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

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

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

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

Calcium phosphate nanoparticles as intrinsic inorganic antimicrobials: In search of the key particle property

One of the main goals of materials science in the 21st century is the development of materials with rationally designed properties as substitutes for traditional pharmacotherapies. At the same time, there is a lack of understanding of the exact material properties that induce therapeutic effects in biological systems, which limits their rational optimization for the related medical applications. This study sets the foundation for a general approach for elucidating nanoparticle properties as determinants of antibacterial activity, with a particular focus on calcium phosphate nanoparticles. To that end, nine physicochemical effects were studied and a number of them were refuted, thus putting an end to frequently erred hypotheses in the literature. Rather than having one key particle property responsible for eliciting the antibacterial effect, a complex synergy of factors is shown to be at work, including (a) nanoscopic size; (b) elevated intracellular free calcium levels due to nanoparticle solubility; (c) diffusivity and favorable electrostatic properties of the nanoparticle surface, primarily low net charge and high charge density; and (d) the dynamics of perpetual exchange of ultrafine clusters across the particle/solution interface. On the positive side, this multifaceted mechanism is less prone to induce bacterial resistance to the therapy and can be a gateway to the sphere of personalized medicine. On a more problematic side, it implies a less intense effect compared to single-target molecular therapies and a difficulty of elucidating the exact mechanisms of action, while also making the rational design of theirs for this type of medical application a challenge

Autologous, Non-Invasively Available Mesenchymal Stem Cells from the Outer Root Sheath of Hair Follicle Are Obtainable by Migration from Plucked Hair Follicles and Expandable in Scalable Amounts

Background: Regenerative therapies based on autologous mesenchymal stem cells (MSC) as well as stem cells in general are still facing an unmet need for non-invasive sampling, availability, and scalability. The only known adult source of autologous MSCs permanently available with no pain, discomfort, or infection risk is the outer root sheath of the hair follicle (ORS). Methods: This study presents a non-invasively-based method for isolating and expanding MSCs from the ORS (MSCORS) by means of cell migration and expansion in air–liquid culture. Results: The method yielded 5 million cells of pure MSCORS cultured in 35 days, thereby superseding prior art methods of culturing MSCs from hair follicles. MSCORS features corresponded to the International Society for Cell Therapy characterization panel for MSCs: adherence to plastic, proliferation, colony forming, expression of MSC-markers, and adipo-, osteo-, and chondro-differentiation capacity. Additionally, MSCORS displayed facilitated random-oriented migration and high proliferation, pronounced marker expression, extended endothelial and smooth muscle differentiation capacity, as well as a paracrine immunomodulatory effect on monocytes. MSCORS matched or even exceeded control adipose-derived MSCs in most of the assessed qualities. Conclusions: MSCORS qualify for a variety of autologous regenerative treatments of chronic disorders and prophylactic cryopreservation for purposes of acute treatments in personalized medicine

Intraovarian regulation of gonadotropin-dependent folliculogenesis depends on notch receptor signaling pathways not involving Delta-like ligand 4 (Dll4)

