Petr Kloucek - Academia.edu (original) (raw)

Papers by Petr Kloucek

Siam Journal on Mathematical Analysis, 2010

We derive a variational principle suitable for tracking free boundaries in fluids. The variationa... more We derive a variational principle suitable for tracking free boundaries in fluids. The variational principle is based on the Lagrangian formulation of the Navier–Stokes equations. The principle is derived from a generalization of the principle of stationary action applied to a Riemannian manifold of volume-preserving flow maps. The dual variational principle for the indicatrices identifying the free boundaries is based on the Wasserstein–Kantorovich metric.

Proceedings of SPIE, Jul 31, 2003

Mathematical Models and Methods in Applied Sciences, Nov 1, 2002

We determine the critical pressure and width of a liquid layer at which the sudden detachment of ... more We determine the critical pressure and width of a liquid layer at which the sudden detachment of bubbles at solid–liquid interfaces occurs. We obtain these values by solving numerically a constrained minimization problem corresponding to the conservation of mass density of gas contained in the bubble attached to a rigid surface, and to the conservation of its free energy.

PLOS ONE, Jan 25, 2021

We present a predictive Geometric Stress Index (pGSI) and its relation to behavioural Entropy (bE... more We present a predictive Geometric Stress Index (pGSI) and its relation to behavioural Entropy (bE). bE is a measure of the complexity of an organism's reactivity to stressors yielding patterns based on different behavioural and physiological variables selected as Surrogate Markers of Stress (SMS). We present a relationship between pGSI and bE in terms of a power law model. This nonlinear relationship describes congruences in complexity derived from analyses of observable and measurable SMS based patterns interpreted as stress. The adjective geometric refers to subdivision(s) of the domain derived from two SMS (heart rate variability and steps frequency) with respect to a positive/negative binary perceptron based on a third SMS (blood oxygenation). The presented power law allows for both quantitative and qualitative evaluations of the consequences of stress measured by pGSI. In particular, we show that elevated stress levels in terms of pGSI leads to a decrease of the bE of the blood oxygenation, measured by peripheral blood oxygenation S p O 2 as a model of SMS.

This study develops a numerical technique for the approximation of the magnetosphere-ionosphere (... more This study develops a numerical technique for the approximation of the magnetosphere-ionosphere (MI) coupling equation, which is a crucial step in the Rice Convection Model (RCM), a physical model that treats plasma in Earth's inner and middle magnetosphere via a multi-fluid approximation. The MI coupling equation is a second-order elliptic boundary value problem that describes conservation of current between the magnetosphere and the ionosphere. The current RCM solver is based on a finite difference scheme and produces unphysical results when the ionospheric conductance has large spatial gradients. We develop an alternative finite element approximation of the MI coupling equation, applying the method of fictitious domains to treat the high-latitude boundary condition along the immersed boundary Γ, a boundary that varies in time and does not align with the computational grid. The result of using fictitious domains is a domain decomposition problem that we solve via a mixed finite element formulation. We compare both a nonconforming and conforming finite element approach within the framework of the mixed formulation. We are able to demonstrate that both the conforming and nonconforming methods generate solutions that are compatible with the current RCM solver when actual RCM data is used. Furthermore, we demonstrate on several analytic test examples that the finite element approximation is more accurate than the finite difference approximation. Therefore, we conclude that the finite element solver is more robust than the finite difference solver. In addition, we provide convergence results for the nonconforming approximation when the conductance coefficients are bounded and measurable, and we use spectral theory from the harmonic Steklov eigenproblem to derive a precise definition of the trace space on the interface Γ. Our overall approximation technique is generalizable to a class of elliptic boundary value problems in which the boundary varies in time or does not align with a fixed grid. Finally, our numerical solver can be modified for use in the RCM-Jupiter that is currently being developed.

We consider a variational principle suitable for tracking boundaries of gas bubbles in liquids an... more We consider a variational principle suitable for tracking boundaries of gas bubbles in liquids and its consequences. The principle is derived from a generalization of the Principle of Stationary Action applied to a Riemannian manifold of volume preserving flow maps. The dual variational principle for the markers tracking the free surfaces is induced by the Wasserstein-Kantorovich metric. This later variational principle provides means to compute the dynamics of free, implicit, surfaces without explicitly solving for the fields and quantities which define them. The presented theory suggests the following approximate evolution equation for the characteristic function of the gas, written in the Lagrangian frame of reference, ρ G (∂ tt χ(x, t) − λ∂ t χ(x, t)) = div (χ(x, t) ((ρ G − ρ L) g + α∇H(x, t))) , x ∈ S(∇χ), t > 0, where S(∇χ) represents the set of points on the gas-liquid interfaces, and H denotes the mean curvature of the interface. The constants α and λ denote the surface tension and Rayleigh's friction dissipation constants, respectively. The density of the liquid and gas are denoted ρ L and ρ G. The gravitational force is denoted g. The regularized version of this equation is given, for some ǫ > 0, by ρ G (∂ tt s ǫ (x, t) − λ∂ t s ǫ (x, t)) = div s ǫ (x, t) (ρ G − ρ L) g + ∇ 2α0 ǫ DW (s ǫ (x, t)) − 2α 0 ǫ ∆ s ǫ (x, t) , x ∈ Ω, t > 0, DW (s) = s(1 − s)(1 − 2s), and α 0 = 3α.

