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Since the first volume of this work came out in Germany in 1924, this book, together with its second volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's second and final revision of 1953.
Abstract An analytical algorithm, called SETTLE, for resetting the positions and velocities to satisfy the holonomic constraints on the rigid water model is presented. This method is still based on the Cartesian coordinate system and can be used in place of SHAKE and RATTLE. We implemented this algorithm in the SPASMS package of molecular mechanics and dynamics. Several series of molecular dynamics simulations were carried out to examine the performance of the new algorithm in comparison with the original RATTLE method. It was found that SETTLE is of higher accuracy and is faster than RATTLE with reasonable tolerances by three to nine times on a scalar machine. Furthermore, the performance improvement ranged from factors of 26 to 98 on a vector machine since the method presented is not iterative. © 1992 by John Wiley & Sons, Inc.
It now appears that the general nature of the deviations from uniformity in the spectrum of a complicated nucleus is essentially the same in all regions of the spectrum and over the entire Periodic Table. This behavior, moreover, is describable in terms of standard Hamiltonian ensembles which could be generated on the basis of simple information-theory concepts, and which give also a good account of fluctuation phenomena of other kinds and, apparently, in other many-body systems besides nuclei. The main departures from simple behavior are ascribable to the moderation of the level repulsion by effects due to symmetries and collectivities, for the description of which more complicated ensembles are called for. One purpose of this review is to give a self-contained account of the theory, using methods---sometimes approximate---which are consonant with the usual theory of stochastic processes. Another purpose is to give a proper foundation for the use of ensemble theory, to make clear the origin of the simplicities in the observable fluctuations, and to derive other general fluctuation results. In comparing theory and experiment, the authors give an analysis of much of the nuclear-energy-level data, as well as an extended discussion of observable effects in nuclear transitions and reactions and in the low-temperature thermodynamics of aggregates of small metallic particles.
During the last few years, considerable interest has been focused on the phase that waves accumulate when the equations governing the waves vary slowly. The recent flurry of activity was set off by a paper by Michael Berry, where it was found that the adiabatic evolution of energy eigenfunctions in quantum mechanics contains a phase of geometric origin (now known as 'Berry's phase') in addition to the usual dynamical phase derived from Schrödinger's equation. This observation, though basically elementary, seems to be quite profound. Phases with similar mathematical origins have been identified
Turbulence is of vital interest and importance to the study of fluid dynamics Pope (1990). In classical physics, turbulence was first studied carefully for incompressible flows whose evolution was given by the Navier-Stokes equations. One of the most celebrated results of incompressible classical turbulence (CT) is the existence of an inertial range with the cascade of kinetic energy from large to small spatial scales until one reaches scale lengths on the order of the dissipationwave length and the eddies/vortices are destroyed. The Kolmogorov kinetic energy spectrum in this inertial range follows the power law in wave number space.
Progress of Theoretical Physics Vol. 29 No. 2 (1963) pp. 235-254 Coupled Partial-Wave-Dispersion-Relation for Nucleon-Nucleon Scattering and ρ- and ω-meson Contributions Susumu Furuichi Progress of Theoretical Physics Vol. 30 No. 3 (1963) pp. 327-342 Contributions of KK Intermediate State to Nucleon Form Factors Ghanshyam Prasad Singh