In view of its influence on the acoustic radiation force, we investigate the microstreaming around a small solid elastic particle in an ultrasonic standing wave in dependence of its material properties and shape. The configuration is axisymmetric, making it accessible to numerical methods, such as the finite element method. The results reveal a transition from viscous scattering- to microstreaming-dominated acoustic radiation force that depends on the particle density. When a deviation of the particle shape from a sphere becomes smaller than the viscous boundary layer thickness, we show that the influence of the shape on the viscous contributions to the acoustic radiation force diminishes, allowing the use of theoretical models for a spherical particle. However, extreme asymmetric shape perturbations, such as crowns with sharp edges, can give rise to noticeable viscous contributions for a dense particle that is larger than the viscous boundary layer thickness. We also introduce a hybrid analytical model for the acoustic radiation force on a spherical particle that accounts for the microstreaming and particle compressibility and shows a good agreement with numerical simulations for an arbitrary particle size and density.

The evolution of cooperation has gained more attention after Smith introduced game theory in the study of evolutionary biology. Subsequent works have extensively explained this phenomenon, consistently showing the importance of spatial structure for the evolution of cooperation. Here we analyze the effect of stochasticity on the evolution of cooperation in group-structured populations. We find a simple formula for the fixation probability of cooperators and show that cooperation can be favored by selection if a condition similar to Hamilton's rule is satisfied, which is also valid for strong selection and high migration. In fact, cooperation can be favored even in the absence of population viscosity and in the limit of an infinite number of finite-size groups. We discuss the importance of stochastic fluctuations in helping cooperation. We argue that this may be a general principle because fluctuations favoring the cooperators are often much more impactful than those favoring the defectors.

Kinetics of dilute heterogeneous traffic on a two-lane road is formulated in the framework of Ben-Naim–Krapivsky model and stationary state properties are analytically derived in the asymptotic limit. The heterogeneity is introduced into the model as a quenched disorder in desired speeds of vehicles. The two-lane model assumes that each vehicle or platoon in a lane moves ballistically until it approaches a slow-moving vehicle or platoon and then joins it. Vehicles in a platoon are assumed to escape the platoon at a constant rate by changing lanes after which they continue to move at their desired speeds. Each lane is assumed to have a different escape rate. As the stationary state is approached, the platoon densities in the two lanes become equal, whereas the vehicle densities and fluxes are higher in the lane with lower escape rate. A majority of the vehicles enjoy a free flow if the harmonic mean of the escape rates of the lanes is comparable to average initial flux on the road. The average platoon size is close to unity in the free-flow regime. If the harmonic mean is lower than the average initial flux, then vehicles with desired speeds lower than a characteristic speed $v^{*}$ still enjoy free flow while those vehicles with desired speeds that are greater than $v^{*}$ experience congestion and form platoons behind the slower vehicles. The characteristic speed depends on the mean of escape times $[R=(R_1+R_{-1})/2]$ of the two lanes (represented by 1 and $-1$) as $v^{*}\sim R^{-\frac{1}{\mu +2}}$, where $\mu$ is the exponent of the quenched disorder distribution for desired speed in the small speed limit. The average platoon size in a lane, when $v^{*}\ll 1$, is proportional to $R^{\frac{\mu +1}{\mu +2}}$ plus a lane-dependent correction. Equations for the kinetics of platoon size distribution for two-lane traffic are also studied. It is shown that a stationary state with platoons as large as road length can occur only if the mean escape rate is independent of platoon size.

It is investigated whether non-Markovianity, i.e., the memory effects resulting from the coupling of the system to its environment, can be beneficial for the performance of quantum heat engines. Specifically, two physical models are considered. The first one is a well-known single-qubit Otto engine; the non-Markovian behavior is there implemented by replacing standard thermalization strokes with so-called extremal thermal operations which cannot be realized without the memory effects. The second one is a three-stroke engine in which the cycle consists of two extremal thermal operations and a single qubit rotation. It is shown that the non-Markovian Otto engine can generate more work-per-cycle for a given efficiency than its Markovian counterpart, whereas performance of both setups is superior to the three-stroke engine. Furthermore, both the non-Markovian Otto engine and the three-stroke engine can reduce the work fluctuations in comparison with the Markovian Otto engine, with their relative advantage depending on the performance target. This demonstrates the beneficial influence of non-Markovianity on both the average performance and the stability of operation of quantum heat engines.

