Nonlocal Dynamics Research Articles

Nonlinear nucleus-acoustic waves in strongly coupled degenerate quantum plasmas

We report the evolutionary dynamics of nonlinear nucleus-acoustic wave patterns excitable in a strongly coupled self-gravitating complex quantum degenerate plasma (QDP) systems. It is inertially composed of strongly correlated non-degenerate heavy nuclei and weakly coupled degenerate light nuclei treated classically. It is thermally constituted of non-relativistic and ultra-relativistic degenerate lighter electrons behaving quantum mechanically. Application of nonlinear perturbation analysis results in a conjugated pair of extended Korteweg-de Vries (e-KdV) equations of unique mathematical shape. The constructed numerical tapestry shows the collective excitations of a new conjugational pair of nonlinear eigenmode structures of gravito-electrosatic origin. The electrostatic potential fluctuations evolve as a distinct family of stable periodic symmetric waves resembling regular soliton-antisoliton pulse-trains; in contrast, the gravitational counterparts evolve as a unique extended class of asymmetric oscillatory solitons and non-monotonous compressive dispersive asymmetric pulse-trains. The microphysical influential dependencies of the eigenstructural patterns on various sensible plasma multi-parametric factors are illustratively analyzed in both the non-relativistic (NR) and ultra-relativistic (UR) limits of the non-local quantum electronic dynamics. The applicability of the explored results in wave kinetic phenomenological processes naturalistically relevant in diversified compact astro-objects and their ambient hydrodynamic atmospheres is summarily outlined.

Human mobility in bike-sharing systems: Structure of local and non-local dynamics.

The understanding of human mobility patterns in different transportation modes is an interdisciplinary research field with a direct impact in aspects as varied as urban planning, traffic optimization, sustainability, the reduction of operating costs as well as the mitigation of pollution in urban areas. In this paper, we study the global activity of users in bike-sharing systems operating in the cities of Chicago and New York. For this transportation mode, we explore the temporal and spatial characteristics of the mobility of cyclists. In particular, through the analysis of origin-destination matrices, we characterize the spatial structure of the displacements of users. We apply a mobility model for the global activity of the system that classifies the displacements between stations in local and non-local transitions. In local transitions, cyclists move in a region around each station whereas, in the non-local case, bike users travel with long-range displacements in a similar way to Lévy flights. We reproduce the spatial dynamics by using Monte Carlo simulations. The obtained results are similar to the observed in real data and reveal that the model implemented captures important characteristics of the global spatial dynamics in the systems analyzed.

The effect of boundaries and impurity on a system with non-local hop dynamics

We study a one-dimensional lattice model of particles which interact with each other via hard-core repulsion, and which can make long hops in addition to the usual nearest neighbour hopping dynamics. The parameter p gives the probability for long hops and the p = 0 limit leads to the well studied totally asymmetric simple exclusion process (TASEP). The first part of this study describes the combined effect of open boundaries and long hops on the steady state of the system. Apart from the usual low density (LD), high density (HD) and maximum current (MC) phases, the introduction of a finite p leads to a new possibility-an empty road (ER) phase with particles clearing out faster than they enter. The variation in the phase diagram with p is interesting, with the LD and MC phases vanishing at large values of p while the ER and HD phases divide the parameter space into 1/2. In the second part of this study, we look at the combined effect of long hops and static/dynamic impurities. The boundaries are taken to be periodic for simplicity. We see that the system with a static impurity and with 0 < p < 1 shows a phase transition from a shock phase characterised by finite densities on either side of the shock (HD–LD phase) to a phase where the density on one side of the shock is zero (HD-ER phase). We also study the effect of a dynamic impurity, introduced via a slow particle. Here, the system undergoes a phase transition from a homogeneous phase to a shock phase depending on the density, the speed of the particle, as well as the probability p. The shock phase dominates the phase diagram at large values of p. All our studies involve numerical simulations which are supported by mean field theory arguments. The mean field approximation works well qualitatively and correctly identifies the possible phases, while the quantitative agreement with numerics varies, depending on parameter values.

On the nano-structural dependence of nonlocal dynamics and its relationship to the upper limit of nonlocal scale parameter

