while others either arrive dead in the water or take hold only to wither and die? Modern diffusion studies have focused primarily on the structural aspects of diffusion, or the existence of tangible points of contact between adopters and adoptees, as well as the environmental contexts that modulate such interactions. But as Strang and Soule (1998:276) note, “[S]tructural opportunities for meani...

We present a solver of 3D two-fluid plasma model for the simulation short-pulse laser interactions with plasma. This resolves equations ideal gas closure. also include Bhatnagar-Gross-Krook collision model. Our is based on PseudoSpectral Time-Domain (PSTD) method to solve Maxwell's curl equations. use Strang splitting integrate Euler source term: while are solved composite scheme mixing Lax-Fri...

In many transport-chemistry models, a huge system of ODE's of the advection-diffusion-reaction type has to be integrated in time. Typically, this is done with the help of operator splitting. Operator splitting is attractive for complex large-scale transport-chemistry models because it allows to handle different processes separately in different parts of the computer program. Rosenbrock schemes ...

We prove convergence of the Hamiltonian Particle-Mesh (HPM) method, initially proposed by J. Frank, G. Gottwald, and S. Reich, on a periodic domain when applied to the irrotational shallow water equations as a prototypical model for barotropic compressible fluid flow. Under appropriate assumptions, most notably sufficiently fast decay in Fourier space of the global smoothing operator, and a Str...

This paper offers a simple, entirely prognostic, ocean circulation model based on the separation of the complete dynamics, including sound waves, into elementary Poisson brackets. For example, one bracket corresponds to the propagation of sound waves in a single direction. Other brackets correspond to the rotation of the velocity vector by individual components of the vorticity and to the actio...

We establish improved uniform error bounds on a second-order Strang time-splitting method which is equivalent to an exponential wave integrator for the long-time dynamics of nonlinear Klein--Gordon equation (NKGE) with weak cubic nonlinearity, whose strength characterized by $\varepsilon^2$ $0 < \varepsilon \leq 1$ dimensionless parameter. Actually, when \ll 1$, NKGE $O(\varepsilon^2)$ nonlinea...

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.[delete if co-registered] Contributions Heather Strang and Lawrence W. Sherman contributed to the writing and revising of this Review. Daniel J. Woods and Barak A...

We analyze operator splitting methods applied to scalar equations with a nonlinear advection operator, and a linear (local or nonlocal) diffusion operator or a linear dispersion operator. The advection velocity is determined from the scalar unknown itself and hence the equations are so-called active scalar equations. Examples are provided by the surface quasi-geostrophic and aggregation equatio...