Transport in simple networks described by integrable discrete nonlinear Schr\"Aodinger equation

We elucidate the case in which the Ablowitz-Ladik (AL) type discrete nonlinear Schr\"Aodinger equa- tion (NLSE) on simple networks (e.g., star graphs and tree graphs) becomes completely integrable just as in the case of a simple 1-dimensional (1-d) discrete chain. The strength of cubic nonlinearity is different from bond to bond, and networks are assumed to have at least two semi-infinite bonds with one of them working as an incoming bond. The present work is a nontrivial extension of our preceding one (Sobirov et al, Phys. Rev. E 81, 066602 (2010)) on the continuum NLSE to the discrete case. We find: (1) the solution on each bond is a part of the universal (bond-independent) AL soliton solution on the 1-d discrete chain, but is multiplied by the inverse of square root of bond-dependent nonlinearity; (2) nonlinearities at individual bonds around each vertex must satisfy a sum rule; (3) under findings (1) and (2), there exist an infinite number of constants of motion. As a practical issue, with use of AL soliton injected through the incoming bond, we obtain transmission probabilities inversely proportional to the strength of nonlinearity on the outgoing bonds

Right-Handed Sector Leptogenesis

Instead of creating the observed baryon asymmetry of the universe by the decay of right-handed (RH) neutrinos to left-handed leptons, we propose to generate it dominantly by the decay of the RH neutrinos to RH leptons. This mechanism turns out to be successful in large regions of parameter space. It may work, in particular, at a scale as low as $\sim$~TeV, with no need to invoke quasi-degenerate RH neutrino masses to resonantly enhance the asymmetry. Such a possibility can be probed experimentally by the observation at colliders of a singlet charged Higgs particle and of RH neutrinos. Other mechanisms which may lead to successful leptogenesis from the RH lepton sector interactions are also briefly presented. The incorporation of these scenarios in left-right symmetric and unified models is discussed.Comment: 14 pages, latex, axodraw; minor clarifications and references added, extended discussion of the signatures at collider

Low-Energy Thermal Leptogenesis in an Extended NMSSM Model

Thermal leptogenesis in the canonical seesaw model in supersymmetry suffers from the incompatibility of a generic lower bound on the mass scale of the lightest right-handed neutrino and the upper bound on the reheating temperature of the Universe after inflation. This is resolved by adding an extra singlet superfield, with a discrete $Z_2$ symmetry, to the NMSSM (Next to Minimal Supersymmetric Standard Model). This generic mechanism is applicable to any supersymmetric model for lowering the scale of leptogenesis.Comment: 16 pages, revtex, 9 eps figure

Converting genetic network oscillations into somite spatial pattern

In most vertebrate species, the body axis is generated by the formation of repeated transient structures called somites. This spatial periodicity in somitogenesis has been related to the temporally sustained oscillations in certain mRNAs and their associated gene products in the cells forming the presomatic mesoderm. The mechanism underlying these oscillations have been identified as due to the delays involved in the synthesis of mRNA and translation into protein molecules [J. Lewis, Current Biol. {\bf 13}, 1398 (2003)]. In addition, in the zebrafish embryo intercellular Notch signalling couples these oscillators and a longitudinal positional information signal in the form of an Fgf8 gradient exists that could be used to transform these coupled temporal oscillations into the observed spatial periodicity of somites. Here we consider a simple model based on this known biology and study its consequences for somitogenesis. Comparison is made with the known properties of somite formation in the zebrafish embryo . We also study the effects of localized Fgf8 perturbations on somite patterning.Comment: 7 pages, 7 figure

An Integrated Linkage Map of Three Recombinant Inbred Populations of Pea (Pisum sativum L.)

