There have been increasing reports that the diffusion coefficient of macromolecules depends on time and fluctuates randomly. Here a method is developed to elucidate this fluctuating diffusivity from trajectory data. Time-averaged mean-square displacement (MSD), a common tool in single-particle-tracking (SPT) experiments, is generalized to a second-order tensor with which both magnitude and orientation fluctuations of the diffusivity can be clearly detected. This method is used to analyze the center-of-mass motion of four fundamental polymer models: the Rouse model, the Zimm model, a reptation model, and a rigid rodlike polymer. It is found that these models exhibit distinctly different types of magnitude and orientation fluctuations of diffusivity. This is an advantage of the present method over previous ones, such as the ergodicity-breaking parameter and a non-Gaussian parameter, because with either of these parameters it is difficult to distinguish the dynamics of the four polymer models. Also, the present method of a time-averaged MSD tensor could be used to analyze trajectory data obtained in SPT experiments.

The force fluctuations experienced by a boundary wall subjected to a lid-driven cavity flow are investigated by means of numerical simulations based on the discrete-element method. The time-averaged dynamics inside the cavity volume and the resulting steady force on the wall are governed by the boundary macroscopic inertial number, the latter being derived from the shearing velocity and the confinement pressure imposed at the top. The force fluctuations are quantified through measuring both the autocorrelation of force time series and the distributions of grain-wall forces, at distinct spatial scales from particle scale to wall scale. A key result is that the grain-wall force distributions are entirely driven by the boundary macroscopic inertial number, whatever the spatial scale considered. In particular, when the wall scale is considered, the distributions are found to evolve from nearly exponential to nearly Gaussian distributions by decreasing the macroscopic inertial number. The transition from quasistatic to dense inertial flow is well identified through remarkable changes in the shapes of the distributions of grain-wall forces, accompanied by a loss of system memory in terms of the mesoscale force transmitted toward the wall.

The interaction of dense plasmas with an intense laser under a strong external magnetic field has been investigated. When the cyclotron frequency for the ambient magnetic field is higher than the laser frequency, the laser's electromagnetic field is converted to the whistler mode that propagates along the field line. Because of the nature of the whistler wave, the laser light penetrates into dense plasmas with no cutoff density, and produces superthermal electrons through cyclotron resonance. It is found that the cyclotron resonance absorption occurs effectively under the broadened conditions, or a wider range of the external field, which is caused by the presence of relativistic electrons accelerated by the laser field. The upper limit of the ambient field for the resonance increases in proportion to the square root of the relativistic laser intensity. The propagation of a large-amplitude whistler wave could raise the possibility for plasma heating and particle acceleration deep inside dense plasmas.

Models of bacterial growth tend to be “irreversible,” allowing for the number of bacteria in a colony to increase but not to decrease. By contrast, models of molecular self-assembly are usually “reversible,” allowing for the addition and removal of particles to a structure. Such processes differ in a fundamental way because only reversible processes possess an equilibrium. Here we show at the mean-field level that dynamic trajectories of reversible and irreversible growth processes are similar in that both feel the influence of attractors, at which growth proceeds without limit but the intensive properties of the system are invariant. Attractors of both processes undergo nonequilibrium phase transitions as model parameters are varied, suggesting a unified way of describing typical properties of reversible and irreversible growth. We also establish a connection at the mean-field level between an irreversible model of growth (the magnetic Eden model) and the equilibrium Ising model, supporting the findings made by other authors using numerical simulations.

Self-organizing behavior has been widely reported in both natural and artificial systems, typically distinguishing between temporal organization (synchronization) and spatial organization (swarming). Swarming has been experimentally observed in systems of magnetotactic bacteria under the action of external magnetic fields. Here we present a model of ensembles of magnetotactic bacteria in which hydrodynamic interactions lead to temporal synchronization in addition to the swarming. After a period of stabilization during which the bacteria form a quasiregular hexagonal lattice structure, the entire swarm begins to rotate in a direction opposite to the direction of the rotation of the magnetic field. We thus illustrate an emergent mechanism of macroscopic motion arising from the synchronized microscopic rotations of hydrodynamically interacting bacteria, reminiscent of the recently proposed concept of swarmalators.