When a fluid is subject to an external field, as is the case near an interface or under spatial confinement, then the density becomes spatially inhomogeneous. Although the one-body density provides much useful information, a higher level of resolution is provided by the two-body correlations. These give a statistical description of the internal microstructure of the fluid and enable calculation of the average interparticle force, which plays an essential role in determining both the equilibrium and dynamic properties of interacting fluids. We present a theoretical framework for the description of inhomogeneous (classical) many-body systems, based explicitly on the two-body correlation functions. By consideration of local Noether-invariance against spatial distortion of the system we demonstrate the fundamental status of the Yvon-Born-Green (YBG) equation as a local force-balance within the fluid. Using the inhomogeneous Ornstein-Zernike equation we show that the two-body correlations are density functionals and, thus, that the average interparticle force entering the YBG equation is also a functional of the one-body density. The force-based theory we develop provides an alternative to standard density functional theory for the study of inhomogeneous systems both in- and out-of-equilibrium. We compare force-based density profiles to the results of the standard potential-based (dynamical) density functional theory. In-equilibrium, we confirm both analytically and numerically that the standard approach yields profiles that are consistent with the compressibility pressure, whereas the force-density functional gives profiles consistent with the virial pressure. For both approaches we explicitly prove the hard-wall contact theorem that connects the value of the density profile at the hard-wall with the bulk pressure. The structure of the theory offers deep insights into the nature of correlation in dense and inhomogeneous systems.

We report on the dynamical buckling of a spherical shell (a table-tennis ball) impinging in normal incidence on a rigid surface (a glass plate). Experimentally, we observe and decipher the geometrical characteristics of the shell profile in the contact region along with global metrics such as the contact duration and the coefficient of restitution of the linear velocity. We determine, in particular, the onset of the ball buckling instability. We find that, just like in quasi-statics, the shell buckles when the crushing exceeds about twice the thickness of the shell. In addition, for launching conditions resulting in the ball elastic buckling, a drop in the restitution coefficient is observed. A companion numerical finite elements study is set to monitor the different sources of energy and reveals that the added energy loss is mainly due to the friction between the shell surface and the solid substrate.

An important and incompletely answered question is whether a high-order rogue wave (RW) can be excited by the collision of first-order RWs, especially for its generation and propagation mechanisms. In this paper, the evolution properties of collisions between RWs are studied numerically for two-component coupled Bose-Einstein condensates. We find that whether a second-order RW can be successfully excited strongly depends on the location and time of the first-order RWs encountered. Only when the highest peaks of two RWs meet at the same position at the same time, can the standard second-order RW be triggered and its structure is in good agreement with the exact solution. Further, we demonstrate that such results are also applicable to the collision of subordinate RWs. This paper not only reveals the collision properties of RWs, but also provides a feasible scheme to generate higher-order RWs for experimental realization.

Here we analyze the evolutionary process in the presence of continuous influx of genotypes with submaximum fitness from the outside to the given habitat with finite resources. We show that strong influx from the outside allows the low-fitness genotype to win the competition with the higher fitness genotype, and in a finite population, drive the latter to extinction. We analyze a mathematical model of this phenomenon and obtain the conditions for the transition from the high-fitness to the low-fitness genotype caused by the influx of the latter. We calculate the time to extinction of the high-fitness genotype in a finite population with two alleles and find the exact analytical dynamics of extinction for the case of many genes with epistasis. We solve a related quasispecies model for a single peak (random) fitness landscape as well as for a symmetric fitness landscape. In the symmetric landscape, a nonperturbative effect is observed such that even an extremely low influx of the low-fitness genotype drastically changes the steady state fitness distribution. A similar nonperturbative phenomenon is observed for the allele fixation time as well. The identified regime of influx-driven evolution appears to be relevant for a broad class of biological systems and could be central to the evolution of prokaryotes and viruses.

We study the morphing of three-dimensional objects within the framework of nonlinear elasticity with large distortions. A distortion field induces a target metric, and the configuration which is effectively realized by a material body is the one that minimizes the distance, measured through the elastic energy, between the target metric and the actual one. Morphing through distortions might have a paramount feature: the resulting configurations might be stress-free; if this is the case, the distortions field is called compatible. We maintain that the morphing through compatible distortions is a key strategy exploited by many soft biological materials, which can exhibit very large shape-change in response to distortions controlled by stimuli such as chemicals or temperature changes, while keeping their stress state almost null. Thus, the study of compatible distortions, and of the related shape-changes, is quite important. Here, we show a blueprint for stress-free morphing based on the notions of metric tensor and of Riemann curvature which can be used to design large morphing of three-dimensional objects.

