Search results for "Integrator"

Multiple time step integrators and momentum conservation

1997

Abstract By use of the standard Liouville operator formalism, we derive a new symplectic multiple time step integrator for Hamiltonian systems with disparate masses, which, in contrast to previous algorithms, conserves the total momentum exactly, and is only moderately slower. The new scheme is tested numerically by application to Molecular Dynamics simulations of a polymer melt whose monomers have different masses, and compared to earlier algorithms.

Multiscale Particle Method in Solving Partial Differential Equations

2007

A novel approach to meshfree particle methods based on multiresolution analysis is presented. The aim is to obtain numerical solutions for partial differential equations by avoiding the mesh generation and by employing a set of particles arbitrarily placed in problem domain. The elimination of the mesh combined with the properties of dilation and translation of scaling and wavelets functions is particularly suitable for problems governed by hyperbolic partial differential equations with large deformations and high gradients.

Reprint of: Approximate Taylor methods for ODEs

2018

Abstract A new method for the numerical solution of ODEs is presented. This approach is based on an approximate formulation of the Taylor methods that has a much easier implementation than the original Taylor methods, since only the functions in the ODEs, and not their derivatives, are needed, just as in classical Runge–Kutta schemes. Compared to Runge–Kutta methods, the number of function evaluations to achieve a given order is higher, however with the present procedure it is much easier to produce arbitrary high-order schemes, which may be important in some applications. In many cases the new approach leads to an asymptotically lower computational cost when compared to the Taylor expansio…

Roving Robots Gain from an Orientation Algorithm of Fruit Flies and Predict a Fly Decision-Making Algorithm

2014

Simple organisms like bacteria are directly influenced by momentary changes in concentration or strength of sensory signals. In noisy sensory gradients frequent zigzagging reduces the performance of the cell or organism. Drosophila melanogaster flies significantly deviate from a direct response to sensory input when orienting in gradients. A dynamical model has been derived which reproduces fly behaviour. Here we report on an emergent property of the model. Implemented in a robot, the algorithm is sustaining decisions between visual targets. The behaviour was consequently found in wild-type flies, which stay with a once-chosen visual target for considerable longer times than mutant flies wi…

Efficient numerical integration of neutrino oscillations in matter

2016

A special purpose solver, based on the Magnus expansion, well suited for the integration of the linear three neutrino oscillations equations in matter is proposed. The computations are speeded up to two orders of magnitude with respect to a general numerical integrator, a fact that could smooth the way for massive numerical integration concomitant with experimental data analyses. Detailed illustrations about numerical procedure and computer time costs are provided.

High Field Polarization Response in Ferroelectrics: Current Solutions and Challenges

2006

Polarization response including ergodicity breaking and the divergence of relaxation time is reproduced for model Hamiltonians of growing complexity. Systematic derivation of the dynamical equations and its solutions is based on the Fokker-Planck and imaginary time Schrödinger equation techniques with subsequent symplectic integration. Test solutions are addressed to finite size and spatially extended problems with microscopically interpretation of the model parameters as a challenge.

2013

The motion energy sensor has been shown to account for a wide range of physiological and psychophysical results in motion detection and discrimination studies. It has become established as the standard computational model for retinal movement sensing in the human visual system. Adaptation effects have been extensively studied in the psychophysical literature on motion perception, and play a crucial role in theoretical debates, but the current implementation of the energy sensor does not provide directly for modelling adaptation-induced changes in output. We describe an extension of the model to incorporate changes in output due to adaptation. The extended model first computes a space-time r…

Stochastic Dynamics of Ferroelectric Polarization

2008

This study is addressed to the conceptual and technical problems emerging for ferroelectric systems out of thermodynamic equilibrium. The theoretical setup includes a lattice of interacting cells, each cell obeying regular dynamics determined by Ginzburg-Landau model Hamiltonians whereas relaxation toward minimum energy state is reproduced by thermal environment. Representative examples include polarization response of a single lattice cell, birth of a domain as triggered by the ergodicity breaking, and the effect of nonlocal electroelastic interaction all evidenced combining the Fokker-Planck, imaginary time Schrodinger and symplectic integration techniques.

Proposal and design of an in-fiber all-optical fractional integrator

2010

Abstract We theoretically and numerically demonstrate that a single fiber Bragg grating – conveniently apodized and of uniform period – operated in reflection can perform an arbitrary-order fractional integration of an input optical waveform. Analytical expressions were found relating the fractional integration order with the apodization profile of the fiber Bragg grating. This simple device shows a good accuracy calculating the fractional time integral of the complex field of arbitrary input optical waveforms.

Theory and modeling of polarization switching in ferroelectrics

2005

Abstract Kinetics of polarization response in ferroelectrics is reproduced within Langevin, Fokker–Planck and imaginary time Schrodinger equation techniques for energy functionals of growing complexity modeling an assembly of coarse grained particles with attractive first neighbor interaction. Symplectic integration based numerical approach captures dynamic hysteresis, polarization switching, and spatially extended stationary polarization. Solution of relevant nonstationary problem is adapted to large scale parallel computing.