The orientational order in a nematic liquid crystal sample confined to an annular region between two concentric cylinders is investigated by means of lattice Monte Carlo simulations. Strong anchoring and homeotropic orientations, parallel to the radial direction, are implemented at the confining surfaces. The elastic anisotropy is taken into account in the bulk interactions by using the pair potential introduced by Gruhn and Hess [T. Gruhn and S. Hess, Z. Naturforsch. A 51, 1 (1996)] and parametrized by Romano and Luckhurst [S. Romano, Int. J. Mod. Phys. B 12, 2305 (1998); Phys. Lett. A 302, 203 (2002); G. R. Luckhurst and S. Romano, Liq. Cryst. 26, 871 (1999)], i.e., the so-called GHRL potential. In the case of equal elastic constants, a small but appreciable deformation along the cylinder axis direction is observed, whereas when the values of $K_{11}/K_{33}$ if $K_{22}=K_{33}$ are low enough, all the spins in the bulk follow the orientation imposed by the surfaces. For larger values of $K_{11}/K_{33}$, spontaneous deformations, perpendicular to the polar plane, increase significantly. Our findings indicate that the onset of these deformations also depends on the ratio $K_{22}/K_{33}$ and on the radius of the cylindrical surfaces. Although expected from the elastic theory, no tangential component of the deformations was observed in the simulations for the set of parameters analyzed.

Motivated by single molecule experiments, we study thermal unfolding pathways of four proteins, chymotrypsin inhibitor, barnase, ubiquitin, and adenylate kinase, using bond network models that combine bond energies and elasticity. The protein elasticity is described by the Gaussian network model (GNM), to which we add prescribed bond binding energies that are assigned to all (nonbackbone) connecting bonds in the GNM of native state and assumed identical for simplicity. Using exact calculation of the Helmholtz free energy for this model, we consider bond rupture single events. The bond designated for rupture is chosen by minimizing the free-energy difference for the process, over all (nonbackbone) bonds in the network. Plotting the free-energy profile along this pathway at different temperatures, we observe a few major partial unfolding, metastable or stable, states, that are separated by free-energy barriers and change role as the temperature is raised. In particular, for adenylate kinase we find three major partial unfolding states, which is consistent with single molecule FRET experiments [Pirchi et al., Nat. Commun. 2, 493 (2011)] for which hidden Markov analysis reveals between three and five such states. Such states can play a major role in enzymatic activity.

Many single-molecule experiments for molecular motors comprise not only the motor but also large probe particles coupled to it. The theoretical analysis of these assays, however, often takes into account only the degrees of freedom representing the motor. We present a coarse-graining method that maps a model comprising two coupled degrees of freedom which represent motor and probe particle to such an effective one-particle model by eliminating the dynamics of the probe particle in a thermodynamically and dynamically consistent way. The coarse-grained rates obey a local detailed balance condition and reproduce the net currents. Moreover, the average entropy production as well as the thermodynamic efficiency is invariant under this coarse-graining procedure. Our analysis reveals that only by assuming unrealistically fast probe particles, the coarse-grained transition rates coincide with the transition rates of the traditionally used one-particle motor models. Additionally, we find that for multicyclic motors the stall force can depend on the probe size. We apply this coarse-graining method to specific case studies of the ${\text{F}}_1$-ATPase and the kinesin motor.

