Carlos Conca

University of Chile · Departamento de Ingeniería Matemática

Background An effective strategy for arboviral control consists in transfecting Aedes aegypti mosquitoes with the intracellular bacteria Wolbachia pipientis , which reduces host viral susceptibility and spreads itself into wild populations via reproductive manipulations. However, the prospect of losing the efficacy of this strategy underscores the...

Background: One of the main lessons of the COVID-19 pandemic is that we must prepare to face another pandemic like it. Consequently, this paper aims to develop a general framework consisting of epidemiological modeling and a practical identifiability approach to assess combined vaccination and non-pharmaceutical interventions (NPIs) strategies for...

Genomic surveillance of infectious diseases allows monitoring circulating and emerging variants and quantifying their epidemic potential. However, due to the high costs associated with genomic sequencing, only a limited number of samples can be analysed. Thus, it is critical to understand how sampling impacts the information generated. Here, we com...

Genomic surveillance of infectious diseases allows monitoring circulating and emerging variants and quantifying their epidemic potential. However, due to the high costs associated with genomic sequencing, only a limited number of samples can be analysed. Thus, it is critical to understand how sampling impacts the information generated. Here, we com...

In this work, we introduce Bloch waves to study the homogenization process in a class of simple laminates which are obtained as a particular Hashin-Shtrikman microstructure involving translations and dilations in only one direction. This makes this class of microstructures non necessarily periodic in the direction of lamination. We derive explicit...

In this paper, we use spectral methods by introducing the Bloch waves to study the homogenization process in the non-periodic class of generalized Hashin-Shtrikman micro-structures \cite[page no. 281]{T}, which incorporates both translation and dilation with a family of scales, including one subclass of laminates. We establish the classical homogen...

A growing body of evidence indicates that dietary polyphenols could be used as an early intervention to treat glucose-insulin (G-I) dysregulation. However, studies report heterogeneous information, and the targets of the intervention remain largely elusive. In this work, we provide a general methodology to quantify the effects of any given polyphen...

The first step in our sensing of smell is the conversion of chemical odorants into electrical signals. This happens when odorants stimulate ion channels along cilia, which are long thin cylindrical structures in our olfactory system. Determining how the ion channels are distributed along the length of a cilium is beyond current experimental methods...

Arboviral diseases such as Zika and Dengue have been on the rise mainly due to climate change, and the development of new treatments and strategies to limit their spreading is needed. The use of Wolbachia

We study the problem of minimizing the first eigenvalue of the p-Laplacian operator for a two-phase material in a bounded open domain Ω⊂RN, N⩾2 assuming that the amount of the best material is limited. We provide a relaxed formulation of the problem and prove some smoothness results for these solutions. As a consequence we show that if Ω is of clas...

We study the stationary Stokes and Navier-Stokes equations with nonhomogeneous Navier boundary conditions in a bounded domain Ω⊂R3 of class C1,1. We prove the existence and uniqueness of weak and strong solutions in W1,p(Ω) and W2,p(Ω) for all 1<p<∞, considering minimal regularity on the friction coefficient α. Moreover, we deduce uniform estimates...

We consider the optimal arrangement of two diffusion materials in a bounded open set $\Omega\subset \mathbb{R}^N$ in order to maximize the energy. The diffusion problem is modeled by the $p$-Laplacian operator. It is well known that this type of problems has no solution in general and then that it is necessary to work with a relaxed formulation. In...

We consider the Robin boundary value problem \({\mathrm {div}}\,(A\nabla u) = {\mathrm {div}}\,\varvec{f}+F\) in \(\Omega \), a \(C^1\) domain, with \((A\nabla u - \varvec{f})\cdot {\varvec{n}}+ \alpha u = g\) on \(\Gamma \), where the matrix A belongs to \(VMO ({\mathbb {R}}^3) \), and discover the uniform estimates on \(\Vert u\Vert _{W^{1,p}(\Om...

We present a new basis of representation for the graphene honeycomb structure that facilitates the solution of the eigenvalue problem by reducing it to one dimension. We define spaces in these geometrical basis that allow us to solve the Hamiltonian in the edges of the lattice. We conclude that it is enough to analyze a one-dimensional problem in a...

