Numerical resolution of an exact heat conduction model with a delay term

In this paper we analyze, from the numerical point of view, a dynamic thermoelastic problem. Here, the so-called exact heat conduction model with a delay term is used to obtain the heat evolution. Thus, the thermomechanical problem is written as a coupled system of partial differential equations, and its variational formulation leads to a system written in terms of the velocity and the temperature fields. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced by using the classical finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A priori error estimates are proved, from which the linear convergence of the algorithm could be derived under suitable additional regularity conditions. Finally, a two-dimensional numerical example is solved to show the accuracy of the approximation and the decay of the discrete energy.Peer ReviewedPostprint (published version

Uniqueness for a high order ill posed problem

In this work, we study a high order derivative in time problem. First, we show that there exists a sequence of elements of the spectrum which tends to infinity and therefore, it is ill posed. Then, we prove the uniqueness of solutions for this problem by adapting the logarithmic arguments to this situation. Finally, the results are applied to the backward in time problem for the generalized linear Burgers’ fluid, a couple of heat conduction problems and a viscoelastic model.Agencia Estatal de Investigación | Ref. PGC2018-096696-B-I00Agencia Estatal de Investigación | Ref. PID2019-105118GB-I0

On the instability for an incremental problem in elastodynamics

Financiado para publicación en acceso aberto: Universidade de Vigo/CISUGIn this short note, we consider some issues regarding the instability of some elastodynamical problems when the elasticity tensor is not positive definite. By using the so-called logarithmic convexity argument, we prove the instability of solutions when the time derivative of the elasticity tensor is semi-definite negative or it satisfies another restriction on the coefficients. The uniqueness of the solution is also concluded. Finally, a simple one-dimensional example is provided to demonstrate the numerical behaviour of the instability.Ministerio de Ciencia, Innovación y Universidades | Ref. PID2019-105118GB-I0

Fast spatial behavior in higher order in time equations and systems

Financiado para publicación en acceso aberto: Universidade de Vigo/CISUGIn this work, we consider the spatial decay for high-order parabolic (and combined with a hyperbolic) equation in a semi-infinite cylinder. We prove a Phragmén-Lindelöf alternative function and, by means of some appropriate inequalities, we show that the decay is of the type of the square of the distance to the bounded end face of the cylinder. The thermoelastic case is also considered when the heat conduction is modeled using a high-order parabolic equation. Though the arguments are similar to others usually applied, we obtain new relevant results by selecting appropriate functions never considered before.Agencia Estatal de Investigación | Ref. PGC2018-096696-B-I00Agencia Estatal de Investigación | Ref. PID2019-105118GB-I0

Uniqueness for a high order ill posed problem

In this work, we study a high order derivative in time problem. First, we show that there exists a sequence of elements of the spectrum which tends to infinity and therefore, it is ill posed. Then, we prove the uniqueness of solutions for this problem by adapting the logarithmic arguments to this situation. Finally, the results are applied to the backward in time problem for the generalized linear Burgers’ fluid, a couple of heat conduction problems and a viscoelastic modelPeer ReviewedPostprint (published version

On the instability for an incremental problem in elastodynamics

In this short note, we consider some issues regarding the instability of some elastodynamical problems when the elasticity tensor is not positive definite. By using the so-called logarithmic convexity argument, we prove the instability of solutions when the time derivative of the elasticity tensor is semi-definite negative or it satisfies another restriction on the coefficients. The uniqueness of the solution is also concluded. Finally, a simple one-dimensional example is provided to demonstrate the numerical behaviour of the instability.Peer ReviewedPostprint (published version

Fast spatial behavior in higher order in time equations and systems

In this work, we consider the spatial decay for high-order parabolic (and combined with a hyperbolic) equation in a semi-infinite cylinder. We prove a Phragmén-Lindelöf alternative function and, by means of some appropriate inequalities, we show that the decay is of the type of the square of the distance to the bounded end face of the cylinder. The thermoelastic case is also considered when the heat conduction is modeled using a high-order parabolic equation. Though the arguments are similar to others usually applied, we obtain new relevant results by selecting appropriate functions never considered beforePeer ReviewedPostprint (published version

