Following the recent proposal made by [J. Bouttier et al., Phys. Rev. E 76, 041140 (2007)], we study analytically the mobility properties of a single vacancy in the close-packed dimer model on the square lattice. Using the spanning web representation, we find determinantal expressions for various observable quantities. In the limiting case of large lattices, they can be reduced to the calculation of Toeplitz determinants and minors thereof. The probability for the vacancy to be strictly jammed and other diffusion characteristics are computed exactly.

Motivated by the interest in the role of stiff polymers like actin in cellular processes and as components of biopolymer networks like the cytoskeleton, we present a statistical mechanical study of the twist elasticity of stiff polymers. We obtain simple, approximate analytical forms for the writhe distribution at zero applied force. We also derive simple analytical expressions for the torque-twist relation and discuss buckling of stiff polymers due to the applied torques. The theoretical predictions presented here can be tested against single-molecule experiments on neurofilaments and cytoskeletal filaments like actin and microtubules.

In this paper we derive analytically the evolution equation of the interface for a model of surface growth with relaxation to the minimum (SRM) in complex networks. We were inspired by the disagreement between the scaling results of the steady state of the fluctuations between the discrete SRM model and the Edward-Wilkinson process found in scale-free networks with degree distribution $P\left(k\right)\sim k^{-\lambda }$ for $\lambda <3$ [Pastore y Piontti et al., Phys. Rev. E 76, 046117 (2007)]. Even though for Euclidean lattices the evolution equation is linear, we find that in complex heterogeneous networks nonlinear terms appear due to the heterogeneity and the lack of symmetry of the network; they produce a logarithmic divergency of the saturation roughness with the system size as found by Pastore y Piontti et al. for $\lambda <3$.

Chemical turbulence in the oscillatory catalytic CO oxidation on Pt(110) is suppressed by means of focused laser light. The laser locally heats the platinum surface which leads to a local increase of the oscillation frequency, and to the formation of a pacemaker which emits target waves. These waves slowly entrain the medium and suppress the spatiotemporal chaos present in the absence of laser light. Our experimental results are confirmed by a detailed numerical analysis of one- and two-dimensional media using the Krischer-Eiswirth-Ertl model for CO oxidation on Pt(110). Different control regimes are identified and the dispersion relation of the system is determined using the pacemaker as an externally tunable wave source.

We study the electrical and hydraulic conductivity percolation exponents in a Gaussian fracture using the method proposed in Plouraboué et al. [Phys. Rev. E 73, 036305 (2006)]. Nonuniversal conductivity percolation exponents are found: they differ from the theoretical predictions for infinite system size for frozen power-law distributions of local conductivities, as with their finite size corrections. In the hydraulic case, we also find that the probability density function of the conductivity follows a power-law distribution near the percolation threshold.

The exact dynamics of a system coupled to an environment can be described by an integro-differential stochastic equation for the reduced density. The influence of the environment is incorporated through a mean field which is both stochastic and nonlocal in time and where the standard two-time correlation functions of the environment appear naturally. Since no approximation is made, the presented theory incorporates exactly dissipative and non-Markovian effects. Applications to the spin-boson model coupled to a heat bath with various coupling regimes and temperature show that the presented stochastic theory can be a valuable tool to simulate exactly the dynamics of open quantum systems. Links with the stochastic Schrödinger equation method and possible extensions to “imaginary time” propagation are discussed.

Full analytical models of heat engines and refrigerators in linear irreversible thermodynamics can be defined by means of a chain of coupled heat devices. In this way it is possible to derive results and techniques of finite-time thermodynamics, like endoreversible efficiencies and the usual models of irreversible heat devices, in terms of an endoreversible energy converter plus a heat leak between external reservoirs. Also, a counterintuitive relationship is found between the global behavior of the chain and the individual performance of the devices: it is not necessary nor generally possible to impose the same operation regime on every device to achieve a desired overall performance.

