This paper presents a mathematical formulation for computing the gravitational potential of a cuboid (or right rectangular prism) with uniform density. The resulting analytical expressions are valid inside, on and outside the cuboid. The methodology systematically organizes logarithmic and arctangent terms using a hexagonal graph approach, promoting numerical stability and correct sign allocation. We provide a structured pseudocode algorithm to facilitate computational implementation, and actual codes written in Python, Matlab and Julia. We also introduce a test, that we call a Laplacian test, used to validate our algorithm and codes. Keywords: Gravitational Potential, Cuboid, Hexagonal Graph, Finite Differences, Laplacian Test.

The angular Doppler effect was introduced by Garetz. While the usual Doppler effect is caused by the translational motion of the emitter, the angular Doppler effect is caused by the rotational motion of the emitter. It results into the frequency shift of a circularly-polarized light. In the present paper we analyze the angular Doppler effect caused by the rotational motion of ions in a magnetic field. We demonstrate that for the spectral lines emitted by ions, this effect results in the shift of the σ-components of the Zeeman triplet observed along the magnetic field. We compare the angular Doppler shift in this situation with the fine structure splitting. We show (by the example of He+) that the angular Doppler shift can exceed the fine structure splitting at sub-Giga Gauss magnetic fields. Magnetic fields of this magnitude and even much higher were theoretically expected to develop and were indeed measured in experiments studying relativistic laser-plasma interactions. Magnetic fields of this magnitude and even much higher occur in neutron stars, some of them having helium in their tiny atmospheres. These are the physical situations relevant to our findings.

The most accepted theory for the evolution of the Cosmos is the Big Bang theory, which suggests that, at the beginning, the entire mass-energy of the Cosmos was concentrated within an extremely small, dense and hot singularity. Here, we present a new physical formula that, although obtained in an extremely simple way, has significant implications in Cosmology. This equation indicates that the mass of the Cosmos has grown proportionally with time. This growth equates to a Planck mass for each unit of Planck Time, which is, the mass of 200 000 suns per second. Finally the total energy of the Cosmos is demonstrated to be zero.

In this study, we have estimated the interfacial barrier height (Φb) of Indium Tin Oxide (ITO) coated glass/Malachite Green (MG) dye/Aluminium (Al) based organic device and subsequently we have also observed the effect of carboxylfunctionalized SWCNT (COOH-SWCNT) on the Φb. Presence of COOH-SWCNT reduces the interfacial barrier height as SWCNT acts as filler and provides easy path for charge percolation. We have used ITO coated glass and aluminium as front electrode and back electrode respectively to form the organic device. This organic device has been prepared with and without COOH-SWCNT by using spin coating technique. We have measured the steady state current-Voltage (<i>I</i>-<i>V</i>) characteristics of the device to estimate the interfacial barrier height (Φb) of the device. Φb is reduced from 0.67 eV to 0.59 eV in the presence of COOH-SWCNT. We have also estimated the Φb by using Norde’s Method. This method also shows a reduction of interfacial barrier height from 0.72 eV to 0.64 eV due to incorporation of COOH-SWCNT. Both the methods show good consistency with each other. Reduction of the interfacial barrier height in presence of COOH-SWCNT indicates the enhancement of charge injection through the metal-organic dye interface. By suitable doping or addition of COOH-SWCNT within the MG dye it is possible to reduce the barrier height and enhance the current injection through metal-organic dye interface.

On the evident tripartite equivalency of the light speed and time and distance as a natural paradigm introduced here it is deduced the natural metric tensor of the universe via Mach's mechanics (metric fully governed by measurable universe) included to the fully variable light speed and fully variable gravitational G accompanied with Planckian quantum gravity in natural quantization of the space-time and we see the quantum modes of the gravitational fields by combination of the Planck and Mach and Einstein-Riemannian physics introducing new universal constants. We see a new cosmology on the base of the variable light speed universe via conservation of the total matter of the universe expanding stationary via permanent cyclical transformation of the observable baryonic matter to background ether and the background ether to the observable baryonic matter required by equation of the continuity for equilibrium, creating homogeneity and isotropy and flattening of the universe and reasoning also a universal background minimum temperature creating cosmic microwave background as a black body radiation. Ultimately it is obvious that our universe is a large version of the Planckian mini universe and also we see variable Planck length correlated to the gravitational potential energy.

