A systematic algorithm to reduce the potential energy surface is presented, which is based on successive inversions of virial data, so that the molecular dynamics is capable of preserving the thermodynamics of the system. The algorithm is tested by reducing the potential energy surface of diatomic molecules that interact through a non-spherically symmetric potential, into an effective potential which is spherically symmetric, showing that all rotational degrees of freedom of the molecules can be disregarded from the thermodynamic point of view, as long as the virial expansion is a good description of the system. Furthermore, our analysis allows us to understand how we can make use of the non-uniqueness of the solution of an inverse problem to generate simplified models.

We numerically discovered around 100 distinct nonrelativistic collisionless periodic three-body orbits in the Coulomb potential in vacuo, with vanishing angular momentum, for equal-mass ions with equal absolute values of charges. These orbits are classified according to their symmetry and topology, and a linear relation is established between the periods, at equal energy, and the topologies of orbits. Coulombic three-body orbits can be formed in ion traps, such as the Paul, or the Penning one, where one can test the period vs topology prediction.

The percolation transition in growing networks can be of infinite order, following the Berezinskii-Kosterlitz-Thouless (BKT) transition. Examples can be found in diverse systems, including coauthorship networks and protein interaction networks. Here, we investigate how such an infinite-order percolation transition is changed by the global suppression (GS) effect. We find that the BKT infinite-order transition breaks down, but the features of infinite-order, second-order, and first-order transitions all emerge in a single framework. Owing to the GS effect, the transition point $p_c$ is delayed, below which the critical region is extended. The power-law behavior of the cluster size distribution reaches the state with the exponent $\tau =2$ at $p_c$, suggesting that the system has the maximum diversity of cluster sizes and a first-order percolation transition occurs at $p_c$.

Many proteins assemble into homomultimeric structures, with a number of subunits that can vary substantially among phylogenetic lineages. As protein-protein interactions require productive encounters among subunits, such variation might partially be explained by variation in cellular protein abundance. Protein abundance in turn depends on the intrinsic rates of production and decay of mRNA and protein molecules, as well as rates of cell growth and division. Using a stochastic framework for prediction of the multimeric state of a protein as a function of these processes and the free energy associated with interface-interface binding, we demonstrate agreement with a wide class of proteins using E. coli proteome data. As such, this platform, which links protein quaternary structure with biochemical rates governing gene expression, protein association and dissociation, and cell growth and division, can be extended to evolutionary models for the emergence and diversification of multimers. While it is tempting to think of multimerization as adaptive, the diversity of multimeric states raises the question of its functional role and impact on fitness. As a force driving selection, we consider the possible increase in enzymatic activity of proteins arising strictly as a consequence of interface-interface binding—namely, enhanced stability to degradation, substrate binding affinity, or catalytic rate of multimers with respect to monomers without invoking further conformational changes, as in allostery. For fixed cost of protein production, we find a benefit conferred by multimers that is dependent on context and can therefore become different in diverging lineages.

A stability and bifurcation analysis of a kinetic equation indicates that the flocking bifurcation of the two-dimensional Vicsek model exhibits an interplay between parabolic and hyperbolic behavior. For box sizes smaller than a certain large value, flocking appears continuously from a uniform disordered state at a critical value of the noise. Because of mass conservation, the amplitude equations describing the flocking state consist of a scalar equation for the density disturbance from the homogeneous particle density (particle number divided by box area) and a vector equation for a current density. These two equations contain two timescales. At the shorter scale, they are a hyperbolic system in which time and space scale in the same way. At the longer, diffusive, timescale, the equations are parabolic. The bifurcating solution depends on the angle and is uniform in space as in the normal form of the usual pitchfork bifurcation. We show that linearization about the latter solution is described by a Klein-Gordon equation in the hyperbolic timescale. Then there are persistent oscillations with many incommensurate frequencies about the bifurcating solution; they produce a shift in the critical noise and resonate with a periodic forcing of the alignment rule. These predictions are confirmed by direct numerical simulations of the Vicsek model.

