arXiv subjects

Mayer Humi

Publications and source records attributed to Mayer Humi.

At least 19 recordsLinked to original sources

arXiv2025

Lorentz Invariant Equations for Multiplets and Their Gauge

This paper explores the existence of kinematical gauge transformations for Lorentz invariant equations which describe a multiplet of two spin $\frac{1}{2}$ particles. For this multiplet the additional gauge invariance can be in form of three different groups of transformation. This gauge is absent when the particles are treated separately. Some basic properties of the solutions for these "multiplet equations" are analyzed.

physics.gen-ph↗

arXiv2022

Reduction of Stratified Axi-Symmetric Euler-Poisson Equations Under Symmetry

The paper considers Euler-Poisson equations which govern the steady state of a self gravitating, rotating, axi-symmetric fluid under the additional assumption that it is incompressible and stratified. In this setting we show that the original system of six nonlinear partial differential equations can be reduced to two equations, one for the mass density and the other for gravitational field. This reduction is carried out in cylindrical coordinates. As a result we are able to derive also expressions for the pressure as a function of the density. The resulting equations are then solved analytically. These analytic solutions are used then to determine the shape of the rotating star (or interstellar cloud) by applying the boundary condition that the pressure is zero at the boundary.

math.AP↗

arXiv2019

Climate Modeling and Bifurcation

Many papers and monographs were written about the modeling the Earth climate and its variability. However there is still an obvious need for a module that presents the fundamentals of climate modeling to students at the undergraduate level. The present educational paper attempts to fill in this gap. To this end we collect in this paper the relevant climate data and present a simple zero and one dimensional models for the mean temperature of the Earth. These models can exhibit bifurcations from the present Earth climate to an ice age or a "Venus type of climate". The models are accompanied by Matlab programs which enable the user to change the models parameters and explore the impact that these changes might have on their predictions on Earth climate.

physics.pop-ph↗

arXiv2018

Axisymmetric, Rotating and Stratified Star

The paper considers Euler-Poisson equations which govern the steady state of a self gravitating, rotating, axi-symmetric stars under the additional assumption that it is composed of incompressible stratified fluid. The original system of six nonlinear equations is reduced to two equations, one for the mass density and the other for gravitational field. This reduction is carried out separately in cylindrical and spherical coordinates. As a "byproduct" we derive also expressions for the pressure. The resulting equations are then solved approximately and these analytic solutions are used then to determine the shape of the rotating star.

astro-ph.SR↗

arXiv2018

Structure of Polytropic Stars in General Relativity

The inner structure of a star or a primordial interstellar cloud is a major topic in classical and relativistic physics. The impact that General Relativistic principles have on this structure has been the subject of many research papers. In this paper we consider within the context of General Relativity a prototype model for this problem by assuming that a star consists of polytropic gas. To justify this assumption we observe that stars undergo thermodynamically irreversible processes and emit heat and radiation to their surroundings. Due to the emission of this energy it is worthwhile to consider an idealized model in which the gas is polytropic. To find interior solutions to the Einstein equations of General Relativity in this setting we derive a single equation for the cumulative mass distribution of the star and use Tolman-Oppenheimer-Volkoff equation to derive formulas for the isentropic index and coefficient. Using these formulas we present analytic and numerical solutions for the polytropic structure of self-gravitating stars and examine their stability. We prove also that when the thermodynamics of a star as represented by the isentropic index and coefficient is known, the corresponding matter density within the star is uniquely determined.

gr-qc↗

arXiv2016

Spherical Isentropic Protostars in General Relativity

In the process of protostar formation, astrophysical gas clouds undergo thermodynamically irreversible processes and emit heat and radiation to their surroundings. Due the emission of this energy one can envision an idealized situation in which the gas entropy remains nearly constant. In this setting, we derive in this paper interior solutions to the Einstein equations of General Relativity for spheres which consist of isentropic gas. To accomplish this objective we derive a single equation for the cumulative mass distribution in the protostar. From a solution of this equation one can infer readily the coefficients of the metric tensor. In this paper we present analytic and numerical solutions for the structure of the isentropic self-gravitating gas. In particular we look for solutions in which the mass distribution indicates the presence of shells, a possible precursor to solar system formation. Another possible physical motivation for this research comes from the observation that gamma ray bursts are accompanied by the ejection of large amounts of thermodynamically active gas at relativistic velocities. Under these conditions it is natural to use the equations of general relativity to inquire about the structure of the ejected mass.

gr-qc↗

arXiv2015

Satellite Orbits and Relative Motion in Levi-Civita Coordinates

In this paper we consider satellite trajectories in central force field with quadratic drag using two formalisms. The first using polar coordinates in which the angular momentum plays a dominant role. The second is in Levi-Civita coordinates in which the energy plays a central role. We then unify these two formalisms by introducing polar coordinates in Levi-Civita space and derive a new equation for satellite orbits in which energy and and angular momentum are on equal footing {and thus characterize the orbit by its two invariants}. In the second part of the paper we derive in Levi-Civita coordinates a linearized equation for the relative motion of two satellites whose trajectories are in the same plane. We carry out also a numerical verification of these equations.

