Two stable dynamical states of trajectories of an underdamped particle, under appropriate conditions, appear naturally in a sinusoidal potential when driven by a low-amplitude biharmonic external field. These states are quite stable at low temperatures but make transitions between them as the temperature is raised. The proper choice of the biharmonic drive makes it possible for the system to show, at the same time, both the phenomena of stochastic resonance and the ratchet effect. The ratchet effect, in this case a consequence of the biharmonic drive, is obtained over a large domain of parameter space. However, stochastic resonance can be obtained only over a restricted (sub)domain of parameter space, and it owes its existence largely to the existence of the two dynamical states.

We propose an alternative conceptual design for a graphene-based quantum engine, driven by a superposition of mechanical strain and an external magnetic field. Engineering of strain in a nanoscale graphene flake creates a gauge field with an associated uniform pseudomagnetic field. The strain-induced pseudomagnetic field can be combined with a real magnetic field, leading to the emergence of discrete relativistic Landau levels within the single-particle picture. The interlevel distance and hence their statistical population can be modulated by quasistatically tuning the magnetic field along a sequence of reversible transformations that constitute a quantum mechanical analog of the classical Otto cycle.

We have studied the presence of plateaus on the low-temperature magnetization of an antiferromagnetic spin-1 chain, as an external uniform magnetic field is varied. A crystal-field interaction is present in the model and the exchange constants follow a random quenched (Bernoulli or Gaussian) distribution. Using a transfer-matrix technique we calculate the largest Lyapunov exponent and, from it, the magnetization at low temperatures as a function of the magnetic field, for different values of the crystal field and the width of the distributions. For the Bernoulli distribution, the number of plateaus increases, with respect to the uniform case [Litaiff et al., Solid State Commun. 147, 494 (2008)] and their presence can be linked to different ground states, when the magnetic field is varied. For the Gaussian distributions, the uniform scenario is maintained, for small widths, but the plateaus structure disappears as the width increases.

On the Moon, water molecules and other volatiles are thought to migrate along ballistic trajectories. Here, this migration process is described in terms of a two-dimensional partial differential equation for the surface concentration, based on the probability distribution of thermal ballistic hops. A random-walk model, a corresponding diffusion coefficient, and a continuum description are provided. In other words, a surface-bounded exosphere is described purely in terms of quantities on the surface, which can provide computational and conceptual advantages. The derived continuum equation can be used to calculate the steady-state distribution of the surface concentration of volatile water molecules. An analytic steady-state solution is obtained for an equatorial ring; it reveals the width and mass of the pileup of molecules at the morning terminator.

Small-angle neutron scattering (SANS) and dynamic light scattering (DLS) studies have been carried out to investigate the effect of an electrolyte on the phase behavior of anionic silica nanoparticles with two globular proteins—cationic lysozyme [molecular weight (MW) 14.7 kDa] and anionic bovine serum albumin (MW 66.4 kDa). The results are compared with our earlier published work on similar systems without any electrolyte [I. Yadav, S. Kumar, V. K. Aswal, and J. Kohlbrecher, Phys. Rev. E 89, 032304 (2014)]. Both the nanoparticle-protein systems transform to two phase at lower concentration of protein in the presence of an electrolyte. The autocorrelation function in DLS suggests that the diffusion coefficient (D) of a nanoparticle-protein system decreases in approaching two phase with the increase in protein concentration. This variation in D can be attributed to increase in attractive interaction and/or overall increase in the size. Further, these two contributions (interaction and structure) are determined from the SANS data. The changes in the phase behavior of nanoparticle-protein systems in the presence of an electrolyte are explained in terms of modifications in both the repulsive and attractive components of interaction between nanoparticles. In a two-phase system individual silica nanoparticles coexist along with their fractal aggregates.

We present a probabilistic cellular automaton (PCA) model to study solid-on-solid interface growth in which the transition rules depend on the local morphology of the profile obtained from the interface representation of the PCA. We show that the model is able to reproduce a wide range of patterns whose critical roughening exponents are associated to different universality classes, including random deposition, Edwards-Wilkinson, and Kardar-Parisi-Zhang. By means of the growth exponent method, we consider a particular set of the model parameters to build the two-dimensional phase diagram corresponding to a planar cut of the higher dimensional parameter space. A strong indication of phase transition between different universality classes can be observed, evincing different regimes of deposition, from layer-by-layer to Volmer-Weber and Stransk-Krastanov-like modes. We expect that this model can be useful to predict the morphological properties of interfaces obtained at different surface deposition problems, since it allows us to simulate several experimental situations by setting the values of the specific transition probabilities in a very simple and direct way.

