The basic reproduction number ${\mathcal{R}}_0$ is a standard indicator of infection control in epidemiology. Although ${\mathcal{R}}_0$ has been studied extensively for deterministic epidemic models, it has not been formulated accurately for models adopting network structures. Here, we extend a four-compartment model that includes commonly used epidemic models to a Markov process on networks. By examining the Markov process in detail, we derive a canonical formula for ${\mathcal{R}}_0$ involving two probability values. Numerical calculations show that the derived formula is a better approximation than the conventional formula when the network is very sparse. We propose this as a standard formula for controlling infections that can only be transmitted through intimate contact, where contacts between individuals can be described as a sparse network.

We have explored a variety of synchronization domains and observed phase-flip transition in a pair of coupled 1-pentanol drops as a function of the volume mismatch. Both experimental observations and numerical studies are presented. The experiments were carried out in a rectangular channel in a ferroin deionized water solution premixed with some volume of pentanol. A single pentanol drop ($\ge 3\mu \mathrm{L}$) performs back and forth oscillations along the length of the channel due to the well-known Marangoni forces. In the present work, for a pair of drops, the drop 1 volume was changed from 3 to 5 $\mu \mathrm{L}$ in steps of $1\mu \mathrm{L}$, whereas the drop 2 volume was varied from 1 to 3 $\mu \mathrm{L}$ in steps of $0.5\mu \mathrm{L}$. A systematic investigation of all the possible combinations of the drop volumes showed the presence of three different types of synchrony—in-phase, antiphase, and phase-switched. In-phase synchronization was robust for a volume mismatch of $>3.0\mu \mathrm{L}$ between the two drops. On the other hand, antiphase synchronization was robust when the volume mismatch was $<2.0\mu \mathrm{L}$. The phase-switched state is a synchronized state involving a phase-flip transition in the time domain. This state was observed for the intermediate range of volume mismatch. Numerically, the system has been investigated using two Stuart-Landau oscillators interacting via a coupling function in the form of Lennard-Jones potential. The numerical results suitably capture both in-phase and antiphase oscillations for a pair of volume-mismatched pentanol drops.

We have studied the localization of waves in a one-dimensional lattice consisting of impurities where the spacing between consecutive impurities can take certain values with given probabilities. In general, such a distribution of impurities induces correlations in the disorder. In particular, with a power-law distribution of spacing, this system is used as a model for light propagation in Lévy glasses. We introduce a method of calculating the Lyapunov exponent which overcomes limitations in the previous studies and can be easily extended to higher orders of perturbation theory. We obtain the Lyapunov exponent up to fourth order of perturbation and discuss the range of validity of perturbation theory, transparent states, and anomalous energies which are characterized by divergences in different orders of the expansion. We also carry out numerical simulations which are in agreement with our analytical results.

The adsorption of a single $\mathit{AB}$ random copolymer (RC) chain onto an inhomogeneous $ab$ surface with a regular periodic pattern is studied theoretically. The problem is considered within the simplest model of a partially directed random walk in two dimensions by using the method of generating functions and the annealed approximation for the averaging over disorder in the RC sequence. The existence of the “optimal” RC composition and the degree of correlation in the monomer sequence, at which the inverse transition temperature has a local minimum, is shown. This is characteristic for symmetric and weakly asymmetric surfaces, whereas for surfaces with pronounced asymmetry there is no such local minimum. The best adsorbate for a strongly asymmetric surface is the homopolymer composed of monomer units that are complimentary to the majority sites on the surface. The results for the adsorption transition point obtained in the annealed approximation are compared with the numerical results for random-periodic $AB$-copolymers with a long period being a quenched random sequence of $A$ and $B$ units. The comparison shows that the annealed approximation provides a very good quantitative estimate of the adsorption transition point.

