Spatiotemporal Solutions Research Articles

Spatiotemporal soliton solutions in three dimensional combined linear-harmonic potentials with varying sources

Spatiotemporal soliton solutions in three dimensional combined linear-harmonic potentials with varying sources

Assessing spatiotemporal risks of nonpoint source pollution via soil erosion: a coastal case in the Yellow River Delta, China.

Nonpoint source pollution (NPSP) has always been the dominant threat to regional waters. Based on empirical models of the revised universal soil loss equation and the phosphorus index, an NPSP risk assessment model denoted as SL-NPSRI was developed. The surface soil pollutant loss was estimated by simulating the rain-runoff topographic process, and the influence of path attenuation was quantified. A case study in the Yellow River Delta and corresponding field surveys of soil pollutants and water quality showed that the established model can be applied to evaluate the spatial heterogeneity of NPSP. NPSP usually occurs during high-intensity rainfall periods and in larger estuaries. Summer rainfall increased pollutant transport into the sea from late July to mid-August and caused estuarine dilution. Higher NPSP risks often correspond to coastal areas with lower vegetation coverage, higher soil erodibility, and higher soil pollutant concentrations. Agricultural NPSP originating from cropland significantly increase the pollutant fluxes. Therefore, area-specific land use management and vegetation coverage improvement, and temporal-specific strategies can be explored for NPSP control during source-transport hydrological processes. This research provides a novel insight for coastal NPSP simulations by comprehensively analyzing the soil erosion process and its associated pollutant loss effects, which can be useful for targeted spatiotemporal solutions.

Bifurcations in a General Delay Sel’kov–Schnakenberg Reaction–Diffusion System

The dynamics of a delay Sel’kov–Schnakenberg reaction–diffusion system are explored. The existence and the occurrence conditions of the Turing and the Hopf bifurcations of the system are found by taking the diffusion coefficient and the time delay as the bifurcation parameters. Based on that, the existence of codimension-2 bifurcations including Turing–Turing, Hopf–Hopf and Turing–Hopf bifurcations are given. Using the center manifold theory and the normal form method, the universal unfolding of the Turing–Hopf bifurcation at the positive constant steady-state is demonstrated. According to the universal unfolding, a Turing–Hopf bifurcation diagram is shown under a set of specific parameters. Furthermore, in different parameter regions, we find the existence of the spatially inhomogeneous steady-state, the spatially homogeneous and inhomogeneous periodic solutions. Discretization of time and space visualizes these spatio-temporal solutions. In particular, near the critical point of Hopf–Hopf bifurcation, the spatially homogeneous periodic and inhomogeneous quasi-periodic solutions are found numerically.

Turing-Hopf Bifurcation Analysis in a Diffusive Ratio-Dependent Predator-Prey Model with Allee Effect and Predator Harvesting.

This paper investigates the complex dynamics of a ratio-dependent predator-prey model incorporating the Allee effect in prey and predator harvesting. To explore the joint effect of the harvesting effort and diffusion on the dynamics of the system, we perform the following analyses: (a) The stability of non-negative constant steady states; (b) The sufficient conditions for the occurrence of a Hopf bifurcation, Turing bifurcation, and Turing-Hopf bifurcation; (c) The derivation of the normal form near the Turing-Hopf singularity. Moreover, we provide numerical simulations to illustrate the theoretical results. The results demonstrate that the small change in harvesting effort and the ratio of the diffusion coefficients will destabilize the constant steady states and lead to the complex spatiotemporal behaviors, including homogeneous and inhomogeneous periodic solutions and nonconstant steady states. Moreover, the numerical simulations coincide with our theoretical results.

