Jaime H Ortega

University of Chile · Departamento de Ingeniería Matemática

Supercritical CO2 injection and dissolution into deep brine aquifers allow its sequestration within geological formations. After injection, CO2 gas phase is buoyancy-driven over the denser aqueous brine, reaching an apparent gravitational stable distribution. However, CO2 dissolution in brine propels convection since the mixture is even denser than...

In this work, we are interested in analyzing the well-known Calderón problem, which is an inverse boundary value problem of determining a coefficient function of an elliptic partial differential equation from the knowledge of the associated Dirichlet-to-Neumann map on the boundary of a domain. We consider the discrete version of the Calderon invers...

The sudden generation of wave disturbances in the ocean is associated with a change in the pressure field in the liquid layer. Consequently, compression-type of waves, known as acoustic-gravity waves, form and radiate at the speed of sound, carrying information on the event source, namely its magnitude and location. This information can be recorded...

The rice leaf, combining the surface properties of lotus leaves and shark skin, presents outstanding superhydrophobic properties motivating its biomimesis. We created a novel biomimetic rice-leaf superhydrophobic surface by a three-level hierarchical structure, using for a first time stereolithographic (SLA) 3D printed channels (100µm width) with a...

In this work, we are interested in analyzing the well-known Calderón problem, which is an inverse boundary value problem of determining a coefficient function of an elliptic partial differential equation from the knowledge of the associated Dirichlet-to-Neumann map on the boundary of a domain. We consider the discrete version of the Calderon invers...

In this work we study the semi-discrete linearized Benjamin-Bona-Mahony equation (BBM) which is a model for propagation of one-dimensional, unidirectional, small amplitude long waves in non-linear dispersive media. In particular, we derive a stability estimate which yields a unique continuation property. The proof is based on a Carleman estimate fo...

For underground mine, the current usual technique for ore extraction is block caving, which generates and induces seismic activity in the mine. To understand block caving method is one of the most challenging problems in underground mining. This method relies on gravity to break and transport large amounts of ore and waste. The state of art in dama...

Block caving is an ore extraction technique used in the copper mines of Chile. It uses gravity to ease the breaking of rocks, and to facilitate the extraction from the mine of the resulting mixture of ore and waste. To simulate this extraction process numerically and better understand its impact on the mine environment, we study 3 variational model...

In this article, we deal with a class of geometric inverse problems for bottom detection by one single measurement on the free surface in water waves. We found upper and lower bounds for the size of the region enclosed between two different bottoms, in terms of Neumann and/or Dirichlet data on the free surface. Starting from the general water-waves...

In this article we deal with a class of inverse problem for the bottom detection by one single measurement on the free surface in water-waves. We start from the general water-waves system in bounded domains with side walls, and rewrite the system as an elliptic problem in a bounded domain with Neumann homogeneous condition on the rigid boundary. Th...

Worldwide the mining activity is facing lower grades, deeper ore bodies and stronger stresses within increasing massive operations. These challenges have several technical difficulties, uncertainties and associated systemic risks, which can affect the business survival and the long-term sustainability of the operation. For underground mine, the cur...

In this work, we investigate numerically the perturbative effects of cell aperture in heat transport and thermal dissipation rate for a vertical Hele-Shaw geometry, which is used as an analogue representation of a planar vertical fracture at the laboratory scale. To model the problem, we derive a two-dimensional set of equations valid for this geom...

We study the problem of source reconstruction for a linear elasticity problem applied to seismicity induced by mining. We assume the source is written as a variable separable function f(x)g(t). We first present a simple proof a local decay result for elasticity in the case of homogeneous media. We then extend the source time reversal method, origin...

The present paper aims at providing a numerical strategy to deal with Partial Differential Equation(PDE)-constrained optimization problems solved with the adjoint method. It is done throughout a coupled system formulation of the constraint PDE and the adjoint model. The resulting model is a non-conservative hyperbolic system and thus a finite volum...

In this work, we present an exploratory study of stability of an open pit mine in the north of Chile with the use of data mining. It is important to note that the study of slope stability is a subject of great interest to mining companies, this is due to the importance in the safety of workers and the protection of infrastructures, whether private...

The present paper aims at providing a numerical strategy to deal with PDE-constrained optimization problems solved with the adjoint method. It is done through out a unified formulation of the constraint PDE and the adjoint model. The resulting model is a non-conservative hyperbolic system and thus a finite volume scheme is proposed to solve it. In...

In this work, we present a modified Time-Reversal Mirror (TRM) Method, called Source Time Reversal (STR), to find the spatial distribution of a seismic source induced by mining activity. This methodology is based on a known full description of the temporal dependence of the source, the Duhamel’s principle, and the time-reverse property of the wave...