The discharge of elongated particles from a silo with rotating bottom is investigated numerically. The introduction of a slight transverse shear reduces the flow rate $Q$ by up to 70% compared with stationary bottom, but the flow rate shows a modest increase by further increasing the external shear. Focusing on the dependency of flow rate $Q$ on orifice diameter $D$, the spheres and rods show two distinct trends. For rods, in the small-aperture limit $Q$ seems to follow an exponential trend, deviating from the classical power-law dependence. These macroscopic observations are in good agreement with our earlier experimental findings [Phys. Rev. E 103, 062905 (2021)]. With the help of the coarse-graining methodology we obtain the spatial distribution of the macroscopic density, velocity, kinetic pressure, and orientation fields. This allows us detecting a transition from funnel to mass flow pattern caused by the external shear. Additionally, averaging these fields in the region of the orifice reveals that the strong initial decrease in $Q$ is mostly attributed to changes in the flow velocity, while the weakly increasing trend at higher rotation rates is related to increasing packing fraction. Similar analysis of the grain orientation at the orifice suggests a correlation of the flow rate magnitude with the vertical orientation and the packing fraction at the orifice with the order of the grains. Lastly, the vertical profile of mean acceleration at the center of the silo denotes that the region where the acceleration is not negligible shrinks significantly due to the strong perturbation induced by the moving wall.

Low-temperature gaseous plasmas exhibit great potential in designing tunable and reconfigurable electromagnetic devices. In this paper, based on an overdense-underdense core-shell plasma structure, tunable Kerker-type invisibility for a radiation-enhanced electrically small antenna is achieved, where dominant scattering direction can be mutated between backward and forward while omnidirectional invisibility and signal enhancement are maintained. Moreover, by electromagnetic multipole decompositions, it is shown that the underdense outer plasma with a negative polarizability is able to weaken the strength and modulate the phase of the electric dipolar scattering component $\left(a_1\right)$, while the magnetic dipolar term $\left(b_1\right)$ nearly remains unchanged. Consequently, quasi-first and -second Kerker conditions are fulfilled near the cutoff band of $a_1$.

Self-propelled rods are a facet of the field of active matter relevant to many physical systems ranging in scale from shaken granular media and bacterial alignment to the flocking dynamics of animals. In this paper we develop a model for nematic alignment of self-propelled rods interacting through binary collisions. We avoid phenomenological descriptions of rod interaction in favor of rigorously using a set of microscopic-level rules. Under the assumption that each collision results in a small change to a rod's orientation, we derive the Fokker-Planck equation for the evolution of the kinetic density function. Using analytical and numerical methods, we study the emergence of the nematic order from a homogeneous, uniform steady state of the mean-field equation. We compare the level of orientational noise needed to destabilize this nematic order and compare our results to an existing phenomenological model that does not explicitly account for the physical collisions of rods. We show the presence of an additional geometric factor in our equations reflecting a reduced collision rate between nearly aligned rods that reduces the level of noise at which nematic order is destroyed, suggesting that alignment that depends on purely physical collisions is less robust.

We propose two different approaches for introducing the information temperature of binary $N\mathrm{th}$-order Markov chains. The first approach is based on a comparison of Markov sequences with equilibrium Ising chains at given temperatures. The second approach uses probabilities of finite-length subsequences of symbols occurring, which determine their entropies. The derivative of the entropy with respect to the energy gives the information temperature measured on the scale of introduced energy. For the case of a nearest-neighbor spin-symbol interaction, both approaches give similar results. However, the method based on the correspondence of the $N$-step Markov and Ising chains appears to be very cumbersome for $N>3$. We also introduce the information temperature for the weakly correlated one-parametric Markov chains and present results for the stepwise and power memory functions. An application of the developed method to obtain the information temperature of some literary texts is given.