Rimming flow in a rotating horizontal cylinder with phase change at the interface

The two-dimensional solutions and stability analysis are presented for an evaporating thin viscous liquid film flowing inside a uniformly heated rotating horizontal cylinder. A non-linear, fourth-order, partial differential evolution equation is obtained by simplifying mass, momentum, and energy conservation equations within the lubrication approximation. The effect of evaporation, gravity, viscous drag, surface tension, thermocapillary stress, and intermolecular forces has been taken into account. The numerical solutions of the model are validated against the existing experimental as well as the numerical results, along with the analytical result for the limiting cases of the present model. The film thickness model is solved to elucidate two-dimensional spatiotemporal solutions and their stability for a wide range of thermal and other parameters. The evaporative mass flux at the liquid–air interface results in unsteady solutions which are oscillatory in nature, and the amplitude of the oscillations increases with an increase in the evaporative flux. The film ruptures after some time and the rupture time is found to be inversely proportional to the evaporation number, a non-dimensional number quantifying the rate of evaporation. The linear stability analysis shows that the thermocapillary stresses as well as the long-range molecular forces destabilize the film. A negative disjoining pressure is shown to reduce the rupture time and vice versa. Evaporation (condensation) plays a destabilizing (stabilizing) role in the thin film flow. Non-linear computations are carried out for the steady profiles, validating the growth rates obtained from the linear stability analysis.

Dynamics of spatiotemporal soliton solutions to a generalized nonlinear Schrödinger equation with inhomogeneous coefficients

In this paper, we study the dynamics of spatiotemporal soliton solutions to a generalized nonlinear Schrödinger equation with inhomogeneous coefficients in analytical and numerical forms. The characteristics and physical applications of the soliton solutions are investigated under different modulations of the coefficients depicting diffraction, potential, nonlinearity, source, and gain. We find that structures of these soliton solutions can be effectively manipulated by appropriately selecting the source term. Besides, the impact of gate effect on soliton propagation is investigated by employing the hyper-Gaussian and rectangle functions as diffraction coefficients. The results show that (i) the hyper-Gaussian modulation can be replaced by the rectangle modulation for large exponent and (ii) the solitons undergo a broadening in width and a sudden decrease in amplitude when passing through the gate functions. Our findings may have potential applications for the investigation of soliton control in the fields of nonlinear optics and Bose–Einstein condensations.

Spatio-Temporal Information Extraction and Geoparsing for Public Chinese Resumes

As an important carrier of individual information, the resume is an important data source for studying the spatio-temporal evolutionary characteristics of individual and group behaviors. This study focuses on spatio-temporal information extraction and geoparsing from resumes to provide basic technical support for spatio-temporal research based on resume text. Most current studies on resume text information extraction are oriented toward recruitment work, such as the automated information extraction, classification, and recommendation of resumes. These studies ignore the spatio-temporal information of individual and group behaviors implied in resumes. Therefore, this study takes the public resumes of teachers in key universities in China as the research data, proposes a set of spatio-temporal information extraction solutions for electronic resumes of public figures, and designs a spatial entity geoparsing method, which can effectively extract and spatially locate spatio-temporal information in the resumes. To verify the effectiveness of the proposed method, text information extraction models such as BiLSTM-CRF, BERT-CRF, and BERT-BiLSTM-CRF are selected to conduct comparative experiments, and the spatial entity geoparsing method is verified. The experimental results show that the precision of the selected models on the named entity recognition task is 96.23% and the precision of the designed spatial entity geoparsing method is 97.91%.

Optical spatiotemporal solitary wave solutions of the generalized (3+1)-dimensional Gross–Pitaevskii equation with distributed coefficients

In this work, the extended Jacobi elliptic function expansion approach is used to analyze a generalized [Formula: see text]-dimensional Gross–Pitaevskii equation with distributed time-dependent coefficients because of its use in the Bose–Einstein condensation. The Gross–Pitaevskii equation plays a significant role in Bose–Einstein condensation, where it characterizes the dynamics of the condensate wave function. By using this approach with a homogeneous balance principle, the spatiotemporal soliton solutions and exact extended traveling-wave solutions of governing equation have been successfully obtained. A few double periodic, trigonometric and hyperbolic function solutions from the Jacobi elliptic function solutions have been found under specific constraints on a parameter. It is obvious that the proposed approach is the most straightforward, efficient and useful way to handle numerous nonlinear models that arise in applied physics and mathematics in order to generate various exact solutions. A case with variable gain, constant diffraction and parabolic potential strength has been considered in this study to derive exact solutions. Numerous novel varieties of traveling-wave solutions have been revealed in this work, including the double periodic singular, the periodic singular, the dark singular, the dark kink singular, the periodic solitary singular and the singular soliton solutions and these newly obtained results differ from those previously investigated for this governing equation. In addition to addressing a scientific explanation of the analytical work, the results have been graphically presented by 3D plots and contour plots for some suitable parameter values to understand the physical meaning of the derived solutions. Due to their applicability to a variety of quantum systems, the acquired solutions are of considerable importance.

