Finite element analysis of laminated plates and shells, volume 1

The finite element method is used to investigate the static behavior of laminated composite flat plates and cylindrical shells. The analysis incorporates the effects of transverse shear deformation in each layer through the assumption that the normals to the undeformed layer midsurface remain straight but need not be normal to the mid-surface after deformation. A digital computer program was developed to perform the required computations. The program includes a very efficient equation solution code which permits the analysis of large size problems. The method is applied to the problem of stretching and bending of a perforated curved plate

Partition Function Zeros of a Restricted Potts Model on Lattice Strips and Effects of Boundary Conditions

We calculate the partition function $Z(G,Q,v)$ of the $Q$-state Potts model exactly for strips of the square and triangular lattices of various widths $L_y$ and arbitrarily great lengths $L_x$, with a variety of boundary conditions, and with $Q$ and $v$ restricted to satisfy conditions corresponding to the ferromagnetic phase transition on the associated two-dimensional lattices. From these calculations, in the limit $L_x \to \infty$, we determine the continuous accumulation loci ${\cal B}$ of the partition function zeros in the $v$ and $Q$ planes. Strips of the honeycomb lattice are also considered. We discuss some general features of these loci.Comment: 12 pages, 12 figure

Inherent Mach-Zehnder interference with "which-way" detection for single particle scattering in one dimension

We study the coherent transport of single photon in a one-dimensional coupled-resonator-array, "non-locally" coupled to a two-level system. Since its inherent structure is a Mach-Zehnder interferometer, we explain the destructive interference phenomenon of the transmission spectrums according to the effect of which-way detection. The quantum realization of the present model is a nano-electromechanical resonator arrays with two nearest resonators coupled to a single spin via their attached magnetic tips. Its classical simulation is a waveguide of coupled defected cavity array with double couplings to a side defected cavity.Comment: 5 papges, 4 figure

The BcB_c Decays to PP-wave Charmonium by Improved Bethe-Salpeter Approach

We re-calculate the exclusive semileptonic and nonleptonic decays of $B_c$ meson to a $P$-wave charmonium in terms of the improved Bethe-Salpeter (B-S) approach, which is developed recently. Here the widths for the exclusive semileptonic and nonleptonic decays, the form factors, and the charged lepton spectrums for the semileptonic decays are precisely calculated. To test the concerned approach by comparing with experimental measurements when the experimental data are available, and to have comparisons with the other approaches the results obtained by the approach and those by some approaches else as well as the original B-S approach, which appeared in literature, are comparatively presented and discussed.Comment: 33 pages, 5 figures, 3 table

Search for Bc(ns)B_c(ns) via the Bc(ns)→Bc(ms)π+π−B_c(ns)\to B_c(ms)\pi^+\pi^- transition at LHCb and Z0Z_0 factory

It is interesting to study the characteristics of the whole family of $B_c$ which contains two different heavy flavors. LHC and the proposed $Z^0$ factory provide an opportunity because a large database on the $B_c$ family will be achieved. $B_c$ and its excited states can be identified via their decay modes. As suggested by experimentalists, $B_c^*(ns)\to B_c+\gamma$ is not easy to be clearly measured, instead, the trajectories of $\pi^+$ and $\pi^-$ occurring in the decay of $B_c(ns)\to B_c(ms)+\pi^+\pi^-$ ($n>m$) can be unambiguously identified, thus the measurement seems easier and more reliable, therefore this mode is more favorable at early running stage of LHCb and the proposed $Z^0$ factory. In this work, we calculate the rate of $B_c(ns)\to B_c(ms)+\pi^+\pi^-$ in terms of the QCD multipole-expansion and the numerical results indicate that the experimental measurements with the luminosity of LHC and $Z^0$ factory are feasible.Comment: 12 pages, 1 figures and 4 tables, acceptted by SCIENCE CHINA Physics, Mechanics & Astronomy (Science in China Series G