This paper studies a two-lane totally asymmetric simple exclusion process, in which particles could jump between the two lanes with asymmetric rates. In the weak coupling situation, the rates are inversely proportional to system size $L$. The appearance of localized shock in one lane and the discontinuous phase transition as revealed by Juhász [Phys. Rev. E 76, 021117 (2007)] are also reproduced. The density profiles and phase diagrams are constructed in the hydrodynamic limit, by numerically solving the steady state equations. The phase diagram in our model exhibits asymmetry, which is different from the symmetric one in Juhász’s model. We have studied the phase boundary and discontinuous line analytically. The analytical results are in good agreement with that obtained from numerical integration. We also study the strong coupling situation, in which the lane changing rates are independent of $L$. Results completely different from that arising from weak coupling are presented. Furthermore, features different from that of the model presented by Pronina and Kolomeisky [Physica A 372, 12 (2006)] are revealed.

We study conserved one-dimensional models of particle diffusion, attachment, and detachment from clusters, where the detachment rates decrease with increasing cluster size as $\gamma \left(m\right)\sim m^{-k}$, $k>0$. Heuristic scaling arguments based on random walk properties show that the typical cluster size scales as ${\left(t/\text{ln}t\right)}^z$, with $z=1/\left(k+2\right)$. The coarsening of neighboring clusters is characterized by initial symmetric flux of particles between them followed by an effectively asymmetric flux due to the unbalanced detachment rates, which leads to the above logarithmic corrections. Small clusters have densities of order $t^{-mz\left(1\right)}$, with $z\left(1\right)=k/\left(k+2\right)$. Thus for $k<1$, the small clusters (mass of order unity) are statistically dominant and the average cluster size does not scale as the size of typically large clusters does. We also solve the master equation of the model under an independent interval approximation, which yields cluster distributions and exponent relations and gives the correct dominant coarsening exponent after suitable changes to incorporate effects of correlations. The coarsening of typical large clusters is described by the distribution $P_t\left(m\right)\sim 1/t^{y}f\left(m/t^z\right)$, with $y=2z$. All results are confirmed by simulation, which also illustrates the unusual features of cluster size distributions, with a power-law decay for small masses and a negatively skewed peak in the scaling region. The detachment rates considered here can apply in the presence of strong attractive interactions, and recent applications suggest that even more rapid rate decays are also physically realistic.

We report an unusual electroconvection in the nematic phase of a bent-core liquid crystal. In a voltage-frequency diagram, two frequency regions exhibiting prewavy stripe patterns were found, as reported by Wiant et al. We found that these stripes never show extinction dark when cells were rotated under crossed polarizers. Based on the color interchange in between neighboring stripes by the rotation of the cells or an analyzer, twisted molecular orientation is suggested; i.e., the directors are alternately twisted from the top to the bottom surfaces with a pretilt angle in adjacent stripes, which is an analogue of the twisted (splayed) structure observed in surface-stabilized ferroelectric liquid crystal cells. The transmittance spectra calculated using the $4\times 4$ matrix method from the model structure are consistent with the experimental observation.

In this paper, we will study theoretically and experimentally the anisotropy of the thermal diffusivity in nematic liquid crystals. We will show that the Baalss-Hess conformal transformation [D. Baalss and S. Hess, Phys. Rev. Lett. 57, 86 (1986)], can be used to obtain a free of adjustable parameters equation that describes the anisotropy of the heat diffusion in these materials. The results of this theory will be compared with experimental data. This study will partially confirm the widely known experimental evidences that indicate that the thermal diffusivity is larger in the director direction than in the one perpendicular to it. For calamitic nematic phases this is true; for discotic nematic ones the reverse situation would be found; the diffusivity would become larger in the direction perpendicular to the director. We will also present experimental data supporting this theoretical prediction.The data comprehend the calamitic and discotic nematic lyotropic phases and a nematic thermotropic phase.

We describe the relationship between the shape of the phase-resetting curve (PRC) and the degree of stochastic synchronization observed between a pair of uncoupled general oscillators receiving partially correlated Poisson inputs in addition to inputs from independent sources. We use perturbation methods to derive an expression relating the shape of the PRC to the probability density function (PDF) of the phase difference between the oscillators. We compute various measures of the degree of synchrony and cross correlation from the PDF’s and use the same to compare and contrast differently shaped PRCs, with respect to their ability to undergo stochastic synchronization. Since the shape of the PRC depends on underlying dynamical details of the oscillator system, we utilize the results obtained from the analysis of general oscillator systems to study specific models of neuronal oscillators. It is shown that the degree of stochastic synchronization is controlled both by the firing rate of the neuron and the membership of the PRC (type I or type II). It is also shown that the circular variance for the integrate and fire neuron and the generalized order parameter for a hippocampal interneuron model have a nonlinear relationship to the input correlation.

