Long Time-Step Particle Pushing in Drift Approximation without Orbit Averaging

1998 ◽  
Vol 145 (1) ◽  
pp. 41-60 ◽  
Author(s):  
Michael V. Smolsky
Keyword(s):  
Time Step ◽  
Long Time ◽  
Particle Pushing

scholarly journals A 2-DIMENSIONAL CELLULAR AUTOMATON FOR AGENTS MOVING FROM ORIGINS TO DESTINATIONS

2005 ◽  
Vol 16 (12) ◽  
pp. 1849-1860 ◽  
Author(s):  
NAJEM MOUSSA
Keyword(s):  
Cellular Automaton ◽  
Cluster Size ◽  
Bimodal Distribution ◽  
Minimal Distance ◽  
Time Step ◽  
Neighbor Site ◽  
Model Dynamics ◽  
Long Time ◽  
Freely Moving ◽  
Small Clusters

We develop a two-dimensional cellular automaton (CA) as a simple model for agents moving from origins to destinations. Each agent moves towards an empty neighbor site corresponding to the minimal distance to its destination. The stochasticity or noise (p) is introduced in the model dynamics, through the uncertainty in estimating the distance from the destination. The friction parameter "μ" is also introduced to control the probability that movement of all involved agents to the same site (conflict) is denied at each time step. This model displays two states; namely the freely moving and the jamming state. If μ is large and p is low, the system is in the jamming state even if the density is low. However, if μ is large and p is high, a freely moving state takes place whenever the density is low. The cluster size and the travel time distributions in the two states are studied in detail. We find that only very small clusters are present in the freely moving state, while the jamming state displays a bimodal distribution. At low densities, agents can take a very long time to reach their destinations if μ is large and p is low (jamming state); but long travel times are suppressed if p becomes large (freely moving state).

Long-time symplectic integration: the example of four-vortex motion

1991 ◽  
Vol 432 (1886) ◽  
pp. 481-494 ◽  
Keyword(s):  
Fourth Order ◽  
Initial Conditions ◽  
Hamiltonian Formulation ◽  
Superior Performance ◽  
Integration Time ◽  
Characteristic Time Scale ◽  
Symplectic Integration ◽  
Time Step ◽  
Long Time ◽  
Runge Kutta

Detailed comparisons are made between long-time numerical integration of the motion of four identical point vortices obtained using both a fourth-order symplectic integration method of the implicit Runge-Kutta type and a standard fourth-order explicit Runge-Kutta scheme. We utilize the reduced hamiltonian formulation of the four-vortex problem due to Aref & Pomphrey. Initial conditions which give both fully chaotic and also quasi-periodic motions are considered over integration times of order 10 6 -10 7 times the characteristic time scale of the evolution. The convergence, as the integration time step is decreased, of the Poincaré section is investigated. When smoothness of the section compared to the converged image, and the fractional change in the hamiltonian H are used as diagnostic indicators, it is found that the symplectic scheme gives substantially superior performance over the explicit scheme, and exhibits only an apparent qualitative degrading in results up to integration time steps of order the minimum timescale of the evolution. It is concluded that this performance derives from the symplectic rather than the implicit character of the method.

Multiple Time Step Brownian Dynamics for Long Time Simulation of Biomolecules

2003 ◽  
Vol 29 (8) ◽  
pp. 471-478 ◽  
Author(s):  
Tadashi Ando ◽  
Toshiyuki Meguro ◽  
Ichiro Yamato
Keyword(s):  
Brownian Dynamics ◽  
Multiple Time ◽  
Time Step ◽  
Multiple Time Step ◽  
Time Simulation ◽  
Long Time

Sewer system flow components identification using signal processing

2010 ◽  
Vol 62 (1) ◽  
pp. 106-114
Author(s):  
F. A. Dorval ◽  
B. Chocat ◽  
E. Emmanuel ◽  
G. Lipeme Kouyi
Keyword(s):  
Signal Processing ◽  
Time Series Data ◽  
Continuous Model ◽  
Series Data ◽  
Time Step ◽  
Sewer System ◽  
Long Time ◽  
Recorded Data ◽  
Flow Components ◽  
Main Components

The development of a continuous model to simulate the behaviour of sewer systems requires detailed information on each component of the flows contributing to the global discharge. In this paper authors investigate a novel method based on signal processing and long time series data implemented with a 2 min time step (flow rate, conductivity, pH and turbidity) in order to identify the dry weather components in a separated stormwater sewer system draining an industrial catchment. The wavelet analysis is applied to the recorded data to identify main components in dry weather flow after the removing of the signal noise. This paper highlights also a method to detect inflow into sewer system and shows how hydrological modelling can be used to characterise the relevant components. These techniques could be used as a basis for several applications.