Biparental recombinant inbred line (RIL) populations are sets of genetically stable lines and have a simple population structure that facilitates the dissection of the genetics of interesting traits. On the other hand, populations derived from multiparent intercrosses combine both greater diversity and higher numbers of recombination events than RILs. Here, we describe a simple population structure: a three-way recombinant inbred population combination. This structure was easy to produce and was a compromise between biparental and multiparent populations. We show that this structure had advantages when analyzing cultivar crosses, and could achieve a mapping resolution of a few genes

Non-conservative Evolution of Cataclysmic Variables

We suggest a new mechanism to account for the loss of angular momentum in binaries with non-conservative mass exchange. It is shown that in some cases the loss of matter can result in increase of the orbital angular momentum of a binary. If included into consideration in evolutionary calculations, this mechanism appreciably extends the range of mass ratios of components for which mass exchange in binaries is stable. It becomes possible to explain the existence of some observed cataclysmic binaries with high donor/accretor mass ratio, which was prohibited in conservative evolution models.Comment: LaTeX, 32 pages, to be published in Astron. Z

Nucleation of a sodium droplet on C60

We investigate theoretically the progressive coating of C60 by several sodium atoms. Density functional calculations using a nonlocal functional are performed for NaC60 and Na2C60 in various configurations. These data are used to construct an empirical atomistic model in order to treat larger sizes in a statistical and dynamical context. Fluctuating charges are incorporated to account for charge transfer between sodium and carbon atoms. By performing systematic global optimization in the size range 1<=n<=30, we find that Na_nC60 is homogeneously coated at small sizes, and that a growing droplet is formed above n=>8. The separate effects of single ionization and thermalization are also considered, as well as the changes due to a strong external electric field. The present results are discussed in the light of various experimental data.Comment: 17 pages, 10 figure

Curvature fluctuations and Lyapunov exponent at Melting

We calculate the maximal Lyapunov exponent in constant-energy molecular dynamics simulations at the melting transition for finite clusters of 6 to 13 particles (model rare-gas and metallic systems) as well as for bulk rare-gas solid. For clusters, the Lyapunov exponent generally varies linearly with the total energy, but the slope changes sharply at the melting transition. In the bulk system, melting corresponds to a jump in the Lyapunov exponent, and this corresponds to a singularity in the variance of the curvature of the potential energy surface. In these systems there are two mechanisms of chaos -- local instability and parametric instability. We calculate the contribution of the parametric instability towards the chaoticity of these systems using a recently proposed formalism. The contribution of parametric instability is a continuous function of energy in small clusters but not in the bulk where the melting corresponds to a decrease in this quantity. This implies that the melting in small clusters does not lead to enhanced local instability.Comment: Revtex with 7 PS figures. To appear in Phys Rev

The Effective Fragment Molecular Orbital Method for Fragments Connected by Covalent Bonds

We extend the effective fragment molecular orbital method (EFMO) into treating fragments connected by covalent bonds. The accuracy of EFMO is compared to FMO and conventional ab initio electronic structure methods for polypeptides including proteins. Errors in energy for RHF and MP2 are within 2 kcal/mol for neutral polypeptides and 6 kcal/mol for charged polypeptides similar to FMO but obtained two to five times faster. For proteins, the errors are also within a few kcal/mol of the FMO results. We developed both the RHF and MP2 gradient for EFMO. Compared to ab initio, the EFMO optimized structures had an RMSD of 0.40 and 0.44 {\AA} for RHF and MP2, respectively.Comment: Revised manuscrip

Neutron-Anti-Neutron Oscillation: Theory and Phenomenology

The discovery of neutrino masses has provided strong hints in favor of the possibility that B-L symmetry is an intimate feature of physics beyond the standard model. I discuss how important information about this symmetry as well as other scenarios for TeV scale new physics can be obtained from the baryon number violating process, neutron-anti-neutron oscillation. This article presents an overview of different aspects of neutron-anti-neutron oscillation and is divided into the following parts : (i) the phenomenon; (ii) the physics, (iii) plausible models and (iv) applications to cosmology. In particular, it is argued how the discovery of $n-\bar{n}$ oscillation can significantly affect our thinking about simple grand unified theory paradigms for physics beyond the standard model, elucidate the nature of forces behind neutrino mass and provide a new microphysical view of the origin of matter in the universe.Comment: 34 pages; 7 figures; Invited review for the issue on "Fundamental Neutron Physics" by J. Phys.