Physics-Informed Deep Learning for Solving Coupled Electron and Phonon Boltzmann Transport Equations

Electron-phonon (e-ph) coupling and transport are ubiquitous in modern electronic devices. The coupled electron and phonon Boltzmann transport equations (BTEs) hold great potential for the simulation of thermal transport in metal and semiconductor systems. However, solving the BTEs is often computationally challenging owing to their high dimensional complexity and a wide span of heat carrier properties, which hinder large-scale thermal modeling at the device level. In this work, we present a physics-informed neural network framework for solving the coupled electron and phonon BTEs. Instead of relying on labeled data, the proposed framework directly learns the spatiotemporal solutions (i.e., the electron and phonon distribution functions) within a parameterized space by enforcing physical laws. The efficacy of this framework is demonstrated through its ability to accurately resolve temperature profiles in low-dimensional thermal transport problems and visualize the ultrafast electron and phonon dynamics in laser heating experiments on thin metal films. The results indicate that our approach can accurately describe nonequilibrium e-ph energy transfer with improved efficiency, opening alternative avenues for the predictive design and optimization of micro- and nanostructures.

Boundedness, stability and pattern formation for a predator-prey model with Sigmoid functional response and prey-taxis

This article concerns the structure of the nonconstant steady states for a predator-prey model of Leslie-Gower type with Sigmoid functional and prey-taxis subject to the homogeneous Neumann boundary condition. The existence of bounded classical global solutions is discussed in bounded domains with arbitrary spatial dimension and any prey-taxis sensitivity coefficient. The local stability of the homogeneous steady state is analyzed to show that the prey-taxis sensitivity coefficient destabilizes the stability of the homogeneous steady state when prey defends. Then we study the existence and stability of the nonconstant positive steady state of the system over 1D domain by applying the bifurcation theory and present properties of local branches such as pitchfork and turning direction. Moreover, we discuss global bifurcation, homogeneous steady state solutions, nonconstant steady states solutions, spatio-temporal periodic solutions and spatio-temporal irregular solutions which demonstrate the coexistence and spatial distribution of prey and predator species. Finally, we perform numerical simulations to illustrate and support our theoretical analysis.

Turing‐Turing and Turing‐Hopf bifurcations in a general diffusive Brusselator model

AbstractA general reaction‐diffusion Brusselator model subject to homogeneous Neumann boundary conditions is investigated in this paper. First, the stability of the unique positive equilibrium is studied, and we identify the existence of the Hopf bifurcation. Then, occurrence conditions of the Turing instability, the Turing‐Turing, and the Turing‐Hopf bifurcations are established. To explore the spatiotemporal solutions resulting from the bifurcation, the amplitude equations of the Turing‐Turing and the Turing‐Hopf bifurcations are established via the method of multiple time scale. It is found that the model admits the nonconstant steady state, the mixed nonconstant steady state, the spatially homogeneous periodic solution, and the spatially nonhomogeneous periodic solution. As such, the nonhomogeneous spatiotemporal solutions appear in the model. In the end, numerical simulations verify the validity of the theoretical results.

