Universal analytic properties of noise. Introducing the J-Matrix formalism

We propose a new method in the spectral analysis of noisy time-series data for damped oscillators. From the Jacobi three terms recursive relation for the denominators of the Pad\'e Approximations built on the well-known Z-transform of an infinite time-series, we build an Hilbert space operator, a J-Operator, where each bound state (inside the unit circle in the complex plane) is simply associated to one damped oscillator while the continuous spectrum of the J-Operator, which lies on the unit circle itself, is shown to represent the noise. Signal and noise are thus clearly separated in the complex plane. For a finite time series of length 2N, the J-operator is replaced by a finite order J-Matrix J_N, having N eigenvalues which are time reversal covariant. Different classes of input noise, such as blank (white and uniform), Gaussian and pink, are discussed in detail, the J-Matrix formalism allowing us to efficiently calculate hundreds of poles of the Z-transform. Evidence of a universal behaviour in the final statistical distribution of the associated poles and zeros of the Z-transform is shown. In particular the poles and zeros tend, when the length of the time series goes to infinity, to a uniform angular distribution on the unit circle. Therefore at finite order, the roots of unity in the complex plane appear to be noise attractors. We show that the Z-transform presents the exceptional feature of allowing lossless undersampling and how to make use of this property. A few basic examples are given to suggest the power of the proposed method.Comment: 14 pages, 8 figure

Brans-Dicke gravity and the capture of stars by black holes: some asymptotic results

In the context of star capture by a black hole, a new noticeable difference between Brans-Dicke theory and general relativity gravitational radiation is pointed out. This feature stems from the non-stationarity of the black hole state, barring Hawking's theorem.Comment: 4 pages. Submitted to Classical and Quantum Gravit

Far-infrared and submillimeter-wave conductivity in electron-doped cuprate La_{2-x}Ce_xCuO_4

We performed far-infrared and submillimeter-wave conductivity experiments in the electron-doped cuprate La_{2-x}Ce_xCuO_4 with x = 0.081 (underdoped regime, T_c = 25 K). The onset of the absorption in the superconducting state is gradual in frequency and is inconsistent with the isotropic s-wave gap. Instead, a narrow quasiparticle peak is observed at zero frequency and a second peak at finite frequencies, clear fingerprints of the conductivity in a d-wave superconductor. A far-infrared conductivity peak can be attributed to 4Delta_0, or to 2Delta_0 + Delta_spin, where Delta_spin is the resonance frequency of the spin-fluctuations. The infrared conductivity as well as the suppression of the quasiparticle scattering rate below T_c are qualitatively similar to the results in the hole-doped cuprates.Comment: 5 pages, 4 figures include

Transmission electron microscopy investigation of segregation and critical floating-layer content of indium for island formation in InGaAs

We have investigated InGaAs layers grown by molecular-beam epitaxy on GaAs(001) by transmission electron microscopy (TEM) and photoluminescence spectroscopy. InGaAs layers with In-concentrations of 16, 25 and 28 % and respective thicknesses of 20, 22 and 23 monolayers were deposited at 535 C. The parameters were chosen to grow layers slightly above and below the transition between the two- and three-dimensional growth mode. In-concentration profiles were obtained from high-resolution TEM images by composition evaluation by lattice fringe analysis. The measured profiles can be well described applying the segregation model of Muraki et al. [Appl. Phys. Lett. 61 (1992) 557]. Calculated photoluminescence peak positions on the basis of the measured concentration profiles are in good agreement with the experimental ones. Evaluating experimental In-concentration profiles it is found that the transition from the two-dimensional to the three-dimensional growth mode occurs if the indium content in the In-floating layer exceeds 1.1+/-0.2 monolayers. The measured exponential decrease of the In-concentration within the cap layer on top of the islands reveals that the In-floating layer is not consumed during island formation. The segregation efficiency above the islands is increased compared to the quantum wells which is explained tentatively by strain-dependent lattice-site selection of In. In addition, In0.25Ga0.75As quantum wells were grown at different temperatures between 500 oC and 550 oC. The evaluation of concentration profiles shows that the segregation efficiency increases from R=0.65 to R=0.83.Comment: 16 pages, 6 figures, 1 table, sbmitted in Phys. Rev.

