A piecewise conservative method for unconstrained convex optimization

Computational Optimization and Applications - We consider a continuous-time optimization method based on a dynamical system, where a massive particle starting at rest moves in the conservative...     

The Allen–Cahn equation with dynamic boundary conditions and mass constraints

The Allen–Cahn equation, coupled with dynamic boundary conditions, has recently received a good deal of attention. The new issue of this paper is the setting of a rather general mass constraint, which may involve either the solution inside the domain or its trace on the boundary. The system of nonlinear partial differential equations can be formulated as a variational inequality. The presence of the constraint in the evolution process leads to additional terms in the equation and the boundary condition containing a suitable Lagrange multiplier. A well‐posedness result is proved for the related initial value problem. Copyright © 2014 John Wiley & Sons, Ltd.     

A mathematical study of the plasticity effects in muscle contraction

Hill's three-element model of contracting muscle is expanded by replacing the series and the parallel elastic elements with elastoplastic elements. The contractile element is structurally described making use of the sliding filament theory. The resulting mathematical model is formulated in terms of an evolution variational inequality for a nonlinear and nonlocal transport-type operator. The existence and uniqueness of the solution are described along with a numerical approach.This work was supported by M.P.I. (fondi per la ricerca scientifica) and by I.A.N. of C.N.R. Pavia.     

Scalable silicon nanowire photodetectors

This paper presents photodetectors having vertically stacked electrodes with sub-micron (300 nm) separation based on silicon nanowire (SiNW) nanocomposites. The thin-film-like devices are made using standard photolithography instead of electron beam lithography and thus are amenable to scalable low-cost manufacturing. The processing technique is not limited to SiNWs and can be extended to different nanowires (NWs) (e.g., ZnO, CdSe) and substrates. The current–voltage characteristics show Schottky behaviour that is dependent on the properties of the contact metal and that of the pristine SiNWs. This makes these devices suitable for examination of electronic transport in SiNWs. Preliminary results for light sensitivity show promising photoresponse that is a function of effective NW density.     

The motion of a solid with large deformations

We study the motion of a solid with large deformations. The solid may be loaded on its surface by needles, rods, beams, plates… Therefore it is wise to choose a third-gradient theory for the body. Stretch matrix of the polar decomposition has to be symmetric. This is an internal constraint which introduces a reaction stress in the Piola–Kirchhoff–Boussinesq stress. We prove that there exists a motion that satisfies the complete equations of Mechanics in a convenient variational framework. This motion is local-in-time because it may be interrupted by crushing, resulting in a discontinuity of velocity with respect to time, i.e., an internal collision.     

Solution Layer Deposition: A Technique for the Growth of Ultra‐Pure Manganese Oxides on Silica at Room Temperature

With the ever increasing miniaturization in microelectronic devices, new deposition techniques are required to form high‐purity metal oxide layers. Herein, we report a liquid route to specifically produce thin and conformal amorphous manganese oxide layers on silicon substrate, which can be transformed into a manganese silicate layer. The undesired insertion of carbon into the functional layers is avoided through a solution metal–organic chemistry approach named Solution Layer Deposition (SLD). The growth of a pure manganese oxide film by SLD takes place through the decoordination of ligands from a metal–organic complex in mild conditions, and coordination of the resulting metal atoms on a silica surface. The mechanism of this chemical liquid route has been elucidated by solid‐state ²⁹Si MAS NMR, XPS, SIMS, and HRTEM.     

Decay of geometry for Fibonacci critical covering maps of the circle

We study the growth of Dfⁿ(f(c)) when f is a Fibonacci critical covering map of the circle with negative Schwarzian derivative, degree d2 and critical point c of order ℓ>1. As an application we prove that f exhibits exponential decay of geometry if and only if ℓ2, and in this case it has an absolutely continuous invariant probability measure, although not satisfying the so-called Collet–Eckmann condition.