Nonlocal elasticity theory is one of the most popular theoretical approaches to investigate the intrinsic scale effect of nano-materials/structures. The coupling of an internal characteristic length and a material parameter can be regarded as a nonlocal scale parameter in nano-meters. The range of this non-dimensional scale parameter is from zero up to different values previously. There is no doubt that the zero nonlocal scale parameter corresponds to a situation without any nonlocal effect. However, the determination of a peak value for the scale parameter is still uncertain. In fact, we frequently ask a simple but unresolved question, i.e., how strong is the nonlocal scale effect? This question is equivalent to what the maximum value of the nonlocal scale parameter is, since it was introduced to characterize the scale effect theoretically. Until now, various maximum values have been selected without rigorous verifications. In this paper, the nano-structural dependence of nonlocal dynamical behavior is investigated to present the existence of an upper limit for the scale parameter. Through three typical examples, the size-dependent behavior of nonlocal dynamics for various nano-structures is analyzed. The upper limit of the scale parameter can be determined accordingly. It is shown that an interval for the scale parameter in the illustrative examples can be found on the basis of the nonlocal softening physical mechanism, in which the equivalent stiffness of nano-structures is weakened than that predicted by the classical continuum theory. The present study contributes to a fuzzy zone in nonlocal elasticity where people are puzzled over the question how to select the upper limit of the nonlocal scale parameter. It is not only beneficial to the refinement of the nonlocal theory of elasticity, and also useful for the exploration of similar theories in nano-mechanics.

Disparity between current and voltage driven capacitively coupled radio frequency discharges

In simulation as well as analytical modeling studies of low-pressure capacitively coupled radio frequency (CCRF) discharges, the assumption of both a driving voltage source or a driving current source is commonly used. It is unclear, however, how and to what extent the choice of the mode of driving, that prescribes either a sinusoidal discharge voltage or a sinusoidal discharge current, itself defines the discharge dynamics that results from these studies. To address this issue, 1d3v cylindrical particle-in-cell/Monte Carlo collisions simulations of asymmetric CCRF discharges are performed in the low pressure regime (p < 2 Pa). We study the nonlocal and nonlinear dynamics of these discharges on a nanosecond timescale. We find that the excitation of the plasma series resonance in the voltage driven case strongly enhances the nonlinear electron power dissipation. However, this resonance is suppressed when a current source is used, because the excitation of harmonics in the RF current is not allowed. Consequently, significant differences between both driving sources are observed in the plasma density as well as in the electron and the power coupling dynamics. We conclude that caution is advised in comparisons between simulations and experiments, as in the former the discharge dynamics is partly defined by the method of driving of the plasma source, while in the latter the addressed resonance phenomena are inherently present at low pressures, since experiments are typically voltage driven.

Kinetic temperature relaxation and nonequilibrium fluctuations in two-dimensional Lennard–Jones systems during nonstationary heat transfer

The kinetic temperature fluctuations in two-dimensional Lennard–Jones systems are compared under equilibrium and nonequilibrium conditions. The calculated relaxation times of the kinetic temperature to the steady state are of the order of 10−11 s and their values decrease with the energy increasing. It is shown that the distribution functions of the relative fluctuations have the form of Gaussian type, the dispersion in a nonsteady state is more than in a steady one. The characteristic times of the fluctuations decay to the steady state levels are in agreement with the typical characteristic times of nonlocal molecular dynamics models describing nonstationary heat transfer.

Violation of Mermin–Ardehali–Belinksii–Klyshko inequality in the three-Jaynes–Cummings model

ABSTRACTIn this paper, we consider the situation that three identical two-level atoms are separately trapped in the three single-mode cavities. Each atom resonantly interacts with cavity via a one-photon hopping. The dynamics of nonlocality in the system is investigated via Mermin–Ardehali–Belinksii–Klyshko inequality. The results show that when three atoms are initially in W state and three-cavity fields are in vacuum states both the quantum state of three atoms and that of three cavities all display nonlocality On the other hand, when three atoms are initially in Greenberger–Horne–Zeilinger state and three-cavity fields are in vacuum states, the quantum state of three atoms and that of three cavities all do not display nonlocality.

Nonlocality and local causality in the Schrödinger equation with time-dependent boundary conditions

We investigate the nonlocal dynamics of a single particle placed in an infinite well with moving walls. It is shown that in this situation, the Schrödinger equation (SE) violates local causality by causing instantaneous changes in the probability current everywhere inside the well. This violation is formalized by designing a gedanken faster-than-light communication device which uses an ensemble of long narrow cavities and weak measurements to resolve the weak value of the momentum far away from the movable wall. Our system is free from the usual features causing nonphysical violations of local causality when using the (nonrelativistic) SE, such as instantaneous changes in potentials or states involving arbitrarily high energies or velocities. We explore in detail several possible artifacts that could account for the failure of the SE to respect local causality for systems involving time-dependent boundary conditions.

Dynamics of measurement-induced nonlocality under decoherence

Measurement Induced Nonlocality (MIN) captures nonlocal effects of a quantum state due to local von Neumann projective measurements, is a bonafide measure of quantum correlation between constituents of a composite system. In this paper, we study the dynamical behavior of entanglement (measured by concurrence), Hilber-Schmidt MIN and fidelity based MIN (FMIN) under local noisy channels such as hybrid (consists of bit, phase, bit and phase flip), generalized amplitude damping (GAD) and depolarizing channels for the initial Bell diagonal state. We observed that while sudden death of entanglement occur in hybrid and GAD channels, MIN and FMIN are more robust against such noise. Finally, we demonstrate the revival of MIN and FMIN after a dark point of time against depolarizing noise.

