Analyticity and criticality results for the eigenvalues of the biharmonic operator

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.Comment: To appear on the proceedings of the conference "Geometric Properties for Parabolic and Elliptic PDE's - 4th Italian-Japanese Workshop" held in Palinuro (Italy), May 25-29, 201

Annihilation of positrons trapped at the (100) and (111) surfaces of Si

We present results of theoretical studies of positron surface states and positron annihilation characteristics at the clean non reconstructed (100) and (111) surfaces of Si performed within the modified atomistic, superposition method. It is found that in the case of non reconstructed semiconductor surfaces, the positron surface state is localized mainly on the vacuum side of the topmost layer. The computed positron surface state energies Eb at the (100) and (111) surfaces of Si are -2.81 and -2.69 eV. In addition, calculations of the positron work functions with respect to the vacuum for bulk Si(100) and Si(111) yielded 2.34 and 2.23 eV, respectively demonstrating the stability of positron surface state on these surfaces. The positron surface state lifetime as well as probabilities for a positron trapped in a surface state to annihilate with relevant core-level electrons are computed for both surfaces, and compared with available experimental data

Biochemical Reaction Rules with Constraints

International audienceWe propose React(C), an expressive programming language for stochastic modeling and simulation in systems biology, that is based on biochemical reactions with constraints. We prove that React(C) can express the stochastic pi-calculus, in contrast to previous rule-based programming languages, and further illustrate the high expressiveness of React(C). We present a stochastic simulator for React(C) independently of the choice of the constraint language C. Our simulator must decide for a given reaction rule whether it can be applied to the current biochemical solution. We show that this decision problem is NP-complete for arbitrary constraint systems C, and that it can be solved in polynomial time for rules of bounded arity. In practice, we propose to solve this problem by constraint programming

Biophysical model to predict lung delivery from a dual bronchodilator dry-powder inhaler

A biophysical lung model was designed to predict inhaled drug deposition in patients with obstructive airway disease, and quantitatively investigate sources of deposition variability. Different mouth-throat anatomies at varying simulated inhalation flows were used to calculate the lung dose of indacaterol/glycopyrronium [IND/GLY] 110/50 µg (QVA149) from the dry-powder inhaler Breezhaler®. Sources of variability in lung dose were studied using computational fluid dynamics, supported by aerosol particle sizing measurements, particle image velocimetry and computed tomography. Anatomical differences in mouth-throat geometries were identified as a major source of inter-subject variability in lung deposition. Lung dose was similar across inhalation flows of 30–120 L/min with a slight drop in calculated delivery at high inspiratory flows. Delivery was relatively unaffected by inhaler inclination angle. The delivered lung dose of the fixed-dose combination IND/GLY matched well with corresponding monotherapy doses. This biophysical model indicates low extra-thoracic drug loss and consistent lung delivery of IND/GLY, independent of inhalation flows. This is an important finding for patients across various ages and lung disease severities. The model provides a quantitative, mechanistic simulation of inhaled therapies that could provide a test system for estimating drug delivery to the lung and complement traditional clinical studies

Theoretical study of the positron surface state at an alkali-metal surface

We present a quantum mechanical analysis of positrons trapped in a bound state at the (100) surface of bulk Cs, based on the treatment of a positron as a single charged particle trapped in an image potential-correlation well in the proximity of the surface atoms. The image-potential-induced positron surface state is calculated using the corrugated-mirror model in full three-dimensional geometry. Calculations show that the positron bound state is delocalized in the surface plane, but is strongly localized perpendicular to the surface mainly in the region between the top and the second layers of Cs atoms. The positron binding energy Eb in the surface state is computed to be 4.92 eV. Calculations on the positron annihilation rates for different Cs core levels are performed using the independent particle model. The positron surface state lifetime is calculated using the local density approximation method. The annihilation probabilities of a positron trapped at the Cs(100) surface with Cs 4p and 4d core electron levels are computed to be 0.065% and 0.22%, respectively. © 1995

Study of positron surface states on the alkali-metal-covered transition-metal surface

We present a first-principles study of annihilation probabilities of surface trapped positrons with core electrons at the Cu(100) surface with sub-monolayers of Cs adsorbed. Image-potential-induced positron surface states are calculated using a corrugated-mirror model in a full three-dimensional geometry. These states are studied for various arrangements of Cs atoms below and above the critical alkali-metal coverage of approximately 0.7 physical monolayer. Computer simulations of the deposition of Cs atoms are used to show that hexagonal close-packed Cs islands are formed at about 0.7 physical monolayer coverage of Cs. It is found that the abrupt decrease in the positron annihilation rate with Cu 3p electrons observed experimentally results from a metallization of the Cs islands. This causes a shift in the localization of the positron bound state from the Cs Cu interface to the vacuum side of the Cs overlayer, with the corresponding abrupt decrease in the positron annihilation probability with Cu electrons. Annihilation probabilities for positrons with Cs electrons are also computed and compared with experiment. © 1995

Finite Element Convergence for the Joule Heating Problem with Mixed Boundary Conditions

We prove strong convergence of conforming finite element approximations to the stationary Joule heating problem with mixed boundary conditions on Lipschitz domains in three spatial dimensions. We show optimal global regularity estimates on creased domains and prove a priori and a posteriori bounds for shape regular meshes.Comment: Keywords: Joule heating problem, thermistors, a posteriori error analysis, a priori error analysis, finite element metho

Computing the first eigenpair of the p-Laplacian via inverse iteration of sublinear supersolutions

We introduce an iterative method for computing the first eigenpair $(\lambda_{p},e_{p})$ for the $p$-Laplacian operator with homogeneous Dirichlet data as the limit of $(\mu_{q,}u_{q})$ as $q\rightarrow p^{-}$, where $u_{q}$ is the positive solution of the sublinear Lane-Emden equation $-\Delta_{p}u_{q}=\mu_{q}u_{q}^{q-1}$ with same boundary data. The method is shown to work for any smooth, bounded domain. Solutions to the Lane-Emden problem are obtained through inverse iteration of a super-solution which is derived from the solution to the torsional creep problem. Convergence of $u_{q}$ to $e_{p}$ is in the $C^{1}$-norm and the rate of convergence of $\mu_{q}$ to $\lambda_{p}$ is at least $O(p-q)$. Numerical evidence is presented.Comment: Section 5 was rewritten. Jed Brown was added as autho

Spatial Heterogeneity of Autoinducer Regulation Systems

Autoinducer signals enable coordinated behaviour of bacterial populations, a phenomenon originally described as quorum sensing. Autoinducer systems are often controlled by environmental substances as nutrients or secondary metabolites (signals) from neighbouring organisms. In cell aggregates and biofilms gradients of signals and environmental substances emerge. Mathematical modelling is used to analyse the functioning of the system. We find that the autoinducer regulation network generates spatially heterogeneous behaviour, up to a kind of multicellularity-like division of work, especially under nutrient-controlled conditions. A hybrid push/pull concept is proposed to explain the ecological function. The analysis allows to explain hitherto seemingly contradicting experimental findings