This paper describes the construction of equilibrium configurations for smectic-$A$ liquid crystals subjected to nonuniform physical boundary conditions, with two-dimensional dependence on the director and layer normal, and a nonlinear layer function. Euler-Lagrange equations are constructed that describe key properties of liquid crystals confined between two boundaries exhibiting spatial imperfections. The results of the model are shown to be consistent with previous published findings in simple domains while results are obtained on how the structure of the liquid crystals changes in response to boundary perturbations. Domain sizes are considered representing those currently used in applications while predictions in smaller domains at the limit of current technologies are also made. In particular, it is shown that the curvature along a boundary impacts on the liquid crystal's structure distant from the boundary feature and therefore previously developed mathematical models, that essentially reduced the problem to a single spatial dimension, cannot be used in such circumstances. Consequences for practical applications are briefly discussed.

With materials of anisotropic electrical conductivity, it is possible to generate a dynamo with a simple velocity field, of the type precluded by Cowling's theorems with isotropic materials. Following a previous study by Ruderman and Ruzmaikin [M. S. Ruderman and A. A. Ruzmaikin, Magnetic field generation in an anisotropically conducting fluid, Geophys. Astrophys. Fluid Dyn. 28, 77 (1984)], who considered the dynamo effect induced by a uniform shear flow, we determine the conditions for the dynamo threshold when a solid plate is sliding over another one, both with anisotropic electrical conductivity. We obtain numerical solutions for a general class of anisotropy and obtain the conditions for the lowest magnetic Reynolds number, using a collocation Chebyshev method. In a particular geometry of anisotropy and wave number, we also derive an analytical solution, where the eigenvectors are just combinations of four exponential functions. An explicit analytical expression is obtained for the critical magnetic Reynolds number. Above the critical magnetic Reynolds number, we have also derived an analytical expression for the growth rate showing that this is a “very fast” dynamo, extrapolating on the “slow” and “fast” terminology introduced by Vainshtein and Zeldovich [S. I. Vainshtein and Y. B. Zeldovich, Reviews of topical problems: Origin of magnetic fields in astrophysics (turbulent “dynamo” mechanisms), Sov. Phys. Usp. 15, 159 (1972)].

We study dipolarly coupled three-dimensional spin systems in both the microcanonical and the canonical ensembles by introducing appropriate numerical methods to determine the microcanonical temperature and by realizing a canonical model of heat bath. In the microcanonical ensemble, we show the existence of a branch of stable antiferromagnetic states in the low-energy region. Other metastable ferromagnetic states exist in this region: by externally perturbing them, an effective negative specific heat is obtained. In the canonical ensemble, for low temperatures, the same metastable states are unstable and reach a new branch of more robust metastable states which is distinct from the stable one. Our statistical physics approach allows us to put some order in the complex structure of stable and metastable states of dipolar systems.

We investigate conformations and dynamics of a polymer considering its monomers to be active Brownian particles. This active polymer shows very intriguing physical behavior which is absent in an active Rouse chain. The chain initially shrinks with active force, which starts swelling on further increase in force. The shrinkage followed by swelling is attributed purely to excluded-volume interactions among the monomers. In the swelling regime, the chain shows a crossover from the self-avoiding behavior to the Rouse behavior with scaling exponent ${\nu }_a\approx 1/2$ for end-to-end distance. The nonmonotonicity in the structure is analyzed through various physical quantities; specifically, radial distribution function of monomers, scattering time, as well as various energy calculations. The chain relaxes faster than the Rouse chain in the intermediate force regime, with a crossover in variation of relaxation time at large active force as given by a power law ${\tau }_r\sim {\text{Pe}}^{-4/3}$ (Pe is Péclet number).

Hermitian operators with exact zero modes subject to non-Hermitian perturbations are considered. Specific focus is on the distribution of the former zero eigenvalues of the Hermitian operators. The broadening of these zero modes is found to follow an elliptic Gaussian random matrix ensemble of fixed size, where the symmetry class of the perturbation determines the behavior of the modes. This distribution follows from a central limit theorem of matrices and is shown to be robust to deformations.

