Increase Of Time Step Research Articles

Large time step discrete-time modeling of sharp wave activity in hippocampal area CA3

Reduced models of neuronal spiking activity simulated with a fixed integration time step are frequently used in studies of spatio-temporal dynamics of neurobiological networks. The choice of fixed time step integration provides computational simplicity and efficiency, especially in cases dealing with large number of neurons and synapses operating at a different level of activity across the population at any given time. A network model tuned to generate a particular type of oscillations or wave patterns is sensitive to the intrinsic properties of neurons and synapses and, therefore, commonly susceptible to changes in the time step of integration. In this study, we analyzed a model of sharp-wave activity in the network of hippocampal area CA3, to examine how an increase of the integration time step affects network behavior and to propose adjustments of intrinsic properties of neurons and synapses that help minimize or remove the damage caused by the time step increase.

Numerical Simulation of Visually Guided Landing Based on a Honeybee Motion Model

We verified the validity of a bio-inspired strategy for visually guided landing and its mathematical model proposed M.V. Srinivasan et al. by numerical simulation. We studied the influence of temporal discretization and the values of the supported optical flow on the landing duration and its result (from smooth to crash). An algorithm for landing simulation was developed taking into account accepted assumptions of the model. Two formulas (sine and tangent) were derived to calculate the distance and the speed of the flying robot, ensuring the constancy of the optical flow at given time steps. A limitation was found in the very value of the optical flow (threshold value), when exceeding this, the strategy leads to a hard touchdown or a crash (at near zero distance the speed is not close to zero). It was shown that the threshold value of the optical flow decreases with increasing time step in both formulas. However, calculating the distance using sine formula has a significantly lower threshold value of the optical flow than the calculation using the tangent formula. It was found that landing occurs faster if we use the sine formula at equal values of the optical flow. Nevertheless, the smooth landing ends at lower threshold values of the optical flow than using the tangent formula. As a result, using a larger value of the optical flow, a faster smooth landing can be achieved using the tangent formula.

Coherence evolution in two-dimensional quantum walk on lattice

We investigate the evolution of the [Formula: see text] norm coherence in two-dimensional quantum walk on lattices for Fourier, Grover and Hadamard coins. Our study shows that the coherence of both the whole system and the position subsystem increases quadratically with the number of steps. We also analyze the influence of three kinds of noises, i.e. broken links, lattice congestion and lattice traps, on the two-dimensional quantum walk. The result shows that the increase of coherence with the number of steps gradually inclines to be linear as the probabilities of broken links and lattice congestion increase. In the quantum walk on trapped lattices, the coherence increases with the increasing time step before the crossover time [Formula: see text] and then gradually decreases after [Formula: see text].

Molecular dynamics based enhanced sampling of collective variables with very large time steps.

Enhanced sampling techniques that target a set of collective variables and that use molecular dynamics as the driving engine have seen widespread application in the computational molecular sciences as a means to explore the free-energy landscapes of complex systems. The use of molecular dynamics as the fundamental driver of the sampling requires the introduction of a time step whose magnitude is limited by the fastest motions in a system. While standard multiple time-stepping methods allow larger time steps to be employed for the slower and computationally more expensive forces, the maximum achievable increase in time step is limited by resonance phenomena, which inextricably couple fast and slow motions. Recently, we introduced deterministic and stochastic resonance-free multiple time step algorithms for molecular dynamics that solve this resonance problem and allow ten- to twenty-fold gains in the large time step compared to standard multiple time step algorithms [P. Minary et al., Phys. Rev. Lett. 93, 150201 (2004); B. Leimkuhler et al., Mol. Phys. 111, 3579-3594 (2013)]. These methods are based on the imposition of isokinetic constraints that couple the physical system to Nosé-Hoover chains or Nosé-Hoover Langevin schemes. In this paper, we show how to adapt these methods for collective variable-based enhanced sampling techniques, specifically adiabatic free-energy dynamics/temperature-accelerated molecular dynamics, unified free-energy dynamics, and by extension, metadynamics, thus allowing simulations employing these methods to employ similarly very large time steps. The combination of resonance-free multiple time step integrators with free-energy-based enhanced sampling significantly improves the efficiency of conformational exploration.

