Time Evolution Research Articles

Introducing and analyzing a new combined version of the unstable Schrödinger equations with strong and weak stability effects

In the literature, two types of unstable nonlinear Schrodinger equations have been independently developed and studied. Each was derived by incorporating either a self-effect term or a time-space dispersion term into the standard nonlinear Schrodinger equation. Both models describe the time evolution of disturbances in unstable media. The primary contribution of this work is the combination of these two types into a single, new unstable version of the nonlinear Schrodinger equation. This new model is analyzed using two effective methods: the rational sine-cosine and the rational sinh-cosh functions. Additionally, a comparison test of the embedded unstable terms is conducted to assess their respective impacts on the stability of the Schrodinger model. Finally, graphical analyses, including 2D and 3D plots, are performed to validate the study’s findings.

Heavy-quark diffusion in 2+1D and glasmalike plasmas: Evidence of a transport peak

We examine how plasma excitations affect the heavy-quark diffusion coefficient in 2+1-dimensional and glasmalike plasmas, akin to the preequilibrium matter describing relativistic heavy-ion collisions at early times. We find that the transport coefficient 2κ transverse to and κz along the beam direction display a qualitatively different evolution. We attribute this to the underlying excitation spectra of these systems, thus providing evidence for the existence of nonperturbative properties in the spectrum. This is accomplished by first reconstructing the diffusion coefficients using gauge-fixed correlation functions, which accurately reproduces the time evolution of 2κ and κz. We then modify these excitation spectra to study the impact of their nonperturbative features on the transport coefficients. In particular, we find evidence for a novel transport peak in the low-frequency spectrum that is crucial for heavy-quark diffusion. We also demonstrate that gluonic excitations are broad while scalar excitations associated with κz are narrow and strongly enhanced at low momenta. Our findings indicate that the large values and dynamical properties of transport coefficients in the glasma could originate from genuinely nonperturbative features in the spectrum. Published by the American Physical Society 2024

Non-autonomous exact solutions and dynamic behaviors for the variable coefficient nonlinear Schrödinger equation with external potential

Abstract The nonlinear Schrödinger(NLS) equation represents a nonlinear dynamical system, which is usually used to describe nonlinear waves in deep water, self-focusing of intense lasers contained in electrolytes, and so on. The exact solutions of the variable coefficient nonlinear Schrödinger equation with external potential are considered. The variable coefficient nonlinear Schrödinger equation is transformed into a constant coefficient nonlinear equation by using the similarity transformation method, the exact solutions of the constant coefficient nonlinear equation are generated by using the homogeneous balance method. We obtain one-soliton, two-soliton, kink type soliton, bright soliton, parabolic soliton and rogue wave solutions. A ‘stepped’ type soliton solution is obtained in this paper, which is a novel type solution and different from the solutions of most nonlinear Schrödinger equations. Some special dynamic behaviors of solitons of the variable coefficient nonlinear Schrödinger equation with external potential are obtained via selecting some free functions. We found that the numerical simulation result is consistent with the exact solution through illustrating the time evolution of bright soliton solution.

Data Migration and security in cloud

Data migration and security in the cloud" refers to the process of transferring data from an on-premises system to a cloud environment while prioritizing security measures to protect sensitive information during transit and once stored in the cloud, including implementing strong access controls, encryption, and regular monitoring to prevent data breaches and ensure compliance with relevant regulations. In this time of digital evolution, cloud migration and its security have become essential topics that cannot be avoided. With more companies turning to cloud services for support, the demand for large-scale data storage and data management has also increased. Along with this rising need, the risk of cyber attacks on cloud data has also increased. To better protect yourself from these risks, it’s essential to ensure that you and your organization are up-to-date on the latest security technologies and safety precautions. Keywords : Data Migration, Data Security, cloud, ETL, Data Integration

State-and-Evolution Detection Model for Characterizing Farmland Spatial Pattern Variation in Hengyang Using Long Time Series Remote Sensing Product

