We introduce “bond-counting” potentials, which provide an elementary description of covalent bonding. These simplistic potentials are intended for studies of the mechanisms behind a variety of phase transitions in elemental melts, including the liquid-liquid phase transitions (LLPTs) in phosphorus and bismuth. As a first study employing such potentials, an analytic solution of a one-dimensional model system is presented, including its thermodynamic properties and its structure factor. In the simplest case, the chemical valency of each atom is 1, and either single atoms or diatomic molecules are present. At low temperatures and moderate pressures, the system consists almost exclusively of molecules, and single atoms act as topological defects. A slightly more complicated case involves a valency of 2, with either single or double bonding. This system exhibits a first-order LLPT from a molecular to a polymeric phase as in phosphorus. In this case, the one-dimensional model system exhibits phase separation for finite-sized systems at low temperatures. A variant of this system also exhibits a nonequilibrium phase transformation upon heating the molecular condensed phase, qualitatively similar to boiling in white phosphorus.

The dynamics of a freely diffusing particle in a two-dimensional channel with cross-sectional area $A\left(x\right)$ can be effectively described by a one-dimensional diffusion equation under the action of a potential of mean force $U\left(x\right)=-k_{B}Tln\left[A\left(x\right)\right]$ (where $k_{B}T$ is the thermal energy) in a system with a spatially dependent diffusion coefficient $D\left(x\right)$. Several attempts to derive expressions relating $D\left(x\right)$ to $A\left(x\right)$ and its derivatives have been made, which were based on considering stationary flows in periodic channels. Here we take an alternative approach and consider non-steady-state single-particle diffusion in an open periodic channel. The approach allows us to express $D\left(x\right)$ as a series of terms of increasing powers of $\epsilon$–a parameter associated with the aspect ratio of the channel. When the expansion is truncated at the leading term, we recover the expression suggested by Zwanzig [J. Phys. Chem. 96, 3926 (1992)] for $D\left(x\right)$. Furthermore, comparison of the first few terms in our expansion for $D\left(x\right)$ with the one proposed by Kalinay and Percus [Phys. Rev. E 74, 041203 (2006)] shows that they are consistent with each other. In the limit of long-wavelength channels ($\epsilon \ll 1$), the expansion converges rapidly and the leading approximation provides a very accurate description of the two-dimensional dynamics. For short-wavelength channels, the expansion does not converge and the validity of the effective one-dimensional description is questionable.

Recent density functional theory simulations showed that metals have a hitherto overlooked symmetry termed “hidden scale invariance” [Hummel et al., Phys. Rev. B 92, 174116 (2015)]. This scaling property implies the existence of lines in the thermodynamic phase diagram, so-called isomorphs, along which structure and dynamics are invariant to a good approximation when given in properly reduced units. This means that the phase diagram becomes effectively one-dimensional with regard to several physical properties. This paper investigates consequences and implications of the isomorph theory in six metallic crystals: Au, Ni, Cu, Pd, Ag, and Pt. The data are obtained from molecular dynamics simulations employing many-body effective medium theory (EMT) to model the atomic interactions realistically. We test the predictions from isomorph theory for structure and dynamics by means of the radial distribution and the velocity autocorrelation functions, as well as the prediction of instantaneous equilibration after a jump between two isomorphic state points. Many properties of crystals tend to be dominated by defects, and many of the properties associated with these defects are expected to be isomorph invariant as well. This is investigated in this paper for the case of vacancy diffusion. In regard to the perfect crystal properties, we find the predicted invariance of structure and also, though less perfectly, of dynamics. We show results on the variation of the density-scaling exponent $\gamma$, which can be related to the Grüneisen parameter, for all six metals. We consider large density changes up to a factor of two, corresponding to very high pressures. Unlike systems modeled using the Lennard-Jones potential where the density-scaling exponent $\gamma$ is almost constant, this quantity varies substantially when using the EMT potential and is also strongly material dependent.

