We employ a time-domain method to compute the near field on a contour enclosing infinitely long cylinders of arbitrary cross section and constitution. We therefore recover the cylindrical Hankel coefficients of the expansion of the field outside the circumscribed circle of the structure. The recovered coefficients enable the wideband analysis of complex systems, e.g., the determination of the radar cross section becomes straightforward. The prescription for constructing such a numerical tool is provided in great detail. The method is validated by computing the scattering coefficients for a homogeneous circular cylinder illuminated by a plane wave, a problem for which an analytical solution exists. Finally, some radiation properties of an optical antenna are examined by employing the proposed technique.

Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and nonequilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first-order behaviors in two different classes of models: The first are generalized epidemic processes that describe in their spatially embedded version—either on or off a regular lattice—compact or fractal cluster growth in random media at zero temperature. A random graph version of these processes is mapped onto a model previously proposed for complex social contagion. We compute detailed phase diagrams and compare our numerical results at the tricritical point in $d=3$ with field theory predictions of Janssen et al. [Phys. Rev. E 70, 026114 (2004)]. The second class consists of exponential (“Hamiltonian,” i.e., formally equilibrium) random graph models and includes the Strauss and the two-star model, where “chemical potentials” control the densities of links, triangles, or two-stars. When the chemical potentials in either graph model are $\mathcal{O}\left(\log N\right)$, the percolation transition can coincide with a first-order phase transition in the density of links, making the former also discontinuous. Hysteresis loops can then be of mixed order, with second-order behavior for decreasing link fugacity, and a jump (first order) when it increases.

This paper illustrates how the tools of equilibrium statistical mechanics can help to describe a far-from-equilibrium problem: the jamming transition in frictionless granular materials. Edwards ideas consist of proposing a statistical ensemble of volume and stress fluctuations through the thermodynamic notion of entropy, compactivity, $X$, and angoricity, $A$ (two temperature-like variables). We find that Edwards thermodynamics is able to describe the jamming transition (J point) in frictionless packings. Using the ensemble formalism we elucidate the following: (i) We test the combined volume-stress ensemble by comparing the statistical properties of jammed configurations obtained by dynamics with those averaged over the ensemble of minima in the potential energy landscape as a test of ergodicity. Agreement between both methods supports the idea of ergodicity and “thermalization” at a given angoricity and compactivity. (ii) A microcanonical ensemble analysis supports the maximum entropy principle for grains. (iii) The intensive variables $A$ and $X$ describe the approach to jamming through a series of scaling relations as $A\to 0^{+}$ and $X\to 0^{-}$. Due to the force-strain coupling in the interparticle forces, the jamming transition is probed thermodynamically by a “jamming temperature” $T_{\mathrm{J}}$ composed of contributions from $A$ and $X$. (iv) The thermodynamic framework reveals the order of the jamming phase transition by showing the absence of critical fluctuations at jamming in static observables like pressure and volume, and we discuss other critical scenarios for the jamming transition. (v) Finally, we elaborate on a comparison with relevant studies by Gao, Blawzdziewicz, and O’Hern [Phys. Rev. E 74, 061304 (2006)], showing a breakdown of equiprobability of microstates obtained via fast quenches. A network analysis of the energy landscape reveals the origin of the inhomogeneities in the uneven distribution of the areas of the basins. Such inhomogeneities are also found in other out-of-equilibrium systems like Lennard-Jones glasses and their existence does not preclude the use of statistical mechanics for jammed systems.