On a mixture of an MGT viscous material and an elastic solid

A lot of attention has been paid recently to the study of mixtures and also to the Moore–Gibson–Thompson (MGT) type equations or systems. In fact, the MGT proposition can be used to describe viscoelastic materials. In this paper, we analyze a problem involving a mixture composed by a MGT viscoelastic type material and an elastic solid. To this end, we first derive the system of equations governing the deformations of such material. We give the suitable assumptions to obtain an existence and uniqueness result. The semigroups theory of linear operators is used. The paper concludes by proving the exponential decay of solutions with the help of a characterization of the exponentially stable semigroups of contractions and introducing an extra assumption. The impossibility of location is also shown.Peer ReviewedPostprint (published version

Seguridad operacional y gestión del operador para habilitar el uso de sistemas aéreos no tripulados (UAS) como herramientas geomáticas

[EN] Potential civil applications of Unmanned Aircraft Systems (UAS), commonly known as drones, have risen steeply during the last decade, mainly due to their versatility and capability of spatial data gathering. Nonetheless, real use of UAS is quite restricted nowadays, primarily due to safety and regulatory constraints. This multidisciplinary project aims to perform specific safety assessments using the SORA methodology adopted by the European Aviation Safety Agency (EASA) and develop documentation and procedures for operators to follow, complying with all required safety and regulatory requirements. As a result, DEURPAS-UPV is the first Spanish drone operator belonging to a university to be authorized by Spanish civil aviation agency (AESA-Agencia Estatal de Seguridad Aérea), to perform drone flights in urban areas, in controlled airspace and during the night. In addition, DEURPAS-UPV has performed the first authorized experimental transport operations using drones in Spain. The results from safety assessment and designed procedures have been successfully applied to the operation of Safety and Emergency service providers, such as Valencia Local Police Corps and the Valencian Emergency and Safety Response Agency (AVSRE - Agencia Valenciana de Seguridad y Respuesta a las Emergencias). Overall, this project has served as an enabler for more complex and safer UAS operations, from the operator’s point of view, which will help break the barriers related to the use of these aircraft, with huge potential in geomatics applications.[ES] Las aplicaciones civiles de los sistemas aéreos no tripulados (UAS), comúnmente conocidos como drones, han aumentado considerablemente durante la última década, principalmente debido a su versatilidad y capacidad de recopilación de datos espaciales. Sin embargo, el uso real de los UAS está bastante restringido hoy en día, principalmente debido a las restricciones de seguridad y legislativas. Este proyecto multidisciplinar tiene como objetivo realizar evaluaciones de seguridad específicas utilizando la metodología SORA adoptada por la Agencia Europea de Seguridad Aérea (EASA) y desarrollar documentación y procedimientos para que los operadores los sigan, cumpliendo con todos los requisitos de seguridad y normativos exigidos. Como resultado, DEURPAS-UPV es el primer operador español de drones perteneciente a una universidad que ha sido autorizado por la Agencia Estatal de Seguridad Aérea (AESA), para realizar vuelos con drones en zonas urbanas, en espacio aéreo controlado y durante la noche. Además, DEURPAS-UPV ha realizado las primeras operaciones experimentales de transporte con drones autorizadas en España. Los resultados de la evaluación de seguridad y los procedimientos diseñados se han aplicado con éxito a la operación de proveedores de servicios de Seguridad y Emergencias, como el Cuerpo de Policía Local de Valencia y la Agencia Valenciana de Segurida y Respuesta a las Emergencias (AVSRE). En general, este proyecto ha servido para facilitar operaciones con UAS más complejas y seguras, desde el punto de vista del operador, lo que ayudará a romper las barreras relacionadas con el uso de estas aeronaves, con un enorme potencial en aplicaciones geomáticas.This work was supported by the Generalitat Valenciana under Grant DECRETO 63/2020 and Universitat Politècnica de València under Grant PAID-01-1.Vera, N.; Quintanilla, I.; Vidal, J.; Fernández, B. (2021). Operational safety and operator management to enable the use of unmanned aircraft systems (UAS) as geomatics tools. En Proceedings 3rd Congress in Geomatics Engineering. Editorial Universitat Politècnica de València. 194-200. https://doi.org/10.4995/CiGeo2021.2021.12724OCS19420

n2 of dissipative couplings are sufficient to guarantee the exponential decay in elasticity

In this paper, we prove that the solutions to the problem determined by an elastic material with n2 coupling dissipative mechanisms decay in an exponential way for every (bounded) geometry of the body, where n is the dimension of the domain, and whenever the coupling coefficients satisfy a suitable condition. We also give several examples where the solutions do not decay when the rank of the matrix of the coupling mechanisms is less than n2 (2 in dimension 2 and 6 in dimension 3)Peer ReviewedPostprint (published version