When poking a thin shell-like structure, like a plastic water bottle, experience shows that an initial axisymmetric dimple forms around the indentation point. The ridge of this dimple, with increasing indentation, eventually buckles into a polygonal shape. The polygon order generally continues to increase with further indentation. In the case of spherical shells, both the underlying axisymmetric deformation and the buckling evolution have been studied in detail. However, little is known about the behavior of general geometries. In this work we describe the geometrical and mechanical features of the axisymmetric ridge that forms in indented general shells of revolution with non-negative Gaussian curvature and the conditions for circumferential buckling of this ridge. We show that under the assumption of “mirror buckling,” a single unified description of this ridge can be written if the problem is nondimensionalized using the local slope of the undeformed shell midprofile at the ridge radial location. However, in dimensional form the ridge properties evolve in quite different ways for different midprofiles. Focusing on the indentation of shallow shells of revolution with constant Gaussian curvature, we use our theoretical framework to study the properties of the ridge at the circumferential buckling threshold and evaluate the validity of the mirror buckling assumption against a linear stability analysis on the shallow shell equations, showing very good agreement. Our results highlight that circumferential buckling in indented thin shells is controlled by a complex interplay between the geometry and the stress state in the ridge. The results of our study will provide greater insight into the mechanics of thin shells. This could enable indentation to be used as a means to measure the mechanical properties of a wide range of shell geometries or used to design shells with specific mechanical behaviors.

In this work, a two-dimensional droplet confined between two parallel electrodes under the combined effects of a nonuniform electric field and unipolar charge injection is numerically investigated using the lattice Boltzmann method (LBM). Under the non-Ohmic regime, the interfacial tension and electric forces at the droplet surface cooperate with the volumetric Coulomb force, leading to complex deformation and motion of the droplet while at the same time inducing a bulk electroconvective flow. After we validate the model by comparing with analytical solutions at the hydrostatic state, we perform a quantitative analysis on the droplet deformation factor $D$ and bulk flow stability criteria $T_{\mathrm{c}}$ under different parameters, including the electric capillary number Ca, the electric Rayleigh number $T$, the permittivity ratio ${\varepsilon }_r$, and the mobility ratio $K_r$. It is found that the bulk flow significantly modifies the magnitude of $D$, which in turn decreases $T_c$ of the electroconvective flow. For a droplet repelled by the anode, ${\varepsilon }_r>1$, an interesting linear relationship can be observed in the $D$-Ca curves. However, for a droplet attracted to the anode, ${\varepsilon }_r<1$, the system is potentially unstable. After first evolving into a quasisteady state, the droplet successively experiences steady flow, periodic flow, second steady flow, and oscillatory flow with increasing $T$. Moreover, discontinuities can be observed in the $D\text{−}T$ curves due to the transitions of bulk flow.

The developing field of stochastic thermodynamics extends concepts of macroscopic thermodynamics such as entropy production and work to the microscopic level of individual trajectories taken by a system through phase space. The scheme involves coupling the system to an environment—typically a source of Markovian noise that affects the dynamics of the system. Here we extend this framework to consider a non-Markovian environment, one whose dynamics have memory and which create additional correlations with the system variables, and illustrate this with a selection of simple examples. Such an environment produces a rich variety of behavior. In particular, for a case of thermal relaxation, the distributions of entropy produced under the non-Markovian dynamics differ from the equivalent case of Markovian dynamics only by a delay time. When a time-dependent external work protocol is turned on, the system's correlations with the environment can either assist or hinder its approach to equilibrium, and affect its production of entropy, depending on the coupling strength between the system and environment.

We consider an isolated circular dry patch formed in an evaporating liquid layer and investigate local viscous flows in both liquid and air near the contact line which is the boundary of the dry patch. Flow patterns in the liquid deviate significantly from the predictions of single-phase models even when the air-to-liquid dynamic viscosity ratio is small. In particular, the separatrices in the liquid flow patterns at large contact angles disappear completely for a range of realistic viscosity ratios when the shear stress on the air side of the interface is accounted for. Experimentally observed motion of microdroplets near the contact line under combined action of gravity and moist air flow is described using our local flow model. We demonstrate that analysis of droplet trajectories leads to unambiguous determination of the local evaporative flux profile. A numerical finite-element approach for the steady diffusion equation is then used to extract the same flux profile from the global solution for concentration field in the limiting case of very thin liquid layer and small contact angle. The local evaporation rate is underpredicted by the numerical method, most likely due to the neglect of convective mass transfer in the air.