Since the early years of the linear elastic theory of fracture [linear elastic fracture mechanics (LEFM)], scientists have sought to understand and predict how fast cracks grow in a material or slip fronts propagate along faults. While shear cracks can travel faster than the shear wave speed, the Rayleigh wave speed is the limiting speed theoretically predicted for tensile failure. This work uncovers the existence of supershear episodes in the tensile (mode I) rupture of linearly elastic materials beyond the maximum allowable (sub-Rayleigh) speed predicted by the classical theory of dynamic fracture. While the admissible rupture speeds predicted by LEFM are verified for smooth crack fronts, we present numerically how a supershear burst can emerge from a discontinuity in crack front curvature. Using a spectral formulation of the three-dimensional elastodynamic equations coupled with a cohesive model of fracture, we study how these short-lived bursts create shock waves persisting far from the discontinuity site. This study provides insight on crack front instabilities present in the rapid tensile failure of brittle materials due to large distortions of the rupture front.

Due to their potential usefulness in engineering and medical applications, various artificial microswimmers have been proposed. In our previous paper et al. [T. Morita, T. Omori, and T. Ishikawa, Phys. Rev. E 98, 023108 (2018)], we introduced a microcapsule swimmer that underwent amoeboidlike shape deformation under vertical fluid oscillation and showed the advantages of using a solid membrane and fluid oscillation in terms of swimmer controllability. Although the microcapsule was capable of migrating in the Stokes flow regime, the propulsion direction was limited to vertically upward or downward. In this paper, therefore, we attempted to control the propulsion of a microcapsule in an arbitrary direction by imposing biaxial fluid oscillations, which is a major step toward future applications. Numerical results showed that the microcapsule could migrate in the horizontal and vertical directions by imposing biaxial fluid oscillations in the vertical and horizontal planes, respectively. The horizontal propulsion can be understood in terms of effective and recovery strokes, i.e., a stroke swimmer, whereas vertical propulsion is similar to rigid body motion induced by a torque, i.e., a torque swimmer. By sequentially imposing three types of fluid oscillations, we successfully controlled the microswimmer to draw a Π-shaped trajectory. Thus, these results illustrate that the position and trajectory of the microswimmer can be controlled arbitrarily in three dimensions. The knowledge presented in this paper is important for future artificial microswimmer designs.

We introduce a natural way to extend celebrated spin-cluster Monte Carlo algorithms for fast thermal lattice simulations at criticality, such as the Wolff algorithm, to systems in arbitrary fields, be they linear magnetic vector fields or nonlinear anisotropic ones. By generalizing the “ghost spin” representation to one with a “ghost transformation,” global invariance to spin symmetry transformations is restored at the cost of an extra degree of freedom which lives in the space of symmetry transformations. The ordinary cluster-building process can then be run on the representation. We show that this extension preserves the scaling of accelerated dynamics in the absence of a field for Ising, Potts, and $\mathrm{O}\left(n\right)$ models and demonstrate the method's use in modeling the presence of novel nonlinear fields. We also provide a c++ library for the method's convenient implementation for arbitrary models.

Branching processes are widely used to model phenomena from networks to neuronal avalanching. In a large class of continuous-time branching processes, we study the temporal scaling of the moments of the instant population size, the survival probability, expected avalanche duration, the so-called avalanche shape, the $n$-point correlation function, and the probability density function of the total avalanche size. Previous studies have shown universality in certain observables of branching processes using probabilistic arguments; however, a comprehensive description is lacking. We derive the field theory that describes the process and demonstrate how to use it to calculate the relevant observables and their scaling to leading order in time, revealing the universality of the moments of the population size. Our results explain why the first and second moment of the offspring distribution are sufficient to fully characterize the process in the vicinity of criticality, regardless of the underlying offspring distribution. This finding implies that branching processes are universal. We illustrate our analytical results with computer simulations.

