Related papers: Bridging geometries and potentials in DBI cosmolog…
We consider the problem of how to determine the force laws in an amorphous system of interacting particles. Given the positions of the centers of mass of the constituent particles we propose a new algorithm to determine the inter-particle…
The depletion force and depletion potential between two in principle unequal "big" hard spheres embedded in a multicomponent mixture of "small" hard spheres are computed using the Rational Function Approximation method for the structural…
We perform a detailed dynamical system analysis for the behaviour of a Dirac-Born-Infeld (DBI) field in a spatially closed Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmology. The DBI field is characterised by a potential and brane…
Persistence diagrams are efficient descriptors of the topology of a point cloud. As they do not naturally belong to a Hilbert space, standard statistical methods cannot be directly applied to them. Instead, feature maps (or representations)…
There is now strong evidence that the current energy density of the Universe is dominated by dark energy with an equation of state w<-1/3, which is causing accelerated expansion. The build-up of structure within such Universes is subject to…
We obtain exact solutions of the one-dimensional Schrodinger equation for some families of associated Lame potentials with arbitrary energy through a suitable ansatz, which may be appropriately extended for other such a families. The…
Generally making the cosmological scale factor $R$ be a function of the coordinate of the extra dimension $\sigma $ that is also a function of time $t$, we achieve a new kind of cosmic acceleration mechanism depending on extra dimension. We…
We present a new method for dealing with geometrical selection effects in galaxy surveys while using a multifractal framework. The power of multifractal analysis lies in its connection to higher order moments, in that it not only probes…
The consideration of dark energy's quanta, required also by thermodynamics, introduces its chemical potential into the cosmological equations. Isolating its main contribution, we obtain solutions with dark energy decaying to matter or…
We show how several important classical problems, with positive definite potential energy, can be solved by starting from the factorization of the total mechanical energy using complex numbers. In particular, we derive in a new way exact…
We define a scale of weighted Morrey spaces which contains different weighted versions appearing in the literature. This allows us to obtain weighted estimates for operators in a unified way. In general, we obtain results for weights of the…
A generalized definition of superpotential has proposed, which connects two one-dimensional potentials $V_{1}$ and $V_{2}$ with discrete energy spectra completely and where: 1) energy of factorization equals to arbitrary level of spectrum…
In the pursuit of a general formulation for a modified gravitational theory at the non-relativistic level and as an alternative to the dark matter hypothesis, we construct a model valid over a wide variety of astrophysical scales. Through…
We study the solutions of the Einstein equations in (d+2)-dimensions, describing parallel p-branes (p=d-1) in a space with two transverse dimensions of positive gaussian curvature. These solutions generalize the solutions of Deser and…
A family of cosmological solutions with $(n+1)$ Ricci-flat spaces in the theory with several scalar fields and multiple exponential potential is obtained when coupling vectors in exponents obey certain relations. Two subclasses of solutions…
The energy and momentum for different cosmological models using various prescriptions are evaluated. In particular, we have focused our attention on the energy and momentum for gravitational waves and discuss the results. It is concluded…
A new method to determine the bias parameter of galaxies relative to matter is suggested. The method is based on the assumption that gravity is the dominating force which determines the formation of the structure in the Universe. Due to…
The concept of partnership of potentials is studied in detail and in particular the non-uniqueness due to the ambiguity in the election of the factorization energy and in the choice of the solution of certain Riccati equation. We generate…
The cosmographic technique is a powerful model-independent tool for distinguishing between competing cosmological scenarios. The key strengths and weaknesses of standard cosmography are discussed in view of healing the convergence problem…
Multidimensional factorization method is formulated in arbitrary curvilinear coordinates. Particular cases of polar and spherical coordinates are considered and matrix potentials with separating variables are constructed. A new class of…