Person:
Díaz Palencia, José Luis

First Name

José Luis

Last Name

Díaz Palencia

Faculty

Escuela Politécnica Superior

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Now showing 1 - 10 of 22

Analysis and profiles of travelling wave solutions to a Darcy-Forchheimer fluid formulated with a non-linear diffusion.
(AIMS Mathematics, 2022) Rahman, S.; Díaz Palencia, José Luis; Roa González, J.
The intention along the presented analysis is to explore existence, uniqueness, regularity of solutions and travelling waves profiles to a Darcy-Forchheimer fluid flow formulated with a non-linear di usion. Such formulation is the main novelty of the present study and requires the introduction of an appropriate mathematical treatment to deal with the introduced degenerate di usivity. Firstly, the analysis on existence, regularity and uniqueness is shown upon definition of an appropriate test function. Afterwards, the problem is formulated within the travelling wave domain and analyzed close the critical points with the Geometric Perturbation Theory. Based on this theory, exact and asymptotic travelling wave profiles are obtained. In addition, the Geometric Perturbation Theory is used to provide evidences of the normal hyperbolicity in the involved manifolds that are used to get the associated travelling wave solutions. The main finding, which is not trivial in the non-linear di usion case, is related with the existence of an exponential profile along the travelling frame. Eventually, a numerical exercise is introduced to validate the analytical solutions obtained.
Fully bio-based Poly (Glycerol-Itaconic acid) as supporter for PEG based form stable phase change materials.
(Composites Communications, 2021) Yin, Guang-Zhong; Díaz Palencia, José Luis; De-Yi, Wang
A novel fully bio-based Poly (Glycerol-Itaconic acid) (PGI) was designed and highly efficiently synthesized by solvent-free polycondensation. The Poly (ethylene glycol) (PEG) was used as the phase change material (PCM) working substance and encapsulated by the sustainable PGI supporter. PEG chains were tightly encapsulated with the PGI supporting material mainly under hydrogen bonds due to the structural compatibility between PGI and PEG. The PCMs can achieve high form stability and high phase change enthalpies in the same kinds of PCMs. Furthermore, the phase change temperatures and enthalpies of the PCMs can be adjusted conveniently by regulating the PEG content and molecular weight. Notably, this process extremely facilitates the realization of efficient mass production due to the eco-friendly nature, high efficiency and low cost.
Characterization of Traveling Waves Solutions to an Heterogeneous Diffusion Coupled System with Weak Advection.
(Mathematics, 2021) Díaz Palencia, José Luis
The aim of this work is to characterize Traveling Waves (TW) solutions for a coupled system with KPP-Fisher nonlinearity and weak advection. The heterogeneous diffusion introduces certain instabilities in the TW heteroclinic connections that are explored. In addition, a weak advection reflects the existence of a critical combined TW speed for which solutions are purely monotone. This study follows purely analytical techniques together with numerical exercises used to validate or extent the contents of the analytical principles. The main concepts treated are related to positivity conditions, TW propagation speed and homotopy representations to characterize the TW asymptotic behaviour.
Regularity, Asymptotic Solutions and Travelling Waves Analysis in a Porous Medium System to Model the Interaction between Invasive and Invaded Species.
(Mathematics, 2022) Díaz Palencia, José Luis; Roa González, Julián; Ur Rahman, Saeed; Naranjo Redondo, Antonio
This work provides an analytical approach to characterize and determine solutions to a porous medium system of equations with views in applications to invasive-invaded biological dynamics. Firstly, the existence and uniqueness of solutions are proved. Afterwards, profiles of solutions are obtained making use of the self-similar structure that permits showing the existence of a diffusive front. The solutions are then studied within the Travelling Waves (TW) domain showing the existence of potential and exponential profiles in the stable connection that converges to the stationary solutions in which the invasive species predominates. The TW profiles are shown to exist based on the geometry perturbation theory together with an analytical-topological argument in the phase plane. The finding of an exponential decaying rate (related with the advection and diffusion parameters) in the invaded species TW is not trivial in the nonlinear diffusion case and reflects the existence of a TW trajectory governed by the invaded species runaway (in the direction of the advection) and the diffusion (acting in a finite speed front or support).
A mathematical analysis of an extended MHD Darcy–Forchheimer type fluid.
(Scientific Reports, 2022) Díaz Palencia, José Luis
The presented analysis has the aim of introducing general properties of solutions to an Extended Darcy–Forchheimer flow. The Extended Darcy–Forchheimer set of equations are introduced based on mathematical principles. Firstly, the diffusion is formulated with a non-homogeneous operator, and is supported by the addition of a non-linear advection together with a non-uniform reaction term. The involved analysis is given in generalized Hilbert–Sobolev spaces to account for regularity, existence and uniqueness of solutions supported by the semi-group theory. Afterwards, oscillating patterns of Travelling wave solutions are analyzed inspired by a set of Lemmas focused on solutions instability. Based on this, the Geometric Perturbation Theory provides linearized flows for which the eigenvalues are provided in an homotopy representation, and hence, any exponential bundles of solutions by direct linear combination. In addition, a numerical exploration is developed to find exact Travelling waves profiles and to study zones where solutions are positive. It is shown that, in general, solutions are oscillating in the proximity of the null critical state. In addition, an inner region (inner as a contrast to an outer region where solutions oscillate) of positive solutions is shown to hold locally in time.
