of nucleosomes along DNA is an experimentally well-studied phenomenon, presumably induced by twist defects that propagate through the wrapped DNA portion. The diffusion constant depends dramatically on the local mechanical properties of the DNA and the presence of DNA-binding ligands. This has been quantitatively understood by a stochastic three-state model. Future experiments are expected to allow application of forces on the nucleosome that induce a directed sliding. By extending the three-state model, the present work studies theoretically the response of the nucleosome to such external forces and how it is affected by the mechanical properties of the DNA and the presence of DNA-binding ligands.

We study the statistical properties of a simple genetic regulatory network that provides heterogeneity within a population of cells. This network consists of a binary genetic switch in which stochastic flipping between the two switch states is mediated by a “flipping” enzyme. Feedback between the switch state and the flipping rate is provided by a linear feedback mechanism: the flipping enzyme is only produced in the on switch state and the switching rate depends linearly on the copy number of the enzyme. This work generalizes the model of Visco et al. [Phys. Rev. Lett. 101, 118104 (2008)] to a broader class of linear feedback systems. We present a complete analytical solution for the steady-state statistics of the number of enzyme molecules in the on and off states, for the general case where the enzyme can mediate flipping in either direction. For this general case we also solve for the flip time distribution, making a connection to first passage and persistence problems in statistical physics. We show that the statistics are non-Poissonian, leading to a peak in the flip time distribution. The occurrence of such a peak is analyzed as a function of the parameter space. We present a relation between the flip time distributions measured for two relevant choices of initial condition. We also introduce a correlation measure and use this to show that this model can exhibit long-lived temporal correlations, thus providing a primitive form of cellular memory. Motivated by DNA replication as well as by evolutionary mechanisms involving gene duplication, we study the case of two switches in the same cell. This results in correlations between the two switches; these can be either positive or negative depending on the parameter regime.

The influence of cholesterol on lipid bilayer structure is significant and the effect of cholesterol on lipid sorting and phase separation in lipid-raft-forming model membrane systems has been well investigated by microscopy methods on giant vesicles. An important consideration however is the influence of fluorescence illumination on the phase state of these lipids and this effect must be carefully minimized. In this paper, we show that synchrotron x-ray scattering on solution lipid mixtures is an effective alternative technique for the identification and characterization of the $l_o$ (liquid ordered) and $l_d$ (liquid disordered) phases. The high intensity of synchrotron x rays allows the observation of up to 5 orders of diffraction from the $l_o$ phase, whereas only two are clearly visible when the $l_d$ phase alone is present. This data can be collected in $\sim 1\text{min}/\text{sample}$, allowing rapid generation of phase data. In this paper, we measure the lamellar spacing in both the liquid-ordered and liquid-disordered phases simultaneously, as a function of cholesterol concentration in two different ternary mixtures. We also observe evidence of a third gel-phaselike population at $10–12\text{mol}\%$ cholesterol and determine the thickness of the bilayer for this phase. Importantly we are able to look at phase coexistence in the membrane independent of photoeffects.

Given a large network, computing statistics such as clustering coefficient, or modularity, is costly for large networks. When one more edge or vertex is added, traditional methods require that the full (expensive) computation be redone on this slightly modified graph. Alternatively, we introduce here a new approach: under modification to the graph, we update the statistics instead of computing them from scratch. In this paper we provide update schemes for a number of popular statistics, to include degree distribution, clustering coefficient, assortativity, and modularity. Our primary aim is to reduce the computational complexity needed to track the evolving behavior of large networks. As an important consequence, this approach provides efficient methods which may support modeling the evolution of dynamic networks to identify and understand critical transitions. Using the updating scheme, the network statistics can be computed much faster than re-calculating each time that the network evolves. We also note that the update formula can be used to determine which edge or node will lead to the extremal change of network statistics, providing a way of predicting or designing network evolution rules that would optimize some chosen statistic. We present our evolution methods in terms of a network statistics differential notation.

When left overnight undisturbed in a covered beaker, suspensions of polystyrene microspheres were found to undergo a distinctive kind of macroscopically visible phase separation. Microspheres migrated radially, leaving a vertically oriented cylinder near the center of the beaker that was devoid of microspheres. Cylinder formation was preceded by formation of a microsphere-free plate at the suspension surface, which may be the precursor of the cylinder. The cylindrical phase separation was found to depend on illumination, which suggests that low-level photon energy from the laboratory environment is sufficient to drive this surprising pattern formation. So long as suspension parameters were set within certain ranges, the cylindrical pattern occurred regularly.

We present an experimental and theoretical study of multistability of a single-mode laser subject to feedback through phase tuning and amplifier sections integrated on the same chip. Closely above threshold, a regime of tristability of continuous-wave (CW) states is found for multiple ranges of amplifier and phase currents. The separation between the tristable wavelengths agrees with the channel spacing of dense wavelength multiplexing in the $C$ band of optical communication making the device interesting for ternary logic applications. Complementary theoretical investigations in the framework of the paradigmatic Lang-Kobayashi model provide a consistent understanding of the experimental findings and additionally yield an analytic formula expressing the maximum number of coexisting stable CW states by the linewidth-enhancement factor $\alpha$. Tristability belongs to the $\alpha$ range from 5 to 8 in good agreement with experiment.

A plasma model of relaxation of a medium in heavy-ion tracks in condensed matter is proposed. The model is based on three assumptions: the Maxwell distribution of plasma electrons, localization of plasma inside the track nanochannel, and constant values of the plasma electron density and temperature during the x-ray irradiation. The model of multiple ionization of target atoms by a fast projectile ion is used to determine the initial conditions. An analysis of the results of the calculations performed makes it possible to define when the atomic relaxation model is a very rough approximation and the plasma relaxation model must be used. It is demonstrated that the plasma relaxation model adequately describes the x-ray spectra observed upon interaction of a fast ion with condensed target. The comparison with the experimental data justifies the reliability of the plasma relaxation model. Preassumptions of plasma relaxation model are validated by the molecular-dynamics simulation. An x-ray spectral method based on the plasma relaxation model is proposed for diagnostics of the plasma in fast ion tracks. The results obtained can be useful in examining the initial stage of defect formation in solids under irradiation with single fast heavy ions.

We present an efficient and accurate grid method for computations of eigenvalues and eigenfunctions of the generalized spheroidal wave equation. Different from previous studies, our method is based on the expansion of the spheroidal wave function by discrete-variable-representation basis functions constructed from the associated Legendre polynomials. The differential operator can be expressed analytically on the grid points, which are the zeros of the associated Legendre polynomials. The resultant potential matrix is simply diagonal and evaluated directly on the same grid. The corresponding differential equation is thus converted to an eigenvalue problem of a small matrix, whose eigenvalues and eigenvectors are converged very fast. The wave functions can then be evaluated accurately at any desired point from the expansion formula with the computed eigenvectors. Compared to previous methods, our method is direct and efficient for any parameter $c$, either small or large.

Brownian ratchets produce directed motion through rectification of thermal fluctuations and have been used for separation processes and colloidal transport. We propose a flashing ratchet motor that enables the transduction of electrical energy into rotary micromechanical work. This is achieved through torque generation provided by boundary shaping of equipotential surfaces. The present device contrasts to previous implementations that focus on translational motion. Stochastic simulations elucidate the performance characteristics of this device as a function of its geometry. Miniaturization to nanoscale dimensions yields rotational speeds in excess of 1 kHz, which is comparable to biomolecular motors of similar size.