We present a field theory to describe the composition of a surface spontaneously exchanging matter with its bulk environment. By only assuming matter conservation in the system, we show with extensive numerical simulations that, depending on the matter exchange rates, a complex patterned composition distribution emerges on the surface. For one-dimensional systems we show analytically and numerically that coarsening is arrested and as a consequence domains have a characteristic length scale. Our results show that the causes of heterogeneous lipid composition in cellular membranes may be justified in simple physical terms.

The random quantum $q$-state clock and Potts models are studied in two and three dimensions. The existence of Griffiths phases is tested in the two-dimensional case with $q=6$ by sampling the integrated probability distribution of local susceptibilities of the equivalent McCoy-Wu three-dimensional classical models with Monte Carlo simulations. For the random Potts model, numerical evidence of the existence of Griffiths phases is given and the finite-size effects are analyzed. For the clock model, the data also suggest the existence of a Griffiths phase but with much larger finite-size effects. The critical point of the random quantum clock model is then studied with the Strong-Disorder Renormalization Group. Evidence is given that, at strong enough disorder, this critical behavior is governed by the same infinite-disorder fixed point as the Potts model, for all the number of states $q$ considered. At weak disorder, our renormalization group method becomes unstable and does not allow us to make conclusions.

Utilizing surface roughness to manipulate thermal transport has aided important developments in thermoelectrics and heat dissipation in microelectronics. In this paper, through a multiparticle Lorentz gas model, it is found that thermal conductivity oscillates with the increase of surface roughness, and the oscillating thermal conductivity gradually disappears with the increase of nonlinearity. The transmittance analyses reveal that the oscillating thermal conductivity is caused by localized particles due to boundary effects. Nonlinearity will gradually break the localization. Thus, localization still exists in the weak nonlinear system, where there exists an interplay between nonlinear interaction and localization. Furthermore, it is also found that boundary shapes have a great influence on the oscillating thermal conductivity. Finally, we have also studied the oscillating thermal rectification effects caused by rough boundaries. This study gains insight into the boundary effect on thermal transport and provides a mechanism to manipulate thermal conductivity.

We show that cellular automata can classify data by inducing a form of dynamical phase coexistence. We use Monte Carlo methods to search for general two-dimensional deterministic automata that classify images on the basis of activity, the number of state changes that occur in a trajectory initiated from the image. When the number of time steps of the automaton is a trainable parameter, the search scheme identifies automata that generate a population of dynamical trajectories displaying high or low activity, depending on initial conditions. Automata of this nature behave as nonlinear activation functions with an output that is effectively binary, resembling an emergent version of a spiking neuron.

Masks have remained an important mitigation strategy in the fight against COVID-19 due to their ability to prevent the transmission of respiratory droplets between individuals. In this work, we provide a comprehensive quantitative analysis of the impact of mask-wearing. To this end, we propose a novel agent-based model of viral spread on networks where agents may either wear no mask or wear one of several types of masks with different properties (e.g., cloth or surgical). We derive analytical expressions for three key epidemiological quantities: The probability of emergence, the epidemic threshold, and the expected epidemic size. In particular, we show how the aforementioned quantities depend on the structure of the contact network, viral transmission dynamics, and the distribution of the different types of masks within the population. Through extensive simulations, we then investigate the impact of different allocations of masks within the population and tradeoffs between the outward efficiency and inward efficiency of the masks. Interestingly, we find that masks with high outward efficiency and low inward efficiency are most useful for controlling the spread in the early stages of an epidemic, while masks with high inward efficiency but low outward efficiency are most useful in reducing the size of an already large spread. Last, we study whether degree-based mask allocation is more effective in reducing the probability of epidemic as well as epidemic size compared to random allocation. The result echoes the previous findings that mitigation strategies should differ based on the stage of the spreading process, focusing on source control before the epidemic emerges and on self-protection after the emergence.