A numerical model is developed for the motion of superparamagnetic nanoparticles in a non-Newtonian blood flow under the influence of a magnetic field. The rheological properties of blood are modeled by the Carreau flow and viscosity, and the stochastic effects of Brownian motion and red blood cell collisions are considered. The model is validated with existing data and good agreement with experimental results is shown. The effectiveness of magnetic drug delivery in various blood vessels is assessed and found to be most successful in arterioles and capillaries. A range of magnetic field strengths are modeled using equations for both a bar magnet and a point dipole: it is shown that the bar magnet is effective at capturing nanoparticles in limited cases, while the point dipole is highly effective across a range of conditions. A parameter study is conducted to show the effects of changing the dipole moment, the distance from the magnet to the blood vessel, and the initial release point of the nanoparticles. The distance from the magnet to the blood vessel is shown to play a significant role in determining nanoparticle capture rate. The optimal initial release position is found to be located within the tumor radius in capillaries and arterioles to prevent rapid diffusion to the edges of the blood vessel prior to arriving at the tumor and near the edge of the magnet when a bar magnet is used.

To simulate elastic turbulence, where viscoelasticity dominates, numerical solvers introduce an artificial stress diffusivity term to handle the steep polymer stress gradients that ensue. This has recently been shown [A. Gupta and D. Vincenzi, J. Fluid Mech. 870, 405 (2019); V. Dzanic et al., J. Fluid Mech. 937, A31 (2022)] to introduce unphysical artifacts with a detrimental impact on simulations. In this Letter, we propose that artificial diffusion is limited to regions where stress gradients are steep instead of seeking the zero-diffusivity limit. Through the cellular forcing and four-roll mill problem, we demonstrate that this modified artificial diffusivity is devoid of unphysical artifacts, allowing all features of elastic turbulence to be retained. Results are found to conform with direct simulations, reducing the impact of artificial diffusivity from a qualitative scale to a quantitative scale while only requiring a fraction of the numerical resolution.

We derive a formula for the dry adiabatic lapse rate of atmospheres composed of real gases. We restrict our study to those described by a family of two-parameter cubic equations of state and the recent Guevara-Rodríguez noncubic equation. Since our formula depends on the adiabatic curves, we compute them all at once, considering molecules that can move, rotate, and vibrate, for any equation of state. To illustrate our results, we estimate the lapse rate of the troposphere of Titan, obtaining a better approximation to the observed data in some instances, when compared to the estimation provided by the virial expansion up to the third order.

We study the spin-1/2 Ising-XXZ model on a decorated honeycomb lattice composed of five spins per unit cell, one Ising spin, and four Heisenberg spins. This model involving the Heisenberg exchange interaction is one of the few models that can be exactly solvable through the generalized star-triangle transformation. The significance of this model is its close relationship to the fully decorated quantum Heisenberg honeycomb lattice since 4/5 of the particles are Heisenberg spins. We investigate the phase diagram at zero temperature and identify a relevant quantum spin frustrated phase resulting from the contribution of quantum Heisenberg exchange interaction. We obtain an exact residual entropy for the quantum spin frustrated phase, which coincides with the residual entropy of the antiferromagnetic spin-1/2 Ising model on a triangular lattice. We also thoroughly explore its thermodynamic properties, focusing mainly on the frustrated region such as entropy, specific heat, spontaneous magnetization, and critical temperature under several conditions.

In this paper, we first develop the projective truncation approximation (PTA) in the Green's function equation of motion (EOM) formalism for classical statistical models. To implement PTA for a given Hamiltonian, we choose a set of basis variables and projectively truncate the hierarchical EOM. We apply PTA to the one-dimensional ${\varphi }^4$ lattice model. Phonon dispersion and static correlation functions are studied in detail. Using one- and two-dimensional bases, we obtain results identical to and beyond the quadratic variational approximation, respectively. In particular, we analyze the power-law temperature dependence of the static averages in the low- and high-temperature limits, and we give exact exponents.

Transient heat dissipation in close-packed quasi-two-dimensional nanoline and three-dimensional nanocuboid hotspot systems is studied based on the phonon Boltzmann transport equation. It is found that, counterintuitively, the heat dissipation efficiency is not a monotonic function of the distance between adjacent nanoscale heat sources but reaches the highest value when this distance is comparable to the phonon mean free path. This is due to the competition of two thermal transport processes: quasiballistic transport when phonons escape from the nanoscale heat source and the scattering among phonons originating from the adjacent nanoscale heat source.

