Nonextensive Pesin identity. Exact renormalization group analytical results for the dynamics at the edge of chaos of the logistic map

We show that the dynamical and entropic properties at the chaos threshold of the logistic map are naturally linked through the nonextensive expressions for the sensitivity to initial conditions and for the entropy. We corroborate analytically, with the use of the Feigenbaum renormalization group(RG) transformation, the equality between the generalized Lyapunov coefficient $\lambda_{q}$ and the rate of entropy production $K_{q}$ given by the nonextensive statistical mechanics. Our results advocate the validity of the $q$-generalized Pesin identity at critical points of one-dimensional nonlinear dissipative maps.Comment: Revtex, 5 pages, 3 figure

Method of lines transpose: High order L-stable O(N) schemes for parabolic equations using successive convolution

We present a new solver for nonlinear parabolic problems that is L-stable and achieves high order accuracy in space and time. The solver is built by first constructing a single-dimensional heat equation solver that uses fast O(N) convolution. This fundamental solver has arbitrary order of accuracy in space, and is based on the use of the Green's function to invert a modified Helmholtz equation. Higher orders of accuracy in time are then constructed through a novel technique known as successive convolution (or resolvent expansions). These resolvent expansions facilitate our proofs of stability and convergence, and permit us to construct schemes that have provable stiff decay. The multi-dimensional solver is built by repeated application of dimensionally split independent fundamental solvers. Finally, we solve nonlinear parabolic problems by using the integrating factor method, where we apply the basic scheme to invert linear terms (that look like a heat equation), and make use of Hermite-Birkhoff interpolants to integrate the remaining nonlinear terms. Our solver is applied to several linear and nonlinear equations including heat, Allen-Cahn, and the Fitzhugh-Nagumo system of equations in one and two dimensions

Spin dynamics in hole-doped two-dimensional S=1/2 Heisenberg antiferromagnets: ^{63}Cu NQR relaxation in La_{2-x}Sr_xCuO_4 for x≤0.04x\leq 0.04

The effects on the correlated Cu^{2+} S = 1/2 spin dynamics in the paramagnetic phase of La_{2-x}Sr_xCuO_4 (for $x \lesssim 0.04$) due to the injection of holes are studied by means of ^{63}Cu NQR spin-lattice relaxation time T_1 measurements. The results are discussed in the framework of the connection between T_1 and the in-plane magnetic correlation length $\xi_{2D}(x,T)$. It is found that at high temperatures the system remains in the renormalized classical regime, with a spin stiffness constant $\rho_s(x)$ reduced by small doping to an extent larger than the one due to Zn doping. For $x\gtrsim 0.02$ the effect of doping on $\rho_s(x)$ appears to level off. The values for $\rho_s(x)$ derived from T_1 for $T\gtrsim 500$ K are much larger than the ones estimated from the temperature behavior of sublattice magnetization in the ordered phase ($T\leq T_N$). It is argued that these features are consistent with the hypothesis of formation of stripes of microsegregated holes.Comment: 10 pages, 3 figure

Computer-Aided Modeling and Analysis of Power Processing Systems (CAMAPPS), phase 1

The large-signal behaviors of a regulator depend largely on the type of power circuit topology and control. Thus, for maximum flexibility, it is best to develop models for each functional block a independent modules. A regulator can then be configured by collecting appropriate pre-defined modules for each functional block. In order to complete the component model generation for a comprehensive spacecraft power system, the following modules were developed: solar array switching unit and control; shunt regulators; and battery discharger. The capability of each module is demonstrated using a simplified Direct Energy Transfer (DET) system. Large-signal behaviors of solar array power systems were analyzed. Stability of the solar array system operating points with a nonlinear load is analyzed. The state-plane analysis illustrates trajectories of the system operating point under various conditions. Stability and transient responses of the system operating near the solar array's maximum power point are also analyzed. The solar array system mode of operation is described using the DET spacecraft power system. The DET system is simulated for various operating conditions. Transfer of the software program CAMAPPS (Computer Aided Modeling and Analysis of Power Processing Systems) to NASA/GSFC (Goddard Space Flight Center) was accomplished

Magnetic susceptibility study of hydrated and non-hydrated NaxCoO2-yH2O single crystals