Spatiotemporal variation of hydrological drought based on the Optimal Standardized Streamflow Index in Luanhe River basin, China

To establish the drought index objectively and reasonably and evaluate the hydrological drought accurately, firstly, the optimal distribution was selected from nine distributions (normal, lognormal, exponential, gamma, general extreme value, inverse Gaussian, logistic, log-logistic and Weibull), then the Optimal Standardized Streamflow Index (OSSI) was calculated based on the optimal distribution, and last, the spatiotemporal evolution of hydrological drought based on the OSSI series was investigated through the monthly streamflow data of seven hydrological stations during the period 1961–2011 in Luanhe River basin, China. Results suggest: (1) the general extreme value and log-logistic distributions performed prominently in fitting the monthly streamflow of Luanhe River basin. (2) The main periods of hydrological drought in Luanhe River basin were 148–169, 75–80, 42–45, 14–19 and 8–9 months. (3) The hydrological drought had an aggravating trend over the past 51 year and with the increase in timescale, the aggravating trend was more serious. (4) The lower the drought grade was, the broader the coverage area. As for the Luanhe River basin, the whole basin suffered the mild and more serious drought, while the severe and more serious drought only cover some areas. (5) With the increase in time step, the frequency distribution of mild droughts across the basin tended to be concentrated, the frequency of extreme droughts in middle and upper reaches tended to increase and the frequency in downstream tends to decrease. This research can provide powerful references for water resources planning and management and drought mitigation.

An Improved Fuzzy Neural Network for Traffic Speed Prediction Considering Periodic Characteristic

This paper proposes a new method in construction fuzzy neural network to forecast travel speed for multi-step ahead based on 2-min travel speed data collected from three remote traffic microwave sensors located on a southbound segment of a fourth ring road in Beijing City. The first-order Takagi–Sugeno system is used to complete the fuzzy inference. To train the evolving fuzzy neural network (EFNN), two learning processes are proposed. First, a $K$ -means method is employed to partition input samples into different clusters and a Gaussian fuzzy membership function is designed for each cluster to measure the membership degree of samples to the cluster centers. As the number of input samples increases, the cluster centers are modified and membership functions are also updated. Second, a weighted recursive least squares estimator is used to optimize the parameters of the linear functions in the Takagi–Sugeno type fuzzy rules. Furthermore, a trigonometric regression function is introduced to capture the periodic component in the raw speed data. Specifically, the predicted performance between the proposed model and six traditional models are compared, which are artificial neural network, support vector machine, autoregressive integrated moving average model, and vector autoregressive model. The results suggest that the prediction performances of EFNN are better than those of traditional models due to their strong learning ability. As the prediction time step increases, the EFNN model can consider the periodic pattern and demonstrate advantages over other models with smaller predicted errors and slow raising rate of errors.

A Particle Fokker-Planck Algorithm with Multiscale Temporal Discretization for Rarefied and Continuum Gas Flows

AbstractFor gas flows with moderate and low Knudsen numbers, pair-wise collisions in the Boltzmann equation can be approximated by the Langevin model corresponding to the Fokker-Planck equation. Using this simplified collision model, particle numerical schemes, e.g. the Fokker-Planck model (FPM) method, can simulate low Knudsen number gas flows more efficient than those based on the Boltzmann equation, such as the Direct Simulation Monte Carlo (DSMC) method. However, as analyzed in this paper, the transport properties of the FPM method deviate from the physical values as the time step increases, and this problem affects its computational accuracy and efficiency for the simulation of multi-scale flows. Herewe propose a particle Fokker-Planck algorithm with multiscale temporal discretization (MTD-FPM) to overcome the drawbacks of the original FPM method. In the MTD-FPM method, the molecular motion is tracked following the integration scheme of the Langevin model in analogy to the original FPM method. However, to ensure consistent transport coefficients for arbitrary temporal discretization, a time step dependent friction coefficient has been implemented. Several benchmark problems, including Couette, thermal Couette, Poiseuille, and Sod tube flows, are simulated to validate the proposed MTD-FPM method.

