5,535 research outputs found
GloptiPoly 3: moments, optimization and semidefinite programming
We describe a major update of our Matlab freeware GloptiPoly for parsing
generalized problems of moments and solving them numerically with semidefinite
programming
Moment and SDP relaxation techniques for smooth approximations of problems involving nonlinear differential equations
Combining recent moment and sparse semidefinite programming (SDP) relaxation
techniques, we propose an approach to find smooth approximations for solutions
of problems involving nonlinear differential equations. Given a system of
nonlinear differential equations, we apply a technique based on finite
differences and sparse SDP relaxations for polynomial optimization problems
(POP) to obtain a discrete approximation of its solution. In a second step we
apply maximum entropy estimation (using moments of a Borel measure associated
with the discrete solution) to obtain a smooth closed-form approximation. The
approach is illustrated on a variety of linear and nonlinear ordinary
differential equations (ODE), partial differential equations (PDE) and optimal
control problems (OCP), and preliminary numerical results are reported
Critical slowing down and fading away of the piston effect in porous media
We investigate the critical speeding up of heat equilibration by the piston
effect (PE) in a nearly supercritical van der Waals (vdW) fluid confined in a
homogeneous porous medium. We perform an asymptotic analysis of the averaged
linearized mass, momentum and energy equations to describe the response of the
medium to a boundary heat flux. While nearing the critical point (CP), we find
two universal crossovers depending on porosity, intrinsic permeability and
viscosity. Closer to the CP than the first crossover, a pressure gradient
appears in the bulk due to viscous effects, the PE characteristic time scale
stops decreasing and tends to a constant. In infinitly long samples the
temperature penetration depth is larger than the diffusion one indicating that
the PE in porous media is not a finite size effect as it is in pure fluids.
Closer to the CP, a second cross over appears which is characterized by a
pressure gradient in the thermal boundary layer (BL). Beyond this second
crossover, the PE time remains constant, the expansion of the fluid in the BL
drops down and the PE ultimately fades away
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