The mechanism by which spiral wave patterns appear in populations of Dictyostelium was probed experimentally by external chemical perturbation. Spiral waves, which often arise from the breakup of circular waves driven...
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The mechanism by which spiral wave patterns appear in populations of Dictyostelium was probed experimentally by external chemical perturbation. Spiral waves, which often arise from the breakup of circular waves driven by pacemakers, typically entrain those pacemakers. We studied these processes by resetting the waves with a spatially uniform pulse of extrinsic cyclic AMP. A pattern of spirals reappeared if resetting was early in the signaling stage, but only targets emerged following late resetting, in a manner analogous to cardiac defibrillation. This supports recent hypotheses that wave pattern selection naturally occurs by slow temporal variation of the excitability of the cells.
Summary form only given. We used the finite-difference time-domain method to solve Maxwell equations. More specifically, we applied the non-dissipative Yee's algorithm with a duality relation between the spatial r...
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Summary form only given. We used the finite-difference time-domain method to solve Maxwell equations. More specifically, we applied the non-dissipative Yee's algorithm with a duality relation between the spatial representations of the electric and magnetic fields that represents both the differential and integral forms of Maxwell equations. The computational domain consists of 19 photonic lattice cells in the periodic structure for /spl epsi/ in the x and y direction and 8 mesh cells in the z direction. Each photonic lattice cell has been divided into 40/spl times/40 computational mesh cells, but due to duality of the discretization mesh, effectively we determined each field on only 20/spl times/20 points inside a photonic lattice cell. Periodic boundary conditions were used in all three directions. We observed the spatial distribution of the magnetic and electric fields and the movement of the mode resonance through the photonic band gap as the defect radius is changed. In addition, we determined the dependence of the localization (the field energy confined at the defect cell) on frequency (defect radius). We also found well localized defect modes.A defect in the form of an air hole with a modified radius was introduced in the center of a triangular lattice.
We present a numerical study of the localized transverse magnetic (TM) defect modes in a two-dimensional, triangular-lattice photonic crystal. The sample consists of an array of circular, air cylinders in a dielectric...
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We present a numerical study of the localized transverse magnetic (TM) defect modes in a two-dimensional, triangular-lattice photonic crystal. The sample consists of an array of circular, air cylinders in a dielectric medium (GaAs). The defect modes were calculated by using a parallel version of the finite-difference time-domain method on the Yee mesh. To validate our computations the results for the transverse electric case were checked against experimental results and the numerical results using a different method. We study the spatial symmetry for TM modes, obtained by changing the dipole excitation frequency. Also, we vary the defect-cylinder radius to tune the resonant frequency across the band gap. The TM mode is found to be highly localized at the defect in the photonic lattice.
A central problem in the mathematical analysis of fluid dynamics is the asymptotic limit of the fluid flow as viscosity goes to *** is particularly important when boundaries are present since vorticitv is typically ge...
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A central problem in the mathematical analysis of fluid dynamics is the asymptotic limit of the fluid flow as viscosity goes to *** is particularly important when boundaries are present since vorticitv is typically generated at the boundary as a result of boundary layer *** boundary laver theory,developed by Prandtl about a hundred years ago,has become a standard tool in addressing these *** at the mathematical level,there is still a lack of fundamental understanding of these questions and the validity of the boundary layer *** this article,we review recent progresses on the analysis of Prandtl’s equation and the related issue of the zero-viscosity limit for the solutions of the Navier-Stokes *** also discuss some directions where progress is expected in the near future.
Presents two algorithms for LC unconstrained optimization problems which use the second order Dini upper directional derivative. Simplicity of the methods to use and perform; Discussion of related properties of the it...
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Presents two algorithms for LC unconstrained optimization problems which use the second order Dini upper directional derivative. Simplicity of the methods to use and perform; Discussion of related properties of the iteration function.
We extend elasticity theory of filaments to encompass systems, such as bacterial flagella, that display competition between two helical structures of opposite chirality. A general, fully intrinsic formulation of the d...
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We extend elasticity theory of filaments to encompass systems, such as bacterial flagella, that display competition between two helical structures of opposite chirality. A general, fully intrinsic formulation of the dynamics of bend and twist degrees of freedom is developed using the natural frame of space curves, spanning from the inviscid limit to the viscously overdamped regime applicable to cellular biology. Aspects of front propagation found in flagella are discussed.
The dynamics of inertial elastic helical thin rods with noncircular cross sections and arbitrary intrinsic curvature, torsion, and twist is studied. The classical Kirchhoff equations are used together with a perturbat...
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The dynamics of inertial elastic helical thin rods with noncircular cross sections and arbitrary intrinsic curvature, torsion, and twist is studied. The classical Kirchhoff equations are used together with a perturbation scheme at the level of the director basis, and the dispersion relation for helical strips is derived and analyzed. It is shown that all naturally straight helical strips are unstable whereas free-standing helices are always stable. There exists a one-parameter family of stationary helical solutions depending on the ratio of curvature to torsion. A bifurcation analysis with respect to this parameter is performed, and bifurcation curves in the space of elastic parameters are identified. The different modes of instabilities are analyzed.
We obtain an explicit generalization, within Fokker-Planck dynamics, of Einstein's relation between drag, diffusion, and the equilibrium distribution for a spatially homogeneous system, considering both the transv...
We obtain an explicit generalization, within Fokker-Planck dynamics, of Einstein's relation between drag, diffusion, and the equilibrium distribution for a spatially homogeneous system, considering both the transverse and longitudinal diffusion for dimension n>1. We provide a complete characterization of the equilibrium distribution in terms of the drag and diffusion transport coefficients. We apply this analysis to charm quark dynamics in a thermal quark-gluon plasma for the case of collisional equilibration.
Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription and replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twis...
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Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription and replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twist and bend elasticity. Competition between twist injection, twist diffusion, and writhing instabilities is described by coupled PDEs for twist and bend evolution. Analytical and numerical methods elucidate the twist/bend coupling and reveal two regimes separated by a Hopf bifurcation: (i) diffusion-dominated axial rotation, or twirling, and (ii) steady-state crankshafting motion, or whirling. The consequences of these phenomena for self-propulsion are investigated, and experimental tests proposed.
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