Extremum principles in electromagnetic systems

Variational expressions and saddle-point (or "mini-max") principles for linear problems in electromagnetism are proposed. When conservative conditions are considered, well-known variational expressions for the resonant frequencies of a cavity and the propagation constant of a waveguide are revised directly in terms of electric and magnetic field vectors. In both cases the unknown constants are typefied as stationary (but not extremum) points of some energy-like functionals. On the contrary, if dissipation is involved then variational expressions achieve the extremum property. Indeed, we point out that a saddle-point characterizes the unique solution of Maxwell equations subject to impedance-like dissipative boundary conditions. In particular, we deal with the quasi-static problem and the time-harmonic case

Free energies in one-dimensional models of magnetic transitions with hysteresis

3A one-dimensional non-isothermal model for magnetic materials is proposed. It provides a simplified description of transitions from paramagnetic to either ferro- or ferri-magnetic phase which also accounts for hysteresis loops. The temperature enters the model as a parameter leading the transition, so that the compatibility with thermodynamics is ensured by the Clausius-Duhem inequality. Above the critical temperature, the paramagnetic susceptibility is assumed to obey a proper law depending on the material: the Curie-Weiss law for ferromagnets and the Néel-Curie-Weiss law for antiferromagnets and ferrimagnets. At a temperature below the critical point, a bilinear rate-independent o.d.e. rules the evolution of magnetization versus magnetic field strength. Because of the special form of its skeleton curve, the model applies to materials whose major hysteresis loop is not rectangular-shaped. In addition, the explicit form of the minimum and maximum free energies is obtained under isothermal conditions for the paramagnetic and hysteretic regimes. This allows us to highlight the amount of work performed on the system which is stored as magnetic energy change.PACS 64.70.Kb – Solid–solid transitions. PACS 75.30.Cr – Saturation moments and magnetic susceptibilities. PACS 75.60.Ej – Magnetization curves, hysteresis and related effects.openopenBERTI A.; GIORGI C.; VUK E.Berti, Alessia; Giorgi, Claudio; Vuk, Elen

Steady states analysis and exponential stability of an extensible thermoelastic system

In this work we consider a nonlinear model for the vibrations of a thermoelastic beam with fixed ends resting on an elastic foundation. The behavior of the related dissipative system accounts for both the midplane stretching of the beam and the Fourier heat conduction. The nonlinear term enters the motion equation, only, while the dissipation is entirely contributed by the heat equation. Under stationary axial load and uniform external temperature the problem uncouples and the bending equilibria of the beam satisfy a semilinear equation. For a general axial load $p$, the existence of a finite/infinite set of steady states is proved and buckling occurrence is discussed. Finally, long-term dynamics of solutions and exponential stability of the straight position are scrutinized

On some nonlinear models for suspension bridges

In this paper we discuss some mathematical models describing the nonlinear vibrations of different kinds of single-span simply supported suspension bridges and we summarize some results about the longtime behavior of solutions to the related evolution problems. Finally, in connection with the static counterpart of a general string-beam nonlinear model, we present some original results concerning the existence of multiple buckled solutions

Asymptotic dynamics of nonlinear coupled suspension bridge equations

In this paper we study the long-term dynamics of a doubly nonlinear abstract system which involves a single differential operator to different powers. For a special choice of the nonlinear terms, the system describes the motion of a suspension bridge where the road bed and the main cable are modeled as a nonlinear beam and a vibrating string, respectively, and their coupling is carried out by nonlinear springs. The set of stationary solutions turns out to be nonempty and bounded. As the external loads vanish, the null solution of the system is proved to be exponentially stable provided that the axial load does not exceed some critical value. Finally, we prove the existence of a bounded global attractor of optimal regularity in connection with an arbitrary axial load and quite general nonlinear terms

Asymptotic behavior and numerical approximation of a double-suspended bridge system