Nonlinear Analysis-theory Methods & Applications, Feb 1, 1994

Applications of Mathematics, 1988

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Revue médicale suisse, Jan 13, 2021

Revue Médicale Suisse, 2021

The theory of approximation of the microstructures associated with the orthorhombic to monoclinic... more The theory of approximation of the microstructures associated with the orthorhombic to monoclinic and cubic to tetragonal transformations is presented. The error estimates derived in this paper show that macroscopic discrete quantities cannot converge faster then O(ph) in order to allow for the unlimited oscillations to develop. The Discrete Uncertainty Principle is proven. It indicates that we cannot approximate macroscopic and microscopic properties of the laminated microstructures with an unlimited precision at the same time.

We show that the Steepest Descent Algorithm in connection with wiggly energies yields minimizing ... more We show that the Steepest Descent Algorithm in connection with wiggly energies yields minimizing sequences that converge to a global minimum of the associated non-quasiconvex variational integrals. We introduce a multi-level innnite dimensional variant of the Steepest Descent Algorithm designed to compute complex microstructures by forming non-smooth minimizers from the smooth initial guess. We apply this multi-level method to the minimization of the variational problems associated with martensitic branching. 65K10 1 Introduction A continuum description of materials with ne structure often leads to minimization and dynamic problems that are extremely complex. In many cases, the reason is that the scale associated with the crystallographic ((ne) structure is not carried over to the continuum models. In the framework of hyperelasticity, for example, one has to work with scale-free microscopic quantities as a consequence of this deeciency. Often a change in the microscopic internal org...

Applied Mathematics, 2016

Applications of a constitutive framework providing compound complexity analysis and indexing of c... more Applications of a constitutive framework providing compound complexity analysis and indexing of coarse-grained self-similar time series representing behavioural data are presented. A notion of behavioural entropy and hysteresis is introduced as two different forms of compound measures. These measures provide clinically applicable complexity analysis of behavioural patterns yielding scalar characterisation of timevarying behaviours registered over an extended period of time. The behavioural data are obtained using body attached sensors providing non-invasive readings of heart rate, skin blood perfusion, blood oxygenation, skin temperature, movement and steps frequency. The results using compound measures of behavioural patterns of fifteen healthy individuals are presented. The application of the compound measures is shown to correlate with complexity analysis. The correlation is demonstrated using two healthy subjects compared against a control group. This indicates a possibility to use these measures in place of fractional dimensions to provide a finer characterisation of behavioural patterns observed using sensory data acquired over a long period of time.

Page 1. THE TRANSONIC FLOW PROBLEMS STABILITY ANALYSIS AND NUMERICAL RESULTS By Petr Kloucek IMA ... more Page 1. THE TRANSONIC FLOW PROBLEMS STABILITY ANALYSIS AND NUMERICAL RESULTS By Petr Kloucek IMA Preprint Series # 1214 March 1994 Page 2. THE TRANSONIC FLOW PROBLEMS STABILITY ANALYSIS ...

The Los Alamos Computer Science Institute (LACSI) was created to foster computer science and comp... more The Los Alamos Computer Science Institute (LACSI) was created to foster computer science and computational science research efforts at the Los Alamos National Laboratory (LANL) that are both internationally recognized and relevant to the goals of LANL. LACSI is a collaboration between LANL and the Rice University Center for Research on High Performance Software, along with partners at the University of Houston (UH), the University of Illinois at UrbanaChampaign (UIUC), and the University of Tennessee at Knoxville. LACSI has major components on site at LANL and at Rice University.

We prove that the Steepest Descent algorithm applied to the minimization of total stored energies... more We prove that the Steepest Descent algorithm applied to the minimization of total stored energies with rank-one related rotationally symmetric energy wells does not produce relaxing vectorial microstructures with non-trivial Young measures.

The Covid-19 pandemic has a major impact on psychiatry by its social consequences and possible di... more The Covid-19 pandemic has a major impact on psychiatry by its social consequences and possible direct effect of certain forms of Covid-19 on mental health. During this crisis, the accessibility of technology meets a state of necessity, which has propelled telepsychiatry from the shadows into the light. The contribution of several technologies (i.e. virtual reality, actigraphy, computational psychiatry) combining clinical data and neuroscience underlines the great neurobehavioural variability even within the same diagnostic category, calling for greater precision in therapeutic offers as suggested e.g. by developments in neurofeedback. The place of intranasal esketamin in the panoply of antidepressent drug treatments for resistant depression has not yet been defined.

We present a mathematical model describing the thermodynamic behavior of shape memory alloy wires... more We present a mathematical model describing the thermodynamic behavior of shape memory alloy wires, as well as a computational technique to solve the resulting system of partial differential equations. The model consists of conservation equations based on a new Helmholtz free energy potential. The computational technique introduces a viscosity-based continuation method, which allows the model to handle dynamic applications where the temporally local behavior of solutions is desired. Computational experiments document that this combination of modeling and solution techniques appropriately predicts the thermally- and stress-induced martensitic phase transitions, as well as the hysteretic behavior and production of latent heat associated with such materials.

This report describes the research projects and accomplishments made possible through the availab... more This report describes the research projects and accomplishments made possible through the availability of the sixteen processor SGI Origin 2000, purchased in parts with the funds from NSF SCREMS grant NSF 98-72009. To date the SGI Origin 2000 has served as the main computing facility in many interdisciplinary projects involving 48 faculty, research scientists, postdocs, graduate and undergraduate students from six departments at Rice University, as well as several visiting scholars and collaborators from other universities. Computations performed on the SGI Origin 2000 have led to 44 journal articles, proceedings articles, and technical reports. Availability of the SGI Origin 2000 on campus has led to a significant increase in the complexity of the problems we are able to tackle and it has served as the catalyst for several of the research projects described in the report. The sixteen processor SGI Origin 2000 continues to be a widely used and important computing resource on campus