Three dimensional structure from intensity correlations

We develop the analysis of x-ray intensity correlations from dilute ensembles of identical particles in a number of ways. First, we show that the 3D particle structure can be determined if the particles can be aligned with respect to a single axis having a known angle with respect to the incident beam. Second, we clarify the phase problem in this setting and introduce a data reduction scheme that assesses the integrity of the data even before the particle reconstruction is attempted. Finally, we describe an algorithm that reconstructs intensity and particle density simultaneously, thereby making maximal use of the available constraints.Comment: 17 pages, 9 figure

Isgur-Wise function in a QCD potential model with coulombic potential as perturbation

We study heavy light mesons in a QCD inspired quark model with the Cornell potential$-\frac{4\alpha_{S}}{3r}+br+c$. Here we consider the linear term $br$ as the parent and $-\frac{4\alpha_{S}}{3r}+c$ i.e.the Coloumbic part as the perturbation.The linear parent leads to Airy function as the unperturbed wavefunction. We then use the Dalgarno method of perturbation theory to obtain the total wavefunction corrected upto first order with Coulombic peice as the perturbation.With these wavefunctions, we study the Isgur-Wise function and calculate its slope and curvature.Comment: paper has been modified in Airy functions calculation upto o(r^3

Dynamical Anomalous Subvarieties: Structure and Bounded Height Theorems

According to Medvedev and Scanlon, a polynomial $f(x)\in \bar{\mathbb Q}[x]$ of degree $d\geq 2$ is called disintegrated if it is not linearly conjugate to $x^d$ or $\pm C_d(x)$ (where $C_d(x)$ is the Chebyshev polynomial of degree $d$). Let $n\in\mathbb{N}$, let $f_1,\ldots,f_n\in \bar{\mathbb Q}[x]$ be disintegrated polynomials of degrees at least 2, and let $\varphi=f_1\times\ldots\times f_n$ be the corresponding coordinate-wise self-map of $({\mathbb P}^1)^n$. Let $X$ be an irreducible subvariety of $({\mathbb P}^1)^n$ of dimension $r$ defined over $\bar{\mathbb Q}$. We define the \emph{$\varphi$-anomalous} locus of $X$ which is related to the \emph{$\varphi$-periodic} subvarieties of $({\mathbb P}^1)^n$. We prove that the $\varphi$-anomalous locus of $X$ is Zariski closed; this is a dynamical analogue of a theorem of Bombieri, Masser, and Zannier \cite{BMZ07}. We also prove that the points in the intersection of $X$ with the union of all irreducible $\varphi$-periodic subvarieties of $({\mathbb P}^1)^n$ of codimension $r$ have bounded height outside the $\varphi$-anomalous locus of $X$; this is a dynamical analogue of Habegger's theorem \cite{Habegger09} which was previously conjectured in \cite{BMZ07}. The slightly more general self-maps $\varphi=f_1\times\ldots\times f_n$ where each $f_i\in \bar{\mathbb Q}(x)$ is a disintegrated rational map are also treated at the end of the paper.Comment: Minor mistakes corrected, slight reorganizatio