Analyzing farmland landscape pattern variations induced by human activities can support effective decision making by governments to improve land use efficiency. However, research on long-term and continuous spatial process changes in farmland is scarce, and spatial pattern changes in farmlands remain insufficiently understood. Moreover, studies in which researchers have utilized dynamic process analysis to describe farmlands are relatively limited. This study aimed to apply the state-and-evolution detection model (SEDM), generated from long-term remote sensing data, to characterize farmland spatial pattern variations in Hengyang City, Hunan Province. Annual farmland data from 1990 to 2022, change type samples, and auxiliary data were collected, and six types of spatial pattern variations (perforation, dissection, shrinkage, creation, enlargement, and aggregation) were defined for the study area. Subsequently, the SEDM was applied based on four landscape indices. Finally, spatiotemporal evolution features, namely evolution times, evolution duration, and dominant evolution pattern, were quantified. The farmland in the study area exhibited a generally upward trend with fluctuations. The maximum area was followed by shrinkage (S), perforation (P), and enlargement (E). In over 70% of the study area, fewer than three evolution times occurred over three decades. The dominant evolution patterns were P–S, S–P, and E–P for single evolution events, and P–S–P, S–P–S, and P–S–S for double events. The model achieved an overall accuracy of 85%, thus demonstrating its effectiveness in characterizing landscape pattern variations and providing valuable insights for researchers and policy makers to develop strategies for farmland protection.

Travel Time Estimation for Optimal Planning in Internal Transportation

Optimal planning depends on precise and exact estimation of the operation costs of mobile robots. Unfortunately, determining the current and future state of a vehicle implies identifying all the parameters in its model. Rather than broadening the number of factors, in this work we adopt the approach of using a higher-level abstraction model to identify only a few cost parameters. Based on the observation that arc travel times accurately reflect the effect of physical states, this work proposes using them as the key parameters to compute accurate path traversal costs in the context of indoor transportation. This approach eliminates the need to model all factors in order to derive the cost for every robot. The resulting model organizes those parameters in a bilinear state-space form and includes the evolution of actual travel times with changing states. We show that the proposed model accurately estimates arc travel times with respect to actual observations gathered from real robots traversing a few arcs of a traffic network until battery exhaustion. We experimentally obtained minimum-cost paths from random origin and destination nodes when using heuristics and the “closer-to-reality” (bilinear-state version of our model) path costs, finding that it can save an average of 15% in transportation time compared to conventional methods.

Charging, aggregation, and electrostatic dispersion of radioactive and nonradioactive particles in the atmosphere

Abstract. Electrostatic dispersion can significantly impact the microphysical behavior of charged particles and ions until reaching zero space charge. However, although radioactive particles can be strongly charged in air, the influence of electrostatic dispersion has been neglected in understanding their behavior. This study is aimed at investigating the time evolution of the charge and size distributions of radioactive and nonradioactive particles in air and developing simple approaches for applications. With processes involving charging, aggregation, and electrostatic dispersion, a comprehensive population balance model (PBM) has been developed to examine particle charge/size distribution dynamics. It is shown that compared to nonradioactive particles, the charge and size distributions of radioactive particles may evolve differently with time because radioactivity and electrostatic dispersion can significantly affect the charging and aggregation kinetics of the particles. It is found that, after the Fukushima accident, background aerosols in the pathway of radioactive plumes might be highly charged due to ionizing radiation, suggesting that radiation fields may strongly influence in situ measurements of charged atmospheric particles. The comprehensive PBM is simplified, and then the verification and application of the simplified PBMs are discussed. This study provides useful insight into how radioactivity can affect the dynamic behavior of particles in atmospheric systems including radiation sources.

