It has been observed, in earlier computations of bifurcation diagrams for dissipative partial differential equations, that the use of certain explicit approximate inertial forms can give rise to numerical artifacts su...
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We present a fast numerical method for solving the incompressible Euler's equation in two dimensions for the special case when the flow field can be represented by patches of constant vorticity. The method is an a...
We present a fast numerical method for solving the incompressible Euler's equation in two dimensions for the special case when the flow field can be represented by patches of constant vorticity. The method is an adaptive vortex method in which cells (vortex blobs) of multiple scales are used to represent the patches so that the number of vortex blobs needed to approximate the patches is proportional to the length of the boundary curve of the patch and inversely proportional to the width of the smallest blob (cell) used. Points along the boundaries of the patches are advected according to the velocity obtained from the approximating vortices.
We describe a new approach to the Monte-Carlo simulations of two-dimensional gravity. Standard dynamical triangulation technique was combined with results of direct enumeration of the cubic graphs. As a result we were...
We describe a new approach to the Monte-Carlo simulations of two-dimensional gravity. Standard dynamical triangulation technique was combined with results of direct enumeration of the cubic graphs. As a result we were able to build large (128K vertices) statistically independent random graphs directly. The quantitative correspondence between our results and those obtained by standard methods has been observed. The algorithm proved to be so efficient that we were able to conduct all the simulations, which usually require the most powerful computers, on an Iris workstation. An opportunity to generate large random graphs allowed us to observe that the internal geometry of random surfaces is more complicated than simple fractals. External geometry also proved to be rather peculiar.
We report first results of a large-scale simulation of two-dimensional quantum gravity using the dynamical triangulation model for systems of up to sixteen thousand triangles. Our results for the internal geometry sho...
We report first results of a large-scale simulation of two-dimensional quantum gravity using the dynamical triangulation model for systems of up to sixteen thousand triangles. Our results for the internal geometry show an unexpectedly complicated behavior of the internal volume as function of the internal radius. A simple fractal characterization is inadequate to describe the geometry of the states in the system.
A three‐dimensional computational simulator of nonplanar substrates coated with positive photoresists is presented. The model includes four major steps: projection printing, exposure, post‐exposure baking (PEB), and...
A three‐dimensional computational simulator of nonplanar substrates coated with positive photoresists is presented. The model includes four major steps: projection printing, exposure, post‐exposure baking (PEB), and dissolution. Projection printing is based on Hopkins’ classical work. The exposure model employs the full nonlinear wave equation coupled with the photoactive compound (PAC) bleaching rate equation. These equations are solved using a spectral element iterative scheme. The PEB is treated as a material diffusion equation employing ideas introduced by Mack and the dissolution algorithm is our LEAD (least action dissolution) algorithm modified for nonplanar substrates. Several realistic examples are presented displaying final profiles at various dissolution times.
S. Kida, M. Takaoka, F. Hussain; Corrigendum:‘‘Reconnection of two vortex rings’’ [Phys. Fluids A 1, 630 (1989)]Comments, Physics of Fluids A: Fluid Dynamics, V
S. Kida, M. Takaoka, F. Hussain; Corrigendum:‘‘Reconnection of two vortex rings’’ [Phys. Fluids A 1, 630 (1989)]Comments, Physics of Fluids A: Fluid Dynamics, V
An inertial manifold is constructed for the scalar reaction-diffusion equation u t = vu xx +ƒ(u) with a cubic nonlinearity. Uniform bounds are obtained for the number of zeros along solutions to the variational equati...
An inertial manifold is constructed for the scalar reaction-diffusion equation u t = vu xx +ƒ(u) with a cubic nonlinearity. Uniform bounds are obtained for the number of zeros along solutions to the variational equations satisfied by the difference of two elements on the unstable manifolds of equilibria. This uniformity leads to the global parameterization of the attractor as a function defined in the linear unstable manifold of the least stable equilibrium. By the introduction of local techniques near each equilibrium, we succeed in constructing an inertial manifold of lowest possible dimension.
The correspondence principle postulated for the description of hydrodynamic turbulence [Phys. Rev. Lett. 57, 1722 (1986)] combined with the theory of thermal boundary layer [B. Castaing et al. (private communication)]...
The correspondence principle postulated for the description of hydrodynamic turbulence [Phys. Rev. Lett. 57, 1722 (1986)] combined with the theory of thermal boundary layer [B. Castaing et al. (private communication)] is applied to high Rayleigh number convection in a Bénard cell. Quantitative interpretation of recent experimental data [B. Castaing et al. (private communication)] is presented. The predicted intermittency exponent following from comparison of the theory with experiment is 0.175<μ<0.275. A crucial experimental test of the renormalization group theory of turbulence is proposed.
The equations of motion describing inviscid fluid flow are solved numerically in two dimensions for the case where the flow can be described by patches of constant vorticity. The case where the vorticity is described ...
The equations of motion describing inviscid fluid flow are solved numerically in two dimensions for the case where the flow can be described by patches of constant vorticity. The case where the vorticity is described initially by two circular patches is studied in detail. The numerical evidence indicates that when the minimum distance between the two patches is initially less than the radius of the patches a singularity forms in finite time on the boundary curves of the patches. The singularity appears to be a jump discontinuity in the tangent vector of the boundary curve.
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