One of the most important issues in spatial ecology is to understand how spatial synchrony and dispersal-induced stability interact. In the existing studies it is shown that dispersion among identical patches results in spatial synchrony; on the other hand, the combination of spatial heterogeneity and dispersion is necessary for dispersal-induced stability (or temporal stability). Population synchrony and temporal stability are thus often thought of as conflicting outcomes of dispersion. In contrast to the general belief, in this present study we show that mean-field dispersion is conducive to both spatial synchrony and dispersal-induced stability even in identical patches. This simultaneous occurrence of rather conflicting phenomena is governed by the suppression of oscillation states, namely amplitude death (AD) and oscillation death (OD). These states emerge through spatial synchrony of the oscillating patches in the strong-coupling strength. We present an interpretation of the mean-field diffusive coupling in the context of ecology and identify that, with increasing mean-field density, an open ecosystem transforms into a closed ecosystem. We report on the occurrence of OD in an ecological model and explain its significance. Using a detailed bifurcation analysis we show that, depending on the mortality rate and carrying capacity, the system shows either AD or both AD and OD. We also show that the results remain qualitatively the same for a network of oscillators. We identify a new transition scenario between the same type of oscillation suppression states whose geneses differ. In the parameter-mismatched case, we further report on the direct transition from OD to AD through a transcritical bifurcation. We believe that this study will lead to a proper interpretation of AD and OD in ecology, which may be important for the conservation and management of several communities in ecosystems.

We study the stochastic dynamics of a Hodgkin-Huxley neuron model in a regime of coexistent stable equilibrium and a limit cycle. In this regime, noise may suppress periodic firing by switching the neuron randomly to a quiescent state. We show that at a critical value of the injected current, the mean firing rate depends weakly on noise intensity, while the neuron exhibits giant variability of the interspike intervals and spike count. To reveal the dynamical origin of this noise-induced effect, we develop the stochastic sensitivity analysis and use the Mahalanobis metric for this four-dimensional stochastic dynamical system. We show that the critical point of giant variability corresponds to the matching of the Mahalanobis distances from attractors (stable equilibrium and limit cycle) to a three-dimensional surface separating their basins of attraction.

The dual cascade of enstrophy and energy in quasi-two-dimensional turbulence strongly suggests that a viscous but otherwise potential vorticity (PV) conserving system decays selectively toward a state of minimum potential enstrophy. We derive a nonperturbative mean field theory for the dynamics of minimum enstrophy relaxation by constructing an expression for PV flux during the relaxation process. The theory is used to elucidate the structure of anisotropic flows emerging from the selective decay process. This structural analysis of PV flux is based on the requirements that the mean flux of PV dissipates total potential enstrophy but conserves total fluid kinetic energy. Our results show that the structure of PV flux has the form of a sum of a positive definite hyperviscous and a negative or positive viscous transport of PV. Transport parameters depend on zonal flow and turbulence intensity. Turbulence spreading is shown to be related to PV mixing via the link of turbulence energy flux to PV flux. In the relaxed state, the ratio of the PV gradient to zonal flow velocity is homogenized. This homogenized quantity sets a constraint on the amplitudes of PV and zonal flow in the relaxed state. A characteristic scale is defined by the homogenized quantity and is related to a variant of the Rhines scale. This relaxation model predicts a relaxed state with a structure which is consistent with PV staircases, namely, the proportionality between mean PV gradient and zonal flow strength.

The Hasimoto transformation between the classical LIA (local induction approximation, a model approximating the motion of a thin vortex filament) and the nonlinear Schrödinger equation (NLS) has proven very useful in the past, since it allows one to construct new solutions to the LIA once a solution to the NLS is known. In the present paper, the quantum form of the LIA (which includes mutual friction effects) is put into correspondence with a type of complex nonlinear dispersive partial differential equation (PDE) with cubic nonlinearity (similar in form to a Ginsburg-Landau equation, with additional nonlinear terms). Transforming the quantum LIA in such a way enables one to obtain quantum vortex filament solutions once solutions to this dispersive PDE are known. From our quantum Hasimoto transformation, we determine the form and behavior of Stokes waves, a standing one-soliton, traveling waves, and similarity solutions under normal and binormal friction effects. The quantum Hasimoto transformation is useful when normal fluid velocity is relatively weak, so for the case where the normal fluid velocity is dominant we resort to other approaches. We exhibit a number of solutions that exist only in the presence of the normal fluid velocity and mutual friction terms (which would therefore not exist in the limit taken to obtain the classical LIA, decaying into line filaments under such a limit), examples of which include normal fluid driven helices, stationary and propagating topological solitons, and a vortex ring whose radius varies inversely with the normal fluid magnitude. We show that, while chaos may not be impossible under the quantum LIA, it should not be expected to arise from traveling waves along quantum vortex filaments under the quantum LIA formulation.