We develop an irregular lattice mass-spring model to simulate and study the deformation modes of a thin elastic ribbon as a function of applied end-to-end twist and tension. Our simulations reproduce all reported experimentally observed modes, including transitions from helicoids to longitudinal wrinkles, creased helicoids and loops with self-contact, and transverse wrinkles to accordion self-folds. Our simulations also show that the twist angles at which the primary longitudinal and transverse wrinkles appear are well described by various analyses of the Föppl–von Kármán equations, but the characteristic wavelength of the longitudinal wrinkles has a more complex relationship to applied tension than previously estimated. The clamped edges are shown to suppress longitudinal wrinkling over a distance set by the applied tension and the ribbon width, but otherwise have no apparent effect on measured wavelength. Further, by analyzing the stress profile, we find that longitudinal wrinkling does not completely alleviate compression, but caps the magnitude of the compression. Nonetheless, the width over which wrinkles form is observed to be wider than the near-threshold analysis predictions: the width is more consistent with the predictions of far-from-threshold analysis. However, the end-to-end contraction of the ribbon as a function of twist is found to more closely follow the corresponding near-threshold prediction as tension in the ribbon is increased, in contrast to the expectations of far-from-threshold analysis. These results point to the need for further theoretical analysis of this rich thin elastic system, guided by our physically robust and intuitive simulation model.

Traveling-wave electrophoresis (TWE) is a method for transporting charged colloidal particles used in many microfluidic techniques for particle manipulation and fractionation. This method exploits the traveling-wave components of the electric field generated by an array of electrodes subjected to ac voltages with a phase delay between neighboring electrodes. In this article, we propose an alternative way of generating traveling-wave electric fields in microchannels. We apply a rotating electric field around a cylindrical insulating micropillar and the resulting traveling-wave modes induce particle drift around the cylinder. We term this phenomenon insulating traveling-wave electrophoresis (i-TWE) to distinguish it from standard TWE performed with arrays of microelectrodes. We characterized the particle drift experimentally and show a quantitative comparison of the particle velocity with theoretical predictions. Excellent agreement is found when the influence of electro-osmosis on the channel walls is also considered.

Considering an interatomic potential $U\left(\mathbf{q}\right)$, where $\mathbf{q}=[{\mathbf{q}}_1,{\mathbf{q}}_2,\cdots ,{\mathbf{q}}_N]\in {\mathbb{R}}^{3N}$ is a vector describing positions ${\mathbf{q}}_i\in {\mathbb{R}}^3$, it is shown that $U$ can be defined as a function of the interatomic distance variables $r_{ij}=|{\mathbf{q}}_i-{\mathbf{q}}_j|$ provided the potential $U$ satisfies some symmetry assumptions. Moreover, the potential $U$ can be defined as a function of a proper subset of the distance variables $r_{ij}$, provided $N>5$, with the number of distance variables used scaling linearly with the number of atoms $N$.

This work uses the low-dissipation strategy to obtain efficiency at maximum power from a stochastic heat engine performing Carnot-, Stirling- and Ericsson-like cycles at finite time. The heat engine consists of a colloidal particle trapped by optical tweezers, in contact with two thermal baths at different temperatures, namely hot ($T_h$) and cold ($T_c$). The particle dynamics is characterized by a Langevin equation with time-dependent control parameters bounded to a harmonic potential trap. In a low-dissipation approach, the equilibrium properties of the system are required, which in our case, can be calculated through a statelike equation for the mean value ${\langle x^2\rangle }_{\mathrm{eq}}$ coming from a macroscopic expression associated with the Langevin equation.

