STUDY OF THE STABILITY OF PARTICLE MOTION IN STORAGE RINGS. Final Report

During this period, our research was concentrated on the study of beam-beam effects in large storage-ring colliders and coherent synchrotron radiation (CSR) effect in light sources. Our group was involved in and made significant contribution to several international accelerator projects such as the US-LHC project for the design of the LHC interaction regions, the luminosity upgrade of Tevatron and HERA, the design of eRHIC, and the U.S. LHC Accelerator Research Program (LARP) for the future LHC luminosity upgrade

Chaotic transport in time-dependent symplectic maps

The effect of tune modulation in two-dimensional symplectic maps has been studied by using the concept of chaotic transport in terms of flux across resonances. When a single resonance is dominant, the particle escape due to the tune modulation can be characterized by the increment of the flux induced by the modulation. The parameter dependence of the particle escape rate obtained by using the transport theory agrees well with the result of the multiparticle tracking study and the beam study experiments at the CERN Super Proton Synchrotron. This study showed that the transport theory provides a computationally efficient means of studying the particle escape due to the tune modulation and estimating the parameter dependence of the escape rate

Mathematical Model for Length Control by the Timing of Substrate Switching in the Type III Secretion System

A grant from the One-University Open Access Fund at the University of Kansas was used to defray the author's publication fees in this Open Access journal. The Open Access Fund, administered by librarians from the KU, KU Law, and KUMC libraries, is made possible by contributions from the offices of KU Provost, KU Vice Chancellor for Research & Graduate Studies, and KUMC Vice Chancellor for Research. For more information about the Open Access Fund, please see http://library.kumc.edu/authors-fund.xml.Type III Secretion Systems (T3SS) are complex bacterial structures that provide gram-negative pathogens with a unique virulence mechanism whereby they grow a needle-like structure in order to inject bacterial effector proteins into the cytoplasm of a host cell. Numerous experiments have been performed to understand the structural details of this nanomachine during the past decade. Despite the concerted efforts of molecular and structural biologists, several crucial aspects of the assembly of this structure, such as the regulation of the length of the needle itself, remain unclear. In this work, we used a combination of mathematical and computational techniques to better understand length control based on the timing of substrate switching, which is a possible mechanism for how bacteria ensure that the T3SS needles are neither too short nor too long. In particular, we predicted the form of the needle length distribution based on this mechanism, and found excellent agreement with available experimental data from Salmonella typhimurium with only a single free parameter. Although our findings provide preliminary evidence in support of the substrate switching model, they also make a set of quantitative predictions that, if tested experimentally, would assist in efforts to unambiguously characterize the regulatory mechanisms that control the growth of this crucial virulence factor

Construction of a two-parameter empirical model of left ventricle wall motion using cardiac tagged magnetic resonance imaging data

Abstract Background A one-parameter model was previously proposed to characterize the short axis motion of the LV wall at the mid-ventricle level. The single parameter of this model was associated with the radial contraction of myocardium, but more comprehensive model was needed to account for the rotation at the apex and base levels. The current study developed such model and demonstrated its merits and limitations with examples. Materials and methods The hearts of five healthy individuals were visualized using cardiac tagged magnetic resonance imaging (tMRI) covering the contraction and relaxation phases. Based on the characteristics of the overall dynamics of the LV wall, its motion was represented by a combination of two components - radial and rotational. Each component was represented by a transformation matrix with a time-dependent variable α or β. Image preprocessing step and model fitting algorithm were described and applied to estimate the temporal profiles of α and β within a cardiac cycle at the apex, mid-ventricle and base levels. During this process, the tagged lines of the acquired images served as landmark reference for comparing against the model prediction of the motion. Qualitative and quantitative analyses were performed for testing the performance of the model and thus its validation. Results The α and β estimates exhibited similarities in values and temporal trends once they were scaled by the radius of the epicardium (r epi )and plotted against the time scaled by the period of the cardiac cycle (T cardiac ) of each heart measured during the data acquisition. α/r epi peaked at about Δt/T cardiac =0.4 and with values 0.34, 0.4 and 0.3 for the apex, mid-ventricle and base level, respectively. β/r epi similarly maximized in amplitude at about Δt/T cardiac =0.4, but read 0.2 for the apex and - 0.08 for the base level. The difference indicated that the apex twisted more than the base. Conclusion It is feasible to empirically model the spatial and temporal evolution of the LV wall motion using a two-parameter formulation in conjunction with tMRI-based visualization of the LV wall in the transverse planes of the apex, mid-ventricle and base. In healthy hearts, the analytical model will potentially allow deriving biomechanical entities, such as strain, strain rate or torsion, which are typically used as diagnostic, prognostic or predictive markers of cardiovascular diseases including diabetes.Peer Reviewe

