Asymptotic Methods in Non Linear Dynamics

This paper features and elaborates recent developments and modifications in asymptotic techniques in solving differential equation in non linear dynamics. These methods are proved to be powerful to solve weakly as well as strongly non linear cases. Obtained approximate analytical solutions are valid for the whole solution domain. In this paper, limitations of traditional perturbation methods are illustrated with various modified techniques. Mathematical tools such as variational approach, homotopy and iteration technique are discussed to solve various problems efficiently. Asymptotic methods such as Variational Method, modified Lindstedt-Poincare method, Linearized perturbation method, Parameter Expansion method, Homotopy Perturbation method and Perturbation-Iteration methods(singular and non singular cases) have been discussed in various situations. Main emphasis is given on Singular perturbation method and WKB method in various numerical problems.Comment: submit, to appear in Journal of Non Linear Science and Applications, 201

The role of trapped neutrino in dense stelllar matter and kaon condensation

We investigate the effect of neutrino trapping on kaon condensation process and Equation of State (EOS) in a newly formed neutron star which is less than several seconds old. Using nonlinear relativistic mean field model, we find that the presence of neutrino shifts the threshold for kaon condensation and muon production to much higher density. We also studied the energy density and pressure of the syst under trapped neutrino condition and found that it stiffens the EOS of the system which may be responsible for the delayed exploision mechanism of supernovae.Comment: 9 pages, 5 figure

Analytical Derivation of Three Dimensional Vorticity Function for wave breaking in Surf Zone

In this report, Mathematical model for generalized nonlinear three dimensional wave breaking equations was de- veloped analytically using fully nonlinear extended Boussinesq equations to encompass rotational dynamics in wave breaking zone. The three dimensional equations for vorticity distributions are developed from Reynold based stress equations. Vorticity transport equations are also developed for wave breaking zone. This equations are basic model tools for numerical simulation of surf zone to explain wave breaking phenomena. The model reproduces most of the dynamics in the surf zone. Non linearity for wave height predictions is also shown close to the breaking both in shoaling as well as surf zone. Keyword Wave breaking, Boussinesq equation, shallow water, surf zone. PACS : 47.32-yComment: arXiv admin note: substantial text overlap with arXiv:physics/050307

SUSY Dark Matter: Closing The Parameter Space

We consider here the constraints in SUGRA models on the SUSY parameter space due to current experimental bounds on the light Higgs mass m_h, the b-> s gamma decay, the amount of neutralino cold dark matter Omega h^2, and the muon magnetic moment. Models with universal soft breaking (mSUGRA) and non-universal gaugino or Higgs masses at M_G are examined. For mSUGRA, the m_h, b->s gamma and Omega h^2 constraints imply a lower bound on the gaugino mass of m_{1/2}>~300GeV implying the gluino and squarks have mass >~700GeV, and the neutralino >~120GeV. The current status of the Brookhaven muon g - 2 experiment is reviewed, and if the Standard Model (SM) contribution evaluated using the e^+ + e^- data is correct, a 2 sigma bound on the deviation of experiment from the SM produces an upper bound on m_{1/2} that eliminates the "focus point" regions of parameter space. Dark matter (DM) detection cross sections range from 5\times10^{-8} pb to 5\times10^{-10} pb which would be accessible to future planned detectors. The SUSY decay B_s->\mu^+ +\mu^- is seen to be accessible to the Tevatron Run 2B with 15 fb^{-1} luminosity for tanbeta >~30. The most favorable signals of SUSY for linear colliders are stau pair production and neutralino pair production, though it will require an 800GeV machine to cover the full parameter space. Non-universal models can modify some of the above results. Thus a non-universal (heavier) gluino mass at M_G can significantly reduce the lower bound constraints of b\to s gamma and m_h giving rise to a lighter SUSY spectrum. A heavier up Higgs mass can open an additional region with allowed relic density arising from annihilation via the s-channel Z diagram with an O(10) larger DM detector cross section.Comment: 14 pages, latex, 13 figures, Talk at conference Beyond the Desert '02, June, 2002, Oulu, Finlan

Generalized Set of Boussinesq equations for Surf Zone Region

In this report, generalized wave breaking equations are developed using three dimensional fully nonlinear extended Boussinesq equations to encompass rotational dynamics in wave breaking zone. The derivation for vorticity distributions are developed from Reynold based stress equations.Comment: 12 pages, submitted to Coastal Engineerin

