Scaling and Linear Response in the GOY Turbulence model

The GOY model is a model for turbulence in which two conserved quantities cascade up and down a linear array of shells. When the viscosity parameter, $\nu$, is small the model has a qualitative behavior which is similar to the Kolmogorov theories of turbulence. Here a static solution to the model is examined, and a linear stability analysis is performed to obtain response eigenvalues and eigenfunctions. Both the static behavior and the linear response show an inertial range with a relatively simple scaling structure. Our main results are: (i) The response frequencies cover a wide range of scales, with ratios which can be understood in terms of the frequency scaling properties of the model. (ii) Even small viscosities play a crucial role in determining the model's eigenvalue spectrum. (iii) As a parameter within the model is varied, it shows a ``phase transition'' in which there is an abrupt change in many eigenvalues from stable to unstable values. (iv) The abrupt change is determined by the model's conservation laws and symmetries. This work is thus intended to add to our knowledge of the linear response of a stiff dynamical systems and at the same time to help illuminate scaling within a class of turbulence models.Comment: 25 pages, figures on reques

Evaluation of selective sensitivity of EZH2 inhibitors based on synthetic lethality in ARID1A-deficient gastric cancer

博士（医学）福島県立医科大

How the viscous subrange determines inertial range properties in turbulence shell models

We calculate static solutions of the 'GOY' shell model of turbulence and do a linear stability analysis. The asymptotic limit of large Reynolds numbers is analyzed. A phase diagram is presented which shows the range of stability of the static solution. We see an unexpected oscillatory dependence of the stability range upon $\lg \nu$, where $\nu$ is the viscosity. This effect depends upon the discrete structure of the shell model and goes to zero as the separation between the shells is brought to zero. These findings show how viscous effects play a role in determining inertial properties of shell models and give some hints for understanding the effects of viscous dissipation upon real turbulence.Comment: Physica D, in pres

Bias driven coherent carrier dynamics in a two-dimensional aperiodic potential

We study the dynamics of an electron wave-packet in a two-dimensional square lattice with an aperiodic site potential in the presence of an external uniform electric field. The aperiodicity is described by $\epsilon_{\bf m} = V\cos{(\pi\alpha m_x^{\nu_x})}\cos{(\pi\alpha m_y^{\nu_y})}$ at lattice sites $(m_x, m_y)$, with $\pi \alpha$ being a rational number, and $\nu_x$ and $\nu_y$ tunable parameters, controlling the aperiodicity. Using an exact diagonalization procedure and a finite-size scaling analysis, we show that in the weakly aperiodic regime ($\nu_x,\nu_y < 1$), a phase of extended states emerges in the center of the band at zero field giving support to a macroscopic conductivity in the thermodynamic limit. Turning on the field gives rise to Bloch oscillations of the electron wave-packet. The spectral density of these oscillations may display a double peak structure signaling the spatial anisotropy of the potential landscape. The frequency of the oscillations can be understood using a semi-classical approach.Comment: 16 pages, to appear in Phys. Lett.

Clostridium difficile sortase recognizes a (S/P)PXTG sequence motif and can accommodate diaminopimelic acid as a substrate for transpeptidation

AbstractCovalent attachment of surface proteins to the cell wall of Gram-positive bacteria requires a sortase-mediated transpeptidation reaction. In almost all Gram-positive bacteria, the housekeeping sortase, sortase A, recognizes the canonical recognition sequence LPXTG (X=any amino acid). The human pathogen Clostridium difficile carries a single putative sortase gene (cd2718) but neither transpeptidation activity nor specificity of CD2718 has been investigated. We produced recombinant CD2718 and examined its transpeptidation activity in vitro using synthetic peptides and MALDI-ToF(-ToF) MS analysis. We demonstrate that CD2718 has sortase activity with specificity for a (S/P)PXTG motif and can accommodate diaminopimelic acid as a substrate for transpeptidation