A bimetric machian approach to gravitation

We propose a bimetric machian approach to gravitation with a mathematical structure much simpler than the one of Rosen's bimetric theories. We obtain two cosmological models based on the simplest assumption that the Universe be filled of pure dust matter. One of the two cosmological models is compatible with the currently observed value of the density of dust matter, and provides an age of the Universe which is of the order of the inverse of the present Hubble parameter. One also obtains the Schwarzschild-like solution and its Newtonian limit together with the modified three Kepler laws which allow us to find that presently 0.5×10^?10 (yr)^?1 δ(A/A)δ 0.625×10^?10 (yr)^?1, a denoting the semimajor axis of the orbit of the test particle. Lastly we obtain the Newtonian limit of the theory.     

New approach to relativity and gravitation

A theory of gravitation, where the stress-energy tensor of the gravitational field is part of the source term of the geometric curvatures, is presented. The theory predicts correctly all the Newtonian and post-Newtonian effects of gravity currently considered as crucial. For extremely strong and nonstatic fields, such as are presumed to exist in quasars and exploding stars, new predictions differing from those of the conventional theory are implied. In the correspondence limit of special relativity the theory recovers the conservation of energy-momentum properly and seems to represent a more satisfactory extension of special theory of relativity.     

A background-dependent approach to the theory of gravitation

On the basis of a Machian view of nature we find a covariant formulation of Newton's gravitational equation in a general frame which satisfies the requirements (i) of being singular if the density of mass is zero everywhere and (ii) of depending on the parallel transport of the four-momentum density of matter (from the three-space point in which it is defined to any other three-space point, at any fixed time) in such a way that it incorporates the idea that the frame has to be fixeddirectly in connection with the distribution and motion of matter. In Paper II we will use such an equation as starting point in order to find relativistic gravitational equations which are supposed to hold in any conceivable universe, describe a purely geometrical theory of gravitation, and explicitly incorporate Mach's principle.     

Dynamical equations and a new analytical approach in lattice gauge theories

A new analytical approach in lattice gauge theories is presented. It is based on the use of the dynamical equations of the theory. The new method is used to discuss the phase structure of abelian lattice gauge systems, the results show that the new approach is an effective one.     

A geometrical approach to the integrability of soliton equations

A separability criterion in one-degree-of-freedom dynamics, suitable for soliton equations, is given in terms of a geometrical structure on the phase manifold. For solitonic degrees of freedom, i.e., those corresponding to the discrete spectrum of the associated Lax operator, integrability is a priori proved.     

Quantum electrodynamics within the framework of a new four-dimensional symmetry

We discuss quantum electrodynamics within the framework of a new four-dimensional symmetry in which the concept of time, the propagation of light, and the transformation property of many physical quantities are drastically different from those in special relativity. However, they are consistent with experiments. The new framework allows for natural developments of additional concepts. Observers in different frames may use the same grid of clocks, located in any one of the frames, and hence have a universal time.I dedicate this paper to the memory of my beloved father, Hsu Mau-Yuen (1903–1977), whose understanding helped me choose to work on physical problems.Work supported in part by the ERDA, Contract No. E(40-1)3992 and by NASA.     

Wavenumber space and physical space responses of a periodically ribbed plate to a point drive: A discrete approach

An efficient technique to estimate the vibration of and sound radiation from a stiffened fluid-loaded plate excited by a mechanical point force is presented. The process is based on the formulation in the wavenumber domain of the transversal displacement of the plate and of the acoustic pressure in the fluid domain. Analytical expressions can be easily obtained for these fields in the case of an infinite plate with stiffeners uniformly spaced. The approach consists then on using the discrete Fourier Transform to deduce the associated fields in the physical space. This transform necessitates truncation of the wavenumber domain and sampling of these wavenumber fields with adequate criterions to avoid loss of information and aliasing. These criterions are discussed in this paper concerning displacement point results on the plate and pressure point results in a part of the fluid domain “close to” the plate. This technique requires relatively small computing time and provides an efficient tool to analyse the vibro-acoustic behaviour of the stiffened plate, both, in the physical and the wavenumber spaces. A comparison between a case discussed in the literature and some examples are presented to illustrate the validity and interests of this approach.     

Dynamical analogy between economical crisis and earthquake dynamics within the nonextensive statistical mechanics framework

The field of study of complex systems considers that the dynamics of complex systems are founded on universal principles that may be used to describe a great variety of scientific and technological approaches of different types of natural, artificial, and social systems. Several authors have suggested that earthquake dynamics and the dynamics of economic (financial) systems can be analyzed within similar mathematical frameworks. We apply concepts of the nonextensive statistical physics, on time-series data of observable manifestations of the underlying complex processes ending up with these different extreme events, in order to support the suggestion that a dynamical analogy exists between a financial crisis (in the form of share or index price collapse) and a single earthquake. We also investigate the existence of such an analogy by means of scale-free statistics (the Gutenberg–Richter distribution of event sizes). We show that the populations of: (i) fracto-electromagnetic events rooted in the activation of a single fault, emerging prior to a significant earthquake, (ii) the trade volume events of different shares/economic indices, prior to a collapse, and (iii) the price fluctuation (considered as the difference of maximum minus minimum price within a day) events of different shares/economic indices, prior to a collapse, follow both the traditional Gutenberg–Richter law as well as a nonextensive model for earthquake dynamics, with similar parameter values. The obtained results imply the existence of a dynamic analogy between earthquakes and economic crises, which moreover follow the dynamics of seizures, magnetic storms and solar flares.     

