1,720,976 research outputs found
Mixing time for the repeated balls into bins dynamics
Full text linkWe consider a nonreversible finite Markov chain called Repeated Balls-into-Bins (RBB) process. This process is a discrete time conservative interacting particle system with parallel updates. Place initially in L bins rL balls, where r is a fixed positive constant. At each time step a ball is removed from each non-empty bin. Then all these removed balls are uniformly reassigned into bins. We prove that the mixing time of the RBB process is of order L. Furthermore we show that if the initial configuration has o(L) balls per site the equilibrium is attained in o(L) steps
Propagation of chaos for a balls into bins model
Full text linkConsider a finite number of balls initially placed in L bins. At each time step a ball is taken from each non-empty bin. Then all the balls are uniformly reassigned into bins. This finite Markov chain is called Repeated Balls-into-Bins process and is a discrete time interacting particle system with parallel updating. We prove that, starting from a suitable (chaotic) set of initial states, as L → +∞, the numbers of balls in each bin become independent from the rest of the system i.e. we have propagation of chaos. We furthermore study some equilibrium properties of the limiting nonlinear process
On the Dynamical Behavior of the ABC Model
No full textWe consider the ABC dynamics, with equal density of the three species,
on the discrete ring with N sites. In this case, the process is
reversible with respect to a Gibbs measure with a mean field interaction
that undergoes a second order phase transition. We analyze the
relaxation time of the dynamics and show that at high temperature it
grows at most as N(2) while it grows at least as N(3) at low
temperature
Large eddy simulations of a utility-scale horizontal axis wind turbine including unsteady aerodynamics and fluid-structure interaction modelling
Full text linkGrowing horizontal axis wind turbines are increasingly exposed to significant sources of unsteadiness, such as tower shadowing, yawed or waked conditions and environmental effects. Due to increased dimensions, the use of steady tabulated airfoil coefficients to determine the airloads along long blades can be questioned in those numerical fluid models that do not have the sufficient resolution to solve explicitly and dynamically the flow close to the blade. Various models exist to describe unsteady aerodynamics (UA). However, they have been mainly implemented in engineering models, which lack the complete capability of describing the unsteady and multiscale nature of wind energy. To improve the description of the blades' aerodynamic response, a 2D unsteady aerodynamics model is used in this work to estimate the airloads of the actuator line model in our fluid–structure interaction (FSI) solver, based on 3D large eddy simulation. At each section along the actuator lines, a semi-empirical Beddoes-Leishman model includes the effects of noncirculatory terms, unsteady trailing edge separation, and dynamic stall in the dynamic evaluation of the airfoils' aerodynamic coefficients. The aeroelastic response of a utility-scale wind turbine under uniform, laminar and turbulent, sheared inflows is examined with one- and two-way FSI coupling between the blades' structural dynamics and local airloads, with and without the enhanced aerodynamics' description. The results show that the external half of the blade is dominated by aeroelastic effects, whereas the internal one is dominated by significant UA phenomena, which was possible to represent only thanks to the additional model implemented
Quantitative ergodicity for the symmetric exclusion process with stationary initial data
Full text linkWe consider the symmetric exclusion process on the d-dimensional lattice with initial data invariant with respect to space shifts and ergodic. It is then known that as t diverges the distribution of the process at time t converges to a Bernoulli product measure. Assuming a summable decay of correlations of the initial data, we prove a quantitative version of this convergence by obtaining an explicit bound on the Ornstein d-distance. The proof is based on the analysis of a two species exclusion process with annihilation
A two-way coupling method for the study of aeroelastic effects in large wind turbines
Full text linkThe relevant size of state-of-the-art wind turbines suggests a significant Fluid-Structure Interaction. Given the difficulties to measure the phenomena occurring, researchers advocate high-fidelity numerical models exploiting Computational Fluid and Structural Dynamics. This work presents a novel aeroelastic model for wind turbines combining our Large-Eddy Simulation fluid solver with a modal beam-like structural solver. A loose algorithm couples the Actuator Line Model, which represents the blades in the fluid domain, with the structural model, which represents the flexural and torsional deformations. For the NREL 5 MW wind turbine, we compare the results of three sets of simulations. Firstly, we consider one-way coupled simulations where only the fluid solver provides the structural one with the aerodynamic loads; then, we consider two-way coupled simulations where the structural feedback to the fluid solver is made of the bending deformation velocities only; finally, we add to the feedback the torsional deformation. The comparison suggests that one-way coupled simulations tend to overpredict the power production and the structural oscillations. The flapwise blades vibration induces a significant aerodynamic damping in the structural motion, while the nose-down torsion reduces the mean aerodynamic forces, and hence the power, yet without introducing a marked dynamical effect
Convex entropy decay via the Bochner-Bakry-Emery approach
No full textWe develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov processes in discrete settings. When this method applies the relative entropy decays in a convex way. The method is shown to be rather powerful when applied to a class of birth and death processes. We then consider other examples, including inhomogeneous zero-range processes and Bernoulli–Laplace models. For these two models, known results were limited to the homogeneous case, and obtained via the martingale approach, whose applicability to inhomogeneous models is still unclear
Direct numerical simulation of boundary layers over microramps. mach number effects
No full textMicrovortex generators are passive control devices with heights below the boundary-layer thickness that have been proposed to mitigate the detrimental effects of shock-wave/boundary-layer interaction. Despite their demonstrated control effectiveness, several aspects of the flow induced in turbulent boundary layers still need to be characterized thoroughly. In this work, we present a campaign of direct numerical simulations of a turbulent boundary layer on a microramp, to investigate the effect of the Mach number, from subsonic to supersonic regime. We show that the flow topology changes significantly because of compressibility effects, and that typical wake features do not scale linearly with the geometry dimensions but rather depend on the incoming flow conditions. Moreover, we investigate the spectral content in time and space of the wake, which is dominated by the Kelvin-Helmholtz instability developing along the shear layer. For larger Mach numbers, the shedding onset is postponed and exhibits a lower peak frequency that evolves in space. Finally, we extract the spatially coherent structures convected in the wake by means of a dynamic mode decomposition along the characteristics, which represents effectively and efficiently the evolution of the entire field, despite the convective nature of the flow under consideration
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