Projet de conversion et d'unification des titres des Series B. C. & D. de la Dette Ottomane

Taha Toros Arşivi, Dosya No: 71-Duyun-u Umumiyeİstanbul Kalkınma Ajansı (TR10/14/YEN/0033) İstanbul Development Agency (TR10/14/YEN/0033

Bubble concentration on spheres for supercritical elliptic problems

We consider the supercritical Lane-Emden problem (P_\eps)\qquad -\Delta v= |v|^{p_\eps-1} v \ \hbox{in}\ \mathcal{A} ,\quad u=0\ \hbox{on}\ \partial\mathcal{A} where $\mathcal A$ is an annulus in \rr^{2m}, $m\ge2$ and p_\eps={(m+1)+2\over(m+1)-2}-\eps, \eps>0. We prove the existence of positive and sign changing solutions of (P_\eps) concentrating and blowing-up, as \eps\to0, on $(m-1)-$dimensional spheres. Using a reduction method (see Ruf-Srikanth (2010) J. Eur. Math. Soc. and Pacella-Srikanth (2012) arXiv:1210.0782)we transform problem (P_\eps) into a nonhomogeneous problem in an annulus \mathcal D\subset \rr^{m+1} which can be solved by a Ljapunov-Schmidt finite dimensional reduction

Dvoretzky type theorems for multivariate polynomials and sections of convex bodies

In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on $\mathbb R^n$, and improve bounds on the number $n(d,k)$ in the analogous conjecture for odd degrees $d$ (this case is known as the Birch theorem) and complex polynomials. We also consider a stronger conjecture on the homogeneous polynomial fields in the canonical bundle over real and complex Grassmannians. This conjecture is much stronger and false in general, but it is proved in the cases of $d=2$ (for $k$'s of certain type), odd $d$, and the complex Grassmannian (for odd and even $d$ and any $k$). Corollaries for the John ellipsoid of projections or sections of a convex body are deduced from the case $d=2$ of the polynomial field conjecture

Photoabsorption spectra of the diamagnetic hydrogen atom in the transition regime to chaos: Closed orbit theory with bifurcating orbits

With increasing energy the diamagnetic hydrogen atom undergoes a transition from regular to chaotic classical dynamics, and the closed orbits pass through various cascades of bifurcations. Closed orbit theory allows for the semiclassical calculation of photoabsorption spectra of the diamagnetic hydrogen atom. However, at the bifurcations the closed orbit contributions diverge. The singularities can be removed with the help of uniform semiclassical approximations which are constructed over a wide energy range for different types of codimension one and two catastrophes. Using the uniform approximations and applying the high-resolution harmonic inversion method we calculate fully resolved semiclassical photoabsorption spectra, i.e., individual eigenenergies and transition matrix elements at laboratory magnetic field strengths, and compare them with the results of exact quantum calculations.Comment: 26 pages, 9 figures, submitted to J. Phys.

Finite size effects on transport coefficients for models of atomic wires coupled to phonons

We consider models of quasi-1-d, planar atomic wires consisting of several, laterally coupled rows of atoms, with mutually non-interacting electrons. This electronic wire system is coupled to phonons, corresponding, e.g., to some substrate. We aim at computing diffusion coefficients in dependence on the wire widths and the lateral coupling. To this end we firstly construct a numerically manageable linear collision term for the dynamics of the electronic occupation numbers by following a certain projection operator approach. By means of this collision term we set up a linear Boltzmann equation. A formula for extracting diffusion coefficients from such Boltzmann equations is given. We find in the regime of a few atomic rows and intermediate lateral coupling a significant and non-trivial dependence of the diffusion coefficient on both, the width and the lateral coupling. These results, in principle, suggest the possible applicability of such atomic wires as electronic devices, such as, e.g., switches.Comment: 9 pages, 5 figures, accepted for publication in Eur. Phys. J.

Properties of cage rearrangements observed near the colloidal glass transition

We use confocal microscopy to study the motions of particles in concentrated colloidal systems. Near the glass transition, diffusive motion is inhibited, as particles spend time trapped in transient ``cages'' formed by neighboring particles. We measure the cage sizes and lifetimes, which respectively shrink and grow as the glass transition approaches. Cage rearrangements are more prevalent in regions with lower local concentrations and higher disorder. Neighboring rearranging particles typically move in parallel directions, although a nontrivial fraction move in anti-parallel directions, usually from pairs of particles with initial separations corresponding to the local maxima and minima of the pair correlation function $g(r)$, respectively.Comment: 5 pages, 4 figures; text & figures revised in v

Positive Least Energy Solutions and Phase Separation for Coupled Schrodinger Equations with Critical Exponent: Higher Dimensional Case

