We develop a maximum likelihood method to infer relevant physical properties of elongated active particles. Using individual trajectories of advected swimmers as input, we are able to accurately determine their rotational diffusion coefficients and an effective measure of their aspect ratio, also providing reliable estimators for the uncertainties of such quantities. We validate our theoretical construction using numerically generated active trajectories upon no flow, simple shear, and Poiseuille flow, with excellent results. Being designed to rely on single-particle data, our method eases applications in experimental conditions where swimmers exhibit a strong morphological diversity. We briefly discuss some of such ongoing experimental applications, specifically, in the characterization of swimming E. coli in a flow.

Reactive particulate systems are of prime importance in varieties of practical applications in process engineering. As an example this study considers extraction of phosphorous from waste water by calcium silicate hydrate particles in the P-RoC process. For such systems modeling has a large potential to help to optimize process conditions, e.g., particle-size distributions or volume flows. The goal of this study is to present a new generic modeling framework to capture relevant aspects of reactive particle fluid flows using combined lattice Boltzmann method and discrete-element method. The model developed is Euler-Lagrange scheme which consist of three-components viz., a fluid phase, a dissolved reactive substance, and suspended particles. The fluid flow and reactive mass transport are described in a continuum framework using volume-averaged Navier-Stokes and volume-averaged advection-diffusion-reaction equations, respectively, and solved using lattice Boltzmann methods. The volume-averaging procedure ensures correctness in coupling between fluid flow, reactive mass transport, and particle motion. The developed model is validated through series of well-defined benchmarks. The benchmarks include the validation of the model with experimental data for the settling of a single particle in a cavity filled with water. The benchmark to validate the multi-scale reactive transport involves comparing the results with a resolved numerical simulation. These benchmarks also prove that the proposed model is grid convergent which has previously not been established for such coupled models. Finally, we demonstrate the applicability of our model by simulating a suspension of multiple particles in fluid with a dissolved reactive substance. Comparison of this coupled model is made with a one-way coupled simulation where the influence of particles on the fluid flow and the reactive solution transport is not considered. This elucidates the need for the two-way coupled model.

We analyze the flow and clogging of circular grains passing through a small aperture under vibration in two dimensions. Via discrete element method simulations, we show that when grains smaller than the original ones are introduced in the system as an additive, the net flow of the original species can be significantly increased. Moreover, there is an optimal radius of the additive particles that maximizes the effect. This finding may constitute the basis for technological applications not only concerning the flow of granular materials but also regarding active matter, including pedestrian evacuation.

Heat engines performing finite time Carnot cycles are described by positive irreversible entropy functions added to the ideal reversible entropy part. The model applies for macroscopic and microscopic (quantum mechanical) engines. The mathematical and physical conditions for the solution of the power maximization problem are discussed. For entropy models which have no reversible limit, the usual "linear response regime" is not mathematically feasible; i.e., the efficiency at maximum power cannot be expanded in powers of the Carnot efficiency. Instead, a physically less intuitive expansion in powers of the ratio of heat-reservoir temperatures holds under conditions that will be inferred. Exact solutions for generalized entropy models are presented, and results are compared. For entropy generation in endoreversible models, it is proved for all heat transfer laws with general temperature-dependent heat resistances, that minimum entropy production is achieved when the temperature of the working substance remains constant in the isothermal processes. For isothermal transition time $t$, entropy production then is of the form $a/\left[tf\right(t)\pm c]$ and not just equal to $a$/$t$ for the low-dissipation limit. The cold side endoreversible entropy as a function of transition times inevitably experiences singularities. For Newtonian heat transfer with temperature-independent heat conductances, the Curzon-Ahlborn efficiency is exactly confirmed, which—only in this unique case—shows "universality" in the sense of independence from dissipation ratios of the hot and cold sides with coinciding lower and upper efficiency bounds for opposite dissipation ratios. Extended exact solutions for inclusion of adiabatic transition times are presented.