Background: In-situ hybridisation studies demonstrate that Notch receptors and ligands are expressed in granulosa cells (GCs) and in the theca layer vasculature of growing follicles. Notch signaling involves cell-to-cell interaction mediated by transmembrane receptors and ligands. This signaling pathway may represent a novel intraovarian regulator of gonadotropin-dependent follicular development to the preovulatory stage. We hypothesized that blocking Notch pathways would disrupt follicular maturation in the mouse ovary. Methods: Hypophysectomized CD21 female mice were administered pregnant mare serum gonadotropin (PMSG) for 3 days to stimulate follicular development. In one experiment, a pan-notch inhibitor, compound E, was initiated 2 days prior to and throughout stimulation (n = 10), while in a second experiment, a humanized phage Dll4 blocking antibody, YW152F, was used (n = 5). After sacrifice, ovarian histology, serum estradiol levels and uterine weights were compared to controls. The ovarian morphology was evaluated with hematoxylin/eosin staining and immunohistochemistry was performed for Notch1, Notch2, Notch3, Notch4, Jagged1, Dll4, platelet endothelial cell adhesion molecule (PECAM) and alpha-smooth muscle actin (α-SMA) detection. Results: We localized specific Notch ligands and receptors in the following structures: Dll4 is specific to theca layer endothelial cells (ECs); Notch1/Notch4 and Jagged1 are expressed in theca layer ECs and vascular smooth muscle cells (VSMCs), whereas Notch3 is restricted to VSMCs; Notch2 is expressed mostly on GCs of small follicles. Administration of a pan-Notch inhibitor, compound E, inhibits follicular development to the preovulatory stage (8.5 preovulatory follicles in treatment vs. 3.4 preovulatory follicles in control, p < 0.01; average number per ovary) with significant secondary effects on ovarian and uterine weight and estradiol secretion in a setting of uninhibited vascular proliferation, but disorganized appearance of ECs and VSMCs. Inhibition of endothelial Notch1 function through the inactivation of its ligand Dll4 with the blocking antibody YW152F induces mild disorganisation of follicular vasculature, but has no significant effect on gonadotropin-dependent folliculogenesis. Conclusions: Our experiments suggest that the complete blockage of the Notch signaling pathway with compound E impairs folliculogenesis and induces disruption of gonadotropin stimulated angiogenesis. It seems the mechanism involves Notch1 and Notch3, specifically, causing the improper assembly of ECs and VSMCs in the theca layer, although the potential role of non-angiogenic Notch signaling, such as Jagged2 to Notch2 in GCs, remains to be elucidated

Endonuclease heteroduplex mismatch cleavage for detecting mutation genetic variation of trypsin inhibitors in soybean

The objective of this work was to evaluate the genetic variation of trypsin inhibitor in cultivated (Glycine max L.) and wild (Glycine sofa Siebold & Zucc.) soybean varieties. Genetic variations of the Kunitz trypsin inhibitor, represented by a 21-kD protein (KTI), and of the Bowman-Birk trypsin chymotrypsin inhibitor (BBI) were evaluated in cultivated (G. max) and wild (G. sofa) soybean varieties. Endonuclease heteroduplex mismatch cleavage assays were performed to detect mutations in the KTI gene, with a single-stranded specific nuclease obtained from celery extracts (CEL I). The investigated soybean varieties showed low level of genetic variation in KTI and BBI. PCR-RFLP analysis divided the BBI-A type into subtypes A1 and A2, and showed that Tib type of KTI is the dominant type. Digestion with restriction enzymes was not able to detect differences between ti-null and other types of Ti alleles, while the endonuclease heteroduplex mismatch cleavage assay with CEL I could detect ti-null type. The digestion method with CEL I provides a simple and useful genetic tool for SNP analysis. The presented method can be used as a tool for fast and useful screening of desired genotypes in future breeding programs of soybean

Corrigendum: CCR7-dependent trafficking of RORγ+ ILCs creates a unique microenvironment within mucosal draining lymph nodes

Presentation of peptide:MHCII by ​RORγ-expressing group 3 innate lymphoid cells (ILC3s), which are enriched within gut tissue, is required for control of ​CD4 T-cell responses to commensal bacteria. It is not known whether ILC populations migrate from their mucosal and peripheral sites to local draining secondary lymphoid tissues. Here we demonstrate that ILC3s reside within the interfollicular areas of mucosal draining lymph nodes, forming a distinct microenvironment not observed in peripheral lymph nodes. By photoconverting intestinal cells in Kaede mice we reveal constitutive trafficking of ILCs from the intestine to the draining mesenteric lymph nodes, which specifically for the LTi-like ILC3s was ​CCR7-dependent. Thus, ILC populations traffic to draining lymph nodes using different mechanisms