Large deformations are prone to cause irreversible changes in materials structure, generally leading to either material hardening or softening. Aqueous foam is a metastable disordered structure of densely packed gas bubbles. We report on the mechanical response of a foam layer subjected to quasistatic periodic shear at large amplitude. We observe that, upon increasing shear, the shear stress follows a universal curve that is nearly exponential and tends to an asymptotic stress value interpreted as the critical yield stress at which the foam structure is completely remodeled. Relevant trends of the foam mechanical response to cycling are mathematically reproduced through a simple law accounting for the amount of plastic deformation upon increasing stress. This view provides a natural interpretation to stress hardening in foams, demonstrating that plastic effects are present in this material even for minute deformation.

We introduce six families of three-dimensional space-periodic steady solenoidal flows, whose kinetic helicity density is zero at any point. Four families are analytically defined. Flows in four families have zero helicity spectrum. Sample flows from five families are used to demonstrate numerically that neither zero kinetic helicity density nor zero helicity spectrum prohibit generation of large-scale magnetic field by the two most prominent dynamo mechanisms: the magnetic $\alpha$-effect and negative eddy diffusivity. Our computations also attest that such flows often generate small-scale field for sufficiently small magnetic molecular diffusivity. These findings indicate that kinetic helicity and helicity spectrum are not the quantities controlling the dynamo properties of a flow regardless of whether scale separation is present or not.

While the three-dimensional Ising model has defied analytic solution, various numerical methods like Monte Carlo, Monte Carlo renormalization group, and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising Model, with lattice sizes ranging from ${16}^3$ to ${1024}^3$. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, e.g., logarithmic derivatives of magnetization and derivatives of magnetization cumulants, we have obtained the critical inverse temperature $K_c=0.221654626\left(5\right)$ and the critical exponent of the correlation length $\nu =0.629912\left(86\right)$ with precision that exceeds all previous Monte Carlo estimates.

Intracellular components explore the cytoplasm via active motor-driven transport in conjunction with passive diffusion. We model the motion of organelles in narrow tubular cells using analytical techniques and numerical simulations to study the efficiency of different transport modes in achieving various cellular objectives. Our model describes length and time scales over which each transport mode dominates organelle motion, along with various metrics to quantify exploration of intracellular space. For organelles that search for a specific target, we obtain the average capture time for given transport parameters and show that diffusion and active motion contribute to target capture in the biologically relevant regime. Because many organelles have been found to tether to microtubules when not engaged in active motion, we study the interplay between immobilization due to tethering and increased probability of active transport. We derive parameter-dependent conditions under which tethering enhances long-range transport and improves the target capture time. These results shed light on the optimization of intracellular transport machinery and provide experimentally testable predictions for the effects of transport regulation mechanisms such as tethering.

Microorganisms and plants very commonly release toxic secondary chemical compounds (allelochemicals) that inhibit or kill sensitive strains or individuals from their own or other species. In this work we study a model that describes two species interacting through allelopathic suppression and competing for resources. Employing linear stability analysis, the conditions for coexistence or extinction of species in spatially homogeneous systems were determined. We found that the borders between the regimes of bistability, coexistence, and the extinction of the weaker by the stronger competitor, are altered by allelopathic interactions. In addition, traveling wave solutions for one species invasion were obtained considering the spatially explicit nature of the model. Our findings indicate that the minimum speed of the invasion wavefronts depends primarily on the competition coefficients and the parameters characterizing the species' functional responses to their allelochemicals. As a general rule, the species provided with the most effective chemical weapons dominates the population dynamics. Finally, we found a tristability at the coexistence region due to the combination of allelopathy and patchy population distributions in space. So, our model provides a distinct mechanism, independent of social behaviors, that produces such unexpected tristability impossible in classical competition models involving one-to-one individual interactions.

