Papers by Cesar S Lopez-Monsalvo
Journal of Physics A: Mathematical and Theoretical
In this work we show that a Legendre transformation is nothing but a mere change of contact polar... more In this work we show that a Legendre transformation is nothing but a mere change of contact polarization from the point of view of contact geometry. Then, we construct a set of Riemannian and pseudo-Riemannian metrics on a contact manifold by introducing almost contact and para-contact structures and we analyze their isometries. We show that it is not possible to find a class of metric tensors which fulfills two properties: on the one hand, to be polarization independent i.e. the Legendre transformations are the corresponding isometries and, on the other, that it induces a Hessian metric into the corresponding Legendre submanifolds. This second property is motivated by the well known Riemannian structures of the geometric description of thermodynamics which are based on Hessian metrics on the space of equilibrium states and whose properties are related to the fluctuations of the system. We find that to define a Riemannian structure with such properties it is necessary to abandon the...
Entropy, 2015
In this work, we show that the thermodynamic phase space is naturally endowed with a non-integrab... more In this work, we show that the thermodynamic phase space is naturally endowed with a non-integrable connection, defined by all of those processes that annihilate the Gibbs one-form, i.e., reversible processes. We argue that such a connection is invariant under re-scalings of the connection one-form, whilst, as a consequence of the non-integrability of the connection, its curvature is not and, therefore, neither is the associated pseudo-Riemannian geometry. We claim that this is not surprising, since these two objects are associated with irreversible processes. Moreover, we provide the explicit form in which all of the elements of the geometric structure of the thermodynamic phase space change under a re-scaling of the connection one-form. We call this transformation of the geometric structure a conformal gauge transformation. As an example, we revisit the change of the thermodynamic representation and consider the resulting change between the two metrics on the thermodynamic phase space, which induce Weinhold's energy metric and Ruppeiner's entropy metric. As a by-product, we obtain a proof of the well-known conformal relation between Weinhold's and Ruppeiner's metrics along the equilibrium directions. Finally, we find interesting properties of the almost para-contact structure and of its eigenvectors, which may be of physical interest.
arXiv (Cornell University), Jul 8, 2022
We consider the motion of charged particles in the presence of a Dirac magnetic monopole. We use ... more We consider the motion of charged particles in the presence of a Dirac magnetic monopole. We use an extension of Noether's theorem for systems with magnetic forces and integrate explicitly the equations of motion.
Photon Black Holes
We study the relationship between the energy and entropy of a black body photon gas, within an id... more We study the relationship between the energy and entropy of a black body photon gas, within an idealised spherical adiabatic enclosure of radius R, as this is compressed into a self-gravitating regime. We show that this regime approximately coincides with the black hole regime for the system, i.e., R ~ R_{s}, where R_{s} denotes the Schwarzschild radius of the system. The entropy of this system is always below the suggested Holographic bound, even as R \to R_{s}. A plausible quantum configuration for the photon gas at R \to R_{s} is suggested, which satisfies all energy, entropy and temperature black hole conditions. Finally we examine our results from the point of view of recent Loop Quantum Gravity ideas
Secure operating bounds for Wind Energy Conversion Systems working as Conventional Power Generation Plants
IET Generation, Transmission & Distribution, 2019
In this work, it is shown that it is possible to operate a wind energy conversion system (WECS) b... more In this work, it is shown that it is possible to operate a wind energy conversion system (WECS) based on a doubly fed induction generator while operating in a different mode than maximum power tracking. Here, using the recent results on the steady state solution of the torque balance transcendental equation, analytical expressions for all the state variables of the WECS are obtained. In this fashion, closed-form online reference trajectories for the system variables are presented. These analytical formulas can be used to perform power tracking control into the safe operational region of WECS. Moreover, realistic generic case studies are described to depict how these results are useful in systematically assessing the secure operating regime for both, the electric and mechanic components of the WECS.
Covariant thermodynamics & relativity
This thesis deals with the dynamics of irreversible processes within the context of the general t... more This thesis deals with the dynamics of irreversible processes within the context of the general theory of relativity. In particular, we address the problem of the `infinite' speed of propagation of thermal disturbances in a dissipative fluid. Although this problem is not new, its best known solution - the Israel and Stewart second order expansion - has an effective, rather than fundamental, character. The present work builds on the multi-fluid variational approach to relativistic dissipation, pioneered by Carter, and provides a dynamical theory of heat conduction. The novel property of such approach is the thermodynamic interpretation associated with a two-fluid system whose constituents are matter and entropy. The dynamics of this model leads to a relativistic generalisation of the Cattaneo equation; the constitutive relation for causal heat transport. A comparison with the Israel and Stewart model is presented and its equivalence is shown. This discussion provides new insights...
arXiv: General Relativity and Quantum Cosmology, 2020
A class of three dimensional contact manifolds is shown to describe certain types of superconduct... more A class of three dimensional contact manifolds is shown to describe certain types of superconductors. Specializing to a particular para-Sasakian metric on the three-sphere shows it to be a vacuum solution of three-dimensional massive gravity. The geometry is Lorentzian and the manifold enjoys local isometry given by the Heisenberg algebra. The background is shown to support self-gravitating force-free electromagnetic fields of Maxwell-Chern-Simons theory or Abelian Higgs theory.