Turing–Hopf bifurcation co-induced by cross-diffusion and delay in Schnakenberg system

The dynamics of Schnakenberg model subjected to gene expression time delay and cross-diffusion is investigated. It is shown that the presence of cross-diffusion allows the enlarged Turing instability region compared with self-diffusion and the variation of time delay can either lead to destabilization of the positive equilibrium or fail Turing instability through Turing–Hopf bifurcation. A bifurcation analysis of the Schnakenberg model in question has been provided to derive the stable regime, Turing instability regime and also the condition for delay-induced Turing–Hopf bifurcation. With the aid of normal form of Turing–Hopf bifurcation, the spatiotemporal dynamics near this bifurcation point can be divided into six categories where various solutions including stable spatially homogeneous or inhomogeneous periodic solutions, stable steady states and the transition from one type of spatiotemporal patterns to another would exhibit. These spatiotemporal solutions have also been illustrated through some numerical simulations, confirming the theoretical predictions.

Spatio-temporal solutions of a diffusive directed dynamics model with harvesting.

The study considers a directed dynamics reaction-diffusion competition model to study the density of evolution for a single species population with harvesting effect in a heterogeneous environment, where all functions are spatially distributed in time series. The dispersal dynamics describe the growth of the species, which is distributed according to the resource function with no-flux boundary conditions. The analysis investigates the existence, positivity, persistence, and stability of solutions for both time-periodic and spatial functions. The carrying capacity and the distribution function are either arbitrary or proportional. It is observed that if harvesting exceeds the growth rate, then eventually, the population drops down to extinction. Several numerical examples are considered to support the theoretical results.Supplementary InformationThe online version contains supplementary material available at 10.1007/s12190-022-01742-x.

Spatiotemporal optical solitons in a dual-core waveguide amplifier with inter modal dispersion

We obtain spatiotemporal optical solitons in a dual-core waveguide amplifier with inter modal dispersion, which can be described by a (3+1)-dimensional generalized nonlinear Schrödinger equation with modulated coefficients and a varying source. Two types of specific media of physical interest are considered to show the propagation behaviors of solutions. We find that the structures of these spatiotemporal optical soliton solutions can be controlled by tuning the dispersion, nonlinearity, gain, and the source parameters.

Spatio-temporal planning simulation of temporary elevators in construction using a game engine

Designing a reasonable and efficient transportation system of temporary elevators from the perspective of spatio-temporal planning is beneficial for the successful completion of construction projects. Specifically, the determination of the service period and floor of temporary elevators and the consideration of the limited availability of time and space should be taken seriously. The spatio-temporal planning of temporary elevators puts forward higher requirements for the display of planning solutions due to the complexity considering both time and space. However, current display ways are generally abstract, low-dimensional, and static, and even when the 4D model is adopted, the display effect of spatio-temporal planning solutions is still limited. This research presents a spatio-temporal planning simulation of temporary elevators in construction using a game engine to address those challenges. The workflow of the spatio-temporal planning simulation divided into configuration and operation planning consists of three steps: 1) import data into the game engine platform, 2) generate the spatio-temporal planning simulation scheme, and 3) conduct the spatio-temporal planning simulation. The results of the experimental test show that the presented spatio-temporal planning simulation way is intuitive and convenient, various planning elements are clearly shown, and corresponding planning information is efficiently conveyed, which can effectively enhance the display effect of spatio-temporal planning solutions.

Spatiotemporal Vortex Pulses: Angular Momenta and Spin-Orbit Interaction.

Recently, spatiotemporal optical vortex pulses carrying a purely transverse intrinsic orbital angular momentum were generated experimentally [Optica 6, 1547 (2019)OPTIC82334-253610.1364/OPTICA.6.001547; Nat. Photonics 14, 350 (2020)NPAHBY1749-488510.1038/s41566-020-0587-z]. However, an accurate theoretical analysis of such states and their angular-momentum properties remains elusive. Here, we provide such analysis, including scalar and vector spatiotemporal Bessel-type solutions as well as description of their propagational, polarization, and angular-momentum properties. Most importantly, we calculate both local densities and integral values of the spin and orbital angular momenta, and predict observable spin-orbit interaction phenomena related to the coupling between the transverse spin and orbital angular momentum. Our analysis is readily extended to spatiotemporal vortex pulses of other natures (e.g., acoustic).

