In this work we consider a simulation strategy for assembling Janus nanoparticles in oil-in-water emulsion droplets by evaporation based on the dissipative particle dynamics method. Our simple method reproduces all the observed cluster configurations that have been explored experimentally. In addition, the kinetic process of cluster formation is systematically investigated. We observe a structural transition from spherical packings to minimal second-moment configurations via visual inspection and a simple angle parameter. We reveal that the critical volume at which the transition occurs is a cubic function of the number of particles, $N$. Our approach also allows us to anticipate higher-order clusters, overcoming the limitations of the standard methods in the literature. Similarly to small $N$ values, we find that for each $N$ in the range of $16–39$, all final clusters have a unique configuration.

Multiple pendulums are investigated numerically and analytically to clarify the nonuniformity of average kinetic energies of particles. The nonuniformity is attributed to the system having holonomic constraints and it is consistent with the generalized principle of the equipartition of energy. With the use of explicit expression for Hamiltonian of a multiple pendulum, approximate expressions for temporal and statistical average of kinetic energies are obtained, where the average energies are expressed in terms of masses of particles. In a typical case, the average kinetic energy is large for particles near the end of the pendulum and small for those near the root. Moreover, the exact analytic expressions for the average kinetic energy of the particles are obtained for a double pendulum.

The dendritic growth in rechargeable batteries is one of the hurdles for the utilization of high energy-density elements, such as alkaline metals, as the electrode. Herein we explore the preventive role of the curved electrode surface in the cylindrical electrode design versus the flat geometry on the stochastic evolution of the dendritic crystals. In this regard we establish a coarse-grained Monte Carlo paradigm in the polar coordinates $(r,\theta )$, which runs in a larger scale of time and space ($\sim \mu \text{s},\sim \text{nm}$ ) than those of interionic collisions ($\sim \text{f}\text{s}$, Å). Subsequently we track the density and the maximum reach of the microstructures in real time, and we elaborate on the underlying mechanisms for their correlation of the relative dendrite measure with the electrode curvature. Such quantification of the positive impact of the curvature on suppressing dendrites could be utilized as an effective longevity design parameter, particularly for the cases prone to dendritic propagation.

Continuum models like the Helfrich Hamiltonian are widely used to describe fluid bilayer vesicles. Here we study the molecular dynamics compatible dynamics of the vertices of two-dimensional meshes representing the bilayer, whose in-plane motion is only weakly constrained. We show (i) that Jülicher's discretization of the curvature energy offers vastly superior robustness for soft meshes compared to the commonly employed expression by Gommper and Kroll and (ii) that for sufficiently soft meshes, the typical behavior of fluid bilayer vesicles can emerge even if the mesh connectivity remains fixed throughout the simulations. In particular, soft meshes can accommodate large shape transformations, and the model can generate the typical ${\ell }^{-4}$ signal for the amplitude of surface undulation modes of nearly spherical vesicles all the way up to the longest wavelength modes. Furthermore, we compare results for Newtonian, Langevin, and Brownian dynamics simulations of the mesh vertices to demonstrate that the internal friction of the membrane model is negligible, making it suitable for studying the internal dynamics of vesicles via coupling to hydrodynamic solvers or particle-based solvent models.

Inverse Ising inference allows pairwise interactions of complex binary systems to be reconstructed from empirical correlations. Typical estimators used for this inference, such as pseudo-likelihood maximization (PLM), are biased. Using the Sherrington-Kirkpatrick model as a benchmark, we show that these biases are large in critical regimes close to phase boundaries, and they may alter the qualitative interpretation of the inferred model. In particular, we show that the small-sample bias causes models inferred through PLM to appear closer to criticality than one would expect from the data. Data-driven methods to correct this bias are explored and applied to a functional magnetic resonance imaging data set from neuroscience. Our results indicate that additional care should be taken when attributing criticality to real-world data sets.