We report on the generation of an intermittent wave field driven by a horizontally moving wave maker interacting with Faraday waves. The spectrum of the local gravitocapillary surface wave fluctuations displays a power law in frequency for a wide range of forcing parameters. We compute the probability density function of the local surface height increments, which show that they change strongly across time scales. The structure functions of these increments are shown to display power laws as a function of the time lag, with exponents that are nonlinear functions of the order of the structure function. We argue that the origin of this scale-invariant intermittent spectrum is the Faraday wave pattern breakup due to its advection by the propagating gravity waves. Finally, some interpretations are proposed to explain the appearance of this intermittent spectrum.

The inertial locomotion of an elongated model swimmer in a Newtonian fluid is quantified, wherein self-propulsion is achieved via steady tangential surface treadmilling. The swimmer has a length $2l$ and a circular cross section of longitudinal profile $aR\left(z\right)$, where $a$ is the characteristic width of the cross section, $R\left(z\right)$ is a dimensionless shape function, and $z$ is a dimensionless coordinate, normalized by $l$, along the centerline of the body. It is assumed that the swimmer is slender, $\epsilon =a/l\ll 1$. Hence, we utilize slender-body theory to analyze the Navier-Stokes equations that describe the flow around the swimmer. Therefrom, we compute an asymptotic approximation to the swimming speed, $U$, as $U/u_s=1-\beta [V\left(\mathrm{Re}\right)-\frac{1}{2}{\int }_{-1}^{1}zlnR\left(z\right)dz]/ln(1/\epsilon )+O[1/{ln}^2(1/\epsilon )]$, where $u_s$ is the characteristic speed of the surface treadmilling, $\mathrm{Re}$ is the Reynolds number based on the body length, and $\beta$ is a dimensionless parameter that differentiates between “pusher” (propelled from the rear, $\beta <0$) and “puller” (propelled from the front, $\beta >0$) -type swimmers. The function $V\left(\mathrm{Re}\right)$ increases monotonically with increasing $\mathrm{Re}$; hence, fluid inertia causes an increase (decrease) in the swimming speed of a pusher (puller). Next, we demonstrate that the power expenditure of the swimmer increases monotonically with increasing $\mathrm{Re}$. Further, the power expenditures of a puller and pusher with the same value of $\left|\beta \right|$ are equal. Therefore, pushers are superior in inertial locomotion as compared to pullers, in that they achieve a faster swimming speed for the same power expended. Finally, it is demonstrated that the flow structure predicted from our reduced-order model is consistent with that from direct numerical simulation of swimmers at intermediate $\mathrm{Re}$.

A fluctuation relation for the heat exchange of an open quantum system under a thermalizing Markovian dynamics is derived. We show that the probability that the system absorbs an amount of heat from its bath, at a given time interval, divided by the probability of the reverse process (releasing the same amount of heat to the bath) is given by an exponential factor which depends on the amount of heat and the difference between the temperatures of the system and the bath. Interestingly, this relation is akin to the standard form of the fluctuation relation (for forward-backward dynamics). We also argue that the probability of the violation of the second law of thermodynamics in the form of the Clausius statement (i.e., net heat transfer from a cold system to its hot bath) drops exponentially with both the amount of heat and the temperature differences of the baths.

We provide a general theory for the structure of the quantum flow near three-dimensional (3D) nodal lines, i.e., one-dimensional loci where the 3D wave function becomes equal to zero. In suitably defined coordinates (comoving with the nodal line) the generic structure of the flow implies the formation of 3D quantum vortices. We show that such vortices are accompanied by nearby invariant lines of the comoving quantum flow, called $X$ lines, which are normally hyperbolic. Furthermore, the stable and unstable manifolds of the $X$ lines produce chaotic scatterings of nearby quantum (Bohmian) trajectories, thus inducing an intricate form of the quantum current in the neighborhood of each 3D quantum vortex. Generic formulas describing the structure around 3D quantum vortices are provided, applicable to an arbitrary choice of 3D wave function. We also give specific numerical examples as well as a discussion of the physical consequences of chaos near 3D quantum vortices.