We report experimental studies on small angle light scattering (SALS), and rheodielectric and electrorheological properties of a binary mixture of octyloxy cyanobiphenyl and hexyloxy cyanobiphenyl liquid crystals. The mixture exhibits nematic ($N$) to smectic-$A$ (Sm$A$) phase transitions, and then again to a reentrant nematic ($N_{\mathrm{R}}$) phase transition. Rapid shear thinning in the quenched samples in the low shear rate region in the $N$ and Sm$A$ phases observed from SALS experiments is attributed to the realignment of the director within the domains. The domains are elongated along the shear direction at higher shear rates. The temperature variation of the effective viscosity and static dielectric constant reveals the changes in the director orientation across $N$-Sm$A$-$N_{\mathrm{R}}$ phase transitions. At a steady shear rate the effective viscosity increases with the electric field in all the phases and saturates at much higher fields. It also exhibits two anomalous peaks across $N$-Sm$A$-$N_{\mathrm{R}}$ phase transitions beyond a particular field. The shear modulus of the Sm$A$ phase in an intermediate field is significantly larger than that measured at both low and high fields. This enhanced viscoelasticity of the Sm$A$ phase is argued to originate from the increased dislocation density.

The thermal mean-square displacement (MSD) of hydrogen in proteins and its associated hydration water is measured by neutron scattering experiments and used an indicator of protein function. The observed MSD as currently determined depends on the energy resolution width of the neutron scattering instrument employed. We propose a method for obtaining the intrinsic MSD of H in the proteins, one that is independent of the instrument resolution width. The intrinsic MSD is defined as the infinite time value of $\langle r^2\rangle$ that appears in the Debye-Waller factor. The method consists of fitting a model to the resolution broadened elastic incoherent structure factor or to the resolution dependent MSD. The model contains the intrinsic MSD, the instrument resolution width, and a rate constant characterizing the motions of H in the protein. The method is illustrated by obtaining the intrinsic MSD $\langle r^2\rangle$ of heparan sulphate (HS-0.4), ribonuclease A, and staphysloccal nuclase (SNase) from data in the literature.

To solve the combinatorial optimization problems, especially the minimal Vertex-cover problem with high efficiency, is a significant task in theoretical computer science and many other subjects. Aiming at detecting the solution space of Vertex-cover, a new structure named mutual-determination is defined and discovered for Vertex-cover on general graphs, which results in the emergence of strong correlations among the unfrozen nodes. Based on the backbones and mutual-determinations with node ranks by leaf removal, we propose a Mutual-determination and Backbone Evolution Algorithm to achieve the reduced solution graph, which provides a graphical expression of the solution space of Vertex-cover. By this algorithm, the whole solution space and detailed structures such as backbones can be obtained strictly when there is no leaf-removal core on the given graph. Compared with the current algorithms, the Mutual-determination and Backbone Evolution Algorithm performs as well as the replica symmetry one in a certain interval but has a small gap higher than the replica symmetric breaking one and has a relatively small error for the exact results. The algorithm with the mutual-determination provides a new viewpoint to solve Vertex-cover and understand the organizations of the solution spaces, and the reduced solution graph gives an alternative way to catch detailed information of the ground/steady states.

Renormalization-group operators are used to classify stochastic processes on two time scales. Repeated application of one operator is associated with the long-time behavior of the process while the other is associated with the short-time behavior of the process. This approach is shown to be robust even in the presence of nonstationary increments and infinite second moments. Fixed points of the operators can be used for further subclassification of processes when appropriate limits exist. Several processes are classified using the renormalization-group scheme. The processes to be classified include advection-diffusion in an ergodic velocity field, and a model of diffusion in the human bronchial tree.

The figure of merit for refrigerators performing finite-time Carnot-like cycles between two reservoirs at temperature $T_h$ and $T_c$ ($<T_h$) is optimized. It is found that the coefficient of performance at maximum figure of merit is bounded between 0 and $(\sqrt{9+8{\varepsilon }_c}-3)/2$ for the low-dissipation refrigerators, where ${\varepsilon }_c=T_c/(T_h-T_c)$ is the Carnot coefficient of performance for reversible refrigerators. These bounds can be reached for extremely asymmetric low-dissipation cases when the ratio between the dissipation constants of the processes in contact with the cold and hot reservoirs approaches to zero or infinity, respectively. The observed coefficients of performance for real refrigerators are located in the region between the lower and upper bounds, which is in good agreement with our theoretical estimation.