Asymptotic scale-dependent stability of surface quasi-geostrophic vortices: semi-analytic results

ABSTRACTThe scale-dependent stability of surface quasi-geostrophic (SQG) vortices is studied both analytically and numerically. In particular, we study the sensitivity of the stability of SQG vortices on a nondimensional number , namely the square root of the Burger number, which sets the transition scale between different dynamical regimes corresponding to local and nonlocal dynamics. We analyse the stability of two different examples. The first example is given by a Rankine vortex, characterised by constant buoyancy. For this case, asymptotic analysis suggests that the frequencies of the perturbations at scales smaller than the transition scale show a dependence. At scales larger than the transition scale, the frequencies scale instead like . The second example consists of a Rankine vortex shielded by a filament characterised by a different value of constant buoyancy. For this example we study the dispersion relation for the perturbations for the cases in which the inner vortex and the outer filament have different asymptotic properties behaviour.

Analysis of Local Dynamics of Difference and Close to Them Differential-Difference Equations

We study the local dynamics of one class of nonlinear difference equations which is important for applications. Using perturbation theory methods, we construct sets of singularly perturbed differential-difference equations that are close (in a sense) to initial difference equations. For the problem on the stability of the zero equilibrium state and for certain infinite-dimensional critical cases, we propose a method that allows us to construct analogs of normal forms. We mean special nonlinear boundary value problems without small parameters, whose nonlocal dynamics describes the structure of solutions to initial equations in a small neighborhood of the equilibrium state. We show that dynamic properties of difference and close to them differential-difference equations considerably differ.

Multistability in a system of two coupled oscillators with delayed feedback

In this paper, nonlocal dynamics of a system of two differential equations with a compactly supported nonlinearity and delay is studied. For some set of initial conditions asymptotics of solutions of considered system is constructed. By this asymptotics we build a special mapping. Dynamics of this mapping describes dynamics of initial system in general: it is proved that stable cycles of this mapping correspond to exponentially orbitally stable relaxation periodic solutions of initial system of delay differential equations. It is shown that amplitude, period of solutions of initial system, and number of coexisting stable solutions depend crucially on coupling parameter. Algorithm for constructing many coexisting stable solutions is described.

Nonlocal and Light Cone Dynamics Emergent from Information-Propagating Complete Graph

Nonlocal and Light Cone Dynamics Emergent from Information-Propagating Complete Graph

Stress-point method for stabilizing zero-energy modes in non-ordinary state-based peridynamics

Non-ordinary state–based peridynamics is a promising continuum mechanics theory that combines non-local dynamics with conventional material models. Within this theory, the correspondence principle can be invoked to compute deformation gradients from the computed displacement fields. However, correspondence based models are prone to a zero-energy mode. This paper proposes the use of stress points to resolve this issue in the peridynamic family with nearest-neighbor discretizations. Each particle horizon is assigned with stress points at which derivatives of field variables are computed. The method is first demonstrated in a simple 1D problem and is compared with the analytical solution and other control methods. 2D and 3D examples are compared with the finite-element method. Zero-energy modes are shown to be completely damped in all cases. The computation efficiency of the explicit stress-point based peridynamic model is analyzed in the end.

Does vibration amplitude influence the evaluation of nonlocal small scale parameter of single layered graphene sheets?

ABSTRACTThis study aims to evaluate the nonlocal small scale parameter for large amplitude vibration of single layered graphene sheets (SLGSs) comparing nonlinear resonant frequencies obtained via nonlocal continuum and molecular dynamics (MD) simulations. Nonlinear governing equations of motion are numerically solved employing the pseudo-spectral method to obtain the frequency response. Results reveal that the calibrated small scale parameter decreases when the vibration amplitude increases. Also, from MD simulations it is seen that for all length sizes after an ultimate vibration amplitude around 31% length size, the graphene sheets start to fracture.

Nucleation and propagation of thermomagnetic avalanches in thin-film superconductors (Review Article)

Stability of the vortex matter—magnetic flux lines penetrating into the material—in type-II superconductor films is crucially important for their application. If some vortices get detached from pinning centres, the energy dissipated by their motion will facilitate further depinning, and may trigger an electromagnetic breakdown. In this paper, we review recent theoretical and experimental results on development of the above mentioned thermomagnetic instability. Starting from linear stability analysis for the initial critical-state flux distribution we then discuss a numerical procedure allowing to analyze developed flux avalanches. As an example of this approach we consider ultra-fast dendritic flux avalanches in thin superconducting disks. At the initial stage the flux front corresponding to the dendrite's trunk moves with velocity up to 100 km/s. At later stage the almost constant velocity leads to a specific propagation regime similar to ray optics. We discuss this regime observed in superconducting films coated by normal strips. Finally, we discuss dramatic enhancement of the anisotropy of the flux patterns due to specific dynamics. In this way we demonstrate that the combination of the linear stability analysis with the numerical approach provides an efficient framework for understanding the ultra-fast coupled nonlocal dynamics of electromagnetic fields and dissipation in superconductor films.