We performed Monte Carlo simulations of the symbiotic contact process on different spatial dimensions ($d$). On the complete and random graphs (infinite dimension), we observe hysteresis cycles and bistable regions, what is consistent with the discontinuous absorbing-state phase transition predicted by mean-field theory. By contrast, on a regular square lattice, we find no signs of bistability or hysteretic behavior. This result suggests that the transition in two dimensions is rather continuous. Based on our numerical observations, we conjecture that the nature of the transition changes at the upper critical dimension ($d_c$), from continuous ($d<d_c$) to discontinuous ($d>d_c$).

The displacive structural phase transition in a two-dimensional model solid due to Benassi et al. [A. Benassi et al., Phys. Rev. Lett. 106, 256102 (2011)] is analyzed using Monte Carlo simulations and finite-size scaling. The model is shown to be a member of the two-dimensional six-state clock model universality class. Consequently, the model features two phase transitions, implying the existence of three thermodynamically distinct phases, namely, a low-temperature phase with long-range order, an intermediate critical phase with power-law decay of correlations, and a high-temperature phase with short-range order.

Numerous empirical studies show that when people play social dilemma games in the laboratory they often cooperate conditionally, and the frequency of conditional cooperators differs between communities. However, this has not yet been fully explained by social dilemma models in structured populations. Here we model a population as a two-layer multiplex network, where the two layers represent economic and social interactions respectively. Players play a conditional public goods game on the economic layer, their donations to the public good dependent on the donations of their neighbors, and player strategies evolve through a combination of payoff comparison and social influence. We find that both conditional cooperation and social influence lead to increased cooperation in the public goods game, with social influence being the dominant factor. Cooperation is more prevalent both because conditional cooperators are less easily exploited by free-riders than unconditional cooperators, and also because social influence tends to preserve strategies over time. Interestingly the choice of social imitation rule does not appear to be important: it is rather the separation of strategy imitation from payoff comparison that matters. Our results highlight the importance of social influence in maintaining cooperative behavior across populations, and suggest that social behavior is more important than economic incentives for the maintenance of cooperation.

Superposition approaches have generally been proposed to create a dynamic rheological map to access colloidal glassy dynamics beyond experimental time windows. However, the validity of the superposition approaches in colloids near the glass transition is questionable owing to the well-known emergence of a $\beta$-relaxation process there. Here, we employ a time-concentration superposition (TCS) approach, analogous to time-temperature superposition and TCS approaches in molecular systems, utilizing a combination of macroscopic rheological experiments and microscopic Brownian dynamics simulations, where concentration jumps are performed by a sudden growth of particle size [soft polystyrene-poly ($N$-isopropylacrylamide) particles in experiment and nearly hard spheres in simulation] at a fixed number of particles. We have examined whether a characteristic master curve can be obtained through horizontal and vertical shifting of the dynamic data, finding that TCS does not hold for either the experimental or simulation systems. We identify the origin of this breakdown as not only the emergence of a strong $\beta$-relaxation process but also its overlap with the $\alpha$ relaxation in both the experimental soft-sphere and the simulated nearly hard-sphere colloids near the glass transition concentration. Further understanding of the lack of validity of TCS results from analysis of both experimental and simulation data in the framework of the Baumgaertel-Schausberger-Winter (BSW) relaxation spectrum which provide a means to determine the concentration dependences of both the $\alpha$ and the $\beta$ relaxations, which seem to follow TCS themselves.

Using inverse Ising inference we show that the absorbing states of the one-dimensional Manna model can be described by an equilibrium model with an emergent interaction displaying short-ranged repulsion and long-ranged attraction. As the model approaches the critical point the interaction becomes purely repulsive, decaying as $r^{-\alpha }$ and we conjecture the exact value $\alpha =1/2$, suggesting density fluctuations decay as $r^{-3/2}$. We present a simple Gaussian field theory for the long-distance behavior of critical absorbing states and discuss implications for the Manna universality class.

