arXiv subjects

Homero G. Díaz-Marín

Publications and source records attributed to Homero G. Díaz-Marín.

6 recordsLinked to original sources

arXiv2024

Intraspecific and monotone enzyme catalysis with oscillatory substrate and inhibitor supplies

Enzyme catalysis in reactors for industrial applications usually require an external intervention of the species involved in the chemical reactions. We analyze the most elementary open enzyme catalysis with competitive inhibition where a time-dependent inflow of substrate and inhibitor supplies is modeled by almost periodic functions. We prove global stability of an almost periodic solution for the non-autonomous dynamical system arising from the mass-law action. This predicts a well behaved situation in which the reactor oscillates with global stability. This is a first case study in the path toward broader global stability results regarding intraspecific and monotone open reaction networks.

math.DS↗

arXiv2023

Potentials for solenoidal fields using the three-dimensional $φ$-harmonic cyclic algebra

Given a PDE in [10] it is proposed a method for constructing solutions by considering an associative real algebra A, and a suitable affine vector field $φ$ with respect to which the components of all the functions $\mathcal{L}\circφ$ are solutions, where $\mathcal L$ is differentiable in the sense of Lorch with respect to A. When we consider the 3D cyclic algebra and a suitable 3D affine map $φ$ we get families of solutions for the Laplace equation with three independent variables.

math.AP↗

arXiv2019

A Poisson Algebra for Abelian Yang-Mills Fields on Riemannian Manifolds with Boundary

We define a family of observables for abelian Yang-Mills fields associated to compact regions $U \subseteq M$ with smooth boundary in Riemannian manifolds. Each observable is parametrized by a first variation of solutions and arises as the integration of gauge invariant conserved current along admissible hypersurfaces contained in the region. The Poisson bracket uses the integration of a canonical presymplectic current.

math-ph↗

arXiv2018

Quantum Abelian Yang-Mills Theory on Riemannian Manifolds with Boundary

We quantize abelian Yang-Mills theory on Riemannian manifolds with boundaries in any dimension. The quantization proceeds in two steps. First, the classical theory is encoded into an axiomatic form describing solution spaces associated to manifolds. Second, the quantum theory is constructed from the classical axiomatic data in a functorial manner. The target is general boundary quantum field theory, a TQFT-type axiomatic formulation of quantum field theory.

hep-th↗

arXiv2018

Observable currents and a covariant Poisson algebra of physical observables

Observable currents are locally defined gauge invariant conserved currents; physical observables may be calculated integrating them on appropriate hypersurfaces. Due to the conservation law the hypersurfaces become irrelevant up to homology, and the main objects of interest become the observable currents them selves. Gauge inequivalent solutions can be distinguished by means of observable currents. With the aim of modeling spacetime local physics, we work on spacetime domains $U\subset M$ which may have boundaries and corners. Hamiltonian observable currents are those satisfying ${\sf d_v}F=-ι_VΩ_L+{\sf d_h}σ^F$ and a certain boundary condition. The family of Hamiltonian observable currents is endowed with a bracket that gives it a structure which generalizes a Lie algebra in which the Jacobi relation is modified by the presence of a boundary term. If the domain of interest has no boundaries the resulting algebra of observables is a Lie algebra. In the resulting framework algebras of observable currents are associated to bounded domains, and the local algebras obey interesting gluing properties. These results are due to considering currents that defined only locally in field space and to a revision of the concept of gauge invariance in bounded spacetime domains. A perturbation of the field on a bounded spacetime domain is regarded as gauge if: (i) the "first order holographic imprint" that it leaves in any hypersurface locally splitting a spacetime domain into two subdomains is negligible according to the linearized gluing field equation, and (ii) the perturbation vanishes at the boundary of the domain. A current is gauge invariant if the variation in them induced by any gauge perturbation vanishes up to boundary terms.

gr-qc↗

arXiv2015

General Boundary Formulation for $n$-Dimensional Classical Abelian Theory with Corners

We propose a general reduction procedure for classical field theories provided with abelian gauge symmetries in a Lagrangian setting. These ideas come from an axiomatic presentation of the general boundary formulation (GBF) of field theories, mostly inspired by topological quantum field theories (TQFT). We construct abelian Yang-Mills theories using this framework. We treat the case for space-time manifolds with smooth boundary components as well as the case of manifolds with corners. This treatment is the GBF analogue of extended TQFTs. The aim for developing this classical formalism is to accomplish, in a future work, geometric quantization at least for the abelian case.

math-ph↗