We study Seebeck effect in liquid electrolytes, starting from its simple neutral analog—thermodiffusion (so-called Ludwig-Soret or Soret effect). It is observed that when two or more subsystems of mobile particles are subjected to the temperature gradient, various types of them respond to it differently. In the case when these fractions, with different mobility parameters (Soret coefficients), are oppositely charged (a case typical for electrolytes), the nonhomogeneous internal electric field is generated. The latter field prevents these fractions from space separation and determines the intensity of the appearing Seebeck effect.

We study conformational transitions of a polymer on a simple-cubic lattice by calculating the zeros of the exact partition function, up to chain length 24. In the complex temperature plane, two loci of the partition function zeros are found for longer chains, suggesting the existence of both the coil-globule collapse transition and the melting-freezing transition. The locus corresponding to coil-globule transition clearly approaches the real axis as the chain length increases, and the transition temperature could be estimated by finite-size scaling. The form of the logarithmic correction to the scaling of the partition function zeros could also be obtained. The other locus does not show clear scaling behavior, but a supplementary analysis of the specific heat reveals a first-order-like pseudotransition.

The presence of noise can improve the response of certain nonlinear systems to input signals through the effects of stochastic resonance (SR). The optimal noise intensity for SR is proportional to the signal frequency if the signal is periodic, but proportional to the signal intensity if the signal is aperiodic. Here, we demonstrate using linear response theory that the optimal noise intensity for SR is necessarily dependent on the signal intensity even if the signal is periodic. We also demonstrate that the SR curves grow according to the signal intensity from a bell-shaped curve to a plateau, resulting in the emergence of SR without tuning. In particular, we present a theoretical analysis indicating that the SR peak shifts with the signal intensity due to the scaling of the stationary neuronal firings. The growth of SR may serve as a useful design principle for many noise-exploiting applications.

Athermal random fiber networks are usually modeled by representing each fiber as a truss, a Euler-Bernoulli or a Timoshenko beam, and, in the case of cross-linked networks, each cross-link as a pinned, rotating, or welded joint. In this work we study the effect of these various modeling options on the dependence of the overall network stiffness on system parameters. We conclude that Timoshenko beams can be used for the entire range of density and beam stiffness parameters, while the Euler-Bernoulli model can be used only at relatively low network densities. In the high density-high bending stiffness range, strain energy is stored predominantly in the axial and shear deformation modes, while in the other extreme range of parameters, the energy is stored in the bending mode. The effect of the model size on the network stiffness is also discussed.

We experimentally investigate the self-propelled two-dimensional turbulent flows of Escherichia coli suspensions in thin liquid films at two different cell concentrations. It is found that the flow has fluctuating vortices with a broad range of scales and intensities through the nonlinear interaction of the swimming bacteria. Increasing cell concentration increases the total propelling power and the nonlinear interaction. It causes the generation of vortices with larger scale, lower frequency, and higher intensity. It also widens the histograms of the flow velocity and the velocity increment between two spatially separated points with more stretched non-Gaussian tails. From the scaling analysis of the structure function $S_q\left(r\right)$ of the $q$th moment of the velocity increment between two points with spatial separation $r$, nonlinear relations between the scaling exponent ${\zeta }_q$ of $S_q\left(r\right)$ and $q$ are found for both cell concentrations, which manifests the multifractal dynamics. The multifractality can be enhanced by increasing cell concentration.

In an all-to-all network of integrate-and-fire neurons in which there is a disorder in the intrinsic oscillatory frequencies of the neurons, we show that through spike-timing-dependent plasticity the synapses which have the high-frequency neurons as presynaptic tend to be potentiated while the links originated from the low-frequency neurons are weakened. The emergent effective flow of directed connections introduces the high-frequency neurons as the more influential elements in the network and facilitates synchronization by decreasing the synaptic cost for onset of synchronization.

