Three-dimensional stationary cyclic symmetric Einstein–Maxwell solutions; black holes

From a general metric for stationary cyclic symmetric gravitational fields coupled to Maxwell electromagnetic fields within the (2 + 1)-dimensional gravity the uniqueness of wide families of exact solutions is established. Among them, all uniform electromagnetic solutions possessing electromagnetic fields with vanishing covariant derivatives, all fields having constant electromagnetic invariants F_μνF^μν and T_μνT^μν, the whole classes of hybrid electromagnetic solutions, and also wide classes of stationary solutions are derived for a third-order nonlinear key equation. Certain of these families can be thought of as black hole solutions. For the most general set of Einstein–Maxwell equations, reducible to three nonlinear equations for the three unknown functions, two new classes of solutions – having anti-de Sitter spinning metric limit – are derived. The relationship of various families with those reported by different authors’ solutions has been established. Among the classes of solutions with cosmological constant a relevant place is occupied by the electrostatic and magnetostatic Peldan solutions, the stationary uniform and spinning Clement classes, the constant electromagnetic invariant branches with the particular Kamata–Koikawa solution, the hybrid cyclic symmetric stationary black hole fields, and the non-less important solutions generated via SL(2,R)-transformations where the Clement spinning charged solution, the Martinez–Teitelboim–Zanelli black hole solution, and Dias–Lemos metric merit mention.     

Spectral properties of the prototropic forms of fluorescein in aqueous solution

The commonly used fluorescent probe, fluorescein, can exist in seven prototropic forms. We have used global analysis procedures to reanalyze the absorption data of Diehl and Horchak-Morris (Talanta 34, 739–741, 1987) in terms of five alternative ionization models. We identify the forms of fluorescein present in aqueous solution and the pK _a of each ionisation transition. The pK_a values of the neutral xanthene, carboxylic acid, and cationic xanthene groups are 6.3, 3.1–3.4, and 3.1–3.4, respectively, and the pK_a value of lactonization is 2.4. As a consequence, the neutral form of fluorescein is a mixture of the lactone (70%), zwitterionic (15%), and quinoid (15%) forms. A knowledge of the forms present in solution permits the characterization of their spectral properties. It is shown that the quinoid and monoanion forms have similar absorption spectra, while the zwitterion spectrum is similar to that of the cation but blue-shifted by 3 nm. The emission spectra of the monoanion and quinoid forms are also identified and shown to be similar but not identical. A model for the excited-state reactions of fluorescein is presented.     

Isotropization of Bianchi Models and a New FRW Solution in Brans–Dicke Theory

Using scaled variables we are able to integrate an equation valid for isotropic and anisotropic Bianchi type I, V, IX models in Brans–Dicke (BD) theory. We analyze known and new solutions for these models in relation with the possibility that anisotropic models asymptotically isotropize, and/or possess inflationary properties. In particular, a new solution of curved (k 0) Friedmann–Robertson–Walker (FRW) cosmologies in Brans–Dicke theory is analyzed.     

Regular Self-Consistent Geometries with Infinite Quantum Backreaction in 2D Dilaton Gravity and Black Hole Thermodynamics: Unfamiliar Features of Familiar Models

We analyze the rather unusual properties of some exact solutions in 2D dilaton gravity for which infinite quantum stresses on the Killing horizon can be compatible with regularity of the geometry. In particular, the Boulware state can support a regular horizon. We show that such solutions are contained in some well-known exactly solvable models (for example, RST). Formally, they appear to account for an additional coefficient B in the solutions (for the same Lagrangian which contains also traditional solutions) that gives rise to the deviation of temperature T from its Hawking value T _H . The Lorentzian geometry, which is a self-consistent solution of the semiclassical field equations, in such models, is smooth even at B0 and there is no need to put B=0 (T=T _H ) to smooth it out. We show how the presence of B0 affects the structure of spacetime. In contrast to usual black holes, full fledged thermodynamic interpretation, including definite value of entropy, can be ascribed (for a rather wide class of models) to extremal horizons, not to nonextreme ones. We find also new exact solutions for usual black holes (with T=T _H ). The properties under discussion arise in the weak-coupling regime of the effective constant of dilaton-gravity interaction. Extension of features, traced in 2D models, to 4D dilaton gravity leads, for some special models, to exceptional nonextreme black holes having no own thermal properties.     

