Molecular motors are fascinating proteins that use the energy of ATP hydrolysis to drive vesicles and organelles along cytoskeleton filaments toward their final destination within the cell. Several copies of these proteins bind to the cargo and take turns transporting the cargo attaching to and detaching from the track stochastically. Despite the relevance of molecular motors to cell physiology, key aspects of their collective functioning are still unknown. In this work we propose a one-dimensional model for the transport of extensive and smooth organelles driven by molecular motors. We ran numerical simulations to study the behavior of the cargo for different motor configurations, focusing on the transport properties observable in the experiments, e.g., average speed of the organelle and variations in length. We found that active motors drive the cargo using two different mechanisms: Either they locate in front of the cargo and pull the organelle or they situate at the cargo lagging edge and push. Variations in the organelle length is in close relation with the fraction of motors in each configuration, which depends on the resisting load. The results of this model were contrasted with experimental data obtained from the tracking of rodlike mitochondria during active transport in Xenopus laevis melanophores.

Electrically driven nematic liquid crystals layers are ideal contexts for studying the interactions of local topological defects, umbilical defects. In homogeneous samples the number of defects is expected to decrease inversely proportional to time as a result of defect-pair interaction law, so-called coarsening process. Experimentally, we characterize the coarsening dynamics in samples containing glass beads as spacers and show that the inclusion of such imperfections changes the exponent of the coarsening law. Moreover, we demonstrate that beads that are slightly deformed alter the surrounding molecular distribution and attract vortices of both topological charges, thus, presenting a mainly quadrupolar behavior. Theoretically, based on a model of vortices diluted in a dipolar medium, a $\frac{2}{3}$ exponent is inferred, which is consistent with the experimental observations.

Biological plywoods are multifunctional fibrous composites materials, ubiquitous in nature. The chiral fibrous organization is found in chitin (insects), cellulosics (plants), and collagen I (cornea and bone of mammals) and is a solid analog of that of cholesteric liquid crystals. The surface and interfaces of plywoods are distinguished by hierarchical topographies and nanowrinkling. In this paper, we present a theory to model the emergence of these surfaces and interfaces using liquid crystal-based shape equations that directly connect material properties with geometric wrinkling. The model applies to liquid crystal precursors of the plywood solid analoges. We focus on wrinkling geometry, wrinkling mechanics, and the mechanogeometry relationships that underlie multifunctionality ubiquitous in biological surfaces. Scaling wrinkling laws that connect mechanical pressures and stresses to folding and bending are formulated and quantified. A synthesis of the connections between mechanics and geometry is achieved using the topology of stress curves and curvature of the wrinkles. Taken together the results show that anchoring is a versatile surface morphing mechanism with a rich surface bending stress field, two ingredients behind many potential multifunctionalities.

Recent computational and laboratory experiments have shown that brittle-ductile transitions in the notch toughnesses of metallic glasses such as Vitreloy 1 are strongly sensitive to the initial effective disorder (or “fictive”) temperature. Glasses with lower effective temperatures are weak and brittle; those with higher effective temperatures are strong and ductile. The analysis of this phenomenon presented here examines the onset of fracture at the tip of a notch as predicted by the shear-transformation-zone theory of spatially varying plastic deformation. The central ingredient of this analysis is an approximation for the dynamics of the plastic zone formed by stress concentration at the notch tip. This zone first shields the tip but then, with increasing stress, expands suddenly, producing a discontinuous transition between brittle and ductile failure in satisfactory agreement with the numerical and experimental observations.

