Conformal field theory of AdS background with Ramond-Ramond flux

We review a formalism of superstring quantization with manifest six-dimensional spacetime supersymmetry, and apply it to AdS(3) x S-3 backgrounds with Ramond-Ramond flux. The resulting description is a conformal field theory based on a sigma model whose target space is a certain supergroup SU' (2\2).

Theory of optical dispersive shock waves in photorefractive media

The theory of optical dispersive shocks generated in the propagation of light beams through photorefractive media is developed. A full one-dimensional analytical theory based on the Whitham modulation approach is given for the simplest case of a sharp steplike initial discontinuity in a beam with one-dimensional striplike geometry. This approach is confirmed by numerical simulations, which are extended also to beams with cylindrical symmetry. The theory explains recent experiments where such dispersive shock waves have been observed.

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Non-Hermitian multichannel theory of ultracold collisions modified by intense light fields tuned to the red of the trapping transition

We develop a systematic scheme to treat binary collisions between ultracold atoms in the presence of a strong laser field, tuned to the red of the trapping transition. We assume that the Rabi frequency is much less than the spacing between adjacent bound-state resonances, In this approach we neglect fine and hyperfine structures, but consider fully the three-dimensional aspects of the scattering process, up to the partial d wave. We apply the scheme to calculate the S matrix elements up to the second order in the ratio between the Rabi frequency and the laser detuning, We also obtain, fur this simplified multichannel model, the asymmetric line shapes of photoassociation spectroscopy, and the modification of the scattering length due to the light field at low, but finite, entrance kinetic energy. We emphasize that the present calculations can be generalized to treat more realistic models, and suggest how to carry out a thorough numerical comparison to this semianalytic theory. [S1050-2947(98)04902-6].

THEORY OF ELASTICITY OF THE ABRIKOSOV FLUX-LINE LATTICE FOR UNIAXIAL SUPERCONDUCTORS - PARALLEL FLUX LINES

In this paper, we consider the extension of the Brandt theory of elasticity of the Abrikosov flux-line lattice for a uniaxial superconductor for the case of parallel flux lines. The results show that the effect of the anisotropy is to rescale the components of the wave vector k and the magnetic field and order-parameter wave vector cut off by a geometrical parameter previously introduced by Kogan.

THEORY OF ELECTRICAL CHARACTERISTICS OF A SCHOTTKY-BARRIER HAVING EXPONENTIALLY DISTRIBUTED IMPURITY STATES AND METAL-INSULATOR METAL STRUCTURES

The metal-insulator or metal-amorphous semiconductor blocking contact is still not well understood. Here, we discuss the steady state characteristics of a non-intimate metal-insulator Schottky barrier. We consider an exponential distribution (in energy) of impurity states in addition to impurity states at a single energy level within the depletion region. We present analytical expressions for the electrical potential, field, thickness of depletion region, capacitance, and charge accumulated in the depletion region. We also discuss ln I versus V(ap) data. Finally, we compare the characteristics in three cases: (i) impurity states at only a single energy level; (ii) uniform energy distribution of impurity states; and (iii) exponential energy distribution of impurity states.In general, the electrical characteristics of Schottky barriers and metal-insulator-metal structures with Schottky barriers depend strongly on the energy distribution of impurity states.

THEORY OF NON-STEADY-STATE ELECTRICAL CHARACTERISTICS OF METAL-INSULATOR-METAL STRUCTURES WITH SCHOTTKY BARRIERS AND UNIFORMLY DISTRIBUTED INTERFACE IMPURITY STATES

The metal-insulator (or amorphous semiconductor) blocking contact is still not well understood. In the present paper, we discuss the non steady state characteristics of Metal-lnsulator-Metal Structure with non-intimate blocking contacts (i.e. Metal-Oxide-Insulator-Metal Structure). We consider a uniform distribution (in energy) of impurity states in addition to impurity states at a single energy level within the depletion region. We discuss thermal as well as isothermal characteristics and present expressions for the temperature of maximum current (T-m) and a method to calculate the density of uniformly distributed impurity states. The variation of mobility with electrical field has also been considered. Finally we plot the theoretical curves under different conditions. The present results are closing into available experimental results.

On non-linear dynamics and a periodic control design applied to the potential of membrane action

The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualitatively, through the stability diagrams to the action potential of the membrane. Furthermore, we also analyze quantitatively the problem through the evaluation of Floquet multipliers. Finally, the nonlinear periodic problem is controlled, based on the Chebyshev polynomial expansion, the Picard iterative method and on Lyapunov-Floquet transformation (L-F transformation).

