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

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 $\alpha$ 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

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 $\lambda = -2\log(R)+C+O(R\log^2 R)$ with $C=1-4\log 2+27/(2\pi^2)\cdot \zeta(3)$ where $R$ 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

Computational Ground Effect Aerodynamics and Airplane Stability Analysis During Take-off and Landing

Computational simulations of aerodynamic characteristics of the Common Research Model (CRM), representing a typical transport airliner, are conducted using CFD methods in close proximity to the ground. The obtained dependencies on bank angle for aerodynamic forces and moments are further used in stability and controllability analysis of the lateral-directional aircraft motion. Essential changes in the lateral-directional modes in close proximity to the ground have been identified. For example, with approach to the ground, the roll subsidence and spiral eigenvalues are merging creating the oscillatory Roll-Spiral mode with quite significant frequency. This transformation of the lateral-directional dynamics in piloted simulation may affect the aircraft responses to external crosswind, modify handling quality characteristics and improve realism of crosswind landing