Diffusive transport is a universal phenomenon, throughout both biological and physical sciences, and models of diffusion are routinely used to interrogate diffusion-driven processes. However, most models neglect to take into account the role of volume exclusion, which can significantly alter diffusive transport, particularly within biological systems where the diffusing particles might occupy a significant fraction of the available space. In this work we use a random walk approach to provide a means to reconcile models that incorporate crowding effects on different spatial scales. Our work demonstrates that coarse-grained models incorporating simplified descriptions of excluded volume can be used in many circumstances, but that care must be taken in pushing the coarse-graining process too far.

Non-Markovian processes are widespread in natural and human-made systems, yet explicit modeling and analysis of such systems is underdeveloped. We consider a non-Markovian dynamic network with random link activation and deletion (RLAD) and heavy-tailed Mittag-Leffler distribution for the interevent times. We derive an analytically and computationally tractable system of Kolmogorov-like forward equations utilizing the Caputo derivative for the probability of having a given number of active links in the network and solve them. Simulations for the RLAD are also studied for power-law interevent times and we show excellent agreement with the Mittag-Leffler model. This agreement holds even when the RLAD network dynamics is coupled with the susceptible-infected-susceptible spreading dynamics. Thus, the analytically solvable Mittag-Leffler model provides an excellent approximation to the case when the network dynamics is characterized by power-law-distributed interevent times. We further discuss possible generalizations of our result.

We identify a universal mathematical structure in microscopic deterministic traffic models (with identical drivers), and thus we show that all such existing models in the literature, including both the two-phase and three-phase models, can be understood as special cases of a master model by expansion around a set of well-defined ground states. This allows any two traffic models to be properly compared and identified. The three-phase models are characterized by the vanishing of leading orders of expansion within a certain density range, and as an example the popular intelligent driver model is shown to be equivalent to a generalized optimal velocity (OV) model. We also explore the diverse solutions of the generalized OV model that can be important both for understanding human driving behaviors and algorithms for autonomous driverless vehicles.

We articulate an adaptive and reference-free framework based on the principle of random switching to detect and control unstable steady states in high-dimensional nonlinear dynamical systems, without requiring any a priori information about the system or about the target steady state. Starting from an arbitrary initial condition, a proper control signal finds the nearest unstable steady state adaptively and drives the system to it in finite time, regardless of the type of the steady state. We develop a mathematical analysis based on fast-slow manifold separation and Markov chain theory to validate the framework. Numerical demonstration of the control and detection principle using both classic chaotic systems and models of biological and physical significance is provided.

Dynamical systems with multiple, hierarchically long-delayed feedback are introduced and studied extending our previous work [Yanchuk and Giacomelli, Phys. Rev. Lett. 112, 174103 (2014)]. Focusing on the phenomenological model of a Stuart-Landau oscillator with two feedbacks, we show the multiscale properties of its dynamics and demonstrate them by means of a space-time representation. For sufficiently long delays, we derive a normal form describing the system close to the destabilization. The space and temporal variables, which are involved in the space-time representation, correspond to suitable time scales of the original system. The physical meaning of the results, together with the interpretation of the description at different scales, is presented and discussed. In particular, it is shown how this representation uncovers hidden multiscale patterns such as spirals or spatiotemporal chaos. The effect of the delay size and the features of the transition between small and large delays is also analyzed. Finally, we comment on the application of the method and on its extension to an arbitrary, but finite, number of delayed feedback terms.

Two types of random evolution processes are studied for ensembles of the standard map with driving parameter $K$ that determines its degree of stochasticity. For one type of process the parameter $K$ is chosen at random from a Gaussian distribution and is then kept fixed, while for the other type it varies from step to step. In addition, noise that can be arbitrarily weak is added. The ensemble average and the average over noise of the diffusion coefficient are calculated for both types of processes. These two types of processes are relevant for two types of experimental situations as explained in the paper. Both types of processes destroy fine details of the dynamics, and the second process is found to be more effective in destroying the fine details. We hope that this work is a step in the efforts for developing a statistical theory for systems with mixed phase space (regular in some parts and chaotic in other parts).