1+1 spectral problems arising from the Manakov-Santini system

This paper deals with the spectral problem of the Manakov Santini system. The point Lie symmetries of the Lax pair have been identified. Several similarity reductions arise from these symmetries. An important benefit of our procedure is that the study of the Lax pair instead of the partial differential equations yields the reductions of the eigenfunctions and also the spectral parameter. Therefore, we have obtained five interesting spectral problems in 1+1 dimensions

Molecular-beam epitaxy of CrSi_2 on Si(111)

Chromium disilicide layers have been grown on Si(111) in a commercial molecular‐beam epitaxy machine. Thin layers (10 nm) exhibit two epitaxial relationships, which have been identified as CrSi_2(0001)//Si(111) with CrSi_2[1010]//Si[101], and CrSi_2(0001)//Si(111) with CrSi_2[1120]//Si[101]. The latter case represents a 30° rotation of the CrSi_2 layer about the Si surface normal relative to the former case. Thick (210 nm) layers were grown by four different techniques, and the best‐quality layer was obtained by codeposition of Cr and Si at an elevated temperature. These layers are not single crystal; the largest grains are observed in a layer grown at 825 °C and are 1–2 μm across

Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips

We determine the general structure of the partition function of the $q$-state Potts model in an external magnetic field, $Z(G,q,v,w)$ for arbitrary $q$, temperature variable $v$, and magnetic field variable $w$, on cyclic, M\"obius, and free strip graphs $G$ of the square (sq), triangular (tri), and honeycomb (hc) lattices with width $L_y$ and arbitrarily great length $L_x$. For the cyclic case we prove that the partition function has the form $Z(\Lambda,L_y \times L_x,q,v,w)=\sum_{d=0}^{L_y} \tilde c^{(d)} Tr[(T_{Z,\Lambda,L_y,d})^m]$, where $\Lambda$ denotes the lattice type, $\tilde c^{(d)}$ are specified polynomials of degree $d$ in $q$, $T_{Z,\Lambda,L_y,d}$ is the corresponding transfer matrix, and $m=L_x$ ($L_x/2$) for $\Lambda=sq, tri (hc)$, respectively. An analogous formula is given for M\"obius strips, while only $T_{Z,\Lambda,L_y,d=0}$ appears for free strips. We exhibit a method for calculating $T_{Z,\Lambda,L_y,d}$ for arbitrary $L_y$ and give illustrative examples. Explicit results for arbitrary $L_y$ are presented for $T_{Z,\Lambda,L_y,d}$ with $d=L_y$ and $d=L_y-1$. We find very simple formulas for the determinant $det(T_{Z,\Lambda,L_y,d})$. We also give results for self-dual cyclic strips of the square lattice.Comment: Reference added to a relevant paper by F. Y. W

A Model of Quark and Lepton Masses I: The Neutrino Sector

If neutrinos have masses, why are they so tiny? Are these masses of the Dirac type or of the Majorana type? We are already familiar with the mechanism of how to obtain a tiny Majorana neutrino mass by the famous see-saw mechanism. The question is: Can one build a model in which a tiny Dirac neutrino mass arises in a more or less "natural" way? What would be the phenomenological consequences of such a scenario, other than just merely reproducing the neutrino mass patterns for the oscillation data? In this article, a systematic and detailed analysis of a model is presented, with, as key components, the introduction of a family symmetry as well as a new SU(2) symmetry for the right-handed neutrinos. In particular, in addition to the calculations of light neutrino Dirac masses, interesting phenomenological implications of the model will be presented.Comment: 25 (single-spaced) pages, 11 figures, corrected some typos in Table I, added acknowledgement

Grand unification in the minimal left-right symmetric extension of the standard model

The simplest minimal left-right symmetric extension of the standard model is studied in the high energy limit, and some consequences of the grand unification hypothesis are explored assuming that the parity breaking scale is the only relevant energy between the electro-weak scale and the unification point. While the model is shown to be compatible with the observed neutrino phenomenology, the parity breaking scale and the heavy boson masses are predicted to be above 10^7 TeV, quite far from the reach of nowadays experiments. Below that scale only an almost sterile right handed neutrino is allowed with a mass M \approx 100 TeV