The analysis of the dynamics of tracer particles in a complex bath can provide valuable information about the microscopic behavior of the bath. In this work, we study the dynamics of a forced tracer in a colloidal bath by means of Langevin dynamics simulations and a theory model within continuum mechanics. In the simulations, the bath is comprised of quasihard spheres with a volume fraction of $50\%$ immersed in a featureless quiescent solvent, and the tracer is pulled with a constant small force (within the linear regime). The theoretical analysis is based on the Navier-Stokes equation, where a term proportional to the velocity arises from coarse-graining the friction of the colloidal particles with the solvent. As a result, the final equation is similar to the Brinkman model, although the interpretation is different. A length scale appears in the model, $k_0^{-1}$, where the transverse momentum transport crosses over to friction with the solvent. The effective friction coefficient experienced by the tracer grows with the tracer size faster than the prediction from Stokes's law. Additionally, the velocity profiles in the bath decay faster than in a Newtonian fluid. The comparison between simulations and theory points to a boundary condition of effective partial slip at the tracer surface. We also study the fluctuations in the tracer position, showing that it reaches diffusion at long times, with a subdiffusive regime at intermediate times. The diffusion coefficient, obtained from the long-time slope of the mean-squared displacement, fulfills the Stokes-Einstein relation with the friction coefficient calculated from the steady tracer velocity, confirming the validity of the linear response formalism.

Three-dimensional simulations with fully resolved hydrodynamics are performed to study the dynamics of a single squirmer with and without gravity to clarify its motion in the vicinity of a flat plate. In the absence of gravity and chirality, the usual dynamics of a squirmer near a wall are recovered. The introduction of chirality modifies the swimming motion of squirmers, adding a component of motion in the third direction. When sedimentation is considered, different dynamics emerge for different gravity strength regimes. In a moderate gravity regime, neutral squirmers and pullers eventually stop moving and reorient in a direction perpendicular to the plate; by contrast, pushers exhibit continuous motion in a tilted direction. In the strong gravity regime, all squirmers sediment and reorient perpendicular to the plate. In this study, chirality is introduced to model realistic microswimmers, and its crucial effects on the nature of squirmer trajectories, which change from straight to circular, are discussed.

We highlight the unique wavelike character observed in the relaxation dynamics of active systems via a Smoluchowski based theoretical framework and Brownian dynamic simulations. Persistent swimming motion results in wavelike dynamics until the advective swim displacements become sufficiently uncorrelated, at which point the motion becomes a random walk process characterized by a swim diffusivity, $D^{\text{swim}}=U_0^2{\tau }_R/\left[d(d-1)\right]$, dependent on the speed of swimming $U_0$, reorientation time ${\tau }_R$, and reorientation dimension $d$. This change in behavior is described by a telegraph equation, which governs the transition from ballistic wavelike motion to long-time diffusive motion. We study the relaxation of active Brownian particles from an instantaneous source, and provide an explanation for the nonmonotonicity observed in the intermediate scattering function. Using our simple kinetic model we provide the density distribution for the diffusion of active particles released from a line source as a function of time, position, and the ratio of the activity to thermal energy. We extend our analysis to include the effects of an external field on particle spreading to further understand how reorientation events in the active force vector affect relaxation. The strength of the applied external field is shown to be inversely proportional to the decay of the wavelike structure. Our theoretical description for the evolution of the number density agrees with Brownian dynamic simulation data.

We perform dynamic Monte Carlo simulations to investigate the equilibrium dynamics of hard board-like colloidal particles in oblate and prolate nematic liquid crystals. In particular, we characterize the particles' diffusion along the nematic director and perpendicularly to it, and observe a structural relaxation decay that strongly depends on the particle anisotropy. To assess the Gaussianity of their dynamics and eventual occurrence of collective motion, we calculate two- and four-point correlation functions that incorporate the instantaneous values of the diffusion coefficients parallel and perpendicular to the nematic director. Our simulation results highlight the occurrence of Fickian and Gaussian dynamics at short and long times, locate the minimum diffusivity at the self-dual shape, the particle geometry that would preferentially stabilise biaxial nematics, and exclude the existence of dynamically correlated particles.

