Extensive numerical simulations of rigidity percolation with only central forces in large three-dimensional lattices have indicated that many of their topological properties undergo a first-order phase transition at the rigidity percolation threshold $p_{ce}$. In contrast with such properties, past numerical calculations of the elastic moduli of the same lattices had provided evidence for a second-order phase transition. In this paper we present the results of extensive simulation of rigidity percolation in large body-centered cubic (bcc) lattices, and show that as the linear size $L$ of the lattice increases, the elastic moduli close to $p_{ce}$ decrease in a stepwise, discontinuous manner, a feature that is absent in lattices with $L<30$. The number and size of such steps increase with $L$. As $p_{ce}$ is approached, long-range, nondecaying orientational correlations are built up, giving rise to compact, nonfractal clusters. As a result, we find that the backbone of the lattice at $p_{ce}$ is compact with a fractal dimension $D_{bb}\approx 3$. The absence of fractal, scale-invariant clusters, the hallmark of second-order phase transitions, together with the stairwise behavior of the elastic moduli, provide strong evidence that, at least in bcc lattices, many of the topological properties of rigidity percolation as well as its elastic moduli may undergo a first-order phase transition at $p_{ce}$. In relatively small lattices, however, the boundary effects interfere with the nonlocal nature of the rigidity percolation. As a result, only when such effects diminish in large lattices does the true nature of the phase transition emerge.

Deterministic and stochastic evolutionary processes drive adaptation in natural populations. The strength of each component process is determined by the population size: deterministic components prevail in very large populations, while stochastic components are the driving mechanisms in small ones. Many natural populations, however, experience intermittent periods of growth, moving through states in which either stochastic or deterministic processes prevail. This growth is often countered by population bottlenecks, which abound in both natural and laboratory populations. Here we investigate how population bottlenecks shape the process of adaptation. We demonstrate that adaptive trajectories in populations experiencing regular bottlenecks can be naturally scaled in time units of generations; with this scaling the time courses of adaptation, fitness variance, and genetic diversity all become relatively insensitive to the timing of population bottlenecks, provided the bottleneck size exceeds a few thousand individuals. We also include analyses at the genotype level to investigate the impact of population bottlenecks on the predictability and distribution of evolutionary pathways. Irrespective of the timing of population bottlenecks, we find that predictability increases with population size. We also find that predictability of the adaptive pathways increases in increasingly rugged fitness landscapes. Overall, our work reveals that both the adaptation rate and the predictability of evolutionary trajectories are relatively robust to population bottlenecks.

Various electronic devices, which we commonly use, radiate microwaves. Such external perturbation influences the functionality of biomolecules. In an ultralow field, the cumulative response of a molecule is expected only over a time scale of hours. To study the structural dynamics of biomolecules over hours, we adopt a simple methodology for constructing the coarse-grained structure of the protein molecule and solve the Langevin equation under different working potentials. In this approach, each amino acid residue of a biomolecule is mapped onto a number of beads, a few for the backbone, and few for the side chain, depending on the complexity of its chemical structure. We choose the force field in such a way that the dynamics of the protein molecule in the presence of ultralow radiation field of microvolt/nm could be followed over the time frame of 2 h. We apply the model to describe a biomolecule, hen egg white lysozyme, and simulate its structural evolution under ultralow strength electromagnetic radiation. The simulation revealed the finer structural details, like the extent of exposure of bioactive residues and the state of the secondary structures of the molecule, further confirmed from spectroscopic measurements [details are available in Phys. Rev. E 97, 052416 (2018) and briefly described here]. Though tested for a specific system, the model is quite general. We believe that it harnesses the potential in studying the structural dynamics of any biopolymer under external perturbation over an extended time scale.

Deoxyribonucleic acid (DNA) hybridization is at the heart of countless biological and biotechnological processes. Its theoretical modeling played a crucial role, since it has enabled extracting the relevant thermodynamic parameters from systematic measurements of DNA melting curves. In this article, we propose a framework based on statistical physics to describe DNA hybridization and melting in an arbitrary mixture of DNA strands. In particular, we are able to analytically derive closed expressions of the system partition functions for any number $N$ of strings and explicitly calculate them in two paradigmatic situations: (i) a system made of self-complementary sequences and (ii) a system comprising two mutually complementary sequences. We derive the melting curve in the thermodynamic limit ($N\to \infty$) of our description, which provides a full justification for the extra entropic contribution that in classic hybridization modeling was required to correctly describe within the same framework the melting of sequences either self-complementary or not. We thus provide a thorough study comprising limit cases and alternative approaches showing how our framework can give a comprehensive view of hybridization and melting phenomena.

