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Starting from a general transformation for spherically symmetric metrics where g\_11=-1/g\_00, we analyze coordinates with the common property of conformal flatness at constant solid angle element. Three general possibilities arise: one where tortoise coordinate appears as the unique solution, other that includes Kruskal-Szekeres coordinates as a very specific case, but that also allows other similar transformations, and finally a new set of coordinates with very different properties than the other two. In particular, this represents any causal patch of the spherically symmetric metrics in a compactified form. We analyze some relations, taking the Schwarzschild case as prototype, but also contrasting the cosmological de-Sitter and Anti-de-Sitter solutions for the new proposed pulsating coordinates., Comment: 17 pages, 4 figures. Preliminar result was presented in GRG23 Conference (China, 2022). Find the published version (DOI below), improving interpretations and a result about AdS Spacetime in: https://rdcu.be/dz1ftrdcu.be/dz1ft

This paper deals with the modeling and mathematical analysis of vehicular traffic phenomena according to a kinetic theory approach, where the microscopic state of vehicles is described by: (i) position, (ii) velocity, as a continuous variable, and also (iii) activity, namely a variable suited to model the quality of the driver-vehicle micro-system. Interactions at the microscopic scale are modeled by methods of game theory with continuous velocity variable, thus leading to the derivation of mathematical models within the framework of the kinetic theory of active particles. Short-range interactions and mean field interactions are modeled to depict velocity changes related to passing and clustering phenomena. Finally, we perform an analysis of a constructive method to solve the model., Comment: 19 pages, 2 figures

We deduce a model for glioma invasion making use of DTI data and accounting for the dynamics of brain tissue being actively degraded by tumor cells via excessive acidity production, but also according to the local orientation of tissue fibers. Our approach has a multiscale character: we start with a microscopic description of single cell dynamics including biochemical and/or biophysical effects of the tumor microenvironment, translated on the one hand into cell stress and corresponding forces and on the other hand into receptor binding dynamics; these lead on the mesoscopic level to kinetic equations involving transport terms w.r.t. all kinetic variables and eventually, by appropriate upscaling, to a macroscopic reaction-diffusion equation for glioma density with multiple taxis, coupled to (integro-)differential equations characterizing the evolution of acidity and macro- and mesoscopic tissue. Our approach also allows for a switch between fast and slower moving regimes, %diffusion- and drift-dominated regimes, according to the local tissue anisotropy. We perform numerical simulations to investigate the behavior of solutions w.r.t. various scenarios of tissue dynamics and the dominance of each of the tactic terms, also suggesting how the model can be used to perform a numerical necrosis-based tumor grading or support radiotherapy planning by dose painting. We also provide a discussion about alternative ways of including cell level environmental influences in such multiscale modeling approach, ultimately leading in the macroscopic limit to (multiple) taxis.

By using a totally antisymmetric spinor field we generalize Elko theory. We compare our proposed theory with traditional totally antisymmetric spinor field theory based on the Dirac equation. As an application of our formalism we comment about the possibility to link our generalized Elko theory with matroids, qubits and surreal numbers., Comment: Latex, 13 pages, published online in Modern Physics Letters A

We make a number of remarks on linearized gravity with cosmological constant in any dimension, which, we argue, can be useful in a quantum gravity framework. For this purpose we assume that the background space-time metric corresponds to the de Sitter or anti-de Sitter space. Moreover, via the graviton mass and the cosmological constant correspondence, we make some interesting observations, putting special attention on the possible scenario of a graviton-tachyon connection. We compare our proposed formalism with the Novello and Neves approach., Comment: 22 pages, accepted for publication in Rev. Mex. Phys

We show that via the Grassmann-Pl\"ucker relations, the various apparent unrelated concepts, such as duality, matroids, qubits, twistors and surreal numbers are, in fact, deeply connected. Moreover, we conjecture the possibility that these concepts may be considered as underlying mathematical structures in quantum gravity., Comment: 17 pages, published in Frontier in Physics

A compact, portable and large field-of-view gamma camera to identify, locate and quantify gamma-ray emitting radioisotopes in real-time has been developed. The device delivers spectroscopic and imaging capabilities, which allow one to use it in a variety of nuclear waste characterisation scenarios, such as radioactivity monitoring in nuclear power plants and more specifically for the decommissioning of nuclear facilities. The technical development of this apparatus and some examples of its application in field measurements are reported in this article. The performance of the presented gamma-camera is also benchmarked against other conventional techniques.

