Rock-salt SnS and SnSe: Native Topological Crystalline Insulators

Unlike time-reversal topological insulators, surface metallic states with Dirac cone dispersion in the recently discovered topological crystalline insulators (TCIs) are protected by crystal symmetry. To date, TCI behaviors have been observed in SnTe and the related alloys Pb$_{1-x}$Sn$_{x}$Se/Te, which incorporate heavy elements with large spin-orbit coupling (SOC). Here, by combining first-principles and {\it ab initio} tight-binding calculations, we report the formation of a TCI in the relatively lighter rock-salt SnS and SnSe. This TCI is characterized by an even number of Dirac cones at the high-symmetry (001), (110) and (111) surfaces, which are protected by the reflection symmetry with respect to the ($\bar{1}$10) mirror plane. We find that both SnS and SnSe have an intrinsically inverted band structure and the SOC is necessary only to open the bulk band gap. The bulk band gap evolution upon volume expansion reveals a topological transition from an ambient pressure TCI to a topologically trivial insulator. Our results indicate that the SOC alone is not sufficient to drive the topological transition.Comment: 5 pages, 5 figure

Recurrence in 2D Inviscid Channel Flow

I will prove a recurrence theorem which says that any $H^s$ ($s>2$) solution to the 2D inviscid channel flow returns repeatedly to an arbitrarily small $H^0$ neighborhood. Periodic boundary condition is imposed along the stream-wise direction. The result is an extension of an early result of the author [Li, 09] on 2D Euler equation under periodic boundary conditions along both directions

Evaluation and application of the Baldwin-Lomax turbulence model in two-dimensional, unsteady, compressible boundary layers with and without separation in engine inlets

There is a practical need to model high speed flows that exist in jet engine inlets. The boundary layers that form in these inlets may be turbulent or laminar and either separated or attached. Also, unsteady supersonic inlets may be subject to frequent changes in operating conditions. Some changes in the operating conditions of the inlets may include varying the inlet geometry, bleeds and bypasses, and rotating or translating the centerbody. In addition, the inlet may be either started or unstarted. Therefore, a CFD code, used to model these inlets, may have to run for several different cases. Also, since the flow conditions through an unsteady inlet may be continually fluctuating, the CFD code which models these flows may have to be run over many time steps. Therefore, it would be beneficial that the code run quickly. Many turbulence models, however, are cumbersome to implement and require a lot of computer time to run, since they add to the number of differential equations to be solved to model a flow. The Baldwin-Lomax turbulence model is a popular model. It is an algebraic, eddy viscosity model. The Baldwin-Lomax model is used in many CFD codes because it is quick and easy to implement. In this paper, we will discuss implementing the Baldwin-Lomax turbulence model for both steady and unsteady compressible flows. In addition, these flows may be either separated or attached. In order to apply this turbulence model to flows which may be subjected to these conditions, certain modifications should be made to the original Baldwin-Lomax model. We will discuss these modifications and determine whether the Baldwin-Lomax model is a viable turbulence model that produces reasonably accurate results for high speed flows that can be found in engine inlets

A Unique Oscillation Solution to the Solar Neutrino Problem?

A global two-neutrino oscillation fit combining Super-Kamiokande solar neutrino data with the solar neutrino rates measured by Homestake, Gallex/GNO, SAGE and SNO prefers a single allowed area, the Large Mixing Angle solution, at about 95% confidence level. The mass^2 difference between the two mass eigenstates is Delta m^2 approx 3-25 x 10^-5 eV^2, the mixing angle theta is tan^2 theta approx 0.21-0.67.Comment: 10 pages, 3 figures, to be published in the proceedings of the NOON 2001 worksho

Universal Texture of Quark and Lepton Mass Matrices

Against the conventional picture that the mass matrix forms in the quark sectors will take somewhat different structures from those in the lepton sectors, a possibility that all the mass matrices of quarks and leptons have the same form as in the neutrinos is investigated. For the lepton sectors, the model leads to a nearly bimaximal mixing with the prediction |U_{e3}|^2=m_e/2m_\mu=0.0024 and \tan^2\theta_{sol} \simeq m_{\nu 1}/m_{\nu 2}, and so on. For the quark sectors, it can lead to reasonable values of the CKM mixing matrix and masses: |V_{us}|\simeq \sqrt{m_d/m_s}, |V_{ub}| \simeq |V_{cb}|\sqrt{m_u/m_c}, |V_{td}| \simeq |V_{cb}|\cdot |V_{us}|, and so on.Comment: 9 pages, Latex, talk given at The 4th workshop on "Neutrino Oscillations and their Origin" (NOON2003) (Kanazawa, Japan, 10--14 Feb. 2002). To appear in the Proceeding

Summary of Model Predictions for Ue3U_{e3}

We present a short discussion on the expected magnitude of $|U_{e3}|$ in the context of various scenarios proposed to describe neutrino masses and mixing. Generic expectation is relatively large ($>0.05$) values for \ue3 which occur in many well-motivated theoretical scenarios and models.Comment: Updated version of the talk presented at the 5th Workshop on "Neutrino Oscillations and their Origin (NOON2004)", February 11-15, Tokyo, Japa

Complexity and integrability in 4D bi-rational maps with two invariants

In this letter we give fourth-order autonomous recurrence relations with two invariants, whose degree growth is cubic or exponential. These examples contradict the common belief that maps with sufficiently many invariants can have at most quadratic growth. Cubic growth may reflect the existence of non-elliptic fibrations of invariants, whereas we conjecture that the exponentially growing cases lack the necessary conditions for the applicability of the discrete Liouville theorem.Comment: 16 pages, 2 figure

Anomalous U(1): Solving Various Puzzles Of MSSM And SU(5) GUT

We discuss how an anomalous U(1) symmetry when appended to MSSM and SUSY GUTs [e.g. SU(5)] can help overcome a variety of puzzles related to charged fermion masses and mixings, flavor changing processes, proton decay and neutrino oscillations. Proton lifetime for SU(5) GUT, in particular, is predicted in a range accessible to the ongoing or planned searches.Comment: Presented at NOON2001 Workshop, Kashiwa, Japan, 5-8 Dec. 200

Recent K2K Results

The disappearance of nu_mu was studied using the K2K-I dataset, which was taken before July, 2001. We observed indications of neutrino oscillation. The resultant oscillation-parameter region was consistent with the atmospheric neutrino result. The appearance of nu_e was searced for in the same dataset. No excess was found over the expected background.Comment: 8 pages, 9 figures; Presented at the 5th Workshop on Neutrino Oscillations and their Origin (NOON2004), Tokyo, Japan, February 11-15,200

Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations

In this paper we construct the autonomous quad-equations which admit as symmetries the five-point differential-difference equations belonging to known lists found by Garifullin, Yamilov and Levi. The obtained equations are classified up to autonomous point transformations and some simple non-autonomous transformations. We discuss our results in the framework of the known literature. There are among them a few new examples of both sine-Gordon and Liouville type equations.Comment: 27 page