We explore the long-time dynamics of a system of identical charged particles trapped on a closed helix. This system has recently been found to exhibit an unconventional deformation of the linear spectrum when tuning the helix radius. Here we show that the same geometrical parameter can affect significantly also the dynamical behavior of an initially broad excitation for long times. In particular, for small values of the radius, the excitation disperses into the whole crystal whereas within a specific narrow regime of larger radii the excitation self-focuses, assuming finally a localized form. Beyond this regime, the excitation defocuses and the dispersion gradually increases again. We analyze this geometrically controlled nonlinear behavior using an effective discrete nonlinear Schrödinger model, which allows us among others to identify a number of breatherlike excitations.

Previous papers by the authors report that they obtained compact, arbitrarily accurate expressions for two-center, one- and two-electron relativistic molecular integrals expressed over Slater-type orbitals. In the present study, accuracy limits of expressions given are examined for three-center nuclear attraction integrals, which are one-electron, three-center integrals with no analytically closed-form expression. In this work new molecular auxiliary functions are used. They are obtained via Neumann expansion of the Coulomb interaction. The numerical global adaptive method is used to evaluate these integrals for arbitrary values of orbital parameters and quantum numbers. Several methods, such as Laplace expansion of Coulomb interaction, single-center expansion, and the Fourier transformation method, have previously been used to evaluate these integrals considering the values of principal quantum numbers in the set of positive integer numbers. This study of three-center integrals places no restrictions on quantum numbers in all ranges of orbital parameters.

The momentum or velocity autocorrelation function $C\left(t\right)$ for a tagged oscillator in a finite harmonic system decays like that of an infinite system for short times, but exhibits erratic behavior at longer time scales. We introduce the autocorrelation function of the long-time noisy tail of $C\left(t\right)$ (“a correlation of the correlation”), which characterizes the distribution of recurrence times. Remarkably, for harmonic systems with same-mass particles this secondary correlation may coincide with the primary correlation $C\left(t\right)$ (when both functions are normalized) either exactly, or over a significant initial time interval. When the tagged particle is heavier than the rest, the equality does not hold, correlations show nonrandom long-time scale pattern, and higher-order correlations converge to the lowest normal mode.

Synchronized neural bursts are one of the most noticeable dynamic features of neural networks, being essential for various phenomena in neuroscience, yet their complex dynamics are not well understood. With extrinsic electrical and optical manipulations on cultured neural networks, we demonstrate that the regularity (or randomness) of burst sequences is in many cases determined by a (few) low-dimensional attractor(s) working under strong neural noise. Moreover, there is an optimal level of noise strength at which the regularity of the interburst interval sequence becomes maximal—a phenomenon of coherence resonance. The experimental observations are successfully reproduced through computer simulations on a well-established neural network model, suggesting that the same phenomena may occur in many in vivo as well as in vitro neural networks.

In the present work, we combine the notion of parity-time ($\mathcal{PT}$) symmetry with that of supersymmetry (SUSY) for a prototypical case example with a complex potential that is related by SUSY to the so-called Pöschl-Teller potential which is real. Not only are we able to identify and numerically confirm the eigenvalues of the relevant problem, but we also show that the corresponding nonlinear problem, in the presence of an arbitrary power-law nonlinearity, has an exact bright soliton solution that can be analytically identified and has intriguing stability properties, such as an oscillatory instability, which is absent for the corresponding solution of the regular nonlinear Schrödinger equation with arbitrary power-law nonlinearity. The spectral properties and dynamical implications of this instability are examined. We believe that these findings may pave the way toward initiating a fruitful interplay between the notions of $\mathcal{PT}$ symmetry, supersymmetric partner potentials, and nonlinear interactions.

