Planktonic communities are extremely diverse and include a vast number of rare species. The dynamics of these rare species is best described by individual-based models. However, individual-based approaches to planktonic diversity face substantial difficulties, due to the large number of individuals required to make realistic predictions. In this paper, we study the diversity of planktonic communities by means of a spatial coalescence model that incorporates transport by oceanic currents. As a main advantage, our approach requires simulating a number of individuals equal to the size of the sample one is interested in, rather than the size of the entire community. By theoretical analysis and simulations, we explore the conditions upon which our coalescence model is equivalent to individual-based dynamics. As an application, we use our model to predict the impact of chaotic advection by oceanic currents on biodiversity. We conclude that the coalescent approach permits one to simulate marine microbial communities much more efficiently than with individual-based models.

We use direct coupling analysis (DCA) to determine epistatic interactions between loci of variability of the SARS-CoV-2 virus, segmenting genomes by month of sampling. We use full-length, high-quality genomes from the GISAID repository up to October 2021 for a total of over 3 500 000 genomes. We find that DCA terms are more stable over time than correlations but nevertheless change over time as mutations disappear from the global population or reach fixation. Correlations are enriched for phylogenetic effects, and in particularly statistical dependencies at short genomic distances, while DCA brings out links at longer genomic distance. We discuss the validity of a DCA analysis under these conditions in terms of a transient auasilinkage equilibrium state. We identify putative epistatic interaction mutations involving loci in spike.

Stochastic thermodynamics has largely succeeded in characterizing both equilibrium and far-from-equilibrium phenomena. Yet many opportunities remain for application to mesoscopic complex systems—especially biological ones—whose effective dynamics often violate detailed balance and whose microscopic degrees of freedom are often unknown or intractable. After reviewing excess and housekeeping energetics—the adaptive and homeostatic components of a system's dissipation—we extend stochastic thermodynamics with a trajectory class fluctuation theorem for nonequilibrium steady-state, nondetailed-balanced complex systems. We then take up the neurobiological examples of voltage-gated sodium and potassium ion channels to apply and illustrate the theory, elucidating their nonequilibrium behavior under a biophysically plausible action potential drive. These results uncover challenges for future experiments and highlight the progress possible understanding the thermodynamics of complex systems—without exhaustive knowledge of every underlying degree of freedom.

The mobility of a colloidal particle in a slit pore is modified by the particle's hydrodynamic coupling to the bounding surfaces and therefore depends on the particle's position within the pore and its direction of motion. We report holographic particle tracking measurements of colloidal particles' diffusion and sedimentation between parallel horizontal walls that yield the mobility for motions perpendicular to the walls, including its dependence on height within the channel. These measurements complement previous studies that probed colloidal mobility parallel to confining surfaces. When interpreted with effective-medium theory, holographic characterization measurements yield estimates for the sedimenting spheres' densities that can be compared with kinematic values to draw insights into the spheres' compositions. This comparison suggests, for example, that the silica spheres used in this study are slightly porous, but that their pores are too small for water to penetrate.

We describe investigations on the influence of the flexible spacer parity and length of the guest photoactive liquid-crystalline dimers in guest-host mixtures exhibiting photoinduced transitions involving isotropic ($I$), cholesteric ($N^{*}$), and twist grain boundary smectic-$C^{*}$ (TGB$C^{*}$) phases. Despite a small concentration (3 wt. %) of the guest molecules, the transition temperatures and their photodriven shift ($\delta T$) show a strong odd-even parity (of the dimer) dependent effect, with the even-parity systems having a larger value than their odd-parity counterparts; $\delta T$ is larger for the $N^{*}\text{−}\mathrm{TGB}{C}^{*}$ transition than for the $I\text{−}{N}^{*}$ one. The photocalorimetric measurements corroborate these features in addition to showing that, in comparison with the absence-of-ultraviolet (UV) case, the transition enthalpy ($\mathrm{\Delta }H$) of the $I\text{−}{N}^{*}$ transition in the UV-on case is diminished by 33 and 12% for the mixtures with even- and odd-parity dimers, respectively. The duration for relaxation from the isothermal photodriven transition also exhibits general features of an odd-even influence. Molecular dynamics simulations demonstrate the presence of significant conformational heterogeneity and associated shift in the conformational space on photostimulation of the guest molecules. The change in the effective shape and nematic order parameter is more pronounced in the even-parity system.

