We develop a mean field theory fo a system of coupled oscillators with random interactions with variable symmetry. Numerical simulations of the resulting one-dimensional dynamics are in accordance with simulations of the N-oscillator dynamics. We find a transition in dependence on interaction strength J and symmetry parameter µ from a dynamically disordered phase to a phase with static disorder, where all oscillators are frozen in random positions. This transition between the"paramagnetic" phase and the spin glass phase appears to be of first order and is dynamically characterized by chaos (positive Lyapunov exponents) in the former case and regular motion (vanishing Lyapunov exponents) in the latter case. The Lyapunov spectrum shows an interesting symmetry for antisymmetric interaction (µ=-1)
Abstract. A hybrid Schwarz/multigrid method for spectral element solvers to the Poisson equation in R 2 is presented. It extends the additive Schwarz method studied by J. Lottes and P. Fischer (J. Sci. Comput. 24:45-78, 2005) by introducing nonuniform weight distributions based on the smoothed sign function. Using a V-cycle with only one pre-smoothing, the new method attains logarithmic convergence rates in the range from 1.2 to 1.9, which corresponds to residual reductions of almost two orders of magnitude. Compared to the original method, it reduces the iteration count by a factor of 1.5 to 3, leading to runtime savings of about 50 percent. In numerical experiments the method proved robust with respect to the mesh size and polynomial orders up to 32. Used as a preconditioner for the (inexact) CG method it is also suited for anisotropic meshes and easily extended to diffusion problems with variable coefficients.
In our recent paper [Phys. Rev. E 58, 1789 (1998)] we found notable deviations from a power-law decay for the "magnetization" of a system of coupled phase oscillators with random interactions claimed by Daido in Phys. Rev. Lett. 68, 1072 (1992). For another long-time property, the Lyaponov exponent, we found that his numerical procedure showed strong time discretization effects and we suspected a similar effect for the algebraic decay. In the Comment to our paper [preceding paper, Phys. Rev. E 61, 2145 (2000)] Daido made clear that the power law behavior was only claimed for the sample averaged magnetization [Z] and he presented new, more accurate numerical results which provide evidence for a power-law decay of this quantity. Our results, however, were obtained for Z itself and not for [Z]. In addition, we have taken the intrinsic oscillator frequencies as Gaussian random variables, while Daido in his new and apparently also in his earlier simulations used a deterministic approximation to the Gaussian distribution. Due to the differences in the observed quantity and the model assumptions our and Daido's results may be compatible.
We present a simple method to derive a planar, instantaneous body force distribution from a given two-dimensional velocity field without knowledge of the pressure field, under the specific restriction that the body force is dominated by one component only. Spatial integration then completely recovers this component. Particle image velocimetry and direct numerical simulations of a wall jet induced by a known body force were conducted to validate the method, demonstrating a good agreement of the original and reconstructed force fields.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.