The thermodynamic properties of the spin $S=3/2$ ferromagnetic Ising model in the presence of transverse and longitudinal crystal fields (equivalent to the Blume-Capel model with a transverse crystal field) have been studied by using two different approaches: (i) a zero-temperature mapping of the system onto a spin-1/2 quantum Ising model in longitudinal and transverse fields, together with time-independent quantum perturbation theory; and (ii) a standard mean-field approximation within the framework of the Bogoliubov inequality for the free energy. A very rich phase diagram, with different kinds of multicritical behavior, has been obtained. The results show first- and second-order transition lines, tricritical and tetracritical points, critical end points with a two-phase coexistence, double critical end points, and also double noncritical end points. Additionally, the behavior of the magnetization as a function of temperature, over a wide range of values of both longitudinal and transverse crystal fields, has also been analyzed in detail. While large magnitudes of the longitudinal crystal field select the $z$-spin components either in their states $\pm 3/2$ or $\pm 1/2$, it is surprising that a large transverse crystal field induces the spin component in the $z$ direction to values $\pm 1$, which are completely different from any expected natural component. This comes indeed as a result of the zero-temperature mapping of the ground state with the superposition of the states $3/2$ and $-1/2$, in one sector of the Hilbert space, and the states $-3/2$ and $1/2$ on the other disjoint sector of the Hilbert space. This superposition for a large transverse crystal field prevails even for finite temperatures, implying that the exact critical points are obtained for the model on the one-dimensional lattice and the two-dimensional square lattice, and quite accurate estimates can be achieved for the three-dimensional simple cubic lattice.

Exchange fluctuation theorems (XFTs) describe a fundamental symmetry relation for particle and energy exchange between several systems. Here we study the XFTs of a Kitaev chain connected to two reservoirs at the same temperature but different bias. By varying the parameters in the Kitaev chain model, we calculate analytically the full counting statistics of the transport current and formulate the corresponding XFTs for multiple current components. We also demonstrate the XFTs with numerical results. We find that due to the presence of the $\mathcal{U}\left(1\right)$ symmetry breaking terms in the Hamiltonian of the Kitaev chain, various forms of the XFTs emerge, and they can be interpreted in terms of various well-known transport processes.

We study how a quantum heat engine based on a single trapped ion performs in finite time. The always-on thermal environment acts like the hot bath, while the motional degree of freedom of the ion plays the role of the effective cold bath. The hot isochoric stroke is implemented via the interaction of the ion with its hot environment, while a projective measurement of the internal state of the ion is performed as an equivalent to the cold isochoric stroke. The expansion and compression strokes are implemented via suitable change in applied magnetic field. We study in detail how the finite duration of each stroke affects the engine performance. We show that partial thermalization can in fact enhance the efficiency of the engine, due to the residual coherence, whereas faster expansion and compression strokes increase the inner friction and therefore reduce the efficiency.

We revisit the problem of pinning a reaction-diffusion front by a defect, in particular by a reaction-free region. Using collective variables for the front and numerical simulations, we compare the behaviors of a bistable and monostable front. A bistable front can be pinned as confirmed by a pinning criterion, the analysis of the time independent problem, and simulations. Conversely, a monostable front can never be pinned, it gives rise to a secondary pulse past the defect and we calculate the time this pulse takes to appear. These radically different behaviors of bistable and monostable fronts raise issues for modelers in particular areas of biology, as for example, the study of tumor growth in the presence of different tissues.

Collections of cells exhibit coherent migration during morphogenesis, cancer metastasis, and wound healing. In many cases, bigger clusters split, smaller subclusters collide and reassemble, and gaps continually emerge. The connections between cell-level adhesion and cluster-level dynamics, as well as the resulting consequences for cluster properties such as migration velocity, remain poorly understood. Here we investigate collective migration of one- and two-dimensional cell clusters that collectively track chemical gradients using a mechanism based on contact inhibition of locomotion. We develop both a minimal description based on the lattice gas model of statistical physics and a more realistic framework based on the cellular Potts model which captures cell shape changes and cluster rearrangement. In both cases, we find that cells have an optimal adhesion strength that maximizes cluster migration speed. The optimum negotiates a tradeoff between maintaining cell-cell contact and maintaining configurational freedom, and we identify maximal variability in the cluster aspect ratio as a revealing signature. Our results suggest a collective benefit for intermediate cell-cell adhesion.

The Navier-Stokes equations generate an infinite set of generalized Lyapunov exponents defined by different ways of measuring the distance between exponentially diverging perturbed and unperturbed solutions. This set is demonstrated to be similar, yet different, from the generalized Lyapunov exponent that provides moments of distance between two fluid particles below the Kolmogorov scale. We derive rigorous upper bounds on dimensionless Lyapunov exponent of the fluid particles that demonstrate the exponent's decay with Reynolds number Re in accord with previous studies. In contrast, terms of cumulant series for exponents of the moments have power-law growth with Re. We demonstrate as an application that the growth of small fluctuations of magnetic field in ideal conducting turbulence is hyperintermittent, being exponential in both time and Reynolds number. We resolve the existing contradiction between the theory, that predicts slow decrease of dimensionless Lyapunov exponent of turbulence with Re, and observations exhibiting quite fast growth. We demonstrate that it is highly plausible that a pointwise limit for the growth of small perturbations of the Navier-Stokes equations exists.