A master equation was formulated to study intrinsic charge fluctuations of a grain in a plasma as ions and primary electrons are attached to the grain through collisional collection, and secondary electrons are emitted from the grain. Two different plasmas with Maxwellian and non-Maxwellian distributions were considered. The fluctuations could be bistable in either plasma when the secondary electron emission is present, as two stable macrostates, associated with two stable roots of the charge net current, may exist. Metastablity of fluctuations, manifested by the passage of the grain charge between two macrostates, was shown to be possible.

We consider percolation and jamming transitions for particulate systems exposed to compression. For the systems built of particles interacting by purely repulsive forces in addition to friction and viscous damping, it is found that these transitions are influenced by a number of effects, and in particular by the compression rate. In a quasistatic limit, we find that for the considered type of interaction between the particles, percolation and jamming transitions coincide. For cohesive systems, however, or for any system exposed to even slow dynamics, the differences between the considered transitions are found and quantified.

The electric Freedericksz transition is a second-order quadratic effect, which, in a planarly aligned nematic liquid crystal layer, manifests above a threshold field as a homogeneous symmetric distortion with maximum director-tilt in the midplane. We find that, upon excitation by a low frequency $(<0.2\mathrm{Hz})$ square-wave field, the instability becomes spatially and temporally varying. This is demonstrated using calamitic liquid crystals, initially in the 90°-twisted planar configuration. The distortion occurs close to the negative electrode following each polarity switch and, for low-voltage amplitudes, decays completely in time. We use the elastically favorable geometry of Brochard-Leger walls to establish the location of maximum distortion. Thus, at successive polarity changes, the direction of extension of both annular and open walls switches between the alignment directions at the two substrates. For high voltages, this direction is largely along the midplane director, while remaining marginally oscillatory. These results are broadly understood by taking into account the time-varying and inhomogeneous field conditions that prevail soon after the polarity reverses. Polarity dependence of the instability is traced to the formation of intrinsic double layers that lead to an asymmetry in field distribution in the presence of an external bias. Momentary field elevation near the negative electrode following a voltage sign reversal leads to locally enhanced dielectric and gradient flexoelectric torques, which accounts for the surface-like phenomenon observed at low voltages. These spatiotemporal effects, also found earlier for other instabilities, are generic in nature.

A model of filaments of the twist-grain-boundary smectic-$A$ phase (TGBA) arising from the homeotropic smectic-$A$ phase and nucleating on the sample surface is proposed. The model is based on the concept of finite blocks of parallel smectic layers forming a helical structure. The blocks are surrounded by dislocation loops. The model describes the filament structure near the sample surface and the observed inclination of the filament axis with respect to the easy direction of the molecular anchoring on the surface. The model is based on the observations of filament textures of the TGBA phase in a chiral liquid crystalline compound, but can be applied for forming of TGBA filaments in any compound. The compression modulus of the compound has been estimated using such parameters as anchoring energy, estimated from the field necessary to transform the structure into the homeotropic smectic-$A$.

Changes in cell size often accompany multicellular motion in tissue, and cell number density is known to strongly influence collective migration in monolayers. Density fluctuations in other forms of active matter have been explored extensively, but not the potential role of density fluctuations in collective cell migration. Here we investigate collective motion in cell monolayers, focusing on the divergent component of the migration velocity field to probe density fluctuations. We find spatial patterns of diverging and converging cell groups throughout the monolayers, which oscillate in time with a period of approximately 3–4 h. Simultaneous fluorescence measurements of a cytosol dye within the cells show that fluid passes between groups of cells, facilitating these oscillations in cell density. Our findings reveal that cell-cell interactions in monolayers may be mediated by intercellular fluid flow.

