By the end of 2020, a year since the first cases of infection by the Covid-19 virus have been reported; several pharmaceutical companies made significant progress in developing effective vaccines against the Covid-19 virus that has claimed the lives of more than ${10}^6$ people over the world. On the other hand, there is growing evidence of re-infection by the virus, which can cause further outbreaks. In this paper, we apply statistical physics tools to examine theoretically the vaccination rate required to control the pandemic for three different vaccine efficiency scenarios and five different vaccination rates. Also, we study the effect of temporal restrictions or reliefs on the pandemic's outbreak, assuming that re-infection is possible. When examining the efficiency of the vaccination rate of the general population in preventing an additional outbreak of the disease, we find that a high vaccination rate (where 0.3% of the population is vaccinated daily, which is equivalent to $\approx {10}^6$ vaccine doses in the United States daily) is required to gain control over the spread of the virus without further restrictions.

We consider the motion of a Brownian particle in a sawtooth potential dichotomously modulated by a spatially harmonic perturbation. An explicit expression for the Laplace transform of the Green function of an extremely asymmetric sawtooth potential is obtained. With this result, within the approximation of small potential-energy fluctuations, the integration of the relations for the average particle velocity is performed in elementary terms. The obtained analytical result, its high-temperature, low-frequency, and high-frequency asymptotics, as well as numerical calculations performed for a sawtooth potential of an arbitrary symmetry, indicate that in such a system, the frequency-temperature controlling the magnitude and direction of the ratchet velocity becomes possible. We clarify the mechanism of the appearance of additional regions of nonmonotonicity in the frequency dependence of the average velocity, which leads to the appearance of additional ratchet stopping points. This mechanism is a consequence of the competition between the sliding time along the steep slope of the highly asymmetric sawtooth potential and the correlation time of the dichotomous noise.

We consider the ground-state phase diagram of a one-dimensional spin-1/2 $XXZ$ chain with a spatially modulated Dzyaloshinskii-Moriya interaction in the presence of an alternating magnetic field applied along the $\widehat{z}$ axis. The model is studied using the continuum-limit bosonization approach and the finite system exact numerical technique. In the absence of a magnetic field, the ground-state phase diagram of the model includes, besides the ferromagnetic and gapless Luttinger-liquid phases, two gapped phases: the composite $\left(C1\right)$ phase characterized by the coexistence of long-range-ordered (LRO) alternating dimerization and spin chirality patterns, and the composite $\left(C2\right)$ phase characterized by, in addition to the coexisting spin dimerization and alternating chirality patterns, the presence of LRO antiferromagnetic order. In the case of mentioned composite gapped phases, and in the case of a uniform magnetic field, the commensurate-incommensurate type quantum phase transitions from a gapful phase into a gapless phase have been identified and described using the bosonization treatment and finite chain exact diagonalization studies. The upper critical magnetic field corresponding to the transition into a fully polarized state has been also determined. It has been shown that the very presence of a staggered component of the magnetic field vapes the composite $\left(C1\right)$ in favor of the composite gapped $\left(C2\right)$ phase.

Schloegl's second model (also known as the quadratic contact process) on a lattice involves spontaneous particle annihilation at rate $p$ and autocatalytic particle creation at empty sites with $n\ge 2$ occupied neighbors. The particle creation rate for exactly $n$ occupied neighbors is selected here as $n\left(n-1\right)/\left[z\left(z-1\right)\right]$ for lattice coordination number $z$. We analyze this model on a Bethe lattice. Precise behavior for stochastic models on regular periodic infinite lattices is usually surmised from kinetic Monte Carlo simulation on a finite lattice with periodic boundary conditions. However, the persistence of boundary effects for a Bethe lattice complicates this process, e.g., by inducing spatially heterogenous states. This motivates the exploration of various boundary conditions and unconventional simulation ensembles on the Bethe lattice to predict behavior for infinite size. We focus on $z=3$, and predict a discontinuous transition to the vacuum state on the infinite lattice when $p$ exceeds a threshold value of around 0.053.

Temperature fluctuations of a finite system follow the Landau bound $\delta T^2=T^2/C\left(T\right)$ where $C\left(T\right)$ is the heat capacity of the system. In turn, the same bound sets a limit to the precision of temperature estimation when the system itself is used as a thermometer. In this paper, we employ graph theory and the concept of Fisher information to assess the role of topology on the thermometric performance of a given system. We find that low connectivity is a resource to build precise thermometers working at low temperatures, whereas highly connected systems are suitable for higher temperatures. Upon modeling the thermometer as a set of vertices for the quantum walk of an excitation, we compare the precision achievable by position measurement to the optimal one, which itself corresponds to energy measurement.