Diffusion of the orbits in a nonchaotic area-preserving map called a generalized triangle map (GTM) is numerically and analytically investigated. We provide accurate empirical evidence that the mean-squared displacement of the momentum for generic perturbation parameter settings increases sublinearly in time, and that the distribution of the momentum obeys a time-fractional diffusion equation. We show that the diffusion properties in the GTM do not follow any of the known stochastic processes generating sublinear diffusion since two seemingly incompatible features, non-Markovian yet stationary, coexist in the dynamics.

The self-correlation function and corresponding self-intermediate scattering function in Fourier space are important quantities for describing the molecular motions of liquids. This work draws attention to a largely overlooked issue concerning the analysis of these space-time density-density correlation functions of polymers. We show that the interpretation of non-Gaussian behavior of polymers is generally complicated by intrachain averaging of distinct self-dynamics of different segments. By the very nature of the mathematics involved, the averaging process not only conceals critical dynamical information, but also contributes to the observed non-Gaussian dynamics. To fully expose this issue and provide a thorough benchmark of polymer self-dynamics, we perform analyses of coarse-grained molecular dynamics simulations of linear and ring polymer melts as well as several theoretical models using a “two-step” approach, where interchain and intrachain averagings of segmental self-dynamics are separated. While past investigations primarily focused on the average behavior, our results indicate that a more nuanced approach to polymer self-dynamics is clearly required.

The two-dimensional Rayleigh-Taylor instability (RTI) in compressible flow with intermolecular interactions is probed via the discrete Boltzmann method. The effects of interfacial tension, viscosity, and heat conduction are investigated. It is found that the influences of interfacial tension on the perturbation amplitude, bubble velocity, and two kinds of entropy production rates all show differences at different stages of RTI evolution. It inhibits the RTI evolution at the bubble acceleration stage, while at the asymptotic velocity stage, it first promotes and then inhibits the RTI evolution. Viscosity and heat conduction inhibit the RTI evolution. Viscosity shows a suppressive effect on the entropy generation rate related to heat flow at the early stage but a first promotive and then suppressive effect on the entropy generation rate related to heat flow at a later stage. Heat conduction shows a promotive effect on the entropy generation rate related to heat flow at an early stage. Still, it offers a first promotive and then suppressive effect on the entropy generation rate related to heat flow at a later stage. By introducing the morphological boundary length, we find that the stage of exponential growth of the interface length with time corresponds to the bubble acceleration stage. The first maximum point of the interface length change rate and the first maximum point of the change rate of the entropy generation rate related to viscous stress can be used as a criterion for RTI to enter the asymptotic velocity stage.

Control over dispersion of nanoparticles in polymer solutions through porous media is important for subsurface applications such as soil remediation and enhanced oil recovery. Dispersion is affected by the spatial heterogeneity of porous media, the non-Newtonian behavior of polymer solutions, and the Brownian motion of nanoparticles. Here, we use the Euler-Lagrangian method to simulate the flow of nanoparticles and inelastic non-Newtonian fluids (described by Meter model) in a range of porous media samples and injection rates. In one case, we use a fine mesh of more than 3 million mesh points to model nanoparticles transport in a sandstone sample. The results show that the velocity distribution of nanoparticles in the porous medium is non-Gaussian, which leads to the non-Fickian behavior of nanoparticles dispersion. Due to pore-space confinement, the long-time mean-square displacement of nanoparticles depends nonlinearly on time. Additionally, the gradient of shear stress in the pore space of the porous medium dictates the transport behavior of nanoparticles in the porous medium. Furthermore, the Brownian motion of nanoparticles increases the dispersion of nanoparticles along the longitudinal and transverse direction.

The vacuum breakdown by 10-PW-class lasers is studied in the optimal configuration of laser beams in the form of an m-dipole wave, which maximizes the magnetic field. Using 3D PIC simulations we calculated the threshold of vacuum breakdown, which is about 10 PW. We examined in detail the dynamics of particles and identified particle trajectories which contribute the most to vacuum breakdown in such highly inhomogeneous fields. We analyzed the dynamics of the electron-positron plasma distribution on the avalanche stage. It is shown that the forming plasma structures represent concentric toroidal layers and the interplay between particle ensembles from different spatial regions favors vacuum breakdown. Based on the angular distribution of charged particles and gamma photons a way to experimentally identify the process of vacuum breakdown is proposed.