Finite Time Scale Research Articles

On the reaction of planetary altitudinal frontal zone to climatic changes

This article examines the dynamics of the planetary high-altitude frontal zone in two natural climatic periods of the state of the earth's climate system - the stabilization period and the second wave of global warming. A change in the area and intensity of the altitudinal frontal zone in different climatic periods was found. The planetary altitudinal frontal zone area expands and its intensity decreases from the stabilization period to the second wave of global warming. The climatic change in the area of planetary altitudinal frontal zone is opposite to the seasonal dynamics of this characteristic. Climate change in intensity is similar to seasonal change. The mechanism of action of negative feedback (air temperature - dynamics of the planetary altitudinal frontal zone) is discovered and described. For the first time, negative feedback has been applied to predict climate variability at finite time scales.

Enhanced diffusion in soft-walled channels with a periodically varying curvature.

The motion of particles along channels of finite width is known to be hindered by either the presence of energy barriers along the channel direction or by variations in the width of the channel in the transverse direction (rugged channel). Remarkably, when both features are present, they can interact to produce a counterintuitive result: adding energy barriers to a rugged channel can enhance the rate of diffusion along it. This is the result of competing energetic and entropic effects. Under the approximation of particles instantaneously in equilibrium in the transverse direction, one can tailor the energy barriers to the ruggedness to recover free diffusion. However, such fine-tuning and potentially restrictive approximations are not necessary to observe an enhanced rate of diffusion as we demonstrate by adding a range of (non-fine-tuned) energy barriers to a channel of sinusoidally varying curvature. Furthermore, this was observed to hold for systems with a finite characteristic timescale for motion in the transverse direction, thus, suggesting that the phenomenon lends itself to be exploited for practical applications.

Eruption of the Envelope of Massive Stars by Energy Injection with Finite Duration

A significant fraction of supernovae show signatures of dense circumstellar material (CSM). While multiple scenarios for creating a dense CSM exist, mass eruption due to injection of energy at the base of the outer envelope is a likely possibility. We carry out radiation hydrodynamical simulations of eruptive mass loss from a typical red supergiant progenitor with an initial mass of 15 M ⊙, for the first time focusing on the timescale of the injection as well as energy. We find that not only sufficient injection energy but also sufficient rate of energy injection per unit time, L min ∼ 8 × 1040 erg s−1 in this particular model, is required for eruption of unbound CSM. This result suggests that the energy injection rate needs to be greater than the binding energy of the envelope divided by the dynamical timescale for the eruption. The density profile of the resulting CSM, whose shape was analytically and numerically predicted in the limit of instantaneous energy injection, similarly holds for a finite injection timescale. We discuss our findings in the framework of proposed mass outburst scenarios, specifically wave-driven outbursts and common-envelope ejection.

Scaling of the entropy production rate in a φ^{4} model of active matter.

In active φ^{4} field theories the nonequilibrium terms play an important role in describing active phase separation; however, they are irrelevant, in the renormalization group sense, at the critical point. Their irrelevance makes the critical exponents the same as those of the Ising universality class. Despite their irrelevance, they contribute to a nontrivial scaling of the entropy production rate at criticality. We consider the nonequilibrium dynamics of a nonconserved scalar field φ (Model A) driven out-of-equilibrium by a persistent noise that is correlated on a finite timescale τ, as in the case of active baths. We perform the computation of the density of entropy production rate σ and we study its scaling near the critical point. We find that similar to the case of active Model A, and although the nonlinearities responsible for nonvanishing entropy production rates in the two models are quite different, the irrelevant parameter τ makes the critical dynamics irreversible.

Reaction-path statistical mechanics of enzymatic kinetics.

We introduce a reaction-path statistical mechanics formalism based on the principle of large deviations to quantify the kinetics of single-molecule enzymatic reaction processes under the Michaelis-Menten mechanism, which exemplifies an out-of-equilibrium process in the living system. Our theoretical approach begins with the principle of equal a priori probabilities and defines the reaction path entropy to construct a new nonequilibrium ensemble as a collection of possible chemical reaction paths. As a result, we evaluate a variety of path-based partition functions and free energies by using the formalism of statistical mechanics. They allow us to calculate the timescales of a given enzymatic reaction, even in the absence of an explicit boundary condition that is necessary for the equilibrium ensemble. We also consider the large deviation theory under a closed-boundary condition of the fixed observation time to quantify the enzyme-substrate unbinding rates. The result demonstrates the presence of a phase-separation-like, bimodal behavior in unbinding events at a finite timescale, and the behavior vanishes as its rate function converges to a single phase in the long-time limit.