Networks of stochastic leaky integrate-and-fire neurons, both at the mean-field level and in square lattices, present a continuous absorbing phase transition with power-law neuronal avalanches at the critical point. Here we complement these results showing that small-world Watts-Strogatz networks have mean-field critical exponents for any rewiring probability $p>0$. For the ring ($p=0$), the exponents are the same from the dimension $d=1$ of the directed-percolation class. In the model, firings are stochastic and occur in discrete time steps, based on a sigmoidal firing probability function. Each neuron has a membrane potential that integrates the signals received from its neighbors. The membrane potentials are subject to a leakage parameter. We study topologies with a varied number of neuron connections and different values of the leakage parameter. Results indicate that the dynamic range is larger for $p=0$. We also study a homeostatic synaptic depression mechanism to self-organize the network towards the critical region. These stochastic oscillations are characteristic of the so-called self-organized quasicriticality.

We consider a low temperature plasma environment in the low Earth orbital region in the presence of charged space debris particles. The dynamics of $(2+1)$-dimensional nonlinear dust-ion acoustic waves with weak transverse perturbation, generated in the system, is found to be governed by a forced Kadomtsev-Petviashvili equation, where the forcing term depends on charged space debris function. The bending phenomena of some exact dust-ion acoustic solitary wave solutions in the $x-t$ and $x-y$ planes are shown; they result from the consideration of different types of possible localized debris functions. A family of exact pinned accelerated solitary wave solutions has been obtained where the velocity changes over time but the amplitude remains constant. The shape of the debris function also changes during its propagation. Also, a special exact solitary wave solution has been derived for the dust-ion acoustic wave that gets curved in spatial dimensions with the curvature depending upon the nature of the forcing debris function. Such intricate solitary wave solutions may be useful in modeling real experimental data.

Using an asymptotic technique, we develop a generalized version of the class-$B$ Haus partial differential equation mode-locking model that accounts for both the slow gain response to the averaged value of the field intensity and the fast gain dynamics on the scale comparable to the pulse duration. We show that unlike the conventional class-$B$ Haus mode-locked model, our model is able to describe not only $Q$-switched instability of the fundamental mode-locked regime but also the leading edge instability leading to harmonic mode-locked regimes with the increase of the pump power.

We investigate the transition from incoherence to global collective motion in a three-dimensional swarming model of agents with helical trajectories, subject to noise and global coupling. Without noise this model was recently proposed as a generalization of the Kuramoto model and it was found that alignment of the velocities occurs discontinuously for arbitrarily small attractive coupling. Adding noise to the system resolves this singular limit and leads to a continuous transition, either to a directed collective motion or to center-of-mass rotations.

The origin of non-Poissonian or bursty temporal patterns observed in various data sets for human social dynamics has been extensively studied, yet its understanding still remains incomplete. Considering the fact that humans are social beings, a fundamental question arises: Is the bursty human dynamics dominated by individual characteristics or by interaction between individuals? In this paper we address this question by analyzing the Wikipedia edit history to see how spontaneous individual editors are in initiating bursty periods of editing, i.e., individual-driven burstiness, and to what extent such editors' behaviors are driven by interaction with other editors in those periods, i.e., interaction-driven burstiness. We quantify the degree of initiative (DoI) of an editor of interest in each Wikipedia article by using the statistics of bursty periods containing the editor's edits. The integrated value of the DoI over all relevant timescales reveals which is dominant between individual-driven and interaction-driven burstiness. We empirically find that this value tends to be larger for weaker temporal correlations in the editor's editing behavior and/or stronger editorial correlations. These empirical findings are successfully confirmed by deriving an analytic form of the DoI from a model capturing the essential features of the edit sequence. Thus our approach provides a deeper insight into the origin and underlying mechanisms of bursts in human social dynamics.

Nonpharmaceutical measures such as social distancing can play an important role in controlling the spread of an epidemic. In this paper, we use a mathematical model combining human mobility and disease spreading. For the mobility dynamics, we design an agent-based model consisting of pedestrian dynamics with a novel type of force to resemble social distancing in crowded sites. For the spreading dynamics, we consider the compartmental susceptible-exposed-infective $\left(SEI\right)$ dynamics plus an indirect transmission with the footprints of the infectious pedestrians being the contagion factor. We show that the increase in the intensity of social distancing has a significant effect on the exposure risk. By classifying the population into social distancing abiders and nonabiders, we conclude that the practice of social distancing, even by a minority of potentially infectious agents, results in a drastic change in the population exposure risk, but it reduces the effectiveness of the protocols when practiced by the rest of the population. Furthermore, we observe that for contagions for which the indirect transmission is more significant, the effectiveness of social distancing would be reduced. This study can help to provide a quantitative guideline for policy-making on exposure risk reduction.