Chromonic liquid crystals constitute a novel lyotropic phase, whose elastic properties have so far been modeled within the classical Oseen-Frank theory, provided that the twist constant is assumed to be considerably smaller than the saddle-splay constant, in violation of one Ericksen inequality. This paper shows that paradoxical consequences follow from such a violation for droplets of these materials surrounded by an isotropic fluid. For example, tactoids with a degenerate planar anchoring simply disintegrate indefinitely in myriads of smaller ones.

The validity of one-dimensional (1D) models for liquid columns (capillary jets, liquid bridges, and other similar systems) for predicting the dynamics of their breakup into drops is studied when viscosity is not relevant. These models assume a simplified radial dependence, which in turn is supported by the premise that the system is slender enough. However, even though the latter hypothesis does not seem to be fulfilled when the system gets close to breakup, 1D models continue to describe its evolution surprisingly well. Our numerical simulations of a liquid jet confirm this good behavior, even when the liquid jet becomes a sequence of incipient drops joined by filaments. A dynamic definition of the slenderness allows computing the stage until which the liquid jet can be considered slender from the standpoint of 1D models. Beyond that point, a detailed numerical study of mass and energy reveals that the action that each incipient main drop suffers from the two adjacent filaments becomes barely significant. Thus, the drop can be considered to oscillate almost freely, while the filaments remain nearly static. To explain how the 1D models can predict the evolution of a so scarcely slender system as a droplet, we compare the linear modal analysis of the Lee, Cosserat and parabolic 1D models for an inviscid free drop with the 3D analysis in cylindrical coordinates. The frequencies of the oscillation modes with lowest index, the most relevant ones arising from the breakup, are in general well predicted. This happens when the radial dependence of both pressure and axial velocity assumed in 1D models reasonably fit the corresponding 3D exact results. The Cosserat model (and even more the parabolic one) performs better than the Lee model.

An ensemble model of turbulence is proposed. The ensemble consists of flow fields in which the flux of an inviscid conserved quantity, such as energy (or enstrophy in two-dimensional flow fields), across the wave number $k$ is a constant independent of $k$ in an appropriate range. Two-dimensional flow fields of constant enstrophy flux are sampled randomly by a Monte Carlo method. The energy spectra $E_k$ of the flow fields are consistent with the scaling $E_k\propto k^{-3}{[ln(k/k_{\mathrm{b}})]}^{-1/3}$ where $k_{\mathrm{b}}$ is the bottom wave number of the constant-flux range.

The multiphase lattice Boltzmann flux solver (MLBFS) has been proposed to tackle complex geometries with nonuniform meshes. It also has been proven to have good numerical stability for multiphase flows with large density ratios. However, the reason for the good numerical stability of MLBFS at large density ratios has not been well established. The present paper reveals the relation between MLBFS and the macroscopic weakly compressible multiphase model by recovering the macroscopic equations of MLBFS (MEs-MLBFS) with actual numerical dissipation terms. By directly solving MEs-MLBFS, the reconstructed MLBFS (RMLBFS) that involves only macroscopic variables in the computational processes is proposed. The analysis of RMLBFS indicates that by combining the predictor step, the corrector step of MLBFS introduces some numerical dissipation terms which contribute to the good numerical stability of MLBFS. By retaining these numerical dissipation terms, RMLBFS can maintain the numerical stability of MLBFS even at large density ratios.

In this study, a layer of cellophane, subjected to an air-pressure difference, was ruptured using a piercing needle. Accordingly, petal-like fragmentation was observed in the layer via high-speed imaging. Two types of crack-propagation regimes were subsequently observed experimentally. If a tensile stress lower than 20.6 MPa acted on the cellophane diaphragm, a single crack was generated, whose propagation speed was lower than that under higher-stress conditions. For tensile stresses greater than 23.7 MPa, the crack-propagation speed remained constant at approximately 0.86 km/s, even after altering the device size, pressure, and humidity on the low-pressure side. The number of cracks equidistant from the piercing point was expressed as a linear function of the tensile stress acting on the diaphragm.