This paper is devoted to introduce and analyze a new non linear problem describing the vibrations of a double suspended bridge system. The road bed is modeled as a double beam of Woinowsky-Krieger type and the two cables, each connected to a single beam by a distributed system of elastic springs, are modeled as one-sided elastic strings. We achieve the existence and uniqueness of solutions by using the semigroup theory and the exponential decay property is also proved. Then, the model is numerically analyzed, through a variational formulation, by using the finite element method and a first-order time integration scheme. A priori error estimates are obtained and the linear convergence is derived under some suitable additional regularity conditions. Finally, some numerical experiments are performed to verify the behavior of the numerical method.Universidade Vigo/CISU

Accessibility of the Pre-Big-Bang Models to LIGO

The recent search for a stochastic background of gravitational waves with LIGO interferometers has produced a new upper bound on the amplitude of this background in the 100 Hz region. We investigate the implications of the current and future LIGO results on pre-Big-Bang models of the early Universe, determining the exclusion regions in the parameter space of the minimal pre-Big Bang scenario. Although the current LIGO reach is still weaker than the indirect bound from Big-Bang nucleosynthesis, future runs by LIGO, in the coming year, and by Advanced LIGO (~2009) should further constrain the parameter space, and in some parts surpass the Big-Bang nucleosynthesis bound. It will be more diffcult to constrain the parameter space in non-minimal pre-Big-Bang models, which are characterized by multiple cosmological phases in the yet not well understood stringy phase, and where the higher-order curvature and/or quantum-loop corrections in the string effective action should be included.Comment: 8 pages, 8 figure

Shape Effect in the Design of Nanowire Coated Microparticles as Transepithelial Drug Delivery Devices

While the oral drug delivery route has traditionally been the most popular among patients, it is estimated that 90 % of therapeutic compounds possess oral bioavailability limitations. Thus, the development of novel drug carriers for more effective oral delivery of therapeutics is an important goal. Composite particles made by growing nanoscopic silicon wires from the surface of narrowly dispersed, microsized silica beads were previously shown to be able to: (a) adhere well onto the epithelium by interdigitating their nanowires with the apical microvilli; and (b) increase the permeability of Caco-2 cell monolayers with respect to small organic molecules in direct proportion to their concentration. A comparison between the effects of spherical and planar particle morphologies on the permeability of the epithelial cell layer in vitro and in vivo presented the subject of this study. Owing to their larger surface area, the planar particles exhibited a higher drug loading efficiency than their spherical counterparts, while simultaneously increasing the transepithelial permeation of a moderately sized model drug, insulin. The insulin elution profile for planar nanowire-coated particles displayed a continual increase in the cumulative amount of the released drug, approaching a constant release rate for 1 – 4 h period of the elution time. An immunohistochemical study confirmed the ability of planar silica particles coated with nanowires to loosen the tight junction of the epithelial cells to a greater extent than the spherical particles did, thus enabling a more facile transport of the drug across the epithelium. Transepithelial permeability tests conducted for model drugs ranging in size from 0.4 to 150 kDa yielded three categories of molecules depending on their permeation propensities. Insulin belonged to the category of molecules deliverable across the epithelium only with the assistance of nanowire-coated particles. Other groups of drugs, smaller and bigger, respectively, either did not need the carrier to permeate the epithelium or were not able to cross it even with the support from the nanowire-coated particles. Bioavailability of insulin orally administered to rabbits was also found to be increased when delivered in conjunction with the nanowire-coated planar particles

Does overhead irrigation with salt affect growth, yield, and phenolic content of lentil plants?

Overhead irrigation of lentil plants with salt (100 mM NaCl) did not have any significant impact on plant growth, while chlorophyll content and chlorophyll fluorescence parameter F-v/F-m were affected. Under such poor irrigation water quality, the malondialdehyde content in leaves was increased due to the lipid peroxidation of membranes. In seeds, the total phenolic content (TPC) was correlated to their total antioxidant capacity (TAC). High performance liquid chromatography-mass spectrometry (HPLC-MS) detection showed that flavonoids (catechin, epicatechin, rutin, p-coumaric acid, quercetin, kaempferol, gallic acid and resveratrol) appear to be the compounds with the greatest influence on the TAC values. Catechin is the most abundant phenolic compound in lentil seeds. Overhead irrigation with salt reduced the concentration of almost all phenolic compounds analyzed from lentil seed extracts