Data sets in the real world are often complex and to some degree hierarchical, with groups and subgroups of data sharing common characteristics at different levels of abstraction. Understanding and uncovering the hidden structure of these data sets is an important task that has many practical applications. To address this challenge, we present a general method for building relational data trees by exploiting the learning dynamics of the restricted Boltzmann machine. Our method is based on the mean-field approach, derived from the Plefka expansion, and developed in the context of disordered systems. It is designed to be easily interpretable. We tested our method in an artificially created hierarchical data set and on three different real-world data sets (images of digits, mutations in the human genome, and a homologous family of proteins). The method is able to automatically identify the hierarchical structure of the data. This could be useful in the study of homologous protein sequences, where the relationships between proteins are critical for understanding their function and evolution.

Nonequilibrium systems in chemistry and physics are generally modeled with the Boltzmann, Fokker-Planck, and Master equations. There has been a considerable interest in the nonequilibrium distributions of electrons and ions in space physics in different environments as well as in other systems. An often-used empirical model to characterize these distributions, especially in space physics, is the Kappa distribution. There have been numerous efforts to provide a theoretical basis for the Kappa distribution that include the Fokker-Planck equation with specific drift and diffusion coefficients. Alternatively, the maximization of the Tsallis nonextensive entropy provides the desired Kappa distribution. This paper examines three families of Fokker-Planck equations that provide a steady-state Kappa distribution as well as a myriad of other nonequilibrium distributions. The relationship of these works with analogous studies of distributions with asymptotic high-energy tails is also considered. It is clear that the many different nonequilibrium distribution functions that can occur cannot all be rationalized with Gibbs-Boltzmann statistical mechanics, which uniquely gives equilibrium distributions, or with the Tsallis nonextensive entropy, which gives uniquely the Kappa distribution. The current research is directed towards an improved understanding of the origin of nonequilibrium distributions in several specific systems.

Many cellular organelles are membrane-bound structures with complex membrane composition and shape. Their shapes have been observed to depend on the metabolic state of the organelle and the mechanisms that couple biochemical pathways and membrane shape are still actively investigated. Here, we study a model coupling inhomogeneities in the lipid composition and membrane geometry via a generalized Helfrich free energy. We derive the resulting stress tensor, the Green's function for a tubular membrane, and compute the phase diagram of the induced deformations. We then apply this model to study the deformation of mitochondria cristae described as membrane tubes supporting a $p\mathrm{H}$ gradient at its surface. This gradient in turn controls the lipid composition of the membrane via the protonation or deprotonation of cardiolipins, which are acid-based lipids known to be crucial for mitochondria shape and functioning. Our model predicts the appearance of tube deformations resembling the observed shape changes of cristea when submitted to a proton gradient.

Visualization of the adjacency matrix enables us to capture macroscopic features of a network when the matrix elements are aligned properly. Community structure, a network consisting of several densely connected components, is a particularly important feature and the structure can be identified through the adjacency matrix when it is close to a block-diagonal form. However, classical ordering algorithms for matrices fail to align matrix elements such that the community structure is visible. In this study, we propose an ordering algorithm based on the maximum-likelihood estimate of the ordered random graph model. We show that the proposed method allows us to more clearly identify community structures than the existing ordering algorithms.

We combine stochastic thermodynamics, large deviation theory, and information theory to derive fundamental limits on the accuracy with which single cell receptors can estimate external concentrations. As expected, if the estimation is performed by an ideal observer of the entire trajectory of receptor states, then no energy consuming nonequilibrium receptor that can be divided into bound and unbound states can outperform an equilibrium two-state receptor. However, when the estimation is performed by a simple observer that measures the fraction of time the receptor is bound, we derive a fundamental limit on the accuracy of general nonequilibrium receptors as a function of energy consumption. We further derive and exploit explicit formulas to numerically estimate a Pareto-optimal tradeoff between accuracy and energy. We find this tradeoff can be achieved by nonuniform ring receptors with a number of states that necessarily increases with energy. Our results yield a thermodynamic uncertainty relation for the time a physical system spends in a pool of states and generalize the classic Berg-Purcell limit [H. C. Berg and E. M. Purcell, Biophys. J. 20, 193 (1977)] on cellular sensing along multiple dimensions.