Time-nonlocal kinetic equations, jerk and hyperjerk in plasmas and solar physics

The simulation and analysis of nonlocal effects in fluids and plasmas is an inherently complicated problem due to the massive breadth of physics required to describe the nonlocal dynamics. This is a multi-physics problem that draws upon various miscellaneous fields, such as electromagnetism and statistical mechanics. In this paper we strive to focus on one narrow but motivating mathematical way: the derivation of nonlocal plasma-fluid equations from a generalized nonlocal Liouville derivative operator motivated from Suykens's nonlocal arguments. The paper aims to provide a guideline toward modeling nonlocal effects occurring in plasma-fluid systems by means of a generalized nonlocal Boltzmann equation. The generalized nonlocal equations of fluid dynamics are derived and their implications in plasma-fluid systems are addressed, discussed and analyzed. Three main topics were discussed: Landau damping in plasma electrodynamics, ideal MHD and solar wind. A number of features were revealed, analyzed and confronted with recent research results and observations.

Observation of multi-channel non-local transport in J-TEXT plasmas

In cold pulse experiments in J-TEXT, not only are rapid electron temperature increases in the core observed, but also steep rises in the inner density are found. Moreover, some evidence of acceleration of the core toroidal rotation is also observed during the non-local transport process of electron temperature. These new findings of cold pulse experiments in J-TEXT suggest that turbulence spreading is a possible mechanism for the non-local transport dynamics.

Irreversibility inversions in two-dimensional turbulence

In this paper we consider a recent theoretical prediction (Bragg \emph{et al.}, Phys. Fluids \textbf{28}, 013305 (2016)) that for inertial particles in 2D turbulence, the nature of the irreversibility of the particle-pair dispersion inverts when the particle inertia exceeds a certain value. In particular, when the particle Stokes number, ${\rm St}$, is below a certain value, the forward-in-time (FIT) dispersion should be faster than the backward-in-time (BIT) dispersion, but for ${\rm St}$ above this value, this should invert so that BIT becomes faster than FIT dispersion. This non-trivial behavior arises because of the competition between two physically distinct irreversibility mechanisms that operate in different regimes of ${\rm St}$. In 3D turbulence, both mechanisms act to produce faster BIT than FIT dispersion, but in 2D turbulence, the two mechanisms have opposite effects because of the flux of energy from the small to the large scales. We supplement the qualitative argument given by Bragg \emph{et al.} (Phys. Fluids \textbf{28}, 013305 (2016)) by deriving quantitative predictions of this effect in the short time limit. We confirm the theoretical predictions using results of inertial particle dispersion in a direct numerical simulation of 2D turbulence. A more general finding of this analysis is that in turbulent flows with an inverse energy flux, inertial particles may yet exhibit a net downscale flux of kinetic energy because of their non-local in-time dynamics.

Surface Freshwater Limitation Explains Worst Rice Production Anomaly in India in 2002

India is the second-most populous country and the second-most important producer of rice of the world. Most Indian rice production depends on monsoon timing and dynamics. In 2002, the lowest monsoon precipitation of the last 130+ years was observed. It coincided with the worst rice production anomaly recorded by FAOSTAT from 1961 to 2014. In that year, freshwater limitation was blamed as responsible for the yield losses in the southeastern coastal regions. Given the important implication for local food security and international market stability, we here investigate the specific mechanisms behind the effects of this extreme meteorological drought on rice yield at the national and regional levels. To this purpose, we integrate output from the hydrological model, surface, and satellite observations for the different rice cropping cycles into state-of-the-art and novel climate indicators. In particular, we adopt the standardized precipitation evapotranspiration index (SPEI) as an indicator of drought due to the local surface water balance anomalies (i.e., precipitation and evapotranspiration). We propose a new indicator of the renewable surface freshwater availability due to non-local sources, i.e., the standardized river discharge index (SDI) based on the anomalies of modelled river discharge data. We compare these indicators to the soil moisture observations retrieved from satellites. We link all diagnostics to the recorded yields at the national and regional level, quantifying the long-term correlations and the best match of the 2002 anomaly. Our findings highlight the need for integrating non-local surface freshwater dynamics with local rainfall variability to determine the soil moisture conditions in rice fields for yields assessment, modeling, and forecasting.