Radiative corrections to neutrino mass matrix in the Standard Model and beyond

We study the effect of radiative corrections on the structure of neutrino mass matrix. We analyze the renormalization of the matrix from the electroweak scale $m_Z$ to the scale $m_0$ at which the effective operator that gives masses to neutrinos is generated. Apart from Standard Model and MSSM, non-standard extensions of SM are considered at a scale $m_X$ intermediate between $m_Z$ and $m_0$. We find that the dominant structure of the neutrino mass matrix does not change. SM and MSSM corrections produce small (few percents) independent renormalization of each matrix element. Non-standard (flavor changing) corrections can modify strongly small (sub-dominant) matrix elements, which are important for the low energy phenomenology. In particular, we show that all sub-dominant elements can have purely radiative origin, being zero at $m_0$. The set of non-zero elements at $m_0$ can be formed by (i) diagonal elements (unit matrix); (ii) $M_{ee}$ and $M_{\mu\tau}$; (iii)$M_{ee}$ and $\mu\tau$-block elements; (iv) $\mu\tau$-block elements. In the case of unit matrix, both atmospheric and solar mixing angles and mass squared differences are generated radiatively.Comment: 22 pages, 5 eps figures, JHEP3.cls, some clarifications and one reference adde

Symbolic Automata: The Toolkit

Abstract. The symbolic automata toolkit lifts classical automata anal-ysis to work modulo rich alphabet theories. It uses the power of state-of-the-art constraint solvers for automata analysis that is both expres-sive and efficient, even for automata over large finite alphabets. The toolkit supports analysis of finite symbolic automata and transducers over strings. It also handles transducers with registers. Constraint solving is used when composing and minimizing automata, and a much deeper and powerful integration is also obtained by internalizing automata as theories. The toolkit, freely available from Microsoft Research1, has re-cently been used in the context of web security for analysis of potentially malicious data over Unicode characters. Introduction. The distinguishing feature of the toolkit is the use and oper-ations with symbolic labels. This is unlike classical automata algorithms that mostly work assuming a finite alphabet. Adtantages of a symbolic representa-tion are examined in [4], where it is shown that the symbolic algorithms con

On modulational instability and energy localization in anharmonic lattices at finite energy density

The localization of vibrational energy, induced by the modulational instability of the Brillouin-zone-boundary mode in a chain of classical anharmonic oscillators with finite initial energy density, is studied within a continuum theory. We describe the initial localization stage as a gas of envelope solitons and explain their merging, eventually leading to a single localized object containing a macroscopic fraction of the total energy of the lattice. The initial-energy-density dependences of all characteristic time scales of the soliton formation and merging are described analytically. Spatial power spectra are computed and used for the quantitative explanation of the numerical results.Comment: 12 pages, 7 figure

Josephson effect in superconductor/ferromagnet-normal/superconductor structures

The critical current IC of superconductor/ferromagnet-normal/superconductor (S/FN/S) Josephson junctions is calculated in the framework of linearized Usadel equations. The dependence of IC on the distance L between superconductors and thicknesses dF,N of ferromagnetic and normal layers is analyzed. It is shown that IC(L,dF) may exhibit damping oscillations as a function of both arguments. The conditions have been determined under which the decay length and period of oscillation of IC(L) at fixed dF are on the order of decay length of superconducting correlations in the N metal, ξN, that is much larger than in F film. We demonstrate also that the positions of the points L=Ln, at which IC=0 exhibit damping oscillations as a function of dF. The number of transitions from 0 to π states in IC(L,dF) increases under L→Ln. Outside these narrow intervals of L around Ln sign and value of IC are independent on dF for dF≳ξF. This fact is important for possible applications of S/FN/S Josephson junctions and S/FNF/S spin valve Josephson devices

Trees with Given Stability Number and Minimum Number of Stable Sets

We study the structure of trees minimizing their number of stable sets for given order $n$ and stability number $\alpha$. Our main result is that the edges of a non-trivial extremal tree can be partitioned into $n-\alpha$ stars, each of size $\lceil \frac{n-1}{n-\alpha} \rceil$ or $\lfloor \frac{n-1}{n-\alpha}\rfloor$, so that every vertex is included in at most two distinct stars, and the centers of these stars form a stable set of the tree.Comment: v2: Referees' comments incorporate

Segregation in Porous NiTi Made by SHS in Flow Reactor

The research considers the contribution of gases to the surface formation during self-propagating high-temperature synthesis (SHS) of porous titanium nickelide based alloys. The structure of the obtained porous alloys was analyzed using the methods of secondary ion mass spectrometry (SIMS), optical microscopy, scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Nanocrystalline intermetallic oxycarbonitrides of a complicated structure were found on the porous titanium nickelide surface. A dense double gradient layer was found under the outer loose deposits. It is concluded that the dense gradient layer of intermetallic oxycarbonitride provides chemical passivity of the investigated porous alloys. Loose surface deposits of intermetallic oxycarbonitrides ensure successful integration of the alloy into the biological tissue in case of implantation.

Quaternized and Unmodified Chitosans: Hydrodynamic Properties

Molecular properties of N-[(2-hydroxy-3-trimethylammonium)propyl]chitosan (modified chitosan) series with the averaged quaternization degree 90% have been studied in comparison with the unmodified chitosan series by the method of translation isothermal diffusion, viscometry and static light scattering in dilute solutions in 0.33M CH3COOH+0.2M.CH3COONa at pH 3.54. Molecular mass, translation diffusion coefficient, and hydrodynamic size of the homologues samples in the modified/unnmodified series have been determined as well as their chain rigidity and Mark-Kuhn-Houwink equations at acidic pH. It was established that the size of modified chitosan molecules might be smaller than the initial polysaccharide of an equal polymerization degree in the same solvent, which was explained by the change of thermodynamic conditions and the change of the ratio of thermodynamic/electrostatic contributions to the total chain rigidity. Quaternized chitosan molecules displayed the different hydrodynamic behavior in 0.33M CH3COOH+0.2M.CH3COONa and in 0.2M NaCl (neutral pH). Solution properties of quaternized chitosan at neutral pH had been identified as the concentration dependent. The threshold influence of the secondary amino group protonation on the hydrodynamic properties of modified chitosan molecules was detected in 0.2M NaCl at the solute concentration range 0.001-0.004 g/cm3

Quasicondensate and superfluid fraction in the 2D charged-boson gas at finite temperature

The Bogoliubov - de Gennes equations are solved for the Coulomb Bose gas describing a fluid of charged bosons at finite temperature. The approach is applicable in the weak coupling regime and the extent of its quantitative usefulness is tested in the three-dimensional fluid, for which diffusion Monte Carlo data are available on the condensate fraction at zero temperature. The one-body density matrix is then evaluated by the same approach for the two-dimensional fluid with e^2/r interactions, to demonstrate the presence of a quasi-condensate from its power-law decay with increasing distance and to evaluate the superfluid fraction as a function of temperature at weak coupling.Comment: 9 pages, 2 figure