Continuum models of epidemics do not take into account the underlying microscopic network structure of social connections. This drawback becomes extreme during quarantine when most people dramatically decrease their number of social interactions, while others (like cashiers in grocery stores) continue maintaining hundreds of contacts per day. We formulate a two-level model of quarantine. On a microscopic level, we model a single neighborhood assuming a star-network structure. On a mesoscopic level, the neighborhoods are placed on a two-dimensional lattice with nearest-neighbors interactions. The modeling results are compared with the COVID-19 data for several counties in Michigan (USA) and the phase diagram of parameters is identified.

The boson peak is a largely unexplained excitation found universally in the terahertz vibrational spectra of disordered systems; the so-called fracton is a vibrational excitation associated with the self-similar structure of monomers in polymeric glasses. We demonstrate that such excitations can be detected using terahertz spectroscopy. In the case of fractal structures, we determine the infrared light-vibration coupling coefficient for the fracton region and show that information concerning the fractal and fracton dimensions appears in the exponent of the absorption coefficient. Finally, using terahertz time-domain spectroscopy and low-frequency Raman scattering, we experimentally observe these universal excitations in a protein (lysozyme) system that has an intrinsically disordered and fractal structure and argue that the system should be considered a single supramolecule. These findings are applicable to amorphous and fractal objects in general and will be valuable for understanding universal dynamics of disordered systems via terahertz light.

Diffusion in spatially rough, confining, one-dimensional continuous energy landscapes is treated using Zwanzig's proposal, which is based on the Smoluchowski equation. We show that Zwanzig's conjecture agrees with Brownian dynamics simulations only in the regime of small roughness. Our correction of Zwanzig's framework corroborates well with numerical results. A numerical simulation scheme based on our coarse-grained Langevin dynamics offers significant reductions in computational time. The mean first-passage time problem in the case of random roughness is treated. Finally, we address the validity of the separation of length scales assumption for the case of polynomial backgrounds and cosine-based roughness. Our results are applicable to hierarchical energy landscapes such as that of a protein's folding and transport processes in disordered media, where there is clear separation of length scale between smooth underlying potential and its rough perturbation.

In this work, we propose a two-dimensional extension of a previously defined one-dimensional version of a model of particles in counterflowing streams, which considers an adapted Fermi-Dirac distribution to describe the transition probabilities. In this modified and extended version of the model, we consider that only particles of different species can interact, and they hop through the cells of a two-dimensional rectangular lattice with probabilities taking into account diffusive and scattering aspects. We show that for a sufficiently low level of randomness ($\alpha \ge 10$), the system can relax to a mobile self-organized steady state of counterflow (lane formation) or to an immobile state (clogging) if the system has an average density near a certain crossover value (${\rho }_c$). We also show that in the case of imbalance between the species, we can simultaneously have three different situations for the same density value set: (i) an immobile phase, (ii) a mobile pattern organized by lanes, and (iii) a profile with mobility but without lane formation, which essentially is the coexistence of situations (i) and (ii). All of our results were obtained by performing Monte Carlo simulations.

We show that “Malthusian flocks”—i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being “born” and “dying” during their motion—belong to a new universality class in spatial dimensions $d>2$. We calculate the universal exponents and scaling laws of this new universality class to $O\left(\epsilon \right)$ in a $d=4-\epsilon$ expansion and find these are different from the “canonical” exponents previously conjectured to hold for “immortal” flocks (i.e., those without birth and death) and shown to hold for incompressible flocks with spatial dimensions in the range of $2<d\le 4$. We also obtain a universal amplitude ratio relating the damping of transverse and longitudinal velocity and density fluctuations in these systems. Furthermore, we find a universal separatrix in real space ($\mathbf{r}$) between two regions in which the equal-time density correlation $\langle \delta \rho (\mathbf{r},t)\delta \rho (0,t)\rangle$ has opposite signs. Our expansion should be quite accurate in $d=3$, allowing precise quantitative comparisons between our theory, simulations, and experiments.