We provide second- to sixth-order virial coefficients of hard hyperspherocylinders in dependence on their aspect ratio $\nu$. Virial coefficients of an anisotropic geometry in four dimensions are calculated employing an optimized Mayer-sampling algorithm. As the second virial coefficient of a hard particle is identical to its excluded hypervolume, the numerically obtained second virial coefficients can be compared to analytical relations for the excluded hypervolume based on geometric measures of the respective, convex geometry in dependence on its aspect ratio $\nu$.

Epidemics unfold by means of a spreading process from each infected individual to a variable number of secondary cases. It has been claimed that the so-called superspreading events of the COVID-19 pandemic are governed by a power-law-tailed distribution of secondary cases, with no finite variance. Using a continuous-time branching process, we demonstrate that for such power-law-tailed superspreading, the survival probability of an outbreak as a function of both time and the basic reproductive number fulfills a “finite-time scaling” law (analogous to finite-size scaling) with universal-like characteristics only dependent on the power-law exponent. This clearly shows how the phase transition separating a subcritical and a supercritical phase emerges in the infinite-time limit (analogous to the thermodynamic limit). We also quantify the counterintuitive hazards posed by this superspreading. When the expected number of infected individuals is computed removing extinct outbreaks, we find a constant value in the subcritical phase and a superlinear power-law growth in the critical phase.

Phonon transport in square-cross-section nanowires is studied using spectral Monte Carlo simulations. Our results show the evolution of the different transport regimes described by Lévy statistics as a function of the surface roughness–to–thermal wavelength ratio $\sigma /\lambda$. More precisely, the relationship between the Lévy index $\gamma$ describing the mean free path distribution $\mathrm{\Psi }\left(\mathrm{\Lambda }\right)$ and $\sigma /\lambda$ is established for the classical diffusive regime, the superdiffusive regime, and the ballistic regime in the nanowire. Besides the conventional superdiffusive regime that is marked by $\mathrm{\Psi }\left(\mathrm{\Lambda }\right)$ with a single heavy-tailed peak, we reveal an unconventional superdiffusive subregime featuring $\mathrm{\Psi }\left(\mathrm{\Lambda }\right)$ with sawtooth oscillations when $\sigma /\lambda \sim 0.01$. Investigation of the direction of propagation of phonons shows a significant narrowing of the angular distribution around the long axis of the nanowire due to the diffuse scattering at rough boundaries when $\sigma /\lambda >0.1$. These results shed light on the transport mechanisms of quasiballistic phonons and will help in nanowire design for specific applications.

By employing Husimi quasiprobability distributions, we show that a bounded portion of an unbounded phase space induces a finite effective dimension in an infinite-dimensional Hilbert space. We compare our general expressions with numerical results for the spin-boson Dicke model in the chaotic energy regime, restricting its unbounded four-dimensional phase space to a classically chaotic energy shell. This effective dimension can be employed to characterize quantum phenomena in infinite-dimensional systems, such as localization and scarring.

Intervention strategies are of great significance for controlling large-scale outbreaks of epidemics. Since the spread of epidemic depends largely on the movement of individuals and the heterogeneity of the network structure, understanding potential factors that affect the epidemic is fundamental for the design of reasonable intervention strategies to suppress the epidemic. So far, most of previous studies mainly consider intervention strategies on the network composed of a single type of locations, while ignoring the movement behavior of individuals to and from locations that are composed of different types, i.e., residences and public places, which often presents heterogeneous structure. In addition, the transmission rate in public places with different population flows is heterogeneous. Inspired by the above observation, we build a bipartite metapopulation network model and propose intervention strategies based on the importance of public places. With the Markovian Chain approach, we derive the epidemic threshold under intervention strategies. Experimental results show that, compared with the uniform intervention to residences or public places, nonuniform intervention to public places is more effective for suppressing the epidemic with an increased epidemic threshold. Specifically, interventions to public places with large degree can further suppress the epidemic. Our study opens a new path for understanding the spatial epidemic spread and provides guidance for the design of intervention strategies for epidemics in the future.