Existing mathematical models for the glucose-insulin (G-I) dynamics often involve variables that are not susceptible to direct measurement. Standard clinical tests for measuring G-I levels for diagnosing potential diseases are simple and relatively cheap, but seldom give enough information to allow the identification of model parameters within the...

We solve a second-order elliptic equation with quasi-periodic boundary conditions defined on a honeycomb lattice that represents the arrangement of carbon atoms in graphene. Our results generalize those found by Kuchment and Post (Commun Math Phys 275(3):805–826, 2007) to characterize not only the stability but also the instability intervals of the...

Although macrophages are part of the human immune system, it has been remarkably observed in laboratory experiments that decreasing its number can slow down the tumor progression. We analyze through a recently mathematical model proposed in the literature, necessary conditions for aggregation of tumor cells and macrophages. In order to do so, we pr...

Wolbachia are alpha-proteobacteria known to infect arthropods, which are of interest for disease control since they have been associated with improved resistance to viral infection. Although several genomes for different strains have been sequenced, there is little knowledge regarding the relationship between this bacterium and their hosts, particu...

The method of asymptotic partial decomposition of a domain proposed and justified earlier for thin domains (rod structures, tube structures consisting of a set of thin cylinders) generates some special interface conditions between the three-dimensional and one-dimensional parts. In the case of fluid mechanics these conditions prescribe a precompute...

In this work we develop a general mathematical model and devise a practical identifiability approach for gastrointestinal stromal tumor (GIST) metastasis to the liver, with the aim of quantitatively describing therapy failure due to drug resistance. To this end, we have modeled metastatic growth and therapy failure produced by resistance to two sta...

In this paper, we study the stationary Stokes and Navier–Stokes equations with non-homogeneous Navier boundary condition in a bounded domain Ω⊂R³ of class C1,1 from the viewpoint of the behavior of solutions with respect to the friction coefficient α. We first prove the existence of a unique weak solution (and strong) in W1,p(Ω) (and W2,p(Ω)) to th...

In this paper, we introduce a macroscopic quantity, namely the dispersion tensor or the Burnett coefficients in the class of generalized Hashin–Shtrikman micro-structures (Tartar in The general theory of homogenization, volume 7 of Lecture notes of the Unione Matematica Italiana, Springer, Berlin, p 281, 2009). In the case of two-phase materials as...

We consider the stationary Boussinesq system with non-homogeneous Dirichlet boundary conditions in a bounded domain of class with a possibly disconnected boundary. We prove the existence of weak solutions in , strong solutions in and very weak solutions in of the stationary Boussinesq system by assuming that the fluxes of the velocity are sufficien...

This paper studies a semi-linear system of equations in \( {\mathbb{R}}^{N} \), which comes from a mathematical model for a new tax system proposed in Chile’s 2014 Tax Reform. The system of equations involves a non negative coefficients matrix and simultaneously relates the unknown vector with its positive part, and hence the nonlinear nature of th...

We study $W^{1,p}$-estimates of inhomogeneous second order elliptic operator of divergence form with Robin boundary condition in $\mathcal{C}^1$ domain. For any $p>2$, we prove that a weak reverse H\"{o}lder inequality holds which in turn provides the $W^{1,p}$-estimates for solutions with Robin boundary condition, independent of $\alpha$. As a res...

We study the stationary Stokes and Navier-Stokes equations with non-homogeneous Navier boundary condition in a bounded domain $\Omega\subset\mathbb{R}^{3}$ of class $\mathcal{C}^{1,1}$. We prove the existence, uniqueness of weak and strong solutions in $\mathbf{W}^{1,p}(\Omega)$ and $\mathbf{W}^{2,p}(\Omega)$ for all $1<p<\infty$ considering minima...

The authors study an integral inverse problem arising in the biology of the olfactory system. The transduction of an odor into an electrical signal is accomplished by a depolarising influx of ions through cyclic-nucleotide-gated (CNG for short) channels on the cilium membrane. The inverse problem studied in this paper consists in finding the spatia...