Rate effects in sheared disordered solids are studied using molecular dynamics simulations of binary Lennard-Jones glasses in two and three dimensions. In the quasistatic (QS) regime, systems exhibit critical behavior: the magnitudes of avalanches are power-law distributed with a maximum cutoff that diverges with increasing system size $L$. With increasing rate, systems move away from the critical yielding point and the average flow stress rises as a power of the strain rate with exponent $1/\beta$, the Herschel-Bulkley exponent. Finite-size scaling collapses of the stress are used to measure $\beta$ as well as the exponent $\nu$ which characterizes the divergence of the correlation length. The stress and kinetic energy per particle experience fluctuations with strain that scale as $L^{-d/2}$. As the largest avalanche in a system scales as $L^{\alpha }$, this implies $\alpha <d/2$. The diffusion rate of particles diverges as a power of decreasing rate before saturating in the QS regime. A scaling theory for the diffusion is derived using the QS avalanche rate distribution and generalized to the finite strain rate regime. This theory is used to collapse curves for different system sizes and confirm $\beta /\nu$.

Disordered solids respond to quasistatic shear with intermittent avalanches of plastic activity, an example of the crackling noise observed in many nonequilibrium critical systems. The temporal power spectrum of activity within disordered solids consists of three distinct domains: a novel power-law rise with frequency at low frequencies indicating anticorrelation, white-noise at intermediate frequencies, and a power-law decay at high frequencies. As the strain rate increases, the white-noise regime shrinks and ultimately disappears as the finite strain rate restricts the maximum size of an avalanche. A new strain-rate- and system-size-dependent theory is derived for power spectra in both the quasistatic and finite-strain-rate regimes. This theory is validated using data from overdamped two- and three-dimensional molecular dynamics simulations. We identify important exponents in the yielding transition including the dynamic exponent $z$ which relates the size of an avalanche to its duration, the fractal dimension of avalanches, and the exponent characterizing the divergence in correlations with strain rate. Results are related to temporal correlations within a single avalanche and between multiple avalanches.

We study the Brownian motion of a charged colloid, confined between two charged walls, for small separation between the colloid and the walls. The system is embedded in an ionic solution. The combined effect of electrostatic repulsion and reduced diffusion due to hydrodynamic forces results in a specific motion in the direction perpendicular to the confining walls. The apparent diffusion coefficient at short times as well as the diffusion characteristic time are shown to follow a sigmoid curve as a function of a dimensionless parameter. This parameter depends on the electrostatic properties and can be controlled by tuning the solution ionic strength. At low ionic strength, the colloid moves faster and is localized, while at high ionic strength it moves slower and explores a wider region between the walls, resulting in a larger diffusion characteristic time.

We focus on studying the opacity of iron, chromium, and nickel plasmas at conditions relevant to experiments carried out at Sandia National Laboratories [J. E. Bailey et al., Nature (London) 517, 56 (2015)]. We calculate the photoabsorption cross sections and subsequent opacity for plasmas using linear-response time-dependent density functional theory (TD-DFT). Our results indicate that the physics of channel mixing accounted for in linear-response TD-DFT leads to an increase in the opacity in the bound-free quasicontinuum, where the Sandia experiments indicate that models underpredict iron opacity. However, the increase seen in our calculations is only in the range of 5%–10%. Further, we do not see any change in this trend for chromium and nickel. This behavior indicates that channel mixing effects do not explain the trends in opacity observed in the Sandia experiments.

Based on the geometrization of dynamics and self-consistent phonon theory, we develop an analytical approach to derive the Lyapunov time, the reciprocal of the largest Lyapunov exponent, for general nonlinear lattices of coupled oscillators. The Fermi-Pasta-Ulam-Tsingou-like lattices are exemplified by using the method, which agree well with molecular dynamical simulations for the cases of quartic and sextic interactions. A universal scaling behavior of the Lyapunov time with the nonintegrability strength is observed for the quasi-integrable regime. Interestingly, the scaling exponent of the Lyapunov time is the same as the thermalization time, which indicates a proportional relationship between the two timescales. This relation illustrates how the thermalization process is related to the intrinsic chaotic property.