Vesicle budding induced by protein binding that generates an isotropic spontaneous curvature is studied using a mean-field theory. Many spherical buds are formed via protein binding. As the binding chemical potential increases, the proteins first bind to the buds and then to the remainder of the vesicle. For a high spontaneous curvature and/or high bending rigidity of the bound membrane, it is found that a first-order transition occurs between a small number of large buds and a large number of small buds. These two states coexist around the transition point. The proposed scheme is simple and easily applicable to many interaction types, so we investigate the effects of interprotein interactions, the protein-insertion-induced changes in area, the variation of the saddle-splay modulus, and the area-difference-elasticity energy. The differences in the preferred curvatures for curvature sensing and generation are also clarified.

Prompted by the existence of biaxial subphases 1/4, 2/5, and 3/7 [Phys. Rev. E 96, 012701 (2017)], we reconsidered the three-phase frustration and the resulting degeneracy lifting by combining the phase diagram of $\mathrm{Sm}{C}_A^{*}$, $\mathrm{Sm}{C}^{*}$, and $\mathrm{Sm}A$ with the discrete flexoelectric effect. We systematically calculated the phase diagrams and tried to understand the overall picture of the phenomena by means of a simple and intuitively clear way in terms of minimal number of parameters. The treatment naturally explains the highly distorted helical structures of the biaxial subphases as well as the microscopic helical short-pitch of $\mathrm{Sm}{C}_{\alpha }^{*}$ which increases or decreases accordingly with rising temperature. The regular subphase emerging sequence is $\mathrm{Sm}{C}_A^{*}(\mathrm{Sm}{C}_{\alpha }^{*}$)–1/4–$\mathbf{1}/\mathbf{3}$–2/5–3/7–$\mathbf{1}/\mathbf{2}$–$\mathrm{Sm}{C}^{*}(\mathrm{Sm}{C}_{\alpha }^{*}$), where the subphases other than 1/3 and 1/2 may or may not emerge. At the same time, we can see a variety of irregular sequences; in particular, any one of the biaxial subphases may singly emerge between $\mathrm{Sm}{C}_A^{*}(\mathrm{Sm}{C}_{\alpha }^{*}$) and ($\mathrm{Sm}{C}^{*})\mathrm{Sm}{C}_{\alpha }^{*}$. Moreover, the experimentally confirmed extraordinary subphase emerging sequence $\mathrm{Sm}{C}^{*}$–$\mathbf{1}/\mathbf{2}$–$\mathrm{Sm}{C}_{\alpha }^{*}$ appears for particular parameter values. Contrastingly to these affirmative aspects, some calculated results are contradictory to the previously reported experimental results: the change from $\mathrm{Sm}{C}_A^{*}$ and $\mathrm{Sm}{C}^{*}$ to $\mathrm{Sm}{C}_{\alpha }^{*}$ is always continuous, the 6-layer 2/3 subphase is not stabilized, and the subphase emerging sequence $\mathrm{Sm}{C}_A^{*}$–1/3–$\mathrm{Sm}{C}^{*}$ does not appear. The causes of inconsistency and how to resolve them were discussed in comparisons with experimental findings.

The shape of a microchannel during flow through it is instrumental to understanding the physics that govern various phenomena ranging from rheological measurements of fluids to separation of particles and cells. Two commonly used approaches for obtaining a desired channel shape (for a given application) are (i) fabricating the microchannel in the requisite shape and (ii) actuating the microchannel walls during flow to obtain the requisite shape. However, these approaches are not always viable. We propose an alternative, passive approach to a priori tune the elastohydrodynamics in a microsystem toward achieving a predetermined (but not prefabricated) flow geometry when the microchannel is subjected to flow. That is, we use the interaction between a soft solid layer, the viscous flow beneath it, and the shaped rigid wall above it to tune the fluid domain's shape. Specifically, we study a parallel-wall microchannel whose top wall is a slender soft coating of arbitrary thickness attached to a rigid platform. We derive a nonlinear differential equation for the soft coating's fluid-solid interface, which we use to infer how to achieve specific conduit shapes during flow. Using this theory, we demonstrate the tuning of four categories of microchannel geometries, which establishes, via a proof-of-concept, the viability of our modeling framework. We also explore slip length patterning on the rigid bottom wall of the microchannel, a common technique in microfluidics, as an additional “handle” for microchannel shape control. However, we show that this effect is much weaker in practice.