We introduce an integrable spin ladder model and study its exact solution, correlation functions, and entanglement properties. The model supports two particle types (corresponding to the even and odd sublattices), such that the scattering phases are constants: Particles of the same type scatter as free fermions, whereas the interparticle phase shift is a constant tuned by an interaction parameter. Therefore, the spin ladder bears similarities with anyonic models. We present exact results for the spectrum and correlation functions, and we study the sublattice entanglement by numerical means.

An encounter-based approach consists in using the boundary local time as a proxy for the number of encounters between a diffusing particle and a target to implement various surface reaction mechanisms on that target. In this paper, we investigate the effects of stochastic resetting onto diffusion-controlled reactions in bounded confining domains. We first discuss the effect of position resetting onto the propagator and related quantities; in this way, we retrieve a number of earlier results but also provide complementary insights into them. Second, we introduce boundary local time resetting and investigate its impact. Curiously, we find that this type of resetting does not alter the conventional propagator governing the diffusive dynamics in the presence of a partially reactive target with a constant reactivity. In turn, the generalized propagator for other surface reaction mechanisms can be significantly affected. Our general results are illustrated for diffusion on an interval with reactive end points. Further perspectives and some open problems are discussed.

The determination of the pair potential $v\left(\mathbf{r}\right)$ that accurately yields an equilibrium state at positive temperature $T$ with a prescribed pair correlation function $g_2\left(\mathbf{r}\right)$ or corresponding structure factor $S\left(\mathbf{k}\right)$ in $d$-dimensional Euclidean space ${\mathbb{R}}^d$ is an outstanding inverse statistical mechanics problem with far-reaching implications. Recently, Zhang and Torquato [Phys. Rev. E 101, 032124 (2020)] conjectured that any realizable $g_2\left(\mathbf{r}\right)$ or $S\left(\mathbf{k}\right)$ corresponding to a translationally invariant nonequilibrium system can be attained by a classical equilibrium ensemble involving only (up to) effective pair interactions. Testing this conjecture for nonequilibrium systems as well as for nontrivial equilibrium states requires improved inverse methodologies. We have devised an optimization algorithm to precisely determine effective pair potentials that correspond to pair statistics of general translationally invariant disordered many-body equilibrium or nonequilibrium systems at positive temperatures. This methodology utilizes a parameterized family of pointwise basis functions for the potential function whose initial form is informed by small-, intermediate- and large-distance behaviors dictated by statistical-mechanical theory. Subsequently, a nonlinear optimization technique is utilized to minimize an objective function that incorporates both the target pair correlation function $g_2\left(\mathbf{r}\right)$ and structure factor $S\left(\mathbf{k}\right)$ so that the small intermediate- and large-distance correlations are very accurately captured. To illustrate the versatility and power of our methodology, we accurately determine the effective pair interactions of the following four diverse target systems: (1) Lennard-Jones system in the vicinity of its critical point, (2) liquid under the Dzugutov potential, (3) nonequilibrium random sequential addition packing, and (4) a nonequilibrium hyperuniform “cloaked” uniformly randomized lattice. We found that the optimized pair potentials generate corresponding pair statistics that accurately match their corresponding targets with total $L_2$-norm errors that are an order of magnitude smaller than that of previous methods. The results of our investigation lend further support to the Zhang-Torquato conjecture. Furthermore, our algorithm will enable one to probe systems with identical pair statistics but different higher-body statistics, which will shed light on the well-known degeneracy problem of statistical mechanics.

We relate the combinatorics of periodic generalized Dyck and Motzkin paths to the cluster coefficients of particles obeying generalized exclusion statistics, and obtain explicit expressions for the counting of paths with a fixed number of steps of each kind at each vertical coordinate. A class of generalized compositions of the integer path length emerges in the analysis.

The glass transition is described as a phase transition in the system of topologically protected excitations in matter structure. The critical behavior of the system is considered in both static and dynamic cases. It is shown that the proposed model reproduces most of the characteristic thermodynamic and kinetic properties of glass transition: the Vogel-Fulcher-Tammann law, the behavior of susceptibility and nonlinear susceptibilities, and heat capacity behavior as well as the appearance of a boson peak in the frequency dependence of the dynamic structure factor near the glass transition temperature.