Transition from random self-propulsion to rotational motion in a non-Markovian microswimmer

Abstract We study the motion of an inertial microswimmer in a non-Newtonian environment with a finite memory and present the theoretical realization of an unexpected transition from its random self-propulsion to rotational (circular or elliptical) motion. Further, the rotational motion of the swimmer is followed by spontaneous local direction reversals yet with a steady state angular diffusion. Moreover, the advent of this behaviour is observed in the oscillatory regime of the inertia-memory parameter space of the dynamics. We quantify this unconventional rotational motion of microswimmer by measuring the time evolution of direction of its instantaneous velocity or orientation. By solving the generalized Langevin model of non-Markovian dynamics of an inertial active Ornstein-Uhlenbeck particle, we show that the emergence of the rotational (circular or elliptical) trajectory is due to the presence of both inertial motion and memory in the environment.

Physical consequences of Lindbladian invariance transformations

On its own, the invariance properties of Markovian master equations have mostly played a mathematical or computational role in the evaluation of quantum open system dynamics. Because all forms of the equation lead to the same time evolution for the state of the system, the fixation of a particular form has only gained physical meaning when correlated with additional information such as in the evolution of quantum trajectories or the study of decoherence-free subspaces. Here, we show that these symmetry transformations can be exploited, on their own, to optimize practical physical tasks. In particular, we present a general formulation showing how they can be used to change the measurable values of physical quantities regarding the exchange of energy and/or information with the environment. We also analyze examples of optimization in quantum thermodynamics and, finally, discuss practical implementations in terms of quantum trajectories. Published by the American Physical Society 2024

Design of shortcuts to adiabaticity for Bose–Einstein condensate dynamics in soliton Josephson junctions

This article primarily establishes a two-soliton system and employs the Lewis–Riesenfeld invariant inverse control method to achieve shortcuts to adiabaticity (STA) technology. We study an atomic soliton Josephson junctions (SJJs) device and subsequently compare and analyze it with atomic bosonic Josephson junctions. Moreover, we use higher-order expressions of the auxiliary equations to optimize the results and weaken the detrimental effect of the sloshing amplitude. We find that in the adiabatic shortcut evolution of two systems with time-containing tunnelling rates, the SJJs system is more robust over a rather short time evolution. In comparison with linear ramping, the STA technique is easier to achieve with the precise modulation of the quantum state in the SJJs system.

Time-Dependent Nuclear Energy-Density Functional Theory Toolkit for Neutron Star Crust: Dynamics of a Nucleus in a Neutron Superfluid

We present a new numerical tool designed to probe the dense layers of neutron star crusts. It is based on the time-dependent Hartree-Fock-Bogoliubov theory with generalized Skyrme nuclear energy-density functionals of the Brussels-Montreal family. We use it to study the time evolution of a nucleus accelerating through superfluid neutron medium in the inner crust of a neutron star. We extract an effective mass in the low velocity limit. We observe a threshold velocity and specify mechanisms of dissipation: phonon emission, Cooper pairs breaking, and vortex rings creation. These microscopic effects are of key importance for understanding various neutron star phenomena. Moreover, the mechanisms we describe are general and apply also to other fermionic superfluids interacting with obstacles like liquid helium or ultracold gases. Published by the American Physical Society 2024

