Search results for " function"

A regularized Newton method for locating thin tubular conductivity inhomogeneities

2011

We consider the inverse problem of determining the position and shape of a thin tubular object, such as for instance a wire, a thin channel or a curve-like crack, embedded in some three-dimensional homogeneous body from a single measurement of electrostatic currents and potentials on the boundary of the body. Using an asymptotic model describing perturbations of electrostatic potentials caused by such thin objects, we reformulate the inverse problem as a nonlinear operator equation. We establish Frechet differentiability of the corresponding operator, compute its Frechet derivative and set up a regularized Newton scheme to solve the inverse problem numerically. We discuss our implementation…

The Calderón Problem for a Space-Time Fractional Parabolic Equation

2020

In this article we study an inverse problem for the space-time fractional parabolic operator $(\partial_t-\Delta)^s+Q$ with $0<s<1$ in any space dimension. We uniquely determine the unknown bounded...

Jacobian of solutions to the conductivity equation in limited view

2022

Abstract The aim of hybrid inverse problems such as Acousto-Electric Tomography or Current Density Imaging is the reconstruction of the electrical conductivity in a domain that can only be accessed from its exterior. In the inversion procedure, the solutions to the conductivity equation play a central role. In particular, it is important that the Jacobian of the solutions is non-vanishing. In the present paper we address a two-dimensional limited view setting, where only a part of the boundary of the domain can be controlled by a non-zero Dirichlet condition, while on the remaining boundary there is a zero Dirichlet condition. For this setting, we propose sufficient conditions on the bounda…

The Calderón problem for the fractional Schrödinger equation

2020

We show global uniqueness in an inverse problem for the fractional Schr\"odinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness in the partial data problem where the measurements are taken in arbitrary open, possibly disjoint, subsets of the exterior. The results apply in any dimension $\geq 2$ and are based on a strong approximation property of the fractional equation that extends earlier work. This special feature of the nonlocal equation renders the analysis of related inverse problems radically different from the traditional Calder\'on problem.

Using tools effectively despite defective hand posture: A single-case study.

2019

Apraxia, a cognitive disorder of motor control, can severely impair transitive actions (object-related) and may lead to action errors (e.g., rubbing a hammer on a nail instead of pounding it) and hand posture errors (e.g., grasping a tool in a wrong way). Here, we report a rare observation of a left-handed patient, left-lateralized for language, who developed a severe apraxia following a right brain lesion. Interestingly the patient showed a significant number of hand posture errors, while she perfectly demonstrated the actual use of tools. This case stressed the predictions made by the current theories of tool use. According to the manipulation-based approach, the hand posture errors shoul…

Insight into the Mechanism of Action of Marine Cytotoxic Thiazinoquinones

2017

The electrochemical response of four natural cytotoxic thiazinoquinones isolated from the Aplidium species was studied using conventional solution-phase and solid-state techniques, based on the voltammetry of immobilized particles methodology. The interaction with O-2 and electrochemically generated reactive oxygen species (ROS) was electrochemically monitored. At the same time, a molecular modeling study including density functional theory (DFT) calculations was performed in order to analyze the conformational and electronic properties of the natural thiazinoquinones, as well as those of their reduced intermediates. The obtained electrochemical and computational results were analyzed and c…

Synthesis, Characterization, and Catalysis of β3-[(CoIIO4)W11O31(O2)4],10- the First Keggin-Based True Heteropoly Dioxygen (Peroxo) Anion. Spectrosco…

1999

Reactions of hydrogen peroxide with several lacunary polyoxometalates of the 1:11 series, XW11O39m- (X = Co3+, Ga3+, Fe3+, Si4+, and P5+), are reported. Synthetic pathways to new polyoxotungstates incorporating dioxygen moieties (peroxo and/or superoxo) are developed. The key step involves treating lacunary precursors with H2O2 in strongly buffered aqueous solutions. Upon reaction of H2O2 with α-[Co3+W11O39],9- (a) the central tetrahedral Co3+ is reduced to Co2+ and (b) each of the four unshared oxygens surrounding the vacancy are replaced by a peroxide group, yielding salts of the tetraperoxide anion β3-[(Co2+O4)W11O31(O2)4]10- (1). These results are unequivocally established by a combinat…

A quantum mechanics-molecular mechanics study of dissociative electron transfer : The methylchloride radical anion in aqueous solution

2002

The dissociative electron transfer reaction CH3Cl+e−→CH3•+Cl− in aqueous solution is studied by using a QM/MM method. In this work the quantum subsystem (a methylchloride molecule plus an electron) is described using density functional theory while the solvent (300 water molecules) is described using the TIP3P classical potential. By means of molecular dynamics simulations and the thermodynamic integration technique we obtained the potential of mean force (PMF) for the carbon–chlorine bond dissociation of the neutral and radical anion species. Combining these two free energy curves we found a quadratic dependence of the activation free energy on the reaction free energy in agreement with Ma…

Hole Localization and Thermochemistry of Oxidative Dehydrogenation of Aqueous Rutile TiO2(110)

2012

The Silica-Water Interface: How the Silanols Determine the Surface Acidity and Modulate the Water Properties.

2015

Silica is the most abundant metal oxide and the main component of the Earth's crust. Its behavior in contact with water plays a critical role in a variety of geochemical and environmental processes. Despite its key role, the details of the aqueous silica interface at the microscopic molecular level are still elusive. Here we provide such a detailed understanding of the molecular behavior of the silica-water interface, using density functional theory based molecular dynamics (DFTMD) simulations, where a consistent treatment of the electronic structure of solvent and surface is provided. We have calculated the acidity of the silanol groups at the interface directly from the DFTMD simulations,…