A generic history-penalized metabasin escape algorithm that contains no predetermined parameters is presented in this work. The spatial location and volume of imposed penalty functions in the configurational space are determined in self-learning processes as the 3$N$-dimensional potential energy surface is sampled. The computational efficiency is demonstrated using a binary Lennard-Jones liquid supercooled below the glass transition temperature, which shows an $O$(10${}^3$) reduction in the quadratic scaling coefficient of the overall computational cost as compared to the previous algorithm implementation. Furthermore, the metabasin sizes of supercooled liquids are obtained as a natural consequence of determining the self-learned penalty function width distributions. In the case of a bulk binary Lennard-Jones liquid at a fixed density of 1.2, typical metabasins are found to contain about 148 particles while having a correlation length of 3.09 when the system temperature drops below the glass transition temperature.

We present some exact results for branching and annihilating random walks. We compute the nonuniversal threshold value of the annihilation rate for having a phase transition in the simplest reaction-diffusion system belonging to the directed percolation universality class. Also, we show that the accepted scenario for the appearance of a phase transition in the parity conserving universality class must be improved. In order to obtain these results we perform an expansion in the branching rate around pure annihilation, a theory without branching. This expansion is possible because we manage to solve pure annihilation exactly in any dimension.

Biomolecular motors can pull and viscously drag membranes. The resulting elongations include cell protrusions, tether networks, and sensorial tentacles. Here we focus on the extraction of a single tube from a vesicle. Via a force balance coupled to binding kinetics, we analytically determine the phase diagram of tube formation as function of the motor processivity, the surface viscosity of the membrane ${\eta }_m^{\prime }$, and the density of motors on the vesicle $\rho$. Three tubulation mechanisms are identified: (i) tip pulling, due to the accumulation of motors at the leading edge of the membrane, (ii) viscous drag, emergent from the translation of motors along the tube, and (iii) hybrid extraction, such that tip pulling and viscous drag are equally important. For experimental values of ${\eta }_m^{\prime }$ and $\rho$, we find that the growth of bionanotubes tends to be driven by viscous forces, whereas artificial membranes are dominated by tip pulling.

We investigate the multichain version of the chemical master equation, when there are transitions between different states inside the long chains, as well as transitions between (a few) different chains. In the discrete version, such a model can describe the connected diffusion processes with jumps between different types. We apply the Hamilton-Jacobi equation to solve some aspects of the model. We derive exact (in the limit of infinite number of particles) results for the dynamic of the maximum of the distribution and the variance of distribution.

We discuss a schematic model of mode-coupling theory for force-driven active nonlinear microrheology, where a single probe particle is pulled by a constant external force through a dense host medium. The model exhibits both a glass transition for the host and a force-induced delocalization transition, where an initially localized probe inside the glassy host attains a nonvanishing steady-state velocity by locally melting the glass. Asymptotic expressions for the transient density correlation functions of the schematic model are derived, valid close to the transition points. There appear several nontrivial time scales relevant for the decay laws of the correlators. For the nonlinear friction coefficient of the probe, the asymptotic expressions cause various regimes of power-law variation with the external force, and two-parameter scaling laws.

Molecular dynamic simulations of a strongly inhomogeneous system reveals that a single-component soft-sphere fluid can behave as a fragile glass former due to confinement. The self-intermediate scattering function, $F_s(k,t)$, of a Lennard-Jones fluid confined in slit-shaped pores, which can accomodate two to four fluid layers, exhibits a two-step relaxation at moderate temperatures. The mean-squared displacement data are found to follow time-temperature superposition and both the self-diffusivity and late $\alpha$ relaxation times exhibit power-law divergences as the fluid is cooled. The system possesses a crossover temperature and follows the scalings of mode coupling theory for the glass transition. The temperature dependence of the self-diffusivity can be expressed using the Vogel-Fulcher-Tammann equation, and estimates of the fragility index of the system indicates a fragile glass former. At lower temperatures, signatures of additional relaxation processes are observed in the various dynamical quantities with a three-step relaxation observed in the $F_s(k,t)$.