The native state structures of globular proteins are stable and well packed indicating that self-interactions are favored over protein-solvent interactions under folding conditions. We use this as a guiding principle to derive the geometry of the building blocks of protein structures—α helices and strands assembled into $\beta$ sheets—with no adjustable parameters, no amino acid sequence information, and no chemistry. There is an almost perfect fit between the dictates of mathematics and physics and the rules of quantum chemistry. Protein evolution is facilitated by sequence-independent platforms, which can elaborate sequence-dependent functional diversity. Our work highlights the vital role of discreteness in life and may have implications for the creation of artificial life and on the nature of life elsewhere in the cosmos.

Synaptic receptor and scaffold molecules self-assemble into membrane protein domains, which play an important role in signal transmission across chemical synapses. Experiment and theory have shown that the formation of receptor-scaffold domains of the characteristic size observed in nerve cells can be understood from the receptor and scaffold reaction and diffusion processes suggested by experiments. We employ here kinetic Monte Carlo (KMC) simulations to explore the self-assembly of synaptic receptor-scaffold domains in a stochastic lattice model of receptor and scaffold reaction-diffusion dynamics. For reaction and diffusion rates within the ranges of values suggested by experiments we find, in agreement with previous mean-field calculations, self-assembly of receptor-scaffold domains of a size similar to that observed in experiments. Comparisons between the results of our KMC simulations and mean-field solutions suggest that the intrinsic noise associated with receptor and scaffold reaction and diffusion processes accelerates the self-assembly of receptor-scaffold domains, and confers increased robustness to domain formation. In agreement with experimental observations, our KMC simulations yield a prevalence of scaffolds over receptors in receptor-scaffold domains. Our KMC simulations show that receptor and scaffold reaction-diffusion dynamics can inherently give rise to plasticity in the overall properties of receptor-scaffold domains, which may be utilized by nerve cells to regulate the receptor number at chemical synapses.

Protein design is the inverse approach of the three-dimensional (3D) structure prediction for elucidating the relationship between the 3D structures and amino acid sequences. In general, the computation of the protein design involves a double loop: A loop for amino acid sequence changes and a loop for an exhaustive conformational search for each amino acid sequence. Herein, we propose a novel statistical mechanical design method using Bayesian learning, which can design lattice proteins without the exhaustive conformational search. We consider a thermodynamic hypothesis of the evolution of proteins and apply it to the prior distribution of amino acid sequences. Furthermore, we take the water effect into account in view of the grand canonical picture. As a result, on applying the 2D lattice hydrophobic-polar (HP) model, our design method successfully finds an amino acid sequence for which the target conformation has a unique ground state. However, the performance was not as good for the 3D lattice HP models compared to the 2D models. The performance of the 3D model improves on using a 20-letter lattice proteins. Furthermore, we find a strong linearity between the chemical potential of water and the number of surface residues, thereby revealing the relationship between protein structure and the effect of water molecules. The advantage of our method is that it greatly reduces computation time, because it does not require long calculations for the partition function corresponding to an exhaustive conformational search. As our method uses a general form of Bayesian learning and statistical mechanics and is not limited to lattice proteins, the results presented here elucidate some heuristics used successfully in previous protein design methods.

We study how bacteria rectification in microfluidics devices can be optimized by performing experiments with eight ratchets of different shape and size. Results show that curved ratchets perform best and that their radius of curvature influences how well they perform, as it affects the time bacteria spend on the ratchet surface. We find that the optimal bacterial ratchet is a $60\mu \mathrm{m}$ radius semicircle witch $15\mu \mathrm{m}$ concavities. We also show that the angle at which bacteria leave the ratchets can play an important role in their efficiency. Lastly, we reproduce our experimental conditions in a simple numerical simulation to confirm our findings.