Using two models of opinion dynamics, the $q$-voter model with independence and the $q$-voter model with anticonformity, we discuss how the change of disorder from annealed to quenched affects phase transitions on networks. To derive phase diagrams on networks, we develop the pair approximation for the quenched versions of the models. This formalism can be also applied to other quenched dynamics of similar kind. The results indicate that such a change of disorder eliminates all discontinuous phase transitions and broadens ordered phases. We show that although the annealed and quenched types of disorder lead to the same result in the $q$-voter model with anticonformity at the mean-field level, they do lead to distinct phase diagrams on networks. These phase diagrams shift towards each other as the average node degree of a network increases, and eventually, they coincide in the mean-field limit. In contrast, for the $q$-voter model with independence, the phase diagrams move towards the same direction regardless of the disorder type, and they do not coincide even in the mean-field limit. To validate our results, we carry out Monte Carlo simulations on random regular graphs and Barabási-Albert networks. Although the pair approximation may incorrectly predict the type of phase transitions for the annealed models, we have not observed such errors for their quenched counterparts.

We develop a lattice model on the rate of hybridization of the complementary single-stranded DNAs (c-ssDNAs). Upon translational diffusion mediated collisions, c-ssDNAs interpenetrate each other to form correct (cc), incorrect (icc), and trap correct contacts (tcc) inside the reaction volume. Correct contacts are those with exact registry matches, which leads to nucleation and zipping. Incorrect contacts are the mismatch contacts which are less stable compared to tcc, which can occur in the repetitive c-ssDNAs. Although tcc possess registry match within the repeating sequences, they are incorrect contacts in the view of the whole c-ssDNAs. The nucleation rate ($k_N$) is directly proportional to the collision rate and the average number of correct contacts ($\langle n_{cc}\rangle$) formed when both c-ssDNAs interpenetrate each other. Detailed lattice model simulations suggest that $\langle n_{cc}\rangle \propto L/V$ where $L$ is the length of c-ssDNAs and $V$ is the reaction volume. Further numerical analysis revealed the scaling for the average radius of gyration of c-ssDNAs ($R_g$) with their length as $R_g\propto \sqrt{L}$. Since the reaction space will be approximately a sphere with radius equals to $2R_g$ and $V\propto L^{3/2}$, one obtains $k_N\propto \frac{1}{\sqrt{L}}$. When c-ssDNAs are nonrepetitive, the overall renaturation rate becomes as $k_R\propto k_{N}L$, and one finally obtains $k_R\propto \sqrt{L}$ in line with the experimental observations. When c-ssDNAs are repetitive with a complexity of $c$, earlier models suggested the scaling $k_R\propto \frac{\sqrt{L}}{c}$, which breaks down at $c=L$. This clearly suggests the existence of at least two different pathways of renaturation in the case of repetitive c-ssDNAs, viz., via incorrect contacts and trap correct contacts. The trap correct contacts can lead to the formation of partial duplexes which can keep the complementary strands in the close proximity for a prolonged timescale. This is essential for the extended 1D slithering, inchworm movements, and internal displacement mechanisms which can accelerate the searching for the correct contacts. Clearly, the extent of slithering dynamics will be inversely proportional to the complexity. When the complexity is close to the length of c-ssDNAs, the pathway via incorrect contacts will dominate. When the complexity is much less than the length of c-ssDNA, pathway via trap correct contacts would be the dominating one.

