We analyze a set of discrete-time quantum walks for which the displacements on a chain follow binary aperiodic jumps according to three paradigmatic sequences: Fibonacci, Thue-Morse, and Rudin-Shapiro. We use a generalized Hadamard coin, ${\widehat{C}}_H$, as well as a generalized Fourier coin, ${\widehat{C}}_K$. We verify the QW experiences a slowdown of the wave packet spreading, ${\sigma }^2\left(t\right)\sim t^{\alpha }$, by the aperiodic jumps whose exponent, $\alpha$, depends on the type of aperiodicity. Additional aperiodicity-induced effects also emerge, namely, (1) while the superdiffusive regime ($1<\alpha <2$) is predominant, $\alpha$ displays an unusual sensibility with the type of coin operator where the more pronounced differences emerge for the Rudin-Shapiro and random protocols and (2) even though the angle $\theta$ of the coin operator is homogeneous in space and time, there is a nonmonotonic dependence of $\alpha$ with $\theta$. Fingerprints of the aperiodicity in the hoppings are also found when distributional measures such as the Shannon and von Neumann entropies, the Inverse Participation Ratio, the Jensen-Shannon dissimilarity, and the kurtosis are computed, which allow assessing informational and delocalization features arising from these protocols and understanding the impact of linear and nonlinear correlations of the jump sequence in a quantum walk as well. Finally, we argue the spin-lattice entanglement is enhanced by aperiodic jumps.

Totally asymmetric exclusion processes (TASEPs) with open boundaries are known to exhibit moving shocks or delocalized domain walls (DDWs) for sufficiently small equal injection and extraction rates. In contrast, TASEPs in a ring with a single inhomogeneity display pinned shocks or localized domain walls (LDWs) under equivalent conditions [see, e.g., H. Hinsch and E. Frey, Phys. Rev. Lett. 97, 095701 (2006)]. By studying periodic exclusion processes composed of a driven (TASEP) and a diffusive segment, we discuss gradual fluctuation-induced depinning of the LDW, leading to its delocalization and formation of a DDW-like domain wall, similar to the DDWs in open TASEPs in some limiting cases under long-time averaging. This smooth crossover is controlled essentially by the fluctuations in the diffusive segment. Our studies provide an explicit route to control the quantitative extent of domain-wall fluctuations in driven periodic inhomogeneous systems, and should be relevant in any quasi-one-dimensional transport processes where the availability of carriers is the rate-limiting constraint.

Slow dynamic nonlinearity is widely observed in brittle materials with complex heterogeneous or cracked microstructures. It is seen in rocks, concrete, and cracked glass blocks. Unconsolidated structures show the behavior as well: aggregates of glass beads under pressure and a single glass bead confined between two glass plates. A defining feature is the loss of stiffness after a mechanical conditioning, followed by a logarithmic-in-time recovery. Materials observed to exhibit slow dynamics are sufficiently different in microstructure, chemical composition, and scale (ranging from the laboratory to the seismological) to suggest some kind of universality. There lacks a full theoretical understanding of the universality in general and the log(time) recovery in particular. One suspicion has been that the phenomenon is associated with glassy grain boundaries and microcracking. Seminal studies were focused on sandstones and other natural rocks, but in recent years other experimental venues have been introduced with which to inform theory. Here, we present measurements on some simple metallic systems: an unconsolidated aggregate of aluminum beads under a confining pressure, an aluminum bead confined between two aluminum plates, and a steel bead confined between steel plates. Ultrasonic waves are used as probes of the systems, and changes are assessed with coda wave interferometry. Three different methods of low-frequency conditioning are applied; all reveal slow dynamic nonlinearities. Results imply that glassy microstructures and cracking do not play essential roles, as they would appear to be absent in our systems.

Surface wrinkles are commonly observed in soft polymer nanofibers produced in electrospinning. This paper studies the conditions of circumferential wrinkling in polymer nanofibers under axial stretching. A nonlinear continuum mechanics model is formulated to take into account the combined effects of surface energy and nonlinear elasticity of the nanofibers on wrinkling initiation, in which the soft nanofibers are treated as incompressible, isotropically hyperelastic neo-Hookean solid. The critical condition to trigger circumferential wrinkling is determined and its dependencies upon the surface energy, mechanical properties, and geometries of the nanofibers are examined. In the limiting case of spontaneous circumferential wrinkling, the theoretical minimum radius of soft nanofibers producible in electrospinning is determined, which is related closely to the intrinsic length $l_0=\gamma /E$ of the polymer (γ: the surface energy; E: a measure of the elastic modulus), and compared with that of spontaneous longitudinal wrinkling in polymer nanofibers. The present study provides a rational understanding of surface wrinkling in polymer nanofibers and a technical approach for actively tuning the surface morphologies of polymer nanofibers for applications, e.g., high-grade filtration, oil-water separation, tissue scaffolding, etc.

