arXiv subjects

P. Pedram

Publications and source records attributed to P. Pedram.

23 records · Page 2Linked to original sources

arXiv2007

Schrödinger-Wheeler-DeWitt equation in chaplygin gas FRW cosmological model

We present a chaplygin gas Friedmann-Robertson-Walker quantum cosmological model. In this work the Schutz's variational formalism is applied with positive, negative, and zero constant spatial curvature. In this approach the notion of time can be recovered. These give rise to Schrödinger-Wheeler-DeWitt equation for the scale factor. We use the eigenfunctions in order to construct wave packets for each case. We study the time dependent behavior of the expectation value of the scale factor, using the many-worlds interpretations of quantum mechanics.

gr-qc↗

arXiv2007

Long-range correlation and multifractality in Bach's Inventions pitches

We show that it can be considered some of Bach pitches series as a stochastic process with scaling behavior. Using multifractal deterend fluctuation analysis (MF-DFA) method, frequency series of Bach pitches have been analyzed. In this view we find same second moment exponents (after double profiling) in ranges (1.7-1.8) in his works. Comparing MF-DFA results of original series to those for shuffled and surrogate series we can distinguish multifractality due to long-range correlations and a broad probability density function. Finally we determine the scaling exponents and singularity spectrum. We conclude fat tail has more effect in its multifractality nature than long-range correlations.

physics.data-an↗

arXiv2007

Detrended Fluctuation analysis of Bach's Inventions and Sinfonias pitches

Detrended Fluctuation Analysis (DFA), suitable for the analysis of nonstationary time series, is used to investigate power law in some of the Bach's pitches series. Using DFA method, which also is a well-established method for the detection of long-range correlations, frequency series of Bach's pitches have been analyzed. In this view we find same Hurts exponents in the range (0.7-0.8) in his Inventions and sinfonia.

physics.comp-ph↗

arXiv2007

Using Spectral Method as an Approximation for Solving Hyperbolic PDEs

We demonstrate an application of the spectral method as a numerical approximation for solving Hyperbolic PDEs. In this method a finite basis is used for approximating the solutions. In particular, we demonstrate a set of such solutions for cases which would be otherwise almost impossible to solve by the more routine methods such as the Finite Difference Method. Eigenvalue problems are included in the class of PDEs that are solvable by this method. Although any complete orthonormal basis can be used, we discuss two particularly interesting bases: the Fourier basis and the quantum oscillator eigenfunction basis. We compare and discuss the relative advantages of each of these two bases.

math-ph↗

arXiv2006

Refined Spectral Method as an extremely accurate technique for solving 2D time-independent Schrodinger equation

We present a refinement of the Spectral Method by incorporating an optimization method into it and generalize it to two space dimensions. We then apply this Refined Spectral Method as an extremely accurate technique for finding the bound states of the two dimensional time-independent Schrodinger equation. We first illustrate the use of this method on an exactly solvable case and then use it on a case which is not so. This method is very simple to program, fast, extremely accurate (e.g. a relative error of 10^(-15) is easily obtainable in two dimensions), very robust and stable. Most importantly, one can obtain the energies and the wave functions of as many of the bound states as desired with a single run of the algorithm.

math-ph↗