In critical systems, the effect of a localized perturbation affects points that are arbitrarily far from the perturbation location. In this paper, we study the effect of localized perturbations on the solution of the random dimer problem in two dimensions. By means of an accurate numerical analysis, we show that a local perturbation of the optimal covering induces an excitation whose size is extensive with finite probability. We compute the fractal dimension of the excitations and scaling exponents. In particular, excitations in random dimer problems on nonbipartite lattices have the same statistical properties of domain walls in spin glass. Excitations produced in bipartite lattices, instead, are compatible with a loop-erased self-avoiding random walk process. In both cases, we find evidence of conformal invariance of the excitations that is compatible with ${\mathrm{SLE}}_{\kappa }$ with parameter $\kappa$ depending on the bipartiteness of the underlying lattice only.

We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges, but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows for the generation of graphs with extensive numbers of triangles and other network motifs commonly observed in many real-world networks. More specifically, we focus on maximum entropy ensembles under constraints placed on the counts and distributions of atomic subgraphs and derive general expressions for the entropy of such models. We also present a procedure for combining distributions of multiple atomic subgraphs that enables the construction of models with fewer parameters. Expanding the model to include atoms with edge and vertex labels we obtain a general class of models that can be parametrized in terms of basic building blocks and their distributions that include many widely used models as special cases. These models include random graphs with arbitrary distributions of subgraphs, random hypergraphs, bipartite models, stochastic block models, models of multilayer networks and their degree-corrected and directed versions. We show that the entropy for all these models can be derived from a single expression that is characterized by the symmetry groups of atomic subgraphs.

We introduce a general approach for the study of the collective dynamics of noninteracting random walkers on connected networks. We analyze the movement of $R$ independent (Markovian) walkers, each defined by its own transition matrix. By using the eigenvalues and eigenvectors of the $R$ independent transition matrices, we deduce analytical expressions for the collective stationary distribution and the average number of steps needed by the random walkers to start in a particular configuration and reach specific nodes the first time (mean first-passage times), as well as global times that characterize the global activity. We apply these results to the study of mean first-encounter times for local and nonlocal random walk strategies on different types of networks, with both synchronous and asynchronous motion.

In most studies, street networks are considered as undirected graphs while one-way streets and their effect on shortest paths are usually ignored. Here, we first study the empirical effect of one-way streets in about 140 cities in the world. Their presence induces a detour that persists over a wide range of distances and is characterized by a nonuniversal exponent. The effect of one-ways on the pattern of shortest paths is then twofold: they mitigate local traffic in certain areas but create bottlenecks elsewhere. This empirical study leads naturally to considering a mixed graph model of 2d regular lattices with both undirected links and a diluted variable fraction $p$ of randomly directed links which mimics the presence of one-ways in a street network. We study the size of the strongly connected component (SCC) versus $p$ and demonstrate the existence of a threshold $p_c$ above which the SCC size is zero. We show numerically that this transition is nontrivial for lattices with degree less than 4 and provide some analytical argument. We compute numerically the critical exponents for this transition and confirm previous results showing that they define a new universality class different from both the directed and standard percolation. Finally, we show that the transition on real-world graphs can be understood with random perturbations of regular lattices. The impact of one-ways on the graph properties was already the subject of a few mathematical studies, and our results show that this problem has also interesting connections with percolation, a classical model in statistical physics.

We study the efficiency of sliding locomotion for three-link bodies with prescribed joint angle motions. The bodies move with no inertia, under dry (Coulomb) friction that is anisotropic (different in the directions normal and tangent to the links) and directional (different in the forward and backward tangent directions). Friction coefficient space can be partitioned into several regions, each with distinct types of efficient kinematics. These include kinematics resembling lateral undulation with very anisotropic friction, small-amplitude reciprocal kinematics, very large-amplitude kinematics near isotropic friction, and kinematics that are very asymmetric about the flat state. In the two-parameter shape space, zero net rotation for elliptical trajectories occurs mainly with bilateral or antipodal symmetry. These symmetric subspaces have about the same peak efficiency as the full space but with much smaller dimension. Adding the second or third harmonics greatly increases the numbers of local optimal for efficiency, but only modestly increases the peak efficiency. Random ensembles with higher harmonics have efficiency distributions that peak near a certain nonzero value and decay rapidly up to the maximum efficiency. A stochastic optimization algorithm is developed to compute optima with higher harmonics. These are simple closed curves, sharpened versions of the elliptical optima in most cases, and achieve much higher efficiencies mainly for small normal friction. With a linear (viscous) resistance law, the optimal trajectories are similar in much of the friction coefficient space, and relative efficiencies are much lower except with very large normal friction.