Construction of a two-parameter empirical model of left ventricle wall motion using cardiac tagged magnetic resonance imaging data

Background A one-parameter model was previously proposed to characterize the short axis motion of the LV wall at the mid-ventricle level. The single parameter of this model was associated with the radial contraction of myocardium, but more comprehensive model was needed to account for the rotation at the apex and base levels. The current study developed such model and demonstrated its merits and limitations with examples. Materials and methods The hearts of five healthy individuals were visualized using cardiac tagged magnetic resonance imaging (tMRI) covering the contraction and relaxation phases. Based on the characteristics of the overall dynamics of the LV wall, its motion was represented by a combination of two components - radial and rotational. Each component was represented by a transformation matrix with a time-dependent variable α or β. Image preprocessing step and model fitting algorithm were described and applied to estimate the temporal profiles of α and β within a cardiac cycle at the apex, mid-ventricle and base levels. During this process, the tagged lines of the acquired images served as landmark reference for comparing against the model prediction of the motion. Qualitative and quantitative analyses were performed for testing the performance of the model and thus its validation. Results The α and β estimates exhibited similarities in values and temporal trends once they were scaled by the radius of the epicardium (repi)and plotted against the time scaled by the period of the cardiac cycle (Tcardiac) of each heart measured during the data acquisition. α/repi peaked at about Δt/Tcardiac=0.4 and with values 0.34, 0.4 and 0.3 for the apex, mid-ventricle and base level, respectively. β/repi similarly maximized in amplitude at about Δt/Tcardiac=0.4, but read 0.2 for the apex and - 0.08 for the base level. The difference indicated that the apex twisted more than the base. Conclusion It is feasible to empirically model the spatial and temporal evolution of the LV wall motion using a two-parameter formulation in conjunction with tMRI-based visualization of the LV wall in the transverse planes of the apex, mid-ventricle and base. In healthy hearts, the analytical model will potentially allow deriving biomechanical entities, such as strain, strain rate or torsion, which are typically used as diagnostic, prognostic or predictive markers of cardiovascular diseases including diabetes

Influence of electron collisions inside the cathode sheath upon the electron energy spectrum in the negative glow region of a gas discharge

Includes bibliographical references.Computer models have been developed to solve the Boltzmann equation for the electron energy spectrum in both the cathode sheath and the negative glow region of a glow discharge. Electron collisions occurring during acceleration inside the cathode sheath partially determine the structure of the electron energy distribution measured in the negative glow. The relative role of elastic, excitation, and ionization collisions are examined using the computer model. Good qualitative agreement was obtained between calculated electron energy distributions and previous experimental measurements both at the sheath-plasma interface as well as in the negative glow region of the discharge.This work was supported by the National Science Foundation. Quantum Electronics Waves and Beams (ECS-881505I, Dr. L. Goldberg) and the Naval Research Laboratory

Micromechanical Model for Self-Organized Impurity Nanorod Arrays in Epitaxial YBCO Films

A micromechanical model based on the theory of elasticity has been developed to study the configuration of self-assembled impurity nanostructures in high temperature superconducting YBCO films. With the calculated equilibrium strain and elastic energy of the impurity doped film, a phase diagram of lattice mismatches $vs.$ elastic constants of the dopant was obtained for the energetically-preferred orientation of impurity nanorods. The calculation of the nanorod orientation and the film lattice deformation has yielded an excellent agreement with experimental measurements

A fundamental limit for integrated atom optics with Bose-Einstein condensates

The dynamical response of an atomic Bose-Einstein condensate manipulated by an integrated atom optics device such as a microtrap or a microfabricated waveguide is studied. We show that when the miniaturization of the device enforces a sufficiently high condensate density, three-body interactions lead to a spatial modulational instability that results in a fundamental limit on the coherent manipulation of Bose-Einstein condensates.Comment: 6 pages, 3 figure