We study the evolution of a social network with friendly or enmity connections into a balanced state by introducing a dynamical model with an intrinsic randomness, similar to Glauber dynamics in statistical mechanics. We include the possibility of the tension promotion as well as the tension reduction in our model. Such a more realistic situation enables the system to escape from local minima in its energy landscape and thus to exit out of frozen imbalanced states, which are unwanted outcomes observed in previous models. On the other hand, in finite networks the dynamics takes the system into a balanced phase, if the randomness is lower than a critical value. For large networks, we also find a sharp phase transition at the initial positive link density of ${\rho }_0^{*}=1/2$, where the system transitions from a bipolar state into a paradise. This modifies the gradual phase transition at a nontrivial value of ${\rho }_0^{*}\simeq 0.65$, observed in recent studies.

By combining analytical and numerical calculations, we investigate the minimal-energy shape of short DNA loops of approximately 100 base pairs (bp). We show that in these loops the excess twist density oscillates as a response to an imposed bending stress, as recently found in DNA minicircles and observed in nucleosomal DNA. These twist oscillations, here referred to as twist waves, are due to the coupling between twist and bending deformations, which in turn originates from the asymmetry between DNA major and minor grooves. We introduce a simple analytical variational shape that reproduces the exact loop energy up to the fourth significant digit and is in very good agreement with shapes obtained from coarse-grained simulations. We, finally, analyze the loop dynamics at room temperature, and show that the twist waves are robust against thermal fluctuations. They perform a normal diffusive motion, whose origin is briefly discussed.

Since the origin of life, both evolutionary dynamics and rhythms have played a key role in the functioning of living systems. The Crow-Kimura model of periodically changing fitness function has been solved exactly, using integral equation with time-ordered exponent. We also found a simple approximate solution for the two-season case. The evolutionary dynamics accompanied by the rhythms provide important insights into the properties of certain biological systems and processes.

Molecular dynamics simulations are a powerful tool to characterize liquid-solid friction. A slab configuration with periodic boundary conditions in the lateral dimensions is commonly used, where the measured friction coefficient could be affected by the finite lateral size of the simulation box. Here we show that for a very wetting liquid close to its melting temperature, strong finite size effects can persist up to large box sizes along the flow direction, typically $\sim 30$ particle diameters. We relate the observed decrease of friction in small boxes to changes in the structure of the first adsorbed layer, which becomes less commensurable with the wall structure. Although these effects disappear for lower wetting cases or at higher temperatures, we suggest that the possible effect of the finite lateral box size on the friction coefficient should not be automatically set aside when exploring unknown systems.

We study a one-dimensional model for heavy particles in a compressible fluid. The fluid-velocity field is modeled by a persistent Gaussian random function, and the particles are assumed to be weakly inertial. Since one-dimensional fluid-velocity fields are always compressible, the model exhibits spatial trapping regions where particles tend to accumulate. We determine the statistics of fluid-velocity gradients in the vicinity of these traps and show how this allows one to determine the spatial Lyapunov exponent and the rate of caustic formation. We compare our analytical results with numerical simulations of the model and explore the limits of validity of the theory. Finally, we discuss implications for higher-dimensional systems.

The stability of a shear flow imposed along a diffusive interface that separates two miscible liquids (a heavier liquid lies underneath) is studied using direct numerical simulations. The phase-field approach is employed for description of a thermo- and hydrodynamic evolution of a heterogeneous binary mixture. The approach takes into account the dynamic interfacial stresses at a miscible interface and uses the extended Fick's law for setting the diffusion transport (the diffusion flux is proportional to the gradient of chemical potential). The shear flow is unstable to two kinds of instabilities: (1) the Kelvin-Helmholtz instability, with an immovable vortex formed in the middle of an interface (in the vertical direction) and (2) the Holmboe instability, with traveling waves along the interfacial boundary. The development of the Holmboe instability results in a stronger enhancement of molecular mixing between the mixture components. Earlier, the boundaries of these instabilities were determined using the linear stability analysis and employing the concept of a “frozen interface.” In the current work, through the solution of full equations, we obtain the stability boundaries for several sets of governing parameters, showing a greater variety of the possible shapes of the stability diagrams. The Kelvin-Helmholtz instability always occurs at lower gravity effects (lower density contrasts), while the Holmboe instability occurs when gravity is stronger. We show that for some parameters these two instabilities are separated by a zone where the shear flow is stable, and this zone disappears for the other sets of parameters.