We develop a model to investigate analytically and numerically the mechanics of wound opening made in a viscoelastic, isotropic, homogeneous, and incompressive thin tissue. This process occurs just immediately after the wound infliction. Before any active biological action has taken place, the tissue relaxes, and the wound opens mostly due to the initial homeostatic tension of the tissue, its elastic and viscous properties, and the existing friction between the tissue and its substrate. We find that for a circular wound the regimes of deformation are defined by a single adimensional parameter $\lambda$, which characterizes the relative importance of viscosity over friction.

A droplet bouncing on the surface of a vertically vibrating liquid bath can walk horizontally, guided by the waves it generates on each impact. This results in a self-propelled classical particle-wave entity. By using a one-dimensional theoretical pilot-wave model with a generalized wave form, we investigate the dynamics of this particle-wave entity. We employ different spatial wave forms to understand the role played by both wave oscillations and spatial wave decay in the walking dynamics. We observe steady walking motion as well as unsteady motions such as oscillating walking, self-trapped oscillations, and irregular walking. We explore the dynamical and statistical aspects of irregular walking and show an equivalence between the droplet dynamics and the Lorenz system, as well as making connections with the Langevin equation and deterministic diffusion.

The free-energy lattice Boltzmann (LB) method is a multiphase LB approach based on the thermodynamic theory. Compared with traditional free-energy LB models, which employ a nonideal thermodynamic pressure tensor, the chemical-potential-based free-energy LB model has attracted much attention in recent years as it avoids computing the thermodynamic pressure tensor and its divergence. In this paper, we propose an improved wetting boundary condition for the chemical-potential-based free-energy LB model. Different from the original wetting boundary condition in the literature, the improved wetting boundary condition utilizes a surface chemical potential that is compatible with the chemical potential of the fluid domain. Accordingly, the thermodynamic consistency of the chemical-potential-based free-energy LB model can be retained by the improved wetting boundary condition. Numerical simulations are performed for droplets resting on flat and cylindrical surfaces with different contact angles. The numerical results show that the improved wetting boundary condition yields more reasonable results and the maximum spurious velocities are found to be smaller by 2 ∼ 3 orders of magnitude than those produced by the original wetting boundary condition.

We present an extensive Monte Carlo investigation of the metastable lifetime through the reversal of the magnetization of spin-$s$ Ising and Blume-Capel models, where $s=\{1/2,1,3/2,2,5/2,3,7/2\}$. The mean metastable lifetime (or reversal time) is studied as a function of the applied magnetic field, and for both models it is found to obey the Becker-Döring theory, as was initially developed for the case of an $s=1/2$ Ising ferromagnet within the classical nucleation theory. Moreover, the decay of the metastable volume fraction nicely follows Avrami's law for all values of $s$ and for both models considered.

The Yard-Sale Model, a well known wealth exchange model whose observed macroscopic behavior hides many underlying aspects of particular complexity, was studied at the microscopic level. The performance of the agents during the successive transactions allows for the definition of successful or disadvantageous strategies according to the profit they achieve at the end of the process. Optimal strategies were found that maximize the individual wealth of each agent by performing their training through a genetic algorithm. The addition of different levels of rationality given by the amount of available information from their environment showed promising results, at both the microscopic and macroscopic levels. Remarkably, after the training process, the rational agents were able to determine when it would be convenient to interact with their opponents. Additionally, a region of parameters was found for which the distribution of wealth is a power law throughout the whole wealth range. As a general result, the incorporation of rational agents in this type of systems leads to greater inequality at the collective level.

Combinations of gyroscopic forces and nonequilibrium activity have been explored recently in rectifying energy in networks with complex geometries and topologies [Phys. Rev. X 10, 021036 (2020)]. Based on this previous work, here we study the effect of added time-periodic modulations. Numerical calculations show that the time-modulated network generates net energy transport between sites and the surroundings, even in the absence of any temperature gradients. Combining path integral formulation and diagrammatic expansion, we explain how such anomalous energy transport emerges, and show how the transport pattern in complex networks can be connected to relatively simple local structures.