Is an active glass different from a conventional passive glass? To address this, we study the dynamics of a dense binary mixture of soft dumbbells, each subject to an active propulsion force and thermal fluctuations. This dense assembly shows dynamical arrest, first to a translational and then to a rotational glass, as one reduces temperature $T$ or the self-propulsion force $f$. We monitor the dynamics along an iso-relaxation-time contour in the $(T-f)$ plane. We find dramatic differences both in the fragility and in the nature of dynamical heterogeneity, which characterize the onset of glass formation—the activity-induced glass exhibits large swirls or vortices, whose scale is set by activity, and it appears to diverge as one approaches the glass transition. This large collective swirling movement should have implications for collective cell migration in epithelial layers. We construct continuum hydrodynamic equations for the simulated system, and we show that the observed behavior of this growing dynamic length scale can be understood from these equations.

We summarize and numerically compare two approaches for modeling and simulating the dynamics of dry granular matter. The first one, the discrete-element method via penalty (DEM-P), is commonly used in the soft matter physics and geomechanics communities; it can be traced back to the work of Cundall and Strack [P. Cundall, Proc. Symp. ISRM, Nancy, France 1, 129 (1971); P. Cundall and O. Strack, Geotechnique 29, 47 (1979)]. The second approach, the discrete-element method via complementarity (DEM-C), considers the grains perfectly rigid and enforces nonpenetration via complementarity conditions; it is commonly used in robotics and computer graphics applications and had two strong promoters in Moreau and Jean [J. J. Moreau, in Nonsmooth Mechanics and Applications, edited by J. J. Moreau and P. D. Panagiotopoulos (Springer, Berlin, 1988), pp. 1–82; J. J. Moreau and M. Jean, Proceedings of the Third Biennial Joint Conference on Engineering Systems and Analysis, Montpellier, France, 1996, pp. 201–208]. The DEM-P and DEM-C are manifestly unlike each other: They use different (i) approaches to model the frictional contact problem, (ii) sets of model parameters to capture the physics of interest, and (iii) classes of numerical methods to solve the differential equations that govern the dynamics of the granular material. Herein, we report numerical results for five experiments: shock wave propagation, cone penetration, direct shear, triaxial loading, and hopper flow, which we use to compare the DEM-P and DEM-C solutions. This exercise helps us reach two conclusions. First, both the DEM-P and DEM-C are predictive, i.e., they predict well the macroscale emergent behavior by capturing the dynamics at the microscale. Second, there are classes of problems for which one of the methods has an advantage. Unlike the DEM-P, the DEM-C cannot capture shock-wave propagation through granular media. However, the DEM-C is proficient at handling arbitrary grain geometries and solves, at large integration step sizes, smaller problems, i.e., containing thousands of elements, very effectively. The DEM-P vs DEM-C comparison is carried out using a public-domain, open-source software package; the models used are available online.

The dynamics of a film climbing the outside of a vertical cylinder under the competing effects of a thermally driven surface tension gradient and gravity is examined through numerical simulations of a thin-film model for the film height. The model, including boundary conditions, depends on three parameters, the scaled cylinder radius $\widehat{R},$ the upstream film height $h_{\infty },$ and the downstream precursor film thickness $b,$ and reduces to the model for Marangoni driven film climbing a vertical plate in the limit $\widehat{R}\to \infty .$ The axisymmetric advancing front displays dynamics similar to that found along a vertical plate where, depending on $h_{\infty },$ the film forms a single Lax shock, an undercompressive double shock, or a rarefaction-undercompressive shock. A linear stability analysis of the Lax shock reveals the number of fingers that form along the contact line increases linearly with cylinder circumference while no fingers form for sufficiently small cylinders (below $\widehat{R}\approx 1.15$ when $b=0.1$). The substrate curvature controls the height of the Lax shock, bounds on $h_{\infty }$ that define the three distinct solutions, and the maximum growth rate of contact line perturbations to the Lax shock when $\widehat{R}=O\left(1\right),$ whereas the three solutions and the stability of the Lax shock converge to the behavior one observes on a vertical plate when $\widehat{R}\ge O\left(10\right).$ An energy analysis reveals that the azimuthal curvatures of the base state and perturbation, which arise from the annular geometry of the film, promote instability of the advancing contact line.