We present a mechanistic model of drug release from a multiple emulsion into an external surrounding fluid. We consider a single multilayer droplet where the drug kinetics are described by a pure diffusive process through different liquid shells. The multilayer problem is described by a system of diffusion equations coupled via interlayer conditions imposing continuity of drug concentration and flux. Mass resistance is imposed at the outer boundary through the application of a surfactant at the external surface of the droplet. The two-dimensional problem is solved numerically by finite volume discretization. Concentration profiles and drug release curves are presented for three typical round-shaped (circle, ellipse, and bullet) droplets and the dependency of the solution on the mass transfer coefficient at the surface analyzed. The main result shows a reduced release time for an increased elongation of the droplets.

Just over a decade ago Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)] published a provocative paper suggesting that a classical system might be able to simulate the truly fundamental quantum mechanical single- and double-slit experiment. The system they investigated was that of an oil droplet walking on a vibrated oil surface. Their results have since been challenged by Andersen et al. [Phys. Rev. E 92, 013006 (2015)] by pointing to insufficient statistical support and a lack of experimental control over critical parameters. Here we show that the randomness in the original experiment is an artifact of lack of control. We present experimental data from an extensive scan of the parameter space of the system including the use of different size slits and tight control of critical parameters. For the single-slit we find very diverse samples of interference-like patterns but all causal by nature. This also holds for the double-slit. However, an extra interference effect appears here. The origin of this is investigated by blocking either the inlet or the outlet of one slit. Hereby we show that the extra interference is solely due to back-scatter of the associated wave field from the outlet of the slit not passed by the droplet. Recently Pucci et al. [J. Fluid Mech. 835, 1136 (2018)] using a much broader slit also showed that the classical system is basically causal. They, too, observed the extra interference effect for the double-slit. However, the reason behind was not determined. Moreover they claimed the existence of a chaotic regime just below the cri- tical acceleration for spontaneous generation of Faraday surface waves. Our measurements do not support the validity of this claim. However, the drop dynamics turns out to have an interesting multifaceted interaction with the slit structure.

Deeply modulated ion spectra from contaminants present on the target surface were measured at the interaction of ultraintense $(2-5)\times {10}^{20}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ and high-contrast laser pulses $(\lesssim {10}^{-10})$ with thin $(\sim \mu \mathrm{m})$ and ultrathin $(\sim \mathrm{nm})$ targets. This phenomenon, observed over a wide range of laser and target parameters, suggests that it is a generic feature of multispecies ion acceleration at high laser pulse contrast. The modulation is ascribed to the acceleration of various ion species at the rear of the target with steplike density profiles which provide well-separated ion species in the accelerated beam. The observed coincidence of the velocity of the modulated region in the ion spectra with the maximum velocity of another ion with a lower mass-to-charge ratio is consistent with this model. The impact of heavy ions on light ions leads to a spectral “bunching” of light ions. Two-dimensional modeling has shown that high laser contrast prevents backside plasma expansion, which provides a well separated ion species with a steplike density profile that allows for the additional acceleration of “light” ions by the slower moving “heavy”-ion front. Spectral modulations can be controlled by tuning the ratio of heavy to light ions in future experiments with ultrathin rear coatings.

The formation of dynamical states for a collection of dust particles in two dimensions is shown using molecular dynamics simulations. The charged dust particles interact with each other with a Yukawa pair potential mimicking the screening due to plasma. An external radial confining force has also been applied to the dust particles to keep them radially confined. When the particle number is low (say, a few), they get arranged on the radial locations corresponding to multiple rings or shells. For specific numbers, such an arrangement of particles is stationary. However, for several cases, the cluster of dust particles relaxes to a state for which the dust particles on rings display intershell rotation. For a larger number of dust particles (a few hundred, for instance), an equilibrium state with a coherent rigid body displaying angular oscillation of the entire cluster is observed. A detailed characterization of the formation of these states in terms of particle number, coupling parameter, etc., is provided.

Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In this work, we show a consistent approach to solve conditional and unconditional Euclidean (Wiener) Gaussian path integrals that allow us to compute transition probabilities in the semiclassical approximation from the solutions of a system of linear differential equations. Our method is particularly useful for investigating Fokker-Planck dynamics and the physics of stringlike objects such as polymers. To give some examples, we derive the time evolution of the $d$-dimensional Ornstein-Uhlenbeck process and of the Van der Pol oscillator driven by white noise. Moreover, we compute the end-to-end transition probability for a charged string at thermal equilibrium, when an external field is applied.

Efimov states are known to have a discrete real-space scale invariance; working in momentum space we identify the relevant discrete scale invariance for the scattering amplitude defining its Weierstrass function as well. Through the use of the mathematical formalism for discrete scale invariance for the scattering amplitude we identify the scaling parameters from the pole structure of the corresponding zeta function; its zeroth-order pole is fixed by the Efimov physics. The corresponding geometrical fractal structure for Efimov physics in momentum space is identified as a ray across a logarithmic spiral. This geometrical structure also appears in the physics of atomic collapse in the relativistic regime connecting it to Efimov physics. Transforming to logarithmic variables in momentum space we map the three-body scattering amplitude into Bloch states and the ladder of energies of the Efimov states are simply obtained in terms of the Bohr-Sommerfeld quantization rule. Thus through the mapping the complex problem of three-body short-range interaction is transformed to that of a noninteracting single particle in a discrete lattice.

The empirical velocity of a reaction-diffusion front, propagating into an unstable state, fluctuates because of the shot noises of the reactions and diffusion. Under certain conditions these fluctuations can be described as a diffusion process in the reference frame moving with the average velocity of the front. Here we address pushed fronts, where the front velocity in the deterministic limit is affected by higher-order reactions and is therefore larger than the linear spread velocity. For a subclass of these fronts—strongly pushed fronts—the effective diffusion constant $D_f\sim 1/N$ of the front can be calculated, in the leading order, via a perturbation theory in $1/N\ll 1$, where $N\gg 1$ is the typical number of particles in the transition region. This perturbation theory, however, overestimates the contribution of a few fast particles in the leading edge of the front. We suggest a more consistent calculation by introducing a spatial integration cutoff at a distance beyond which the average number of particles is of order 1. This leads to a nonperturbative correction to $D_f$ which even becomes dominant close to the transition point between the strongly and weakly pushed fronts. At the transition point we obtain a logarithmic correction to the $1/N$ scaling of $D_f$. We also uncover another, and quite surprising, effect of the fast particles in the leading edge of the front. Because of these particles, the position fluctuations of the front can be described as a diffusion process only on very long time intervals with a duration $\mathrm{\Delta }t\gg {\tau }_N$, where ${\tau }_N$ scales as $N$. At intermediate times the position fluctuations of the front are anomalously large and nondiffusive. Our extensive Monte Carlo simulations of a particular reacting lattice gas model support these conclusions.

We propose a characterization of quantum many-body chaos: given a collection of simple operators, the set of all possible pair correlations between these operators can be organized into a matrix with a random-matrix-like spectrum. This approach is particularly useful for locally interacting systems, which do not generically show exponential Lyapunov growth of out-of-time-ordered correlators. We demonstrate the validity of this characterization by numerically studying the Sachdev-Ye-Kitaev model and a one-dimensional spin chain with random magnetic field (XXZ model).

We performed a series of molecular dynamics (MD) simulations of phospholipid bilayers under shear flow to estimate the effect of the system size on Kelvin-Helmholtz (KH)-like instability of the bilayer at the molecular scale. To extend the estimation by the MD simulations to the microscale, we introduced linear stability analysis for the fluid–fluid interface consisting of a thin membrane. For both the MD simulations and theoretical model, the critical velocity difference across the bilayer, where instability occurs, decreased with increasing wavelength of the bilayer undulation $\lambda$, which corresponds to the system size. When $\lambda$ was more than about ten times larger than the bilayer thickness, the critical velocity difference in the MD simulations was in quantitative agreement with that obtained by the theoretical model. This means that the theoretical model is applicable for the shear-induced KH-like instability of the bilayer for large $\lambda$. The theoretical model showed that the critical velocity difference for the KH-like instability was proportional to ${\lambda }^{-3/2}$. Based on these results, we discuss the implications of the shear-induced bilayer instability in the shear-induced cell damage observed in experiments.