In this paper, we present some results for existence of global solutions and attractivity for mulidimensional fractional differential equations involving Riemann-Liouville derivative. First, by using a Bielecki type norm and Banach fixed point theorem, we prove a Picard-Lindel\"of type theorem on the existence and uniqueness of solutions. Then, applying the properties of Mittag-Leffler functions, we describe the attractivity of solutions to some classes of Riemann--Liouville linear fractional differential systems.

The work reported here demonstrates that it is possible to accurately determine surface gravities of $\delta$ Sct stars using the frequency content from high precision photometry and a measurement of the parallax. Using a sample of 10 eclipsing binary systems with a $\delta$ Sct component and the unique $\delta$ Sct star discovered with a transiting planet, WASP-33, we were able to refine the $\Delta\nu-\bar\rho$ relation. Using this relation and parallaxes, we obtained independent values for the masses and radii, allowing us to calculate the surface gravities without any constraints from spectroscopic or binary analysis. A remarkably good agreement was found between our results and those published, extracted from the analysis of the radial velocities and light curves of the systems. This reinforces the potential of $\Delta\nu$ as a valuable observable for $\delta$ Sct stars and settles the degeneracy problem for the $\log g$ determination through spectroscopy., Comment: 5 pages, 2 figures, 1 table

We analyse test particle's trajectories around the geometry of a Schwarzschild black hole. In order to resemble sections of jets in the neighborhood of a black hole, we consider the conserved quantities corresponding to constraints imposed on the trajectories of the test particles, namely conic and hyperboloidic trajectories. As expected, the energy and angular momentum are closely related to the solutions in the non-constrained case., Comment: 13 pages, 2 figures

We make a number of observations on Conway surreal number theory which may be useful, for further developments, in both in mathematics and theoretical physics. In particular, we argue that the concepts of surreal numbers and matroids can be linked. Moreover, we established a relation between the Gonshor approach on surreal numbers and tensors. We also comment about the possibility to connect surreal numbers with supesymmetry. In addition, we comment about possible relation between surreal numbers and fractal theory. Finally, we argue that the surreal structure may provide a different mathematical tools in the understanding of singularities in both high energy physics and gravitation., Comment: 19 pages, Latex, to be published in Journal of Modern Physics

The Dirac equation in four time and four space dimensions (or (4+4)-dimensions) is considered. Step by step we show that such an equation admits Majorana and Weyl solutions. In order to obtain the Majorana or Weyl spinors we used a method based on the construction of Clifford algebra in terms of 2x2-matrices. We argue that our approach can be useful in supergravity, superstrings and qubit theory., Comment: 16 pages, Latex, accepted for its publication in International Journal of Geometric Methods in Modern Physics

We develop an alternative Ashtekar formalism in eight dimensions. In fact, using a MacDowell-Mansouri physical framework and a self-dual curvature symmetry we propose an action in eight dimensions in which the Levi-Civita tenor with eight indices plays a key role. We explicitly show that such an action contains number of linear, quadratic and cubic terms in the Riemann tensor, Ricci tensor and scalar curvature. In particular, the linear term is reduced to the Einstein-Hilbert action with cosmological constant in eight dimensions. We prove that such a reduced action is equivalent to the Lovelock action in eight dimensions., Comment: 12 pages, Latex, accepted for publication in Modern Physics Letters A

In this short note, we show that the real function recently proposed by Bruce J. West [Exact solution to fractional logistic equation, Physica A 429 (2015) 103--108] is not an exact solution for the fractional logistic equation., Comment: 7 pages, 4 figures

This paper concerns a model for tumor cell migration through the surrounding extracellular matrix by considering mass balance phenomena involving the chemical interactions produced on the cell surface. The well-posedness of this model is proven. An asymptotic analysis via a suitable hydrodynamic limit completes the description of the macroscopic behaviour.

Using a Lagrangian formalism we establish a relationship between the (n + D + d) dimensional cosmology, black-holes and the Polyakov action for strings. Specifically, we identify these physical scenarios as part of a 2-dimensional metric, which arises from a Lagrangian function with constraints, derived from the Einstein-Hilbert action. In particular, we show that the Friedmann-Robertson-Walker cosmological model and the Schwarzschild solution are both consequence of this Lagrangian., Comment: 7 pages, Latex

In this paper we prove that the fractional derivative or the fractional primitive of a $T$-periodic function cannot be a $\tilde{T}$-periodic function, for any period $\tilde{T}$, with the exception of the zero function., Comment: 12 pages