We report here an alternative kind of fingering instability observed during fracture of an unconfined gel consisting of two cuboids joined by a thin gel disk, and all prepared monolithically. When the blocks are sheared across the joint, fracture ensues with the appearance of fingers at the fracture front. The spacing between the fingers remains independent of the shearing speed, planar shape of the joint, and the shear modulus of gel. Importantly this instability appears without any effect of confinement of the gel block, and its wavelength remains dependent on the lateral size of the disk, in contrast to all known instances of fingering phenomena in confined viscous, elastic, and viscoelastic systems.

Complex systems often exhibit multiple levels of organization covering a wide range of physical scales, so the study of the hierarchical decomposition of their structure and function is frequently convenient. To better understand this phenomenon, we introduce a generalization of information theory that works with hierarchical partitions. We begin revisiting the recently introduced hierarchical mutual information (HMI), and show that it can be written as a level by level summation of classical conditional mutual information terms. Then, we prove that the HMI is bounded from above by the corresponding hierarchical joint entropy. In this way, in analogy to the classical case, we derive hierarchical generalizations of many other classical information-theoretic quantities. In particular, we prove that, as opposed to its classical counterpart, the hierarchical generalization of the variation of information is not a metric distance, but it admits a transformation into one. Moreover, focusing on potential applications of the existing developments of the theory, we show how to adjust by chance the HMI. We also corroborate and analyze all the presented theoretical results with exhaustive numerical computations, and include an illustrative application example of the introduced formalism. Finally, we mention some open problems that should be eventually addressed for the proposed generalization of information theory to reach maturity.

Cell motility plays important roles in a range of biological processes, such as reproduction and infections. Studies have hypothesized that the ulcer-causing bacterium Helicobacter pylori invades the gastric mucus layer lining the stomach by locally turning nearby gel into sol, thereby enhancing its locomotion through the biological barrier. In this work, we present a minimal theoretical model to investigate how heterogeneity created by a swimmer affects its own locomotion. As a generic locomotion model, we consider the swimming of a spherical squirmer in a purely viscous fluid pocket (representing the liquified or degelled region) surrounded by a Brinkman porous medium (representing the mucus gel). The use of the squirmer model enables an exact, analytical solution to this hydrodynamic problem. We obtain analytical expressions for the swimming speed, flow field, and power dissipation of the swimmer. Depending on the details of surface velocities and fluid properties, our results reveal the existence of a minimum threshold size of mucus gel that a swimmer needs to liquify in order to gain any enhancement in swimming speed. The threshold size can be as much as approximately $30\%$ of the swimmer size. We contrast these predictions with results from previous models and highlight the significant role played by the details of surface actuations. In addition to their biological implications, these results could also inform the design of artificial microswimmers that can penetrate into biological gels for more effective drug delivery.

A target design for mitigating the Rayleigh-Taylor instability is proposed for use in high energy density and direct-drive inertial confinement fusion experiments. In this scheme, a thin gold membrane is offset from the main target by several-hundred microns. A strong picket on the drive beams is incident upon this membrane to produce x rays which generate the initial shock through the target. The main drive follows shortly thereafter, passing through the ablated shell and directly driving the main target. The efficacy of this scheme is demonstrated through experiments performed at the OMEGA EP facility, showing a reduction of the Rayleigh-Taylor instability growth which scales exponentially with frequency, suppressing development by at least a factor of 5 for all wavelengths below 100 $\mu \mathrm{m}$. This results in a delay in the time of target perforation by $\sim 40\%$.

In this paper, we develop an efficient and alternative lattice Boltzmann (LB) model for simulating immiscible incompressible $N$-phase flows $(N\ge 2)$ based on the Cahn-Hilliard phase field theory. In order to facilitate the design of LB model and reduce the calculation of the gradient term, the governing equations of the $N$-phase system are reformulated, and they satisfy the conservation of mass, momentum and the second law of thermodynamics. In the present model, $(N-1)$ LB equations are employed to capture the interface, and another LB equation is used to solve the Navier-Stokes (N-S) equations, where a new distribution function for the total force is delicately designed to reduce the calculation of the gradient term. The developed model is first validated by two classical benchmark problems, including the tests of static droplets and the spreading of a liquid lens, the simulation results show that the current LB model is accurate and efficient for simulating incompressible $N$-phase fluid flows. To further demonstrate the capability of the LB model, two numerical simulations, including dynamics of droplet collision for four fluid phases and dynamics of droplets and interfaces for five fluid phases, are performed to test the developed model. The results show that the present model can successfully handle complex interactions among $N$ $(N\ge 2)$ immiscible incompressible flows.

Based on the notion of quantum trajectory, we present a stochastic theoretical framework for Floquet quantum heat engines. As an application, the large deviation functions of two types of stochastic efficiencies for a two-level Floquet quantum heat engine are investigated. We find that the statistics of one efficiency agree well with the predictions of the universal theory of efficiency fluctuations developed by Verley et al. [Phys. Rev. E 90, 052145 (2014)], whereas the statistics of the other efficiency do not. The reason for this discrepancy is attributed to the lack of fluctuation theorems for the latter type of efficiency.