The direct problem of water-wave equations is the problem of determining the surface and its velocity potential, in time T > 0, for a given initial profile and velocity potential, where the profile of the bottom, the bathymetry, is known. In this paper, we study the inverse problem of recovering the shape of the solid bottom boundary of an inviscid...

Objective:: To analyze suicidal behavior and build a predictive model for suicide risk using data mining (DM) analysis. Methods:: A study of 707 Chilean mental health patients (with and without suicide risk) was carried out across three healthcare centers in the Metropolitan Region of Santiago, Chile. Three hundred forty-three variables were stu...

A hydraulic jump is a physical phenomenon commonly observed in nature such as in open channel flows or spillways and is dependent upon the relation between the initial upstream fluid speed and a critical speed characterized by a dimensionless number F known as the Froude number. In this paper we prove the existence of hydraulic jumps for stationary...

In this paper we study the stability and deformation of structures, in particular the wall of an open pit mine is studied by using information obtained from a variety of remote sensors and some extra data, with a novelty approach considering the use of mathematical models and data mining techniques. In particular we present two models to help the s...

During the last years, the neuronavigation, also called image-guided surgery (IGS) or computer-assisted surgery (CAS), has had a tremendous impact improving the performance and safety in the neurosurgery. We can note that the neuronavigation systems use preoperative images, in general MRI images. However, during the operation the position of the ti...

We present an improvement to the standard synthetic schlieren technique to obtain the temperature distribution of a fluid inside of a Hele-Shaw cell. We aim to use the total variation \(L^1\)-norm optical flow method to treat experimental images and to obtain quantitative results of the development of thermal convection inside a cell, by detecting...

In this work we are interested in estimating the size of a cavity D immersed in a bounded domain \Omega, contained in R^d, d=2,3, filled with a viscous fluid governed by the Stokes system, by means of velocity and Cauchy forces on the external boundary of \Omega. More precisely, we establish some lower and upper bounds in terms of the difference be...

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...

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...

This study investigates the effects of different solid models on predictions of brain shift for three craniotomies. We created a generic 3D brain model based on healthy human brain and modeled the brain parenchyma as single continuum and constrained by a practically rigid skull. We have used elastic model, hyperelastic 1st, 2nd, and 3rd Ogden model...

This paper proves the local exact boundary controllability property of a nonlinear system of two coupled Korteweg–de Vries equations which models the interactions of weakly nonlinear gravity waves (see [10]). Following the method in [24], which combines the analysis of the linearized system and the Banach's fixed point theorem, the controllability...

This article considers a hyperbolic equation perturbed by a vanishing viscosity term depending on a small parameter ε>0. We show that the resulting parabolic equation is null-controllable. Moreover, we provide uniform estimates, with respect to ε, for the parabolic controls and we prove their convergence to a control of the limit hyperbolic equatio...

Our research aims at image segmentation using the variational framework of Mumford and Shah, following an approximation proposed by Ambrosio and Tortorelli. This technique circumvents the use of parametric contours and implicit level-set techniques, where its solution may be regarded as a soft segmentation, with a number the levels or colors being...

This paper studies the internal controllability and stabilizability of a family of Boussinesq systems recently proposed by J. L. Bona, M. Chen and J.-C. Saut to describe the two-way propagation of small amplitude gravity waves on the surface of water in a canal. The space of the controllable data for the associated linear system is determined for a...

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...

Undesirable splashing appears in copper converters when air is injected into the molten matte to trigger the conversion process. We consider here a cylindrical container horizontally placed and containing water, where gravity waves on the liquid surface are generated due to water injection through a lateral submerged nozzle. The fluid dynamics in a...

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...

We consider the motion of a rigid body immersed in a bidimensional incompressible perfect fluid. The motion of the fluid is governed by the Euler equations and the conservation laws of linear and angular momentum rule the dynamics of the rigid body. We prove the existence and uniqueness of a global classical solution for this fluid–structure intera...

In this work we consider the inverse problem of the identification of a single rigid body immersed in a fluid governed by the stationary Navier-Stokes equations. It is assumed that friction forces are known on a part of the outer boundary. We first prove a uniqueness result. Then, we establish a formula for the observed friction forces, at first or...

Publicación ISI Email : jortega@dim.uchile.cl; jorge@dim.uchile.cl; smaranda@dim.uchile.cl In this Note, we use the Bloch wave method to study the asymptotic behavior of the solution of the Laplace equation in a periodically perforated domain, under a non-homogeneous Neumann condition on the boundary of the holes, as the hole size goes to zero more...

In this paper, we use the Bloch wave method to study the asymptotic behavior of the solution of the Laplace equation in a periodically perforated domain, under a non-homogeneous Neumann condition on the boundary of the holes, as the size of the holes goes to zero more rapidly than the domain period. This method allows to prove that, when the hole s...