Streaming potential mediated pressure driven electrokinetic transport of Phan-Thien–Tanner fluids in a slit type parallel plate microchannel is studied analytically and semianalytically. Without adopting the traditional considerations of Debye–Hückel linearization approximation for low surface potentials, exact analytical solutions are obtained for the electrostatic potential distribution, velocity, and volumetric flow rates taking into account the full Poisson-Boltzmann equation. The influences of interfacial electrokinetics and viscoelasticity on the streaming potential development, polymeric stress components, shear viscosity, and the hydroelectric energy conversion efficiency are incorporated concurrently. Major findings indicate that the magnitude of the induced streaming potential, volumetric flow rates, and the energy conversion efficiency increases up to a threshold limit of zeta potential of $\zeta \le 6$, however, it follows an asymptotic reduction at the other end of higher zeta potentials $6<\zeta \le 10$. The polymeric stress components and shear viscosity follow a similar trend in the regime of $1\le \zeta \le 10$, which is primarily governed by the streaming potential field. In contrast, the transverse averaged shear viscosity in the range $1\le \zeta \le 10$ obeys an opposite trend by yielding an inverted parabolic shape. Amplification in the Stern layer conductivity yields a progressive reduction in the streaming potential magnitude and the hydroelectric energy conversion efficiency. The effect of the fluid viscoelasticity designated by the Weissenberg number exhibits a linear enhancement in streaming potential, flow rates, and the energy conversion efficiency. Moreover, we show that with the optimal combinations of surface charging and fluid viscoelasticity, it is possible to accomplish a giant augmentation in the hydroelectric energy conversion efficiency and flow rates. The analytical and semianalytical results presented in this investigation are believed to be worthy not only to cater deeper understanding in micro- and nanofluidic transport characteristics but also will act as functional design instrument for the future generation of energy efficient narrow fluidic devices.

The interplay of inertia and elasticity is shown to have a significant impact on the transport of filamentary objects, modeled by bead-spring chains, in a two-dimensional turbulent flow. We show how elastic interactions among inertial beads result in a nontrivial sampling of the flow, ranging from entrapment within vortices to preferential sampling of straining regions. This behavior is quantified as a function of inertia and elasticity and is shown to be very different from free, noninteracting heavy particles, as well as inertialess chains [Picardo et al., Phys. Rev. Lett. 121, 244501 (2018)]. In addition, by considering two limiting cases, of a heavy-headed and a uniformly inertial chain, we illustrate the critical role played by the mass distribution of such extended objects in their turbulent transport.

We present a new model of electron transport in warm and hot dense plasmas which combines the quantum Landau-Fokker-Planck equation with the concept of mean-force scattering. We obtain electrical and thermal conductivities across several orders of magnitude in temperature, from warm dense matter conditions to hot, nondegenerate plasma conditions, including the challenging crossover regime between the two. The small-angle approximation characteristic of Fokker-Planck collision theories is mitigated to good effect by the construction of accurate effective Coulomb logarithms based on mean-force scattering, which allows the theory to remain accurate even at low temperatures, as compared with high-fidelity quantum simulation results. Electron-electron collisions are treated on equal footing as electron-ion collisions. Their accurate treatment is found to be essential for hydrogen, and is expected to be important to other low-$Z$ elements. We find that electron-electron scattering remains influential to the value of the thermal conductivity down to temperatures somewhat below the Fermi energy. The accuracy of the theory seems to falter only for the behavior of the thermal conductivity at very low temperatures due to a subtle interplay between the Pauli exclusion principle and the small-angle approximation as they pertain to electron-electron scattering. Even there, the model is in fair agreement with ab initio simulations.

We propose a method to directly couple molecular dynamics, the finite element method, and particle-in-cell techniques to simulate metal surface response to high electric fields. We use this method to simulate the evolution of a field-emitting tip under thermal runaway by fully including the three-dimensional space-charge effects. We also present a comparison of the runaway process between two tip geometries of different widths. The results show with high statistical significance that in the case of sufficiently narrow field emitters, the thermal runaway occurs in cycles where intensive neutral evaporation alternates with cooling periods. The comparison with previous works shows that the evaporation rate in the regime of intensive evaporation is sufficient to ignite a plasma arc above the simulated field emitters.

Accurately acquiring the three-dimensional (3D) image of a porous medium is an imperative issue for the prediction of multiple physical properties. Considering the inherent nature of the multiscale pores contained in porous media such as tight sandstones, to completely characterize the pore structure, one needs to scan the microstructure at different resolutions. Specifically, low-resolution (LR) images cover a larger field of view (FOV) of the sample, but are lacking small-scale features, whereas high-resolution (HR) images contain ample information, but sometimes only cover a limited FOV. To address this issue, we propose a method for fusing the spatial information from a two-dimensional (2D) HR image into a 3D LR image, and finally reconstructing an integrated 3D structure with added fine-scale features. In the fusion process, the large-scale structure depicted by the 3D LR image is fixed as background and the 2D image is utilized as training image to reconstruct a small-scale structure based on the background. To assess the performance of our method, we test it on a sandstone scanned with low and high resolutions. Statistical properties between the reconstructed image and the target are quantitatively compared. The comparison indicates that the proposed method enables an accurate fusion of the LR and HR images because the small-scale information is precisely reproduced within the large one.

