Molecular Dynamics Simulations of Weak Detonations

Detonation of a three-dimensional reactive non-isotropic molecular crystal is modeled using molecular dynamics simulations. The detonation process is initiated by an impulse, followed by the creation of a stable fast reactive shock wave. The terminal shock velocity is independent of the initiation conditions. Further analysis shows supersonic propagation decoupled from the dynamics of the decomposed material left behind the shock front. The dependence of the shock velocity on crystal nonlinear compressibility resembles solitary behavior. These properties categorize the phenomena as a weak detonation. The dependence of the detonation wave on microscopic potential parameters was investigated. An increase in detonation velocity with the reaction exothermicity reaching a saturation value is observed. In all other respects the model crystal exhibits typical properties of a molecular crystal.Comment: 38 pages, 20 figures. Submitted to Physical Review

Global well-posedness of the KP-I initial-value problem in the energy space

We prove that the KP-I initial value problem is globally well-posed in the natural energy space of the equation

Brain Plasticity following Intensive Bimanual Therapy in Children with Hemiparesis: Preliminary Evidence

Neuroplasticity studies examining children with hemiparesis (CH) have focused predominantly on unilateral interventions. CH also have bimanual coordination impairments with bimanual interventions showing benefits. We explored neuroplasticity following hand-arm bimanual intensive therapy (HABIT) of 60 hours in twelve CH (6 females, mean age 11 ± 3.6 y). Serial behavioral evaluations and MR imaging including diffusion tensor (DTI) and functional (fMRI) imaging were performed before, immediately after, and at 6-week follow-up. Manual skills were assessed repeatedly with the Assisting Hand Assessment, Children’s Hand Experience Questionnaire, and Jebsen-Taylor Test of Hand Function. Beta values, indicating the level of activation, and lateralization index (LI), indicating the pattern of brain activation, were computed from fMRI. White matter integrity of major fibers was assessed using DTI. 11/12 children showed improvement after intervention in at least one measure, with 8/12 improving on two or more tests. Changes were retained in 6/8 children at follow-up. Beta activation in the affected hemisphere increased at follow-up, and LI increased both after intervention and at follow-up. Correlations between LI and motor function emerged after intervention. Increased white matter integrity was detected in the corpus callosum and corticospinal tract after intervention in about half of the participants. Results provide first evidence for neuroplasticity changes following bimanual intervention in CH.This project was funded by grants from Guy’s and St Thomas’ Charity, Marnie Kimelman Trust and ILAN, the Israeli Association for Disabled children. Beit Issie Shapiro funded and provided the camp venue. D. Green was supported by a grant from the Department of Immigration and Absorption during 2010-2011

Cortical Reorganization following Injury Early in Life

The brain has a remarkable capacity for reorganization following injury, especially during the first years of life. Knowledge of structural reorganization and its consequences following perinatal injury is sparse. Here we studied changes in brain tissue volume, morphology, perfusion, and integrity in children with hemiplegia compared to typically developing children, using MRI. Children with hemiplegia demonstrated reduced total cerebral volume, with increased cerebrospinal fluid (CSF) and reduced total white matter volumes, with no differences in total gray matter volume, compared to typically developing children. An increase in cortical thickness at the hemisphere contralateral to the lesion (CLH) was detected in motor and language areas, which may reflect compensation for the gray matter loss in the lesion area or retention of ipsilateral pathways. In addition, reduced cortical thickness, perfusion, and surface area were detected in limbic areas. Increased CSF volume and precentral cortical thickness and reduced white matter volume were correlated with worse motor performance. Brain reorganization of the gray matter within the CLH, while not necessarily indicating better outcome, is suggested as a response to neuronal deficits following injury early in life.Guy’s and St Thomas’ Charity and the Marnie Kimelman Trus

Asymptotic Lower Bounds for a class of Schroedinger Equations

We shall study the following initial value problem: \begin{equation}{\bf i}\partial_t u - \Delta u + V(x) u=0, \hbox{} (t, x) \in {\mathbf R} \times {\mathbf R}^n, \end{equation} $$u(0)=f,$$ where $V(x)$ is a real short--range potential, whose radial derivative satisfies some supplementary assumptions. More precisely we shall present a family of identities satisfied by the solutions to the previous Cauchy problem. As a by--product of these identities we deduce some uniqueness results and a lower bound for the so called local smoothing which becomes an identity in a precise asymptotic sense.Comment: 24 pages. to appear on Comm. Math. Phy

Structural resolvent estimates and derivative nonlinear Schrodinger equations

A refinement of uniform resolvent estimate is given and several smoothing estimates for Schrodinger equations in the critical case are induced from it. The relation between this resolvent estimate and radiation condition is discussed. As an application of critical smoothing estimates, we show a global existence results for derivative nonlinear Schrodinger equations.Comment: 21 page

A class of Schrodinger operators with decaying oscillatory potentials

We discuss Schr\"odinger operators on a half-line with decaying oscillatory potentials, such as products of an almost periodic function and a decaying function. We provide sufficient conditions for preservation of absolutely continuous spectrum and give bounds on the Hausdorff dimension of the singular part of the spectral measure. We also discuss the analogs for orthogonal polynomials on the real line and unit circle.Comment: 18 page