Bistability of the large-scale dynamics in quasi-two-dimensional turbulence

In many geophysical and astrophysical flows, suppression of fluctuations along one direction of the flow drives a quasi-two-dimensional upscale flux of kinetic energy, leading to the formation of strong vortex condensates at the largest scales. Recent studies have shown that the transition towards this condensate state is hysteretic, giving rise to a limited bistable range in which both the condensate state as well as the regular three-dimensional state can exist at the same parameter values. In this work, we use direct numerical simulations of thin-layer flow to investigate whether this bistable range survives as the domain size and turbulence intensity are increased. By studying the time scales at which rare transitions occur from one state into the other, we find that the bistable range grows as the box size and/or Reynolds number$Re$are increased, showing that the bistability is neither a finite-size nor a finite-$Re$effect. We furthermore predict a cross-over from a bimodal regime at low box size, low$Re$to a regime of pure hysteresis at high box size, high$Re$, in which any transition from one state to the other is prohibited at any finite time scale.

Revisiting the averaged problem in the case of mean-motion resonances in the restricted three-body problem

A classical approach to the restricted three-body problem is to analyze the dynamics of the massless body in the synodic reference frame. A different approach is represented by the perturbative treatment: in particular the averaged problem of a mean-motion resonance allows to investigate the long-term behavior of the solutions through a suitable approximation that focuses on a particular region of the phase space. In this paper, we intend to bridge a gap between the two approaches in the specific case of mean-motion resonant dynamics, establish the limit of validity of the averaged problem and take advantage of its results in order to compute trajectories in the synodic reference frame. After the description of each approach, we develop a rigorous treatment of the averaging process, estimate the size of the transformation and prove that the averaged problem is a suitable approximation of the restricted three-body problem as long as the solutions are located outside the Hill’s sphere of the secondary. In such a case, a rigorous theorem of stability over finite but large timescales can be proven. We establish that a solution of the averaged problem provides an accurate approximation of the trajectories on the synodic reference frame within a finite time that depend on the minimal distance to the Hill’s sphere of the secondary. The last part of this work is devoted to the co-orbital motion (i.e., the dynamics in 1:1 mean-motion resonance) in the circular-planar case. In this case, an interpretation of the solutions of the averaged problem in the synodic reference frame is detailed and a method that allows to compute co-orbital trajectories is displayed.

Two-fluid model for a fluid with tetrahedral-octupolar order.

We investigate the macroscopic dynamics of a two-fluid system with tetrahedral order. As all normal-fluid two-fluid systems one has-compared to a simple fluid-the velocity difference between the two subsystems and the concentration of one component as additional macroscopic variables. Depending on the type of system, the concentration can either be a conserved quantity or relax on a long, but finite timescale. Due to the existence of the tetrahedral order such a system breaks parity symmetry. Here we discuss physical systems without preferred direction in real space, meaning that our description applies to optically isotropic materials. We find a number of reversible as well as dissipative dynamic cross-coupling terms due to the additional octupolar order, when compared to a fluid mixture. As the most interesting cross-coupling term from an experimental point of view, we identify a dissipative cross-coupling between the relative velocity and the usual velocity gradients. Applying a shear flow in a plane, this dissipative cross-coupling leads to a velocity difference perpendicular to the shear plane. As a result one can obtain a spatially homogeneous oscillation of the relative velocity. In addition, this induced relative velocity can couple as a function of time and space to the concentration, which gives rise to an overdamped propagating soundlike mode, where the overdamping arises from the fact that velocity difference is a macroscopic variable and not strictly conserved. We also show that electric field gradients are connected with an analogous reversible cross-coupling and can lead in a planar shear geometry to an overdamped propagating mode as well.

Temporal Klein Model for Particle-Pair Creation

This work considers the creation of electron-positron pairs from intense electric fields in vacuum, for arbitrary temporal field variations. These processes can be useful to study quantum vacuum effects with ultra-intense lasers. We use the quantized Dirac field to explore the temporal Klein model. This model is based on a vector potential discontinuity in time, in contrast with the traditional model based on a scalar potential discontinuity in space. We also extend the model by introducing a finite time-scale for potential variations. This allows us to study the transition from a singular electric field spike, with infinitesimal duration, to the opposite case of a static field where the Schwinger formula would apply. The present results are intrinsically non-perturbative. Explicit expressions for pair-creation as a function of the potential time-scales are derived. This work explores the spacetime symmetry associated with pair creation in vacuum: the space symmetry breaking of the old Klein paradox model, in contrast with the time symmetry breaking of the temporal Klein model.