We study in this work the dynamics of a collection of identical hollow spheres (ping-pong balls) that rest on a horizontal metallic grid. Fluidization is achieved by means of a turbulent air current coming from below. The upflow is adjusted so that the particles do not levitate over the grid, resulting in quasi-two-dimensional dynamics. We show that the behavior of diffusion and correlations in this system is particularly rich. Noticeably as well (and related to the complex dynamical behavior), a variety of phases appear, with important peculiarities with respect to analogous setups. We observe gas, liquid, glass, and hexagonal crystal phases. Most notably, we show that the melting of the hexagonal crystal occurs in coexistence with a liquid phase. This strikingly differs from the corresponding transition in a purely two-dimensional systems of air-fluidized disks, for which no phase coexistence has been reported in the literature.

In a recent paper Das et al. [J. Chem. Phys. 147, 164102 (2017)] proposed the Fokker-Planck equation (FPE) for the Brownian harmonic oscillator in the presence of a magnetic field and the non-Markovian thermal bath, respectively. This system has been studied very recently by Hidalgo-Gonzalez and Jiménez-Aquino [Phys. Rev. E 100, 062102 (2019)] and the Fokker-Planck equation was derived using the characteristic function. It includes a few extra terms in the FPE and the authors conclude that their method is accurate compared to the calculation by Das et al. Then we reexamine our calculation and which is present in this comment. The revised calculation shows that both methods give the same result.

Recently in a paper by Hidalgo-Gonzalez and Jiménez-Aquino [Phys. Rev. E 100, 062102 (2019)], the generalized Fokker-Planck equation (GFPE) for a Brownian harmonic oscillator in a constant magnetic field and under the action of time-dependent force fields, has been explicitly calculated using the characteristic function method. Although the problem is linear it is not easy to solve, however, the method of the characteristic function is effective and allows to obtain an exact and precise solution of the problem. Our theoretical result has been compared with the one reported by Das et al. in a recently submitted paper [arXiv:2011.09771] using another solution method. The proposed method consists in constructing the GFPE and then calculating each time-dependent coefficient associated with this equation. However, in a more complicated case, one cannot know a priori the exact number of terms that this equation must contain. The precise number is further provided by the characteristic function method.

The identification of precursors of climatic phenomena has enormous practical importance. Recent work constructs a climate network based on surface air temperature data to analyze the El Niño phenomena. We utilize microtransitions which occur before the discontinuous percolation transition in the network as well as other network quantities to identify a set of reliable precursors of El Niño episodes. These precursors identify 10 out of 13 El Niño episodes occurring in the period of 1979–2018 with an average lead time of approximately 6.4 months. We also find indicators of tipping events in the data.

The properties of freestanding tensionless interfaces and membranes at low bending rigidity $\kappa$ are dominated by strong fluctuations and self-avoidance and are thus outside the range of standard perturbative analysis. We analyze this regime by a simple discretized, self-avoiding membrane model on a frame subject to periodic boundary conditions by use of Monte Carlo simulation and dynamically triangulated surface techniques. We find that at low bending rigidities, the membrane properties fall into three regimes: Below the collapse transition ${\kappa }_{\mathrm{BP}}$ it is subject to branched polymer instability where the framed surface is not defined, in a range below a threshold rigidity ${\kappa }_c$ the conformational correlation function are characterized by power-law behavior with a continuously varying exponent $\alpha , 2<\alpha \le 4$ and above ${\kappa }_c, \alpha =4$ characteristic for linearized bending excitations. Response functions specific heat and area compressibility display pronounced peaks close to ${\kappa }_c$. The results may be important for the description of soft interface systems, such as microemulsions and membranes with in-plane cooperative phenomena.

We study the possibility of achieving the Carnot efficiency in a finite-power underdamped Brownian Carnot cycle. Recently, it was reported that the Carnot efficiency is achievable in a general class of finite-power Carnot cycles in the vanishing limit of the relaxation times. Thus, it may be interesting to clarify how the efficiency and power depend on the relaxation times by using a specific model. By evaluating the heat-leakage effect intrinsic in the underdamped dynamics with the instantaneous adiabatic processes, we demonstrate that the compatibility of the Carnot efficiency and finite power is achieved in the vanishing limit of the relaxation times in the small temperature-difference regime. Furthermore, we show that this result is consistent with a trade-off relation between power and efficiency by explicitly deriving the relation of our cycle in terms of the relaxation times.