Undesirable splashing appears in copper converters when air is injected into the molten matte in order to carry out the conversion process. We consider here a cylin- drical container horizontally placed and containing water, where gravity waves on the liquid surface are generated due to water injection through a lateral submerged nozzle. The fluid...

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...

We present some results for the inverse problem of the identification of a single rigid body immersed in a fluid governed by the stationary Boussinesq equations. First, we establish a uniqueness result. Then, we show the way the observation depends on perturbations of the rigid body and we deduce some consequences. Finally, we present a new method...

We analyze the inverse problem of the identification of a rigid body immersed in a fluid governed by the stationary Boussinesq system. First, we establish a uniqueness result. Then, we present a new method for the partial identification of the body. The proofs use local Carleman estimates, differentiation with respect to domains, data assimilation...

In this article, we develop a model to help a maintenance decision making situation of a given equipment. We propose a novel model to determine optimal life-cycle duration and intervals between overhauls by minimizing global maintenance costs. We consider a situation where the costumer, which owns the equipment, may negotiate a better warranty cont...

We study the following inverse problem: an inaccessible rigid body D is immersed in a viscous fluid, in such a way that D plays the role of an obstacle around which the fluid is flowing in a greater bounded domain Ω, and we wish to determine D (i.e., its form and location) via boundary measurement on the boundary ∂Ω. Both for the stationary and the...

In this work we are interested in the study of controllability and stabilization of the linearized Benjamin-Ono equation with periodic boundary conditions, which is a generic model for the study of weakly nonlinear waves with nonlocal dispersion. It is well known that the Benjamin-Ono equation has infinite number of conserved quantities, thus we co...

In this paper we investigate the motion of a rigid ball in an incompressible perfect fluid occupying ${\mathbb R}^2$. We prove the global in time existence and the uniqueness of the classical solution for this fluid-structure problem. The proof relies mainly on weighted estimates for the vorticity associated with the strong solution of a fluid-stru...

This article is devoted to the ɛ-insensitizing controllability of the heat equation with disjoint control and observation regions. In the 1-D case and for symmetric regions a positive answer is obtained.

In this paper, we study the ε-insensitizing controllability for the functional given by integrating in time the square of the solution of the heat equation in a finite number of points of the domain Ω⊂RN, i.e., when the observation set is reduced to a finite set of points. We reduce the controllability problem to a unique continuation property for...

We have numerically studied the fluid dynamic effects on water in a converter-shaped vessel of air injection from a submerged tuyere. The time dependent and three dimensional simulations of the bi-phase system were carried out using the volume of fluid (VOF) and the standard k-epsilon turbulence models implemented in the commercial solver Fluent. E...

In this note, we clarify a technical point of Ref. 1, devoted to studying a constrained approximate controllability for the heat equation.

In this work we prove the generic simplicity of the spectrum of the clamped plate equation in a bounded regular domain of R d. That is, given Ω ⊂ R d , we show that there exists an arbitrarily small deformation of the domain u, such that all the eigenvalues of the plate system in the deformed domain Ω + u are simple. To prove this result we first p...

We numerically study the growth, rise, and interaction with the upper air-water interface of bubbles generated forcing air through a submerged orifice in a cylindrical vessel with polymeric surface containing quiescent water. The simulations were carried out using the volume of fluid (VOF) technique implemented in the commercial solver Fluent. We s...

In this work, we study an approximate control problem for the heatequation, with a nonstandard but rather natural restriction on thesolution. It is well known that approximate controllability holds. On theother hand, the total mass of the solutions of the uncontrolled system isconstant in time. Therefore, it is natural to analyze whether approximat...

We analyze the multiplicity of the eigenvalues for the Stokes operator in a bounded domain of ℝ2 with Dirichlet boundary conditions. We prove that, generically with respect to the domain, all the eigenvalues are simple. In other words, given a bounded domain of ℝ2, we prove the existence of arbitrarily small deformations of its boundary such that t...

In this work we prove the generic simplicity of the spectrum of the clamped plate equation in a bounded regular domain of ${\mathbb R}^d.$ That is, given $\Omega\subset{\mathbb R}^d,$ we show that there exists an arbitrarily small deformation of the domain $u,$ such that all the eigenvalues of the plate system in the deformed domain $\Omega +u$ are...

In this paper we study the asymptotic behavior of solutions of linear parabolic equations in IR N with periodic coefficients and L 1 initial data, as t → ∞. It was already known that, in a first approximation, solutions behave as the fundamental solution of the homogenized system. We use the Bloch waves decomposition to obtain a complete expansion...