Bio: Rizwan-uddin is an academic researcher from University of Illinois at Urbana–Champaign. The author has contributed to research in topics: Convection–diffusion equation & Boundary value problem. The author has an hindex of 21, co-authored 89 publications receiving 1592 citations. Previous affiliations of Rizwan-uddin include University of Virginia & Urbana University.
Papers published on a yearly basis
TL;DR: The implicit Particle-in-Cell method for the computer simulation of plasma, and its implementation in a three-dimensional parallel code, called iPIC3D, enables kinetic plasma simulations at magnetohydrodynamics time scales.
Abstract: The implicit Particle-in-Cell method for the computer simulation of plasma, and its implementation in a three-dimensional parallel code, called iPIC3D, are presented. The implicit integration in time of the Vlasov-Maxwell system, removes the numerical stability constraints and it enables kinetic plasma simulations at magnetohydrodynamics time scales. Simulations of magnetic reconnection in plasma are presented to show the effectiveness of the algorithm.
01 Jan 2009
TL;DR: In this paper, a closed form analytical double-series solution is presented for the multi-dimensional unsteady heat conduction problem in polar coordinates (2-D cylindrical) with multiple layers in the radial direction.
Abstract: Closed form analytical double-series solution is presented for the multi-dimensional unsteady heat conduction problem in polar coordinates (2-D cylindrical) with multiple layers in the radial direction. Spatially non-uniform, but time-independent, volumetric heat sources are assumed in each layer. Separation of variables method is used to obtain transient temperature distribution. In contrast to Cartesian or cylindrical ( r , z ) coordinates, eigenvalues in the direction perpendicular to the layers do not explicitly depend on those in the other direction. The implication of the above statement is that the imaginary eigenvalues are precluded from the solution of the problem. However, radial (transverse) eigenvalues are implicitly dependent on the angular eigenvalues through the order of the Bessel functions which constitute the radial eigenfunctions. Therefore, for each eigenvalue in the angular direction, corresponding radial eigenvalues must be obtained. Solution is valid for any combination of homogenous boundary condition of the first or second kind in the angular direction. However, inhomogeneous boundary conditions of the third kind are applied in the radial direction. Proposed solution is also applicable to multiple layers with zero inner radius. An illustrative example problem for the three-layer semi-circular annular region is solved. Results along with the isotherms are shown graphically and discussed.
TL;DR: In this article, the drift flux model is used to make the set of equations dimensionless to ensure the mutual independence of the dimensionless variables and parameters: the steady-state inlet velocity v, the inlet subcooling number N sub and the phase change number N pch.
Abstract: Linear and nonlinear mathematical stability analyses of parallel channel density wave oscillations are reported. The two phase flow is represented by the drift flux model. A constant characteristic velocity v 0 ∗ is used to make the set of equations dimensionless to ensure the mutual independence of the dimensionless variables and parameters: the steady-state inlet velocity v , the inlet subcooling number N sub and the phase change number N pch . The exact equation for the total channel pressure drop is perturbed about the steady-state for the linear and nonlinear analyses. The surface defining the marginal stability boundary (MSB) is determined in the three-dimensional equilibrium-solution/operating-parameter space v − N sub − N pch . The effects of the void distribution parameter C 0 and the drift velocity V g j on the MSB are examined. The MSB is shown to be sensitive to the value of C 0 and comparison with experimental data shows that the drift flux model with C 0 > 1 predicts the experimental MSB and the neighboring region of stable oscillations (limit cycles) considerably better than do the homogeneous equilibrium model ( C 0 = 1, V g j = 0 ) or a slip flow model. The nonlinear analysis shows that supercritical Hopf bifurcation occurs for the regions of parameter space studied; hence stable oscillatory solutions exist in the linearly unstable region in the vicinity of the MSB. That is, the stable fixed point v becomes unstable and bifurcates to a stable limit cycle as the MSB is crossed by varying N sub and/or N pch .
TL;DR: In this paper, an analytical double-series solution for the time-dependent asymmetric heat conduction in a multilayer annulus is presented, where real eigenvalues are obtained by virtue of precluded explicit dependence of transverse (radial) eigen values on those in the other direction.
Abstract: In this paper, we present an analytical double-series solution for the time-dependent asymmetric heat conduction in a multilayer annulus. In general, analytical solutions in multidimensional Cartesian or cylindrical r,z coordinates suffer from existence of imaginary eigenvalues and thus may lead to numerical difficulties in computing analytical solution. In contrast, the proposed analytical solution in polar coordinates (2D cylindrical) is “free” from such imaginary eigenvalues. Real eigenvalues are obtained by virtue of precluded explicit dependence of transverse (radial) eigenvalues on those in the other direction. DOI: 10.1115/1.2977553
TL;DR: A new and related complexity measure is developed, sample entropy (SampEn), and a comparison of ApEn and SampEn is compared by using them to analyze sets of random numbers with known probabilistic character, finding SampEn agreed with theory much more closely than ApEn over a broad range of conditions.