The characterization of intermittency in turbulence has its roots in the refined similarity hypotheses of Kolmogorov, and if no proper definition is to be found in the literature, statistical properties of intermittency were studied and models were developed in an attempt to reproduce it. The first contribution of this work is to propose a requirement list to be satisfied by models designed within the Lagrangian framework. Multifractal stochastic processes are a natural choice to retrieve multifractal properties of the dissipation. Among them, we investigate the Gaussian multiplicative chaos formalism, which requires the construction of a log-correlated stochastic process $X_t$. The fractional Gaussian noise of Hurst parameter $H=0$ is of great interest because it leads to a log correlation for the logarithm of the process. Inspired by the approximation of fractional Brownian motion by an infinite weighted sum of correlated Ornstein-Uhlenbeck processes, our second contribution is to propose a stochastic model: $X_t={\int }_0^{\infty }{Y}_t^{x}k\left(x\right)dx$, where $Y_t^x$ is an Ornstein-Uhlenbeck process with speed of mean reversion $x$ and $k$ is a kernel. A regularization of $k\left(x\right)$ is required to ensure stationarity, finite variance, and logarithmic autocorrelation. A variety of regularizations are conceivable, and we show that they lead to the aforementioned multifractal models. To simulate the process, we eventually design a new approach relying on a limited number of modes for approximating the integral through a quadrature $X_t^N={\sum }_{i=1}^N{\omega }_i{Y}_t^{x_i}$, using a conventional quadrature method. This method can retrieve the expected behavior with only one mode per decade, making this strategy versatile and computationally attractive for simulating such processes, while remaining within the proposed framework for a proper description of intermittency.

The subject of the present study is the dynamics of a single cavitation bubble in a spherical liquid cell surrounded by an infinite elastic solid. It is shown that volume confinement strongly affects the manifestation of the classical cavitation Blake threshold. In particular, at liquid cell sizes smaller than some critical size, the cavitation is completely suppressed by volumetric confinement. The system of equations for the dynamics of a confined bubble, accounting for the mass of gas in the bubble, surface tension, liquid compressibility, solid elasticity, and damping due to viscosity in the liquid cell, is derived. The pressure in the solid far away from the bubble is used as an external driving force. Linear analysis of the bubble dynamics, including consideration of the natural frequency and amplitude-phase frequency response of the bubble-in-cell system, is conducted. In the nonlinear case, bifurcation diagrams are considered to determine the dynamic response of small and large bubbles in the states below and above the cavitation threshold, respectively.

The successful prediction of the specific heat of solids is a milestone in the kinetic theory of matter due to Debye. No such success, however, has ever been obtained for the specific heat of liquids, which has remained a mystery for over a century. A theory of specific heat of liquids is derived here using a recently proposed analytical form of the vibrational density of states of liquids, which takes into account saddle points in the liquid energy landscape via the so-called instantaneous normal modes (INMs), corresponding to negative eigenvalues (imaginary frequencies) of the Hessian matrix. The theory is able to explain the typical monotonic decrease in specific heat with temperature observed in liquids in terms of the average INM excitation lifetime decreasing with $T$ (in accordance with the Arrehnius law) and provides an excellent single-parameter fitting to several sets of experimental data for atomic and molecular liquids. It also correlates the height of the liquid energy barrier with the slope of the specific heat in the function of temperature in accordance with the available data. These findings demonstrate that the specific heat of liquids is controlled by the instantaneous normal modes, i.e., by localized unstable (exponentially decaying) vibrational excitations and provide the missing connection among anharmonicity, saddle points in the energy landscape, and the thermodynamics of liquids.