Liouville-Type Results for a Two-Dimensional Stretching Eyring–Powell Fluid Flowing along the z-Axis.
(Mathematics, 2022) Díaz Palencia, José Luis; Rahman, Saeed ur; Nouman, Muhammad
The purpose of this study is to establish Liouville-type results for a three-dimensional incompressible, unsteady flow described by the Eyring–Powell fluid equations. The fluid is studied in a plane Ωp while it moves along the z-axis. Therefore the main functions to analyze are given by u(x,y,z,t) and v(x,y,z,t) , belonging to Ωp . The results are obtained for globally bounded initial data as well as their corresponding derivatives, and the variations in velocity along the z-axis belong to the space L2 and BMO . Under such conditions, Liouville-type results are obtained and extended to Lp, p>2.
Nanocarbon-Based Flame Retardant Polymer Nanocomposites.
(Molecules, 2021) Yang, Yuan; Díaz Palencia, José Luis; Wang, Na; Jiang, Yan; De-Yi, Wang
In recent years, nanocarbon materials have attracted the interest of researchers due to their excellent properties. Nanocarbon-based flame retardant polymer composites have enhanced thermal stability and mechanical properties compared with traditional flame retardant composites. In this article, the unique structural features of nanocarbon-based materials and their use in flame retardant polymeric materials are initially introduced. Afterwards, the flame retardant mechanism of nanocarbon materials is described. The main discussions include material components such as graphene, carbon nanotubes, fullerene (in preparing resins), elastomers, plastics, foams, fabrics, and film–matrix materials. Furthermore, the flame retardant properties of carbon nanomaterials and their modified products are summarized. Carbon nanomaterials not only play the role of a flame retardant in composites, but also play an important role in many aspects such as mechanical reinforcement. Finally, the opportunities and challenges for future development of carbon nanomaterials in flame-retardant polymeric materials are briefly discussed.
Non-homogeneous reaction in a non-linear diffusion operator with advection to model a mass transfer process.
(Journal of Applied Analysis & Computation, 2022) Díaz Palencia, José Luis; Prieto Muñoz, Federico; García Haro, Juan Miguel
It is the objective to provide a mathematical treatment of a nonhomogeneous and non-lipschitz reaction problem with a non-linear diffusion and advection operator, so that it can be applied to a fire extinguishing process in aerospace. The main findings are related with the existence and characterization of a finite propagation support that emerges in virtue of the the non-linear diffusion formulation. It is provided a precise assessment on different times associated to the extinguisher discharge process. Particularly, the time required to activate the discharge, the time required for the extinguisher front to cover the whole domain, the time required to reach a minimum level of concentration so as to extinguish a fire and the time required by the agent to reach some difficult dead zones where the extinguisher propagates only by diffusion and no advection. The equation proposed is firstly discussed from a mathematical perspective to find analytical solutions and propagating profiles. Afterwards, the application exercise is introduced.
Liouville-Type Results for a Three-Dimensional Eyring-Powell Fluid with Globally Bounded Spatial Gradients in Initial Data.
(Mathematics, 2022) Díaz Palencia, José Luis; Rahman, Saeed; Nouman, Muhammad; Roa González, Julián
The analysis in the present paper provides insights into the Liouville-type results for an Eyring-Powell fluid considered as having an incompressible and unsteady flow. The gradients in the spatial distributions of the initial data are assumed to be globally (in the sense of energy) bounded. Under this condition, solutions to the Eyring-Powell fluid equations are regular and bounded under the L2 norm. Additionally, a numerical assessment is provided to show the mentioned regularity of solutions in the travelling wave domain. This exercise serves as a validation of the analytical approach firstly introduced.
Invasive-invaded system of non-Lipschitz porous medium equations with advection.
(International Journal of Biomathematics, 2021) Díaz Palencia, José Luis
This work provides analytical results towards applications in the field of invasive-invaded systems modelled with non-linear diffusion and with advection. The results focus on showing regularity, existence and uniqueness of weak solutions using the condition of a non-linear slightly positive parabolic operator and the reaction-absorption monotone properties. The coupling in the reaction-absorption terms, that characterizes the species interaction, impedes the formulation of a global comparison principle that is shown to exist locally. Additionally, the present work provides analytical solutions obtained as selfsimilar minimal and maximal profiles. A propagating diffusive front is shown to exist until the invaded specie notes the existence of the invasive. When the desertion of the invaded starts, the diffusive front vanishes globally and the non-linear diffusion concentrates only on the propagating tail which exhibits finite speed. Finally, the invaded specie is shown to exhibit an exponential decay along a characteristic curve. Such exponential decay is not trivial in the non-linear diffusion case and confirms that the invasive continues to feed on the invaded during the desertion.