A compressible Rayleigh-Taylor (RT) unstable flow with a diffuse interface where the density varies smoothly supports a multiplicity of unstable eigenmodes that grow exponentially in time. This paper studies two relevant problems in a two-dimensional (2-D) RT flow by use of multimode decomposition. The first one is the excitation of these modes by arbitrarily introduced infinitesimal perturbations. The initial amplitude of each mode is calculated by projecting the introduced perturbation into the eigenvector space, and the obtained initial amplitude can be used to predict the linear evolution of the perturbation accurately, as is confirmed by direct numerical simulations. If the initial perturbation includes pressure or velocity components, then in addition to the growth of the RT mode, a strong acoustic wave package would be radiated to the heavy fluid, whereas a mild acoustic wave package would be radiated to the light fluid. As the second problem, in order to reveal the interaction feature of the unstable normal modes in the nonlinear phase, we perform the multimode decomposition based on the instantaneous perturbation field under the Fourier transformation in the direction tangential to the interface. For the current case studies, the emergence of the bubble-spike structure is mainly attributed to the nonlinear amplification of the odd modes decomposed from the fundamental disturbances. As time advances to the nonlinear phase, the projection to the low-order normal modes possesses less portion of the total energy due to the complexity of the multipeak perturbation profiles.

When a particle moves through a spatially random force field, its momentum may change at a rate which grows with its speed. Suppose moreover that a thermal bath provides friction which gets weaker for large speeds, enabling high-energy localization. The result is a unifying framework for the emergence of heavy tails in the velocity distribution, relevant for understanding the power-law decay in the electron velocity distribution of space plasma or more generally for explaining non-Maxwellian behavior of driven gases. We also find long-time tails in the velocity autocorrelation, indicating persistence at large speeds for a wide range of parameters and implying superdiffusion of the position variable.

A time-dependent generalized Kubo relation is derived by introducing the notion of a diffusion function for a particle confined in a harmonic potential. The relation reduces to the standard Kubo relation as a special case but holds for anomalous diffusion, nonergodic processes, and bounded motion. We analyze in detail the behaviors of the diffusion and memory functions and report a generalized Stokes-Einstein relation concerning anomalous diffusion. Furthermore, we demonstrate that when a high finite-frequency cutoff is imposed on the noise spectral density, a breakdown in ergodicity accompanied by the appearance of nonstationarity in the velocity autocorrelation function occurs in forced systems. This breakdown is taken as explicit evidence for either decay-spring-memory or recovering-force effects leading to nonexponential relaxation kinematics.

The detection of a weak signal in the presence of noise is an important problem that is often studied in terms of the receiver operating characteristic (ROC) curve, in which the probability of correct detection is plotted against the probability for a false positive. This kind of analysis is typically applied to the situation in which signal and noise are stochastic variables; the detection problem emerges, however, also often in a context in which both signal and noise are stochastic processes and the (correct or false) detection is said to take place when the process crosses a threshold in a given time window. Here we consider the problem for a combination of a static signal which has to be detected against a dynamic noise process, the well-known Ornstein-Uhlenbeck process. We give exact (but difficult to evaluate) quadrature expressions for the detection rates for false positives and correct detections, investigate systematically a simple sampling approximation suggested earlier, compare to an approximation by Stratonovich for the limit of high threshold, and briefly explore the case of multiplicative signal; all theoretical results are compared to extensive numerical simulations of the corresponding Langevin equation. Our results demonstrate that the sampling approximation provides a reasonable description of the ROC curve for this system, and it clarifies limit cases for the ROC curve.

Modeling cooperative dynamics using networks of phase oscillators is common practice for a wide spectrum of biological and technological networks, ranging from neuronal populations to power grids. In this paper we study the emergence of stable clusters of synchrony with complex intercluster dynamics in a three-population network of identical Kuramoto oscillators with inertia. The populations have different sizes and can split into clusters where the oscillators synchronize within a cluster, but notably, there is a phase shift between the dynamics of the clusters. We extend our previous results on the bistability of synchronized clusters in a two-population network [I. V. Belykh et al., Chaos 26, 094822 (2016)] and demonstrate that the addition of a third population can induce chaotic intercluster dynamics. This effect can be captured by the old adage “two is company, three is a crowd,” which suggests that the delicate dynamics of a romantic relationship may be destabilized by the addition of a third party, leading to chaos. Through rigorous analysis and numerics, we demonstrate that the intercluster phase shifts can stably coexist and exhibit different forms of chaotic behavior, including oscillatory, rotatory, and mixed-mode oscillations. We also discuss the implications of our stability results for predicting the emergence of chimeras and solitary states.

