Observation of Andreev Surface Bound States in the 3-K phase Region of Sr_2RuO_4

The tunneling spectrum of the superconducting phase with T_c ~ 3.0 K has been measured in the Ru-embedded region of Sr_2RuO_4 using cleaved junctions. A sharp zero-bias conductance peak (ZBCP) has been observed below 3 K. All characteristics of this ZBCP suggest that it originates from Andreev surface bound states, indicating that the pairing in the 3-K phase is also non-s-wave. Below the bulk T_c of Sr_2RuO_4 (~1.5 K), a bell-shaped ZBCP was found. This supports that there is a phase transition in the 3-K phase region near the bulk T_c.Comment: 4 pages, to appear in Phys. Rev. Lett. 87 (2001

Delay-dependent robust stability of stochastic delay systems with Markovian switching

In recent years, stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities (LMIs), which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method

Imprinted Networks as Chiral Pumps

We investigate the interaction between a chirally imprinted network and a solvent of chiral molecules. We find, a liquid crystalline polymer network is preferentially swollen by one component of a racemic solvent. This ability to separate is linked to the chiral order parameter of the network, and can be reversibly controlled via temperature or a mechanical deformation. It is maximal near the point at which the network loses its imprinted structure. One possible practical application of this effect would be a mechanical device for sorting mixed chiral molecules.Comment: 4 pages, 5 figure

Lattice dynamics and electron-phonon coupling in Sr2RuO4

The lattice dynamics in Sr$_2$RuO$_4$ has been studied by inelastic neutron scattering combined with shell-model calculations. The in-plane bond-stretching modes in Sr$_2$RuO$_4$ exhibit a normal dispersion in contrast to all electronically doped perovskites studied so far. Evidence for strong electron phonon coupling is found for c-polarized phonons suggesting a close connection with the anomalous c-axis charge transport in Sr$_2$RuO$_4$.Comment: 11 pages, 8 figures 2 table

Emergence of intrinsic superconductivity below 1.178 K in the topologically non-trivial semimetal state of CaSn3

Topological materials which are also superconducting are of great current interest, since they may exhibit a non-trivial topologically-mediated superconducting phase. Although there have been many reports of pressure-tuned or chemical-doping-induced superconductivity in a variety of topological materials, there have been few examples of intrinsic, ambient pressure superconductivity in a topological system having a stoichiometric composition. Here, we report that the pure intermetallic CaSn3 not only exhibits topological fermion properties but also has a superconducting phase at 1.178 K under ambient pressure. The topological fermion properties, including the nearly zero quasi-particle mass and the non-trivial Berry phase accumulated in cyclotron motions, were revealed from the de Haas-van Alphen (dHvA) quantum oscillation studies of this material. Although CaSn3 was previously reported to be superconducting at 4.2K, our studies show that the superconductivity at 4.2K is extrinsic and caused by Sn on the degraded surface, whereas its intrinsic bulk superconducting transition occurs at 1.178 K. These findings make CaSn3 a promising candidate for exploring new exotic states arising from the interplay between non-trivial band topology and superconductivity, e.g. topological superconductivityComment: 20 pages,4 figure

SDE SIS epidemic model with demographic stochasticity and varying population size

In this paper we look at the two dimensional stochastic differential equation (SDE) susceptible-infected-susceptible (SIS) epidemic model with demographic stochasticity where births and deaths are regarded as stochastic processes with per capita disease contact rate depending on the population size. First we look at the SDE model for the total population size and show that there exists a unique non-negative solution. Then we look at the two dimensional SDE SIS model and show that there exists a unique non-negative solution which is bounded above given the total population size. Furthermore we show that the number of infecteds and the number of susceptibles become extinct in finite time almost surely. Lastly, we support our analytical results with numerical simulations using theoretical and realistic disease parameter values

Solvable senescence model with positive mutations

We build upon our previous analytical results for the Penna model of senescence to include positive mutations. We investigate whether a small but non-zero positive mutation rate gives qualitatively different results to the traditional Penna model in which no positive mutations are considered. We find that the high-lifespan tail of the distribution is radically changed in structure, but that there is not much effect on the bulk of the population. Th e mortality plateau that we found previously for a stochastic generalization of the Penna model is stable to a small positive mutation rate.Comment: 3 figure

Modelling the effect of telegraph noise in the SIRS epidemic model using Markovian switching

We discuss the effect of introducing telegraph noise, which is an example of an environmental noise, into the susceptible-infectious-recovered-susceptible (SIRS) model by examining the model using a finite-state Markov Chain (MC). First we start with a two-state MC and show that there exists a unique nonnegative solution and establish the conditions for extinction and persistence. We then explain how the results can be generalised to a finite-state MC. The results for the SIR (Susceptible-Infectious-Removed) model with Markovian Switching (MS) are a special case. Numerical simulations are produced to confirm our theoretical results