We study the non-Hermitian Hofstadter dynamics of a quantum particle with biased motion on a square lattice in the background of a magnetic field. We show that in quasimomentum space, the energy spectrum is an overlap of infinitely many inequivalent fractals. The energy levels in each fractal are space-filling curves with Hausdorff dimension 2. The band structure of the spectrum is similar to a fractal spider web in contrast to the Hofstadter butterfly for unbiased motion.

Selective energy transport throughout a quantum network connected to more than one reaction center can play an important role in many natural and technological considerations in photosystems. In this work, we propose a method in which an excitation can be transported from the original site of the network to one of the reaction centers arbitrarily using independent sources of dephasing noises. We demonstrate that in the absence of dephasing noises, the coherent evolution of the system does not have any role in energy transport in the network. Therefore, incoherent evolution via application of dephasing noises throughout a selected path of the network leads to complete transferring of the excitation to a desired reaction center.

In analogy to Brownian computers we explicitly show how to construct stochastic models which mimic the behavior of a general-purpose computer (a Turing machine). Our models are discrete state systems obeying a Markovian master equation, which are logically reversible and have a well-defined and consistent thermodynamic interpretation. The resulting master equation, which describes a simple one-step process on an enormously large state space, allows us to thoroughly investigate the thermodynamics of computation for this situation. Especially in the stationary regime we can well approximate the master equation by a simple Fokker-Planck equation in one dimension. We then show that the entropy production rate at steady state can be made arbitrarily small, but the total (integrated) entropy production is finite and grows logarithmically with the number of computational steps.

We develop a generating functional description of the dynamics of non-Markovian individual-based systems in which delay reactions can be terminated before completion. This generalizes previous work in which a path-integral approach was applied to dynamics in which delay reactions complete with certainty. We construct a more widely applicable theory, and from it we derive Gaussian approximations of the dynamics, valid in the limit of large, but finite, population sizes. As an application of our theory we study predator-prey models with delay dynamics due to gestation or lag periods to reach the reproductive age. In particular, we focus on the effects of delay on noise-induced cycles.

Models of three-dimensional space filling based on growth of two-dimensional sheets are proposed. Beginning from planar Eden-style growth of sheets, additional growth modes are introduced. These enable the sheets to form layered or disordered structures. The growth modes can also be combined. An off-lattice kinetic Monte Carlo–based computer algorithm is presented and used to study the kinetics of the new models and the resulting structures. It is possible to study space filling by two-dimensional growth in a three-dimensional domain with arbitrarily oriented sheets; the results agree with previously published models where the sheets are only able to grow in a limited set of directions. The introduction of a bifurcation mechanism gives rise to complex disordered structures that are of interest as model structures for the mesostructure of calcium silicate hydrate in hardened cement paste.

We study the critical behavior of the Sherrington-Kirkpatrick model in transverse field (at finite temperature) using Monte Carlo simulation and exact diagonalization (at zero temperature). We determine the phase diagram of the model by estimating the Binder cumulant. We also determine the correlation length exponent from the collapse of the scaled data. Our numerical studies here indicate that critical Binder cumulant (indicating the universality class of the transition behavior) and the correlation length exponent cross over from their “classical” to “quantum” values at a finite temperature (unlike the cases of pure systems, where such crossovers occur at zero temperature). We propose a qualitative argument supporting such an observation, employing a simple tunneling picture.

We compute statistical properties of the stochastic entropy production associated with the nonstationary transport of heat through a system coupled to a time dependent nonisothermal heat bath. We study the one-dimensional stochastic evolution of a bound particle in such an environment by solving the appropriate Langevin equation numerically, and by using an approximate analytic solution to the Kramers equation to determine the behavior of an ensemble of systems. We express the total stochastic entropy production in terms of a relaxational or nonadiabatic part together with two components of housekeeping entropy production and determine the distributions for each, demonstrating the importance of all three contributions for this system. We compare the results with an approximate analytic model of the mean behavior and we further demonstrate that the total entropy production and the relaxational component approximately satisfy detailed fluctuation relations for certain time intervals. Finally, we comment on the resemblance between the procedure for solving the Kramers equation and a constrained extremization, with respect to the probability density function, of the spatial density of the mean rate of production of stochastic entropy.

We study the bidimensional voter model on a square lattice with numerical simulations. We demonstrate that the evolution takes place in two distinct dynamic regimes; a first approach towards critical site percolation and a further approach towards full consensus. We calculate the time dependence of the two growing lengths, finding that they are both algebraic but with different exponents (apart from possible logarithmic corrections). We analyze the morphology and statistics of clusters of voters with the same opinion. We compare these results to the ones for curvature driven two-dimensional coarsening.