In this article, we study the approximate controllability and homegenization results of a semi-linear elliptic problem with Robin boundary condition in a periodically perforated domain. We prove the existence of minimal norm control using Lions constructive approach, which is based on Fenchel-Rockafeller duality theory, and by means of Zuazua's...

In this work we simulate biofilm structures (“finger-like”, as well as, compact structures) as a result of microbial growth in different environmental conditions. At the same time, the numerical method that we use in order to carry out the computational simulations is new to the biological community, as far as we know. The use of our model sheds li...

In this paper, we study the L² and H¹-approximate controllability and homogenization of a semilinear elliptic boundary value problem in a perforated domain. The principal term in the state equation has rapidly oscillating coefficients and the control region is free from perforations (holes). The observable zone is locally distributed in the perfora...

A classical stationary Boussinesq system with non-homogeneous Dirichlet boundary conditions in a bounded domain Ω.

We consider the inverse problem of detecting the location and the shape of several obstacles immersed in a fluid flowing in a larger bounded domain Ω from partial boundary measurements in the two dimensional case. The fluid flow is governed by the steady-state Stokes equations. We use a topological sensitivity analysis for the Kohn-Vogelius functio...

The authors study a linear inverse problem with a biological interpretation, which is modelled by a Fredholm integral equation of the first kind, where the kernel is represented by step functions. Based on different assumptions, identifiability, stability and reconstruction results are obtained. © 2015, Fudan University and Springer-Verlag Berlin H...

We consider the problem of distributing two conducting materials with a prescribed volume ratio in a given domain so as to minimize the first eigenvalue of an elliptic operator with Dirichlet conditions. The gap between the two conductivities is assumed to be small (low contrast regime). For any geometrical configuration of the mixture, we provide...

One of the main challenges in cancer modelling is to improve the knowledge of tumor progression in areas related to tumor growth, tumor-induced angiogenesis and targeted therapies efficacy. For this purpose, incorporate the expertise from applied mathematicians, biologists and physicians is highly desirable. Despite the existence of a very wide ran...

Cilia are long thin cylindrical structures that extend from an olfactory receptor into the nasal mucus. The transduction of an odor into an electrical signal occurs in the membranes of the cilia. The cyclic-nucleotide-gated (CNG) channels, activated by cyclic adenosine monophosphate (cAMP), allow a depolarizing influx of sodium ions, which initiate...

In this work we propose a new model to simulate biofilm structures (‘‘finger-like’’, as well as, compact structures) as a result of microbial growth in different environmental conditions. At the same time, the numerical method that we use in order to carry out the computational simulations is new to the biological community, as far as we know. The...

In this work, we propose a new model to simulate biofilm structures (‘‘finger-like’’, as well as, compact structures) as a result of microbial growth in different environmental conditions. At the same time, the numerical method that we use to carry out the computational simulations is new to the biological community, as far as we know. The use of o...

In this paper we study a linear inverse problem with a biological interpretation, which is modeled by a Fredholm integral equation of the first kind. When the kernel in the Fredholm equation is represented by step func- tions, we obtain identifiability, stability and reconstruction results. Further- more, we provide a numerical reconstruction algor...

For the parabolic–elliptic Keller–Segel system in 2 it has been proved that if the initial mass is less than 8π/χ, a global solution exists, and in case the initial mass is larger than 8π/χ, blow-up happens. The case of several chemotactic species introduces an additional question: What is the analog for the critical mass obtained for the single s...

In this article we consider the problem of the optimal distribution of two conducting materials with given volume inside a fixed domain, in order to minimize the first eigenvalue (the ground state) of a Dirichlet operator. It is known, when the domain is a ball, that the solution is radial, and it was conjectured that the optimal distribution of th...

The object of discussion of this article is the fourth-order tensor d introduced as a set of macro coefficients associated with fine periodic structures. Focus of attention is its variation on laminated microstructures. Complete bounds are obtained on its quartic form along with the corresponding optimal structures. Differences with corresponding r...

For a class of drift–diffusion systems Kurokiba et al. [M. Kurokiba, T. Nagai, T. Ogawa, The uniform boundedness and threshold for the global existence of the radial solution to a drift–diffusion system, Commun. Pure Appl. Anal. 5 (2006) 97–106.] proved global existence and uniform boundedness of the radial solutions when the L1L1-norm of the initi...