The effects of network topology on the emergence and persistence of infectious diseases have been broadly explored in recent years. However, the influence of the vital dynamics of the hosts (i.e., birth-death processes) on the network structure, and their effects on the pattern of epidemics, have received less attention in the scientific community. Here, we study Susceptible-Infected-Recovered(-Susceptible) [SIR(S)] contact processes in standard networks (of Erdös-Rényi and Barabási-Albert type) that are subject to host demography. Accounting for the vital dynamics of hosts is far from trivial, and it causes the scale-free networks to lose their characteristic fat-tailed degree distribution. We introduce a broad class of models that integrate the birth and death of individuals (nodes) with the simplest mechanisms of infection and recovery, thus generating age-degree structured networks of hosts that interact in a complex manner. In our models, the epidemiological state of each individual may depend both on the number of contacts (which changes through time because of the birth-death process) and on its age, paving the way for a possible age-dependent description of contagion and recovery processes. We study how the proportion of infected individuals scales with the number of contacts among them. Rather unexpectedly, we discover that the result of highly connected individuals at the highest risk of infection is not as general as commonly believed. In infections that confer permanent immunity to individuals of vital populations (SIR processes), the nodes that are most likely to be infected are those with intermediate degrees. Our age-degree structured models allow such findings to be deeply analyzed and interpreted, and they may aid in the development of effective prevention policies.

Very recently, a first-order phase transition, named explosive synchronization (ES), has attracted great attention due to its remarkable novelty in theory and significant impact in applications. However, so far, all observations of ES have been associated with various correlation constraints on system parameters, which restrict its generality and applications. Here we consider heterogeneous networks around Hopf bifurcation point described by chemical reaction-diffusion systems and also by their reduced order parameter versions, the complex Ginzburg-Landau equations, and demonstrate that explosive synchronization can appear as an emergent feature of oscillatory networks, and the restrictions on specific parameter correlations used so far for ES can be lifted entirely. Theoretical analyses and numerical simulations show with a perfect agreement that explosive synchronization can appear in networks with nodes having identical natural frequencies, and necessary correlation conditions for ES can be realized in a self-organized manner by network evolution.

Application to a chaotic erbium-doped fiber laser of the digital encoding technique by control of its emitted symbolic dynamics is numerically tested. Criteria to select the better working conditions and the perturbation to be introduced in any control parameter are proposed. Once they are chosen, the procedure to prepare the system for control and the way to carry it out are described. It is shown that the general method cannot be blindly applied, but it must be adapted to the particular case under analysis for a good performance. Finally, in relation to a possible experimental implementation, influence of noise in the bit error rate of the communication system is discussed.

We study the interplay between network topology and complex space-time patterns and introduce a concept to analytically predict complex patterns in networks of Stuart-Landau oscillators with linear symmetric and instantaneous coupling based solely on the network topology. These patterns consist of partial amplitude death and partial synchronization and are found to exist in large variety for all undirected networks of up to 5 nodes. The underlying concept is proved to be robust with respect to frequency mismatch and can also be extended to larger networks. In addition it directly links the stability of complete in-phase synchronization to only a small subset of topological eigenvalues of a network.

In this article we consider the complete set of synchronized and phase-locked states available to pairs of hydrodynamically coupled colloidal rotors, consisting of spherical beads driven about circular paths in the same, and in opposing senses. Oscillators such as these have previously been used as coarse grained, minimal models of beating cilia. Two mechanisms are known to be important in establishing synchrony. The first involves perturbation of the driving force, and the second involves deformation of the rotor trajectory. We demonstrate that these mechanisms are of similar strength, in the regime of interest, and interact to determine observed behavior. Combining analysis and simulation with experiments performed using holographic optical tweezers, we show how varying the amplitude of the driving force perturbation leads to a transition from synchronized to phase-locked states. Analogies with biological systems are discussed, as are implications for the design of biomimetic devices.

The ability to trap or deflect sliding drops is of great interest in microfluidics, as it has several technological applications, ranging from self-cleaning and fog harvesting surfaces to laboratory-on-a-chip devices. We present a three-dimensional numerical model that describes sliding droplets interacting with wetting defects of variable strength and size. This approach provides relevant insight if compared to simplified analytic models, as it allows us to assess the relevance of the internal degrees of freedom of the droplet. We observe that the deformation of the drop enhances the effective strength and range of the defect, and we quantify this effect by comparison to a point-mass model. We also analyze the role of the steepness and strength of the defect on the drop motion, observing that small, strong defects are more effective at trapping than large, shallow traps of same excess surface energy. Finally, our results show quantitative agreement with previously reported electrowetting experiments, suggesting a universal behavior in droplet trapping that does not depend strongly on the nature of the defect.