We report on the measurement of detailed balance violation in a coupled, noise-driven linear electronic circuit consisting of two nominally identical RC elements that are coupled via a variable capacitance. The state variables are the time-dependent voltages across each of the two primary capacitors, and the system is driven by independent noise sources in series with each of the resistances. From the recorded time histories of these two voltages, we quantify violations of detailed balance by three methods: (1) explicit construction of the probability current density, (2) constructing the time-dependent stochastic area, and (3) constructing statistical fluctuation loops. In comparing the three methods, we find that the stochastic area is relatively simple to implement and computationally inexpensive and provides a highly sensitive means for detecting violations of detailed balance.

Structural defects within amorphous packings of symmetric particles can be characterized using a machine learning approach that incorporates structure functions of radial distances and angular arrangement. This yields a scalar field, softness, that correlates with the probability that a particle is about to be rearranged. However, when particle shapes are elongated, as in the case of dimers and ellipses, we find that the standard structure functions produce imprecise softness measurements. Moreover, ellipses exhibit deformation profiles in stark contrast to circular particles. In order to account for the effects of orientation and alignment, we introduce structure functions to recover the predictive performance of softness, as well as provide physical insight into local and extended dynamics. We study a model disordered solid, a bidisperse two-dimensional granular pillar, driven by uniaxial compression and composed entirely of monomers, dimers, or ellipses. We demonstrate how the computation of softness via a support vector machine extends to dimers and ellipses with the introduction of orientational structure functions. Then we highlight the spatial extent of rearrangements and defects, as well as their cross correlation, for each particle shape. Finally, we demonstrate how an additional machine learning algorithm, recursive feature elimination, provides an avenue to better understand how softness arises from particular structural aspects. We identify the most crucial structure functions in determining softness and discuss their physical implications.

In this work we present a phenomenological model to look for a better understanding of the shock-wave structure in dilute monatomic gases. The model is based on the principles of linear irreversible thermodynamics, where we have been aware of the flow anisotropy caused by the shock-wave propagation. Then a new coupling appears between the stress tensor and the heat flux. The comparisons with the experimental data available for argon as well as the direct simulation Monte Carlo method calculations are done and shown to support our proposal.

We study the Swift–Hohenberg equation (SHE) in the presence of an external field. The application of the field leads to a phase diagram with three phases, i.e., stripe, hexagon, and uniform. We focus on coarsening after a quench from the uniform to stripe or hexagon regions. For stripe patterns, we find that the length scale associated with the order-parameter structure factor has the same growth exponent ($\simeq 1/4$) as for the SHE with zero field. The growth process is slower in the case of hexagonal patterns, with the effective growth exponent varying between $1/6$ and $1/9$, depending on the quench parameters. For deep quenches in the hexagonal phase, the growth process stops at late stages when defect boundaries become pinned.

We study the rare fluctuations or large deviations of time-integrated functionals or observables of an unbiased random walk evolving on Erdös-Rényi random graphs, and construct a modified, biased random walk that explains how these fluctuations arise in the long-time limit. Two observables are considered: the sum of the degrees visited by the random walk and the sum of their logarithm, related to the trajectory entropy. The modified random walk is used for both quantities to explain how sudden changes in degree fluctuations, similar to dynamical phase transitions, are related to localization transitions. For the second quantity, we also establish links between the large deviations of the trajectory entropy and the maximum entropy random walk.

We study the residual entropy of the nearest-neighbor spin-ice model in a magnetic field along the [111] direction using the Wang-Landau Monte Carlo method, with a special attention to dilution effects. For a diluted model, we observe a stepwise decrease of the residual entropy as a function of the magnetic field, which is consistent with the finding of the five magnetization plateaus in a previous replica-exchange Monte Carlo study by Peretyatko et al. [Phys. Rev. B 95, 144410 (2017)]. We find large peaks of the residual entropy due to the degeneracy at the crossover magnetic fields, $h_c/J=0$, 3, 6, 9, and 12, where $h$ and $J$ are the magnetic field and the exchange coupling, respectively. In addition, we also study the residual entropy of the diluted antiferromagnetic Ising models in a magnetic field on the kagome and triangular lattices. We again observe large peaks of the residual entropy, which are associated with multiple magnetization plateaus for the diluted model. Finally, we discuss the interplay of dilution and magnetic fields in terms of the residual entropy.