For a semibounded plasma in a constant magnetic field and interacting with short laser pulse, a kinetic equation is derived, which makes it possible to describe the low-frequency movements of electrons. In the linear approximation in laser radiation intensity the solution of kinetic equation is obtained taking into account mirror reflection of electrons by the plasma surface. Using this solution, we derived low-frequency currents generated by low-frequency field and ponderomotive force that changes during the pulse affect. Under the assumption that characteristic spatial scales of changes in the low-frequency field and ponderomotive force exceed the Larmor radius of electrons, we studied low-frequency currents near the plasma surface. If the electron cyclotron frequency exceeds the inverse pulse duration, then low-frequency currents differ from their values in a homogeneous plasma only at a distance from the surface not exceeding several Larmor radii. Taking this fact into account, a solution to the equation for low-frequency field in the plasma was obtained. The terahertz (THz) magnetic field generated by nonlinear currents is found. It is shown that the maximum value of the generated field is attained at cyclotron frequency comparable with the product of the plasma frequency square and laser pulse duration.

In a recent paper by B. G. da Costa et al. [Phys. Rev. E 102, 062105 (2020)], the phenomenological Langevin equation and the corresponding Fokker-Planck equation for an inhomogeneous medium with a position-dependent particle mass and position-dependent damping coefficient have been studied. The aim of this comment is to present a microscopic derivation of the Langevin equation for such a system. It is not equivalent to that in the commented paper.

It is shown that in the “Comment on ‘Deformed Fokker-Planck equation: Inhomogeneous medium with a position-dependent mass,”’ three crucial observations have gone unnoticed, thus restricting its conclusion on the legitimacy of the Langevin equation for a position-dependent mass, Eq. (46) of da Costa et al. [Phys. Rev. E 102, 062105 (2020)].

The “Brownian bees” model describes a system of $N$-independent branching Brownian particles. At each branching event the particle farthest from the origin is removed so that the number of particles remains constant at all times. Berestycki et al. [arXiv:2006.06486] proved that at $N\to \infty$ the coarse-grained spatial density of this particle system lives in a spherically symmetric domain and is described by the solution of a free boundary problem for a deterministic reaction-diffusion equation. Furthermore, they showed [arXiv:2005.09384] that, at long times, this solution approaches a unique spherically symmetric steady state with compact support: a sphere whose radius ${\ell }_0$ depends on the spatial dimension $d$. Here we study fluctuations in this system in the limit of large $N$ due to the stochastic character of the branching Brownian motion, and we focus on persistent fluctuations of the swarm size. We evaluate the probability density $\mathcal{P}(\ell ,N,T)$ that the maximum distance of a particle from the origin remains smaller than a specified value $\ell <{\ell }_0$ or larger than a specified value $\ell >{\ell }_0$ on a time interval $0<t<T$, where $T$ is very large. We argue that $\mathcal{P}(\ell ,N,T)$ exhibits the large-deviation form $-ln\mathcal{P}\simeq NT{R}_d\left(\ell \right)$. For all $d$'s we obtain asymptotics of the rate function $R_d\left(\ell \right)$ in the regimes $\ell \ll {\ell }_0,\ell \gg {\ell }_0$, and $|\ell -{\ell }_0|\ll {\ell }_0$. For $d=1$ the whole rate function can be calculated analytically. We obtain these results by determining the optimal (most probable) density profile of the swarm, conditioned on the specified $\ell$ and by arguing that this density profile is spherically symmetric with its center at the origin.

The mechanical behavior and cortical tension of single cells are analyzed using electrodeformation relaxation. Four types of cells, namely, MCF-10A, MCF-7, MDA-MB-231, and GBM, are studied, with pulse durations ranging from 0.01 to 10 s. Mechanical response in the long-pulse regime is characterized by a power-law behavior, consistent with soft glassy rheology resulting from unbinding events within the cortex network. In the subsecond short-pulse regime, a single timescale well describes the process and indicates the naive tensioned (prestressed) state of the cortex with minimal force-induced alteration. A mathematical model is employed and the simple ellipsoidal geometry allows for use of an analytical solution to extract the cortical tension. At the shortest pulse of 0.01 s, tensions for all four cell types are on the order of ${10}^{-2}$ N/m.