The Cassie-Wenzel transition of a symmetric binary liquid mixture in contact with a nano-corrugated wall is studied. The corrugation consists of a periodic array of nanopits with square cross sections. The substrate potential is the sum over Lennard-Jones interactions, describing the pairwise interaction between the wall particles $\mathrm{C}$ and the fluid particles. The liquid is composed of two species of particles, $\mathrm{A}$ and $\mathrm{B}$, which have the same size and equal $\mathrm{A}\text{−}\mathrm{A}$ and $\mathrm{B}\text{−}\mathrm{B}$ interactions. The liquid particles interact between each other also via $\mathrm{A}\text{−}\mathrm{B}$ Lennard-Jones potentials. We have employed classical density functional theory to determine the equilibrium structure of binary liquid mixtures in contact with the nano-corrugated surface. Liquid intrusion into the pits is studied as a function of various system parameters such as the composition of the liquid, the strengths of various interparticle interactions, and the geometric parameters of the pits. The binary liquid mixture is taken to be at its mixed-liquid-vapor coexistence. For various sets of parameters the results obtained for the Cassie-Wenzel transition, as well as for the metastability of the two corresponding thermodynamic states, are compared with macroscopic predictions in order to check the range of validity of the macroscopic theories for systems exposed to nanoscopic confinements. Distinct from the macroscopic theory, it is found that the Cassie-Wenzel transition cannot be predicted based on the knowledge of a single parameter, such as the contact angle within the macroscopic theory.

We study the heat current flowing between two baths consisting of harmonic oscillators interacting with a qubit through a spin-boson coupling. An explicit expression for the generating function of the total heat flowing between the right and left baths is derived by evaluating the corresponding Feynman-Vernon path integral by performing the noninteracting blip approximation (NIBA). We recover the known expression, obtained by using the polaron transform. This generating function satisfies the Gallavotti-Cohen fluctuation theorem, both before and after performing the NIBA. We also verify that the heat conductance is proportional to the variance of the heat current, retrieving the well-known fluctuation dissipation relation. Finally, we present numerical results for the heat current.

The transfer entropy and the transfer entropy rate are closely related concepts that measure information exchange between two dynamical systems. These measures allow us to study linear and nonlinear causality relations and can be estimated through the use of different methodologies. However, some of them assume a data model and/or are computationally expensive. This article depicts a methodology to estimate the transfer entropy rate between two systems through the Lempel-Ziv complexity. This methodology offers a set of advantages: It estimates the transfer entropy rate from two single discrete series of measures, it is not computationally expensive, and it does not assume any data model. The simulation results over three different unidirectional coupled dynamical systems suggest that this methodology can be used to assess the direction and strength of the information flow between systems. Moreover, it provides good estimations for short-length time series.

We have discovered here a duality relation between infinitely divisible subordinators which can produce both retarding and accelerating anomalous diffusion in the framework of the special Bernstein function approach. As a consequence, we show that conjugate pairs of Bernstein functions taken as Laplace exponents can produce in a natural way both retarding and accelerating anomalous diffusion (either subdiffusion or superdiffusion). This provides a unified way to control the dynamics of complex biological processes leading to transient anomalous diffusion in single-particle tracking experiments. Moreover, this permits one to explain better the relaxation diagram positioning two different power laws of relaxation, including the celebrated Havriliak-Negami law.

Connecting short-time microscopic dynamics with long-time hydrodynamics in strongly correlated quantum systems is one of the outstanding questions. In particular, it is hard to determine various hydrodynamic coefficients such as the diffusion constant or viscosity starting from a microscopic model: exact quantum simulations are limited to either small system sizes or to short times, which are insufficient to reach asymptotic behavior and so various approximations must be applied. We show that these difficulties, at least for particular models, can be circumvented by using the cluster truncated Wigner approximation (CTWA), which maps quantum Hamiltonian dynamics into classical Hamiltonian dynamics in auxiliary high-dimensional phase space. We apply CTWA to XXZ next-nearest-neighbor spin-1/2 chains and XY spin ladders, and find behavior consisting of short-time spin relaxation which gradually crosses over to emergent diffusive behavior at long times. For a random initial state, we show that CTWA correctly reproduces the whole spin spectral function. Necessary in this construction is sampling from properly fluctuating initial conditions: the Dirac mean-field (variational) ansatz, which neglects such fluctuations, leads to incorrect predictions.