The open asymmetric simple exclusion process (ASEP) has emerged as a paradigmatic model of nonequilibrium behavior, in part due to its complex dynamical behavior and wide physical applicability as a model of driven diffusion. We compare the dynamical phase behavior of the one-dimensional (1D) ASEP and the multi-lane ASEP, a previously unstudied extension of the 1D model that may be thought of as a finite-width strip of the fully two-dimensional (2D) system. Our characterization employs large deviation theory (LDT), matrix product states (MPS), and the density matrix renormalization group (DMRG) algorithm, to compute the current cumulant generating function and its derivatives, which serve as dynamical order parameters. We use this measure to show that when particles cannot exit or enter the lattice vertically, the phase behavior of the multi-lane ASEP mimics that of its 1D counterpart, exhibiting the macroscopic and microscopic signatures of the maximal current, shock, and high-density–low-density coexistence phases. Conversely, when particles are allowed to freely enter and exit the lattice, no such transition is observed. This contrast emphasizes the complex interplay between latitudinal and longitudinal hopping rates and the effect of current biasing. Our results support the potential of tensor networks as a framework to understand classical nonequilibrium statistical mechanics.

Three-dimensional observation of Brownian particles under shear flow is performed with a stereo microscope to examine the nature of the Brownian motion that occurs in the presence of shear flow. From the three-dimensional trajectories of the particles, we clearly demonstrate the occurrence of anomalous diffusion in the flow direction and the coupling of the displacements in the flow and velocity gradient directions. Furthermore, we experimentally obtain the probability distribution function and current density, which also exhibit characteristic features, and compare the obtained results with theoretical results derived using the Fokker-Planck equation.

We systematically simulate and analyze the motion of discrete breatherlike excitations (DBEs) in the nonlinear Schrödinger lattice with random potentials. A universal transient diffusion of the DBEs is observed for short timescales ($t\lesssim {10}^3$). For longer timescales ($t$ up to ${10}^5$), the DBEs become localized. Such localization, depending on the DBE powers, has two different regimes: Regime I is the Anderson-like localization induced by the disorder, while Regime II is an enhanced localization attributed to both the disorder and discreteness. Our study is expected to shed light on understanding the interplay between disorder and strong nonlinearity, from the diffusive transport and localization properties of nonlinear localized excitations in random media.

Much of the community detection literature studies structural communities, communities defined solely by the connectivity patterns of the network. Often networks contain additional metadata which can inform community detection such as the grade and gender of students in a high school social network. In this work, we introduce a tuning parameter to the content map equation that allows users of the Infomap community detection algorithm to control the metadata's relative importance for identifying network structure. On synthetic networks, we show that our algorithm can overcome the structural detectability limit when the metadata are well aligned with community structure. On real-world networks, we show how our algorithm can achieve greater mutual information with the metadata at a cost in the traditional map equation. Our tuning parameter, like the focusing knob of a microscope, allows users to “zoom in” and “zoom out” on communities with varying levels of focus on the metadata.

We consider a one-dimensional elastic membrane, which is pushed by growing filaments. The filaments tend to grow by creating local protrusions in the membrane and this process has surface energy and bending energy costs. Although it is expected that with increasing surface tension and bending rigidity, it should become more difficult to create a protrusion, we find that for a fixed bending rigidity, as the surface tension increases, protrusions are more easily formed. This effect also gives rise to nontrivial dependence of membrane velocity on the surface tension, characterized by a dip and a peak. We explain this unusual phenomenon by studying in detail the interplay of the surface and the bending energy and show that this interplay is responsible for a qualitative shape change of the membrane, which gives rise to the above effect.