The rate of convergence of the jamming densities to their asymptotic high-dimensional tree approximation is studied, for two types of random sequential adsorption (RSA) processes on a $d$-dimensional cubic lattice. The first RSA process has an exclusion shell around a particle of nearest neighbors in all $d$ dimensions ($N1$ model). In the second process the exclusion shell consists of a $d$-dimensional hypercube with length $k=2$ around a particle ($N2$ model). For the $N1$ model the deviation of the jamming density ${\rho }_r\left(d\right)$ from its asymptotic high $d$ value ${\rho }_{\text{asy}}\left(d\right)=\frac{ln(1+2d)}{2d}$ vanishes as ${\left[\frac{ln(1+2d)}{2d}\right]}^{3.41}$. In addition, it has been shown that the coefficients $a_n\left(d\right)$ of the short-time expansion of the occupation density of this model (at least up to $n=6$) are given for all $d$ by a finite correction sum of order $(n-2)$ in $1/d$ to their asymptotic high $d$ limit. The convergence rate of the jamming densities of the $N2$ model to their high $d$ limits ${\rho }_{\text{asy}}\left(d\right)=d\frac{ln3}{3^d}$ is slow. For $2\le d\le 4$ the generalized Palasti approximation provides by far a better approximation. For higher $d$ values the jamming densities converge monotonically to the above asymptotic limits, and their decay with $d$ is clearly faster than the decay as ${(0.432332...)}^d$ predicted by the generalized Palasti approximation.

We consider the overdamped Brownian dynamics of a particle starting inside a square potential well which, upon exiting the well, experiences a flat potential where it is free to diffuse. We calculate the particle's probability distribution function (PDF) at coordinate $x$ and time $t, P(x,t)$, by solving the corresponding Smoluchowski equation. The solution is expressed by a multipole expansion, with each term decaying $t^{1/2}$ faster than the previous one. At asymptotically large times, the PDF outside the well converges to the Gaussian PDF of a free Brownian particle. The average energy, which is proportional to the probability of finding the particle inside the well, diminishes as $E\sim 1/t^{1/2}$. Interestingly, we find that the free energy of the particle, $F$, approaches the free energy of a freely diffusing particle, $F_0$, as $\delta F=F-F_0\sim 1/t$, i.e., at a rate faster than $E$. We provide analytical and computational evidence that this scaling behavior of $\delta F$ is a general feature of Brownian dynamics in nonconfining potential fields. Furthermore, we argue that $\delta F$ represents a diminishing entropic component which is localized in the region of the potential, and which diffuses away with the spreading particle without being transferred to the heat bath.

We consider a system consisting of two interacting classical particles, each one subject to an on-site potential and to a Langevin thermal bath. We analytically calculate the heat current that can be established through the system when the bath temperatures are different, for weak nonlinear forces. We explore the conditions under which the diode effect emerges when inverting the temperature difference. Despite the simplicity of this two-particle diode, an intricate dependence on the system parameters is put in evidence. Moreover, behaviors reported for long chains of particles can be extracted, for instance, the dependence of the flux with the interfacial stiffness and type of forces present, as well as the dependencies on the temperature required for rectification. These analytical results can be a tool to foresee the distinct role that diverse types of nonlinearity and asymmetry play in thermal conduction and rectification.

Collective oscillations and their suppression by external stimulation are analyzed in a large-scale neural network consisting of two interacting populations of excitatory and inhibitory quadratic integrate-and-fire neurons. In the limit of an infinite number of neurons, the microscopic model of this network can be reduced to an exact low-dimensional system of mean-field equations. Bifurcation analysis of these equations reveals three different dynamic modes in a free network: a stable resting state, a stable limit cycle, and bistability with a coexisting resting state and a limit cycle. We show that in the limit cycle mode, high-frequency stimulation of an inhibitory population can stabilize an unstable resting state and effectively suppress collective oscillations. We also show that in the bistable mode, the dynamics of the network can be switched from a stable limit cycle to a stable resting state by applying an inhibitory pulse to the excitatory population. The results obtained from the mean-field equations are confirmed by numerical simulation of the microscopic model.