We study the following nonlinear Schr\"{o}dinger system which is related to Bose-Einstein condensate: {displaymath} {cases}-\Delta u +\la_1 u = \mu_1 u^{2^\ast-1}+\beta u^{\frac{2^\ast}{2}-1}v^{\frac{2^\ast}{2}}, \quad x\in \Omega, -\Delta v +\la_2 v =\mu_2 v^{2^\ast-1}+\beta v^{\frac{2^\ast}{2}-1} u^{\frac{2^\ast}{2}}, \quad x\in \om, u\ge 0, v\ge 0 \,\,\hbox{in \om},\quad u=v=0 \,\,\hbox{on \partial\om}.{cases}{displaymath} Here \om\subset \R^N is a smooth bounded domain, $2^\ast:=\frac{2N}{N-2}$ is the Sobolev critical exponent, -\la_1(\om)0 and $\beta\neq 0$, where \lambda_1(\om) is the first eigenvalue of $-\Delta$ with the Dirichlet boundary condition. When \bb=0, this is just the well-known Brezis-Nirenberg problem. The special case N=4 was studied by the authors in (Arch. Ration. Mech. Anal. 205: 515-551, 2012). In this paper we consider {\it the higher dimensional case $N\ge 5$}. It is interesting that we can prove the existence of a positive least energy solution (u_\bb, v_\bb) {\it for any $\beta\neq 0$} (which can not hold in the special case N=4). We also study the limit behavior of (u_\bb, v_\bb) as $\beta\to -\infty$ and phase separation is expected. In particular, u_\bb-v_\bb will converge to {\it sign-changing solutions} of the Brezis-Nirenberg problem, provided $N\ge 6$. In case \la_1=\la_2, the classification of the least energy solutions is also studied. It turns out that some quite different phenomena appear comparing to the special case N=4.Comment: 48 pages. This is a revised version of arXiv:1209.2522v1 [math.AP

Precision Flavour Physics with B→KννˉB\to K\nu\bar\nu and B→Kl+l−B\to Kl^+l^-

We show that a combined analysis of $B\to K\nu\bar\nu$ and $B\to Kl^+l^-$ allows for new physics tests practically free of form factor uncertainties. Residual theory errors are at the level of several percent. Our study underlines the excellent motivation for measuring these modes at a Super Flavour Factory.Comment: 26 pages, 2 figure

The Spin Glass Transition : Exponents and Dynamics

Numerical simulations on Ising Spin Glasses show that spin glass transitions do not obey the usual universality rules which hold at canonical second order transitions. On the other hand the dynamics at the approach to the transition appear to take up a universal form for all spin glasses. The implications for the fundamental physics of transitions in complex systems are addressed.Comment: 4 pages (Latex) with 3 figures (postscript), accepted for publication in Physica

Thermal Plasticity of the Kelp Laminaria digitata (Phaeophyceae) Across Life Cycle Stages Reveals the Importance of Cold Seasons for Marine Forests

Phenotypic plasticity (genotype × environment interaction) is an especially important means for sessile organisms to cope with environmental variation. While kelps, the globally most productive group of seaweeds, generally possess a wide thermal performance range, kelp populations at their warm distribution limits are threatened by ocean warming. Here, we investigated effects of temperature during ontogeny of the kelp Laminaria digitata across haploid gametophyte and diploid sporophyte life cycle stages in five distinct genetic lines. We hypothesized that thermal plasticity increases trait performance of juvenile sporophytes in experimental temperatures that match the temperature experienced during gametogenesis and recruitment, and that plasticity differs among genetic lines (genetic variation for plasticity). We applied a full-factorial experimental design to generate different temperature histories by applying 5 and 15°C during meiospore germination, gametogenesis of parental gametophytes and recruitment of offspring sporophytes (19–26 days), and juvenile sporophyte rearing (91–122 days). We then tested for thermal plasticity among temperature history treatments at 5 and 15°C in a final 12-day experiment assessing growth, the storage compound mannitol, carbon and nitrogen contents, and fluorometric responses in 3–4 month old sporophytes for five genetic lines. Our study provides evidence for the importance of cold temperatures at early development on later sporophyte performance of L. digitata. Gametogenesis and recruitment at 5°C promoted higher growth of offspring sporophytes across experimental temperatures. While photosynthetic capacity was higher at 15°C, carbon and nitrogen storage were higher at 5°C, both showing fast acclimation responses. We identified an important role of genetic variation for plasticity in shaping L. digitata’s thermal plasticity. Trait performance at 5 or 15°C (reaction norm slopes) differed among genetic lines, even showing opposite response patterns. Interestingly, genetic variation for plasticity was only significant when sporophytes were reared at 5°C. Thus, we provide evidence that the cold-temperate to Arctic kelp species, L. digitata, which possesses a wide temperature tolerance between 0 and 23°C, is impaired by warm temperature during gametogenesis and recruitment, reducing growth of juvenile sporophytes and expression of variable thermal plasticity in the wild