Abstract: Entropy, as it relates to dynamical systems, is the rate of information production. Methods for estimation of the entropy of a system represented by a time series are not, however, well suited to analysis of the short and noisy data sets encountered in cardiovascular and other biological studies. Pincus introduced approximate entropy (ApEn), a set of measures of system complexity closely related to entropy, which is easily applied to clinical cardiovascular and other time series. ApEn statistics, however, lead to inconsistent results. We have developed a new and related complexity measure, sample entropy (SampEn), and have compared ApEn and SampEn by using them to analyze sets of random numbers with known probabilistic character. We have also evaluated cross-ApEn and cross-SampEn, which use cardiovascular data sets to measure the similarity of two distinct time series. SampEn agreed with theory much more closely than ApEn over a broad range of conditions. The improved accuracy of SampEn statistics should make them useful in the study of experimental clinical cardiovascular and other biological time series.
TL;DR: Although a variety of univariate statistics are included, certain topics that are important in medical research are not, and there is little or no discussion of multiple regression, life-table techniques, or pooling of studies.
Abstract: This book attempts to achieve a difficult goal: to teach statistics to the novice so as to impart a liking and understanding of statistics. The book is geared toward a medical audience, since most examples are from the medical literature. The structure of the book consists of the following elements in each chapter: a small number of statistical rules of thumb, followed by a nontechnical explanation, a demonstration of how to work through the mechanics of doing the statistical test in question, a summary, and sample problems to be solved by the reader. (The answers, with explanations, are provided in an appendix.) Although a variety of univariate statistics are included, certain topics that are important in medical research are not. For example, there is little or no discussion of multiple regression, life-table techniques, or pooling of studies. These omissions, especially of multiple regression, are unfortunate. The Primer was derived from
TL;DR: In this paper, the role of turbulence and magnetic fields in star formation in molecular clouds is studied, and it is shown that the SFR depends on four basic parameters: (1) virial parameter αvir; (2) sonic Mach number ; (3) turbulent forcing parameter b, which is a measure for the fraction of energy driven in compressive modes; and (4) plasma with the Alfven Mach number.
Abstract: The role of turbulence and magnetic fields is studied for star formation in molecular clouds. We derive and compare six theoretical models for the star formation rate (SFR)—the Krumholz & McKee (KM), Padoan & Nordlund (PN), and Hennebelle & Chabrier (HC) models, and three multi-freefall versions of these, suggested by HC—all based on integrals over the log-normal distribution of turbulent gas. We extend all theories to include magnetic fields and show that the SFR depends on four basic parameters: (1) virial parameter αvir; (2) sonic Mach number ; (3) turbulent forcing parameter b, which is a measure for the fraction of energy driven in compressive modes; and (4) plasma with the Alfven Mach number . We compare all six theories with MHD simulations, covering cloud masses of 300 to 4 × 106 M ☉ and Mach numbers -50 and -∞, with solenoidal (b = 1/3), mixed (b = 0.4), and compressive turbulent (b = 1) forcings. We find that the SFR increases by a factor of four between and 50 for compressive turbulent forcing and αvir ~ 1. Comparing forcing parameters, we see that the SFR is more than 10 times higher with compressive than solenoidal forcing for simulations. The SFR and fragmentation are both reduced by a factor of two in strongly magnetized, trans-Alfvenic turbulence compared to hydrodynamic turbulence. All simulations are fit simultaneously by the multi-freefall KM and multi-freefall PN theories within a factor of two over two orders of magnitude in SFR. The simulated SFRs cover the range and correlation of SFR column density with gas column density observed in Galactic clouds, and agree well for star formation efficiencies SFE = 1%-10% and local efficiencies = 0.3-0.7 due to feedback. We conclude that the SFR is primarily controlled by interstellar turbulence, with a secondary effect coming from magnetic fields.
TL;DR: The basic principles of particle-tracking microrheology are established, describing the advantages of this approach over more conventional approaches to cell mechanics, and basic concepts of molecular mechanics and polymer physics relevant to themicrorheological response of cells are presented.
Abstract: A multitude of cellular and subcellular processes depend critically on the mechanical deformability of the cytoplasm. We have recently introduced the method of particle-tracking microrheology, which measures the viscoelastic properties of the cytoplasm locally and with high spatiotemporal resolution. Here we establish the basic principles of particle-tracking microrheology, describing the advantages of this approach over more conventional approaches to cell mechanics. We present basic concepts of molecular mechanics and polymer physics relevant to the microrheological response of cells. Particle-tracking microrheology can probe the mechanical properties of live cells in experimentally difficult, yet more physiological, environments, including cells embedded inside a 3D matrix, adherent cells subjected to shear flows, and cells inside a developing embryo. Particle-tracking microrheology can readily reveal the lost ability of diseased cells to resist shear forces.