A geometrical approach for open and closed strings

We show that a candidate for the open string lagrangian proposed earlier has a large tangent space invariance group, in addition to being invariant under extended reparametrization transformations. We also simplify the underlying differential geometry and extend it to the closed string. In the latter case, the well known constraint relating the number of the right and left movers emerges naturally.     

Landau levels in uniaxially strained graphene: A geometrical approach

The effect of strain on the Landau levels (LLs) spectra in graphene is studied, using an effective Dirac-like Hamiltonian which includes the distortion in the Dirac cones, anisotropy and spatial-dependence of the Fermi velocity induced by the lattice change through a renormalized linear momentum. We propose a geometrical approach to obtain the electron’s wave-function and the LLs in graphene from the Sturm–Liouville theory, using the minimal substitution method. The coefficients of the renormalized linear momentum are fitted to the energy bands, which are obtained from a Density Functional Theory (DFT) calculation. In particular, we evaluate the case of Dirac cones with an ellipsoidal transversal section resulting from uniaxially strained graphene along the Arm-Chair (AC) and Zig-Zag (ZZ) directions. We found that uniaxial strain in graphene induces a contraction of the LLs spectra for both strain directions. Also, is evaluated the contribution of the tilting of Dirac cone axis resulting from the uniaxial deformations to the contraction of the LLs spectra.     

A simple geometrical approach to particle production in collisions with nuclei

It is argued that hadron collisions with nuclei are similar to hadron-hadron collisions, having similar properties for the impact parameter distributions and the leading particle spectra. The relevant existing high-energy data, including the universality of multiplicity distributions and the possibility of geometrical scaling in reactions with nuclei, are easily understood in the framework of geometrical models by extending to p-nucleus collisions what was learnt about impact parameter and leading particles in pp collisions. The questions of forward-backward correlations and photo- and electroproduction are briefly discussed.     

A complex minkowski space approach to twistors

This paper is basically a review of known results in twistor theory. Its value is intended to lie in the connections presented between twistor concepts and structures in complex Minkowski space. The relationship of twistor theory to complex null infinity and a new proof of the Kerr theorem are presented; these results are to some extent original.     

Calculation scheme of heavy-ion collisions within the framework of a modified hydrodinamic approach

A hydrodynamic approach to describing heavy-ion collisions with allowance for the emission of the secondary particles is developed. The compression, the expansion, and break-up stages of the resulting hotspot are considered. The formed shock wave has a time-dependent front. The calculated spectra of produced protons are compared with experimental data.     

A background-dependent approach to the theory of gravitation II. Relativistic gravitational equations

On the basis of the results of Paper I and guided by a Machian view of nature, we find new gravitational equations which are background dependent. Such equations describe a purely geometrical theory of gravitation, and their dependence on the background structure is through the total energy-momentum tensor on the past sheet of the light cone of each space-time pointx [θ^μν x, say], i.e., through the integral on the past sheet of the light cone ofx of the parallel transport of the energy-momentum tensor from the space-time point in which it is defined tox along the geodesic connecting the two space-time points. Following Gürsey, we assume that the source of the De Sitter metric is not the cosmological term, but, rather, the energy-momentum tensor of a “uniform distribution of mass scintillations” [T ^μν x, say].T ^μν x, indeed, turns out to be equal to the metric tensor times a constant factor. As a consequence, in any local inhomogeneity A of a space-time whose background structure is determined by the Perfect Cosmological Principle,θ ^μν turns out to be approximately equal to the metric tensor times a constant factor, providedT=g _αβ T ^αβ is sufficiently small and the structure of the past sheet of the light cones of the space-time points belonging to Λ is not too much perturbed by the local gravitational field. As a consequence, in Λ the new equations approximately reduce to Einstein's equations. If one considers a “superuniverse model” in which our universe is considered as a local inhomogeneity in a De Sitter background, then from the above result there follows a fortiori the agreement of the new gravitational equations with the classical tests of gravitation. Furthermore, the dependence on the background structure is such that the new equations (i) incorporate the idea that the frame has to be fixeddirectly in connection with cosmological observations, and (ii) are singular in the absence of matter in the whole space-time. Moreover, (iii) the coupling constant turns out to be dimensionless in natural units (c=1=?), and (iv) a local inertial frame in a De Sitter background is determined by the condition that with respect to it the background structure is homogeneous in space and in time and is Lorentz invariant.