1,844 research outputs found
A simple closure approximation for slow dynamics of a multiscale system: nonlinear and multiplicative coupling
Multiscale dynamics are ubiquitous in applications of modern science. Because
of time scale separation between relatively small set of slowly evolving
variables and (typically) much larger set of rapidly changing variables, direct
numerical simulations of such systems often require relatively small time
discretization step to resolve fast dynamics, which, in turn, increases
computational expense. As a result, it became a popular approach in
applications to develop a closed approximate model for slow variables alone,
which both effectively reduces the dimension of the phase space of dynamics, as
well as allows for a longer time discretization step. In this work we develop a
new method for approximate reduced model, based on the linear
fluctuation-dissipation theorem applied to statistical states of the fast
variables. The method is suitable for situations with quadratically nonlinear
and multiplicative coupling. We show that, with complex quadratically nonlinear
and multiplicative coupling in both slow and fast variables, this method
produces comparable statistics to what is exhibited by an original multiscale
model. In contrast, it is observed that the results from the simplified closed
model with a constant coupling term parameterization are consistently less
precise
Improved linear response for stochastically driven systems
The recently developed short-time linear response algorithm, which predicts
the average response of a nonlinear chaotic system with forcing and dissipation
to small external perturbation, generally yields high precision of the response
prediction, although suffers from numerical instability for long response times
due to positive Lyapunov exponents. However, in the case of stochastically
driven dynamics, one typically resorts to the classical fluctuation-dissipation
formula, which has the drawback of explicitly requiring the probability density
of the statistical state together with its derivative for computation, which
might not be available with sufficient precision in the case of complex
dynamics (usually a Gaussian approximation is used). Here we adapt the
short-time linear response formula for stochastically driven dynamics, and
observe that, for short and moderate response times before numerical
instability develops, it is generally superior to the classical formula with
Gaussian approximation for both the additive and multiplicative stochastic
forcing. Additionally, a suitable blending with classical formula for longer
response times eliminates numerical instability and provides an improved
response prediction even for long response times
Cross sections for geodesic flows and \alpha-continued fractions
We adjust Arnoux's coding, in terms of regular continued fractions, of the
geodesic flow on the modular surface to give a cross section on which the
return map is a double cover of the natural extension for the \alpha-continued
fractions, for each in (0,1]. The argument is sufficiently robust to
apply to the Rosen continued fractions and their recently introduced
\alpha-variants.Comment: 20 pages, 2 figure
Simulator of fuel cells characteristics on the basis of the semiconductor converter
The results of development and research of the simulator of fuel cells characteristics based on the operated pulse converter with direct current and digital alarm processor have been considered. The electrochemical model of fuel cell considering its static and dynamic characteristics is incorporated in the algorithm of the processor work. The specified simulator has on loading terminals the same characteristics of output capacity as a real system. It allows abandoning the use of both the elements and expensive accompanying systems at stages of research, design and realization of independent systems of power supply on the basis of fuel cells
Multilevel Analysis of Oscillation Motions in Active Regions of the Sun
We present a new method that combines the results of an oscillation study
made in optical and radio observations. The optical spectral measurements in
photospheric and chromospheric lines of the line-of-sight velocity were carried
out at the Sayan Solar Observatory. The radio maps of the Sun were obtained
with the Nobeyama Radioheliograph at 1.76 cm. Radio sources associated with the
sunspots were analyzed to study the oscillation processes in the
chromosphere-corona transition region in the layer with magnetic field B=2000
G. A high level of instability of the oscillations in the optical and radio
data was found. We used a wavelet analysis for the spectra. The best
similarities of the spectra of oscillations obtained by the two methods were
detected in the three-minute oscillations inside the sunspot umbra for the
dates when the active regions were situated near the center of the solar disk.
A comparison of the wavelet spectra for optical and radio observations showed a
time delay of about 50 seconds of the radio results with respect to optical
ones. This implies a MHD wave traveling upward inside the umbral magnetic tube
of the sunspot. Besides three-minute and five-minute ones, oscillations with
longer periods (8 and 15 minutes) were detected in optical and radio records.Comment: 17 pages, 9 figures, accepted to Solar Physics (18 Jan 2011). The
final publication is available at http://www.springerlink.co
Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach
In this paper we consider the problem of deriving approximate autonomous
dynamics for a number of variables of a dynamical system, which are weakly
coupled to the remaining variables. In a previous paper we have used the Ruelle
response theory on such a weakly coupled system to construct a surrogate
dynamics, such that the expectation value of any observable agrees, up to
second order in the coupling strength, to its expectation evaluated on the full
dynamics. We show here that such surrogate dynamics agree up to second order to
an expansion of the Mori-Zwanzig projected dynamics. This implies that the
parametrizations of unresolved processes suited for prediction and for the
representation of long term statistical properties are closely related, if one
takes into account, in addition to the widely adopted stochastic forcing, the
often neglected memory effects.Comment: 14 pages, 1 figur
The Lyapunov exponent in the Sinai billiard in the small scatterer limit
We show that Lyapunov exponent for the Sinai billiard is with where
is the radius of the circular scatterer. We consider the disk-to-disk-map
of the standard configuration where the disks is centered inside a unit square.Comment: 15 pages LaTeX, 3 (useful) figures available from the autho
Computational Simulation of Airfoils Stall Aerodynamics at Low Reynolds Numbers
Experimental results for aerodynamic static hysteresis at stall conditions
obtained in the TsAGI's T-124 low-turbulence wind tunnel for NACA0018
are presented and analysed. Computational predictions of aerodynamic
static hysteresis are made using the OpenFOAM simulations considering
di erent grids, turbulence models and solvers. Comparisons of compu-
tational simulation results with experimental wind tunnel data are made
for 2D NACA0018 and NACA0012 airfoils at low Reynolds numbers Re =
(0.3-1.0) millions. The properties of the proposed phenomenological bifurca-
tion model for simulation of aerodynamic loads at the existence of static
hysteresis are discussed
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