We report intermittent large spiking events in a heterogeneous network of forced Josephson junctions under the influence of repulsive interaction. The response of the individual junctions has been inspected instead of the collective response of the ensemble, which reveals the large spiking events in a subpopulation with characteristic features of extreme events (EE). The network splits into three clusters of junctions, one in coherent libration, one in incoherent rotational motion, and another subpopulation originating EE, which resembles a chimeralike pattern. EE migrates spatially from one to another subpopulation of junctions with the repulsive strength. The origin of EE in a subpopulation and chimera pattern is a generic effect of distributed damping parameter and repulsive interaction, which we verify with another network of the Liénard system. EE originates in the subpopulation via a local riddling of in-phase synchronization. The probability density function of event heights confirms the rare occurrence of large events and the return time of EE as expressed by interevent intervals in the subgroup follows a Poisson distribution. The mechanism of the origin of such a unique clustering is explained qualitatively.

Following the paper exploring the Anderson localization of monochromatically perturbed kicked quantum maps [Phys. Rev. E 97, 012210 (2018)], the delocalization-localization transition phenomena in polychromatically perturbed quantum maps (QM) is investigated focusing particularly on the dependency of critical phenomena on the number $M$ of the harmonic perturbations, where $M+1=d$ corresponds to the spatial dimension of the ordinary disordered lattice. The standard map and the Anderson map are treated and compared. As the basis of analysis, we apply the self-consistent theory (SCT) of the localization for our systems, taking a plausible hypothesis on the mean-free-path parameter which worked successfully in the analyses of the monochromatically perturbed QMs. We compare in detail the numerical results with the predictions of the SCT by largely increasing $M$. The numerically obtained index of critical subdiffusion $t^{\alpha }$ ($t$:time) agrees well with the prediction of one-parameter scaling theory $\alpha =2/(M+1)$, but the numerically obtained critical exponent of localization length significantly deviates from the SCT prediction. Deviation from the SCT prediction is drastic for the critical perturbation strength of the transition: If $M$ is fixed, then the SCT presents plausible prediction for the parameter dependence of the critical value, but its value is $1/(M-1)$ times smaller than the SCT prediction, which implies existence of a strong cooperativity of the harmonic perturbations with the main mode.

Lies can have a negating impact on governments, companies, and the society as a whole. Understanding the dynamics of lying is therefore of crucial importance across different fields of research. While lying has been studied before in well-mixed populations, it is a fact that real interactions are rarely well-mixed. Indeed, they are usually structured and thus best described by networks. Here we therefore use the Monte Carlo method to study the evolution of lying in the sender-receiver game in a one-parameter family of networks, systematically covering complete networks, small-world networks, and one-dimensional rings. We show that lies that benefit the sender at a cost to the receiver, the so-called black lies, are less likely to proliferate on networks than they do in well-mixed populations. Honesty is thus more likely to evolve, but only when the benefit for the sender is smaller than the cost for the receiver. Moreover, this effect is particularly strong in small-world networks, but less so in the one-dimensional ring. For lies that favor the receiver at a cost to the sender, the so-called altruistic white lies, we show that honesty is also more likely to evolve than it is in well-mixed populations. But contrary to black lies, this effect is more expressed in the one-dimensional ring, whereas in small-world networks it is present only when the cost to the sender is greater than the benefit for the receiver. Last, for lies that benefit both the sender and the receiver, the so-called Pareto white lies, we show that the network structure actually favors the evolution of lying, but this only occurs when the benefit for the sender is slightly greater than the benefit for the receiver. In this case again the small-world topology acts as an amplifier of the effect, while other network topologies fail to do the same. In addition to these main results we discuss several other findings, which together show clearly that the structure of interactions and the overall topology of the network critically determine the dynamics of lying.

Cofilin and ADF are cytoskeleton remodeling proteins that cooperatively bind and fragment actin filaments. Bound cofilin molecules do not directly interact with each other, indicating that cooperative binding of cofilin is mediated by the actin filament lattice. Cofilactin is therefore a model system for studying allosteric regulation of self-assembly. How cofilin binding changes structural and mechanical properties of actin filaments is well established. Less is known about the interaction energies and the thermodynamics of filament fragmentation, which describes the collective manner in which the cofilin concentration controls mean actin filament length. Here, we provide a general thermodynamic framework for allosteric regulation of self-assembly, and we use the theory to predict the interaction energies of experimental actin filament length distributions over a broad range of cofilin binding densities and for multiple cofilactin variants. We find that bound cofilin induces changes in nearby actin-actin interactions, and that these allosteric effects are propagated along the filament to affect up to four neighboring cofilin-binding sites (i.e., beyond nearest-neighbor allostery). The model also predicts that cofilin differentially stabilizes and destabilizes longitudinal versus lateral actin-actin interactions, and that the magnitude, range, asymmetry, and even the sign of these interaction energies can be altered using different actin and cofilin mutational variants. These results demonstrate that the theoretical framework presented here can provide quantitative thermodynamic information governing cooperative protein binding and filament length regulation, thus revealing nanometer length-scale interactions from micron length-scale “wet-lab” measurements.