To study the significance of advection in the transport of solutes, or particles, within thin biological gaps (channels), we examine theoretically the process driven by stochastic fluid flow caused by random thermal structural motion, and we compare it with transport via diffusion. The model geometry chosen resembles the synaptic cleft; this choice is motivated by the cleft's readily modeled structure, which allows for well-defined mechanical and physical features that control the advection process. Our analysis defines a Péclet-like number, ${\mathcal{A}}^D$, that quantifies the ratio of time scales of advection versus diffusion. Another parameter, ${\mathcal{A}}^M$, is also defined by the analysis that quantifies the full potential extent of advection in the absence of diffusion. These parameters provide a clear and compact description of the interplay among the well-defined structural, geometric, and physical properties vis-$\grave{a}$-vis the advection versus diffusion process. For example, it is found that ${\mathcal{A}}^D\sim 1/R^2$, where $R$ is the cleft diameter and hence diffusion distance. This curious, and perhaps unexpected, result follows from the dependence of structural motion that drives fluid flow on $R$. ${\mathcal{A}}^M$, on the other hand, is directly related (essentially proportional to) the energetic input into structural motion, and thereby to fluid flow, as well as to the mechanical stiffness of the cleftlike structure. Our model analysis thus provides unambiguous insight into the prospect of competition of advection versus diffusion within biological gaplike structures. The importance of the random, versus a regular, nature of structural motion and of the resulting transient nature of advection under random motion is made clear in our analysis. Further, by quantifying the effects of geometric and physical properties on the competition between advection and diffusion, our results clearly demonstrate the important role that metabolic energy (ATP) plays in this competitive process.

A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore networks to general geometric domains can be considered and that the (free random walk) central limit theorem can be generalized to cover also the nonfree case. The latter gives rise to a continuum-limit description of the diffusive motion where the effect of partially absorbing barriers is accounted for in a natural and non-Markovian way that, in contrast to the traditional approach, quantifies the absorptivity of a barrier in terms of a dimensionless parameter in the range 0 to 1. The generalized theorem gives two general analytic expressions for the continuum-limit propagator: an infinite sum of Gaussians and an infinite sum of plane waves. These expressions entail the known method-of-images and Laplace eigenfunction expansions as special cases and show how the presence of partially absorbing barriers can lead to phenomena such as line splitting and band gap formation in the plane wave wave-number spectrum.

It has been recently shown [E. Lerner, G. Düring, and E. Bouchbinder, Phys. Rev. Lett. 117, 035501 (2016)] that the nonphononic vibrational modes of structural glasses at low frequencies $\omega$ are quasilocalized and follow a universal density of states $D\left(\omega \right)\sim {\omega }^4$. Here we show that the gapless nature of the observed density of states depends on the existence of internal stresses that generically emerge in glasses due to frustration, thus elucidating a basic element underlying this universal behavior. Similarly to jammed particulate packings, low-frequency modes in structural glasses emerge from a balance between a local elasticity term and an internal stress term in the dynamical matrix, where the difference between them is orders of magnitude smaller than their typical magnitude. By artificially reducing the magnitude of internal stresses in a computer glass former in three dimensions, we show that a gap is formed in the density of states below which no vibrational modes exist, thus demonstrating the crucial importance of internal stresses. Finally, we show that while better annealing the glass upon cooling from the liquid state significantly reduces its internal stresses, the self-organizational processes during cooling render the gapless $D\left(\omega \right)\sim {\omega }^4$ density of state unaffected.

