The Effects of Additives on the Physical Properties of Electroformed Nickel and on the Stretch of Photoelectroformed Nickel Components

The process of nickel electroforming is becoming increasingly important in the manufacture of MST products, as it has the potential to replicate complex geometries with extremely high fidelity. Electroforming of nickel uses multi-component electrolyte formulations in order to maximise desirable product properties. In addition to nickel sulphamate (the major electrolyte component), formulation additives can also comprise nickel chloride (to increase nickel anode dissolution), sulphamic acid (to control pH), boric acid (to act as a pH buffer), hardening/levelling agents (to increase deposit hardness and lustre) and wetting agents (to aid surface wetting and thus prevent gas bubbles and void formation). This paper investigates the effects of some of these variables on internal stress and stretch as a function of applied current density.Comment: Submitted on behalf of TIMA Editions (http://irevues.inist.fr/tima-editions

Curved planar quantum wires with Dirichlet and Neumann boundary conditions

We investigate the discrete spectrum of the Hamiltonian describing a quantum particle living in the two-dimensional curved strip. We impose the Dirichlet and Neumann boundary conditions on opposite sides of the strip. The existence of the discrete eigenvalue below the essential spectrum threshold depends on the sign of the total bending angle for the asymptotically straight strips.Comment: 7 page

Quantum waveguides with a lateral semitransparent barrier: spectral and scattering properties

We consider a quantum particle in a waveguide which consists of an infinite straight Dirichlet strip divided by a thin semitransparent barrier on a line parallel to the walls which is modeled by a $\delta$ potential. We show that if the coupling strength of the latter is modified locally, i.e. it reaches the same asymptotic value in both directions along the line, there is always a bound state below the bottom of the essential spectrum provided the effective coupling function is attractive in the mean. The eigenvalues and eigenfunctions, as well as the scattering matrix for energies above the threshold, are found numerically by the mode-matching technique. In particular, we discuss the rate at which the ground-state energy emerges from the continuum and properties of the nodal lines. Finally, we investigate a system with a modified geometry: an infinite cylindrical surface threaded by a homogeneous magnetic field parallel to the cylinder axis. The motion on the cylinder is again constrained by a semitransparent barrier imposed on a ``seam'' parallel to the axis.Comment: a LaTeX source file with 12 figures (11 of them eps); to appear in J. Phys. A: Math. Gen. Figures 3, 5, 8, 9, 11 are given at 300 dpi; higher resolution originals are available from the author

Polymers in Curved Boxes

We apply results derived in other contexts for the spectrum of the Laplace operator in curved geometries to the study of an ideal polymer chain confined to a spherical annulus in arbitrary space dimension D and conclude that the free energy compared to its value for an uncurved box of the same thickness and volume, is lower when $D < 3$, stays the same when $D = 3$, and is higher when \mbox{$D > 3$}. Thus confining an ideal polymer chain to a cylindrical shell, lowers the effective bending elasticity of the walls, and might induce spontaneous symmetry breaking, i.e. bending. (Actually, the above mentioned results show that {\em {any}} shell in $D = 3$ induces this effect, except for a spherical shell). We compute the contribution of this effect to the bending rigidities in the Helfrich free energy expression.Comment: 20 pages RevTeX, epsf; 4 figures; submitted to Macromoledule

Perturbations of eigenvalues embedded at threshold: one, two and three dimensional solvable models

We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians showing eigenvalues and resonances at the threshold of the continuous spectrum and we analyze the effect of various type of perturbations on the spectral singularities. We provide algorithms to obtain convergent series expansions for the coordinates of the singularities.Comment: 20 page

On the spectrum of a bent chain graph

We study Schr\"odinger operators on an infinite quantum graph of a chain form which consists of identical rings connected at the touching points by $\delta$-couplings with a parameter $\alpha\in\R$. If the graph is "straight", i.e. periodic with respect to ring shifts, its Hamiltonian has a band spectrum with all the gaps open whenever $\alpha\ne 0$. We consider a "bending" deformation of the chain consisting of changing one position at a single ring and show that it gives rise to eigenvalues in the open spectral gaps. We analyze dependence of these eigenvalues on the coupling $\alpha$ and the "bending angle" as well as resonances of the system coming from the bending. We also discuss the behaviour of the eigenvalues and resonances at the edges of the spectral bands.Comment: LaTeX, 23 pages with 7 figures; minor changes, references added; to appear in J. Phys. A: Math. Theo