The Hubble constant has been added in addition to the three fundamental constants (speed of light, gravitational constant and Planck constant) used by Max Planck, for derivation of the Planck mass by dimensional analysis. As a result, a general solution is found for the mass dimension expression m = γp m0, where m0 ≡ mp is the Planck mass, γ = 1.23×10-61 is a small dimensionless quantity and p is an arbitrary parameter in the interval [–1, 1]. The Planck mass mp = 2.17×10-8 kg, mass of the Hubble sphere MH ~ 1053 kg, minimum quantum of mass/energy mG = 2.68×10-69 kg, Weinberg mass mW = 1.08×10-28 kg, mass of hypothetical quantum gravity atom MG = 3.8×1012 kg, Eddington mass limit of stars ME = 6.6×1032 kg and some more masses potentially important for the physics and astrophysics represent particular solutions for values of p, expressed as fractions with small numerators and nominators.

In this study we explore the various aspects involved in nuclear detonations occurring around compact objects and the energetics involved. We discuss the possibility of sub-Chandrasekhar white dwarfs detonating due to the buildup of a layer of hydrogen on the CO white dwarf by accreting from a companion star to explain observed deviations such as subluminous type Ia. We also detail some of the energetics involved that will make such scenarios plausible. Also an alternate model for gamma ray bursts is suggested. For a very close binary system, the white dwarf (close to Chandrasekhar mass limit) can detonate due to tidal heating, leading to a supernova. Material falling on to the neutron star at relativistic velocities can cause its collapse to a magnetar or quark star or black hole leading to a gamma ray burst. As the material smashes on to the neutron star, it is dubbed the Smashnova model. Here the supernova is followed by a gamma ray burst.

We consider the dynamical system, fn+1 = u(fn), (1) (where usually n, is time) defined by a continuous map u. Our target is to find a flow of the system for each initial state f0, i.e., we seek continuous solutions of (1), with the same smoothness degree as u. We start with the introduction of continued forms which are a generalization of continued fractions. With the use of continued forms and a modulator function (i.e., weight function) m, we construct a sequence of smooth functions, which come arbitrarily close to a smooth flow of (1). The limit of this sequence is a functional transform, Km[u], of u, with respect to m. The functional transform is a solution of (1), in the sense that, Km[u] (y + c), is a flow of (1) for each translation constant c. Here we present the first part of our work where we consider a subclass of dissipative dynamical systems in the sence that they have wandering sets of positive measure. In particular we consider strictly increasing real univariate maps, u: D⟶D, D = (a+∞), where, a≤0, or, a=-∞, with the property, u(x)-x≥ε>0, which implies that u, has no real fixed points. We briefly give some mathematical and physical applications and we discuss some open problems. We demonstrate the method on the simple non-linear dynamical system, fn+1 = (fn)2+1.

The study proposes a quantum approach to explain existence and main features of the gravitational waves radiated by an isolated two body orbiting system. The quantum eigenvalues of such a system are calculated with the help of the space-time quantum uncertainty, without additional hypotheses via an “ab initio” model. The approach is deliberately non-relativistic: The model does not implement any relativistic assumption and shows that the mere quantum approach is enough to get energy loss and orbit radius contraction coincident with that early inferred by Einstein. However the outcomes of the model also show features typical of the quantum systems, which are purposely discussed.

We calculate the Newtonian gravitational potential and field of a cubic, homogeneous asteroid and we a pply it to the orbit of possible satellites. Large astronom ical objects such as stars or planets, naturally te nd to form spherical shapes due to the dominance of the gravit ational forces, but as a thought experiment, we con sider the properties of a planet in the form of a perfect cub e. We investigate the formation of stable orbits ar ound such cubic objects, for the case of a static as well as a rotating cube employing the method of Poincare sections. The calculation of the gravitational field around non-s pherical objects has a significant role in space mi ssions to investigate asteroid belt objects that require calc ulating orbits around a large non-spherical mass. T he calculation of such non-spherical fields also has r elevance in identifying deposits or beds of ores in side the Earth, by measuring gravitational anomalies.