We study how walls confining active fluids interact with asymmetric passive objects placed in their bulk. We show that the objects experience nonconservative long-ranged forces mediated by the active bath. To leading order, these forces can be computed using a generalized image theorem. The walls repel asymmetric objects, irrespective of their microscopic properties or their orientations. For circular cavities, we demonstrate how this may lead to the localization of asymmetric objects in the center of the cavity, something impossible for symmetric ones.

The biaxial phase in nematic liquid crystals has been elusive for several decades after its prediction in the 1970s. A recent experimental breakthrough was achieved by Liu et al. [Proc. Natl. Acad. Sci. USA 113, 10479 (2016)] in a liquid-crystalline medium with magnetic nanoparticles. They exploited the different length scales of dipolar and magnetonematic interactions to obtain an equilibrium state where the magnetic moments are at an angle to the nematic director. This tilt introduces a second distinguished direction for orientational ordering or biaxiality in the two-component system. Using coarse-grained Ginzburg-Landau free-energy models for the nematic and magnetic fields, we provide a theoretical framework which allows for the manipulation of morphologies and quantitative estimates of biaxial order.

The two-dimensional $XY$ model with Dzyaloshinskii-Moriya interaction has been studied through extensive Monte Carlo simulations. A hybrid algorithm consisting of single-spin Metropolis and Swendsen-Wang cluster-spin updates has been employed. Single histogram techniques have been used to obtain the thermodynamic variables of interest and finite-size-scaling analysis has led to the phase transition behavior in the thermodynamic limit. Fluctuating boundary conditions have been utilized in order to match the incommensurability between the spin structures and the finite lattice sizes due to the Dzyaloshinskii-Moriya interaction. The effects of the fluctuating boundary conditions have been analyzed in detail in both commensurate and incommensurate cases. The Berezinskii-Kosterlitz-Thouless transition temperature has been obtained as a function of the Dzyaloshinskii-Moriya interaction and the results are in excellent agreement with the exact equation for the transition line. The spin-spin correlation function critical exponent has been computed as a function of the Dzyaloshinskii-Moriya interaction and temperature. In the incommensurate cases, optimal sizes for the finite lattices and the distribution of the boundary shift angle have been extracted. Analysis of the low temperature configurations and the corresponding vortex-antivortex pairs have also been addressed in some regions of the phase diagram.

When the unconditioned process is a diffusion living on the half-line $x\in ]-\infty ,a[$ in the presence of an absorbing boundary condition at position $x=a$, we construct various conditioned processes corresponding to finite or infinite horizon. When the time horizon is finite $T<+\infty$, the conditioning consists in imposing the probability distribution $P^{*}(y,T)$ to be surviving at time $T$ at the position $y\in ]-\infty ,a[$, as well as the probability distribution ${\gamma }^{*}\left(T_a\right)$ of the absorption time $T_a\in [0,T]$. When the time horizon is infinite $T=+\infty$, the conditioning consists in imposing the probability distribution ${\gamma }^{*}\left(T_a\right)$ of the absorption time $T_a\in [0,+\infty [$, whose normalization $[1-S^{*}\left(\infty \right)]$ determines the conditioned probability $S^{*}\left(\infty \right)\in [0,1]$ of forever-survival. This case of infinite horizon $T=+\infty$ can be thus reformulated as the conditioning of diffusion processes with respect to their first-passage-time properties at position $a$. This general framework is applied to the explicit case where the unconditioned process is the Brownian motion with uniform drift $\mu$ to generate stochastic trajectories satisfying various types of conditioning constraints. Finally, we describe the links with the dynamical large deviations at Level 2.5 and the stochastic control theory.

We investigate the long-term relaxation of one-dimensional (1D) self-gravitating systems, using both kinetic theory and $N$-body simulations. We consider thermal and Plummer equilibria, with and without collective effects. All combinations are found to be in clear agreement with respect to the Balescu–Lenard and Landau predictions for the diffusion coefficients. Interestingly, collective effects reduce the diffusion by a factor $\sim 10$. The predicted flux for Plummer equilibrium matches the measured one, which is a remarkable validation of kinetic theory. We also report on a situation of quasikinetic blocking for the same equilibrium.