Effet d’un programme d’activité physique intermittent de haute intensité sur la perte de masse grasse abdominale chez la femme DT2 ménopausée

Contexte : A la ménopause, la diminution des taux d’estrogènes favorise un dépôt de masse grasse (MG) abdominal (sous-cutané et viscéral). La MG viscérale est corrélée aux maladies cardio-vasculaires (MCV). Ce risque est accentué chez les sujets présentant un diabète de type 2 (DT2).Objectif : Comparer deux modalités d’entraînement, continu de moyenne intensité (SSE) vs. intermittent de haute intensité (HIIE), sur la perte de MG abdominale (dont viscérale) chez des femmes DT2 ménopausées.Matériels et méthode : Seize femmes DT2 ménopausées (69±1ans; IMC : 31±1 kg/m²) ont été réparties aléatoirement en deux groupes. Pendant quatre mois, deux fois par semaine, 8 d’entre elles ont réalisé un entraînement SSE (40 min de pédalage à 50% de la FCmax de réserve), et 8 ont réalisé un entraînement HIIE (8s de sprint suivies de 12s de récupération active, pendant 20 min). Pré (T0) et post entraînement (T4), la composition corporelle et la MG abdominale totale ont été mesurées par DXA (Dual Energy X-ray Absorptiometry). La MG viscérale a été estimée à partir de la méthode de Martin et Jensen1. A T0 et T4, les apports énergétiques et le niveau d’activité physique ont été déterminés (questionnaires et accéléromètrie validée2 intégrée sur smartphone).Résultats : Après 16 semaines d’intervention, sans modification des apports énergétiques et du niveau d’activité physique total, une perte de MG totale et un gain de masse maigre est observé (effet temps, p<0.05). La diminution de MG abdominale est supérieure dans le groupe HIIE (0.32% ± 2.07 vs 8.32 % ± 2.19, p<0.05) et la perte de MG viscérale n’est observée que dans le groupe HIIE (p<0.05).Conclusion : L’entraînement de type HIIE apparait comme un programme alternatif intéressant chez la femme DT2 ménopausée en diminuant significativement la MG abdominale totale et viscérale

On a semiclassical formula for non-diagonal matrix elements

Let $H(\hbar)=-\hbar^2d^2/dx^2+V(x)$ be a Schr\"odinger operator on the real line, $W(x)$ be a bounded observable depending only on the coordinate and $k$ be a fixed integer. Suppose that an energy level $E$ intersects the potential $V(x)$ in exactly two turning points and lies below $V_\infty=\liminf_{|x|\to\infty} V(x)$. We consider the semiclassical limit $n\to\infty$, $\hbar=\hbar_n\to0$ and $E_n=E$ where $E_n$ is the $n$th eigen-energy of $H(\hbar)$. An asymptotic formula for $$, the non-diagonal matrix elements of $W(x)$ in the eigenbasis of $H(\hbar)$, has been known in the theoretical physics for a long time. Here it is proved in a mathematically rigorous manner.Comment: LaTeX2

An effective mass theorem for the bidimensional electron gas in a strong magnetic field

We study the limiting behavior of a singularly perturbed Schr\"odinger-Poisson system describing a 3-dimensional electron gas strongly confined in the vicinity of a plane $(x,y)$ and subject to a strong uniform magnetic field in the plane of the gas. The coupled effects of the confinement and of the magnetic field induce fast oscillations in time that need to be averaged out. We obtain at the limit a system of 2-dimensional Schr\"odinger equations in the plane $(x,y)$, coupled through an effective selfconsistent electrical potential. In the direction perpendicular to the magnetic field, the electron mass is modified by the field, as the result of an averaging of the cyclotron motion. The main tools of the analysis are the adaptation of the second order long-time averaging theory of ODEs to our PDEs context, and the use of a Sobolev scale adapted to the confinement operator