Given a set of standard binary patterns and a defective pattern, the binary pattern retrieval task is to find the closest pattern to the defective one among these standard patterns. The associative-memory network of Kuramoto oscillators consisting of a Hebbian coupling term and a second-order Fourier term can be applied to this task. When the memorized patterns stored in the Hebbian coupling are mutually orthogonal, recent studies show that the network is capable of distinguishing the memorized patterns from most other patterns. However, the orthogonality usually fails in real situations. In this paper, we present a unified approach for the application of this model in pattern retrieval problems with any general set of standard patterns. By subgrouping the standard patterns and employing an orthogonal lift of each subgroup, this approach makes use of the theory in the case of mutually orthogonal memorized patterns. In particular, the error-free retrieval can be guaranteed, which requires that the retrieved pattern must coincide with one of the standard patterns. As illustrative simulations, pattern retrieval tests for partly sheltered Arabic number symbols are presented.

Correlation functions of components of second-order tensor fields in isotropic systems can be reduced to an isotropic fourth-order tensor field characterized by a few invariant correlation functions (ICFs). It is emphasized that components of this field depend in general on the coordinates of the field vector variable and thus on the orientation of the coordinate system. These angular dependencies are distinct from those of ordinary anisotropic systems. As a simple example of the procedure to obtain the ICFs we discuss correlations of time-averaged stresses in isotropic glasses where only one ICF in reciprocal space becomes a finite constant $e$ for large sampling times and small wave vectors. It is shown that $e$ is set by the typical size of the frozen-in stress components normal to the wave vectors, i.e., it is caused by the symmetry breaking of the stress for each independent configuration. Using the presented general mathematical formalism for isotropic tensor fields this finding explains in turn the observed long-range stress correlations in real space. Under additional but rather general assumptions $e$ is shown to be given by a thermodynamic quantity, the equilibrium Young modulus $E$. We thus relate for certain isotropic amorphous bodies the existence of finite Young or shear moduli to the symmetry breaking of a stress component in reciprocal space.

In this paper, we investigate the crowd evacuation from a room on the basis of the mean field game theory. In particular, effects of the predictability of pedestrians on the evacuation process are considered by applying the Cristiani-Santo-Mensi method as a solver of the Hamilton-Jacobi-Bellman equation coupled with the Fokker-Planck equation. Some numerical tests of the crowd evacuation from a room are implemented in order to investigate effects of the predictability, mass diffusion, interactive force and domain, and form of the running cost function on the evacuation process. Finally, we investigate effects of the predictability on the evacuation process, when two exits are opened and closed, alternatively.

We study the entrainment of a localized pattern to an external signal via its coupling to zero modes associated with broken symmetries. We show that when the pattern breaks internal symmetries, entrainment is governed by a multiple degrees-of-freedom dynamical system that has a universal structure, defined by the symmetry group and its breaking. We derive explicitly the universal locking dynamics for entrainment of patterns breaking internal phase symmetry, and calculate the locking domains and the stability and bifurcations of entrainment of complex Ginzburg-Landau solitons by an external pulse.

In the present paper, we investigate the effects of disorder on the reversal time ($\tau$) of classical anisotropic Heisenberg ferromagnets in three dimensions by means of Monte Carlo simulations. Starting from the pure system, our analysis suggests that $\tau$ increases with increasing anisotropy strength. On the other hand, for the case of randomly distributed anisotropy, generated from various statistical distributions, a set of results is obtained: (i) For both bimodal and uniform distributions, the variation of $\tau$ with the strength of anisotropy strongly depends on temperature. (ii) At lower temperatures, the decrement in $\tau$ with increasing width of the distribution is more prominent. (iii) For the case of normally distributed anisotropy, the variation of $\tau$ with the width of the distribution is nonmonotonic, featuring a minimum value that decays exponentially with the temperature. Finally, we elaborate on the joint effect of longitudinal ($h_z$) and transverse ($h_x$) fields on $\tau$, which appear to obey a scaling behavior of the form $\tau h_z^n\sim f\left(h_x\right)$.