In this article we consider the problem of the optimal distribution of two conducting materials with given volume inside a fixed domain, in order to minimize the first eigenvalue (the ground state) of a Dirichlet operator. It is known, when the domain is a ball, that the solution is radial, and it was conjectured that the optimal distribution of th...

This paper is devoted to a geometrical inverse problem associated with a fluid–structure system. More precisely, we consider the interaction between a moving rigid body and a viscous and incompressible fluid. Assuming a low Reynolds regime, the inertial forces can be neglected and, therefore, the fluid motion is modelled by the Stokes system. We fi...

For the Keller–Segel model, it was conjectured by Childress and Percus (1984, Chemotactic collapse in two dimensions. In Lecture Notes in Biomath. Vol. 55, Springer, Berlin-Heidelberg-New York, 1984, pp. 61–66) that in a two-dimensional domain there exists a critical number C such that if the initial mass is strictly less than C, then the solution...

Ferritin plays a key role in the regulation of iron cellular levels, acting as the main intracellular iron storage protein. Studying the mechanism used by ferritin to store iron will lead to a better understanding of cellular iron homeostasis. We propose a kinetic model for iron storage in ferritin based on the main reactions for ferritin and iron,...

A first set of macro coefficients known as the homogenized coefficients appear in the homogenization of PDE on periodic structures. If energy is increased or scale is decreased, these coefficients do not provide adequate approximation. Using Bloch decomposition, it is first realized that the above coefficients correspond to the lowest energy and th...

We study the existence of local and global mild solutions of the fractional-order differential equations in an arbitrary Banach space by using the semigroup theory and the Schauder fixed-point theorem. We also give some examples to illustrate the applications of abstract results.

Supplemental Figure S1: In vivo ferritin's iron content in sucrose gradient fractions. Caco-2 cells were grown in 7 cm2 culture plates for 7 days in media containing 2, 4, 6, 10, 20 or 40 μM of total iron. Cell homogenates were prepared as described and cleared by centrifugation (Arredondo et al., 1997). Supernatants, corresponding to the cytosolic...

Iron is essential for the maintenance of basic cellular processes. In the regulation of its cellular levels, ferritin acts as the main intracellular iron storage protein. In this work we present a mathematical model for the dynamics of iron storage in ferritin during the process of intestinal iron absorption. A set of differential equations were es...

In this paper, we consider a moving rigid solid immersed in a potential fluid. The fluid-solid system fills the whole two dimensional space and the fluid is assumed to be at rest at infinity. Our aim is to study the inverse problem, initially introduced in [3], that consists in recovering the position and the velocity of the solid assuming that the...

In this paper we shall study a fractional integral equation in an arbitrary Banach space X. We used the analytic semigroups theory of linear operators and the fixed point method to establish the existence and uniqueness of solutions of the given problem. We also prove the existence of global solution. The existence and convergence of the Faedo–Gale...

Modelamiento matemático de crecimiento de tumores, acoplado con angiogénesis tumoral y su uso en la investigación de nuevas estrategias de tratamiento del cáncer Resumen Considerando la importancia del cáncer a nivel mundial, es necesario planear estrategias para estudiar y controlar esta enfermedad. Sin embargo, es difícil tener un pronóstico y tr...

The pioneering works of Murat and Tartar (Topics in the mathematical modeling of composite materials. PNLDE 31. Birkhäuser, Basel, 1997) go a long way in showing, in general, that problems of optimal design may not admit solutions if microstructural designs are excluded from consideration. Therefore, assuming, tactilely, that the problem of minimiz...

In this paper, we consider the macroscopic quantity, namely the dispersion tensor associated with a periodic structure in one dimension (see Refs. 5 and 7). We describe the set in which this quantity lies, as the microstructure varies preserving the volume fraction.

En esta comunicación se propone un nuevo modelo para la formación de una biopelícula y se estudian los aspectos numéricos de su simulación computacional. Nuestro modelo está basado en tres aspectos fundamentales: primero, se incorpora un mecanismo de transporte de nutrientes hacia la biopelícula; segundo, se incorpora un mecanismo de consumo y de c...