The excess free energy of a molecular cluster is a key quantity in models of the nucleation of droplets from a metastable vapor phase; it is often viewed as the free energy arising from the presence of an interface between the two phases. We show how this quantity can be extracted from simulations of the mechanical disassembly of a cluster using guide particles in molecular dynamics. We disassemble clusters ranging in size from 5 to 27 argonlike Lennard-Jones atoms, thermalized at 60 K, and obtain excess free energies, by means of the Jarzynski equality, that are consistent with previous studies. We only simulate the cluster of interest, in contrast to approaches that require a series of comparisons to be made between clusters differing in size by one molecule. We discuss the advantages and disadvantages of the scheme and how it might be applied to more complex systems.

A meshless lattice Boltzmann numerical method is proposed. The collision and streaming operators of the lattice Boltzmann equation are separated, as in the usual lattice Boltzmann models. While the purely local collision equation remains the same, we rewrite the streaming equation as a pure advection equation and discretize the resulting partial differential equation using the Lax-Wendroff scheme in time and the meshless local Petrov-Galerkin scheme based on augmented radial basis functions in space. The meshless feature of the proposed method makes it a more powerful lattice Boltzmann solver, especially for cases in which using meshes introduces significant numerical errors into the solution, or when improving the mesh quality is a complex and time-consuming process. Three well-known benchmark fluid flow problems, namely the plane Couette flow, the circular Couette flow, and the impulsively started cylinder flow, are simulated for the validation of the proposed method. Excellent agreement with analytical solutions or with previous experimental and numerical results in the literature is observed in all the simulations. Although the computational resources required for the meshless method per node are higher compared to that of the standard lattice Boltzmann method, it is shown that for cases in which the total number of nodes is significantly reduced, the present method actually outperforms the standard lattice Boltzmann method.

In a recent paper by D. Dantchev, J. Bergknoff, and J. Rudnick [Phys. Rev. E 89, 042116 (2014)], the problem of the Casimir force in the $\mathrm{O}\left(n\right)$ model on a slab with free boundary conditions, investigated earlier by us [Europhys. Lett. 100, 10004 (2012)], is reconsidered using a mean-spherical model with separate constraints for each layer. The authors (i) question the applicability of the Ginzburg-Landau-Wilson approach to the low-temperature regime, arguing for the superiority of their model compared to the family of ${\varphi }^4$ models $A$ and $B$ whose numerically exact solutions we determined both for values of the coupling constant $0<g<\infty$ and for $g=\infty$. They (ii) report consistency of their results with ours in the critical region and a strong manifestation of universality but (iii) point out discrepancies with our results in the region below $T_c$. Here we refute (i) and prove that our model $B$ with $g=\infty$ is identical to their spherical model. Hence evidence for the reported universality is already contained in our paper. Moreover, the results we determined for anyone of the models $A$ and $B$ for various thicknesses $L$ are all numerically exact. (iii) is due to their misinterpretation of our results for the scaling limit. We also show that their low-temperature expansion, which does not hold inside the scaling regime, is limited to temperatures lower than they anticipated.

The preceding Comment raises a few points concerning our paper [Phys. Rev. E 89, 042116 (2014)]. In this Reply we stress that although Diehl et al. [Europhys. Lett. 100, 10004 (2012) and Phys. Rev. E 89, 062123 (2014)] use three different models to study the Casimir force for the $\mathrm{O}(n\to \infty )$ model with free boundary conditions we study a single model over the entire range of temperatures from above the bulk critical temperature $T_c$ to absolute temperatures down to $T=0$. The use of a single model renders more transparent the crossover from effects dominated by critical fluctuations in the vicinity of the bulk transition temperature to effects controlled by Goldstone modes at low temperatures. Contrary to the assertion in the Comment, we make no claim for the superiority of our model over any of those considered by Diehl et al. [Europhys. Lett. 100, 10004 (2012) and Phys. Rev. E 89, 062123 (2014)]. We also present additional evidence supporting our conclusion in Dantchev et al. [Phys. Rev. E 89, 042116 (2014)] that the temperature range in which our low-temperature analytical expansion for the Casimir force increases as $L$ grows and remains accurate for values of the ratio $T/T_c$ that become closer and closer to unity, whereas $T$ remains well outside of the critical region.

