Large-amplitude inviscid fluid motion in an accelerating container

Study of dynamic behavior of the liquid-vapor interface of an inviscid fluid in an accelerating cylindrical container includes an analytical-numerical method for determining large amplitude motion. The method is based on the expansion of the velocity potential in a series of harmonic functions with time dependent coefficients

Propagation of the phase of solar modulation

The phase of the 11 year galactic cosmic ray variation, due to a varying rate of emission of long lived propagating regions of enhanced scattering, travels faster than the scattering regions themselves. The radial speed of the 11 year phase in the quasi-steady, force field approximation is exactly twice the speed of the individual, episodic decreases. A time dependent, numerical solution for 1 GeV protons at 1 and 30 Au gives a phase speed which is 1.85 times the propagation speed of the individual decreases

Existence and uniqueness of limit cycles in a class of second order ODE's with inseparable mixed terms

We prove a uniqueness result for limit cycles of the second order ODE $\ddot x + \dot x \phi(x,\dot x) + g(x) = 0$. Under mild additional conditions, we show that such a limit cycle attracts every non-constant solution. As a special case, we prove limit cycle's uniqueness for an ODE studied in \cite{ETA} as a model of pedestrians' walk. This paper is an extension to equations with a non-linear $g(x)$ of the results presented in \cite{S}

Uncertainty quantification in steady state simulations of a molten salt system using polynomial chaos expansion analysis

Uncertainty Quantification (UQ) of numerical simulations is highly relevant in the study and design of complex systems. Among the various approaches available, Polynomial Chaos Expansion (PCE) analysis has recently attracted great interest. It belongs to nonintrusive spectral projection methods and consists of constructing system responses as polynomial functions of the stochastic inputs. The limited number of required model evaluations and the possibility to apply it to codes without any modification make this technique extremely attractive. In this work, we propose the use of PCE to perform UQ of complex, multi-physics models for liquid fueled reactors, addressing key design aspects of neutronics and thermal fluid dynamics. Our PCE approach uses Smolyak sparse grids designed to estimate the PCE coefficients. To test its potential, the PCE method was applied to a 2D problem representative of the Molten Salt Fast Reactor physics. An in-house multi-physics tool constitutes the reference model. The studied responses are the maximum temperature and the effective multiplication factor. Results, validated by comparison with the reference model on 103 Monte-Carlo sampled points, prove the effectiveness of our PCE approach in assessing uncertainties of complex coupled models

Normal forms approach to diffusion near hyperbolic equilibria

We consider the exit problem for small white noise perturbation of a smooth dynamical system on the plane in the neighborhood of a hyperbolic critical point. We show that if the distribution of the initial condition has a scaling limit then the exit distribution and exit time also have a joint scaling limit as the noise intensity goes to zero. The limiting law is computed explicitly. The result completes the theory of noisy heteroclinic networks in two dimensions. The analysis is based on normal forms theory.Comment: 21 page

Positrons in Cosmic Rays from Dark Matter Annihilations for Uplifted Higgs Regions in MSSM

We point out that there are regions in the MSSM parameter space which successfully provide a dark matter (DM) annihilation explanation for observed positron excess (e.g. PAMELA), while still remaining in agreement with all other data sets. Such regions (e.g. the uplifted Higgs region) can realize an enhanced neutralino DM annihilation dominantly into leptons via a Breit-Wigner resonance through the CP-odd Higgs channel. Such regions can give the proper thermal relic DM abundance, and the DM annihilation products are compatible with current antiproton and gamma ray observations. This scenario can succeed without introducing any additional degrees of freedom beyond those already in the MSSM.Comment: 11 pages, 9 figure

Extended Quintessence with non-minimally coupled phantom scalar field

We investigate evolutional paths of an extended quintessence with a non-minimally coupled phantom scalar field $\psi$ to the Ricci curvature. The dynamical system methods are used to investigate typical regimes of dynamics at the late time. We demonstrate that there are two generic types of evolutional scenarios which approach the attractor (a focus or a node type critical point) in the phase space: the quasi-oscillatory and monotonic trajectories approach to the attractor which represents the FRW model with the cosmological constant. We demonstrate that dynamical system admits invariant two-dimensional submanifold and discussion that which cosmological scenario is realized depends on behavior of the system on the phase plane $(\psi, \psi')$. We formulate simple conditions on the value of coupling constant $\xi$ for which trajectories tend to the focus in the phase plane and hence damping oscillations around the mysterious value $w=-1$. We describe this condition in terms of slow-roll parameters calculated at the critical point. We discover that the generic trajectories in the focus-attractor scenario come from the unstable node. It is also investigated the exact form of the parametrization of the equation of state parameter $w(z)$ (directly determined from dynamics) which assumes a different form for both scenarios.Comment: revtex4, 15 pages, 9 figures; (v2) published versio