Models of Passive and Reactive Tracer Motion: an Application of Ito Calculus

By means of Ito calculus it is possible to find, in a straight-forward way, the analytical solution to some equations related to the passive tracer transport problem in a velocity field that obeys the multidimensional Burgers equation and to a simple model of reactive tracer motion.Comment: revised version 7 pages, Latex, to appear as a letter to J. of Physics

Calculation of renormalized viscosity and resistivity in magnetohydrodynamic turbulence

A self-consistent renormalization (RG) scheme has been applied to nonhelical magnetohydrodynamic turbulence with normalized cross helicity $\sigma_c =0$ and $\sigma_c \to 1$. Kolmogorov's 5/3 powerlaw is assumed in order to compute the renormalized parameters. It has been shown that the RG fixed point is stable for $d \ge d_c \approx 2.2$. The renormalized viscosity $\nu^*$ and resistivity $\eta^*$ have been calculated, and they are found to be positive for all parameter regimes. For $\sigma_c=0$ and large Alfv\'{e}n ratio (ratio of kinetic and magnetic energies) $r_A$, $\nu^*=0.36$ and $\eta^*=0.85$. As $r_A$ is decreased, $\nu^*$ increases and $\eta^*$ decreases, untill $r_A \approx 0.25$ where both $\nu^*$ and $\eta^*$ are approximately zero. For large $d$, both $\nu^*$ and $\eta^*$ vary as $d^{-1/2}$. The renormalized parameters for the case $\sigma_c \to 1$ are also reported.Comment: 19 pages REVTEX, 3 ps files (Phys. Plasmas, v8, 3945, 2001

Drug design of novel molecules using a bioisosteric and de novo techniques - a comparison

Rational drug design is an area of science that evolves continuously in order to answer contemporary demands for a decrease in novel drug discovery turnover time. Multiple drug design modalities exist which may be exploited in response to the parameters of specific drug design projects. Bioisosteric modification of existing molecules and de novo design are two such approaches, both of which were employed in parallel in this study which aimed to compare their scope and efficiency using Tricyclic Antidepressants (TCAs) and Selective Serotonin Reuptake Inhibiting (SSRIs) molecules as case studies. Results indicated that bioisosterically modified structures did not have a higher affinity for their cognate receptor when compared to the template structure while the de novo design yielded molecules that were markedly different to the template from a structural perspective, and which also bound to the cognate receptor with an affinity superior to that of the template. This study showed therefore that bioisosteric modification is of utility when minor structural variations are considered sufficiently relative to a template molecule, and could consequently be of utility in the acquisition of new patents, in the reduction of toxicity, or in the attainment of improved biological profiles. It indicated furthermore, the role of the de novo approach in the successful exploration of novel pharmacophoric space and in the generation of molecular structures with an affinity significantly greater than that of lead molecules for a target receptor.peer-reviewe

Probing the role of Nd3+ ions in the weak multiferroic character of NdMn2O5 by optical spectroscopies

Raman and infrared spectroscopies are used as local probes to study the dynamics of the Nd-O bonds in the weakly multiferroic NdMn2O5 system. The temperature dependence of selected Raman excitations reveals the splitting of the Nd-O bonds in NdMn2O5. The Nd3+ ion crystal field (CF) excitations in NdMn2O5 single crystals are studied by infrared transmission as a function of temperature, in the 1800-8000 cm-1 range, and under an applied magnetic field up to 11 T. The frequencies of all 4Ij crystal-field levels of Nd3+ are determined. We find that the degeneracy of the ground-state Kramers doublet is lifted ({\Delta}0 ~7.5 cm-1) due to the Nd3+-Mn3+ interaction in the ferroelectric phase, below TC ~ 28 K. The Nd3+ magnetic moment mNd(T) and its contribution to the magnetic susceptibility and the specific heat are evaluated from {\Delta}0(T) indicating that the Nd3+ ions are involved in the magnetic and the ferroelectric ordering observed below ~ 28 K. The Zeeman splitting of the excited crystal field levels of the Nd3+ ions at low temperature is also analyzed.Comment: This paper is accepted for publication as a Regular Article in Physical Review