When a cylindrical rod is placed on a flat and hot surface with a constant temperature, it can reach a steady state after certain time. In the steady state, though the temperature field inside the rod is inhomogeneous, it does not change with time. The inhomogeneous temperature change in the rod may induce inhomogeneous thermal expansion in it. Recent experiments have determined that if the rod is slightly curved, the inhomogeneous thermal expansion in the rod can drive its continuous and self-sustained rolling on a hot surface. It has been further shown that if the rod is bent to a closed torus and placed on a hot surface, the torus everts or inverts continuously due to the cross-coupling between the thermal field and the cyclic rotation. Such cyclic eversion or inversion of a torus can be regarded as a zero-elastic-energy mode because both the elastic energy and the shape of the torus remain unchanged during the rotation. In this article, we develop a coupled mechanics theory to model the continuous self-sustained eversion or inversion of a viscoelastic torus on a hot surface. We hope our modeling will inspire more novel designs of elastic motors being capable of zero-energy mode motion and help to quantitatively predict their performance.

A numerical model for laser-matter interactions in the warm dense matter regime is presented with broad applications, e.g., ablation, thermionic emission, and radiation. A unique approach is adopted, in which a complete set of collisional and transport data is calculated using a quantum model and incorporated into the classical two-temperature model for the electron and lattice-ion temperatures. The data set was produced by the average atom model that combines speed, conceptual simplicity, and straightforward numerical development. Such data are suitable for use in the warm dense matter regime, where most of the laser-matter interactions at moderate intensities occur, thus eliminating deficiencies of previous models, e.g., interpolation between solid and ideal plasma regimes. In contrast to other works, we use a more rigorous definition of solid and plasma states of the metal, based on the physical condition of the lattice, crystalline (ordered) versus melted (disordered), rather than a definition based on electron temperature. The synergy between the two-temperature and average atom models has been demonstrated on a problem involving heating and melting of the interior of Al by a short-pulse laser with duration 0.1–1 ps and laser fluences $1\times {10}^3-3\times {10}^4\mathrm{J}/{\mathrm{m}}^2\left(0.1\text{–}3\mathrm{J}/\mathrm{c}{\mathrm{m}}^2\right)$. The melting line, which separates the solid and plasma regimes, has been tracked in time and space. The maximum melting depth has been determined as a function of laser fluence: $l_{\mathrm{melt}}\left(\mu \mathrm{m}\right)\cong 4\times {10}^{3}F\left(\frac{\mathrm{J}}{{\mathrm{m}}^2}\right)$.

We present a comprehensive numerical study on the kinetics of phase transition that is characterized by two nonconserved scalar order parameters coupled by a special linear-quadratic interaction. This particular Ginzburg-Landau theory has been proposed to describe the coupled charge and magnetic transition in nickelates and the collinear stripe phase in cuprates. The inhomogeneous state of such systems at low temperatures consists of magnetic domains separated by quasimetallic domain walls where the charge order is reduced. By performing large-scale cell dynamics simulations, we find a two-stage phase-ordering process in which a short period of independent evolution of the two order parameters is followed by a correlated coarsening process. The long-time growth and coarsening of magnetic domains is shown to follow the Allen-Cahn power law. We further show that the nucleation-and-growth dynamics during phase transformation to the ordered states is well described by the Kolmogorov-Johnson-Mehl-Avrami theory in two dimensions. On the other hand, the presence of quasimetallic magnetic domain walls in the ordered states gives rise to a very different kinetics for transformation to the high-temperature paramagnetic phase. In this scenario, the phase transformation is initiated by the decay of magnetic domain walls into two insulator-metal boundaries, which subsequently move away from each other. Implications of our findings to recent nano-imaging experiments on nickelates are also discussed.

We apply the derivative expansion of the effective action in the exact renormalization group equation up to fourth order to the $Z_2$ and $\text{O}\left(N\right)$ symmetric scalar models in $d=3$ Euclidean dimensions. We compute the critical exponents $\nu$, $\eta$, and $\omega$ using polynomial expansion in the field. We obtain our predictions for the exponents employing two regulators widely used in exact renormalization group computations. We apply Wynn's epsilon algorithm to improve the predictions for the critical exponents, extrapolating beyond the next-to-next-to-leading order prediction of the derivative expansion.