We consider two aspects in climatic science where bistability between the two stable states of the systems is observed. One is the transition between the glacial and the interglacial period in Earth's glacial cycle. Another is the thermohaline circulation in the North Atlantic ocean. Both of these phenomena can be modeled by the overdamped dynamics of a Brownian particle in a double-well potential subject to periodic forcing. For the former case, the two wells represent two different climates and the periodic forcing is sufficiently weak not to cause a transition between the two states without the effect of the noise. Whereas in case of the latter phenomenon, the two states correspond to the two different conditions of the flow and the strength of the periodic forcing is high enough to give rise to hysteresis in the system. We propose that one important component of the dynamics, short-term fluctuations related to weather, in both of these cases, depends on the current climatic state of the system. This leads to introduction of the state-dependent diffusion coefficients in the dynamics because the diffusion coefficient represents the strength of the fluctuations. We justify our argument by analyzing the ${\delta }^{18}\mathrm{O}$ record for the glacial cycle model. We have shown that this consideration can produce certain features in the dynamics which agree with the real observations in case of both glacial cycles and thermohaline flow.

Field-theoretical calculations performed in an approximation scheme often present a spurious dependence of physical quantities on some unphysical parameters associated with the details of the calculation setup (such as the renormalization scheme or, in perturbation theory, the resummation procedure). In the present article, we propose to reduce this dependence by invoking conformal invariance. Using as a benchmark the three-dimensional Ising model, we show that, within the derivative expansion at order 4, performed in the nonperturbative renormalization group formalism, the identity associated with this symmetry is not exactly satisfied. The calculations which best satisfy this identity are shown to yield critical exponents which coincide to a high accuracy with those obtained by the conformal bootstrap. Additionally, this work gives a strong justification to the success of a widely used criterion for fixing the appropriate renormalization scheme, namely the principle of minimal sensitivity.

We study random walks with stochastic resetting to the initial position on arbitrary networks. We obtain the stationary probability distribution as well as the mean and global first passage times, which allow us to characterize the effect of resetting on the capacity of a random walker to reach a particular target or to explore a finite network. We apply the results to rings, Cayley trees, and random and complex networks. Our formalism holds for undirected networks and can be implemented from the spectral properties of the random walk without resetting, providing a tool to analyze the search efficiency in different structures with the small-world property or communities. In this way, we extend the study of resetting processes to the domain of networks.

In the study of dynamical systems on networks or graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that, instead of microscopic details of the individual nodes or vertices, rather make the influence of the network coupling topology visible. The master stability function is an important such tool to achieve this goal. Here, we generalize the master stability approach to hypergraphs. A hypergraph coupling structure is important as it allows us to take into account arbitrary higher-order interactions between nodes. As, for instance, in the theory of coupled map lattices, we study Laplace-type interaction structures in detail. Since the spectral theory of Laplacians on hypergraphs is richer than on graphs, we see the possibility of different dynamical phenomena. More generally, our arguments provide a blueprint for how to generalize dynamical structures and results from graphs to hypergraphs.

Attraction between the polycyclic aromatic surface elements of carbon nanotubes (CNTs) and the aromatic nucleotides of deoxyribonucleic acid (DNA) leads to reversible adsorption (physisorption) between the two, a phenomenon related to hybridization. We propose a Hamiltonian formulation for the zipper model that accounts for the DNA-CNT interactions and allows for the processing of experimental data, which has awaited an available theory for a decade.

A unique feature of colloid particles and biopolymers is the molecule's intrinsic rigidity characterized by a molecular-level length scale. Under extreme confinement conditions at cellular scales or in nanodevices, these molecules can display orientational ordering accompanied by severe density depletion. Conventional liquid-crystal theories, such as the Oseen-Frank or Landau–de Gennes theories, cannot capture the essential molecular-level properties: the boundary effects, which extend to a distance of the rigidity length scale, and the drastic variations of the inhomogeneous molecular density. Here we show, based on a simple interpretation of the Onsager model, that rodlike molecules in extreme annular confinement produce unusual liquid-crystal defect structures that are independent phases from the patterns usually seen in a weaker confinement environment.

Based on simplifications of previous numerical calculations [H. Graf and H. Löwen, Phys. Rev. E 59, 1932 (1999)], we propose algebraic free energy expressions for the smectic-A liquid crystal phase and the crystal phases of hard spherocylinders. Quantitative agreement with simulations is found for the resulting equations of state. The free energy expressions can be used to straightforwardly compute the full phase behavior for all aspect ratios and to provide a suitable benchmark for exploring how attractive interrod interactions mediate the phase stability through perturbation approaches such as free-volume or van der Waals theory.

Packing of particles in confined environments is a common problem in multiple fields. Here, based on the two-dimensional Hertzian particle model, we study the packing of deformable spherical particles under compression and reveal the crucial role of stress as an ordering field in regulating particle arrangement. Specifically, under increasing compression, the squeezed particles spontaneously organize into regular packings in the sequence of triangular and square lattices, pentagonal tessellation, and the reentrant triangular lattice. The rich ordered patterns and complex structures revealed in this work suggest a fruitful organizational strategy based on the interplay of external stress and intrinsic elastic instability of particle arrays.