Magnetic seed generation by plasma heat flux in accretion disks

Magnetic batteries are potential sources that may drive the generation of a seed magnetic field, even if this field is initially zero. These batteries can be the result of nonaligned thermodynamic gradients in plasmas, as well as of special and general-relativistic effects. So far, magnetic batteries have only been studied in ideal magnetized fluids. We studied the nonideal fluid effects introduced by the energy flux in the vortical dynamics of a magnetized plasma in curved space-time. We propose a novel mechanism for generating a heat-flux-driven magnetic seed within a simple accretion disk model around a Schwarzschild black hole. We used the 3+1 formalism for the splitting of the space-time metric into space-like and time-like components. We studied the vortical dynamics of a magnetized fluid with a heat flux in the Schwarzschild geometry in which thermodynamic and hydrodynamic quantities are only dependent on the radial coordinate. Assuming that the magnetic field is initially zero, we estimated the linear time evolution of the magnetic field due to the inclusion of nonideal fluid effects. When the thermodynamic and hydrodynamic quantities vary only radially, the effect of the coupling between the heat flux, the space-time curvature, and the fluid velocity acts as the primary driver for an initial linearly time-growing magnetic field. The plasma heat flux completely dominates the magnetic field generation at a specific distance from the black hole, where the fluid vorticity vanishes. This distance depends on the thermodynamical properties of the Keplerian plasma accretion disk. These properties control the strength of the nonideal effects in the generation of seed magnetic fields. We find that heat flux is the main driver of a seed magnetic field in black hole accretion disks if the geometry, plasma dynamics, and thermodynamics share the same axial symmetry. This suggests that nonideal fluid effects may play a major role in the magnetization of astrophysical plasmas.

An amplitude equation for the conserved-Hopf bifurcation-Derivation, analysis, and assessment.

We employ weakly nonlinear theory to derive an amplitude equation for the conserved-Hopf instability, i.e., a generic large-scale oscillatory instability for systems with two conservation laws. The resulting equation represents in the conserved case the equivalent of the complex Ginzburg-Landau equation obtained in the nonconserved case as an amplitude equation for the standard Hopf bifurcation. Considering first the case of a relatively simple symmetric two-component Cahn-Hilliard model with purely nonreciprocal coupling, we derive the nonlinear nonlocal amplitude equation with real coefficients and show that its bifurcation diagram and time evolution well agree with the results for the full model. The solutions of the amplitude equation and their stability are analytically obtained, thereby showing that in such oscillatory phase separation, the suppression of coarsening is universal. Second, we lift the two restrictions and obtain the amplitude equation in the generic case. It has complex coefficients and also shows very good agreement with the full model as exemplified for some transient dynamics that converges to traveling wave states.

2D/3D heterojunction carrier dynamics and interface evolution for efficient inverted perovskite solar cells

The 2D/3D heterojunction perovskites have garnered increasing attention due to their exceptional moisture and thermal stability. However, few works have paid attention to the influence of the subsequent change process of 2D/3D heterojunction PSC on the stability of PSCs. Moreover, the evolution of the interface and carrier dynamic behavior of the 2D/3D perovskite films with long-term operation has not been systematically developed before. In this work, the effects of 2D/3D heterojunction evolution on the interface of perovskite films and different carrier dynamics during 2D/3D evolution are systematically analyzed for the first time. The decomposition of 2D/3D heterojunction in the perovskite film will have a certain impact on the surface and carrier dynamics behavior of perovskite. During the evolution of 2D/3D heterojunction, PbI2 crystals will appear, which will improve the interfacial energy level matching between the electron transport layer and perovskite film. With a long evolution time, some holes will appear on the surface of perovskite film. The open circuit voltage (VOC) of PSCs increased from 1.14 to 1.18 V and the PCE increased to 23.21% after 300 h storage in the nitrogen atmosphere, and maintained 89% initial performance for with 3000 h stability test in N2 box. This discovery has a significant role in promoting the development of inverted heterojunction PSCs and constructing the revolution mechanism of charge carrier dynamic.