Collisional damping of electron plasma waves, the primary damping for high phase velocity waves, is proportional to the electron-ion collision rate, ${\nu }_{\mathrm{ei},\mathrm{th}}$. Here, it is shown that the damping rate normalized to ${\nu }_{\mathrm{ei},\mathrm{th}}$ depends on the charge state, $Z$, on the magnitude of ${\nu }_{\mathrm{ei},\mathrm{th}}$ and the wave number $k$ in contrast with the commonly used damping rate in plasma wave research. Only for weak collision rates in low-$Z$ plasmas for which the electron self-collision rate is comparable to the electron-ion collision rate is the damping rate given by the commonly accepted value. The result presented here corrects the result presented in textbooks at least as early as 1973. The complete linear theory requires the inclusion of both electron-ion pitch-angle and electron-electron scattering, which itself contains contributions to both pitch-angle scattering and thermalization.

Analogies between fluid flows and granular flows are useful because they pave the way for continuum treatments of granular media. However, in practice it is impossible to predict under what experimental conditions the dynamics of fluids and granulates are qualitatively similar. In the case of unsteadily driven systems no such analogy is known. For example, in a partially filled container subject to horizontal oscillations liquids slosh, whereas granular media of complex particles exhibit large-scale convection rolls. We here show that smooth monodisperse steel spheres exhibit liquidlike sloshing dynamics. Our findings highlight the role of particle material and geometry for the dynamics and phase transitions of the system.

We define stochastic bridges as conditional distributions of stochastic paths that leave a specified point in phase-space in the past and arrive at another one in the future. These can be defined relative to either forward or backward stochastic differential equations and with the inclusion of arbitrary path-dependent weights. The underlying stochastic equations are not the same except in linear cases. Accordingly, we generalize the theory of stochastic bridges to include time-reversed and weighted stochastic processes. We show that the resulting stochastic bridges are identical, whether derived from a forward or a backward time stochastic process. A numerical algorithm is obtained to sample these distributions. This technique, which uses partial stochastic equations, is robust and easily implemented. Examples are given, and comparisons are made to previous work. In stochastic equations without a gradient drift, our results confirm an earlier conjecture, while generalizing this to cases with path-dependent weights. An example of a two-dimensional stochastic equation with no potential solution is analyzed and numerically solved. We show how this method can treat unexpectedly large excursions occurring during a tunneling or escape event, in which a system escapes from one quasistable point to arrive at another one at a later time.

We show that eigenenergies and energy eigenstates play different roles in the equilibration process of an isolated quantum system. Their roles are revealed numerically by exchanging the eigenenergies between an integrable model and a nonintegrable model. We find that the structure of eigenenergies of a nonintegrable model characterized by nondegeneracy ensures that quantum revival occurs rarely whereas the energy eigenstates of a nonintegrable model suppress the fluctuations for the equilibrated quantum state. Our study is aided with a quantum entropy that describes how randomly a wave function is distributed in quantum phase space. We also demonstrate with this quantum entropy the validity of Berry's conjecture for energy eigenstates. This implies that the energy eigenstates of a nonintegrable model appear indeed random.

We derive a kinetic equation for rarefied diatomic gases whose molecules have a permanent dipole moment. Estimating typical parameters of such gases, we show that quantum effects cannot be neglected when describing the rotation of molecules, which we thus approximate by quantum rotators. The intermolecular potential is assumed to involve an unspecified short-range repulsive component and a long-range dipole-dipole Coulomb interaction. In the kinetic equation derived, the former and the latter give rise, respectively, to the collision integral and a self-consistent electric field generated collectively by the dipoles (as in the Vlasov model of plasma). It turns out that the characteristic period of the molecules' rotation is much shorter than the time scale of the collective electric force and the latter is much shorter than the time scale of the collision integral, which allows us to average the kinetic equation over rotation. In the averaged model, collisions and interaction with the collective field affect only those rotational levels of the molecules that satisfy certain conditions of synchronism. It is then shown that the derived model does not describe condensation; i.e., permanent dipoles of molecules cannot exert the level of intermolecular attraction necessary for condensation. It is argued that an adequate model of condensation must include the temporary dipoles that molecules induce on each other during interaction, and that this model must be quantum, not classical.

