Tags » Mathematical Physics

Electromagnetic 3D subsurface imaging with source sparsity for a synthetic object [IMA]


This paper concerns electromagnetic 3D subsurface imaging in connection with sparsity of signal sources. We explored an imaging approach that can be implemented in situations that allow obtaining a large amount of data over a surface or a set of orbits but at the same time require sparsity of the signal sources. 207 more words

Instrumentation And Methods For Astrophysics

Ernst formulation of axisymmetric fields in $f(R)$ gravity: applications to neutron stars and gravitational waves [CL]


The Ernst formulation of the Einstein equations is generalised to accommodate $f(R)$ theories of gravity. It is shown that, as in general relativity, the axisymmetric $f(R)$ field equations for a vacuum spacetime that is either stationary or cylindrically symmetric reduce to a single, non-linear differential equation for a complex-valued scalar function. 88 more words

High Energy Astrophysical Phenomena

Exact power series solutions of the structure equations of the general relativistic isotropic fluid stars with linear barotropic and polytropic equations of state [CL]


Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. 233 more words

Solar And Stellar Astrophysics

On dynamical systems approaches and methods in $f(R)$ cosmology [CL]


We discuss dynamical systems approaches and methods applied to flat Robertson-Walker models in $f(R)$-gravity. We argue that a complete description of the solution space of a model requires a global state space analysis that motivates globally covering state space adapted variables. 169 more words

Cosmology And Nongalactic Astrophysics

Relation between Legendre polynomial Generating function and Legendre differential equation

In the last couple of days I’ve had a little spare time, so I decided to admire a couple of mathematical tools used in the theory of Electrodynamics. 1,236 more words