Solving Finite-Element Time-Domain Problems With GaBP

In this paper, a new finite element Gaussian belief propagation (FGaBP) method is presented for time-domain applications. The unconditionally stable Newmark time-stepping scheme is combined with FGaBP for this purpose. As shown empirically, the method converges for increasing time step sizes without losing stability. The combined FGaBP-time stepping is able to retain the parallel scalability from FGaBP as in previous work. In addition, this paper also shows that lossy material properties can be easily supported by the method with minimal changes to its formulation.

Validation of a non-conforming monolithic fluid-structure interaction method using phase-contrast MRI.

This paper details the validation of a non‐conforming arbitrary Lagrangian‐Eulerian fluid‐structure interaction technique using a recently developed experimental 3D fluid‐structure interaction benchmark problem. Numerical experiments for steady and transient test cases of the benchmark were conducted employing an inf‐sup stable and a general Galerkin scheme. The performance of both schemes is assessed. Spatial refinement with three mesh refinement levels and fluid domain truncation with two fluid domain lengths are studied as well as employing a sequence of increasing time step sizes for steady‐state cases. How quickly an approximate steady‐state or periodic steady‐state is reached is investigated and quantified based on error norm computations. Comparison of numerical results with experimental phase‐contrast magnetic resonance imaging data shows very good overall agreement including governing of flow patterns observed in the experiment.

Mechanics of Cadherin Unbinding using Coarse-Grained Models

Cell-cell adhesion is mediated by calcium-dependent proteins called cadherins, which are important in neuronal connectivity and tissue integrity. Cadherins are modular proteins with large extracellular domains that have typically been modeled using all-atom molecular dynamics (MD) simulations. However, these simulations are computationally expensive and most of them only include small fragments of these cadherin extracellular domains. To overcome these limitations, we used a coarse-grained (CG) model with the MARTINI force field to study large cadherin complexes over long time scales. All-atom MD simulations were used to find optimal parameters for an elastic network model that stabilized the protein secondary structure. The CG model allowed for a 5x increase in timestep and a 10-fold reduction of system sizes. Using this model we studied the dynamics and elastic response of classical cadherins and clustered protocadherins. In these simulations, the extracellular domains of classical cadherins straightened before unbinding, while protocadherins slipped past each other during unbinding. Overall, our results confirm that our model is an effective simulation tool for studying of the mechanics of cadherin complexes.

Role of Core Electrons in Quantum Dynamics Using TDDFT.

The explicit simulation of time dependent electronic processes requires computationally onerous routes involving the temporal integration of motion equations for the charge density. Efficiency optimization of these methods typically relies on increasing the integration time-step and on the reduction of the computational cost per step. The implicit representation of inner electrons by effective core potentials-or pseudopotentials-is a standard practice in localized-basis quantum-chemistry implementations to improve the efficiency of ground-state calculations, still preserving the quality of the output. This article presents an investigation on the impact that effective core potentials have on the overall efficiency of real time electron dynamics with TDDFT. Interestingly, the speedups achieved with the use of pseudopotentials in this kind of simulation are on average much more significant than in ground-state calculations, reaching in some cases a factor as large as 600×. This boost in performance originates from two contributions: on the one hand, the size of the density matrix, which is considerably reduced, and, on the other, the elimination of high-frequency electronic modes, responsible for limiting the maximum time-step, which vanish when the core electrons are not propagated explicitly. The latter circumstance allows for significant increases in time-step, that in certain cases may reach up to 3 orders of magnitude, without losing any relevant chemical or spectroscopic information.