Formation and competition of associations are studied in a six-species ecological model where each species has two predators and two prey. Each site of a square lattice is occupied by an individual belonging to one of the six species. The evolution of the spatial distribution of species is governed by iterated invasions between the neighboring predator-prey pairs with species specific rates and by site exchange between the neutral pairs with a probability $X$. This dynamical rule yields the formation of five associations composed of two or three species with proper spatiotemporal patterns. For large $X$ a cyclic dominance can occur between the three two-species associations whereas one of the two three-species associations prevails in the whole system for low values of $X$ in the final state. Within an intermediate range of $X$ all the five associations coexist due to the fact that cyclic invasions between the two-species associations reduce their resistance temporarily against the invasion of three-species associations.

We derive an analytic formula for the lateral dynamics of solitons in a general inhomogeneous nonlinear media, and show that it can be valid over tens of diffraction lengths. In particular, we show that solitons centered at a lattice maximum can be “mathematically unstable” but “physically stable.” We also derive an analytic upper bound for the critical velocity for tunneling, which is valid even when the standard Peierls-Nabarro potential approach fails.

We investigate the distribution of magnetic fields around dense solid plasmas generated by intense $p$-polarized laser ($\sim {10}^{16}\text{W}{\text{cm}}^{-2}$, 100 fs) irradiation of magnetic tapes, using high sensitivity magneto-optical microscopy. By investigating the effect of irradiation on the magnetic tape, we present evidence for axial magnetic fields and map out the spatial distribution of these fields around the laser generated plasma. By using the axial magnetic field distribution as a diagnostic tool we uncover evidence for angular momentum associated with the plasma.

The discovery of community structure is a common challenge in the analysis of network data. Many methods have been proposed for finding community structure, but few have been proposed for determining whether the structure found is statistically significant or whether, conversely, it could have arisen purely as a result of chance. In this paper we show that the significance of community structure can be effectively quantified by measuring its robustness to small perturbations in network structure. We propose a suitable method for perturbing networks and a measure of the resulting change in community structure and use them to assess the significance of community structure in a variety of networks, both real and computer generated.

We present a microscopic derivation of self-consistent equations of Anderson localization in a disordered medium of finite size. The derivation leads to a renormalized, position-dependent diffusion coefficient. The position dependence of the latter is due to the position dependence of return probability in a bounded medium.

Using physical arguments, I derive the physically correct equations of motion for a classical charged particle from the Lorentz-Abraham-Dirac equations (LAD) which are well known to be physically incorrect. Since a charged particle can classically not be a point particle because of the Coulomb field divergence, my derivation allows for that by imposing a basic condition on the external force. That condition ensures that the particle’s finite size charge distribution appears as a point charge to the external force. Finite radius charge distributions are known not to lead to differential equations of motion. The present work is in agreement with the results by [H. Spohn, Europhys. Lett. 50, 287 (2000)] and by others. An example, uniform acceleration, demonstrates what the above basic condition entails. For clarity of the argument, I discuss the nonrelativistic case before the relativistic one.

The motion of solitons is studied in the Toda lattice with a local defect due to a change in coupling constants. We demonstrate that the generation of the trapped defect mode by the incident soliton is strongly suppressed under a certain condition. The effect is explained by the fact that, under this condition, the defect mode vanishes in the linear limit. In the same case, the soliton remains stable, traveling through a periodic array of defects; otherwise, it decays.

We examine a simple hard-disk fluid with no long-range interactions on the two-dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is frustrated, allowing us to construct a tractable, one-parameter model of disordered monodisperse hard disks. We extend free-area theory and the virial expansion to this regime, deriving the equation of state for the system, and compare its predictions with simulations near an isostatic packing in the curved space. Additionally, we investigate packing and dynamics on triply periodic, negatively curved surfaces with an eye toward real biological and polymeric systems.