Numerical analysis of an unconditionally energy-stable reduced-order finite element method for the Allen-Cahn phase field model

In this paper, a reduced-order finite element (FE) method preserving the unconditional energy-stability is proposed to simulate the Allen-Cahn phase field model, based on the proper orthogonal decomposition (POD) method with the snapshot technique. We first derive the full order FE formulation of the Allen-Cahn model and compute its FE full solutions, from which we choose a few spatio-temporal solutions as snapshots. Based on the POD technique, we then build a set of optimal POD bases maximizing the energy content in the original ensemble data, and in the new low-dimensional space spanned by the POD bases, we establish a low-order numerical model of stable reduced-order FE (SROFE) formulation for the Allen-Cahn phase field model. We also prove error estimates of the SROFE solutions of the Allen-Cahn phase field model. Finally, some numerical results are provided to test the validity of the SROFE formulation.

MVFNet: Multi-View Fusion Network for Efficient Video Recognition

Conventionally, spatiotemporal modeling network and its complexity are the two most concentrated research topics in video action recognition. Existing state-of-the-art methods have achieved excellent accuracy regardless of the complexity meanwhile efficient spatiotemporal modeling solutions are slightly inferior in performance. In this paper, we attempt to acquire both efficiency and effectiveness simultaneously. First of all, besides traditionally treating H x W x T video frames as space-time signal (viewing from the Height-Width spatial plane), we propose to also model video from the other two Height-Time and Width-Time planes, to capture the dynamics of video thoroughly. Secondly, our model is designed based on 2D CNN backbones and model complexity is well kept in mind by design. Specifically, we introduce a novel multi-view fusion (MVF) module to exploit video dynamics using separable convolution for efficiency. It is a plug-and-play module and can be inserted into off-the-shelf 2D CNNs to form a simple yet effective model called MVFNet. Moreover, MVFNet can be thought of as a generalized video modeling framework and it can specialize to be existing methods such as C2D, SlowOnly, and TSM under different settings. Extensive experiments are conducted on popular benchmarks (i.e., Something-Something V1 & V2, Kinetics, UCF-101, and HMDB-51) to show its superiority. The proposed MVFNet can achieve state-of-the-art performance with 2D CNN's complexity.

Turing patterns in a diffusive Holling–Tanner predator-prey model with an alternative food source for the predator

In this manuscript, we consider temporal and spatio-temporal modified Holling–Tanner predator-prey models with predator-prey growth rate as a logistic type, Holling type II functional response and alternative food sources for the predator. From our result of the temporal model, we identify regions in parameter space in which Turing instability in the spatio-temporal model is expected and we show numerical evidence where the Turing instability leads to spatio-temporal periodic solutions. Subsequently, we analyse these instabilities. We use simulations to illustrate the behaviour of both the temporal and spatio-temporal model.

Technical and tactical measures to reduce unwanted catches in mixed fisheries: Do the opinions of Irish fishers align with management advice?

The introduction of the Landing Obligation in Europe has increased the need for fishers to adopt more selective fishing practices, to avoid unwanted catches that would previously have been legally discarded. Modelling, experiments and trials have been conducted by scientists, often in collaboration with industry, to determine how gear modifications, changes in fishing tactics, and alterations to spatio-temporal exploitation patterns can assist in reducing unwanted catches. Yet voluntary uptake of resultant recommendations is often poor or slow. During semi-structured interviews with fishers and industry representatives from the Irish demersal fishing industry we discussed their views with regard to the effectiveness of such measures in reducing unwanted catches. Opinions varied between respondents. There was broad agreement that larger mesh sizes are vital for reducing discards, which aligns with current management advice. Other selectivity devices were viewed less favourably due to the difficulties associated with correctly setting up and maintaining gear to ensure effective operation. The benefits of spatio-temporal solutions were recognised despite a lack of formal management advice with regards to such measures. A lack of trust between fishers, as well as fear of providing additional information to authorities which could be used against them, led to a guarded response for resources such as more formal information sharing schemes. While our results indicate individuals have their own tactics and preferences to reduce unwanted catches, understanding broad industry perspectives towards technical and tactical measures to reduce discards is important if scientists and policy makers are to best support industry to increase selectivity.