Contribution of Pressure to the Energy-Momentum Density in a Moving Perfect Fluid -- a Physical Perspective

In the energy-momentum density expressions for a relativistic perfect fluid with a bulk motion, one comes across a couple of pressure-dependent terms, which though well known, are to an extent, lacking in their conceptual basis and the ensuing physical interpretation. In the expression for the energy density, the rest mass density along with the kinetic energy density of the fluid constituents due to their random motion, which contributes to the pressure as well, are already included. However, in a fluid with a bulk motion, there are, in addition, a couple of explicit, pressure-dependent terms in the energy-momentum densities, whose presence to an extent, is shrouded in mystery, especially from a physical perspective. We show here that one such pressure-dependent term appearing in the energy density, represents the work done by the fluid pressure against the Lorentz contraction during transition from the rest frame of the fluid to another frame in which the fluid has a bulk motion. This applies equally to the electromagnetic energy density of electrically charged systems in motion and explains in a natural manner an apparently paradoxical result that the field energy of a charged capacitor system decreases with an increase in the system velocity. The momentum density includes another pressure-dependent term, that represents an energy flow across the system, due to the opposite signs of work being done by pressure on two opposite sides of the moving fluid. From Maxwell's stress tensor we demonstrate that in the expression for electromagnetic momentum of an electric charged particle, it is the presence of a similar pressure term, arising from electrical self-repulsion forces in the charged sphere, that yields a natural explanation for the famous, more than a century old, 4/3 factor in the electromagnetic mass.

General Formulation of Eliminating Unusual Amplitude Growth for Structure-Dependent Integration Algorithms

An unusual amplitude growth of the steady-state response for structures with high natural frequencies was found in explicit or semi-explicit structure-dependent integration algorithms with unconditional stability, second-order accuracy and no overshoot. This paper proposes a general formulation for eliminating such an unusual amplitude growth, by incorporating the load-dependent term into the displacement recursive formula without changing the numerical properties of the integration algorithm. Compared with the existing formulation using the local truncation error for eliminating the unusual amplitude growth, the proposed formulation has the advantages of less symbolic operations, while naturally including the existing formulation. In addition, it is observed that the coefficients of the load-dependent term are proportional to the limit values of the displacement coefficients in the displacement recursive formula as the natural frequency of the system tends to infinity. Then, the general formulation of the load-dependent term is tested for 15 structure-dependent integration algorithms to verify its correctness. Finally, numerical examples of linear and nonlinear multiple-degrees-of-freedom systems illustrate that the general formulation can remove effectively and conveniently the unusual amplitude growth for dynamic response analyses.

Spontaneous and gravitational baryogenesis

Some problems of spontaneous and gravitational baryogenesis are discussed. Gravity modification due to the curvature-dependent term in gravitational baryogenesis scenario is considered. It is shown that the interaction of baryonic fields with the curvature scalar leads to strong instability of the gravitational equations of motion and as a result to noticeable distortion of the standard cosmology.

Modified interaction radius and touching spheres schemes for the determination of impact parameter in Coulomb excitation experiments

The parametrization schemes based on interaction radius and touching spheres (ts) commonly used for the determination of minimum value of impact parameter [Formula: see text] in the above barrier Coulomb excitation experiments are modified by incorporating an energy-dependent term. The modification leads to about 13% improvement in the value of [Formula: see text] for a variety of projectile target combinations at above Coulomb barrier incident energies.

RETURN-PREDICTING FACTORS FOR US TREASURIES: ON THE SIMILARITY OF "TENTS" AND "BATS"

Different authors find optically very different patterns ("tents" and "bats") when excess returns from US Treasuries are regressed against forward rates. A separate source of disagreement is whether the recent tent-shaped factor found by Cochrane & Piazzesi (2004, 2005, 2008) is fundamentally different from the slope (in yields) explanatory factor for the time-dependent term premia that has been identified since the early 1990s. We show that "tent" and "bat" patterns produce predictions of excess returns that are economically indistinguishable, both locally and globally. We also argue that, if the slope (in yield space) is indeed the most important explanatory factor for excess returns, then a simple transformation of the loadings of the forwards rates on the slope factor naturally recovers an approximate tent shape in forward-rate space. However, a transformation from a slope factor in yields to loadings for forward rates does not easily produce a bat pattern. This may provide indirect corroboration to Cochrane & Piazzesi's (2004) claim that the bat factor is a result of near colinearity for smoothed data, and that the "tent" solution is intrinsically different from the "bat" solution.