Food webs are used to describe feeding relationships in an ecosystem. Simple and complex dynamica... more Food webs are used to describe feeding relationships in an ecosystem. Simple and complex dynamical behavior can be displayed in food web chains. From an ecological viewpoint, unstable and chaotic behavior are two dynamical problems of food web ecosystems that may require the introduction of control actions to drive the system to the desired behavior. In this work, we introduce a robust feedback control approach for control and synchronization of populations in food webs. The control design is based on a cascade control structure in conjunction with a simple and robust feedback. Numerical simulations on two case studies, a three trophic food chain model and a bioreactor model with four microbial populations.
A two-fluid model for relativistic heat conduction
Three years ago it was presented in these proceedings the relativistic dynamics of a multi-fluid ... more Three years ago it was presented in these proceedings the relativistic dynamics of a multi-fluid system together with various applications to a set of topical problems [1]. In this talk, I will start from such dynamics and present a covariant formulation of relativistic thermodynamics which provides us with a causal constitutive equation for the propagation of heat in a relativistic setting.
We show that the Thurston geometries are vacuum solutions to the New Massive Gravity equations of... more We show that the Thurston geometries are vacuum solutions to the New Massive Gravity equations of motion. We analyze their Lorentzian counterparts as well.
We show that the Thurston geometries are vacuum solutions to the New Massive Gravity equations of... more We show that the Thurston geometries are vacuum solutions to the New Massive Gravity equations of motion. We analyze their Lorentzian counterparts as well.
Physics Letters B, 2021
The defining property of every three-dimensional e-contact manifold is shown to be equivalent to ... more The defining property of every three-dimensional e-contact manifold is shown to be equivalent to requiring the fulfillment of London's equation in 2+1 electromagnetism. To illustrate this point, we show that every such manifold that is also K-contact and η-Einstein is a vacuum solution to the most general quadratic-curvature gravity action, in particular of New Massive Gravity. As an example we analyze S 3 equipped with a contact structure together with an associated metric tensor such that the canonical generators of the contact distribution are null. The resulting Lorentzian metric is shown to be a vacuum solution of three-dimensional massive gravity. Moreover, by coupling the New Massive Gravity action to Maxwell-Chern-Simons we obtain a class of charged solutions stemming directly from the para-contact metric structure. Finally, we repeat the exercise for the Abelian Higgs theory.
Physics Letters B, 2021
The defining property of every three-dimensional e-contact manifold is shown to be equivalent to ... more The defining property of every three-dimensional e-contact manifold is shown to be equivalent to requiring the fulfillment of London's equation in 2+1 electromagnetism. To illustrate this point, we show that every such manifold that is also K-contact and η-Einstein is a vacuum solution to the most general quadratic-curvature gravity action, in particular of New Massive Gravity. As an example we analyze S 3 equipped with a contact structure together with an associated metric tensor such that the canonical generators of the contact distribution are null. The resulting Lorentzian metric is shown to be a vacuum solution of three-dimensional massive gravity. Moreover, by coupling the New Massive Gravity action to Maxwell-Chern-Simons we obtain a class of charged solutions stemming directly from the para-contact metric structure. Finally, we repeat the exercise for the Abelian Higgs theory.
Revista de la Escuela de Física, Jan 16, 2019
In this manuscript, we present the variational derivation of Maxwell's equations by means of the ... more In this manuscript, we present the variational derivation of Maxwell's equations by means of the variational bi-complex. We use this exercise to introduce the reader to the formulation of geometric variational problems and their implementation in a Computer Algebra System. En este trabajo presentamos la derivación variacional de las ecuaciones de Maxwell por medio del bi-complejo variacional. Usamos este ejercicio para introducir al lector a la formulación geométrica de problemas variacionales y su implementación en un Sistema de Algebra Computacional.
An upper wavelength cut off for the light absorption spectrum of black holes
In this work, we use the fact that kinematics of light propagation in a non-dispersive medium ass... more In this work, we use the fact that kinematics of light propagation in a non-dispersive medium associated with a bi-metric spacetime is expressed by means of a 1-parameter family of contact transformations. We present a general technique to find such transformations and explore some explicit examples for Minkowski and anti-deSitter spacetimes geometries.
Journal of Mathematical Physics, 2014
General Relativity and Gravitation, 2013
Revista de la Escuela de Física, 2019
A method to describe exact solutions of the Einstein-Maxwell field equations in terms of relativi... more A method to describe exact solutions of the Einstein-Maxwell field equations in terms of relativistic thin disks constituted by two perfect charged fluids is presented. Describing the surface of the disk as a single charged fluid we find explicit expressions for the rest energies, the pressures and the electric charge densities of the two fluids. An explicit example is given. The particular case of the thin disks composed by two charged perfect fluids with barotropic equation of state is also presented.
arXiv: Mathematical Physics, 2020
In this work we show that a Legendre transformation is nothing but a mere change of symplectic po... more In this work we show that a Legendre transformation is nothing but a mere change of symplectic polarization from the point of view of contact geometry. Then, we construct a set of Riemannian and pseudo-Riemannian metrics on a contact manifold by introducing almost contact and para-contact structures and we analyze their isometries. We show that it is not possible to find a class of metric tensors which fulfills two properties: on the one hand, to be polarization independent i.e. the Legendre transformations are the corresponding isometries and, on the other, that it induces a Hessian metric into the corresponding Legendre submanifolds. This second property is motivated by the well known Riemannian structures of the geometric description of thermodynamics which are based on Hessian metrics on the space of equilibrium states and whose properties are related to the fluctuations of the system. We find that to define a Riemannian structure with such properties it is necessary to abandon ...
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Papers by Cesar S Lopez-Monsalvo