We develop theoretical equivalences between stochastic and deterministic models for populations of individual cells stratified by age. Specifically, we develop a hierarchical system of equations describing the full dynamics of an age-structured multistage Markov process for approximating cell cycle time distributions. We further demonstrate that the resulting mean behavior is equivalent, over large timescales, to the classical McKendrick-von Foerster integropartial differential equation. We conclude by extending this framework to a spatial context, facilitating the modeling of traveling wave phenomena and cell-mediated pattern formation. More generally, this methodology may be extended to myriad reaction-diffusion processes for which the age of individuals is relevant to the dynamics.

Chirality can endow nonequilibrium active matter with unique features and functions. Here, we explore the chiral dynamics in biphasic active nematics composed of self-rotating units that continuously inject energy and angular momentum at the microscale. We show that the self-rotation of units can regularize the boundaries between two phases, rendering sinusoidal-like interfaces, which allow lateral wave propagation and are characterized by chains of ordered antiferromagnetic cross-interface flow vortices. Through the spontaneous coordination of counter-rotating units across the interfaces, topological defects excited by activity are sorted spatiotemporally, where positive defects are locally trapped at the interfaces but, unexpectedly, are transported laterally in a unidirectional rather than wavy mode, whereas inertial negative defects remain spinning in the bulks. Our findings reveal that individual chirality could be harnessed to modulate interfacial morphodynamics in active systems and suggest a potential approach toward controlling topological defects for programmable microfluidics and logic operations.

The purpose of this article is to describe the physical mechanism responsible for the appearance of both spatially periodic and kinklike distortions in a homogeneously aligned microsized nematic volume under the effect of crossed electric and magnetic fields. Numerical studies were carried out to describe the dynamic reorientation of the ${\mathrm{director}}^{\prime }\mathrm{s}$ field in a thick liquid crystal (LC) cell ($\sim 200\mu \text{m}$) under the effect of a large electric field $\mathbf{\text{E}}$ ($\sim 1.0\text{V}/\mu \text{m}$) directed at an angle $\alpha$ close to a right angle to magnetic field $\mathbf{\text{B}}$ ($\sim 7.0\text{T}$). It is shown that under the effect of $\mathbf{\text{E}}$ directed at $\alpha \sim 89.{96}^{\circ }$ to $\mathbf{\text{B}}$, at least two scenarios of reorientation of the director field can be realized. First, in response to the suddenly applied electric field, spatially periodic patterns can appear in an initially uniformly aligned nematic domain. Second, when the same crossed external fields are applied at the smaller angle $\alpha \sim 88.{81}^{\circ }$ to each other, the mode of uniform director reorientation is dominated. In the case when the electric field $E\gg E_{\mathrm{th}}$ is applied orthogonally to both horizontal bounding surfaces of the LC cell and the magnetic field is turned off, in the microsized nematic volume the distortion in the form of the kinklike wave spreading normally to the horizontal bounding surfaces with the velocity in a few meters per second can be excited.

It is well established that application of an oscillatory excitation with zero time-average but temporal asymmetry can yield net drift. To date this temporal symmetry breaking and net drift has been explored primarily in the context of point particles, nonlinear optics, and quantum systems. Here, we present two new experimental systems where the impact of temporally asymmetric force excitations can be readily observed with mechanical motion of macroscopic objects: (1) solid centimeter-scale objects placed on a uniform flat surface made to vibrate laterally, and (2) charged colloidal particles in water placed between parallel electrodes with an applied oscillatory electric potential. In both cases, net motion is observed both experimentally and numerically with nonantiperiodic, two-mode, sinusoids where the frequency modes are the ratio of odd and even numbers (e.g., $2\mathrm{Hz}$ and $3\mathrm{Hz}$). The observed direction of motion is always the same for the same applied waveform, and is readily reversed by changing the sign of the applied waveform, for example, by swapping which electrode is powered and grounded. We extend these results to other nonlinear mechanical systems, and we discuss the implications for facile control of object motion using tunable periodic driving forces.

Prestrained elastic networks arise in a number of biological and technological systems ranging from the cytoskeleton of cells to tensegrity structures. Motivated by this observation, we here consider a minimal model in one dimension to set the stage for understanding the response of such networks as a function of the prestrain. To this end we consider a chain [one-dimensional (1D) network] of elastic springs upon which a random, zero mean, finite variance prestrain is imposed. Numerical simulations and analytical predictions quantify the magnitude of the contraction as a function of the variance of the prestrain, and show that the chain always shrinks. To test these predictions, we vary the topology of the chain, consider more complex connectivity and show that our results are relatively robust to these changes.