Magnetic properties of single crystalline Zn1−xCoxO thin films

We report on the magnetic properties of single crystalline thin films of Zn_1−xCo_xO (x=0.003–0.14) grown by plasma-assisted molecular beam epitaxy. In order to understand the role of intermediate charge carriers in the magnetic properties of this material two types of films were fabricated, with and without Ga-codoping. Magnetic measurements were made between 2 and 300 K in fields up to 5 T with a Quantum Design SQUID magnetometer. We found that all the tested films exhibit paramagnetic behavior following the Curie–Weiss law, χ=C/(T−θ), with negative Curie–Weiss temperatures and that this behavior holds even under strong n-doping. We show that the magnetization data, M(H), in function of the Co content provide additional evidence in favor of the antiferromagnetic Co–Co interaction in this material. We also observe that these data exhibit an ‘easy plane’ magnetic anisotropy for all the studied Co concentrations. Finally, we develop a simple cluster model, in order to describe the magnetic properties of ZnCoO, which is found to be in good agreement with our experiments.     

Spectroscopic Study of DHDA Complex Formation of d- and f-Electron Metal Ions in Methanol Solution

Synthesis and spectral characterization of N,N′-Bis(2,4-dihydroxobenzylidene)1,2-diaminobenzene (DHDA) complexes with chosen f- and d-metal ions are described. Physico-chemical properties of a series of complexes: DHDA–La(NO₃)₃, DHDA–Eu(NO₃)₃. DHDA–Yb(NO₃)₃, DHDA–Cu(NO₃)₂, DHDA–Zn(NO₃)₂, DHDA–Co(NO₃)₂, were studied in methanol solution using UV-VIS, IR and fluorescence spectroscopy. Based on the absorption spectra the conditional stability constants of the metal complexes were determined.     

(Z N×) n−1 generalization of the chiral Potts model

We show that theR-matrix which intertwines twon-by-N ^n–1 state cyclicL-operators related with a generalization ofU _q(sl(n)) algebra can be considered as a Boltzmann weight of four-spin box for a lattice model with two-spin interaction just as theR-matrix of the checkerboard chiral Potts model. The rapidity variables lie on the algebraic curve of the genusg=N ^{2(n–1)((n–1)N-n)+1} defined by 2n–3 independent moduli. This curve is a natural generalization of the curve which appeared in the chiral Potts model. Factorization properties of theL-operator and its connection to the SOS models are also discussed.     

Understanding of a-Si:H(p)/c-Si(n) heterojunction solar cell through analysis of cells with point-contacted p/n junction

We fabricated point-contacted a-Si:H(p)/c-Si(n) heterojunction solar cells using patterned SiO₂ and investigated their electrical properties using the light current–voltage (I–V) curve and Suns-V_oc measurements. The light I–V curves showed bias-dependent changes according to the applied voltage in the point-contacted cells, especially in the samples with a long distance between the point-contacted junctions. The Suns-V_oc measurements showed that the bias-dependence of the light I–V curves did not originate from the recombination in the SiO₂/Si or a-Si:H(p)/c-Si(n) interface, but from the series resistances. It is possible to explain the bias-dependent light I–V curve in terms of the conductivity of a-Si:H(p) and difference in the electrical contact properties between a-Si:H(p), ZnO and c-Si(n). These results mean that the electrical properties of the a-Si:H(p) layer and the contact properties with this layer are also critical to obtain a high J_sc and fill factor in n-type based Si heterojunction solar cells.     

A Self-Consistent Ornstein–Zernike Approximation for the Edwards–Anderson Spin-Glass Model

We propose a self-consistent Ornstein–Zernike approximation for studying the Edwards–Anderson spin glass model. By performing two Legendre transforms in replica space, we introduce a Gibbs free energy depending on both the magnetizations and the overlap order parameters. The correlation functions and the thermodynamics are then obtained from the solution of a set of coupled partial differential equations. The approximation becomes exact in the limit of infinite dimension and it provides a potential route for studying the stability of the high-temperature phase against replica-symmetry breaking fluctuations in finite dimensions. As a first step, we present the predictions for the freezing temperature T _f and for the zero-field thermodynamic properties and correlation length above T _f as a function of dimensionality.     

Spectral/hp least-squares finite element formulation for the Navier–Stokes equations

We consider the application of least-squares finite element models combined with spectral/hp methods for the numerical solution of viscous flow problems. The paper presents the formulation, validation, and application of a spectral/hp algorithm to the numerical solution of the Navier–Stokes equations governing two- and three-dimensional stationary incompressible and low-speed compressible flows. The Navier–Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity or velocity gradients as additional independent variables and the least-squares method is used to develop the finite element model. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton’s method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method. Spectral convergence of the L₂ least-squares functional and L₂ error norms is verified using smooth solutions to the two-dimensional stationary Poisson and incompressible Navier–Stokes equations. Numerical results for flow over a backward-facing step, steady flow past a circular cylinder, three-dimensional lid-driven cavity flow, and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation.     