We have rigorously analyzed the stability of the efficient cell dynamics simulations (CDS) method by making use of the special properties of the local averaging operator $\langle \langle *\rangle \rangle -*$ in matrix form. Besides resolving a theoretical issue that has puzzled many over the past three decades, this analysis has considerable practical value: It relates CDS directly to finite-difference approximations of the Cahn-Hilliard-Cook equations and provides a straightforward recipe for replacing the original two- or three-dimensional (2D or 3D) averaging operators in CDS by an equivalent (in terms of stability) discrete Laplacian with superior isotropy and scaling behavior. As such, we open up a route to suppress the unphysical reflection of the computational grid in CDS results (grid artifacts). We found that proper rescaling of discrete Laplacians, needed to employ them in CDS, is equivalent to introducing a well-chosen time step in CDS. In turn, our analysis provides stability conditions for phase-field simulations based on the Cahn-Hilliard-Cook equations. Subsequently, we have quantitatively compared the isotropy and scaling behavior of several discrete 2D or 3D Laplacians, thereby extending the significance of this work to general field-based methodology. We found that all considered discrete Laplacians have equivalent scaling behavior along the Cartesian directions. In addition, and somewhat surprisingly, known “isotropic” discrete Laplacians, i.e., isotropic up to fourth order in $\left|\mathbf{k}\right|$, become quite anisotropic for larger wave vectors, whereas “less isotropic” discrete Laplacians (second order) are only slightly anisotropic on the whole $\left|\mathbf{k}\right|$ range. We identified a hard limit to the accuracy with which the discrete Laplacian can emulate the two important properties of the optimal (continuum) Laplacian, as an improvement of the isotropy, by introducing additional points to the stencil, will negatively affect the scaling behavior. Within this limitation, the discrete compact Laplacians in the $DnQm$ class known from lattice hydrodynamics, $D2Q9$ in 2D and $D3Q19$ in 3D, are found to be optimal in terms of isotropy. However, by being only slightly anisotropic on the whole range and enabling larger time steps, the discrete Laplacians that relate to the local averaging operator of Oono and Puri (2D) and Shinozaki and Oono (3D) as well as the less familiar 3D discrete $BvV$ Laplacian developed for dynamic density functional theory are valid alternatives.

The effect of shape asymmetry of microswimmers on their adsorption capacity at confining channel walls is studied by a simple dumbbell model. For a shape polarity of a forward-swimming cone, like the stroke-averaged shape of a sperm, extremely long wall retention times are found, caused by a nonvanishing component of the propulsion force pointing steadily into the wall, which grows exponentially with the self-propulsion velocity and the shape asymmetry. A direct duality relation between shape asymmetry and wall curvature is proposed and verified. Our results are relevant for the design microswimmer with controlled wall-adhesion properties. In addition, we confirm that pressure in active systems is strongly sensitive to the details of the particle-wall interactions.

We develop a framework that casts the point water-vegetation dynamics under stochastic rainfall forcing as a continuous-time random walk (CTRW), which yields an evolution equation for the joint probability density function (PDF) of soil-moisture and biomass. We find regime shifts in the steady-state PDF as a consequence of changes in the rainfall structure, which flips the relative strengths of the system attractors, even for the same mean precipitation. Through an effective potential, we quantify the impact of rainfall variability on ecosystem resilience and conclude that amplified rainfall regimes reduce the resilience of water-stressed ecosystems, even if the mean annual precipitation remains constant.