We report a detailed semianalytical treatment to investigate the dynamics of a single cavity soliton (CS) and two copropagating CSs separately in a Kerr mediated passive optical fiber resonator which is driven by a phase-modulated pump. The perturbation is dealt with by introducing Rayleigh's dissipation function in the framework of a variational principle that results in a set of coupled ordinary differential equations describing the evolution of individual soliton parameters. We further derive closed-form expressions for quick estimation of the temporal trajectory, drift velocity, and the phase shift accumulated by the CS due to the externally modulated pump. We also extend the variational approach to solve a two-soliton interaction problem in the absence as well as in the presence of the externally modulated field. In the absence of a phase-modulated field, the two copropagating solitons can attract, repulse, or propagate independently depending on their initial delay. The final state of interaction can be predicted through a second-order differential equation which is derived by the variational method. While in the presence of the phase-modulated field, the two-soliton interaction can result in annihilation, merging, breathing, or a two-soliton state depending on the detuning frequency and the pump power. Variational treatment analytically predicts these states and portrays the related dynamics that agrees with the full numerical simulation carried out by solving the normalized Lugiato-Lefever equation. The results obtained through this variational approach will enrich the understanding of complex pulse dynamics under a phase-modulated driving field in passive dissipative systems.

A living cell senses its environment and responds to external signals. In this paper, we study theoretically the precision at which cells can determine the position of a spatially localized transient extracellular signal. To this end, we focus on the case where the stimulus is converted into the release of a small molecule that acts as a second messenger, for example, ${\mathrm{Ca}}^{2+}$, and activates kinases that change the activity of enzymes by phosphorylating them. We analyze the spatial distribution of phosphorylation events using stochastic simulations as well as a mean-field approach. Kinases that need to bind to the cell membrane for getting activated provide more accurate estimates than cytosolic kinases. Our results could explain why the rate of ${\mathrm{Ca}}^{2+}$ detachment from the membrane-binding conventional protein kinase $\mathrm{C}\alpha$ is larger than its phosphorylation rate.

A nonhorizontal slope in the isotherm has been observed in the two-phase coexisting region of the first-order liquid-expanded (LE)–liquid-condensed (LC) phase transition in Langmuir monolayers for many decades. We show that the simple analysis of a phenomenological Landau free energy involving the coupling-energy contributions of molecular lateral density $\left(\rho \right)$ with spontaneous collective chain tilt (θ) and two-dimensional strain $\left({\varepsilon }_s\right)$ inside the LC domain enables one to understand the origin of a nonhorizontal straight-line slope in the LE-LC phase coexistence region of the isotherm. The presence of $\rho -{\varepsilon }_s$ coupling must be essential for the appearance of the straight-line shape of a nonhorizontal plateau in the isotherm. Moreover, it is found from the comparison of the two-dimensional contour plots of the free energy that an LE phase may persist significantly even at the later stage of the straight-line regime beyond a transition midpoint surface pressure in the presence of this coupling. The persistence of the LE phase may lead to the delay of transition progress as manifested more clearly by the appearance of a compressibility plateau in the coexistence region that indicates the existence of persistent equilibrium density fluctuations in the monolayer.

Crack growth in heterogeneous materials sometimes exhibits crackling dynamics, made of successive impulselike events with specific scale-invariant time and size organization reminiscent of earthquakes. Here, we examine this dynamics in a model which identifies the crack front with a long-range elastic line driven in a random potential. We demonstrate that, under some circumstances, fracture grows intermittently, via scale-free impulse organized into aftershock sequences obeying the fundamental laws of statistical seismology. We examine the effects of the driving rate and system overall stiffness (unloading factor) onto the scaling exponents and cutoffs associated with the time and size organization. We unravel the specific conditions required to observe a seismiclike organization in the crack propagation problem. Beyond failure problems, implications of these results to other crackling systems are finally discussed.

