Extremality of mass in the bimetric theory of gravitation

In the bimetric theory of gravitation, the static spherically symmetric case involving matter characterized by density and pressure is considered. It is found that the condition that the mass be stationary under small variations of the field variables (including the density) for a fixed number of baryons leads to the field equations and to the equilibrium condition. If one considers only solutions of the field equations, then the mass for a fixed baryon number is stationary (one can expect it to be extremal in most cases) if the equilibrium condition holds.Dedicated to Achille Papapetrou on the occasion of his retirement.     

Plane waves in the bimetric gravitation theory

Field equations for plane waves are set up and some solutions are obtained. Transverse, longitudinal, and mixed waves are possible. In the purely transverse case the energy density is positive definite. In the purely longitudinal case it may be negative. However, in one example investigated it is positive if the Riemannian metric tensor satisfies a condition corresponding to space-time having satisfactory physical properties.     

Rotordynamic analysis using the Complex Transfer Matrix: An application to elastomer supports using the viscoelastic correspondence principle

Numerous methods are available to calculate rotordynamic whirl frequencies, including analytic methods, finite element analysis, and the transfer matrix method. The typical real-valued transfer matrix (RTM) suffers from several deficiencies, including lengthy computation times and the inability to distinguish forward and backward whirl. Though application of complex coordinates in rotordynamic analysis is not novel per se, specific advantages gained from using such coordinates in a transfer matrix analysis have yet to be elucidated. The present work employs a complex coordinate redefinition of the transfer matrix to obtain reduced forms of the elemental transfer matrices in inertial and rotating reference frames, including external stiffness and damping. Application of the complex-valued state variable redefinition results in a reduction of the 8×8 RTM to the 4×4 Complex Transfer Matrix (CTM). The CTM is advantageous in that it intrinsically separates forward and backward whirl, eases symbolic manipulation by halving the transfer matrices’ dimension, and provides significant improvement in computation time. A symbolic analysis is performed on a simple overhung rotor to demonstrate the mathematical motivation for whirl frequency separation. The CTM?s utility is further shown by analyzing a rotordynamic system supported by viscoelastic elastomer rings. Viscoelastic elastomer ring supports can provide significant damping while reducing the cost and complexity associated with conventional components such as squeeze film dampers. The stiffness and damping of a viscoelastic damper ring are determined herein as a function of whirl frequency using the viscoelastic correspondence principle and a constitutive fractional calculus viscoelasticity model. The CTM is then employed to obtain the characteristic equation, where the whirl frequency dependent stiffness and damping of the elastomer supports are included. The Campbell diagram is shown, demonstrating the CTM?s ability to intrinsically separate synchronous whirl direction for a non-trivial rotordynamic system. Good agreement is found between the CTM results and previously obtained analytic and experimental results for the elastomer ring supported rotordynamic system.     

Adiabatic polarization energy in a simple dense fluid

In this note we prey300505 sent the results of a calculation of the adiabatic electrostatic polarization energy, P⁺, of Xe⁺ in fluid Ar over the density range 0.1–1.4 g cm^?3. P₊ was expressed in terms of Lekner's screening function which, within the framework of the Kirkwood approximation, is determined by the (neutral) solute-solvent and the solvent-solvent pair correlation functions. The density dependence of P₊ can be quite well approximated (within ≈10%) by the Born charging energy with the effective ionic radius being identified with the effective hard-core diameter for the (neutral) solute-solvent separation. The P₊ data, together with experimental spectroscope results for the density dependence of the ionization potential of Xe and of CH₃I, result in preliminary information concerning the ground state energy of the quasi-free electron in fluid Ar over a wide density range.     

Composite quarks and leptons as solutions of anomaly constraints

We provide models for composite fermions which satisfy the anomaly constraints of 't Hooft. All the decoupling requirements are satisfied as preons acquire a mass. The spectrum of the composite fermions is far richer than the preon's while maintaining asymptotic freedom. The available symmetries contain SU(3) × SU(2) × U(1) and the composite particles include the ordinary quarks and leptons along with additional unobserved (presumably heavy) fermions.     

Magnetization plateau and quantum phase transitions in a spin-orbital model

A spin-orbital chain with different Landé g factors and one-ion anisotropy is studied in the context of the thermodynamical Bethe ansatz. It is found that there exists a magnetization plateau resulting from the different Landé g factors. Detailed phase diagram in the presence of an external magnetic field is presented both numerically and analytically. For some values of the anisotropy, the four-component system undergoes five consecutive quantum phase transitions when the magnetic field varies. We also study the magnetization in various cases, especially its behaviors in the vicinity of the critical points. For the SU(4) spin-orbital model, explicit analytical expressions for the critical fields are derived, with excellent accuracy compared with numerics.Received: 8 January 2004, Published online: 8 June 2004PACS: 75.30.Kz Magnetic phase boundaries (including magnetic transitions, metamagnetism, etc.) - 71.27. + a Strongly correlated electron systems; heavy fermions - 75.10.Jm Quantized spin models     

Inclusive ϱ0 production in νp charged-current interactions

Using data from the Fermilab 15 ft hydrogen bubble chamber, we have studied inclusive ?⁰ production in antineutrino-proton charged-current interactions. We measure (0.21 ± 0.03) ?⁰/event, corresponding to ?⁰/π^?=0.12 ± 0.02. As a function of Q² and for hadronic masses above a threshold region, the ?⁰/π^? ratio shows little variation. At least 50% of the ?⁰'s are consistent with coming from the current fragmentation region. The results agree reasonably well with the predictions of the quark fragmentation model of Feynman and field.     

Additive representations of non-additive measures and the choquet integral

This paper studies some new properties of set functions (and, in particular, “non-additive probabilities” or “capacities”) and the Choquet integral with respect to such functions, in the case of a finite domain. We use an isomorphism between non-additive measures on the original space (of states of the world) and additive ones on a larger space (of events), and embed the space of real-valued functions on the former in the corresponding space on the latter. This embedding gives rise to the following results:

the Choquet integral with respect to any totally monotone capacity is an average over minima of the integrand;

the Choquet integral with respect to any capacity is the difference between minima of regular integrals over sets of additive measures;

under fairly general conditions one may define a “Radon-Nikodym derivative” of one capacity with respect to another;

the “optimistic” pseudo-Bayesian update of a non-additive measure follows from the Bayesian update of the corresponding additive measure on the larger space.

We also discuss the interpretation of these results and the new light they shed on the theory of expected utility maximization with respect to non-additive measures.