0000000000237337
AUTHOR
B. H. Lavenda
showing 8 related works from this author
Hyperbolic nature of uniformly rotating systems and their relation to gravity
2008
Special relativity corresponds to hyperbolic geometry at constant velocity while the so-called general relativity corresponds to hyperbolic geometry of uniformly accelerated systems. Generalized expressions for angular momentum, centrifugal and Coriolis forces are found in hyperbolic space, which reduce to the usual expressions of Euclidean space when the absolute constant tends to infinity. Gravity enters only in the specification of the absolute constant. A uniformly rotating disc corresponds exactly to hyperbolic geometry with a constant negative Gaussian curvature. The angle defect is related to Lorentz contraction of objects normal to the radial direction. Lobachevsky's angle of parall…
The Khuri-Jones Threshold Factor as an Automorphic Function
2013
The Khuri-Jones correction to the partial wave scattering amplitude at threshold is an automorphic function for a dihedron. An expression for the partial wave amplitude is obtained at the pole which the upper half-plane maps on to the interior of semi-infinite strip. The Lehmann ellipse exists below threshold for bound states. As the system goes from below to above threshold, the discrete dihedral (elliptic) group of Type 1 transforms into a Type 3 group, whose loxodromic elements leave the fixed points 0 and $\infty$ invariant. The transformation of the indifferent fixed points from -1 and +1 to the source-sink fixed points 0 and $\infty$ is the result of a finite resonance width in the im…
Geometric Entropies of Mixing (EOM)
2005
Trigonometric and trigonometric-algebraic entropies are introduced. Regularity increases the entropy and the maximal entropy is shown to result when a regular $n$-gon is inscribed in a circle. A regular $n$-gon circumscribing a circle gives the largest entropy reduction, or the smallest change in entropy from the state of maximum entropy which occurs in the asymptotic infinite $n$ limit. EOM are shown to correspond to minimum perimeter and maximum area in the theory of convex bodies, and can be used in the prediction of new inequalities for convex sets. These expressions are shown to be related to the phase functions obtained from the WKB approximation for Bessel and Hermite functions.
The Lineage of String Theory
2011
The Regge trajectories, upon which string theory is based, behave as rigid rotators rather than vibrating strings. The same relation, between the angular momentum, and the square of the mass, can be found in gravity, the electroweak, and strong interactions. The angle deficit for cosmic strings is shown to be an angle excess that is related to the increase of the circumference of a uniformly rotating disc. Schr\"odinger's time independent equation with a centrifugal barrier gives an automorphic function that can be constructed as the ratio of its two independent solutions for values of the angular momentum lying outside of their positive, integer values. If the fixed points 0 and $\infty$ i…
The thermodynamics governing 'endoreversible' engines
2006
The thermodynamics of the Curzon-Ahlborn engine, which is a prototype of endoreversible engines, is elucidated. In particular, their criterion for adiabatic equilibration is revised. The so-called irreversibility of endoreversible engines arises from the selection of the coldest reservoir for heat rejection. Rather, if the reservoirs are allowed to come into thermal and mechanical contact, a mean value results which optimizes the work output and heat uptake, and is entirely reversible. The Carnot efficiency cannot be beaten because nothing is as cold as the coldest reservoir.
Errors in the Bag Model of Strings, and Regge Trajectories Represent the Conservation of Angular Momentum in Hyperbolic Space
2011
The MIT bag model is shown to be wrong because the bag pressure cannot be held constant, and the volume can be fixed in terms of it. The bag derivation of Regge's trajectories is invalidated by an integration of the energy and angular momentum over all values of the radius up to $r_0=c/\omega$. This gives the absurd result that "total" angular momentum decreases as the frequency increases. The correct expression for the angular momentum is obtained from hyperbolic geometry of constant negative curvature $r_0$. When the square of the relativistic mass is introduced, it gives a negative intercept which is the Euclidean value of the angular momentum. Regge trajectories are simply statements of…
Aberration and radiation pressure in the Klein and Poincare models
2008
Aberration and radiation pressure reflected by a moving mirror are examples of the Klein and Poincar\'e models of hyperbolic geometry, respectively. Reflection at a moving mirror produces a two-way Dopper shift. Its one-way counterpart, aberration, has nothing to do with the radiation pressure on a moving mirror, but, rather with the pressure on a completely absorbing surface. Both pressures vanish when the angle of parallelism is reached. Two-way, second-order Doppler shifts can be used to establish experimentally the existence of an angle of parallelism.
Entropies of Mixing and the Lorenz Order
2005
Entropies of mixing can be derived directly from the parent distributions of extreme value theory. They correspond to pseudo-additive entropies in the case of Pareto and power function distributions, while to the Shannon entropy in the case of the exponential distribution.The former tend to the latter when their shape parameters tend to infinity and zero, respectively. Hence processes whose entropies of mixing are pseudo-additive entropies majorize, in the Lorenz order sense, those whose entropy is the Shannon entropy. In the case of the arcsine distribution, maximal properties of regular polygons correspond to maximum entropy of mixing.