Elements of statistical physics formalism were applied to mutagenic and carcinogenic processes associated with cellular DNA; these are lesion (damage) creation, mutation creation, and cellular neoplastic (cancer) transformation. The probabilities of all state changes were strictly related to potential barrier heights between energetic states of DNA molecules. Barriers can be modified when radiation adaptive response mechanisms are applied, which are associated with a radiobiological quantity called radiosensitivity. It was discussed that radiosensitivity is determined by the cell's response to radiation resulting in three potential dose-response scenarios: linear, threshold, or hormetic. The type of dose-response is of critical importance in the development of radiation protection standards and individual radiation risk assessment. It is shown that the different scenarios describe different limits of the same underlying phenomena and the cell can respond in a linear, threshold, or hormetic way regarding its radiosensitivity. Finally, the dissipative adaptation mechanism is discussed in the context of proliferating cancer cells.

The spread of opinions, memes, diseases, and “alternative facts” in a population depends both on the details of the spreading process and on the structure of the social and communication networks on which they spread. One feature that can change spreading dynamics substantially is heterogeneous behavior among different types of individuals in a social network. In this paper, we explore how antiestablishment nodes (e.g., hipsters) influence the spreading dynamics of two competing products. We consider a model in which spreading follows a deterministic rule for updating node states (which indicate which product has been adopted) in which an adjustable probability $p_{\mathrm{Hip}}$ of the nodes in a network are hipsters, who choose to adopt the product that they believe is the less popular of the two. The remaining nodes are conformists, who choose which product to adopt by considering which products their immediate neighbors have adopted. We simulate our model on both synthetic and real networks, and we show that the hipsters have a major effect on the final fraction of people who adopt each product: even when only one of the two products exists at the beginning of the simulations, a small fraction of hipsters in a network can still cause the other product to eventually become the more popular one. To account for this behavior, we construct an approximation for the steady-state adoption fractions of the products on $k$-regular trees in the limit of few hipsters. Additionally, our simulations demonstrate that a time delay $\tau$ in the knowledge of the product distribution in a population, as compared to immediate knowledge of product adoption among nearest neighbors, can have a large effect on the final distribution of product adoptions. Using a local-tree approximation, we derive an analytical estimate of the spreading of products and obtain good agreement if a sufficiently small fraction of the population consists of hipsters. In all networks, we find that either of the two products can become the more popular one at steady state, depending on the fraction of hipsters in the network and on the amount of delay in the knowledge of the product distribution. Our simple model and analysis may help shed light on the road to success for antiestablishment choices in elections, as such success—and qualitative differences in final outcomes between competing products, political candidates, and so on—can arise rather generically in our model from a small number of antiestablishment individuals and ordinary processes of social influence on normal individuals.

We map a class of well-mixed stochastic models of biochemical feedback in steady state to the mean-field Ising model near the critical point. The mapping provides an effective temperature, magnetic field, order parameter, and heat capacity that can be extracted from biological data without fitting or knowledge of the underlying molecular details. We demonstrate this procedure on fluorescence data from mouse T cells, which reveals distinctions between how the cells respond to different drugs. We also show that the heat capacity allows inference of the absolute molecule number from fluorescence intensity. We explain this result in terms of the underlying fluctuations, and we demonstrate the generality of our work.

