Jitendra C. Parikh

Gravitational energy of a stringy charged black hole

Abstract It is known that a static, spherically symmetric stringy charged black hole has several different properties than that of the Reissner-Nordstrom black hole. In this letter we obtain the gravitational energy of the stringy charged black hole and observe that the total energy is positive and is confined to the interior of the black hole. This is in contrast to the result for the Reissner-Nordstrom black hole, where the total gravitational energy is positive but is shared by its interior as well as exterior. Consequently, unlike the case of the Reissner-Nordstrom black hole, the effective gravitational mass experienced by a neutral test particle situated at any finite distance in the gravitational field of the stringy charged black hole is positive.

A conformal scalar dyon black hole solution

Abstract An exact solution of Einstein-Maxwell-conformal scalar field equations is given, which is a black hole solution and has three parameters: scalar charge, electric charge, and magnetic charge. Switching off the magnetic charge parameter yields the solution given by Bekenstein. In addition the energy of the conformal scalar dyon black hole is obtained.

Wavelet analysis and scaling properties of time series.

We propose a wavelet based method for the characterization of the scaling behavior of nonstationary time series. It makes use of the built-in ability of the wavelets for capturing the trends in a data set, in variable window sizes. Discrete wavelets from the Daubechies family are used to illustrate the efficacy of this procedure. After studying binomial multifractal time series with the present and earlier approaches of detrending for comparison, we analyze the time series of averaged spin density in the 2D Ising model at the critical temperature, along with several experimental data sets possessing multifractal behavior.

Space symmetry in light nuclei. II. SU(4) isospin--spin averages

Abstract The validity of the Wigner supermultiplet scheme in the d-s shell is investigated for nuclei with neutron excess using the spectral distribution methods of French. Averages of the Hamiltonian H and H 2 over states belonging to a definite SU(4) symmetry, isospin and spin are used to determine ground state energies and low lying spectra of nuclei. Intensities of various irreducible representations of SU(4) near the ground state are evaluated and these provide a measure of symmetry breaking. We find that the symmetry in nuclei with neutron excess is no worse than that for the lowest isospin ones. The results obtained are compared with the Franzini-Radicati mass formula.

Calculations of the giant dipole resonance for sd-shell nuclei in the open-shell random phase approximation

Abstract The systematics of the giant dipole resonance have been calculated in the open-shell RPA for all the self-conjugate sd-shell nuclei, using (i) a phenomenological Rosenfeld interaction, (ii) Barret, Hewitt and McCarthy G -matrix elements and (iii) Kuo G -matrix elements. The excitations are based on shell model ground states for all nuclei except 28 Si for which a projected Hartree-Fock ground state was used.

Unitary group decomposition of hamiltonian operators. II. SU (4) irreducible tensors, norms and their energy variation and symmetry breaking

SU(6) ⊗ SU(4) tensor decomposition of effective interactions in the 2s-1d shell has been carried out to examine the relative importance of the various irreducible tensors in many-particle spaces. For this purpose norms of the irreducible tensors are evaluated in many-particle spaces. Variation of the expectation value of the square of the irreducible tensor parts with excitation energy has also been examined using the polynomial expansion method. A new measure of symmetry breaking that is theoretically more sound is derived which includes in its definition partial width as well as internal width. This is used to study SU(4) symmetry mixing in nuclei.

The quadrupole collectivity and possible existence of macroscopic SU(3) symmetry in some collective shell model states

Abstract The shell model eigenfunctions for low-lying states of 56 Fe and 54 Cr are analyzed to illustrate that the “collective” states of these nuclei can be described as the coupling of a small number of low-lying collective states of the proton and neutron groups. A truncation scheme for doing shell model calculations which would take advantage of the multipole collectivity of the low-lying states of the proton and neutron states is discussed. Finally, it is suggested that the rotational features observed even in the heavy deformed nuclei could be a consequence of the existence of what might be called an approximate “macroscopic” SU(3) symmetry.

Mixing of SU(3) symmetry for nuclei in the ds-shell

Abstract Spectral distribution methods of French are applied to evaluate intensities near the ground state of different SU(3) representations for the ds-shell nuclei. For nuclei with 20 ⩽ A ⩽ 24 there is a dominant symmetry but for the heavier ones large admixtures are present.

Dynamic Predictions from Time Series Data — An Artificial Neural Network Approach

A hybrid approach, incorporating concepts of nonlinear dynamics in artificial neural networks (ANN), is proposed to model a time series generated by complex dynamic systems. We introduce well-known features used in the study of dynamic systems — time delay τ and embedding dimension d — for ANN modeling of time series. These features provide a theoretical basis for selecting the optimal size for the number of neurons in the input layer. The main outcome of the new approach for such problems is that to a large extent it defines the ANN architecture, models the time series and gives good prediction. As a consequence, we have an integrated and systematic data-driven scheme for modeling time series data. We illustrate our method by considering computer generated periodic and chaotic time series. The ANN model developed gave excellent quality of fit for the training and test sets as well as for iterative dynamic predictions for future values of the two time series. Further, computer experiments were conducted by introducing Gaussian noise of various degrees in the two time series, to simulate real world effects. We find that up to a limit introduction of noise leads to a smaller network with good generalizing capability.

Instability of the plasma oscillations in finite temperature perturbative QCD

We use linear-response dielectric theory to show that the baryon-poor QCD plasma based on the perturbative vacuum is unstable, even at a high temperature. If deconfinement occurs in nuclear collisions or the early universe, it is not accompanied by the restoration of the perturbative vacuum.