We report on experiments aiming at characterizing erosion and deposition processes on a tilted granular bed. We investigate the existence of the neutral angle, that is, the critical angle at which erosion exactly balances accretion after the passage of a granular avalanche of a finite mass. Experiments show in particular that the neutral angle depends on both avalanche mass and shape but is rather insensitive to the bed length. This result strongly suggests that the effective friction between the static and mobile granular phases cannot be taken as an intrinsic property that is only material dependent but should be considered a flow-dependent property. Interestingly, for a given avalanche mass, the net erosion rate increases linearly with the angular deviation from the neutral angle. We also compare our data with the predictions of the erosion-deposition model introduced by Bouchaud, Cates, Ravi Prakash, and Edwards (BCRE) [J. Phys. I 4, 1283 (1994)]. We show that the predictions drawn from the modified version of the BCRE model proposed by Boutreux and de Gennes, in which the local erosion rate between the static and mobile phases is independent of the flow thickness, are in remarkable agreement with the experimental results.

We present a theory of electrostatic fluctuations in two-component plasmas where electrons and ions are described by Maxwellian distribution functions at unequal temperatures. Based on the exact solution of the Landau kinetic equation, that includes electron-electron, electron-ion, and ion-ion collision integrals, the dynamic form factor, $S(\vec{k},\omega )$, is derived for weakly coupled plasmas. The collective plasma responses at ion-acoustic, Langmuir, and entropy mode resonances are described for arbitrary wave numbers and frequencies in the entire range of plasma collisionality. The collisionless limit of $S(\vec{k},\omega )$ and the strong-collision result based on the fluctuation-dissipation theorem and classical transport at $T_e=T_i$ are recovered and discussed. Results of several Thomson scattering experiments in the broad range of plasma parameters are described and discussed by means of our theory for $S(\vec{k},\omega )$.

We study energy transport in the paradigmatic Hamiltonian mean-field (HMF) model and other related long-range interacting models using molecular dynamics simulations. We show that energy diffusion in the HMF model is subdiffusive in nature, which confirms a recently obtained intriguing result that, despite being globally interacting, this model is a thermal insulator in the thermodynamic limit. Surprisingly, when additional nearest-neighbor interactions are introduced to the HMF model, an energy superdiffusion is observed. We show that these results can be consistently explained by studying energy localization due to thermally generated intrinsic localized excitation modes (discrete breathers) in nonlinear discrete systems. Our analysis for the HMF model can also be readily extended to more generic long-range interacting models where the interaction strength decays algebraically with the (shortest) distance between two lattice sites. This reconciles many of the apparently counterintuitive results presented recently [C. Olivares and C. Anteneodo, Phys. Rev. E 94, 042117 (2016); D. Bagchi, Phys. Rev. E 95, 032102 (2017)] concerning energy transport in two such long-range interacting models.

Crackling noise can be initiated by competing or coexisting mechanisms. These mechanisms can combine to generate an approximate scale invariant distribution that contains two or more contributions. The overall distribution function can be analyzed, to a good approximation, using maximum-likelihood methods and assuming that it follows a power law although with nonuniversal exponents depending on a varying lower cutoff. We propose that such distributions are rather common and originate from a simple superposition of crackling noise distributions or exponential damping.

In an elliptic billiard, we find avoided level crossings taking place over wide ranges, which are of a Demkov type for generations of eigenfunctions localized on an islands chain and its pair unstable periodic orbit. For a proof of the existence of avoided level crossings, first, we show that the quantized eigenvalue of the unstable periodic orbit, obtained by the Einstein-Brillouin-Keller quantization rule, passes the eigenvalues of bouncing-ball modes localized on the unstable periodic orbit after Demkov type avoided level crossings so that pairs of bouncing-ball modes are sequentially generated. Next, by using a perturbed Hamiltonian, we show that off-diagonal elements in Hamiltonian are nonzero, which give rise to an interaction between two eigenfunctions. Last, we verify that the observed phenomenon is Fermi resonance: that is, the quantum number difference of two normal modes equals the periodic orbits, where eigenfunctions are localized after an avoided level crossing.

We propose a model for the mechanical behavior of protein materials. Based on a limited number of experimental macromolecular parameters (persistence and contour length) we obtain the macroscopic behavior of keratin fibers (human, cow, and rabbit hair), taking into account the damage and residual stretches effects that are fundamental in many functions of life. We also show the capability of our approach to describe the main dissipation and permanent strain effects observed in the more complex spider silk fibers. The comparison between our results and the data obtained experimentally from cyclic tests demonstrates that our model is robust and is able to reproduce with a remarkable accuracy the experimental behavior of all protein materials we tested.