arXiv subjects

P. Padilla

Publications and source records attributed to P. Padilla.

5 recordsLinked to original sources

arXiv2021

Extending Friedmann equations using fractional derivatives using a Last Step Modification technique: the case of a matter dominated accelerated expanding Universe

We present a toy model for extending the Friedmann equations of relativistic cosmology using fractional derivatives. We do this by replacing the integer derivatives, in a few well-known cosmological results with fractional derivatives leaving their order as a free parameter. All this with the intention to explain the current observed acceleration of the Universe. We apply the Last Step Modification technique of fractional calculus to construct some useful fractional equations of cosmology. The fits of the unknown fractional derivative order and the fractional cosmographic parameters to SN Ia data shows that this simple construction can explain the current accelerated expansion of the Universe without the use of a dark energy component with a MOND-like behaviour using Milgrom's acceleration constant which sheds light into to the non-necessity of a dark matter component as well.

gr-qc↗

arXiv2021

Low-Loss Reconfigurable Phase Shifter in Gap-Waveguide Technology for mm-Wave Applications

In this brief, we present a low-loss mechanically reconfigurable phase shifter implemented in gap-waveguide technology for mm-wave frequencies. The proposed design gives a practical implementation of tuning elements inside the waveguide providing alternatives to the use of the E-plane split waveguide at high frequencies in order to avoid leakage losses. The depicted phase shifter design is based on a H-plane split waveguide. The phase shift is controlled by means of a tuning screw, which exerts pressure on a flexible metallic strip inserted inside the waveguide. The flexible strip bends with different curvature radii and determines the phase shift at the output port. Cost-effective manufacturing and simple implementation of the flexible metallic strip are achieved by means of the gap-waveguide design. A prototype has been manufactured for validation purposes. Good impedance matching is achieved from 64 GHz to 75 GHz providing a 15.8% impedance bandwidth. The results show a maximum phase shift of 250$^{o}$ with a maximum and mean insertion loss (IL) of 3 dB and 1.7 dB, respectively.

eess.SP↗

arXiv2016

Measuring social complexity and the emergence of cooperation from entropic principles

Assessing quantitatively the state and dynamics of a social system is a very difficult problem. It is of great importance for both practical and theoretical reasons such as establishing the efficiency of social action programs, detecting possible community needs or allocating resources. In this paper we propose a new general theoretical framework for the study of social complexity, based on the relation of complexity and entropy in combination with evolutionary dynamics to asses the dynamics of the system. Imposing the second law of thermodynamics, we study the conditions under which cooperation emerges and demonstrate that it depends of relative importance of local and global fitness. As cooperation is a central concept in sustainability, this thermodynamic-informational approach allows new insights and means to asses it using the concept of Helmholtz free energy. Finally we introduce a new set of equations that consider the more general case where the social system change both in time and space, and relate our findings to sustainability.

physics.soc-ph↗

arXiv2001

Quantum Collapse of a Small Dust Shell

The full quantum mechanical collapse of a small relativistic dust shell is studied analytically, asymptotically and numerically starting from the exact finite dimensional classical reduced Hamiltonian recently derived by Háj{\'ı}ček and Kuchař. The formulation of the quantum mechanics encounters two problems. The first is the multivalued nature of the Hamiltonian and the second is the construction of an appropriate self adjoint momentum operator in the space of the shell motion which is confined to a half line. The first problem is solved by identifying and neglecting orbits of small action in order to obtain a single valued Hamiltonian. The second problem is solved by introducing an appropriate lapse function. The resulting quantum mechanics is then studied by means of analytical and numerical techniques. We find that the region of total collapse has very small probability. We also find that the solution concentrates around the classical Schwarzschild radius. The present work obtains from first principles a quantum mechanics for the shell and provides numerical solutions, whose behavior is explained by a detailed WKB analysis for a wide class of collapsing shells.

gr-qc↗

arXiv2000

The Effect of low Momentum Quantum Fluctuations on a Coherent Field Structure

In the present work the evolution of a coherent field structure of the Sine-Gordon equation under quantum fluctuations is studied. The basic equations are derived from the coherent state approximation to the functional Schrödinger equation for the field. These equations are solved asymptotically and numerically for three physical situations. The first is the study of the nonlinear mechanism responsible for the quantum stability of the soliton in the presence of low momentum fluctuations. The second considers the scattering of a wave by the Soliton. Finally the third problem considered is the collision of Solitons and the stability of a breather. It is shown that the complete integrability of the Sine-Gordon equation precludes fusion and splitting processes in this simplified model. The approximate results obtained are non-perturbative in nature, and are valid for the full nonlinear interaction in the limit of low momentum fluctuations. It is also found that these approximate results are in good agreement with full numerical solutions of the governing equations. This suggests that a similar approach could be used for the baby Skyrme model, which is not completely integrable. In this case the higher space dimensionality and the internal degrees of freedom which prevent the integrability will be responsable for fusion and splitting processes. This work provides a starting point in the numerical solution of the full quantum problem of the interaction of the field with a fluctuation.

hep-ph↗