Hydrodynamics of the Kuramoto-Sivashinsky Equation in Two Dimensions

The large scale properties of spatiotemporal chaos in the 2d Kuramoto-Sivashinsky equation are studied using an explicit coarse graining scheme. A set of intermediate equations are obtained. They describe interactions between the small scale (e.g., cellular) structures and the hydrodynamic degrees of freedom. Possible forms of the effective large scale hydrodynamics are constructed and examined. Although a number of different universality classes are allowed by symmetry, numerical results support the simplest scenario, that being the KPZ universality class.Comment: 4 pages, 3 figure

Metallothionein 1E mRNA is highly expressed in oestrogen receptor-negative human invasive ductal breast cancer

Metallothioneins (MTs), a group of ubiquitous metalloproteins, comprise isoforms encoded by ten functional genes in humans. Different MT isoforms possibly play different functional roles during development or under various physiological conditions. The MT-1E isoform mRNA has been recently shown to be differentially expressed in oestrogen receptor (OR)-positive and OR-negative breast cancer cell lines. In this study, we evaluated MT-1E mRNA expression via semi-quantitative RT-PCR in 51 primary invasive ductal breast cancer tissues, concurrently with OR-positive and progesterone receptor (PR)-positive MCF7 cells, OR-negative and PR-negative MDA-MB-231 cells and PR-transfected MDA-MB-231 breast cancer cells (ABC28). We demonstrated significantly higher MT-1E mRNA expression in OR-negative compared with OR-positive breast cancer tissues (P= 0.026). MCF7 cells lacked MT-1E mRNA expression, while both OR- and PR-negative MDA-MD-231 cells exhibited a high level of MT-1E mRNA expression. The level of MT-1E mRNA expression in progesterone-treated and -untreated ABC28 cells remained similar as the parental cell line MDA-MB-231-C2 cells. The results suggest that MT-1E may have specific and functional roles in OR-negative invasive ductal breast cancers, possibly mediated via effector genes downstream of the oestrogen receptor, but not through the PR pathway. © 2000 Cancer Research Campaig

Model For Polygonal Hydraulic Jumps

We propose a phenomenological model for the polygonal hydraulic jumps discovered by Ellegaard et al., based on the known flow structure for the type II hydraulic jumps with a "roller" (separation eddy) near the free surface in the jump region. The model consists of mass conservation and radial force balance between hydrostatic pressure and viscous stresses on the roller surface. In addition, we consider the azimuthal force balance, primarily between pressure and viscosity, but also including non-hydrostatic pressure contributions from surface tension in light of recent observations by Bush et al. The model can be analyzed by linearization around the circular state, resulting in a parameter relationship for nearly circular polygonal states. A truncated, but fully nonlinear version of the model can be solved analytically. This simpler model gives rise to polygonal shapes that are very similar to those observed in experiments, even though surface tension is neglected, and the condition for the existence of a polygon with N corners depends only on a single dimensionless number {\phi}. Finally, we include time-dependent terms in the model and study linear stability of the circular state. Instability occurs for suffciently small Bond number and the most unstable wave length is expected to be roughly proportional to the width of the roller as in the Rayleigh-Plateau instability.Comment: 17 pages; Phys. Rev. E (2012

Crossover from Quarter-Filling to Half-Filling in a One-Dimensional Electron System with a Dimerized and Quarter-Filled Band

The interplay between quarter-filled and half-filled umklapp scattering has been examined by applying the renormalization group method to a one-dimensional quarter-filled electron system with dimerization, on-site (U) and nearest-neighbor (V) repulsive interactions. The phase diagram on the U-V plane is obtained at absolute zero temperature where the Mott insulator (the charge ordered insulator) is found for smaller (larger) V. By choosing the moderate parameter in the region of Mott insulator, it is shown that the resistivity exhibits a crossover from behavior of quarter-filling to that of half-filling with decreasing temperature.Comment: 4 pages, 4 figures, submitted to J. Phys. Soc. Jp

On perturbations of Dirac operators with variable magnetic field of constant direction

We carry out the spectral analysis of matrix valued perturbations of 3-dimensional Dirac operators with variable magnetic field of constant direction. Under suitable assumptions on the magnetic field and on the pertubations, we obtain a limiting absorption principle, we prove the absence of singular continuous spectrum in certain intervals and state properties of the point spectrum. Various situations, for example when the magnetic field is constant, periodic or diverging at infinity, are covered. The importance of an internal-type operator (a 2-dimensional Dirac operator) is also revealed in our study. The proofs rely on commutator methods.Comment: 12 page