When a binary liquid is confined by a strongly repulsive wall, the local density is depleted near the wall and an interface similar to that between the liquid and its vapor is formed. This analogy suggests that the composition of the binary liquid near this interface should exhibit spatial modulation similar to that near a liquid-vapor interface even if the interactions of the wall with the two components of the liquid are the same. The Guggenheim adsorption relation quantifies the concentrations of two components of a binary mixture near a liquid-vapor interface and qualitatively states that the majority (minority) component enriches the interface for negative (positive) mixing energy if the surface tensions of the two components are not very different. From molecular dynamics simulations of binary mixtures with different compositions and interactions we find that the Guggenheim relation is qualitatively satisfied at wall-induced interfaces for systems with negative mixing energy at all state points considered. For systems with positive mixing energy, this relation is found to be qualitatively valid at low densities, while it is violated at state points with high density where correlations in the liquid are strong. This observation is validated by a calculation of the density profiles of the two components of the mixture using density functional theory with the Ramakrishnan-Yussouff free-energy functional. Possible reasons for the violation of the Guggenheim relation are discussed.

Experimental evidence shows that in gene transcription RNA polymerase has the possibility to be stalled at a certain position of the transcription template. This may be due to the template damage or protein barriers. Once stalled, polymerase may backtrack along the template to the previous nucleotide to wait for the repair of the damaged site, simply bypass the barrier or damaged site and consequently synthesize an incorrect messenger RNA, or degrade and detach from the template. Thus, the effective transcription rate (the rate to synthesize correct product mRNA) and the transcription effectiveness (the ratio of the effective transcription rate to the effective transcription initiation rate) are both influenced by polymerase stalling events. So far, no theoretical model has been given to discuss the gene transcription process including polymerase stalling. In this study, based on the totally asymmetric simple exclusion process, the transcription process including polymerase stalling is analyzed theoretically. The dependence of the effective transcription rate, effective transcription initiation rate, and transcription effectiveness on the transcription initiation rate, termination rate, as well as the backtracking rate, bypass rate, and detachment (degradation) rate when stalling, are discussed in detail. The results showed that backtracking restart after polymerase stalling is an ideal mechanism to increase both the effective transcription rate and the transcription effectiveness. Without backtracking, detachment of stalled polymerase can also help to increase the effective transcription rate and transcription effectiveness. Generally, the increase of the bypass rate of the stalled polymerase will lead to the decrease of the effective transcription rate and transcription effectiveness. However, when both detachment rate and backtracking rate of the stalled polymerase vanish, the effective transcription rate may also be increased by the bypass mechanism.

We analyze how to value future costs and benefits when they must be discounted relative to the present. We introduce the subject for the nonspecialist and take into account the randomness of the economic evolution by studying the discount function of three widely used processes for the dynamics of interest rates: Ornstein-Uhlenbeck, Feller, and log-normal. Besides obtaining exact expressions for the discount function and simple asymptotic approximations, we show that historical average interest rates overestimate long-run discount rates and that this effect can be large. In other words, long-run discount rates should be substantially less than the average rate observed in the past, otherwise any cost-benefit calculation would be biased in favor of the present and against interventions that may protect the future.

We introduce an approach based on algebraic topological methods that allow an accurate characterization of jamming in dynamical systems with queues. As a prototype system, we analyze the traffic of information packets with navigation and queuing at nodes on a network substrate in distinct dynamical regimes. A temporal sequence of traffic density fluctuations is mapped onto a mathematical graph in which each vertex denotes one dynamical state of the system. The coupling complexity between these states is revealed by classifying agglomerates of high-dimensional cliques that are intermingled at different topological levels and quantified by a set of geometrical and entropy measures. The free-flow, jamming, and congested traffic regimes result in graphs of different structure, while the largest geometrical complexity and minimum entropy mark the edge of the jamming region.

This work is divided into two parts. In the first one, a study of radiative properties (such as monochromatic and the Rosseland and Planck mean opacities, monochromatic emissivities, and radiative power loss) and of the average ionization and charge state distribution of xenon plasmas in a range of plasma conditions of interest in laboratory astrophysics and extreme ultraviolet lithography is performed. We have made a particular emphasis in the analysis of the validity of the assumption of local thermodynamic equilibrium and the influence of the atomic description in the calculation of the radiative properties. Using the results obtained in this study, in the second part of the work we have analyzed a radiative shock that propagated in xenon generated in an experiment carried out at the Prague Asterix Laser System. In particular, we have addressed the effect of plasma self-absorption in the radiative precursor, the influence of the radiation emitted from the shocked shell and the plasma self-emission in the radiative precursor, the cooling time in the cooling layer, and the possibility of thermal instabilities in the postshock region.