Stumped nature hyperjerk system with fractional order and exponential nonlinearity: Analog simulation, bifurcation analysis and cryptographic applications

This article presents the construction and consumption of hyperjerk system having chaotic nature with the commensurate ordered fractional derivative on rapidly digitalized emerging technologies. The system analyzed analytically using Lipschitz condition and numerically with the help of predictor corrector approaches. Originality of constructed system is confirmed using log error plots which gives satisfactory small values on finite time scale. The dynamical performances of the complex system are termed in multiple phase planes by the mean of their significant nature. Stability and bifurcation analysis around the fractional derivative is also studies for the various parameter of system to check the visibility of chaotic solution. The system is also designed in analog circuit simulator with the aid of operational amplifier, anti-parallel semiconductor diodes for validation of the system. With the help of random number generators (RNGs), binary array generated from the hyperjerk system and plugged in to the NIST 800–22 test suite to measure the randomness. The array having high randomness is used as strong cypher key for the cryptographic execution straightforwardly in both direction encryption and decryption.

Agent-based modeling: Population limits and large timescales.

Modeling, simulation, and analysis of interacting agent systems is a broad field of research, with existing approaches reaching from informal descriptions of interaction dynamics to more formal, mathematical models. In this paper, we study agent-based models (ABMs) given as continuous-time stochastic processes and their pathwise approximation by ordinary and stochastic differential equations (SDEs) for medium to large populations. By means of an appropriately adapted transfer operator approach, we study the behavior of the ABM process on long time scales. We show that, under certain conditions, the transfer operator approach allows us to bridge the gap between the pathwise results for large populations on finite timescales, i.e., the SDE limit model, and approaches built to study dynamical behavior on long time scales like large deviation theory. The latter provides a rigorous analysis of rare events including the associated asymptotic rates on timescales that scale exponentially with the population size. We demonstrate that it is possible to reveal metastable structures and timescales of rare events of the ABM process by finite-length trajectories of the SDE process for large enough populations. This approach has the potential to drastically reduce computational effort for the analysis of ABMs.

Entropy production in model colloidal suspensions under shear via the fluctuation theorem.

Dissipative systems often exhibit novel and unexpected properties. This is, for instance, the case of simple liquids, which, when subjected to shear and after reaching a steady state, can exhibit a negative entropy production over finite length scales and timescales. This result, among others, is captured by nonequilibrium relations known as fluctuation theorems. Using nonequilibrium molecular dynamics simulations, we examine how, by fine-tuning the properties of the components of a complex fluid, we can steer the nonequilibrium response of the fluid. More specifically, we show how we control the nonequilibrium probability distribution for the shear stress and, in turn, how often states with a negative entropy production can occur. To achieve this, we start by characterizing how the size for the liquid matrix impacts the probability of observing negative entropy states, as well as the timescale over which these can be observed. We then measure how the addition of larger particles to this liquid matrix, i.e., simulating a model colloidal suspension, results in an increase in the occurrence of such states. This suggests how modifications in the composition of the mixture and in the properties of its components lead to an increase in the probability of observing states of negative entropy production and, thus, for the system to run in reverse.

Spin-glass magnetism of the non-equiatomic CoCrFeMnNi high-entropy alloy

The CoCrFeMnNi high-entropy alloy (HEA) is a magnetically concentrated crystalline system with all lattice sites magnetic, containing randomness (five different types of spins are randomly positioned on the lattice) and frustration (a consequence of mixed ferromagnetic and antiferromagnetic interactions). The sample material was prepared as a non-equiatomic, fully random solid solution of the five magnetic elements and we have studied experimentally the nature of the magnetic state. Upon cooling, no long-range magnetic ordering takes place, but the spin system undergoes a kinetic freezing transition to a spin glass phase, where below the spin freezing temperature Tf≈ 20 K, ergodicity of the system is broken. The observed broken-ergodicity phenomena include zero-field-cooled – field-cooled magnetization splitting in low magnetic fields, a frequency-dependent cusp in the ac susceptibility, an ultraslow time-decay of the thermoremanent magnetization and the memory effect, where the state of the spin system reached upon isothermal aging at a certain temperature can be retrieved after a reverse temperature cycle. All these phenomena are associated with the out-of-equilibrium dynamics of a nonergodic, frustrated system of coupled spins that approach thermal equilibrium, but can never reach it on a finite experimental time scale, so that we are observing only transient effects of partial equilibration within localized spin domains.