Cyclic predator-prey systems have been shown to give rise to rich, and novel, space-time patterns, as, for example, coarsening domains with nontrivial in-domain dynamics. In this work, we study numerically the responses of a cyclic six-species model, characterized by the formation of spirals inside coarsening domains, to two different types of perturbations: changing the values of the predation and reproduction rates as well as changing the interaction scheme. For both protocols, we monitor the time evolution of the system after the onset of the perturbation through the measurement of dynamical correlation functions and time-dependent densities of empty sites. In this way, we gain insights into the complex responses to different perturbations in a system in which spirals, which are due to the formation of cyclic alliances, dominate the dynamics inside the coarsening domains.

We establish the power output and efficiency of a single-particle nanomachine whose characteristic component is a nonlinear potential $U\left(r\right)\propto {\left|r\right|}^{\alpha }$. We do so by considering multi-temperature “elliptic” and Carnot-like cycles. In both protocols we verify the linear case $\alpha =2$ corresponds to a threshold situation. In the former, it establishes the transition from a machine behavior—wherefrom we can extract work—to a refrigerator performance. Last but not least, a closer look at the isentropic lines of these systems sets clear parameter value limitations to the definition of a Carnot cycle using such type of mechanical system. An observation that goes beyond standard thermodynamic conditions, where the existence of a Carnot cycle must be material independent.

We report the occurrence of vibrational resonance (VR) for a particle placed in a nonlinear asymmetrical Remoissenet-Peyrard potential substrate whose shape is subjected to deformation. We focus on the possible influence of deformation on the occurrence of vibrational resonance (VR) and show evidence of deformation-induced double resonances. By an approximate method involving direct separation of the time scales, we derive the equation of slow motion and obtain the response amplitude. We validate the theoretical results by numerical simulation. Besides revealing the existence of deformation-induced VR, our results show that the parameters of the deformed potential have a significant effect on the VR and can be employed to either suppress or modulate the resonance peaks, thereby controlling the resonances. By exploring the time series, the phase space structures, and the bifurcation of the attractors in the Poincaré section, we demonstrate that there are two distinct dynamical mechanisms that can give rise to deformation-induced resonances, viz., (i) monotonic increase in the size of a periodic orbit and (ii) bifurcation from a periodic to a quasiperiodic attractor.

Planar graphs and their spatial embedding—planar maps—are used in many different fields due to their ubiquity in the real world (leaf veins in biology, street patterns in urban studies, etc.) and they are also fundamental objects in mathematics and combinatorics. These graphs have been well described in the literature, but we do not have so far a clear way to cluster them in different families. A typology of planar maps would be very useful and would allow us to monitor their changes, to compare them with each other, or to correlate their structure with other properties. Using an algorithm which merges recursively the smallest areas in the graph with the largest ones, we plot the Gini coefficient of areas of cells and obtain a profile associated with each network. We test the relevance of these “Gini profiles” on simulated networks and on real street networks of Barcelona, New York, and Tokyo, and discuss their main properties. We also apply this method to the case of Paris at different dates which allows us to follow the structural changes of this system. Finally, we discuss the important ingredient of spatial heterogeneity of real-world planar graphs and test some ideas on Manhattan and Tokyo. Our results show that the Gini profile encodes various information about the structure of the corresponding planar map and represents a good candidate for constructing relevant classes of these objects.

In this paper, magnetic resonance velocimetry is used to measure the spatially resolved velocity and velocity fluctuations for granular flow in a Couette cell for four different particle sizes. The largest particles studied ($d_p=1.7\mathrm{mm}$) showed significant slip at the inner wall. The remaining particles showed no slip and all exhibit the same behavior in the profiles of the mean velocity and variance of velocity. The measurements demonstrate that the velocity and variance in velocity scale with the inner wall velocity $U$; the variance does not scale with $U^2$. The experimental data were compared with a kinetic theory based model of granular flow and a hydrodynamic model. It was found that the shear rate scales with an exponent of 1.5–2.0 with respect to the velocity fluctuations $\sqrt{\langle u_y^2\rangle }$, compared with the value of 1.0 expected from kinetic theory. The difference in the exponent is consistent with the effect of collective dynamics as described by the hydrodynamic model.