This study is a direct follow-up of the paper by Heifetz and Guha [Phys. Rev. E 100, 043105 (2019)] on a minimal nonlinear dynamical system, describing a prototype of linearized two-dimensional shear instability. In that paper, the authors describe the instability in terms of an action at a distance between two vorticity waves, each of which propagates counter to its local mean flow as well as counter to the other. Here we add to the model the effect of mutual interaction between the waves and the mean flow, where growth of the waves reduces the mean shear and vice versa. This addition yields oscillatory Hamiltonian dynamics, including states of phase slipping and libration with finite-size wave amplitude oscillations. We find that wave–mean-flow dynamics emerging from unstable normal modes in the linearized stage are doomed to librate around the antiphased neutral configuration in which the waves hinder each other's counterpropagation rate. We discuss as well how the given dynamics relates to familiar models of phase oscillators.

At the molecular level fluid motions are, by first principles, described by time reversible laws. On the other hand, the coarse grained macroscopic evolution is suitably described by the Navier-Stokes equations, which are inherently irreversible, due to the dissipation term. Here, a reversible version of three-dimensional Navier-Stokes is studied, by introducing a fluctuating viscosity constructed in such a way that enstrophy is conserved, along the lines of the paradigm of microcanonical versus canonical treatment in equilibrium statistical mechanics. Through systematic simulations we attack two important questions: (a) What are the conditions that must be satisfied in order to have a statistical equivalence between the two nonequilibrium ensembles? (b) What is the empirical distribution of the fluctuating viscosity observed by changing the Reynolds number and the number of modes used in the discretization of the evolution equation? The latter point is important also to establish regularity conditions for the reversible equations. We find that the probability to observe negative values of the fluctuating viscosity becomes very quickly extremely small when increasing the effective Reynolds number of the flow in the fully resolved hydrodynamical regime, at difference from what was observed previously.

An initially planar shock wave propagating into a medium of nonuniform density will be perturbed, leading to the generation of postshock velocity perturbations. Using numerical simulations we study this phenomenon in the case of highly nonuniform density (order-unity normalized variance, ${\sigma }_{\rho }/\overline{\rho }\sim 1$) and strong shocks (shock Mach numbers ${\overline{M}}_s\gtrsim 10$). This leads to a highly disrupted shock and a turbulent postshock flow. We simulate this interaction for a range of shock drives and initial density configurations meant to mimic those which might be presently achieved in experiments. Theoretical considerations lead to scaling relations, which are found to reasonably predict the postshock turbulence properties. The turbulent velocity dispersion and turbulent Mach number are found to depend on the preshock density dispersion and shock speed in a manner consistent with the linear Richtymer-Meshkov instability prediction. We also show a dependence of the turbulence generation on the scale of density perturbations. The postshock pressure and density, which can be substantially reduced relative to the unperturbed case, are found to be reasonably predicted by a simplified analysis that treats the extended shock transition region as a single normal shock.

The spectral characteristics of high-order harmonics generated by the interaction of a linearly polarized relativistic laser pulse with a plasma grating target are investigated. Through particle-in-cell simulations and an analytical model, it is shown that a plasma grating target with periodic structure can select special harmonics with integer multiples of the grating frequency, and that low-order harmonics with frequencies being integer times of the laser frequency are generated nearly parallel to the target surface from a Fresnel zone plate target with an aperiodic structure. Spectral control of the harmonics can be achieved by introducing a correction factor $\beta$ to the radius formula of the Fresnel zone plate, which can create a slightly detuned plasma grating, and then only the narrow-band harmonics can be selected nearly parallel to the target surface. The center order of the narrow-band harmonics can be tuned by adjusting the correction factor $\beta$, while the bandwidth of the harmonics can be selected by adjusting the other parameter ${\lambda }_f$ of the detuned plasma grating.