159,046 research outputs found
Stochastic macromodeling for hierarchical uncertainty quantification of nonlinear electronic systems
A hierarchical stochastic macromodeling approach is proposed for the efficient variability analysis of complex nonlinear electronic systems. A combination of the Transfer Function Trajectory and Polynomial Chaos methods is used to generate stochastic macromodels. In order to reduce the computational complexity of the model generation when the number of stochastic variables increases, a hierarchical system decomposition is used. Pertinent numerical results validate the proposed methodology
Fluid flow dynamics under location uncertainty
We present a derivation of a stochastic model of Navier Stokes equations that
relies on a decomposition of the velocity fields into a differentiable drift
component and a time uncorrelated uncertainty random term. This type of
decomposition is reminiscent in spirit to the classical Reynolds decomposition.
However, the random velocity fluctuations considered here are not
differentiable with respect to time, and they must be handled through
stochastic calculus. The dynamics associated with the differentiable drift
component is derived from a stochastic version of the Reynolds transport
theorem. It includes in its general form an uncertainty dependent "subgrid"
bulk formula that cannot be immediately related to the usual Boussinesq eddy
viscosity assumption constructed from thermal molecular agitation analogy. This
formulation, emerging from uncertainties on the fluid parcels location,
explains with another viewpoint some subgrid eddy diffusion models currently
used in computational fluid dynamics or in geophysical sciences and paves the
way for new large-scales flow modelling. We finally describe an applications of
our formalism to the derivation of stochastic versions of the Shallow water
equations or to the definition of reduced order dynamical systems
From chemical Langevin equations to Fokker-Planck equation: application of Hodge decomposition and Klein-Kramers equation
The stochastic systems without detailed balance are common in various
chemical reaction systems, such as metabolic network systems. In studies of
these systems, the concept of potential landscape is useful. However, what are
the sufficient and necessary conditions of the existence of the potential
function is still an open problem. Use Hodge decomposition theorem in
differential form theory, we focus on the general chemical Langevin equations,
which reflect complex chemical reaction systems. We analysis the conditions for
the existence of potential landscape of the systems. By mapping the stochastic
differential equations to a Hamiltonian mechanical system, we obtain the
Fokker-Planck equation of the chemical reaction systems. The obtained
Fokker-Planck equation can be used in further studies of other steady
properties of complex chemical reaction systems, such as their steady state
entropies.Comment: 6 pages, 0 figure, submitted to J. Phys. A: Math. Theo
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