Two-dimensional ASEP model to study density profiles in CVD growth

The growth of two-dimensional (2D) transition metal dichalcogenides using chemical vapor deposition has been an area of intense study, primarily due to the scalability requirements for potential device applications. One of the major challenges of such growths is the large-scale thickness variation of the grown film. To investigate the role of different growth parameters computationally, we use a 2D asymmetric simple-exclusion process (ASEP) model with open boundaries as an approximation to the dynamics of deposition on the coarse-grained lattice. The variations in concentration of particles (growth profiles) at the lattice sites in the grown film are studied as functions of parameters like injection and ejection rate of particles from the lattice, time of observation, and the right bias difference between the hopping probabilities towards right and towards left) imposed by the carrier gas. In addition, the deposition rates at a given coarse-grained site is assumed to depend on the occupancy of that site. The effect of the maximum deposition rate, i.e., the deposition rate at a completely unoccupied site on the substrate, has been explored. The growth profiles stretch horizontally when either the evolution time or the right bias is increased. An increased deposition rate leads to a step-like profile, with the higher density region close to the left edge. In 3D, the growth profiles become more uniform with the increase in the height of the precursor with respect to the substrate surface. These results qualitatively agree with the experimental observations.

Phylogenetic Diversity of Plant and Insect Communities on Islands.

Interactions between plants and insects have long fascinated scientists. While some plants rely on insects for pollination and seed dispersal, insects rely on plants for food or as a habitat. Despite extensive research investigating pair-wise species interactions, few studies have characterized plant and insect communities simultaneously, making it unclear if diverse plant communities are generally associated with diverse insect communities. This work aims to better understand the historical and evolutionary relationships between plant and insect phylogenetic diversity (PD) on islands. We hypothesized that phylogenetically diverse plant communities (i.e., high PD) support diverse insect communities, with the relationship varying with island isolation, area, age, and latitude. Species lists for plants and insects were compiled from the published literature, and plant PD was calculated using ´standardized mean pairwise distance´ (SES.MPD) and ´standardized mean nearest taxon distance´ (SES.MNTD). For insects, PD was estimated using the number of genera, families, and orders. We found that plant diversity in evolutionary recent times (SES.MNTD) is associated with recent insect diversity (number of genera), but no relationship was found between plant and insect diversity across whole phylogenies (plant SES.MPD vs. number of insect families). Distant islands generally support high PD of plants (high SES.MPD and SES.MNTD) and insects (low number of genera). Plant and insect PD was generally high on small islands, except for plant SES.MPD revealing no relationship with island size. Insect PD was somewhat higher on young islands (low number of families), whereas there was no relationship between island age and plant PD. Plant SES.MPD was higher on high latitude islands, yet we did not find significant relationships between the latitude and the metrics of insect PD or plant SES.MNTD. These findings suggest that protecting high plant PD may also help conserve high insect PD, with a focus on small and distant islands as potential hotspots of phylogenetic diversity across multiple taxa.

Dust ring and gap formation by gas flow induced by low-mass planets embedded in protoplanetary disks

The observed dust rings and gaps in protoplanetary disks could be imprints of forming planets. Even low-mass planets in the 1-10 Earth-mass regime, which have not yet carved deep gas gaps, can generate such dust rings and gaps by driving a radially-outward gas flow, as shown in previous work. However, understanding the creation and evolution of these dust structures is challenging due to dust drift and diffusion, requiring an approach beyond previous steady state models. Here we investigate the time evolution of the dust surface density influenced by the planet-induced gas flow, based on post-processing three-dimensional hydrodynamical simulations. We find that planets larger than a dimensionless thermal mass of m = 0.05, corresponding to 0.3 Earth mass at 1 au or 1.7 Earth masses at 10 au, generate dust rings and gaps, provided that solids have small Stokes numbers (St ≲ 10−2) and that the disk midplane is weakly turbulent (αdiff ≲10−4). As dust particles pile up outside the orbit of the planet, the interior gap expands with time when the advective flux dominates over diffusion. Dust gap depths range from a factor of a few to several orders of magnitude, depending on planet mass and the level of midplane particle diffusion. We constructed a semi-analytic model describing the width of the dust ring and gap, and then compared it with the observational data. We find that up to 65% of the observed wide-orbit gaps could be explained as resulting from the presence of a low-mass planet, assuming αdiff = 10−5 and St = 10−3. However, it is more challenging to explain the observed wide rings, which in our model would require the presence of a population of small particles (St = 10−4). Further work is needed to explore the role of pebble fragmentation, planet migration, and the effect of multiple planets.

