Acceleration stochastic model

Despite the ability of the GLM to reproduce any realizable Reynolds-stress model, Pope (2002b) has shown that it is not consistent with DNS data for homogeneous turbulent shear flow. In order to overcome this problem, and to incorporate the Reynolds-number effects observed in DNS, a stochastic model for the acceleration can be formulated (Pope 2002a Pope 2003). However, it remains to be seen how well such models will perform for more complex inhomogeneous flows. In particular, further research is needed to determine the functional forms of the coefficient matrices in both homogeneous and inhomogeneous turbulent flows. 

In general the method of confidence intervals (Zacks, 1971, Ch. 10) may be suggested for approaching a problem of this kind. As it follows from the nature of the stochastic model, an increase in input load of phosphorus does not necessarily lead to an acceleration of the eutrophication process. The same input load, however, may lead to a major increase in algae biomass (as was probably the case in 1982). 

The structural response is evaluated in the time domain and the excitation is given in terms of a stochastic model of the input ground acceleration time history. In what follows, the model by (Atkinson Silva 2003) is implemented. The site seismic hazard is expressed as a function of M and R for given local soil conditions a further PDF p(Z) is introduced, to model the uncertainty in the ground motion time history for a given M and R. Therefore (0) is given by (0) = p(0s Ds, Ms) p(M)p(R)p(X) and the integral in Equation 11 can be written as ... 

A Tuned Mass Damper (TMD) is one of the simplest and the most rehable passive device for vibration control in a wide range of applications, and for this reason many optimization criteria have been proposed for this specific device. Essentially, a TMD consists in an additional mass connected to a main system by a spring and a damper. The main system, excited by a base acceleration, is modelled as a stochastic stationary coloured noise and introducing the global space state vector ... 

The acceleration is modeled as stochastic process defined as filtered white noise. With respect to Equation 8,... 

We shall see that a conditional acceleration model in the form of (6.48) is equivalent to a stochastic Lagrangian model for the velocity fluctuations whose characteristic correlation time is proportional to e/k. As discussed below, this implies that the scalar flux (u,

joint velocity, composition PDF level, and thus that a consistent scalar-flux transport equation can be derived from the PDF transport equation. 

Erratum A stochastic Lagrangian model for acceleration in turbulent flow [Phys. Fluids 14, 2360 (2002)]. Physics of Fluids 15, 269. 

A role of other parameters of the model is investigated by Kuzovkov [26], It is demonstrated that an increase of the ratio a//3 for a fixed lj0 = (cr/3)1/2 and the control parameter k acts to accelerate a change of the focal regime for chaotic. Simultaneously, the amplitudes of oscillations in concentration for particles of different kinds are no longer close. A study of the stochastic Lotka-Volterra model performed here shows that irregular concentration motion observed experimentally in the Belousov-Zhabotinsky systems [8] indeed could take place in a system with mono- and bimolecular stages and two intermediate products only. 

Tenneti, S., Fox, R. O. Subramaniam, S. 2012 Stochastic acceleration model for gas-solid flows at moderate Reynolds numbers. Journal of Fluid Mechanics (submitted). 

Particle-based simulation techniques include atomistic MD and coarse-grained molecular dynamics (CG-MD). Accelerated dynamics methods, such as hyperdynamics and replica exchange molecular dynamics (REMD), are very promising for circumventing the timescale problem characteristic of atomistic simulations. Structure and dynamics at the mesoscale level can be described within the framework of coarse-grained particle-based models using such methods as stochastic dynamics (SD), dissipative particle dynamics (DPD), smoothed-particle hydrodynamics (SPH), lattice molecular dynamics (LMD), lattice Boltzmann method (IBM), multiparticle collision dynamics (MPCD), and event-driven molecular dynamics (EDMD), also referred to as collision-driven molecular dynamics or discrete molecular dynamics (DMD). 

Sorella was able to improve this method significantly by making use of the Hessian matrix. He termed this method stochastic reconfiguration with Hessian acceleration (SRH) and showed in an application to spin lattice models that it is much more efficient than original stochastic reconfiguration-based method and more efficient than the simple Newton-Raphson method. ... 

To simulate the slow-pressure phenomena, a stochastic mixing and reorientation model can be used. It describes the dissipation and the observed tendency of the Reynolds stresses to become isotropic. The stochastic mixing model is similar to that used for the scalar dissipation, whereas the reorientation process is described in analogy with collisions between Maxwellian molecules, i.e., conserving both momentum and energy. Pope [1985] developed an alternative model for the conditional acceleration term, based on the generalized Langevin model. 

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