Atom-optics kicked rotor represents an experimentally reliable version of the paradigmatic quantum kicked rotor system. In this system, a periodic sequence of kicks are imparted to the cold atomic cloud. After a short initial diffusive phase the cloud settles down to a stationary state due to the onset of dynamical localization. In this paper, to explore the interplay between localized and diffusive phases, we experimentally implement a modification to this system in which the sign of the kick sequence is flipped after every $M$ kicks. This is achieved in our experiment by allowing free evolution for half the Talbot time after every $M$ kicks. Depending on the value of $M$, this modified system displays a combination of enhanced diffusion followed by asymptotic localization. This is explained as resulting from two competing processes—localization induced by standard kicked rotor type kicks, and diffusion induced by the half Talbot time evolution. The experimental and numerical simulations agree with one another. The evolving states display localized but nonexponential wave function profiles. This provides another route to quantum control in the kicked rotor class of systems.

In this article we develop an algorithm for the efficient simulation of electrolytes in the presence of physical boundaries. In previous work the discrete ion stochastic continuum overdamped solvent (DISCOS) algorithm was derived for triply periodic domains, and was validated through ion-ion pair correlation functions and Debye-Hückel-Onsager theory for conductivity, including the Wien effect for strong electric fields. In extending this approach to include an accurate treatment of physical boundaries we must address several important issues. First, the modifications to the spreading and interpolation operators necessary to incorporate interactions of the ions with the boundary are described. Next we discuss the modifications to the electrostatic solver to handle the influence of charges near either a fixed potential or dielectric boundary. An additional short-ranged potential is also introduced to represent interaction of the ions with a solid wall. Finally, the dry diffusion term is modified to account for the reduced mobility of ions near a boundary, which introduces an additional stochastic drift correction. Several validation tests are presented confirming the correct equilibrium distribution of ions in a channel. Additionally, the methodology is demonstrated using electro-osmosis and induced-charge electro-osmosis, with comparison made to theory and other numerical methods. Notably, the DISCOS approach achieves greater accuracy than a continuum electrostatic simulation method. We also examine the effect of under-resolving hydrodynamic effects using a “dry diffusion” approach, and find that considerable computational speedup can be achieved with a negligible impact on accuracy.

Investigating the potential benefits of the use of magnetic fields in inertial confinement fusion experiments has given rise to experimental platforms like the Magnetized Liner Inertial Fusion approach at the Z-machine (Sandia National Laboratories) or its laser-driven equivalent at OMEGA (Laboratory for Laser Energetics). Implementing these platforms at MegaJoule-scale laser facilities, such as the Laser MegaJoule (LMJ) or the National Ignition Facility (NIF), is crucial to reaching self-sustained nuclear fusion and enlarges the level of magnetization that can be achieved through a higher compression. In this paper, we present a complete design of an experimental platform for magnetized implosions using cylindrical targets at LMJ. A seed magnetic field is generated along the axis of the cylinder using laser-driven coil targets, minimizing debris and increasing diagnostic access compared with pulsed power field generators. We present a comprehensive simulation study of the initial B field generated with these coil targets, as well as two-dimensional extended magnetohydrodynamics simulations showing that a 5 T initial B field is compressed up to 25 kT during the implosion. Under these circumstances, the electrons become magnetized, which severely modifies the plasma conditions at stagnation. In particular, in the hot spot the electron temperature is increased (from 1 keV to 5 keV) while the density is reduced (from $40{\mathrm{g}/\mathrm{cm}}^3$ to $7{\mathrm{g}/\mathrm{cm}}^3$). We discuss how these changes can be diagnosed using x-ray imaging and spectroscopy, and particle diagnostics. We propose the simultaneous use of two dopants in the fuel (Ar and Kr) to act as spectroscopic tracers. We show that this introduces an effective spatial resolution in the plasma which permits an unambiguous observation of the B-field effects. Additionally, we present a plan for future experiments of this kind at LMJ.