The emergence of directed motion is investigated in a system consisting of a sphere immersed in a viscous fluid and subjected to time-periodic forces of zero average. The directed motion arises from the combined action of a nonlinear drag force and the applied driving forces, in the absence of any periodic substrate potential. Necessary conditions for the existence of such directed motion are obtained and an analytical expression for the average terminal velocity is derived within the adiabatic approximation. Special attention is paid to the case of two mutually perpendicular forces with sinusoidal time dependence, one with twice the period of the other. It is shown that, although neither of these two forces induces directed motion when acting separately, when added together, the resultant force generates directed motion along the direction of the force with the shortest period. The dependence of the average terminal velocity on the system parameters is analyzed numerically and compared with that obtained using the adiabatic approximation. Among other results, it is found that, for appropriate parameter values, the direction of the average terminal velocity can be reversed by varying the forcing strength. Furthermore, certain aspects of the observed phenomenology are explained by means of symmetry arguments.

We propose a unified framework to evaluate and quantify the search time of multiple random searchers traversing independently and concurrently on complex networks. We find that the intriguing behaviors of multiple random searchers are governed by two basic principles—the logarithmic growth pattern and the harmonic law. Specifically, the logarithmic growth pattern characterizes how the search time increases with the number of targets, while the harmonic law explores how the search time of multiple random searchers varies relative to that needed by individual searchers. Numerical and theoretical results demonstrate these two universal principles established across a broad range of random search processes, including generic random walks, maximal entropy random walks, intermittent strategies, and persistent random walks. Our results reveal two fundamental principles governing the search time of multiple random searchers, which are expected to facilitate investigation of diverse dynamical processes like synchronization and spreading.

In the current paper, phospholipid bilayers are modeled using coarse-grained molecular dynamics simulations with the MARTINI force field. The extracted molecular trajectories are analyzed using Fourier analysis of the undulations and orientation vectors to establish the differences between the two approaches for evaluating the bending modulus. The current work evaluates and extends the implementation of the Fourier analysis for molecular trajectories using a weighted horizon-based averaging approach. The effect of numerical parameters in the analysis of these trajectories is explored by conducting parametric studies. Computational modeling results are validated against experimentally characterized bending modulus of lipid membranes using a shape fluctuation analysis. The computational framework is then used to estimate the bending moduli for different types of lipids (phosphocholine, phosphoethanolamine, and phosphoglycerol). This work provides greater insight into the numerical aspects of evaluating the bilayer bending modulus, provides validation for the orientation analysis technique, and explores differences in bending moduli based on differences in the lipid nanostructures.

Chromatin remodelers are molecular motors that play essential roles in the regulation of nucleosome positioning and chromatin accessibility. These machines couple the energy obtained from the binding and hydrolysis of ATP to the mechanical work of manipulating chromatin structure through processes that are not completely understood. Here we present a quantitative analysis of nucleosome repositioning by the imitation switch (ISWI) chromatin remodeler and demonstrate that nucleosome stability significantly impacts the observed activity. We show how DNA damage induced changes in the affinity of DNA wrapping within the nucleosome can affect ISWI repositioning activity and demonstrate how assay-dependent limitations can bias studies of nucleosome repositioning. Together, these results also suggest that some of the diversity seen in chromatin remodeler activity can be attributed to the variations in the thermodynamics of interactions between the remodeler, the histones, and the DNA, rather than reflect inherent properties of the remodeler itself.

While magnetic nanoparticles suspended in Newtonian solvents (ferrofluids) have been intensively studied in recent years, the effects of viscoelasticity of the surrounding medium on the nanoparticle dynamics are much less understood. Here we investigate a mesoscopic model for the orientational dynamics of isolated magnetic nanoparticles subject to external fields, viscous and viscoelastic friction, as well as the corresponding random torques. We solve the model analytically in the overdamped limit for weak viscoelasticity. By comparison to Brownian dynamics simulations we establish the limits of validity of the analytical solution. We find that viscoelasticity not only slows down the magnetization relaxation, shifts the peak of the imaginary magnetic susceptibility ${\chi }^{″}$ to lower frequencies, and increases the magnetoviscosity but also leads to nonexponential relaxation and a broadening of ${\chi }^{″}$. The model we study also allows us to test a recent proposal for using magnetic susceptibility measurements as a nanorheological tool using a variant of the Germant-DiMarzio-Bishop relation. We find for the present model and certain parameter ranges that the relation of the magnetic susceptibility to the shear modulus is satisfied to a good approximation.

