Search results for "equation"

Quantum dynamics by the constrained adiabatic trajectory method

2011

We develop the constrained adiabatic trajectory method (CATM) which allows one to solve the time-dependent Schr\"odinger equation constraining the dynamics to a single Floquet eigenstate, as if it were adiabatic. This constrained Floquet state (CFS) is determined from the Hamiltonian modified by an artificial time-dependent absorbing potential whose forms are derived according to the initial conditions. The main advantage of this technique for practical implementation is that the CFS is easy to determine even for large systems since its corresponding eigenvalue is well isolated from the others through its imaginary part. The properties and limitations of the CATM are explored through simple…

From Random Walker to Vehicular Traffic: Motion on a Circle

2014

Driving of cars on a highway is a complex process which can be described by deterministic and stochastic forces. It leads to equations of motion with asymmetric interaction and dissipation as well as to new energy flow law already presented at previous TRAFFIC AND GRANULAR FLOW meetings. Here we consider a model, where motion of an asymmetric random walker on a ring with periodic boundary conditions takes place. It is related to driven systems with active particles, energy input and depot. This simple model can be further developed towards more complicated ones, describing vehicular or pedestrian traffic. Three particular cases are considered, starting with discrete coordinate and time, the…

Comments on “Measurement of dimensionless Chezy coefficient in step-pool reach (Case study of Dizin River in Iran)” by Torabizadeh A., Tahershamsi A.…

2018

This paper is a comment on a previous published paper.

Discussion of “Modified Hazen–Williams and Darcy–Weisbach Equations for Friction and Local Head Losses along Irrigation Laterals” by John D. Valiantz…

2007

Flow Resistance in Step-Pool Rills

2017

Rills evolve morphologically, and the adjustment of rill channel geometry to flow affects the relationships among velocity, discharge, and slope. The resistance to flow in step-pool rills is mainly due to form-induced mechanisms and, in comparison, grain resistance is of minor significance. Previous studies on rill flow resistance have been performed exclusively for grainresistance conditions and use a stream flow equation. In this study, a new flow resistance equation, deduced by applying dimensional analysis and self-similarity theory, was applied to rill flow in step-pool channels. First, the incomplete self-similarity hypothesis was used for establishing a power flow velocity profile wh…

Stability in a System subject to Noise with Regulated Periodicity

2011

The stability of a simple dynamical system subject to multiplicative one-side pulse noise with hidden periodicity is investigated both analytically and numerically. The stability analysis is based on the exact result for the characteristic functional of the renewal pulse process. The influence of the memory effects on the stability condition is analyzed for two cases: (i) the dead-time-distorted poissonian process, and (ii) the renewal process with Pareto distribution. We show that, for fixed noise intensity, the system can be stable when the noise is characterized by high periodicity and unstable at low periodicity.

Two competing species in super-diffusive dynamical regimes

2010

The dynamics of two competing species within the framework of the generalized Lotka-Volterra equations, in the presence of multiplicative alpha-stable Lévy noise sources and a random time dependent interaction parameter, is studied. The species dynamics is characterized by two different dynamical regimes, exclusion of one species and coexistence of both, depending on the values of the interaction parameter, which obeys a Langevin equation with a periodically fluctuating bistable potential and an additive alpha-stable Lévy noise. The stochastic resonance phenomenon is analyzed for noise sources asymmetrically distributed. Finally, the effects of statistical dependence between multiplicative …

Noise enhanced stability in fluctuating metastable states Phys. Rev. E69, 061103 (2004)

2004

We derive general equations for the nonlinear relaxation time of Brownian diffusion in randomly switching potential with a sink. For piece-wise linear dichotomously fluctuating potential with metastable state, we obtain the exact average lifetime as a function of the potential parameters and the noise intensity. Our result is valid for arbitrary white noise intensity and for arbitrary fluctuation rate of the potential. We find noise enhanced stability phenomenon in the system investigated: The average lifetime of the metastable state is greater than the time obtained in the absence of additive white noise.We obtain the parameter region of the fluctuating potential where the effect can be ob…

Dielectric Relaxation of a Polybutadiene Melt at a Crystalline Graphite Surface: Atomistic Molecular Dynamics Simulations

2014

Dielectric experiments are an indispensable tool to further our understanding of the relaxation behavior of polymers, not only in bulk samples but also in confined situations. A chemically realistic Molecular Dynamics simulation, in which all information about molecular motions is available, can shed light onto the questions of heterogeneity and anisotropy of the underlying molecular relaxation processes which lead to the ensemble averaged experimental dielectric signal. In this contribution, we present a careful analysis of the dielectric response of a weakly polar and confined polymer, 1,4-polybutadiene between graphite walls. The relaxation of the segmental dipole moments was obtained in…

An EKF Based Method for Path Following in Turbulent Air

2017

An innovative use of the Extended Kalman Filter (EKF) is proposed to perform both accurate path following and adequate disturbance rejection in turbulent air. The tuned up procedure employs simultaneously two different EKF: the first one estimates gust disturbances, the second one estimates modified aircraft parameters. The first filter, by using measurements gathered in turbulent air, estimates both aircraft states and wind components. The second one, by using the estimated disturbances, obtains command laws that are able to reject disturbances. The predictor of the second EKF uses the estimated wind components to solve motion equations in turbulent air. Besides a set of unknown stability …