Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs

Algorithms are presented for the tanh- and sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and PDEs in terms of Jacobi's elliptic functions. For systems with parameters, the algorithms determine the conditions on the parameters so that the differential equations admit polynomial solutions in tanh, sech, combinations thereof, Jacobi's sn or cn functions. Examples illustrate key steps of the algorithms. The new algorithms are implemented in Mathematica. The package DDESpecialSolutions.m can be used to automatically compute new special solutions of nonlinear PDEs. Use of the package, implementation issues, scope, limitations, and future extensions of the software are addressed. A survey is given of related algorithms and symbolic software to compute exact solutions of nonlinear differential equations.Comment: 39 pages. Software available from Willy Hereman's home page at http://www.mines.edu/fs_home/whereman

Spectra of Quarkonia at Finite Temperature

Finite-temperature spectra of heavy quarkonia are calculated by combining potential model and thermofield dynamics formalisms. The mass spectra of the heavy quarkonia with various quark contents are calculated. It is found that binding mass of the quarkonium decreases as temperature increases.Comment: 12 pages, 1 figure. To appear Mod.Phys.Lett.

Modelling of carbon dioxide absorption into aqueous ammonia solution in a wetted wall column

© 2015 Universiti Putra Malaysia Press. In this paper, a mathematical model is developed based on mass and momentum balance for carbon dioxide absorption into aqueous ammonia solution. The model is simplified based on the assumption that the CO2 absorption into aqueous ammonia is a pseudo-first-order reaction. Laplace transform method is applied in order to solve the partial differential model equation. Finally, the CO2 molar flux is expressedas a function of partial pressure of CO2, concentration of aqueous ammonia, temperature and gas-liquidcontact area. Variation of CO2 molar flux with partial pressure of CO2 and temperature is discussedand a comparison is performed with experimental data from literature. Variation of CO2 molar flux isalso shown with gas-liquid contact area. The calculated flux from the model follows the same trend asthat of the experimental data reported in literature and the accuracy is within the accepted limit. The mathematical model is very helpful to predict the CO2 molar flux as a function of partial pressure of CO2, concentration of aqueous ammonia, temperature and gas-liquid contact area

Local Hall effect in hybrid ferromagnetic/semiconductor devices

We have investigated the magnetoresistance of ferromagnet-semiconductor devices in an InAs two-dimensional electron gas system in which the magnetic field has a sinusoidal profile. The magnetoresistance of our device is large. The longitudinal resistance has an additional contribution which is odd in applied magnetic field. It becomes even negative at low temperature where the transport is ballistic. Based on the numerical analysis, we confirmed that our data can be explained in terms of the local Hall effect due to the profile of negative and positive field regions. This device may be useful for future spintronic applications.Comment: 4 pages with 4 fugures. Accepted for publication in Applied Physics Letter

Gravitational lensing statistical properties in general FRW cosmologies with dark energy component(s): analytic results

Various astronomical observations have been consistently making a strong case for the existence of a component of dark energy with negative pressure in the universe. It is now necessary to take the dark energy component(s) into account in gravitational lensing statistics and other cosmological tests. By using the comoving distance we derive analytic but simple expressions for the optical depth of multiple image, the expected value of image separation and the probability distribution of image separation caused by an assemble of singular isothermal spheres in general FRW cosmological models with dark energy component(s). We also present the kinematical and dynamical properties of these kinds of cosmological models and calculate the age of the universe and the distance measures, which are often used in classical cosmological tests. In some cases we are able to give formulae that are simpler than those found elsewhere in the literature, which could make the cosmological tests for dark energy component(s) more convenient.Comment: 14 pages, no figure, Latex fil

On the YM and QCD spectra from five dimensional strings

We consider a non-critical five dimensional string setup which could provide a dual description of QCD in the limit of large number of colors and flavors. The model corresponds to N_c color D3-branes and N_f D4/anti D4-brane pairs supporting flavor degrees of freedom. The matching of the string model spectrum with the dual field theory one is considered. We discuss the consequences of the possible matching of the gravity modes with the light glueballs and the interpretation of the brane spectrum in Yang-Mills and QCD.Comment: 21 pages; V2: added corrections and references to match the published versio

Dynamic Behavior in Piezoresponse Force Microscopy

Frequency dependent dynamic behavior in Piezoresponse Force Microscopy (PFM) implemented on a beam-deflection atomic force microscope (AFM) is analyzed using a combination of modeling and experimental measurements. The PFM signal comprises contributions from local electrostatic forces acting on the tip, distributed forces acting on the cantilever, and three components of the electromechanical response vector. These interactions result in the bending and torsion of the cantilever, detected as vertical and lateral PFM signals. The relative magnitudes of these contributions depend on geometric parameters of the system, the stiffness and frictional forces of tip-surface junction, and operation frequencies. The dynamic signal formation mechanism in PFM is analyzed and conditions for optimal PFM imaging are formulated. The experimental approach for probing cantilever dynamics using frequency-bias spectroscopy and deconvolution of electromechanical and electrostatic contrast is implemented.Comment: 65 pages, 15 figures, high quality version available upon reques