Artificial neural networks are universal function approximators. They can forecast dynamics, but they may need impractically many neurons to do so, especially if the dynamics is chaotic. We use neural networks that incorporate Hamiltonian dynamics to efficiently learn phase space orbits even as nonlinear systems transition from order to chaos. We demonstrate Hamiltonian neural networks on a widely used dynamics benchmark, the Hénon-Heiles potential, and on nonperturbative dynamical billiards. We introspect to elucidate the Hamiltonian neural network forecasting.

We consider the dynamics of relativistic spin-half particles in quantum graphs with transparent branching points. The system is modeled by combining the quantum graph concept with the one of transparent boundary conditions applied to the Dirac equation on metric graphs. Within such an approach, we derive simple constraints, which turn the usual Kirchhoff-type boundary conditions at the vertex equivalent to the transparent ones. Our method is applied to quantum star graph. An extension to more complicated graph topologies is straightforward.

A data-driven framework is developed to represent chaotic dynamics on an inertial manifold (IM) and applied to solutions of the Kuramoto-Sivashinsky equation. A hybrid method combining linear and nonlinear (neural-network) dimension reduction transforms between coordinates in the full state space and on the IM. Additional neural networks predict time evolution on the IM. The formalism accounts for translation invariance and energy conservation, and substantially outperforms linear dimension reduction, reproducing very well key dynamic and statistical features of the attractor.

We present analytical results for the structural evolution of random networks undergoing contraction processes via generic node deletion scenarios, namely, random deletion, preferential deletion, and propagating deletion. Focusing on configuration model networks, which exhibit a given degree distribution $P_0\left(k\right)$ and no correlations, we show using a rigorous argument that upon contraction the degree distributions of these networks converge towards a Poisson distribution. To this end, we use the relative entropy $S_t=S[P_t\left(k\right)\left|\right|\pi \left(k\right|{\langle K\rangle }_t)]$ of the degree distribution $P_t\left(k\right)$ of the contracting network at time $t$ with respect to the corresponding Poisson distribution $\pi \left(k\right|{\langle K\rangle }_t)$ with the same mean degree ${\langle K\rangle }_t$ as a distance measure between $P_t\left(k\right)$ and Poisson. The relative entropy is suitable as a distance measure since it satisfies $S_t\ge 0$ for any degree distribution $P_t\left(k\right)$, while equality is obtained only for $P_t\left(k\right)=\pi \left(k\right|{\langle K\rangle }_t)$. We derive an equation for the time derivative $d{S}_t/dt$ during network contraction and show that the relative entropy decreases monotonically to zero during the contraction process. We thus conclude that the degree distributions of contracting configuration model networks converge towards a Poisson distribution. Since the contracting networks remain uncorrelated, this means that their structures converge towards an Erdős-Rényi (ER) graph structure, substantiating earlier results obtained using direct integration of the master equation and computer simulations [Tishby et al., Phys. Rev. E 100, 032314 (2019)]. We demonstrate the convergence for configuration model networks with degenerate degree distributions (random regular graphs), exponential degree distributions, and power-law degree distributions (scale-free networks).

We study the large-amplitude response of classical molecules to electromagnetic radiation, showing the universality of the transition from linear to nonlinear response and breakup at sufficiently large amplitudes. We demonstrate that a range of models, from the simple harmonic oscillator to the successful Peyrard-Bishop-Dauxois type models of DNA, which include realistic effects of the environment (including damping and dephasing due to thermal fluctuations), lead to characteristic universal behavior: formation of domains of dissociation in driving force amplitude-frequency space, characterized by the presence of local boundary minima. We demonstrate that by simply following the progression of the resonance maxima in this space, while gradually increasing intensity of the radiation, one must necessarily arrive at one of these minima, i.e., a point where the ultrahigh spectral selectivity is retained. We show that this universal property, applicable to other oscillatory systems, is a consequence of the fact that these models belong to the fold catastrophe universality class of Thom's catastrophe theory. This in turn implies that for most biostructures, including DNA, high spectral sensitivity near the onset of the denaturation processes can be expected. Such spectrally selective molecular denaturation could find important applications in biology and medicine.

