Physical Mathematics

Each of welding processes has some disadvantages and limitations; For instance existence of welding imperfections that might be due to poor workmanship or design issues such as cracks, porosity, lack of fusion, incomplete penetration, spatters and others. Failure of Schenectady T2 tanker in 1943 is a good example of brittle fracture where the crack initiated due to presence of notches in steels that are sensitive at low temperature

In this paper we introduce a new technique for constructing solutions of the ultra-relativistic Euler equations. The Riemann invariants are formulated. We also give some applications of the Riemann invariants. We firstly study the geometric properties of the solution in Riemann invariants coordinates. The other application of Riemann invariants, representing the ultra-relativistic Euler equations in diagonal form, which admits the existence of global smooth solution for the ultra-relativistic Euler equations.

The derivation of Lorentz Transformation Equations in the Special Theory of Relativity, besides being explicitly based on the two postulates of that theory is also critically based on an implicit premise that the detection of a light signal/particle at a point in space at an instant of time is an event that is not exclusive to any inertial reference frame but it is capable of being measured by the observers in other inertial reference frames as well. This paper explains how this untested paradoxical premise vitiates the entire theory and suggests its replacement with a contrary postulate that the detection of light in an inertial reference frame is an event that is exclusive to that frame. This paper shows that if that contrary postulate is accepted, then the absoluteness of space and time declared by Newton can coexist with the absoluteness of the speed of light in vacuum declared by Einstein without any conflict between them.

Several different gravitational laws can be derived that fall within a spectrum that covers an extreme from elliptical partial differential equations for Newtonian gravitation to hyperbolic or wave equations demonstrated by other laws from Jefimenko to Einstein’s relativity. If each of these equations is valid for specific conditions at a considerable distance from space, then there is an interesting counterpoint with similar physical mathematical behavior that may be analogous between gravity and say, fluid dynamics. Here, Newtonian gravitation appears mathematically similar to subsonic flow while the other laws mathematically are comparable to supersonic flow. This evaluation advocates identifying experiments that may observe creating an inhomogeneous gravitational field that mathematically result in producing gravitational shocks or waves embedded in regions with merging different distinct strength gravitational fields. If such shocks are feasible, exploiting these gravitational shocks in a propulsion system would create thrust to possibly shadow or repel gravitation. Variations in energy to generate mass may create these distinct and separate gravitational fields for these gravitational shocks. Such an investigation is warranted for mankind to exploit developing this embryonic technology that potentially may develop an exotic space propulsor capable of moving faster than light (FTL).

Here, the nuclear fractional integro differential equation is considered. Then, the numerical solution of the linear fractional integro differential operator m m LΦ = λ Φ is discussed. In addition, the eigenvalues (EVs) and the corresponding eigenfunctions (EFs) are obtained for the nuclear integral equation (NIE). Finally, the relation between the fractional coefficient and the potential function is obtained.

Perspective variances cause conflicts of understanding between all people and are especially evident among the many builders of gravity theories. External Gravity theory provides a 180 degree change of perspective relative to current theories. While consistent with experience, External Gravity Theory rebuilds gravity and its flow direction and source by focusing on the actions of the structure of space rather than actions caused by matter. The flow of gravity is broken down into beams for increased analysis potential. Another name for External Gravitation would be Beam Theory. Of the many revelations found with gravity beams, the focus of this paper is on the solution of gravity measurements during eclipses which led to the dual eclipse bump anomaly.

We develop further our fibre bundle construct of non-commutative space-time on a Minkowski base space. We assume space-time is non-commutative due to the existence of additional non-commutative algebraic structure at each point x of space-time, forming a quantum operator ‘fibre algebra’ A(x). This structure then corresponds to the single fibre of a fibre bundle. A gauge group acts on each fibre algebra locally, while a ‘section’ through this bundle is then a quantum field of the form {A(x);x∈M} with M the underlying space-time manifold. In addition, we assume a local algebra O(D) corresponding to the algebra of sections of such a principal fibre bundle with base space a finite and bounded subset of space-time, D. The algebraic operations of addition and multiplication are assumed defined fibrewise for this algebra of sections

The result of the Lorentz Transformation on a classical formula is that an observer in reference frame A observes the same phenomena in reference frame B like an observer in reference frame B observing the phenomena in reference frame A. Is that true? In this article I demonstrate at the Doppler effect that this is valid even for ‘absolute’ velocities belonging to a reference frame outside of A and B. I suggest to test whether the geometric means of frequencies belong to the frames A and B or to a reference frame outside of A and B by an experiment at CERN. In the latter case this would have significant implications in space-time modelling

A discrete path in space-time can be considered as a series of applications of the translation subgroup of the Poincare group. If there is a local mapping from this translation group into a neighbourhood of the identity of a quantum Weyl algebra fibre bundle, then the whole classical path can be lifted into the fibre bundle to form a unique quantum field as a section through the fibres. Under the further assumptions of scale relativity, we also show that a discrete closed loop in space time, corresponding to two classical paths sharing the same end points, is renormalisable and the finite limit has anomalous dimension equal to the fractal dimension. We end by introducing the possibility of a ‘push forward’ connection on the bundle O(D) of Ehresmann type.

We continue to develop further a new mathematical approach to the quantisation of general field theories such as general relativity and modified gravity. Treating quantum fields as fibre bundles, we discuss operators acting on each fibre that generate a ‘Fibre Algebra’. The algebras of two types of operators are considered in detail, namely observables as generic physical variables and more specialised quantum operators suitable for describing particles, symmetries and transformations. We then introduce quantum states of these operators and examine their properties. By establishing a link between the commutativity and group cohomology of the translational group as a local gauge group, we show that this leads to unitary representations. of the local gauge group of diffeomorphisms under very general topological conditions; as well the construction of generalised symmetric quantum states invariant under this group action. Discussion of these results in the context of loop quantum gravity and other current theories highlights constraints on the local nature of space-time.

Dark can’t be on the same sentence of a Hypothesis. Let’s surmise here an alternative model in which the time turn around the space with non-zero angular momentum. Then, there should be a center and we may observe anisotropies, and indeed although they are not explicit in space, but are observed over time, and we identify a beginning and an arrow-of-time. If so, to preserve the metrics invariance through scale, estimated distances to deep galaxies may be corrected by replacing the FLRW metrics by another logarithmic based, according to now a days observations in supernovae Ia range up to 0.2

Matter is actually under numerous investigations because of our misunderstanding on some observed phenomena, especially at the astronomic and cosmological scales. In the present article, a scalar field theory is investigated to explain the mass of particles from a global point of view. An universal mechanism is developed and a general relation is eventually proposed that enables to make some accurate predictions for the mass of composite particles. Numerical values are provided including predictions for existing particles, with discrete energy spectrum in relation to large-scale phenomena.