Semi-implicit iterative methods for low Mach number turbulent reacting flows: Operator splitting versus approximate factorization

Two formally second-order accurate, semi-implicit, iterative methods for the solution of scalar transport–reaction equations are developed for Direct Numerical Simulation (DNS) of low Mach number turbulent reacting flows. The first is a monolithic scheme based on a linearly implicit midpoint method utilizing an approximately factorized exact Jacobian of the transport and reaction operators. The second is an operator splitting scheme based on the Strang splitting approach. The accuracy properties of these schemes, as well as their stability, cost, and the effect of chemical mechanism size on relative performance, are assessed in two one-dimensional test configurations comprising an unsteady premixed flame and an unsteady nonpremixed ignition, which have substantially different Damköhler numbers and relative stiffness of transport to chemistry. All schemes demonstrate their formal order of accuracy in the fully-coupled convergence tests. Compared to a (non-)factorized scheme with a diagonal approximation to the chemical Jacobian, the monolithic, factorized scheme using the exact chemical Jacobian is shown to be both more stable and more economical. This is due to an improved convergence rate of the iterative procedure, and the difference between the two schemes in convergence rate grows as the time step increases. The stability properties of the Strang splitting scheme are demonstrated to outpace those of Lie splitting and monolithic schemes in simulations at high Damköhler number; however, in this regime, the monolithic scheme using the approximately factorized exact Jacobian is found to be the most economical at practical CFL numbers. The performance of the schemes is further evaluated in a simulation of a three-dimensional, spatially evolving, turbulent nonpremixed planar jet flame.

An implicit numerical scheme for the simulation of three-dimensional two-phase flows in light water nuclear reactors

ABSTRACTAn implicit numerical scheme is presented for solving the two-fluid model widely used in the analysis of a gas–liquid two-phase flow in light water nuclear reactors (LWRs). The pressure equation is established by combining the momentum and mass conservation equations. The implicit calculation of each governing equation is separated into phase- and space-link steps. In the phase-link step, the interfacial momentum and heat transfers are implicitly calculated. Then the solution accounting for the convection and diffusion terms is calculated simultaneously in space. The phase- and space-link steps are repeated for convergence. The numerical scheme is implemented in CUPID, which is a multidimensional two-phase flow analysis code for LWRs, and verified against a set of conceptual two-phase flow problems which include typical thermal hydraulic phenomena in LWRs. Calculations are performed using four numerical schemes, semi-implicit ICE and SMAC schemes, an implicit scheme, and an implicit scheme with increased time step size, and the results are discussed.

A point kinetics model for dynamic simulations of next generation nuclear reactor

An accurate, fast-running and stable six-group, point kinetics (PK) model is developed and applied successfully to the dynamic simulation of the operation of the prismatic core, high temperature next generation nuclear plant (NGNP) reactor. The model is unrestricted by the size of the time step, which could be as much as several seconds, accounts for Doppler Broadening and the fuel and graphite temperature reactivity feedbacks, and includes an active neutron source for zero-power reactor startup. An efficient and robust numerical technique that approximates the exponential matrix using 7th order-accurate Padé(3,3) function with a discretization error on the order of (Δt)3, solves the coupled nonlinear and stiff six-groups point kinetics equations. The PK model handles reactivity insertions in excess of a prompt critical, ρ/β¯> $1.0, with unrestrictive time step size. Model results are successfully benchmarked using the Inhour solution for a step insertion of external reactivity. To simulate the transient response of the NGNP reactor following an external reactivity insertion and during a startup, the PK model is coupled to 84-nodes thermal-hydraulics model of the reactor, also developed in this work. With a 2 s time step, the error of predicting the reactor thermal power is ∼0.001%, increasing exponentially to ∼0.08% and ∼1.5% with increased time step size to 5 and 8 s, respectively. The present PK model has been successfully incorporated into MELCOR-H2 nuclear reactor analysis code to simulate transient operation of Very High Temperature Reactor (VHTR) for electricity generation, using a Closed Brayton Cycle turbomachinery, and the co-generation of hydrogen using Sulfur Iodine (SI) thermochemical processes.