We study the active to absorbing phase transition (AAPT) in a simple two-component model system for a species and its mutant. We uncover the nontrivial critical scaling behavior and weak dynamic scaling near the AAPT that shows the significance of mutation and highlights the connection of this model with the well-known directed percolation universality class. Our model should be a useful starting point to study how mutation may affect extinction or survival of a species.

When playing games in groups, it is an advantage for individuals to have accurate statistical information on the strategies of their opponents. Such information may be obtained by remembering previous interactions. We consider a rock-paper-scissors game in which agents are able to recall their last $m$ interactions, used to estimate the behavior of their opponents. At critical memory length, a Hopf bifurcation leads to the formation of stable limit cycles. In a mixed population, agents with longer memories have an advantage, provided the system has a stable fixed point, and there is some asymmetry in the payoffs of the pure strategies. However, at a critical concentration of long memory agents, the appearance of limit cycles destroys their advantage. By introducing population dynamics that favors successful agents, we show that the system evolves toward the bifurcation point.

The viscosity of fluids is generally understood in terms of kinetic mechanisms, i.e., particle collisions, or thermodynamic ones as imposed through structural distortions upon, e.g., applying shear. Often the latter are more relevant, which allows a simpler theoretical description, and, e.g., (damped) Brownian particles can be considered good fluid model systems. We formulate a general theoretical approach for rheology in confinement, based on microscopic equations of motion and classical density functional theory. Specifically, we discuss the viscosity for the case of two parallel walls in relative motion as a function of the wall-to-wall distance, analyzing its relation to the slip length found for a single wall. The previously observed [A. A. Aerov and M. Krüger, J. Chem. Phys. 140, 094701 (2014).] deficiency of inhomogeneous (unphysical) stresses under naive application of shear in confinement is healed when hydrodynamic interactions are included.

We present a sharp-interface model of two-dimensional ramified growth during quasisteady electrodeposition. Our model differs from previous modeling methods in that it includes the important effects of extended space-charge regions and nonlinear electrode reactions. The electrokinetics is described by a continuum model, but the discrete nature of the ions is taken into account by adding a random noise term to the electrode current. The model is validated by comparing its behavior in the initial stage with the predictions of a linear stability analysis. The main limitations of the model are the restriction to two dimensions and the assumption of quasisteady transport.

Due to elastic anisotropy, two-dimensional patterning of substrates can promote weak azimuthal alignment of adjacent nematic liquid crystals. Here we consider how such alignment can be achieved using a periodic square lattice of circular or elliptical motifs. In particular, we examine ways in which the lattice and motif can combine to favor differing orientations. Using Monte Carlo simulation and continuum elasticity we find, for circular motifs, that the coverage fraction controls both the polar anchoring angle and a transition in the azimuthal orientation. If the circles are generalized to ellipses, arbitrary control of the effective easy axis and effective anchoring potential becomes achievable by appropriate tuning of the ellipse motif relative to the periodic lattice patterning. This has possible applications in both monostable and bistable liquid crystal device contexts.

The activity of pancreatic $\beta$ cells can be described by biological networks of coupled nonlinear oscillators that, via electrochemical synchronization, release insulin in response to augmented glucose levels. In this work, we analyze the emergent behavior of regular and percolated $\beta$-cells clusters through a stochastic mathematical model where “functional” networks arise. We show that the emergence and robustness of the synchronized dynamics depend both on intrinsic and extrinsic parameters. In particular, cellular noise level, glucose concentration, network spatial architecture, and cell-to-cell coupling strength are the key factors for the generation of a rhythmic and robust activity. Their role in the functional network topology associated with $\beta$-cells clusters is analyzed and discussed.

We perform a comprehensive analysis of the spectral statistics of the molecular resonances in ${}^{166}\mathrm{Er}$ and ${}^{168}\mathrm{Er}$ observed in recent ultracold collision experiments [Frisch et al., Nature (London) 507, 475 (2014)] with the aim of determining the chaoticity of this system. We calculate different independent statistical properties to check their degree of agreement with random matrix theory (RMT), and analyze if they are consistent with the possibility of having missing resonances. The analysis of the short-range fluctuations as a function of the magnetic field points to a steady increase of chaoticity until $B\sim 30$ G. The repulsion parameter decreases for higher magnetic fields, an effect that can be interpreted as due to missing resonances. The analysis of long-range fluctuations allows us to be more quantitative and estimate a $20\%–25\%$ fraction of missing levels. Finally, a study of the distribution of resonance widths provides additional evidence supporting missing resonances of small width compared with the experimental magnetic field resolution. We conclude that further measurements with increased resolution will be necessary to give a final answer to the problem of missing resonances and the agreement with RMT.