In superionic compounds one component premelts, providing high ionic conductivity to solid-state electrolytes. Here we find sublattice melting in colloidal crystals of oppositely charged particles that are highly asymmetric in size and charge in salt solutions. The small particles in ionic compounds melt when the temperature increases, forming a superionic phase. These delocalized small particles in a crystal of large oppositely charged particles, in contrast to superionic phases in atomic systems, form crystals with nonelectroneutral stoichiometric ratios. This generates structures with multiple domains of ionic crystals in percolated superionic phases with adjustable stoichiometries.

A computational technique was developed to simulate wettable particles trapped at a fluid-fluid interface under gravity. The proposed technique combines the improved smoothed profile-lattice Boltzmann method (iSP-LBM) for the treatment of moving solid-fluid boundaries and the free-energy LBM for the description of isodensity immiscible two-phase flows. We considered five benchmark problems in two-dimensional systems, including a stationary drop, a wettable particle trapped at a fluid-fluid interface in the absence or presence of gravity, two freely moving particles at a fluid-fluid interface in the presence of gravity (i.e., capillary floatation forces), and two vertically constrained particles at a fluid-fluid interface (i.e., capillary immersion forces). The simulation results agreed well with theoretical estimations, demonstrating the efficacy of the proposed technique.

We study the sandpile model on three-dimensional spanning Ising clusters with the temperature $T$ treated as the control parameter. By analyzing the three-dimensional avalanches and their two-dimensional projections (which show scale-invariant behavior for all temperatures), we uncover two universality classes with different exponents (an ordinary BTW class, and ${\mathrm{SOC}}_{T=\infty }$), along with a tricritical point (at $T_c$, the critical temperature of the host) between them. The transition between these two criticalities is induced by the transition in the support. The ${\mathrm{SOC}}_{T=\infty }$ universality class is characterized by the exponent of the avalanche size distribution ${\tau }^{T=\infty }=1.27\pm 0.03$, consistent with the exponent of the size distribution of the Barkhausen avalanches in amorphous ferromagnets Durin and Zapperi [Phys. Rev. Lett. 84, 4705 (2000)]. The tricritical point is characterized by its own critical exponents. In addition to the avalanche exponents, some other quantities like the average height, the spanning avalanche probability (SAP), and the average coordination number of the Ising clusters change significantly the behavior at this point, and also exhibit power-law behavior in terms of $\epsilon \equiv \frac{T-T_c}{T_c}$, defining further critical exponents. Importantly, the finite-size analysis for the activity (number of topplings) per site shows the scaling behavior with exponents $\beta =0.19\pm 0.02$ and $\nu =0.75\pm 0.05$. A similar behavior is also seen for the SAP and the average avalanche height. The fractal dimension of the external perimeter of the two-dimensional projections of avalanches is shown to be robust against $T$ with the numerical value $D_f=1.25\pm 0.01$.

Phase coherence is an important measure in nonlinear science. Whereas there is no generally accepted definition for phase and therefore for phase coherence, many works associate this feature with topological aspects of the systems, such as having a well-defined rotating center. Given the relevance of this concept for synchronization problems, one aim of this paper is to argue by means of a couple of counterexamples that phase coherence is not related to the topology of the attractor. A second aim is to introduce a phase-coherence measure based on recurrence plots, for which probabilities of recurrences for two different trajectories are similar for a phase-coherent system and dissimilar for non-phase-coherent systems. The measure does not require a phase variable defined a priori.