We investigate the Joule expansion of an interacting quantum gas in an energy eigenstate. The Joule expansion occurs when two subsystems of different particle density are allowed to exchange particles. We demonstrate numerically that the subsystems in their energy eigenstates evolves unitarily into the global equilibrium state in accordance with the eigenstate thermalization hypothesis. We find that the quantum gas changes its temperature after the Joule expansion with a characteristic inversion temperature $T_{\mathrm{I}}$. The gas cools down (heats up) when the initial temperature is higher (lower) than $T_{\mathrm{I}}$, implying that $T_{\mathrm{I}}$ is a stable fixed point, which is contrasted to the behavior of classical gases. Our work exemplifies that transport phenomena can be studied at the level of energy eigenstates.

Quantum systems whose classical counterparts are chaotic typically have highly correlated eigenvalues and level statistics that coincide with those from ensembles of full random matrices. A dynamical manifestation of these correlations comes in the form of the so-called correlation hole, which is a dip below the saturation point of the survival probability's time evolution. In this work, we study the correlation hole in the spin-boson (Dicke) model, which presents a chaotic regime and can be realized in experiments with ultracold atoms and ion traps. We derive an analytical expression that describes the entire evolution of the survival probability and allows us to determine the time scales of its relaxation to equilibrium. This expression shows remarkable agreement with our numerical results. While the initial decay and the time to reach the minimum of the correlation hole depend on the initial state, the dynamics beyond the hole up to equilibration is universal. We find that the relaxation time of the survival probability for the Dicke model increases linearly with system size.

This work aims to investigate the influence of $p\mathrm{H}$ on the mechanism of assembly of macromolecules. We studied the effect of the $p\mathrm{H}$ on the interaction of two polyelectrolytes of opposed charge, having the same size, by means of dissipative particle dynamics method. The system consisted of a strong cationic and a weak anionic polyelectrolyte in an aqueous solution containing monovalent counterions. The analysis was made by varying the $p\mathrm{H}$ of the solution, which modifies the charge fraction of the weak anionic polyelectrolyte with a dissociation acid constant $p\mathrm{Ka}$ of 5.5, while the polycation is fully charged in all the $p\mathrm{H}$ range used, characteristic of a strong polyelectrolyte. In order to describe the influence of $p\mathrm{H}$ on the complexation process, we have analyzed the pair radial distribution functions polyanion-counterion, polycation-counterion, and polyanion-polycation. The complex conformation was studied by means of the radius of gyration and the end-to-end distance of both chains as the $p\mathrm{H}$ varied from 1 to 14. A relevant finding obtained here was the relationship between the radial distribution functions and the counterion release from the polyelectrolytes, which leads to a reduction in the size of the complex when $p\mathrm{H}$ increased. Surprisingly, a transition from an extended to a compact polyelectrolyte complex was obtained when the $p\mathrm{H}$ reached the dissociation acid constant $p\mathrm{Ka}$ of the weak polyelectrolyte. This systematic study can help to understand a large number of more realistic problems in biological systems such as protein complex, chromatin phase transition, or in complex systems applied in biomedical science.

Elastic crystalline membranes exhibit a buckling transition from sphere to polyhedron. However, their morphologies are restricted to convex polyhedra and are difficult to externally control. Here we study morphological changes of closed crystalline membranes of superparamagnetic particles. The competition of magnetic dipole-dipole interactions with the elasticity of this magnetoelastic membrane leads to concave morphologies. Interestingly, as the magnetic field strength increases, the symmetry of the buckled membrane decreases from 5-fold to 3-fold, to 2-fold and, finally, to 1-fold rotational symmetry. This gives the ability to switch the membrane morphology between convex and concave shapes with specific symmetry and provides promising applications for membrane shape control in the design of actuatable microcontainers for targeted delivery systems.

We present an elementary, general, and semiquantitative description of relaxation to Gaussian and generalized Gibbs states in lattice models of fermions or bosons with quadratic Hamiltonians. Our arguments apply to arbitrary initial states that satisfy a mild condition on clustering of correlations. We also show that similar arguments can be used to understand relaxation (or its absence) in systems with time-dependent quadratic Hamiltonians and provide a semiquantitative description of relaxation in quadratic periodically driven (Floquet) systems.