Cells need to reliably sense external ligand concentrations to achieve various biological functions such as chemotaxis or signaling. The molecular recognition of ligands by surface receptors is degenerate in many systems, leading to crosstalk between ligand-receptor pairs. Crosstalk is often thought of as a deviation from optimal specific recognition, as the binding of noncognate ligands can interfere with the detection of the receptor's cognate ligand, possibly leading to a false triggering of a downstream signaling pathway. Here we quantify the optimal precision of sensing the concentrations of multiple ligands by a collection of promiscuous receptors. We demonstrate that crosstalk can improve precision in concentration sensing and discrimination tasks. To achieve superior precision, the additional information about ligand concentrations contained in short binding events of the noncognate ligand should be exploited. We present a proofreading scheme to realize an approximate estimation of multiple ligand concentrations that reaches a precision close to the derived optimal bounds. Our results help rationalize the observed ubiquity of receptor crosstalk in molecular sensing.

We study the axisymmetric response of a complete spherical shell under homogeneous compressive pressure $p$ to an additional point force. For a pressure $p$ below the classical critical buckling pressure $p_c$, indentation by a point force does not lead to spontaneous buckling but an energy barrier has to be overcome. The states at the maximum of the energy barrier represent a subcritical branch of unstable stationary points, which are the transition states to a snap-through buckled state. Starting from nonlinear shallow shell theory, we obtain a closed analytical expression for the energy barrier height, which facilitates its effective numerical evaluation as a function of pressure by continuation techniques. We find a clear crossover between two regimes: For $p/p_c\ll 1$ the postbuckling barrier state is a mirror-inverted Pogorelov dimple, and for $(1-p/p_c)\ll 1$ the barrier state is a shallow dimple with indentations smaller than shell thickness and exhibits extended oscillations, which are well described by linear response. We find systematic expansions of the nonlinear shallow shell equations about the Pogorelov mirror-inverted dimple for $p/p_c\ll 1$ and the linear response state for $(1-p/p_c)\ll 1$, which enable us to derive asymptotic analytical results for the energy barrier landscape in both regimes. Upon approaching the buckling bifurcation at $p_c$ from below, we find a softening of an ideal spherical shell. The stiffness for the linear response to point forces vanishes $\propto {(1-p/p_c)}^{1/2}$; the buckling energy barrier vanishes $\propto {(1-p/p_c)}^{3/2}$; and the shell indentation in the barrier state vanishes $\propto {(1-p/p_c)}^{1/2}$. This makes shells sensitive to imperfections which can strongly reduce $p_c$ in an avoided buckling bifurcation. We find the same softening scaling in the vicinity of the reduced critical buckling pressure also in the presence of imperfections. We can also show that the effect of axisymmetric imperfections on the buckling instability is identical to the effect of a point force that is preindenting the shell. In the Pogorelov limit, the energy barrier maximum diverges $\propto {(p/p_c)}^{-3}$ and the corresponding indentation diverges $\propto {(p/p_c)}^{-2}$. Numerical prefactors for proportionalities both in the softening and the Pogorelov regime are calculated analytically. This also enables us to obtain results for the critical unbuckling pressure and the Maxwell pressure.

We analyze the effect of a small inclination on the well-studied problem of two-dimensional binary fluid convection in a horizontally extended closed rectangular box with a negative separation ratio, heated from below. The horizontal component of gravity generates a shear flow that replaces the motionless conduction state when inclination is not present. This large-scale flow interacts with the convective currents resulting from the vertical component of gravity. For very small inclinations the primary bifurcation of this flow is a Hopf bifurcation that gives rise to chevrons and blinking states similar to those obtained with no inclination. For larger but still small inclinations this bifurcation disappears and is superseded by a fold bifurcation of the large-scale flow. The convecton branches, i.e., branches of spatially localized states consisting of counterrotating rolls, are strongly affected, with the snaking bifurcation diagram present in the noninclined system destroyed already at small inclinations. For slightly larger but still small inclinations we obtain small-amplitude localized states consisting of corotating rolls that evolve continuously when the primary large-scale flow is continued in the Rayleigh number. These localized states lie on a solution branch with very complex behavior strongly dependent on the values of the system parameters. In addition, several disconnected branches connecting solutions in the form of corotating rolls, counterrotating rolls, and mixed corotating and counterrotating states are also obtained.