The Markovian approach, which assumes exponentially distributed interinfection times, is dominant in epidemic modeling. However, this assumption is unrealistic as an individual's infectiousness depends on its viral load and varies over time. In this paper, we present a Susceptible-Infected-Recovered-Vaccinated-Susceptible epidemic model incorporating non-Markovian infection processes. The model can be easily adapted to accurately capture the generation time distributions of emerging infectious diseases, which is essential for accurate epidemic prediction. We observe noticeable variations in the transient behavior under different infectiousness profiles and the same basic reproduction number ${\mathcal{R}}_0$. The theoretical analyses show that only ${\mathcal{R}}_0$ and the mean immunity period of the vaccinated individuals have an impact on the critical vaccination rate needed to achieve herd immunity. A vaccination level at the critical vaccination rate can ensure a very low incidence among the population in the case of future epidemics, regardless of the infectiousness profiles.

Macromolecule crowding has a prominent impact on a series of biochemical processes in the cell. It is also expected to promote macromolecular complexation induced by excluded volume effects, which conflicts with recent advances in the thermodynamic interaction between inert, synthetic polymers, and nucleic acids. Along this line, a method combining high-resolution magnetic tweezers and extended crowder-oxDNA model was applied to resolve these discrepancies by systematically studying the kinetics and thermodynamics of the folding-unfolding transition for an individual DNA hairpin in a crowded environment. More specifically, from the magnetic tweezers-based experiments, the linear dependence of the critical force of the DNA hairpin on the polyethylene glycol (PEG) concentration was demonstrated, which is consistent with the results based on the crowder-oxDNA model in which the Lennard-Jones potential was adopted to express the interaction between the crowders and the DNA hairpin. These consistencies highlight that the excluded volume effects are mainly responsible for the interaction between PEG and the DNA hairpin, which is different from the interaction between dextran and the DNA hairpin. In the meantime, the dependence of the folding rate on the molecule weight of PEG, which was different from fluorescence resonance energy transfer-based results, was identified. The proposed method opens a path to detect the interaction between an inert, synthetic molecule, and the DNA hairpin, which is important to accurately mimic the cytosolic environments using mixtures of different inert molecules.

The paper is devoted to the study of the nodal surfaces of the wave functions for fermion systems. Using the quantum Monte Carlo method, implicit equations of nodal surfaces for some $s$-electron systems containing two–five electrons are numerically obtained. The obtained results are in agreement with the provisions of other researchers. An original method for constructing nodal surfaces is proposed, which is convenient for the implementation of quantum Monte Carlo.

For a four-stroke asymmetrically driven quantum Otto engine with working medium modeled by a single qubit, we study the bounds on nonequilibrium fluctuations of work and heat. We find strict relations between the fluctuations of work and individual heat for hot and cold reservoirs in arbitrary operational regimes. Focusing on the engine regime, we show that the ratio of nonequilibrium fluctuations of output work to input heat from the hot reservoir is both upper and lower bounded. As a consequence, we establish a hierarchical relation between the relative fluctuations of work and heat for both cold and hot reservoirs and further make a connection with the thermodynamic uncertainty relations. We discuss the fate of these bounds also in the refrigerator regime. The reported bounds, for such asymmetrically driven engines, emerge once both the time-forward and the corresponding reverse cycles of the engine are considered on an equal footing. We also extend our study and report bounds for a parametrically driven harmonic oscillator Otto engine.

In a previous paper, we used a recent extension of the periodic-orbit dividing surfaces method to distinguish the reactive and nonreactive parts in a three-dimensional (3D) Caldera potential-energy surface. Furthermore, we detected the phenomenon of dynamical matching in a 3D Caldera potential-energy surface. This happened for a specific value of the radius $r$ of the periodic orbit dividing surfaces ($r=0.25$). In this paper, we demonstrated that the chemical ratios of the number of reactive and nonreactive trajectories to the total number of trajectories converges for a range of the radius $r$ of the periodic-orbit dividing surfaces. This is important not only for validating the previous paper and to confirm that the method can detect the phenomenon of dynamical matching independently of the chosen radius of the construction of the dividing surface but also for investigating the application of the method to other Hamiltonian models.