On the Stability and CPU Time of the Implicit Runge-Kutta Schemes for Steady State Simulations

AbstractImplicit time integration schemes are popular because their relaxed stability constraints can result in better computational efficiency. For time-accurate unsteady simulations, it has been well recognized that the inherent dispersion and dissipation errors of implicit Runge-Kutta schemes will reduce the computational accuracy for large time steps. Yet for steady state simulations using the time-dependent governing equations, these errors are often overlooked because the intermediate solutions are of less interest. Based on the model equationdy/dt=(μ+iλ)yof scalar convection diffusion systems, this study examines the stability limits, dispersion and dissipation errors of four diagonally implicit Runge-Kutta-type schemes on the complex (μ+iλ)Δtplane. Through numerical experiments, it is shown that, as the time steps increase, the A-stable implicit schemes may not always have reduced CPU time and the computations may not always remain stable, due to the inherent dispersion and dissipation errors of the implicit Runge-Kutta schemes. The dissipation errors may decelerate the convergence rate, and the dispersion errors may cause large oscillations of the numerical solutions. These errors, especially those of high wavenumber components, grow at large time steps. They lead to difficulty in the convergence of the numerical computations, and result in increasing CPU time or even unstable computations as the time step increases. It is concluded that an optimal implicit time integration scheme for steady state simulations should have high dissipation and low dispersion.

On the connection between dissipative particle dynamics and the Itô-Stratonovich dilemma.

Dissipative Particle Dynamics (DPD) is a popular simulation model for investigating hydrodynamic behavior of systems with non-negligible equilibrium thermal fluctuations. DPD employs soft core repulsive interactions between the system particles, thus allowing them to overlap. This supposedly permits relatively large integration time steps, which is an important feature for simulations on large temporal scales. In practice, however, an increase in the integration time step leads to increasingly larger systematic errors in the sampling statistics. Here, we demonstrate that the prime origin of these systematic errors is the multiplicative nature of the thermal noise term in Langevin's equation, i.e., the fact that it depends on the instantaneous coordinates of the particles. This lead to an ambiguity in the interpretation of the stochastic differential Langevin equation, known as the Itô-Stratonovich dilemma. Based on insights from previous studies of the dilemma, we propose a novel algorithm for DPD simulations exhibiting almost an order of magnitude improvement in accuracy, and nearly twice the efficiency of commonly used DPD Langevin thermostats.

Short-Term Speed Prediction Using Remote Microwave Sensor Data: Machine Learning versus Statistical Model

Recently, a number of short-term speed prediction approaches have been developed, in which most algorithms are based on machine learning and statistical theory. This paper examined the multistep ahead prediction performance of eight different models using the 2-minute travel speed data collected from three Remote Traffic Microwave Sensors located on a southbound segment of 4th ring road in Beijing City. Specifically, we consider five machine learning methods: Back Propagation Neural Network (BPNN), nonlinear autoregressive model with exogenous inputs neural network (NARXNN), support vector machine with radial basis function as kernel function (SVM-RBF), Support Vector Machine with Linear Function (SVM-LIN), and Multilinear Regression (MLR) as candidate. Three statistical models are also selected: Autoregressive Integrated Moving Average (ARIMA), Vector Autoregression (VAR), and Space-Time (ST) model. From the prediction results, we find the following meaningful results: (1) the prediction accuracy of speed deteriorates as the prediction time steps increase for all models; (2) the BPNN, NARXNN, and SVM-RBF can clearly outperform two traditional statistical models: ARIMA and VAR; (3) the prediction performance of ANN is superior to that of SVM and MLR; (4) as time step increases, the ST model can consistently provide the lowest MAE comparing with ARIMA and VAR.