We have measured the magnetic susceptibility of single crystal samples of non-hydrated NaxCoO2 (x ~ 0.75, 0.67, 0.5, and 0.3) and hydrated Na0.3CoO2-yH2O (y ~ 0, 0.6, 1.3). Our measurements reveal considerable anisotropy between the susceptibilities with H||c and H||ab. The derived anisotropic g-factor ratio (g_ab/g_c) decreases significantly as the composition is changed from the Curie-Weiss metal with x = 0.75 to the paramagnetic metal with x = 0.3. Fully hydrated Na0.3CoO2-1.3H2O samples have a larger susceptibility than non-hydrated Na0.3CoO2 samples, as well as a higher degree of anisotropy. In addition, the fully hydrated compound contains a small additional fraction of anisotropic localized spins.Comment: 6 pages, 5 figure

Geometrization of the Gauge Connection within a Kaluza-Klein Theory

Within the framework of a Kaluza-Klein theory, we provide the geometrization of a generic (Abelian and non-Abelian) gauge coupling, which comes out by choosing a suitable matter fields dependence on the extra-coordinates. We start by the extension of the Nother theorem to a multidimensional spacetime being the direct sum of a 4-dimensional Minkowski space and of a compact homogeneous manifold (whose isometries reflect the gauge symmetry); we show, how on such a ``vacuum'' configuration, the extra-dimensional components of the field momentum correspond to the gauge charges. Then we analyze the structure of a Dirac algebra as referred to a spacetime with the Kaluza-Klein restrictions and, by splitting the corresponding free-field Lagrangian, we show how the gauge coupling terms outcome.Comment: 10 pages, no figure, to appear on Int. Journ. Theor. Phy

Neutron scattering study of novel magnetic order in Na0.5CoO2

We report polarized and unpolarized neutron scattering measurements of the magnetic order in single crystals of Na0.5CoO2. Our data indicate that below T_N=88 K the spins form a novel antiferromagnetic pattern within the CoO2 planes, consisting of alternating rows of ordered and non-ordered Co ions. The domains of magnetic order are closely coupled to the domains of Na ion order, consistent with such a two-fold symmetric spin arrangement. Magnetoresistance and anisotropic susceptibility measurements further support this model for the electronic ground state.Comment: 4 pages, 4 figure

Phase Separation of the Two-Dimensional t-J model

The boundary of phase separation of the two-dimensional t-J model is investigated by the power-Lanczos method and Maxwell construction. The method is similar to a variational approach and it determines the lower bound of the phase separation boundary with $J_c/t=0.6\pm 0.1$ in the limit $n_e\sim 1$. In the physical interesting regime of high T_c superconductors where $0.3<J/t<0.5$ there is no phase separation.Comment: LaTex 5 pages, 4 figure

Analysis and design of a high power, digitally-controlled spacecraft power system

The progress to date on the analysis and design of a high power, digitally controlled spacecraft power system is described. Several battery discharger topologies were compared for use in the space platform application. Updated information has been provided on the battery voltage specification. Initially it was thought to be in the 30 to 40 V range. It is now specified to be 53 V to 84 V. This eliminated the tapped-boost and the current-fed auto-transformer converters from consideration. After consultations with NASA, it was decided to trade-off the following topologies: (1) boost converter; (2) multi-module, multi-phase boost converter; and (3) voltage-fed push-pull with auto-transformer. A non-linear design optimization software tool was employed to facilitate an objective comparison. Non-linear design optimization insures that the best design of each topology is compared. The results indicate that a four-module, boost converter with each module operating 90 degrees out of phase is the optimum converter for the space platform. Large-signal and small-signal models were generated for the shunt, charger, discharger, battery, and the mode controller. The models were first tested individually according to the space platform power system specifications supplied by NASA. The effect of battery voltage imbalance on parallel dischargers was investigated with respect to dc and small-signal responses. Similarly, the effects of paralleling dischargers and chargers were also investigated. A solar array and shunt model was included in these simulations. A model for the bus mode controller (power control unit) was also developed to interface the Orbital replacement Unit (ORU) model to the platform power system. Small signal models were used to generate the bus impedance plots in the various operating modes. The large signal models were integrated into a system model, and time domain simulations were performed to verify bus regulation during mode transitions. Some changes have subsequently been incorporated into the models. The changes include the use of a four module boost discharger, and a new model for the mode controller, which includes the effects of saturation. The new simulations for the boost discharger show the improvement in bus ripple that can be achieved by phase-shifted operation of each of the boost modules