Intrinsic equations for a generalized relaxed elastic line on an oriented surface in the galilean space

In this article, we derive the intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean 3-dimensional space G₃. These equations will give direct and more geometric approach to questions concerning about generalized relaxed elastic lines on an oriented surface in G₃.     

Lentivirus-mediated transgene delivery to the hippocampus reveals sub-field specific differences in expression

Background  

In the adult hippocampus, the granule cell layer of the dentate gyrus is a heterogeneous structure formed by neurons of different ages, morphologies and electrophysiological properties. Retroviral vectors have been extensively used to transduce cells of the granule cell layer and study their inherent properties in an intact brain environment. In addition, lentivirus-based vectors have been used to deliver transgenes to replicative and non-replicative cells as well, such as post mitotic neurons of the CNS. However, only few studies have been dedicated to address the applicability of these widespread used vectors to hippocampal cells in vivo. Therefore, the aim of this study was to extensively characterize the cell types that are effectively transduced in vivo by VSVg-pseudotyped lentivirus-based vectors in the hippocampus dentate gyrus.     

An adeno-associated viral vector transduces the rat hypothalamus and amygdala more efficient than a lentiviral vector

Background  

This study compared the transduction efficiencies of an adeno-associated viral (AAV) vector, which was pseudotyped with an AAV1 capsid and encoded the green fluorescent protein (GFP), with a lentiviral (LV) vector, which was pseudotyped with a VSV-G envelop and encoded the discosoma red fluorescent protein (dsRed), to investigate which viral vector transduced the lateral hypothalamus or the amygdala more efficiently. The LV-dsRed and AAV1-GFP vector were mixed and injected into the lateral hypothalamus or into the amygdala of adult rats. The titers that were injected were 1 × 10⁸ or 1 × 10⁹ genomic copies of AAV1-GFP and 1 × 10⁵ transducing units of LV-dsRed.     

Backlund transformations and exact solutions for a nonlinear elliptic equation modelling isothermal magnetostatic atmosphere

The equations of magnetostatic equilibria for a plasma in agravitational field are investigated analytically. For equilibriawith an ignorable spatial coordinate, the equations reduce toa single nonlinear elliptic equation for the magnetic potentialu known as the Grad-Shafranov equation. By specifying the arbitraryfunctions in this equation, a Liouville equation is obtained.Bäcklund transformations are described and applied to obtainexact solutions for the Liouville equation modelling an isothermalmagnetostatic atmosphere, in which the current density J isproportional to the exponential of the magnetic potential andmoveover falls off exponentially with distance vertical to thebase with an e-folding distance equal to the gravitational scaleheight.     

Eliminating islands in high-pressure free-boundary stellarator magnetohydrodynamic equilibrium solutions

Magnetic islands in free-boundary stellarator equilibria are suppressed using a procedure that iterates the plasma equilibrium equations and, at each iteration, adjusts the coil geometry to cancel resonant fields produced by the plasma. The coils are constrained to satisfy certain measures of engineering acceptability and the plasma is constrained to ensure kink stability. As the iterations continue, the coil geometry and the plasma simultaneously converge to an equilibrium in which the island content is negligible. The method is applied with success to a candidate plasma and coil design for the National Compact Stellarator Experiment [Phys. Plasmas 8, 2083 (2001)]].     

Geometrical constraints on finite-time Lyapunov exponents in two and three dimensions

Constraints are found on the spatial variation of finite-time Lyapunov exponents of two- and three-dimensional systems of ordinary differential equations. In a chaotic system, finite-time Lyapunov exponents describe the average rate of separation, along characteristic directions, of neighboring trajectories. The solution of the equations is a coordinate transformation that takes initial conditions (the Lagrangian coordinates) to the state of the system at a later time (the Eulerian coordinates). This coordinate transformation naturally defines a metric tensor, from which the Lyapunov exponents and characteristic directions are obtained. By requiring that the Riemann curvature tensor vanish for the metric tensor (a basic result of differential geometry in a flat space), differential constraints relating the finite-time Lyapunov exponents to the characteristic directions are derived. These constraints are realized with exponential accuracy in time. A consequence of the relations is that the finite-time Lyapunov exponents are locally small in regions where the curvature of the stable manifold is large, which has implications for the efficiency of chaotic mixing in the advection-diffusion equation. The constraints also modify previous estimates of the asymptotic growth rates of quantities in the dynamo problem, such as the magnitude of the induced current. (c) 2001 American Institute of Physics.     

Metallic stripe in two dimensions: stability and spin-charge separation

The problems of charge stripe formation, spin-charge separation, and stability of the antiphase domain wall (ADW) associated with a stripe are addressed using an analytical approach to the t- J(z) model. We show that a metallic stripe together with its ADW is the ground state of the problem in the low doping regime. The stripe is described as a system of spinons and magnetically confined holons strongly coupled to the two dimensional spin environment with holon-spin-polaron elementary excitations filling a one-dimensional band.     

Reversible state transfer between light and a single trapped atom

We demonstrate the reversible mapping of a coherent state of light with a mean photon number (-)n approximately equal to 1.1 to and from the hyperfine states of an atom trapped within the mode of a high-finesse optical cavity. The coherence of the basic processes is verified by mapping the atomic state back onto a field state in a way that depends on the phase of the original coherent state. Our experiment represents an important step toward the realization of cavity QED-based quantum networks, wherein coherent transfer of quantum states enables the distribution of quantum information across the network.     

Controlling DNA orientation on mixed ssDNA/OEG SAMs

We present and characterize a mixed self-assembled monolayer (SAM) consisting of single-stranded oligonucleotide (ssDNA)- and oligo(ethylene glycol) (OEG)-terminated thiols. The ssDNA/OEG SAMs are prepared by simultaneous coadsorption from a common thiol solution over a broad range of compositions. Electron spectroscopy for chemical analysis (ESCA) is used to measure the surface coverage of ssDNA, whereas surface plasmon resonance (SPR) sensor is used to measure the hybridization of complementary ssDNA and protein resistance. Through the complementary use of these techniques, we find that the composition of OEG in the assembly solution controls a key parameter: the surface coverage of ssDNA on the surface. There is evidence that it influences the orientation of the immobilized ssDNA probes. Lower OEG concentrations yield a surface with higher ssDNA coverage and less favorable orientation, whereas higher OEG concentrations produce a surface with lower DNA coverage and more favorable orientation. Competition between these two effects controls the hybridization efficiency of the ssDNA surface. Compared to ssDNA surfaces prepared with other diluent thiols, the use of OEG improves the protein resistance of the surface, making it more broadly applicable.     

Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity

Localization to the ground state of axial motion is demonstrated for a single, trapped atom strongly coupled to the field of a high finesse optical resonator. The axial atomic motion is cooled by way of coherent Raman transitions on the red vibrational sideband. An efficient state detection scheme enabled by strong coupling in cavity QED is used to record the Raman spectrum, from which the state of atomic motion is inferred. We find that the lowest vibrational level of the axial potential with zero-point energy variant Planck's over 2 h omega a/2kB = 13 microK is occupied with probability P0 approximately 0.95.