The results presented in this study are aimed at the theoretical estimate of the interactions between a spherical microbial cell and the colloidal cell imprints in terms of the Derjaguin, Landau, Vervey, and Overbeek (DLVO) surface forces. We adapted the Derjaguin approximation to take into account the geometry factor in the colloidal interaction between a spherical target particle and a hemispherical shell at two different orientations with respect to each other. We took into account only classical DLVO surface forces, i.e., the van der Waals and the electric double layer forces, in the interaction of a spherical target cell and a hemispherical shell as a function of their size ratio, mutual orientation, distance between their surfaces, their respective surface potentials, and the ionic strength of the aqueous solution. We found that the calculated interaction energies are several orders higher when match and recognition between the target cell and the target cell imprint is achieved. Our analysis revealed that the recognition effect of the hemispherical shell towards the target microsphere comes from the greatly increased surface contact area when a full match of their size and shape is produced. When the interaction between the surfaces of the hemishell and the target cell is attractive, the recognition greatly amplifies the attraction and this increases the likelihood of them to bind strongly. However, if the surface interaction between the cell and the imprint is repulsive, the shape and size match makes this interaction even more repulsive and thus decreases the likelihood of binding. These results show that the surface chemistry of the target cells and their colloidal imprints is very important in controlling the outcome of the interaction, while the shape recognition only amplifies the interaction. In the case of nonmonotonous surface-to-surface interaction we discovered some interesting interplay between the effects of shape match and surface chemistry which is discussed in the paper. The results from this study establish the theoretical basis of cell shape recognition by colloidal cell imprints which, combined with cell killing strategies, could lead to an alternative class of cell shape selective antimicrobials, antiviral, and potentially anticancer therapies.

For a symmetric ion permselective system, in terms of geometry and bulk concentrations, the system response is also symmetric under opposite electric field polarity. In this work we derive an analytical solution for the concentration distribution, electric potential, and current-voltage response for a four-layered system comprised of two microchambers connected by two permselective regions of varying properties. It is shown that any additional asymmetry in the system, in terms of the geometry, bulk concentration, or surface charge property of the permselective regions, results in current rectification. Our work is divided into two parts: when both permselective regions have the same surface charge sign and the case of opposite signs. For the same sign case we are able to show that the system behaves as a dialytic battery while accounting for field-focusing effects. For the case of opposite signs (i.e., bipolar membrane), our system exhibits the behavior of a bipolar diode where the magnitude of the rectification can be of order ${10}^2-{10}^3$.

The isentropic expansion of an instantaneously and homogeneously heated foil is calculated using a 1D fluid model. The initial temperature and density are assumed to be in the vicinity of the critical temperature and solid density, respectively. The fluid is assumed to satisfy the van der Waals equation of state with an arbitrary number of degrees of freedom. Self-similar Riemann solutions are found. With a larger number of degrees of freedom $f$, depending on the initial dimensionless entropy ${\tilde{s}}_0$, a richer family of foil expansion behaviors have been found. We calculate the domain in parameter space where these behaviors occur. In total, eight types of rarefaction waves are found and described.

Dynamics of low-temperature water in nanostructured materials is important to a variety of phenomena, ranging from transport in cement and asphaltene, to conformational dynamics of proteins in “crowded” cellular environments, survival of microorganisms at very low temperatures, and diffusion in nanogeoscience. Using silicon-carbide nanotubes as a prototype of nanostructured materials, extensive molecular dynamics simulations were carried out to study the cage correlation function $C\left(t\right)$ and self-diffusivity $D$ of supercooled water in the nanotubes. $C\left(t\right)$, which measures changes in the atomic surroundings inside the nanotube, follows the Kohlrausch-Williams-Watts law, $C\left(t\right)\sim exp[-{(t/\tau )}^{\beta }]$, where $\tau$ is a relaxation time and $\beta$ is a topological exponent. For the temperature range $220\text{K}<T\le 273$ K, we find $\beta \simeq 0.438$, in excellent agreement with and confirming the prediction by Phillips [Rep. Prog. Phys. 59, 1133 (1996)], $\beta =3/7$. The self-diffusivity manifests a transition around 230 K, very close to 228 K, the temperature at which a fragile-to-strong dynamic crossover is supposed to happen. Thus the results indicate that water does not freeze in the nanotube over the studied temperature range, and that the Stokes-Einstein relation breaks down.