Nonlinear Approximations to Critical and Relaxation Processes

We develop nonlinear approximations to critical and relaxation phenomena, complemented by the optimization procedures. In the first part, we discuss general methods for calculation of critical indices and amplitudes from the perturbative expansions. Several important examples of the Stokes flow through 2D channels are brought up. Power series for the permeability derived for small values of amplitude are employed for calculation of various critical exponents in the regime of large amplitudes. Special nonlinear approximations valid for arbitrary values of the wave amplitude are derived from the expansions. In the second part, the technique developed for critical phenomena is applied to relaxation phenomena. The concept of time-translation invariance is discussed, and its spontaneous violation and restoration considered. Emerging probabilistic patterns correspond to a local breakdown of time-translation invariance. Their evolution leads to the time-translation invariance complete (or partial) restoration. We estimate the typical time extent, amplitude and direction for such a restorative process. The new technique is based on explicit introduction of origin in time as an optimization parameter. After some transformations, we arrive at the exponential and generalized exponential-type solutions (Gompertz approximants), with explicit finite time scale, which is only implicit in the initial parameterization with polynomial approximation. The concept of crash as a fast relaxation phenomenon, consisting of time-translation invariance breaking and restoration, is advanced. Several COVID-related crashes in the time series for Shanghai Composite and Dow Jones Industrial are discussed as an illustration.

Simulations of Asymmetric Membranes Illustrate Cooperative Leaflet Coupling and Lipid Adaptability

Biological membranes are composed of lipid bilayers that are often asymmetric with regards to the lipid composition and/or aqueous solvent they separate. Studying lipid asymmetry both experimentally and computationally is challenging. Molecular dynamics simulations of lipid bilayers with asymmetry are difficult due to finite system sizes and time scales accessible to simulations. Due to the very slow flip-flop rate for phospholipids, one must first choose how many lipids are on each side of the bilayer, but the resulting bilayer may be unstable (or metastable) due to differing tensile and compressive forces between leaflets. Here we use molecular dynamics simulations to investigate a number of different asymmetric membrane systems, both with atomistic and coarse-grained models. Asymmetries studied include differences in number of lipids, lipid composition (unsaturated and saturated tails and different headgroups), and chemical gradients between the aqueous phases. Extensive analysis of the bilayers’ properties such as area per lipid, density, and lateral pressure profiles are used to characterize bilayer asymmetry. We also address how cholesterol (which flip-flops relatively quickly) influences membrane asymmetries. Our results show how each leaflet is influenced by the other and can mitigate the structural changes to the bilayer overall structure. Cholesterol can respond to changes in bilayer asymmetry to alleviate some of the effect on the bilayer structure, but that will alter its leaflet distribution, which in turn affects its chemical potential. Ionic imbalances are shown to have a modest change in bilayer structure, despite large changes in the electrostatic potential. Bilayer asymmetry can also induce a modest electrostatic potential across the membrane. Our results highlight the importance of membrane asymmetry on bilayer properties, the influence of lipid headgroups, tails and cholesterol on asymmetry, and the ability of lipids to adapt to different environments.

Classical dynamics of three-body systems in the Efimov potential

We investigate the classical nonrelativistic dynamics of three bodies in Efimov's $\ensuremath{-}1/{R}^{2}$ potential in three spatial dimensions, with a view towards semiclassical quantization and insight into the geometry of Efimov states. Without the short-distance cutoff, these dynamics are superintegrable, which allows an exact integration of the equations of motion for arbitrary initial conditions. We show that periodic orbits necessarily lead to exactly vanishing binding energy of the bound states, in disagreement with Efimov's quantum-mechanical results. A scaling anomaly demands that the quantum dynamics of three bodies in this potential be augmented by additional boundary conditions affecting all three particles at the short-distance cutoff point, i.e., near the triple collision. We discuss the inherent difficulties in the definition of appropriate three-body boundary conditions in three spatial dimensions and briefly discuss their consequences for (quasi)periodic orbits. Consequently, the classical orbits corresponding to Efimov states cannot be exactly periodic, but must have a finite timescale (lifetime), associated with the time it takes the system's hyperradius to fall to zero, or to the cutoff value, which is typically much longer than the (quasi)period of the hyperangular motion. The scaling properties of the lifetime are in agreement with the quantum-mechanical predictions of the half-life (width) of Efimov states surrounded by an ultracold gas. Detailed spatiotemporal evolution of the system is generally unpredictable beyond the three-body collision point, even though global conservation laws ensure that the system's hyperradius must be periodic.