Near-infrared photorefractivity in Cr-doped potassium sodium strontium barium niobate single crystal

We report on the photorefractive properties of a Cr-doped (K_1–x Na _x )_2A–2 (Sr _y Ba_1–y )_2–A Nb₁₀O₃₀ (x=0.586, y=0.659, A=1.12) single crystal in the near-infrared spectrum. The sample exhibits photorefractivity for wavelengths up to at least 840 nm where the steady-state two-beam coupling gain is found to be larger than 2 cm^–1. Photorefractive gain and decay rate are measured as a function of wavelength, grating spacing and intensity. The wavelength dependence of gain fluctuations in two-beam coupling are also measured.     

General Relativity as a (Constrained) Yang-Mills Theory and a Novel Gravity with Torsion

We show that General Relativity (GR) with cosmological constant may be formulated as a rather simple constrained SO(D – 1, 2) (or SO(D, 1))-Yang-Mills (YM) theory. Furthermore, the spin connections of the Cartan-Einstein formulation for GR appear as solutions of a genuine SO(D – 1,1)-YM. We also present a theory of gravity with torsion as the most natural extension of this result. The theory comes out to be strictly an YM-theory upon relaxation of a suitable constraint. This work sets out to enforce the close connection between YM theories and GR by means of an alternative construction.     

Finitized Conformal Spectra of the Ising Model on the Klein Bottle and Möbius Strip

We study the conformal spectra of the critical square lattice Ising model on the Klein bottle and Möbius strip using Yang–Baxter techniques and the solution of functional equations. In particular, we obtain expressions for the finitized conformal partition functions in terms of finitized Virasoro characters. This demonstrates that Yang–Baxter techniques and functional equations can be used to study the conformal spectra of more general exactly solvable lattice models in these topologies. The results rely on certain properties of the eigenvalues which are confirmed numerically.     

Multiple Instantons Representing Higher-Order Chern–Pontryagin Classes,II

This paper is a continuation of an earlier study on the generalized Yang–Mills instantons over 4m-dimensional spheres. We will first present a discussion on the generalized Yang–Mills equations, the higher-order Chern–Pontryagin classes, c _2m , and the self-dual or anti-self-dual equations. We will then obtain some sharp asymptotic estimates for the self-dual or anti-self-dual equations within the Witten–Tchrakian framework which relates the integer value of c _2m to the number of vortices of the solution to a reduced 2-dimensional Abelian Higgs system over the Poincaré half-plane. We will prove that, indeed, for any integer N, there exists a 2|N|-parameter family of the generalized self-dual or anti-self-dual instantons realizing the topology c _2m =N. Furthermore, for the purpose of accommodating more general solutions, we establish a removable singularity theorem which enables us to extend the solutions obtained on a 4m-dimensional Euclidean space with an integral bound to the Hölder continuous solutions on a 4m-dimensional sphere.Research supported in part by PSC-CUNY Research Award 32Research supported in part by NSF under grants DMS–9972300 and DMS–9729992 through IAS     

The Ising Model on a Quenched Ensemble of c=−5 Gravity Graphs

We study with Monte Carlo methods an ensemble of c=–5 gravity graphs, generated by coupling a conformal field theory with central charge c=–5 to two-dimensional quantum gravity. We measure the fractal properties of the ensemble, such as the string susceptibility exponent _s and the intrinsic fractal dimension d _H. We find _s=–1.5(1) and d _H=3.36(4), in reasonable agreement with theoretical predictions. In addition, we study the critical behavior of an Ising model on a quenched ensemble of the c=–5 graphs and show that it agrees, within numerical accuracy, with theoretical predictions for the critical behavior of an Ising model coupled dynamically to two-dimensional quantum gravity, with a total central charge of the matter sector c=–5.     