SEMICLASSICAL THEORY OF MAGNETIZATION FOR A 2-DIMENSIONAL NONINTERACTING ELECTRON-GAS

We compute the semiclassical magnetization and susceptibility of non-interacting electrons, confined by a smooth two-dimensional potential and subjected to a uniform perpendicular magnetic field, in the general case when their classical motion is chaotic. It is demonstrated that the magnetization per particle m(B) is directly related to the staircase function N(E), which counts the single-particle levels up to energy E. Using Gutzwiller's trace formula for N, we derive a semiclassical expression for m. Our results show that the magnetization has a non-zero average, which arises from quantum corrections to the leading-order Weyl approximation to the mean staircase and which is independent of whether the classical motion is chaotic or not. Fluctuations about the average are due to classical periodic orbits and do represent a signature of chaos. This behaviour is confirmed by numerical computations for a specific system.

Conjectures and theorems in the theory of entire functions

Motivated by the recent solution of Karlin's conjecture, properties of functions in the Laguerre-Polya class are investigated. The main result of this paper establishes new moment inequalities fur a class of entire functions represented by Fourier transforms. The paper concludes with several conjectures and open problems involving the Laguerre-Polya class and the Riemann xi -function.

Signaling path of the action of AVP on distal K+ secretion

Background. Previous studies from our laboratory have shown that luminal perfusion with arginine vasopressin (AVP) stimulates distal tubule secretory potassium flux (J(K)) via V1 receptors (Am J Physiol 278: F809- F816, 2000). In the present work, we investigate the cell signaling mechanism of this process.Methods. In vivo stationary microperfusion was performed in rat cortical distal tubules and luminal K was measured using double K+ resin/reference microelectrodes.Results. In control conditions, J(K) was 0.71 +/- 0.05 nmol. cm(-2).second(-1); this process was inhibited (14%) by 10(-5) mol/L 8-bromo-cyclic adenosine monophosphate (cAMP), and increased by 35% with 10(-8) mol/L phorbol ester [phorbol 12-myristate 13-acetate (PMA), which activates protein kinase C (PKC)]. During luminal perfusion with 10(-11) mol/L AVP, J(K) increased to 0.88 +/- 0.08 nmol. cm(-2).seconds(-1). In the presence of 10(-11) mol/L AVP, J(K) was not affected by 10(-4) mol/L H89, a blocker of protein kinase A (PKA), but was inhibited (45%) by 10(-5) mol/L staurosporine, an inhibitor of PKC, and by 41% during perfusion with 5 x 10(-5) mol/L of the cell Ca2+ chelator bis (2-aminophenoxy) ethane-tetraacetic acid (BAPTA). In order to study the role of Ca2+-dependent K channels in the luminal hormonal action, the tubules were perfused with 5 mmol/L tetraethylammonium chloride (TEA) or 10(-7) mol/L iberiotoxin, in the presence of AVP, and JK was significantly reduced by both agents. Iberiotoxin reduced AVP-stimulated J(K) by 36.4%, and AVP-independent J(K) (after blocking V1 receptors) by only 16%.Conclusion. The results suggest that the luminal V1-receptor effect of AVP on J(K) was mediated by the phospholipase C (PLC)/ Ca2+/PKC signaling path and not by adenylate cyclase/cAMP/PKA, therefore probably acting on maxi-potassium channels.

Theory of electrical characteristics for metal-oxide-insulator Schottky barrier and metal-insulator-metal structures

The metal-insulator or metal-amorphous semiconductor blocking contact is still not well understood. Here, the intimate metal-insulator and metal-oxide-insulator contact are discussed. Further, the steady-state characteristics of metal-oxide-insulator-metal structures are also discussed. Oxide is an insulator with wider energy band gap (about 50 Å thick). A uniform energetic distribution of impurities is considered in addition to impurities at a single energy level inside the surface charge region at the oxide-insulator interface. Analytical expressions are presented for electrical potential, field, thickness of the depletion region, capacitance, and charge accumulated in the surface charge region. The electrical characteristics are compared with reference to relative densities of two types of impurities. ln I is proportional to the square root of applied potential if energetically distributed impurities are relatively important. However, distribution of the electrical potential is quite complicated. In general energetically distributed impurities can considerably change the electrical characteristics of these structures.