Dark matter and Consequences of SUSY

We examine here the constraints from the amount of relic density of neutralino dark matter and other experiments have on the SUSY parameter space for the mSUGRA model and for models with non-universal soft breaking at the GUT scale. In mSUGRA, the allowed amount of dark matter restricts the SUSY parameter space to a narrow band in m_0 - m_{1/2} (except at very large \tan\beta). The Higgs mass and b-> s\gamma constraints produce a lower bound of m_{1/2}>~{\sim} 300GeV and if the muon magnetic moment anomaly can be interpreted as a 3\sigma deviation from the Standard Model, one also obtains an upper bound of m_{1/2} <~900 GeV, making the SUSY spectrum well accessible to the LHC. The B_s->\mu \mu decay is seen to be accessible to the Tevatron Run2B with 15 fb^{-1} for \tan\beta>~30. However, only parts of the spectrum will be accessible to the NLC if it's energy is below 800GeV. Non-universal soft breaking opens new regions of parameter space. Thus the m_{1/2} lower bound constraint of b->s\gamma and also the Higgs mass can be reduced greatly if the gluino mass is assumed larger at the GUT scale (allowing for a lighter gaugino spectrum), and non-universal Higgs soft breaking masses at the GUT scale can open new allowed regions at relatively low m_{1/2} and high m_0 where dark matter detection cross sections may be increased by a factor of ten or more.Comment: 11 pages, latex, 10 figures, Plenary talk at SUSY02 (DESY, June 17-23, 2002

Dark Matter Detection Rates In SUGRA Models

Direct detection of Milky Way wimps are discussed within the framework of R-parity conserving SUGRA models with grand unification at M_G. Two questions are discussed: what SUGRA models can account for the DAMA data if this data is confirmed, and is the full SUGRA parameter space accessible to future planned detectors. Experimental constraints of the Higgs mass bound, the b-> s\gamma bound, relic density constraints (including all co-annihilation channels), etc. are imposed. In addition, the effect of the possible muon g - 2 anomaly are examined. For mSUGRA, we find that the Higgs mass and b\to s\gamma constraint puts a lower bound m_{1/2} > (300 - 400) GeV (i.e. m_{\tilde\chi^0_1} > (120 - 160) GeV) for \tan\beta < 50, and thus the largest theoretical neutralino-proton cross sections still lie significantly below the DAMA 3\sigma lower bound. (Predictions for \tan\beta> 50 become sensitive to the precise value of m_t and m_b.) If in addition one imposes the muon anomaly constraint, \mu must be positive and an upper bound of m_{1/2}< 850 GeV for \tan\beta < 50 is obtained. More generally, if \mu >0 and m_{1/2} < 1 TeV, the cross sections are >~ 10^{-10} pb, and hence this parameter space would be mostly accessible to planned high sensitivity detectors. For non-minimal SUGRA models, the cross sections can be considerably larger, and a simple SU(5) model with non-universal soft breaking in the Higgs and third generation is seen to give cross sections in the DAMA range for \tan\beta >~ 15 with m_{\tilde\chi^0_1} > 80 GeV, and minimum cross sections >~10^{-10} pb for \mu > 0.Comment: 14 pages, latex, 8 figures, talk at COSMO-01, Rovaniemi, Finland, August 29 - September 4, 200

Numerical Studies of Particle Laden Flow in Dispersed Phase

To better understand the hydrodynamic flow behavior in turbulence, Particle-Fluid flow have been studied using our Direct Numerical(DNS) based software DSM on MUSCL-QUICK and finite volume algorithm. The particle flow was studied using Eulerian-Eulerian Quasi Brownian Motion(QBM) based approach. The dynamics is shown for various particle sizes which are very relevant to spray mechanism for Industrial applications and Bio medical applications.Comment: 9 pages, 12 Figures, submitted to International Journal for Numerical Methods in Fluid

Yukawa Textures in Heterotic M-Theory

We examine the structure of the Yukawa couplings in the 11 dimensional Horava-Witten M-theory based on non-standard embeddings. We find that the CKM and quark mass hierarchies can be explained in M Theory without introducing undue fine tuning. A phenomenological example is presented satisfying all CKM and quark mass data requiring the 5-branes cluster near the second orbifold plane, and that the instanton charges of the physical orbifold plane vanish. The latter condition is explicitly realized on a Calabi-Yau manifold with del Pezzo base dP_7.Comment: 3 pages, latex, talk at DPF 2000, Columbus, OH, August 9-12, 200

Yukawa Textures in Horava-Witten M-Theory

Recent advances in 11 dimensional Horava-Witten M-theory based on non-standard embeddings with torus fibered Calabi-Yau manifolds have allowed the construction of three generation models with Wilson line breaking to the Standard Model gauge symmetry. Central to these constructions is the existence of a set of 5-branes in the bulk. We examine within this framework the general structure of the matter Yukawa couplings and show that M-theory offers an alternate possible way of achieving the CKM and quark mass hierarchies without introducing undue fine tuning or (as in conventional analysis) small parameters raised to high powers. A phenomenological example is presented in accord with all CKM and quark mass data requiring mainly that the 5-branes cluster near the second orbifold plane, and that the instanton charges of the physical orbifold plane vanish. An explicit example of a three generation model with vanishing physical plane instanton charges based on a torus fibered Calabi-Yau three fold with a del Pezzo base $dP_7$ and Wilson line breaking is constructed.Comment: 28 pages, Revte