On Markov operators preserving polynomials

The paper is concerned with a special class of positive linear operators acting on the space C(K)$C(K)$ of all continuous functions defined on a convex compact subset K   of R^d${\mathbf{R}}^d$, d?1$d?1$, having non-empty interior. Actually, this class consists of all positive linear operators T   on C(K)$C(K)$ which leave invariant the polynomials of degree at most 1 and which, in addition, map polynomials into polynomials of the same degree. Among other things, we discuss the existence of such operators in the special case where K is strictly convex by also characterizing them within the class of positive projections. In particular we show that such operators exist if and only if ∂K   is an ellipsoid. Furthermore, a characterization of balls of R^d${\mathbf{R}}^d$ in terms of a special class of them is furnished. Additional results and illustrative examples are presented as well.     

Nonequilibrium thermodynamics and the optimal path to turbulence in shear flows

We determine the initial condition on the laminar-turbulent boundary closest to the laminar state using nonlinear optimization for plane Couette flow. Resorting to the general evolution criterion of nonequilibrium systems we optimize the route to the statistically steady turbulent state, i.e., the state characterized by the largest entropy production. This is the first time information from the fully turbulent state is included in the optimization procedure. We demonstrate that the optimal initial condition is localized in space for realistic flow domains.     

Extraordinary magnetic field effect in bent-core liquid crystals

A bent-core mesogen that forms a cybotactic nematic phase exhibits a giant magnetic field-induced shift of its nematic-isotropic and smectic-C-nematic transition temperatures: ΔT(H) = 4 K for H = 10 kOe. In contrast with molecular nematics, in cybotactic nematics the field couples with the anisotropic susceptibility of clusters containing several hundred partially ordered molecules. X-ray diffraction data corroborate a quantitative estimate of inferred cluster size (～300 molecules). The results represent an unequivocal demonstration of the cluster picture of the nematic phase of this class of nonlinear liquid crystals.     

Electrodeposited Co-Pt thin films for magnetic hard disks

ew baths for Co-Pt electrodeposition have been developed and developed and ECD thin films (≤0.3μm) have been prepared and characterized structurally (XRD), morphologically (SEM), chemically (EDS) and magnetically (VSM); their improved corrosion, oxidation and wear resistance have been ascertained. Such alloys appear suitable candidates for magnetic storage systems, from all technological viewpoints. The originally formulated baths contain Co-NH₃-citrate complexes and Pt-p salt (Pt(NH₃)₂(NO₂)₂). Co-Pt thin films of fcc structure are deposited obtaining microcrystallites of definite composition. At Pt 30 at% we obtain fcc films with a=0.369 nm, H_C=80 kA m, and high squareness; increasing Co and decreasing Pt content in the bath it is possible to reduce the Pt content of the deposit, obtaining fcc structures containing two types of microcrystals with a = 0.3615 nm and a = 0.369 nm deposited simultaneously. NaH₂PO₂ additions to the bath have a stabilizing influence on the fcc structure of a = 0.3615 nm, Pt 20 at% and H_C as high as 200 kA/m, with hysteresis loops suitable for both longitudinal or perpendicular recording, depending on the thickness. We have prepared 2.5 in. hard disks for magnetic recording with ECD Co-Pt 20 at% with a polished and texturized ACD Ni-P underlayer. Pulse response, 1F & 2F frequency and frequency sweep response behaviour, as well as noise and overwrite characteristics have been measured for both our disks and high-standard sputtered Co-Cr-Ta production disks, showin improved D₅₀ for Co-Pt ECD disks. The signal-to-noise ratio could be improved by pulse electrodeposition and etching post-treatments.     

Space-resolved low frequency dynamics in entangled polymers

A T_1ρ filter for the NMR imaging of solid polymers is presented. T_1ρ is the relaxation time in the rotating frame, which is sensitive to the molecular motion and whose spectral density falls in the range of slow dynamics, namely motion characterized by correlation times ranging between 10⁻² and 10⁻⁵ s. The method allows one to obtain a good spatial resolution without the need of strong field gradients and without the effects related to the spatial encoding manipulation of the spin system.     

Search for medium modifications of the rho meson

The photoproduction of vector mesons on various nuclei has been studied using the CLAS detector at Jefferson Laboratory. The vector mesons, rho, omega, and varphi, are observed via their decay to e;{+}e;{-}, in order to reduce the effects of final-state interactions in the nucleus. Of particular interest are possible in-medium effects on the properties of the rho meson. The rho mass spectrum is extracted from the data on various nuclei, 2H, C, Fe, and Ti. We observe no significant mass shift and some broadening consistent with expected collisional broadening for the rho meson.     

Approximation of some Feller semigroups associated with a modification of Szász–Mirakjan–Kantorovich operators

We deepen the study of a sequence (C _n ) _n≧1 of positive linear operators, first introduced in [4], that generalize the classical Szász–Mirakjan–Kantorovich operators. In particular, we present some qualitative properties and an asymptotic formula for such a sequence. Moreover, we prove that, under suitable assumptions, the C ₀-semigroups generated by the second order differential operator $$V_l(u)(x)=xu''(x)+\frac{l}{2} u'(x)\quad (x \geqq 0,\ l \in [0, 2]) $$ on suitable domains of continuous or integrable functions may be approximated by means of iterates of the C _n ’s.     

Nonlinearities in tilt and layer displacements of planar lipid bilayers

A novel continuum model is proposed to describe the deformations of a planar lipid bilayer suspended across a circular pore. The model is derived within a new theoretical framework for smectic A liquid crystals in which the usual director n , which defines the average orientation of the molecules, is not constrained to be normal to the layers. The free energy is defined by considering the elastic splay of the director, the bending and compression of the lipid bilayer, the cost of tilting the director with respect to the layer normal, the surface tension, and the weak anchoring of the director. Variational methods are used to derive the equilibrium equations and boundary conditions. The resulting boundary value problem is then solved numerically to compute the fully nonlinear displacement of the layers and tilt of the lipid molecules. A parametric study shows that an increase in surface tension produces a decrease in the deformation of the lipid bilayers while an opposite effect is obtained when increasing the anchoring strength.