Intracellular protein patterns regulate a variety of vital cellular processes such as cell division and motility, which often involve dynamic cell-shape changes. These changes in cell shape may in turn affect the dynamics of pattern-forming proteins, hence leading to an intricate feedback loop between cell shape and chemical dynamics. While several computational studies have examined the rich resulting dynamics, the underlying mechanisms are not yet fully understood. To elucidate some of these mechanisms, we explore a conceptual model for cell polarity on a dynamic one-dimensional manifold. Using concepts from differential geometry, we derive the equations governing mass-conserving reaction–diffusion systems on time-evolving manifolds. Analyzing these equations mathematically, we show that dynamic shape changes of the membrane can induce pattern-forming instabilities in parts of the membrane, which we refer to as regional instabilities. Deformations of the local membrane geometry can also (regionally) suppress pattern formation and spatially shift already existing patterns. We explain our findings by applying and generalizing the local equilibria theory of mass-conserving reaction–diffusion systems. This allows us to determine a simple onset criterion for geometry-induced pattern-forming instabilities, which is linked to the phase-space structure of the reaction–diffusion system. The feedback loop between membrane shape deformations and reaction–diffusion dynamics then leads to a surprisingly rich phenomenology of patterns, including oscillations, traveling waves, and standing waves, even if these patterns do not occur in systems with a fixed membrane shape. Our paper reveals that the local conformation of the membrane geometry acts as an important dynamical control parameter for pattern formation in mass-conserving reaction-diffusion systems.

High-intensity laser solid interactions are capable of generating attosecond light bursts via high-harmonic generation—most work focuses on single beam interactions. In this paper, we perform a numerical investigation on the role of wavelength and polarization in relativistic, high-harmonic generation from normal-incidence, two-beam interactions off plasma mirrors. We find that the two-beam harmonic-generation mechanism is a robust process described by a set of well-defined selection rules. We demonstrate that the emitted harmonics from normal-incidence interactions exhibit an intensity optimization when the incident fields are of equal intensity for two-color circularly polarized fields.

A resolvable quantum many-body Hamiltonian is introduced that mimics the behavior of the autocatalytic chemical reaction $A+B\rightleftarrows 2B$ involving two different molecular species, $A$ and $B$. The model also describes two nonlinearly coupled modes of an optical cavity. Consistent with the current understanding of the relaxation dynamics of integrable systems in isolation, the wave function following a quantum quench exhibits irreversibility with retention of the memory about its initial conditions. Salient features of the model include a marked similarity with conventional quantum decay and a total $B$-to-A conversion, with associated classical-like behavior of the wave function, when the initial state does not contain $A$-type molecules.

A complete understanding of the statistics of the work done by quenching a parameter of a quantum many-body system is still lacking in the presence of an initial quantum coherence in the energy basis. In this case, the work can be represented by a class of quasiprobability distributions. Here, we try to clarify the genuinely quantum features of the process by studying the work quasiprobability for an Ising model in a transverse field. We consider both a global and local quench by focusing mainly on the thermodynamic limit. We find that, while for a global quench there is a symmetric noncontextual representation with a Gaussian probability distribution of work, for a local quench we can get quantum contextuality as signaled by a negative fourth moment of the work. Furthermore, we examine the critical features related to a quantum phase transition and the role of the initial quantum coherence as a useful resource.

Large deviation theory provides the framework to study the probability of rare fluctuations of time-averaged observables, opening new avenues of research in nonequilibrium physics. Some of the most appealing results within this context are dynamical phase transitions (DPTs), which might occur at the level of trajectories in order to maximize the probability of sustaining a rare event. While macroscopic fluctuation theory has underpinned much recent progress on the understanding of symmetry-breaking DPTs in driven diffusive systems, their microscopic characterization is still challenging. In this work we shed light on the general spectral mechanism giving rise to continuous DPTs not only for driven diffusive systems, but for any jump process in which a discrete ${\mathbb{Z}}_n$ symmetry is broken. By means of a symmetry-aided spectral analysis of the Doob-transformed dynamics, we provide the conditions whereby symmetry-breaking DPTs might emerge and how the different dynamical phases arise from the specific structure of the degenerate eigenvectors. In particular, we show explicitly how all symmetry-breaking features are encoded in the subleading eigenvectors of the degenerate subspace. Moreover, by partitioning configuration space into equivalence classes according to a proper order parameter, we achieve a substantial dimensional reduction which allows for the quantitative characterization of the spectral fingerprints of DPTs. We illustrate our predictions in several paradigmatic many-body systems, including (1) the one-dimensional boundary-driven weakly asymmetric exclusion process (WASEP), which exhibits a particle-hole symmetry-breaking DPT for current fluctuations, (2) the three- and four-state Potts model for spin dynamics, which displays discrete rotational symmetry-breaking DPTs for energy fluctuations, and (3) the closed WASEP which presents a continuous symmetry-breaking DPT into a time-crystal phase characterized by a rotating condensate.