In a world of hardening borders, nations may deprive themselves of enjoying the benefits of cooperative immigrants. Here we analyze the effect of efficient cooperative immigrants on a population playing public goods games. We considered a population structured on a square lattice with individuals playing public goods games with their neighbors. The demographics are determined by stochastic birth, death, and migration. The strategies spread through imitation dynamics. Our model shows that cooperation among natives can emerge due to social contagion of good role-model agents that can provide better quality public goods. Only a small fraction of efficient cooperators, among immigrants, is enough to trigger cooperation across the native population. We see that native cooperation achieves its peak at moderate values of immigration rate. Such efficient immigrant cooperators act as nucleation centers for the growth of cooperative clusters, which eventually dominate defection.

We investigate the effects of array geometry and flow orientation on transport of finite-sized particles in ordered arrays using Stokesian dynamics simulations. We find that quiescent diffusion is independent of array geometry over the range of volume fraction of the nanoposts examined. Longitudinal dispersion under flow depends on the direction of incident flow relative to the array lattice vectors. Taylor-Aris behavior is recovered for flow along the lattice directions, whereas a nonmonotonic dependence of the dispersion coefficient on the Péclet number is obtained for flow orientations slightly perturbed from certain lattice vectors, owing to a competition between directional locking and spatial velocity variations.

Traditionally the study of dynamics of glass-forming materials has been focused on the structural α relaxation. However, in recent years experimental evidence has revealed that a secondary β relaxation belonging to a special class, called the Johari-Goldstein (JG) β relaxation, has properties strongly linked to the primary α relaxation. By invoking the principle of causality, the relation implies the JG β relaxation is fundamental and indispensable for generating the α relaxation, and the properties of the latter are inherited from the former. The JG β relaxation is observed together with the α relaxation mostly by dielectric spectroscopy. The macroscopic nature of the data allows the use of arbitrary or unproven procedures to analyze the data. Thus the results characterizing the JG β relaxation and the relation of its relaxation time ${\tau }_{\beta }$ to the α-relaxation time ${\tau }_{\alpha }$ obtained can be equivocal and controversial. Coming to the rescue is the nuclear resonance time-domain-interferometry (TDI) technique covering a wide time range (${10}^{-9}–{10}^{-5}\mathrm{s}$) and a scattering vector $q$ range ($9.6–40\mathrm{n}{\mathrm{m}}^{-1}$). TDI experiments have been carried out on four glass formers, ortho-terphenyl [M. Saito et al., Phys. Rev. Lett. 109, 115705 (2012)], polybutadiene [T. Kanaya et al., J. Chem. Phys. 140, 144906 (2014)], 5-methyl-2-hexanol [F. Caporaletti et al., Sci. Rep. 9, 14319 (2019)], and 1-propanol [F. Caporaletti et al., Nat. Commun. 12, 1867 (2021)]. In this paper the TDI data are reexamined in conjunction with dielectric and neutron scattering data. The results show the JG β relaxation observed by dielectric spectroscopy is heterogeneous and comprises processes with different length scales. A process with a longer length scale has a longer relaxation time. TDI data also prove the primitive relaxation time ${\tau }_0$ of the coupling model falls within the distribution of the TDI $q$-dependent JG β-relaxation times. This important finding explains why the experimental dielectric JG β-relaxation times ${\tau }_{\beta }\left(T,P\right)$ is approximately equal to ${\tau }_0\left(T,P\right)$ as found in many glass formers at various temperature $T$ and pressure $P$. The result, ${\tau }_{\beta }\left(T,P\right)\approx {\tau }_0\left(T,P\right)$, in turn explains why the ratio ${\tau }_{\alpha }\left(T,P\right)/{\tau }_{\beta }\left(T,P\right)$ is invariant to changes of $T$ and pressure $P$ at constant ${\tau }_{\alpha }\left(T,P\right)$, the α-relaxation time.