The phase-transition behavior of the NP-hard vertex-cover (VC) combinatorial optimization problem is studied numerically by linear programming (LP) on ensembles of random graphs. As the basic Simplex (SX) algorithm suitable for such LPs may produce incomplete solutions for sufficiently complex graphs, the application of cutting-plane (CP) methods is sought. We consider Gomory and $\{0,\frac{1}{2}\}$ cuts. We measure the probability of obtaining complete solutions with these approaches as a function of the average node degree $c$ and observe transition between typically complete and incomplete phase regions. While not generally complete solutions are obtained for graphs of arbitrarily high complexity, the CP approaches still advance the boundary in comparison to the pure SX algorithm, beyond the known replica-symmetry breaking (RSB) transition at $c=e\approx 2.718$. In fact, our results provide evidence for another algorithmic transition at $c\approx 2.90\left(2\right)$. Besides this, we quantify the transition between easy and hard solvability of the VC problem also in terms of numerical effort. Further we study the so-called whitening of the solution, which is a measure for the degree of freedom that single vertices experience with respect to degenerate solutions. Inspection of the quantities related to clusters of white vertices reveals that whitening is affected, only slightly but measurably, by the RSB transition.

In this Letter, we discuss how flow inhomogeneity affects the self-diffusion behavior in granular flows. Whereas self-diffusion scalings have been well characterized in the past for homogeneous shearing, the effect of shear localization and nonlocality of the flow has not been studied. We, therefore, present measurements of self-diffusion coefficients in discrete numerical simulations of steady, inhomogeneous, and collisional shearing flows of nearly identical, frictional, and inelastic spheres. We focus on a wide range of dense solid volume fractions, that correspond to geophysical and industrial shearing flows that are dominated by collisional interactions. We compare the measured values first with a scaling based on shear rate and, then, on a scaling based on the granular temperature. We find that the latter does much better than the former in collapsing the data. The results lay the foundations of diffusion models for inhomogeneous shearing flows, which should be useful in treating problems of mixing and segregation.

Stochastic resetting can be naturally understood as a renewal process governing the evolution of an underlying stochastic process. In this work, we formally derive well-known results of diffusion with resets from a renewal theory perspective. Parallel to the concepts from renewal theory, we introduce the conditioned backward $B$ and forward $F$ times being the times since the last and until the next reset, respectively, given that the current state of the system $X\left(t\right)$ is known. These magnitudes are introduced with the paradigmatic case of diffusion under resetting, for which the backward and forward times are conditioned to the position of the walker. We find analytical expressions for the conditioned backward and forward time probability density functions (PDFs), and we compare them with numerical simulations. The general expressions allow us to study particular scenarios. For instance, for power-law reset time PDFs such that $\phi \left(t\right)\sim t^{-1-\alpha }$, significant changes in the properties of the conditioned backward and forward times happen at half-integer values of $\alpha$ due to the composition between the long-time scaling of diffusion $P(x,t)\sim 1/\sqrt{t}$ and the reset time PDF.

Many dynamical processes of complex systems can be understood as the dynamics of a group of nodes interacting on a given network structure. However, finding such interaction structure and node dynamics from time series of node behaviors is tough. Conventional methods focus on either network structure inference task or dynamics reconstruction problem, very few of them can work well on both. This paper proposes a universal framework for reconstructing network structure and node dynamics at the same time from observed time-series data of nodes. We use a differentiable Bernoulli sampling process to generate a candidate network structure, and we use neural networks to simulate the node dynamics based on the candidate network. We then adjust all the parameters with a stochastic gradient descent algorithm to maximize the likelihood function defined on the data. The experiments show that our model can recover various network structures and node dynamics at the same time with high accuracy. It can also work well on binary, discrete, and continuous time-series data, and the reconstruction results are robust against noise and missing information.

Information propagation on networks is a central theme in social, behavioral, and economic sciences, with important theoretical and practical implications, such as the influence maximization problem for viral marketing. Here we consider a model that unifies the classical independent cascade models and the linear threshold models, and generalize them by considering continuous variables and allowing feedback in the dynamics. We then formulate its influence maximization as a mixed integer nonlinear programming problem and adopt derivative-free methods. Furthermore, we show that the problem can be exactly solved in the special case of linear dynamics, where the selection criterion is closely related to the Katz centrality, and propose a customized direct search method with local convergence. We then demonstrate the close to optimal performance of the customized direct search numerically on both synthetic and real networks.