Transition of synchronization state during the quasiperiodic route to chaos in coupled friction-induced continuous oscillators

Friction-induced vibration, particularly associated with the squealing problem in disk brake systems, has been a longstanding challenge in the automotive industry. In our research, we employed the synchronization theory to gain insights into the interaction between two coupled cantilever beams attached with tip masses. This proposed model emulates the dynamics of a mountain bike disk brake assembly. The work explores a range of collective behaviors, including synchronized periodic, multi-periodic, quasiperiodic, as well as desynchronized chaotic and quasiperiodic oscillations. Despite numerous studies reported on the synchronization phenomenon in discrete friction-induced oscillatory systems, there appears to be a lack of similar research on continuous systems. This work stands as the first of its kind in exploring the dynamics of synchronization between two coupled continuous systems exhibiting a quasiperiodic route to chaos. A bifurcation study is conducted utilizing the Poincaré points corresponding to the local maxima of oscillation amplitude with respect to the zero-velocity crossing. The results showed the existence of narrow multi-periodic windows during the quasiperiodic route at several locations. Additionally, the existence of multiple quasiperiodic attractors exhibiting different states of synchronization for the same set of parameters is observed. We analyzed the time evolution of the cumulative instantaneous phase difference between the coupled signals and identified distinct states of synchronization possessed by the system. The coupled system undergoes interesting phenomena such as complete phase lock, intermittent phase lock, and phase drifting. Moreover, the transition occurring to the state of synchronization during the quasiperiodic route to chaos is studied employing the phase locking value, the Pearson linear correlation coefficient, and the relative mean frequency. Notably, our findings revealed that while the Pearson correlation can effectively identify both the mode and strength of synchronization, other measures such as phase lock value and relative mean frequency only reflect synchronization strength.

Topological pumping in an inhomogeneous Aubry-André model

The Aubry-André model is a fundamental theoretical model that exhibits interesting topological features. In this paper, we examine topologically protected boundary states in the inhomogeneous off-diagonal Aubry-André model. In contrast to the homogeneous case, the inhomogeneity triggers boundary states at phase boundaries that separate two distinct non-trivial topological domains. Remarkably, the topological character of the boundary states is predicted through topological pumping, where a boundary state is transferred from one boundary across the bulk region to the other by adiabatically tuning the pump parameter. Moreover, the role of the off-diagonal modulation strength (λ) on the transfer efficiency of the topological pumping is addressed. To support our results, we investigate the time evolution of a continuous-time quantum walk and show that its spread rate and λ are inversely related. Our work provides a new avenue to harness topological features of the Aubry-André model, where topological pumping can be used for robust quantum transport.

Modeling of drug release, erosion and diffusion fronts movement in high viscosity HPMC matrices containing a cellulolytic enzyme

A formerly developed mathematical model describing drug release from hydrophilic matrices (HMs) took into account resistance to drug release given by its dissolution and by the presence of a growing gel layer. Such a model was applied to previously reported release data obtained from HMs made of hydroxypropyl methylcellulose (HPMC), where acetaminophen was used as model drug and a cellulolytic product was added as “active” excipient to attain zero-order release kinetics. The Levich theory applied to acetaminophen intrinsic dissolution rate (IDR) data highlighted the suitability of such a drug for modeling purposes, given its good surface wettability. First assessment of the model ability to describe drug release from the abovementioned systems was carried out on partially coated matrices, representing a simplified physical frame, but results were then confirmed on uncoated systems. Experimental and model release data showed good agreement; therefore, the release-describing equation was combined with that of the global mass balance to obtain two new equations related to erosion and diffusion fronts time evolution. Changes over time in the dissolution and gel contributions to total resistance, calculated using model output parameters, highlighted that the enzyme, through its hydrolytic activity on HPMC, was responsible for a time-dependent reduction of the resistance component related to gel layer.