The collective dynamics of externally driven $N_{\mathrm{p}}$-colloidal systems ($1\le N_{\mathrm{p}}\le 4$) in a confined viscous fluid have been investigated using three-dimensional direct numerical simulations with fully resolved hydrodynamics. The dynamical modes of collective particle motion are studied by changing the particle Reynolds number as determined by the strength of the external driving force and the confining wall distance. For a system with $N_{\mathrm{p}}=3$, we found that at a critical Reynolds number a dynamical mode transition occurs from the doublet-singlet mode to the triplet mode, which has not been reported experimentally. The dynamical mode transition was analyzed in detail from the following two viewpoints: (1) spectrum analysis of the time evolution of a tagged particle velocity and (2) the relative acceleration of the doublet cluster with respect to the singlet particle. For a system with $N_{\mathrm{p}}=4$, we found similar dynamical mode transitions from the doublet-singlet-singlet mode to the triplet-singlet mode and further to the quartet mode.

In thermotropic chiral $\mathrm{Sm}\text{−}{A}^{*}$ phases, an electric field along the smectic layers breaks the $D_{\infty }$ symmetry of the $\mathrm{Sm}\text{−}{A}^{*}$ phase and induces a tilt of the liquid crystal director. This so-called electroclinic effect (ECE) was first reported by Garoff and Meyer in 1977 and attracted substantial scientific and technological interest due to its linear and submicrosecond electro-optic response [S. Garoff and R. B. Meyer, Phys. Rev. A 19, 338 (1979)]. We now report the observation of an ECE in the pretransitional regime from a lyotropic chiral lamellar $L_{\alpha }^{*}$ phase into a lyo-$\mathrm{Sm}\text{−}{C}^{*}$ phase, the lyotropic analog to the thermotropic $\mathrm{Sm}\text{−}{C}^{*}$ phase which was recently discovered by Bruckner et al. [Angew. Chem. Int. Ed. 52, 8934 (2013)]. We further show that the observed ECE has all signatures of its thermotropic counterpart, namely (i) the effect is chiral in nature and vanishes in the racemic $L_{\alpha }$ phase, (ii) the effect is essentially linear in the sign and magnitude of the electric field, and (iii) the magnitude of the effect diverges hyperbolically as the temperature approaches the critical temperature of the second order tilting transition. Specific deviations between the ECEs in chiral lamellar and chiral smectic phases are related to the internal field screening effect of electric double layers formed by inevitable ionic impurities in lyotropic phases.

The coalescence, and subsequent satellite formation, of two inviscid droplets is studied numerically. The initial drops are taken to be of equal and different sizes, and simulations have been carried out with and without the presence of an electrical field. The main computational challenge is the tracking of a free surface that changes topology. Coupling level set and boundary integral methods with an embedded potential flow model, we seamlessly compute through these singular events. As a consequence, the various coalescence modes that appear depending upon the relative ratio of the parent droplets can be studied. Computations of first stage pinch-off, second stage pinch-off, and complete engulfment are analyzed and compared to recent numerical studies and laboratory experiments. Specifically, we study the evolution of bridge radii and the related scaling laws, the minimum drop radii evolution from coalescence to satellite pinch-off, satellite sizes, and the upward stretching of the near cylindrical protrusion at the droplet top. Clear evidence of partial coalescence self-similarity is presented for parent droplet ratios between 1.66 and 4. This has been possible due to the fact that computational initial conditions only depend upon the mother droplet size, in contrast with laboratory experiments where the difficulty in establishing the same initial physical configuration is well known. The presence of electric forces changes the coalescence patterns, and it is possible to control the satellite droplet size by tuning the electrical field intensity. All of the numerical results are in very good agreement with recent laboratory experiments for water droplet coalescence.