Interaction-impeded relaxation in the presence of finite-temperature baths

We study the interplay between interactions and finite-temperature dephasing baths. We consider a double well with strongly interacting bosons coupled, via the density, to a bosonic bath. Such a system, when the bath has infinite temperature and instantaneous decay of correlations, relaxes with an emerging algebraic behavior with exponent 1/2. Here we show that, because of the finite-temperature baths and of the choice of spectral densities, such an algebraic relaxation may occur for a shorter duration and the characteristic exponent can be lower than 1/2. These results show that the interaction-induced impeding of relaxation is stronger and more complex when the bath has finite temperature and/or nonzero timescale for the decay of correlations.

Quantum many-body scar states with emergent kinetic constraints and finite-entanglement revivals

We construct a set of exact, highly excited eigenstates for a nonintegrable spin-1/2 model in one dimension that is relevant to experiments on Rydberg atoms in the antiblockade regime. These states provide a new solvable example of quantum many-body scars: their sub-volume-law entanglement and equal energy spacing allow for infinitely long-lived coherent oscillations of local observables following a suitable quantum quench. While previous works on scars have interpreted such oscillations in terms of the precession of an emergent macroscopic SU(2) spin, the present model evades this description due to a set of emergent kinetic constraints in the scarred eigenstates that are absent in the underlying Hamiltonian. We also analyze the set of initial states that give rise to periodic revivals, which persist as approximate revivals on a finite timescale when the underlying model is perturbed. Remarkably, a subset of these initial states coincides with the family of area-law entangled Rokhsar-Kivelson states shown by Lesanovsky to be exact ground states for a class of models relevant to experiments on Rydberg-blockaded atomic lattices.

Microscopic theory of the influence of strong attractive forces on the activated dynamics of dense glass and gel forming fluids.

We theoretically study the nonmonotonic (re-entrant) activated dynamics associated with a finite time scale kinetically defined repulsive glass to fluid to attractive glass transition in high volume fraction particle suspensions interacting via strong short range attractive forces. The classic theoretical "projection" approximation that replaces all microscopic forces by a single effective force determined solely by equilibrium pair correlations is revisited based on the "projectionless dynamic theory" (PDT). A hybrid-PDT approximation is formulated that explicitly quantifies how attractive forces induce dynamical constraints, while singular hard core interactions are treated based on the projection approach. Both the effects of interference between repulsive and attractive forces, and structural changes due to attraction-induced bond formation that competes with caging, are included. Combined with the microscopic Elastically Collective Nonlinear Langevin Equation (ECNLE) theory of activated relaxation, the resultant approach appears to properly capture both the re-entrant dynamic crossover behavior and the strong nonmonotonic variation of the activated structural relaxation time with attraction strength and range at very high volume fractions as observed experimentally and in simulations. Testable predictions are made. Major differences compared to both ideal mode coupling theory and ECNLE theory based on the full force projection approximation are identified. Calculations are also performed for smaller time and length scale intracage dynamics relevant to the non-Gaussian parameter based on analyzing the dynamic free energy that controls particle trajectories. Implications of the new theory for thermal glass forming liquids with relatively long range attractive forces are briefly analyzed.

Dynamics of strongly interacting systems: From Fock-space fragmentation to many-body localization

We study the $t{-}V$ disordered spinless fermionic chain in the strong coupling regime, $t/V\rightarrow 0$. Strong interactions highly hinder the dynamics of the model, fragmenting its Hilbert space into exponentially many blocks in system size. Macroscopically, these blocks can be characterized by the number of new degrees of freedom, which we refer to as movers. We focus on two limiting cases: Blocks with only one mover and the ones with a finite density of movers. The former many-particle block can be exactly mapped to a single-particle Anderson model with correlated disorder in one dimension. As a result, these eigenstates are always localized for any finite amount of disorder. The blocks with a finite density of movers, on the other side, show an MBL transition that is tuned by the disorder strength. Moreover, we provide numerical evidence that its ergodic phase is diffusive at weak disorder. Approaching the MBL transition, we observe sub-diffusive dynamics at finite time scales and find indications that this might be only a transient behavior before crossing over to diffusion.