Dependable numerical results from long-time simulations require stable numerical integration schemes. For Hamiltonian systems, this is achieved with symplectic integrators, which conserve the symplectic condition and exactly solve for the dynamics for an approximate Hamiltonian. The conventional generating function formalism used for Hamiltonian systems is problematic for magnetic systems, as the Hamiltonian is not easily separable. This paper presents a derivation of symplectic integrators from a discretized action. Using this method, it is shown that the integrator due to Boris is a symplectic integrator in the non-relativistic limit, and a relativistic integrator is derived.
A recurrent and central theme in discussions of the quality of life in urban areas is the supposed relationship between population density (people per acre), household crowding (people per room) and social problems. The usual assumption is that these forms of congestion are stressful to individuals and that the resultant stress is manifested in increased rates of physical, psychological and social disorders. Studies in animal biology are the major source of information linking crowding and density to stress pathology. The relatively consistent findings of these investigations indicate that crowding is associated with heightened neurological activity and hormonal aberrations, a decrease in normal reproductive behaviour, increased aggression, and higher morbidity and mortality rates (Calhoun
Studying single-particle dynamics over many periods of oscillations is a well-understood problem solved using symplectic integration. Such integration schemes derive their update sequence from an approximate Hamiltonian, guaranteeing that the geometric structure of the underlying problem is preserved. Simulating a self-consistent system over many oscillations can introduce numerical artifacts such as grid heating. This unphysical heating stems from using non-symplectic methods on Hamiltonian systems. With this guidance, we derive an electrostatic algorithm using a discrete form of Hamilton's Principle. The resulting algorithm, a gridless spectral electrostatic macroparticle model, does not exhibit the unphysical heating typical of most particlein-cell methods. We present results of this using a two-body problem as an example of the algorithm's energy-and momentum-conserving properties.
The flow induced in a long cylinder by an axially discharging round turbulent jet was investigated experimentally with applications to crude oil storage in the U.S. strategic petroleum reserves (SPR). It was found that the flow does not reach a true steady state, but vacillates periodically. Digital video recordings and particle image velocimetry were used to map the flow structures and velocity/vorticity fields, from which the frequency of jet switching, jet stopping distance, mean flow, turbulence characteristics, and the influence of end-wall boundary conditions were inferred. The results were parameterized using the characteristic length D and velocity J 1/2 /D scales based on the jet kinematic momentum flux J and cylinder width D. The scaling laws so developed could be used to extrapolate laboratory observations to SPR flows.
Three groups of mother-son dyads interacted with the Interpersonal Game Test. Each group consisted of 10 dyads in which the sons had been designated as aggressive, withdrawn, or controls on the basis of therapists' ratings and scores on a behavioral checklist. Various patterns of interacting were identified (e.g., competitive, dominant-submissive) and some differences in mother-son interactions seemed related to aggression/withdrawal in children. The potential advantages of a procedure such as the Interpersonal Game Test over more conventional procedures for assessing family interactions were discussed.
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