In this article we deal with the problem of distributing two conducting materials in a given domain, with their proportions being fixed, so as to minimize the first eigenvalue of a Dirichlet operator. When the design region is a ball, it is known that there is an optimal distribution of materials which does not involve the mixing of the materials....

En esta comunicación se propone un nuevo modelo para la formación de una biopelícula y se estudian los aspectos numéricos de su simulación computacional. Nuestro modelo está basado en tres aspectos fundamentales: primero, se incorpora un mecanismo de transporte de nutrientes hacia la biopelícula; segundo, se incorpora un mecanismo de consumo y de c...

RESUMEN En este artículo se proponen dos métodos numéricos para resolver un sistema de ecuaciones en derivadas parciales formado por una ecuación del tipo parabólica, y otra hiperbólica. Estos métodos están basados en dos aproximaciones teóricas de la solución de la ecuación parabólica del sistema, y en un uso adecuado de un esquema de diferencias...

This work deals with the study of an inverse geometric problem in fluid mechanics. In particular, we are interested in the numerical reconstruction of a rigid body which is immersed in a cavity, filled with a fluid, by means of measurements of the Cauchy forces and the velocity of the fluid on one part of the exterior boundary. This problem was stu...

This article was published in an uncorrected form because the publisher did not receive the authors' corrections contained in an e-mail lost in transit between the two parties. The PDF shows the corrections that the authors would like to have been made.

We study a direct integral decomposition for the spaces L 2 (O) and H 1 (O) based on (ξ,Y * )-periodic functions. Using this decomposition we can write the Green’s operator (associated to the classical Stokes system in fluid mechanics) in terms of a family of self-adjoint compact operators which depend on the parameter ξ. As a consequence, we obtai...

In this Note we investigate the problem of the detection of a moving obstacle in a perfect fluid occupying a bounded domain in R2 from the measurement of the velocity of the fluid on one part of the boundary. We show that when the obstacle is a ball, we may identify the position and the velocity of its center of mass from a single boundary measurem...

In this work, we consider low contrast periodic media and we study the dependence of the effective or homogenized tensor and the dispersion tensor in terms of the microstructure. We treat both one-dimensional structures and some laminated structures in higher dimension. Interesting properties of the sign of these coefficients are found. Surprisingl...

This write-up is a review of some old and some recent developments in the homogenization of fluid flows modelled by Stokes, NavierÐStokes, Euler, Advection-Diffusion equations. Oscillations may enter these systems through domains, the coefÞcients or through the initial data. Various phenomena involved in the homogenization process are highlighted....

In this work, we study the Bloch wave decomposition for the Stokes equations in a periodic media in R-d. We prove that, because of the incompressibility constraint, the Bloch eigenvalues, as functions of the Bloch frequency xi, are not continuous at the origin. Nevertheless, when xi goes to zero in a fixed direction, we exhibit a new limit spectral...

This paper presents a comprehensive mathematical model of transport phenomena which occur along a tuyere of the Teniente converter during injection of oxygen-enriched air. Inlet pressure, gas velocity and temperature, the dimensions of the tuyere, and the properties of gas are the basic data. From these inputs, temperature distribution of the refra...

The aim of this work is to demonstrate a curious property of general periodic structures. It is well known that the corresponding homogenized matrix is positive definite. We calculate here the next order Burnett coefficients associated with such structures. We prove that these coefficients form a tensor which is negative semidefinite. We also provi...

This paper deals with a numerical study of classical homogenization of elliptic linear operators with periodic oscillating coefficients (period εY). The importance of such problems in engineering applications is quite well-known. A method introduced by Conca and Vanninathan [SIAM J. Appl. Math. 1997; 57:1639–1659] based on Bloch waves that homogeni...

In this article we study the asymptotic behaviour of the eigenvalues of a family of nonlinear monotone elliptic operators of the form A(epsilon) = - div(a(epsilon) (x, del u)), which are sub-differentials of even, positively homogeneous convex functionals, under the assumption that the operators G-converge to art operator A(hom) = div(a(hom) (x, de...