By performing dynamic Monte Carlo simulations, we investigate the microrheology of isotropic suspensions of hard-core colloidal cuboids. In particular, we infer the local viscoelastic behavior of these fluids by studying the dynamics of a probe spherical particle that is incorporated in the host phase and is dragged by an external force. This technique, known as active microrheology, allows one to characterize the microscopic response of soft materials upon application of a constant force, whose intensity spans here three orders of magnitude. By tuning the geometry of cuboids from oblate to prolate as well as the system density, we observe different responses that are quantified by measuring the effective friction perceived by the probe particle. The resulting friction coefficient exhibits a linear regime at forces that are much weaker and larger than the thermal forces, whereas a nonlinear, force-thinning regime is observed at intermediate force intensities.

We experimentally study the unjamming dynamics of strongly compressed particle rafts confined between two fixed walls and two movable barriers. The back barrier is made of an elastic band, whose deflection indicates the local stress. The front barrier is pierced by a gate, whose opening triggers local unjamming. Prior to gate opening, the rafts are quasistatically compressed by moving only one of the two barriers, in the vicinity of which folds form. Using high-speed imaging, we follow the raft relaxation with folded, jammed, and unjammed areas and measure the velocity fields inside and outside the confined domain. Two very different behaviors develop. For rafts compressed by the back barrier, only partial unjamming occurs. At the end of the process, many folds remain and the back stress does not relax. The flow develops mostly along the compression axis and the particles passing the gate form a dense raft whose width is the gate width. For rafts compressed at the front, quasitotal unjamming is observed. Almost no folds persist and only minimal stress remains, if any. The particles flow along the compression axis but also normally to it and form a rather circular and not dense assembly. Both the force chain network orientation and the initial fold location could cause the unjamming difference. Other effects, such as a different pressure field or simple steric hindrance, cannot be excluded.

Thermocapillary convection is a common flow in space. Experiments regarding thermocapillary convection were previously carried out in a large-scale liquid bridge with a diameter of 20 mm on the Tiangong-2 space station, and the transition process to chaos was systematically studied. Under microgravity conditions, gravity is greatly weakened, and the transition process of the flow is very slow. This allows for the opportunity to study the bifurcation process in detail. It has been found that there are abundant nonlinear physical phenomena associated with the changing geometric parameters in thermocapillary convection systems. The transition mechanisms interact with each other, leading to various transition routes. The phase space trajectories, the Lyapunov exponents, and correlation dimensions are calculated to distinguish the chaotic state under a variety of conditions. Through the chaotic dynamics analysis, the chaotic characteristics of the entire transition process are quantitatively discussed.

The engineering features of transmitting mediums and their impact on different characteristics of a quantum system play a significant role in the efficient performance of nonlocal protocols. For this purpose, the dynamics of open quantum systems and coupling mediums remain a pathway. In this work, we investigate the dynamics of quantum correlations using negativity, uncertainty-induced nonlocality, and local quantum Fisher information in a hybrid qubit-qutrit thermal state when coupled with a magnetic field and influenced by random telegraph noise. Different features of the system parameters are taken into account while designing longer preservation of qubit-qutrit correlations. We show that the temperature has an inverse impact on the initial values of negativity, uncertainty-induced nonlocality, and local quantum Fisher information. When the magnetic field is characterized by different features, the entanglement, nonlocality, and Fisher information show a variety of dynamical maps, assuring their distinct nature. In addition, the qubit-qutrit correlations undergo repeated revivals when the configuration is restricted to the non-Markovian regime. On the other hand, an exponential drop with a single minimum is observed in the Markovian regime of the coupled field. Most importantly, our findings reveal that the present coupled fields have several advantages that can be leveraged to generate the optimal degree of entanglement, nonlocality, and local quantum Fisher information preservation in quantum dynamical maps.