A Q2Q1 integrated finite element method with the semi‐implicit consistent CSF for solving incompressible two‐phase flows with surface tension effect

SummaryAn integrated finite element method (FEM) is proposed to simulate incompressible two‐phase flows with surface tension effects, and three different surface tension models are applied to the FEM to investigate spurious currents and temporal stability. A Q2Q1 element is adopted to solve the continuity and Navier–Stokes equations and a Q2‐iso‐Q1 to solve the level set equation. The integrated FEM solves pressure and velocity simultaneously in a strongly coupled manner; the level set function is reinitialized by adopting a direct approach using interfacial geometry information instead of solving a conventional hyperbolic‐type equation. In addition, a consistent continuum surface force (consistent CSF) model is utilized by employing the same basis function for both surface tension and pressure variables to damp out spurious currents and to estimate the accurate pressure distribution. The model is further represented as a semi‐implicit manner to improve temporal stability with an increased time step. In order to verify the accuracy and robustness of the code, the present method is applied to a few benchmark problems of the static bubble and rising bubble with large density and viscosity ratios. The Q2Q1‐integrated FEM coupled with the semi‐implicit consistent CSF demonstrates the significantly reduced spurious currents and improved temporal stability. The numerical results are in good qualitative and quantitative agreements with those of the existing studies. Copyright © 2015 John Wiley & Sons, Ltd.

Reactive transport LBM model for CO2 injection in fractured reservoirs

A geochemical LBM model has been developed to simulate the CO2 injection in homogeneous porous media in our previous work. That model has the ability to investigate the coupled reactive transport processes with reactants and products ions transport, matrix dissolution, and dissolution induced porosity change. In the present work, the model is extended to study the reactive transport properties in “fractured” media. Two kinds of fractures are investigated: one is straightforward along the centerline, and the other is inclined. The reaction rate distribution and evolution are analyzed at different time steps. The dissolution property of fracture edges is also studied, the bottom edge dissolution rate is generally higher than that of the upper edge in inclined fractured media. The porosity change becomes more and more obvious with the increase of time steps, as well as the edge porosity profiles. For the different fracture width, the dissolution rate and edge porosity become higher with the increase of fracture width. All the results show that the present model has the capability to numerically investigate CO2 injection and reactive transport in fractured reservoirs.

Hybrid short-term freeway speed prediction methods based on periodic analysis

Short-term traffic speed forecasting is an important issue for developing Intelligent Transportation Systems applications. So far, a number of short-term speed prediction approaches have been developed. Recently, some multivariate approaches have been proposed to consider the spatial and temporal correlation of traffic data. However, as traffic data often demonstrates periodic patterns, the existing methodologies often fail to take into account spatial and temporal information as well as the periodic features of traffic data simultaneously in the multi-step prediction. This paper comprehensively evaluated the multi-step prediction performance of space time (ST) model, vector autoregression (VAR), and autoregressive integrated moving average (ARIMA) models using the 5 minute freeway speed data collected from five loop detectors located on an eastbound segment of Interstate 394 freeway, in Minnesota. To further consider the cyclical characteristics of freeway speed data, hybrid prediction approaches were proposed to decompose speed into two different components: a periodic trend and a residual part. A trigonometric regression function is introduced to capture the periodic component and the residual part is modeled by the ST, VAR, and ARIMA models. The prediction results suggest that for multi-step freeway speed prediction, as the time step increases, the ST model demonstrates advantages over the VAR and ARIMA models. Comparisons among the ST, VAR, ARIMA, and hybrid models demonstrated that modeling the periodicity and the residual part separately can better interpret the underlining structure of the speed data. The proposed hybrid prediction approach can accommodate the periodic trends and provide more accurate prediction results when the forecasting horizon is greater than 30 min.