We study spatial correlations between oscillator phases in the steady state of a Kuramoto model, in which phase oscillators that are randomly distributed in space interact with constant strength but within a limited range. Such a model could be relevant, for example, in the synchronization of gene expression oscillations in cells, where only oscillations of neighboring cells are coupled through cell-cell contacts. We analytically infer spatial phase-phase correlation functions from the known steady-state distribution of oscillators for the case of homogenous frequencies and show that these can contain information about the range and strength of interactions, provided the noise in the system can be estimated. We suggest a method for the latter, and also explore when correlations appear to be ergodic in this model, which would enable an experimental measurement of correlation functions to utilize temporal averages. Simulations show that our techniques also give qualitative results for the model with heterogenous frequencies. We illustrate our results by comparison with experimental data on genetic oscillations in the segmentation clock of zebrafish embryos.

We investigate the thermalization of a two-component scalar field across a second-order phase transition under extremely fast quenches. We find that vortices start developing once the thermal bath sets the control parameter to its final value in the nonsymmetric phase. Specifically, we find that vortices emerge as the fluctuating field relaxes and departs macroscopically from its symmetric configuration. The density of primordial vortices at the relaxation time is a decreasing function of the final temperature of the quench. Subsequently, vortices and antivortices annihilate at a rate that eventually determines the total thermalization time. This rate decreases if the theory contains a discrete anisotropy term, which otherwise leaves the primordial vortex density unaffected. Our results thus establish a link between the topological processes involved in the vortex dynamics and the delay in the thermalization of the system.

Via extensive Monte Carlo simulations along with systematic analyses of corrections to scaling, we estimate the order parameter critical exponent $\beta$ of absorbing phase transitions in systems with two symmetric absorbing states. The value of $\beta$ was conjectured to be $\frac{13}{14}\approx 0.93$ and Monte Carlo simulation studies in the literature have repeatedly reproduced values consistent with the conjecture. In this paper, we systematically estimate $\beta$ by analyzing the effective exponent after finding how strong corrections to scaling are. We show that the widely accepted numerical value of $\beta$ is not correct. Rather, we obtain $\beta =1.020\left(5\right)$ from different models with two symmetric absorbing states.

The motion of individual weaver ants from Oecophylla smaragdina was tracked within a small arena to study the algorithm that these ants use for navigation. The arena, a floor tile, was either clean or partly covered by a mild chemical repellent. Statistical properties of the observed motion of the ant can be described by a model that is analogous to the Langevin theory of the motion of Brownian particles. With each time step, the velocity of the ant changes by a random vector with a robust probability distribution. When the average ant encounters the chemical repellent it responds, like a particle seeing a potential energy barrier, by initially slowing before recovering towards its equilibrium state of motion. The model accounts for most qualitative properties of motion with a small number of parameters.

Since the early work of Hagen [G. H. L. Hagen, Ber. Verhandl. K. Preuss. Akad. Wiss. Berlin 17, 35 (1852)] and Beverloo et al. [W. Beverloo et al., Chem. Eng. Sci. 15, 260 (1961)], the flow rate of granular material discharging through a circular orifice from a silo has been described by means of dimensional analysis and experimental fits and explained through the free-fall arch model. Here, in contrast to the traditional approach, we derive a differential equation based on the energy balance of the system. This equation is consistent with the well-known Beverloo rule due to a compensation of energy terms. Moreover, this equation can be used to explore different conditions for silo discharges. In particular, we show how the effect of friction on the flow rate can be predicted. The theory is validated using discrete element method simulations.

Until now most studies of discrete plasticity have focused on systems that are assumed to be driven by a monotonically increasing force; in many real systems, however, the driving force includes damped oscillations or oscillations induced by the propagation of discrete events or “slip avalanches.” In both cases, these oscillations may obscure the true dynamics. Here we effectively consider both cases by investigating the effects of damped oscillations in the external driving force on avalanche dynamics. We compare model simulations of slip avalanches under mean-field dynamics with observations in slip-avalanche experiments on slowly compressed micrometer-sized Au specimens using open-loop force control. The studies show very good agreement between simulations and experiments. We find that an oscillatory external driving force changes the average avalanche shapes only for avalanches with durations close to the period of oscillation of the external force. This effect on the avalanche shapes can be addressed in experiments by choosing suitable specimen dimensions so that the mechanical resonance does not interact with the avalanche dynamics. These results are important for the interpretation of avalanche experiments with built-in oscillators, and for the prediction and analysis of avalanche dynamics in systems with resonant vibrations.