Discrete element methods require appropriate models for particle-particle collisions. Usually, researchers use soft-sphere types of models where the collision dynamics is solved numerically. This makes the simulation computationally expensive. In this paper, however, we show a hard-sphere model that uses ready analytic formulas that relate the pre- and postcollisional velocities of the particles in contact. This hard-sphere model is an extension of an existing model that uses three input parameters. For this, we applied the linear-spring soft-sphere model, where analytic relations can be found. These relations were implemented into the standard hard-sphere model. As a result, we obtain a robust hard-sphere model that is more accurate than the standard one and is still computationally cheap.

We present a kinetic model for nonideal fluids, where the local thermodynamic pressure is imposed through appropriate rescaling of the particle's velocities, accounting for both long- and short-range effects and hence full thermodynamic consistency. The model features full Galilean invariance together with mass, momentum, and energy conservation and enables simulations ranging from subcritical to supercritical flows, which is illustrated on various benchmark flows such as anomalous shock waves or shock droplet interaction.

In models in statistical physics, the dynamics often slows down tremendously near the critical point. Usually, the correlation time $\tau$ at the critical point increases with system size $L$ in power-law fashion: $\tau \sim L^z$, which defines the critical dynamical exponent $z$. We show that this also holds for the two-dimensional bond-diluted Ising model in the regime $p>p_c$, where $p$ is the parameter denoting the bond concentration, but with a dynamical critical exponent $z\left(p\right)$ which shows a strong $p$ dependence. Moreover, we show numerically that $z\left(p\right)$, as obtained from the autocorrelation of the total magnetization, diverges when the percolation threshold $p_c=1/2$ is approached: $z\left(p\right)-z\left(1\right)\sim {(p-p_c)}^{-2}$. We refer to this observed extremely fast increase of the correlation time with size as super slowing down. Independent measurement data from the mean-square deviation of the total magnetization, which exhibits anomalous diffusion at the critical point, support this result.

A computer simulation was used to study the random sequential adsorption of identical discorectangles onto a continuous plane. The problem was analyzed for a wide range of discorectangle aspect ratios ($\varepsilon \in [1;100]$). We studied the anisotropic deposition, i.e., the orientations of the deposited particles were uniformly distributed within some interval such that the particles were preferentially aligned along a given direction. The kinetics of the changes in the packing fraction found at different values of such the alignment are discussed. Partial ordering of the discorectangles significantly affected the packing fraction at the jamming state, ${\phi }_{\text{j}}$, and shifted the cusps in the ${\phi }_{\text{j}}\left(\varepsilon \right)$ dependencies. The structure of the jammed state was analyzed using the adsorption of disks of different diameters into the porous space between the deposited discorectangles. The analysis of the connectivity between the discorectangles was performed assuming a core-shell structure of particles.

In this paper we investigate the effects of diffusion on the dynamics of a single focal adhesion at the leading edge of a crawling cell by considering a simplified model of sliding friction. Using a mean-field approximation, we derive an effective single-particle system that can be interpreted as an overdamped Brownian particle with spatially dependent stochastic resetting. We then use renewal and path-integral methods from the theory of stochastic resetting to calculate the mean sliding velocity under the combined action of diffusion, active forces, viscous drag, and elastic forces generated by the adhesive bonds. Our analysis suggests that the inclusion of diffusion can sharpen the response to changes in the effective stiffness of the adhesion bonds. This is consistent with the hypothesis that force fluctuations could play a role in mechanosensing of the local microenvironment.