We consider an Ehrenfest approximation for a particle in a double-well potential in the presence of an external environment schematized as a finite resource heat bath. This allows us to explore how the limitations in the applicability of Ehrenfest dynamics to nonlinear systems are modified in an open system setting. Within this framework, we have identified an environment-induced spontaneous symmetry breaking mechanism, and we argue that the Ehrenfest approximation becomes increasingly valid in the limit of strong coupling to the external reservoir, either in the form of an increasing number of oscillators or increasing temperature. The analysis also suggests a rather intuitive picture for the general phenomenon of quantum tunneling and its interplay with classical thermal activation processes, which may be of relevance in physical chemistry, ultracold atom physics, and fast-switching dynamics such as in superconducting digital electronics.

We study a stochastic dynamics of systems with hard excitement of auto-oscillations possessing a bistability mode with coexistence of the stable equilibrium and limit cycle. A principal difference in the results of the impact of additive and parametric random disturbances is shown. For the stochastic van der Pol oscillator with increasing parametric noise, qualitative transformations of the probability density function form “crater”-“$\mathrm{peak}+\mathrm{crater}$”-“peak” are demonstrated by numerical simulation. An analytical investigation of such $\mathrm{P}$ bifurcations is carried out for the stochastic Hopf-like model with hard excitement of self-oscillations. A detailed parametric description of the response of this model on the additive and multiplicative noise and corresponding stochastic bifurcations are presented and discussed.

A theoretical model is developed that describes nonlinear spherical pulsations and translational motions of two interacting bubbles at arbitrary separation distances between the bubbles. The derivation of the model is based on the multipole expansion of the bubble velocity potentials and the use of the Lagrangian formalism. The model consists of four coupled ordinary differential equations. Two of them are modified Rayleigh-Plesset equations for the radial oscillations of the bubbles and the other two describe the translational displacement of the bubble centers. The equations are not subject to the assumption that the distance between the bubbles is large compared to the bubble radii and hence make it possible to simulate the bubble dynamics starting from large separation distances up to contact between the bubbles providing that the deviation of the bubble shape from sphericity is negligible. Numerical simulations are carried out to demonstrate the capabilities of the developed model. It is shown that the correct modeling of the translational dynamics of the bubbles at small separation distances requires terms accurate up to ninth order in the inverse separation distance. Physical mechanisms are analyzed that lead to the change of the direction of the relative translational motion of the bubbles in finite-amplitude acoustic fields.

We conduct numerical experiments on spreading of viscoelastic droplets on a flat surface. Our work considers a Giesekus fluid characterized by a shear-thinning viscosity and an Oldroyd-B fluid, which is close to a Boger fluid with constant viscosity. Our results qualitatively agree with experimental observations in that both shear thinning and elasticity enhances contact line motion, and that the contact line motion of the Boger fluid obeys the Tanner-Voinov-Hoffman relation. Excluding inertia, the spreading speed shows strong dependence on rheological properties, such as the viscosity ratio between the solvent and the polymer suspension, and the polymeric relaxation time. We also discuss how elasticity can affect contact line motion. The molecular migration theory proposed in the literature is not able to explain the agreement between our simulations and experimental results.

This paper is concerned with the evaluation of two Lagrangian measures which arise in oscillatory or fluctuating shear flows when the fluctuating field is rotational and the spectrum of wave numbers which comprise it is continuous. The measures are the drift and pseudomomentum. Phillips [J. Fluid Mech. 430, 209 (2001)] has shown that the measures are, in such instances, succinctly expressed in terms of Lagrangian integrals of Eulerian space-time correlations. But they are difficult to interpret, and the present work begins by expressing them in a more insightful form. This is achieved by assuming the space-time correlations are separable as magnitude, determined by one-point velocity correlations, and spatial diminution. The measures then parse into terms comprised of the mean Eulerian velocity, one-point velocity correlations, and a family of integrals of spatial diminution, which in turn define a series of Lagrangian time and velocity scales. The pseudomomentum is seen to be strictly negative and related to the turbulence kinetic energy, while the drift is mixed and strongly influenced by the Reynolds stress. Both are calculated for turbulent channel flow for a range of Reynolds numbers and appear, as the Reynolds number increases, to approach a terminal form. At all Reynolds numbers studied, the pseudomomentum has a sole peak located in wall units in the low teens, while at the highest Reynolds number studied, ${\mathrm{Re}}_{\tau }=5200$, the drift is negative in the vicinity of that peak, positive elsewhere, and largest near the rigid boundary. In contrast, the time and velocity scales grow almost logarithmically over much of the layer. Finally, the drift and pseudomomentum are discussed in the context of coherent wall layer structures with which they are intricately linked.