2,008,921 research outputs found
Scaling Relations for the Cosmological "Constant" in Five-Dimensional Relativity
When the cosmological "constant" is derived from modern five-dimensional
relativity, exact solutions imply that for small systems it scales in
proportion to the square of the mass. However, a duality transformation implies
that for large systems it scales as the inverse square of the mass
Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
The development in the study of supersymmetric many-particle quantum systems
with inverse-square interactions is reviewed. The main emphasis is on quantum
systems with dynamical OSp(2|2) supersymmetry. Several results related to
exactly solved supersymmetric rational Calogero model, including shape
invariance, equivalence to a system of free superoscillators and non-uniqueness
in the construction of the Hamiltonian, are presented in some detail. This
review also includes a formulation of pseudo-hermitian supersymmetric quantum
systems with a special emphasis on rational Calogero model. There are quite a
few number of many-particle quantum systems with inverse-square interactions
which are not exactly solved for a complete set of states in spite of the
construction of infinitely many exact eigen functions and eigenvalues. The
Calogero-Marchioro model with dynamical SU(1,1|2) supersymmetry and a quantum
system related to short-range Dyson model belong to this class and certain
aspects of these models are reviewed. Several other related and important
developments are briefly summarized.Comment: LateX, 65 pages, Added Acknowledgment, Discussions and References,
Version to appear in Jouranl of Physics A: Mathematical and Theoretical
(Commissioned Topical Review Article
Stress Wave Anisotropy in Centered Square Highly Nonlinear Granular Systems
Highly ordered, close packed granular systems present a nonlinear dynamic behavior stemming from the Hertzian contact interaction between particles. We investigated the propagation of elastic stress waves in an uncompressed, centered square array of spherical and cylindrical particles. We show, via experiments and numerical simulations, that systematic variations of the mass and stiffness ratios of the spherical and cylindrical particles lead to large variations in the characteristics of the propagating stress wave fronts traveling through the system. The ability to control the stress wave front properties in these granular systems may allow for the development of new wave-tailoring materials including systems capable of redirecting impact energy
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