We show that the presence of a Coriolis force in a rotating linear lattice imposes a nonreciprocal propagation of the phononic heat carriers. Using this effect we propose the concept of Coriolis linear thermal circulator which can control the circulation of a heat current. A simple model of three coupled harmonic masses on a rotating platform permits us to demonstrate giant circulating rectification effects for moderate values of the angular velocities of the platform.

We investigate numerically the mechanisms governing horizontal dragging of a rigid cylinder buried inside granular matter, with particular emphasis on enumerating drag and lift forces that resist cylinder movement. The recently proposed particle finite element method is employed, which combines the robustness of classical continuum mechanics formulations in terms of representing complex aspects of the material constitutive behavior, with the effectiveness of discrete element methods in simulating ultralarge deformation problems. The investigation focuses on the effect of embedment depth, cylinder roughness, granular matter macromechanical properties, and of the magnitude of the cylinder's horizontal displacement on the amplitude of the resisting forces, which are discussed in light of published experimental data. Interpretation of the results provides insight on how the material flow around the cylinder affects the developing resistance, and a mechanism is proposed to describe the development of a steady-state drag force at large horizontal movements of the cylinder.

The fast lubrication dynamics method is applied to simulate the motion and deposition of charge-stabilized 100-nm-diam particles into sediment films from aqueous dispersions. Colloidal interactions are incorporated with a Yukawa potential and the effects of the screened-Coulomb potential strength and Péclet number (which controls the sedimentation driving force) on particle orientation are quantified with a sixfold bond order parameter. The effect of sediment growth rate on the order parameter is determined and related to a competition between the electrostatic interaction strength and sedimentation driving force. Increasing the electrostatic interaction strength and decreasing the Péclet number lead to lower sediment growth rates and consequently greater sixfold bond order. Our work demonstrates the feasibility of including lubrication interactions in dynamic simulations of sediment films and suggests that these interactions play a central role in the kinetics of film microstructure development and consequently in the degree of order within the film.

Transitions in the qualitative behavior of chemical reaction dynamics with a decrease in molecule number have attracted much attention. Here, a method based on a Markov process with a tridiagonal transition matrix is applied to the analysis of this transition in reaction dynamics. The transition to bistability due to the small-number effect and the mean switching time between the bistable states are analytically calculated in agreement with numerical simulations. In addition, a novel transition involving the reversal of the chemical reaction flow is found in the model under an external flow, and also in a three-component model. The generality of this transition and its correspondence to biological phenomena are also discussed.

We examine the existence and properties of charge flipping vortices (CFVs), vortices which periodically flip the topological charge, in three-site (trimer) and six-site (hexamer) discrete nonlinear Schrödinger lattices. We demonstrate numerically that CFVs exist as exact quasiperiodic solutions in continuous families which connect two different stationary solutions without topological charge, and that it is possible to interpret the dynamics of certain CFVs as the result of perturbations of these stationary solutions. The CFVs are calculated with high numerical accuracy and we may therefore accurately determine many of their properties, such as their energy and linear stability, and the CFVs are found to be stable over large parameter regimes. We also show that, like in earlier studies for lattices with a multiple of four sites, trimer and hexamer CFVs can be obtained by perturbing stationary constant amplitude vortices with certain linear eigenmodes. However, in contrast to the former case where the perturbation could be infinitesimal, the magnitude of the perturbations for trimers and hexamers must overcome a quite large threshold value. These CFVs may be interpreted as exact quasiperiodic CFVs, with a small perturbation applied. The concept of a charge flipping energy barrier is introduced and discussed.