One-dimensional localized sequences of bound (coupled) traveling pulses, wave trains with a finite number of pulses, are described in a piecewise-linear reaction-diffusion system of the FitzHugh-Nagumo type with linear cross-diffusion terms of opposite signs. The simplest case of two bound pulses, the paired-pulse waves (pulse pairs), is solved analytically. The solutions contain oscillatory tails in the wave profiles so that the pulse pairs consist of a double-peak core and wavy edges. Several pulse pairs with different profile shapes and propagation speeds can appear for the same parameter values of the model when the cross diffusion is dominant. The more general case of many bound pulses, multipulse waves, is studied numerically. It is shown that, dependent on the values of the cross-diffusion coefficients, the multipulse waves upon collision can pass through one another with unchanged size and shape, exhibiting soliton behavior. Moreover, multipulse collisions with the system boundaries can generate a rich variety of wave transformations: the transition from the multipulse waves to pulse-front waves and further to simple fronts or to annihilation as well the transition to solitary pulses or to multipulse waves with lower numbers of pulses. Analytical and numerical results for the pulse pairs agree well with each other.

The nucleoprotein filament (NPF) is the fundamental element of homologous recombination (HR), a major mechanism for the repair of double-strand DNA breaks in the cell. The NPF is made of the damaged DNA strand surrounded by recombinase proteins, and its sensitivity to base-pairing mismatches is a crucial feature that guarantees the fidelity of the repair. The concurrent recombinases are also essential for several steps of HR. In this work, we used torque-sensitive magnetic tweezers to probe and apply mechanical constraints to single nucleoprotein filaments (NPFs). We demonstrated that the NPF undergoes structural transitions from a stretched to a compact state, and we measured the corresponding mechanochemical signatures. Using an active two-state model, we proposed a free-energy landscape for the NPF transition. Using this quantitative model, we explained both how the sensitivity of the NPF to the homology length is regulated by its structural transition and how the cooperativity of Rad51 favors selectivity to relatively long homologous sequences.

We report on the enhancement of the hydrodynamic damping of gravity waves at the surface of a fluid layer as they interact with a turbulent vortex flow in a sloshing experiment. Gravity surface waves are excited by oscillating horizontally a square container holding our working fluid (water). At the bottom of the container, four impellers in a quadrupole configuration generate a vortex array at moderate to high Reynolds number, which interact with the wave. We measure the surface fluctuations using different optical nonintrusive methods and the local velocity of the flow. In our experimental range, we show that as we increase the angular velocity of the impellers, the gravity wave amplitude decreases without changing the oscillation frequency or generating transverse modes. This wave dissipation enhancement is contrasted with the increase of the turbulent velocity fluctuations from particle image velocimetry measurements via a turbulent viscosity. To rationalize the damping enhancement a periodically forced shallow water model including viscous terms is presented, which is used to calculate the sloshing wave resonance curve. The enhanced viscous dissipation coefficient is found to scale linearly with the measured turbulent viscosity. Hence, the proposed scheme is a good candidate as an active surface gravity wave dampener via vortex flow reconfiguration.

We find the moment generating function (mgf) of the nonequilibrium work for open systems undergoing a thermal process, i.e., when the stochastic dynamics maps thermal states into time-dependent thermal states. The mgf is given in terms of a temperaturelike scalar satisfying a first-order ordinary differential equation. We apply the result to some paradigmatic situations: a levitated nanoparticle in a breathing optical trap, a Brownian particle in a box with a moving piston, and a two-state system driven by an external field, where the work mgfs are obtained for different timescales and compared with Monte Carlo simulations.

Detrended fluctuation analysis (DFA) is one of the most widely used tools for the detection of long-range dependence in time series. Although DFA has found many interesting applications and has been shown to be one of the best performing detrending methods, its probabilistic foundations are still unclear. In this paper, we study probabilistic properties of DFA for Gaussian processes. Our main attention is paid to the distribution of the squared error sum of the detrended process. We use a probabilistic approach to derive general formulas for the expected value and the variance of the squared fluctuation function of DFA for Gaussian processes. We also get analytical results for the expected value of the squared fluctuation function for particular examples of Gaussian processes, such as Gaussian white noise, fractional Gaussian noise, ordinary Brownian motion, and fractional Brownian motion. Our analytical formulas are supported by numerical simulations. The results obtained can serve as a starting point for analyzing the statistical properties of DFA-based estimators for the fluctuation function and long-memory parameter.