In recent years situations where elsewise identical particles demix when different degrees of freedom do not thermalize have become a research focus in nonequilibrium statistical mechanics. The majority of these models are formulated in the context of active particles, but the phenomenon also occurs for particles without driving. All the models studied so far share the property that they do not obey microscopic reversibility, and it may be thought that this is a necessary condition for such demixing to occur. We show here that such a demixing transition also occurs in a mixture of otherwise identical particles moving at two fixed but different speeds according to a time-reversible quasi-Newtonian dynamics. The mechanical instability underlying this behavior is generated by the lack of thermalization between the two subsystems, which is shared by all systems showing this behavior.

Herein, a method is proposed to determine the azimuthal anchoring energies of surface liquid crystals (LCs), as they gradually change orientation from a vertical to a horizontal state owing to an increase in the voltage applied to each LC cell. The LC cells are characterized using the direction of the Williams roll pattern related to the midplane LC director of the conduction regime of the electrohydrodynamic convection patterns of LCs. The application of the midplane LC directions, obtained from the direction of the roll patterns, to the Ericksen-Leslie equation produces the precise values of the surface anchoring strength. The hybrid type 90°-twisted nematic LC cell, composed of homeotropic and homogeneous LC alignment layers on the top and bottom substrates, respectively, was used to find the azimuthal anchoring energy of the surface LCs, indicated by voltages at the initially vertically aligned LC state. It was observed that the surface azimuthal anchoring energy on the homeotropic layer increased with an increase in voltage. We expect that the proposed technique may be excellent in terms of ease of use, simplicity, and accuracy because the azimuthal anchoring energy can be visually evaluated through the roll pattern.

We develop the geometric description of submanifolds in Newton-Cartan spacetime. This provides the necessary starting point for a covariant spacetime formulation of Galilean-invariant hydrodynamics on curved surfaces. We argue that this is the natural geometrical framework to study fluid membranes in thermal equilibrium and their dynamics out of equilibrium. A simple model of fluid membranes that only depends on the surface tension is presented and, extracting the resulting stresses, we show that perturbations away from equilibrium yield the standard result for the dispersion of elastic waves. We also find a generalization of the Canham-Helfrich bending energy for lipid vesicles that takes into account the requirements of thermal equilibrium.

The lattice Boltzmann method (LBM) has been formulated as a powerful numerical tool to simulate incompressible fluid flows. However, it is still a critical issue for the LBM to overcome the discrete effects on boundary conditions successfully for curved no-slip walls. In this paper, we focus on the discrete effects of curved boundary conditions within the framework of the multiple-relaxation-time (MRT) model. We analyze in detail a single-node curved boundary condition [Zhao et al., Multiscale Model. Simul. 17, 854 (2019)] for predicting the Poiseuille flow and derive the numerical slip at the boundary dependent on a free parameter as well as the distance ratio and the relaxation times. An approach by virtue of the free parameter is then proposed to eliminate the slip velocity while with uniform relaxation parameters. The theoretical analysis also indicates that for previous curved boundary schemes only with the distance ratio and the halfway bounce-back (HBB) boundary scheme, the numerical slip cannot be removed with uniform relaxation times virtually. We further carried out some simulations to validate our theoretical derivations, and the numerical results for the case of straight and curved boundaries confirm our theoretical analysis. Finally, for fluid flows with curved boundary geometries, resorting to more degrees of freedom from the boundary scheme may have more potential to eliminate the discrete effect at the boundary with uniform relaxation times.

Lévy walks (LWs) are spatiotemporally coupled random-walk processes describing superdiffusive heat conduction in solids, propagation of light in disordered optical materials, motion of molecular motors in living cells, or motion of animals, humans, robots, and viruses. We here investigate a key feature of LWs—their response to an external harmonic potential. In this generic setting for confined motion we demonstrate that LWs equilibrate exponentially and may assume a bimodal stationary distribution. We also show that the stationary distribution has a horizontal slope next to a reflecting boundary placed at the origin, in contrast to correlated superdiffusive processes. Our results generalize LWs to confining forces and settle some longstanding puzzles around LWs.