Drop-carrier particles (DCPs) are solid microparticles designed to capture uniform microscale drops of a target solution without using costly microfluidic equipment and techniques. DCPs are useful for automated and high-throughput biological assays and reactions, as well as single-cell analyses. Surface energy minimization provides a theoretical prediction for the volume distribution in pairwise droplet splitting, showing good agreement with macroscale experiments. We develop a probabilistic pairwise interaction model for a system of such DCPs exchanging fluid volume to minimize surface energy. This leads to a theory for the number of pairwise interactions of DCPs needed to reach a uniform volume distribution. Heterogeneous mixtures of DCPs with different sized particles require fewer interactions to reach a minimum energy distribution for the system. We optimize the DCP geometry for minimal required target solution and uniformity in droplet volume.

In this paper, we first present a multiple-relaxation-time lattice Boltzmann (MRT-LB) model for one-dimensional diffusion equation where the D1Q3 (three discrete velocities in one-dimensional space) lattice structure is considered. Then through the theoretical analysis, we derive an explicit four-level finite-difference scheme from this MRT-LB model. The results show that the four-level finite-difference scheme is unconditionally stable, and through adjusting the weight coefficient ${\omega }_0$ and the relaxation parameters $s_1$ and $s_2$ corresponding to the first and second moments, it can also have a sixth-order accuracy in space. Finally, we also test the four-level finite-difference scheme through some numerical simulations and find that the numerical results are consistent with our theoretical analysis.

The regularized class of lattice Boltzmann methods (LBMs) leverage the potency of the standard lattice-Bhatnagar-Gross-Krook method by filtering out spurious nonhydrodynamic moments from the moment space; this is achieved through evaluating regularized populations via a multiscale or a Hermite polynomial expansion approach. In this paper, we propose an alternative approach for evaluating the lattice populations. This approach is based on a kinetic theory that is consistent with nonequilibrium thermodynamics and obeys the Onsager-reciprocity principle. The proposed method is verified and validated for a number of canonical problems such as the athermal shock tube, the double periodic shear layer, the lid driven cavity, flow past square cylinder, and Poiseuille flow at nonvanishing Knudsen numbers. Additionally, the proposed method is compared to existing regularized LBM schemes and is shown to yield significant improvement in the stability and accuracy of the simulations.

Nanoscale heat engines are subject to large fluctuations which affect their precision. The thermodynamic uncertainty relation (TUR) provides a trade-off between output power, fluctuations, and entropic cost. This trade-off may be overcome by systems exhibiting quantum coherence. This Letter provides a study of the TUR in a prototypical quantum heat engine, the Scovil–Schulz-DuBois maser. Comparison with a classical reference system allows us to determine the effect of quantum coherence on the performance of the heat engine. We identify analytically regions where coherence suppresses fluctuations, implying a quantum advantage, as well as regions where fluctuations are enhanced by coherence. This quantum effect cannot be anticipated from the off-diagonal elements of the density matrix. Because the fluctuations are not encoded in the steady state alone, TUR violations are a consequence of coherence that goes beyond steady-state coherence. While the system violates the conventional TUR, it adheres to a recent formulation of a quantum TUR. We further show that parameters where the engine operates close to the conventional limit are prevalent and TUR violations in the quantum model are not uncommon.

We present the results of a quantitative study of the phase behavior of a model polymer chain with side spheres using two independent computer simulation techniques. We find that the mere addition of side spheres results in key modifications of standard polymer behavior. One obtains a marginally compact phase at low temperatures; the structures in this phase are reduced in dimensionality and are ordered, they include strands assembled into sheets and a variety of helices, and at least one of the transitions on lowering the temperature to access these ordered states is found to be first order. Our model serves to partially bridge conventional polymer phases with biomolecular phases.

The site-bond percolation problem in two-dimensional kagome lattices has been studied by means of theoretical modeling and numerical simulations. Motivated by considerations of cluster connectivity, two distinct schemes (denoted as $S\cap B$ and $S\cup B$) have been considered. In $S\cap B$ ($S\cup B$), two points are connected if a sequence of occupied sites and ($\mathit{or}$) bonds joins them. Analytical and simulation approaches, supplemented by analysis using finite-size scaling theory, were used to calculate the phase boundaries between the percolating and nonpercolating regions, thus determining the complete phase diagram of the system in the ($p_s,p_b$) space. In the case of the $S\cap B$ model, the obtained results are in excellent agreement with previous theoretical and numerical predictions. In the case of the $S\cup B$ model, the limiting curve separating percolating and nonpercolating regions is reported here.