Georgia College & State University

About: Georgia College & State University is a education organization based out in Milledgeville, Georgia, United States. It is known for research contribution in the topics: Population & Higher education. The organization has 950 authors who have published 1591 publications receiving 37027 citations.

Near-threshold deuteron photodisintegration: An indirect determination of the Gerasimov-Drell-Hearn sum rule and forward spin polarizability ( γ 0 ) for the deuteron at low energies

Abstract: It is shown that a measurement of the analyzing power obtained with linearly polarized \ensuremath{\gamma}-rays and an unpolarized target can provide an indirect determination of two physical quantities. These are the Gerasimov-Drell-Hearn (GDH) sum rule integrand for the deuteron and the sum rule integrand for the forward spin polarizability (${\ensuremath{\gamma}}_{0}$) near photodisintegration threshold. An analysis of data for the $d(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}},n)p$ reaction and other experiments is presented. A fit to the world data analyzed in this manner gives a GDH integral value of $\ensuremath{-}603\ifmmode\pm\else\textpm\fi{}43\ensuremath{\mu}$b between the photodisintegration threshold and 6 MeV. This result is the first confirmation of the large contribution of the ${}^{1}{S}_{0}(M1)$ transition predicted for the deuteron near photodisintegration threshold. In addition, a sum rule value of 3.75\ifmmode\pm\else\textpm\fi{}0.18 fm${}^{4}$ for ${\ensuremath{\gamma}}_{0}$ is obtained between photodisintegration threshold and 6 MeV. This is a first indirect confirmation of the leading-order effective field theory prediction for the forward spin-polarizability of the deuteron.

Non-linear noise excitation for some space-time fractional stochastic equations in bounded domains

Abstract: In this paper we study non-linear noise excitation for the following class of space-time fractional stochastic equations in bounded domains: $$\partial^\beta_tu_t(x)=- u(-\Delta)^{\alpha/2} u_t(x)+I^{1-\beta}_t[\lambda \sigma(u)\stackrel{\cdot}{F}(t,x)]$$ in $(d+1)$ dimensions, where $ u>0, \beta\in (0,1)$, $\alpha\in (0,2]$. The operator $\partial^\beta_t$ is the Caputo fractional derivative, $-(-\Delta)^{\alpha/2} $ is the generator of an isotropic stable process and $I^{1-\beta}_t$ is the fractional integral operator. The forcing noise denoted by $\stackrel{\cdot}{F}(t,x)$ is a Gaussian noise. The multiplicative non-linearity $\sigma:\RR{R}\to\RR{R}$ is assumed to be globally Lipschitz continuous. These equations were recently introduced by Mijena and Nane(J. Mijena and E. Nane. Space time fractional stochastic partial differential equations. Stochastic Process Appl. 125 (2015), no. 9, 3301--3326). We first study the existence and uniqueness of the solution of these equations {and} under suitable conditions on the initial function, we {also} study the asymptotic behavior of the solution with respect to the parameter $\lambda$. In particular, our results are significant extensions of those in Foondun et al (M. Foondun, K. Tian and W. Liu. On some properties of a class of fractional stochastic equations. Preprint available at arxiv.org 1404.6791v1.), Foondun and Khoshnevisan (M. Foondun and D. Khoshnevisan. Intermittence and nonlinear parabolic stochastic partial differential equations, Electron. J. Probab. 14 (2009), no. 21, 548--568.), Nane and Mijena (J. Mijena and E. Nane. Space time fractional stochastic partial differential equations. Stochastic Process Appl. 125 (2015), no. 9, 3301--3326; J. B. Mijena, and E.Nane. Intermittence and time fractional partial differential equations. Submitted. 2014).

Numerical Solution of Multiple Nonlinear Volterra Integral Equations

Abstract: We analyze a discretization method for solving nonlinear integral equations that contain multiple integrals. These equations include integral equations with a Volterra series, instead of a single integral term, on one side of the equation. We prove existence and uniqueness of solutions, and convergence and estimates of the order of convergence for the numerical methods of solution.