The spread of behavior in a society has two major features: the synergy of multiple spreaders and the dominance of hubs. While strong synergy is known to induce mixed-order transitions (MOTs) at percolation, the effects of hubs on the phenomena are yet to be clarified. By analytically solving the generalized epidemic process on random scale-free networks with the power-law degree distribution $p_k\sim k^{-\alpha }$, we clarify how the dominance of hubs in social networks affects the conditions for MOTs. Our results show that, for $\alpha <4$, an abundance of hubs drive MOTs, even if a synergistic spreading event requires an arbitrarily large number of adjacent spreaders. In particular, for $2<\alpha <3$, we find that a global cascade is possible even when only synergistic spreading events are allowed. These transition properties are substantially different from those of cooperative contagions, which are another class of synergistic cascading processes exhibiting MOTs.

There is a growing interest in cylindrical structures of hard and soft particles. A promising new method to assemble such structures has recently been introduced by Lee et al. [Lee, Gizynski, and Grzybowski, Adv. Mater. 29, 1704274 (2017)]. They used rapid rotations around a central axis to drive spheres of lower density than the surrounding fluid towards the axis. This resulted in different structures as the number of spheres is varied. Here, we present comprehensive analytic energy calculations for such self-assembled structures, based on a generic soft sphere model, from which we obtain a phase diagram. It displays interesting features, including peritectoid points. These analytic calculations are complemented by preliminary numerical simulations for finite sample sizes with soft spheres. A similar analytic approach could be used to study packings of spheres inside cylinders of fixed dimensions, but with a variation in the number of spheres.

Separating ignition of the central hot spot from propagating burn in the surrounding dense fuel is crucial to conclusively assess the achievement of ignition in inertial confinement fusion (ICF). We show that the transition from hot spot ignition to the onset of propagating burn occurs when the alpha heating within the hot spot has amplified the fusion yield by $15\times$ to $25\times$ with respect to the compression-only case without alpha energy deposition. This yield amplification corresponds to a value of the fractional alpha energy $f_{\alpha }\approx 1.4$ ($f_{\alpha }=0.5$ alpha energy/hot spot energy). The parameter $f_{\alpha }$ can be inferred in ICF experiments by measuring the neutron yield, hot spot size, temperature, and burn width. This ignition threshold is measurable and applicable to all ICF implosions of deuterium and tritium targets both direct and indirect drive. The results of this Rapid Communication can be used to set the goals of the ICF effort with respect to the first demonstration of thermonuclear ignition.

We study the stochastic dynamics of infinitely many globally interacting units made of $q$ states distributed uniformly along a ring that is externally driven. While repulsive interactions always lead to uniform occupations, attractive interactions give rise to much richer phenomena: We analytically characterize a Hopf bifurcation which separates a high-temperature regime of uniform occupations from a low-temperature one where all units coalesce into a single state. For odd $q$, below the critical temperature starts a synchronization regime which ends via a second phase transition at lower temperatures, while for even $q$ this intermediate phase disappears. We find that interactions have no effects except below critical temperature for attractive interactions. A thermodynamic analysis reveals that the dissipated work is reduced in this regime, whose temperature range is shown to decrease as $q$ increases. The $q$ dependence of the power-efficiency trade-off is also analyzed.

In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a unified theoretical framework for the drift of such patterns under small external perturbations, in terms of overlap integrals between the perturbation and the adjoint critical eigenfunctions of the linearized operator (i.e., response functions). For spiral waves, the finite radius of the spiral tip trajectory and spiral wave meander are taken into account. Different coordinate systems can be chosen, depending on whether one wants to predict the motion of the spiral-wave tip, the time-averaged tip path, or the center of the meander flower. The framework is applied to analyze the drift of a meandering spiral wave in a constant external field in different regimes.