A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions

We discuss a deformation of Sasakian structure in the presence of totally skew-symmetric torsion by introducing odd dimensional manifolds whose metric cones are K\"ahler with torsion. It is shown that such a geometry inherits similar properties to those of Sasakian geometry. As an example of them, we present an explicit expression of local metrics and see how Sasakian structure is deformed by the presence of torsion. We also demonstrate that our example of the metrics admits the existence of hidden symmetries described by non-trivial odd-rank generalized closed conformal Killing-Yano tensors. Furthermore, using these metrics as an {\it ansatz}, we construct exact solutions in five dimensional minimal (un-)gauged supergravity and eleven dimensional supergravity. Finally, we discuss the global structures of the solutions and obtain regular metrics on compact manifolds in five dimensions, which give natural generalizations of Sasaki--Einstein manifolds $Y^{p,q}$ and $L^{a,b,c}$. We also discuss regular metrics on non-compact manifolds in eleven dimensions.Comment: 38 pages, 1 table, v2: version to appear in Class. Quant. Gra

Regeneration of Alveolar Type I and II Cells from Scgb1a1-Expressing Cells following Severe Pulmonary Damage Induced by Bleomycin and Influenza

The lung comprises an extensive surface of epithelia constantly exposed to environmental insults. Maintaining the integrity of the alveolar epithelia is critical for lung function and gaseous exchange. However, following severe pulmonary damage, what progenitor cells give rise to alveolar type I and II cells during the regeneration of alveolar epithelia has not been fully determined. In this study, we have investigated this issue by using transgenic mice in which Scgb1a1-expressing cells and their progeny can be genetically labeled with EGFP. We show that following severe alveolar damage induced either by bleomycin or by infection with influenza virus, the majority of the newly generated alveolar type II cells in the damaged parenchyma were labeled with EGFP. A large proportion of EGFP-expressing type I cells were also observed among the type II cells. These findings strongly suggest that Scgb1a1-expressing cells, most likely Clara cells, are a major cell type that gives rise to alveolar type I and II cells during the regeneration of alveolar epithelia in response to severe pulmonary damage in mice..Singapore. National Research FoundationSingapore–MIT Alliance for Research and Technology (Infectious Disease-IRG research programme

The Entropy for General Extremal Black Holes

We use the Kerr/CFT correspondence to calculate the entropy for all known extremal stationary and axisymmetric black holes. This is done with the help of two ansatzs that are general enough to cover all such known solutions. Considering only the contribution from the Einstein-Hilbert action to the central charge(s), we find that the entropy obtained by using Cardy's formula exactly matches with the Bekenstein-Hawking entropy.Comment: Minor corrections, section 5 refined, references added

Two body non-leptonic Λb\Lambda_b decays in quark model with factorization ansatz

The two body non-leptonic $\Lambda_b$ decays are analyzed in factorization approximation, using quark model, $\xi = 1 / N_c$ as a free parameter. It is shown that the experimental branching ratio for $\Lambda_b \longrightarrow \Lambda {J/\psi}$ restricts $\xi$ and this ratio can be understood for a value of $\xi$ which lies in the range $0 \leq \xi \leq 0.5$ suggested by two body B meson decays. The branching ratios for $\Lambda_b \longrightarrow \Lambda_{c} D^*_s(D_s)$ are predicted to be larger than the previous estimates. Finally it is pointed that CKM-Wolfenstein parameter $\rho^2 + \eta^2$, where $\eta$ is CP phase, can be determined from the ratio of widths of $\Lambda_b \longrightarrow \Lambda \bar{D}$ and $\Lambda_b \longrightarrow \Lambda {J/\psi}$ or that of $\Lambda_b \longrightarrow p D_s$ and $\Lambda_b \longrightarrow \Lambda_c D_s$ independent of the parameter $\xi$.Comment: 18 pages, latex, 1 figure available on request, please send any questions or comments to [email protected]

Microscopic theory of quantum dot interactions with quantum light: local field effect

A theory of both linear and nonlinear electromagnetic response of a single QD exposed to quantum light, accounting the depolarization induced local--field has been developed. Based on the microscopic Hamiltonian accounting for the electron--hole exchange interaction, an effective two--body Hamiltonian has been derived and expressed in terms of the incident electric field, with a separate term describing the QD depolarization. The quantum equations of motion have been formulated and solved with the Hamiltonian for various types of the QD excitation, such as Fock qubit, coherent fields, vacuum state of electromagnetic field and light with arbitrary photonic state distribution. For a QD exposed to coherent light, we predict the appearance of two oscillatory regimes in the Rabi effect separated by the bifurcation. In the first regime, the standard collapse--revivals phenomenon do not reveal itself and the QD population inversion is found to be negative, while in the second one, the collapse--revivals picture is found to be strongly distorted as compared with that predicted by the standard Jaynes-Cummings model. %The model developed can easily be extended to %%electromagnetic excitation. For the case of QD interaction with arbitrary quantum light state in the linear regime, it has been shown that the local field induce a fine structure of the absorbtion spectrum. Instead of a single line with frequency corresponding to which the exciton transition frequency, a duplet is appeared with one component shifted by the amount of the local field coupling parameter. It has been demonstrated the strong light--mater coupling regime arises in the weak-field limit. A physical interpretation of the predicted effects has been proposed.Comment: 14 pages, 7 figure