Solubility and acid-base properties and activity coefficients of chitosan in different ionic media and at different ionic strengths, at T = 25 °C

Studies on the acid-base properties and solubility of a polyammonium polyelectrolyte (chitosan) with different molecular weights (MW 310 and 50 kDa), were performed at T = 25 °C, in the pH range 2.5–7. The protonation of chitosan was investigated by potentiometry ([H⁺]-glass electrode) in NaCl, NaNO₃ and mixed NaNO₃ + Na₂SO₄ ionic media, at different ionic strengths. Protonation constants were calculated as a function of dissociation degree α by means of two different models, namely, a simple linear model and the modified Henderson–Hasselbalch equation. Experimental data were also fitted using a model independent of α (Diprotic-like model), according to which the acid-base properties can be simply described by two protonation constants in all the acidic pH range. The dependence on ionic strength of protonation constants in NaCl aqueous solution was modelled by Specific ion Interaction Theory (SIT). The ion pair formation between protonated chitosan and Cl⁻, NO₃⁻ and SO₄²⁻ was also considered, and the relative formation constants are reported.Solubility investigations were performed in NaCl aqueous solutions in a wide range of ionic strength (0.1 < I/mol L^− 1 < 3.0), with the aim to determine the activity coefficients of neutral species and the Setschenow coefficient of chitosan 310 kDa.     

Algebraic Geometry in Discrete Quantum Integrable Model and Baxter's T–Q Relation

We study the diagonalization problem of certain discrete quantum integrable models by the method of Baxter's T–Q relation from the algebraic geometry aspect. Among those the Hofstadter type model (with the rational magnetic flux), discrete quantum pendulum and discrete sine-Gordon model are our main concern in this report. By the quantum inverse scattering method, the Baxter's T–Q relation is formulated on the associated spectral curve, a high genus Riemann surface in general, arisen from the study of spectrum problem of the system. In the case of degenerated spectral curve where the spectral variables lie on rational curves, we obtain the complete and explicit solution of the T–Q polynomial equation associated to the model, and the intimate relation between the Baxter's T–Q relation and algebraic Bethe Ansatz is clearly revealed. The algebraic geometry of a general spectral curve attached to the model and certain qualitative properties of solutions of the Baxter's T–Q relation are discussed incorporating the physical consideration.     

Spectrophotometric Study of Luminol in Dimethyl Sulfoxide–Potassium Hydroxide

The spectrophotometric study of luminol (LH₂) in dimethyl sulfoxide (DMSO), DMSO-water solutions, and alkaline DMSO and DMSO-water solutions has been done, focusing on the effect of the KOH additon on LH₂ absorption and fluorescence properties. The absorption spectra indicate an acid-base equilibrium, and the luminol dianion (L^2–) formation at 3 × 10^–4 – 2.4 × 10^–3 M KOH. The decrease of the fluorescence intensity and the variation of the excitation spectra of LH₂-DMSO-KOH solutions with KOH concentration have been similarly explained. The acid-base process is reversible. The addition of HCl to the solution with 3.0 × 10^–3 M KOH leads to an increase of the fluorescence intensity to its highest value, observed in pure DMSO. The addition of HCl to the LH₂-DMSO solution leads to the decrease of the fluorescence intensity as a result of the LH⁺ ₃ cation formation. In LH₂-DMSO-water, the fluorescence band is shifted from 405 nm to 424 nm and increased in the intensity. In the presence of KOH (in LH₂-DMSO-water-KOH solution) a new band appears, with the maximum at 485 nm and the band at 405 nm decreased. The changes in fluorescence lifetimes also evidence the different chemical species formed.     

First-principles study of fundamental properties and electronic structure of alloys

We have performed first-principles calculations using full-potential augmented-plane-wave method to investigate the fundamental properties of the Cd_1–xZn_xTe alloys. The composition dependence of the lattice constant and the bulk modulus have been estimated from total energy calculations. By means of the analytical fitting the band structures in the vicinity of the Brillouin center a complete set of effective electron- and hole-masses have also been derived. In order to further understand the effects of the chemical bonding on the above macroscopic properties we then studied the relaxation behaviors and the changes of the electronic states upon alloying for x=0.25 system. The results presented here yield a general understanding of the fundamental properties for the Cd_1–xZn_xTe crystals studies.     

Luminescence from ZnO/MgO nanoparticle structures prepared by solution techniques

The optical and structural properties of mixed ZnO/MgO particles prepared by solution techniques are investigated by the cathodoluminescence and electron microscopy techniques. The samples annealed at 400–1000 °C show well crystalline wurtzite structure of the ZnO (MgZnO) particles with the size in range of 10–100 nm. Annealing at high temperatures (>700 °C) leads to Mg diffusion in ZnO and Mg_xZn_1−xO alloy formation. The blue shifts of the near-band-edge emission as a result of the alloy band gap widening and quantum confinement effect for the small size particles are demonstrated.