We have studied the properties of a sandpile automata under the constraint of height restriction of sand columns. In this sandpile, an active site transfers a grain to a neighboring site if and only if the height of the sand column at the destination site is less than a preassigned value $n_c$. This sandpile was studied by Dickman et al. [Phys. Rev. E 66, 016111 (2002)] in a conserved system with a fixed number of sand grains. In contrast, we have studied the avalanche dynamics of the driven sandpile under the open boundary conditions. The deterministic dynamics of the Bak, Tang, and Wiesenfeld (BTW) sandpile under the height restriction is found to be non-Abelian. Using numerical results, we argue that the steady states of the sandpile are exactly the recurrent states of the BTW sandpile, but occur with nonuniform probabilities. A detailed analysis of the cluster size distributions indicates that the associated exponent values are likely to be different from those of the BTW sandpile. The other differences include that the drop number distribution decays as a power law, and the largest avalanche size grows as the fourth power of the system size.

Controlling complex networks has received much attention in the past two decades. In order to control complex networks in practice, recent progress is mainly focused on the control energy required to drive the associated system from an initial state to any final state within finite time. However, one of the major challenges when controlling complex networks is that the amount of control energy is usually prohibitively expensive. Previous explorations on reducing the control energy often rely on adding more driver nodes to be controlled directly by external control inputs, or reducing the number of target nodes required to be controlled. Here we show that the required control energy can be reduced exponentially by appropriately setting the initial states of uncontrollable nodes for achieving the target control of complex networks. We further present the energy-optimal initial states and theoretically prove their existence for any structure of network. Moreover, we demonstrate that the control energy could be saved by reducing the distance between the energy-optimal states set and the initial states of uncontrollable nodes. Finally, we propose a strategy to determine the optimal time to inject the control inputs, which may reduce the control energy exponentially. Our conclusions are all verified numerically, and shed light on saving control energy in practical control.

We have found that phase transitions occurring between three traffic phases [free flow (F), synchronized flow (S), and wide moving jam (J)] determine the spatiotemporal dynamics of traffic consisting of $100\%$ automated-driving vehicles moving on a two-lane road with an on-ramp bottleneck. This means that three-phase traffic theory is a common framework for the description of traffic states independent of whether human-driving or automated-driving vehicles move in vehicular traffic. To prove this, we have studied automated-driving vehicular traffic with the use of classical Helly's model [Proceedings of the Symposium on Theory of Traffic Flow (Elsevier, Amsterdam, 1959), pp. 207–238] widely applied for automated vehicle motion. Although dynamic rules of the motion of automated-driving vehicles in a road lane are qualitatively different from those of human-driving vehicles, we have revealed that traffic breakdown ($\mathrm{F}\to \mathrm{S}$ transition) at the bottleneck exhibits the nucleation nature, which was observed in empirical field data measured in traffic consisting of $100\%$ human-driving vehicles. The physics of the nucleation nature of the $\mathrm{F}\to \mathrm{S}$ transition in automated-driving traffic is associated with a discontinuity in the rate of lane-changing that causes the discontinuity in the rate of over-acceleration. This discontinuous character of over-acceleration leads to both the existence and self-maintaining of synchronized flow at the bottleneck in automated-driving vehicular traffic as well as to the existence at any time instant of a range of highway capacities between some minimum and maximum capacities. Within the capacity range, an $\mathrm{F}\to \mathrm{S}$ transition can be induced; however, when the maximum capacity is exceeded, then after some time-delay a spontaneous $\mathrm{F}\to \mathrm{S}$ transition occurs at the bottleneck. The phases F, S, and J can coexist each other in space and time.