Learning Complex, Extended Sequences Using the Principle of History Compression

1992 ◽  
Vol 4 (2) ◽  
pp. 234-242 ◽  
Author(s):  
Jürgen Schmidhuber
Keyword(s):  
Divide And Conquer ◽  
Time Lags ◽  
Training Algorithms ◽  
Recurrent Networks ◽  
Time Step ◽  
Neural Network Learning ◽  
Event Sequences ◽  
Network Learning ◽  
Training Sequences ◽  
Long Time

Previous neural network learning algorithms for sequence processing are computationally expensive and perform poorly when it comes to long time lags. This paper first introduces a simple principle for reducing the descriptions of event sequences without loss of information. A consequence of this principle is that only unexpected inputs can be relevant. This insight leads to the construction of neural architectures that learn to “divide and conquer” by recursively decomposing sequences. I describe two architectures. The first functions as a self-organizing multilevel hierarchy of recurrent networks. The second, involving only two recurrent networks, tries to collapse a multilevel predictor hierarchy into a single recurrent net. Experiments show that the system can require less computation per time step and many fewer training sequences than conventional training algorithms for recurrent nets.

scholarly journals A test of numerical instability and stiffness in the parametrizations of the ARPÉGE and ALADIN models

2012 ◽  
Vol 5 (4) ◽  
pp. 4233-4268 ◽  
Author(s):  
M. Tudor
Keyword(s):  
Differential Equations ◽  
Weather Prediction ◽  
Stiff Problem ◽  
Vertical Diffusion ◽  
Time Step ◽  
True Solution ◽  
Weather Forecasts ◽  
Long Time ◽  
Lagrangian Advection ◽  
Nwp Model

Abstract. Meteorological numerical weather prediction (NWP) models solve a system of partial differential equations in time and space. Semi-lagrangian advection scheme in the model dynamics allows for long time-steps. These longer time-steps can result in instabilities occurring in the model physics. A system of differential equations in which some solution components decay more rapidly than others is stiff. In this case it is stability rather than accuracy that restricts the time-step. The vertical diffusion parametrization can cause fast non-meteorological oscillations around the slowly evolving true solution (fibrillations). These are treated with an anti-fibrillation scheme. But small oscillations remain in an operational weather forecasts using ARPÉGE and ALADIN models. It is needed to test of the complete model formulation, as implemented in the operational forecast. In this paper, a simple test is designed. The test reveals if the formulation of particular physical parametrization is a stiff problem or potentially numerically unstable in combination with any other part of the model. When the test is applied to a stable scheme, the solution remains stable. But, applying the test to a potentially unstable scheme yields a solution with fibrillations of substantial amplitude. The parametrizations of a NWP model ARPÉGE were tested one by one to see which one may be the source of unstable model behaviour. The test has identified the stratiform precipitation scheme (a diagnostic Kessler type scheme) as a stiff problem, particularly the term that describes the evaporation of snow.

scholarly journals Assessment of meteorological extremes using a synoptic weather generator and a downscaling model based on analogs

2019 ◽  
Author(s):  
Damien Raynaud ◽  
Benoit Hingray ◽  
Guillaume Evin ◽  
Anne-Catherine Favre ◽  
Jérémy Chardon
Keyword(s):  
Time Series ◽  
Large Scale ◽  
Weather Generator ◽  
Time Step ◽  
Stochastic Weather Generator ◽  
Natural Risk ◽  
Synoptic Weather ◽  
Weather Generators ◽  
Long Time ◽  
Precipitation And Temperature

Abstract. Natural risk studies such as flood risk assessments require long series of weather variables. As an alternative to observed series, which have a limited length, these data can be provided by weather generators. Among the large variety of existing ones, resampling methods based on analogues have the advantage of guaranteeing the physical consistency between local variables at each time step. However, they cannot generate values of predictands exceeding the range of observed values. Moreover, the length of the simulated series is typically limited to the length of the synoptic meteorology records used to characterize the large-scale atmospheric configuration of the generation day. To overcome those limitations, the stochastic weather generator proposed in this study combines two sampling approaches based on atmospheric analogues: (1) a synoptic weather generator in a first step, which recombines days in the 20th century to generate a 1000-year sequence of new atmospheric trajectories and (2) a stochastic downscaling model in a second step, applied to these atmospheric trajectories, in order to simulate long time series of daily regional precipitation and temperature. The method is applied to daily time series of mean areal precipitation and temperature in Switzerland. It is shown that the climatological characteristics of observed precipitation and temperature are adequately reproduced. It also improves the reproduction of extreme precipitation values, overcoming previous limitations of standard analog-based weather generators.

Long-Time-Step Methods for Oscillatory Differential Equations

1998 ◽  
Vol 20 (3) ◽  
pp. 930-963 ◽  
Author(s):  
B. García-Archilla ◽  
J. M. Sanz-Serna ◽  
R. D. Skeel
Keyword(s):  
Differential Equations ◽  
Time Step ◽  
Long Time
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