physics.space-ph↗

arXiv2015

Self Gravitating Incompressible Fluid in Two Dimensions

In this paper we develop two models for the steady states and evolution of two dimensional isothermal self gravitating and rotating incompressible gas which are based on the hydrodynamic equations for stratified fluid. The first model is for the steady states of the gas while the second addresses the time evolution of the gas subject to some constraints. These models reduce the initial five partial differential equations that govern this system to two for the steady state model and to three for the time dependent model. Analytical and numerical solutions of the model equations are used to study the structure of the resulting steady and time dependent states of the fluid with some possible astrophysical applications.

astro-ph.EP↗

arXiv2014

Closed form Solutions to Some Nonlinear equations by a Generalized Cole-Hopf Transformation

In the first part of this paper we linearize and solve the Van der Pol and Lienard equations with some additional nonlinear terms by the application of a generalized form of Cole-Hopf transformation. We then show that the same transformation can be used to linearize Painleve III equation for certain combinations of its parameters. Finally we linearize new forms of Burger's and related convective equations with higher order nonlinearities.

math-ph↗

arXiv2013

On the Solution of the Van der Pol Equation

We linearize and solve the Van der Pol equation (with additional nonlinear terms) by the application of a generalized form of Cole-Hopf transformation. We classify also Lienard equations with low order polynomial coefficients which can be linearized by this transformation.

math-ph↗

arXiv2013

Convective Equations and a Generalized Cole-Hopf Transformation

Differential equations with convective terms such as the Burger's equation appear in many applications and have been the subject of intense research. In this paper we use a generalized form of Cole-Hopf transformation to relate the solutions of some of these nonlinear equations to the solutions of linear equations. In particular we consider generalized forms of Burger's equation and second order nonlinear ordinary differential equations with convective terms which can represent steady state one-dimensional convection.

math-ph↗

arXiv2013

Near Earth Asteroids:The Celestial Chariots

In this paper we put forward a proposal to use Near Earth Objects as radiation shield for deep space exploration. In principle these objects can provide also a spacious habitat for the astronauts and their supplies on their journeys. We undertake also a detailed assessment of this proposal for a mission from Earth to Mars.

physics.pop-ph↗

arXiv2012

A Generalized Cole-Hopf Transformation for Nonlinear ODES

We introduce a hybrid Cole-Hopf-Darboux transformation to relate solutions of nonlinear and linear second order differential equations and derive a sufficient condition for this correspondence. In particular we show that solutions of some nonlinear second order equations are related to the special functions of mathematical physics through this transformation. These nonlinear equations can be viewed as the "class of special nonlinear equations" which correspond to the linear differential equations which define the special functions of mathematical physics.

math-ph↗

arXiv2012

A New Approach to Impulsive Rendezvous near Circular Orbit

A new approach is presented for the problem of optimal impulsive rendezvous of a spacecraft in an inertial frame near a circular orbit in a Newtonian gravitational field. The total characteristic velocity to be minimized is replaced by a related characteristic-value function and this related optimization problem can be solved in closed form. The solution of this problem is shown to approach the solution of the original problem in the limit as the boundary conditions approach those of a circular orbit. Using a form of primer-vector theory the problem is formulated in a way that leads to relatively easy calculation of the optimal velocity increments. A certain vector that can easily be calculated from the boundary conditions determines the number of impulses required for solution of the optimization problem and also is useful in the computation of these velocity increments. Necessary and sufficient conditions for boundary conditions to require exactly three nonsingular non-degenerate impulses for solution of the related optimal rendezvous problem, and a means of calculating these velocity increments are presented. If necessary these velocity increments could be calculated from a hand calculator containing trigonometric functions. A simple example of a three-impulse rendezvous problem is solved and the resulting trajectory is depicted.

physics.space-ph↗

arXiv2012

EMD Algorithm with Approximate Zero Crossings

The classical EMD algorithm has been used extensively in the literature to decompose signals that contain nonlinear waves. However when a signal contain two or more frequencies that are close to one another the decomposition might fail. In this paper we propose a new formulation of this algorithm which is based on the zero crossings of the signal and show that it performs well even when the classical algorithm fail. We address also the filtering properties and convergence rate of the new algorithm versus the classical EMD algorithm.

math.NA↗

arXiv2011

A Modified EMD Algorithm and its Applications

math.NA↗

arXiv2011

Separation of Coupled Systems of Schrodinger Equations by Darboux transformations

Darboux transformations in one independent variable have found numerous applications in various field of mathematics and physics. In this paper we show that the extension of these transformations to two dimensions can be used to decouple systems of Schrodinger equations and provide explicit representation for three classes of such systems. We show also that there is an elegant relationship between these transformations and analytic complex matrix functions.

math-ph↗

arXiv2008

Long's Equation in Terrain Following Coordinates

Long's equation describes two dimensional stratified atmospheric flow over terrain which is represented by the geometry of the domain. The solutions of this equation over simple topography were investigated analytically and numerically by many authors. In this paper we derive a new terrain following formulation of this equation which incorporates the terrain as part of the differential equation rather than the geometry of the domain. This leads to new analytic insights about the solutions of this equation and enable us to compute steady state gravity wave patterns over complex topography.

physics.geo-ph↗