32,266 research outputs found
Computation of unsteady momentum and heat transfer from a fixed circular cylinder in laminar flow
This paper presents a finite difference solution for 2D, low Reynolds number, unsteady flow around and heat transfer from a stationary circular cylinder placed in a uniform flow. The fluid is assumed to be incompressible and of constant property. The governing equations are the Navier-Stokes equations, the continuity equation, a Poisson equation for pressure and the energy equation. The temperature of the cylinder wall is kept constant and the viscous energy dissipation term is neglected in the energy equation. The computed Strouhal numbers, time-mean drag and base pressure coefficients, as well as the average Nusselt numbers compare well with existing experimental results
Stability of Oscillating Hexagons in Rotating Convection
Breaking the chiral symmetry, rotation induces a secondary Hopf bifurcation
in weakly nonlinear hexagon patterns which gives rise to oscillating hexagons.
We study the stability of the oscillating hexagons using three coupled
Ginzburg-Landau equations. Close to the bifurcation point we derive reduced
equations for the amplitude of the oscillation, coupled to the phase of the
underlying hexagons. Within these equation we identify two types of long-wave
instabilities and study the ensuing dynamics using numerical simulations of the
three coupled Ginzburg-Landau equations.Comment: 25 pages, 7 figure
Modeling oscillatory Microtubule--Polymerization
Polymerization of microtubules is ubiquitous in biological cells and under
certain conditions it becomes oscillatory in time. Here simple reaction models
are analyzed that capture such oscillations as well as the length distribution
of microtubules. We assume reaction conditions that are stationary over many
oscillation periods, and it is a Hopf bifurcation that leads to a persistent
oscillatory microtubule polymerization in these models. Analytical expressions
are derived for the threshold of the bifurcation and the oscillation frequency
in terms of reaction rates as well as typical trends of their parameter
dependence are presented. Both, a catastrophe rate that depends on the density
of {\it guanosine triphosphate} (GTP) liganded tubulin dimers and a delay
reaction, such as the depolymerization of shrinking microtubules or the decay
of oligomers, support oscillations. For a tubulin dimer concentration below the
threshold oscillatory microtubule polymerization occurs transiently on the
route to a stationary state, as shown by numerical solutions of the model
equations. Close to threshold a so--called amplitude equation is derived and it
is shown that the bifurcation to microtubule oscillations is supercritical.Comment: 21 pages and 12 figure
Birhythmicity, Synchronization, and Turbulence in an Oscillatory System with Nonlocal Inertial Coupling
We consider a model where a population of diffusively coupled limit-cycle
oscillators, described by the complex Ginzburg-Landau equation, interacts
nonlocally via an inertial field. For sufficiently high intensity of nonlocal
inertial coupling, the system exhibits birhythmicity with two oscillation modes
at largely different frequencies. Stability of uniform oscillations in the
birhythmic region is analyzed by means of the phase dynamics approximation.
Numerical simulations show that, depending on its parameters, the system has
irregular intermittent regimes with local bursts of synchronization or
desynchronization.Comment: 21 pages, many figures. Paper accepted on Physica
Asymptotic Properties of Difference Equations for Isotropic Loop Quantum Cosmology
In loop quantum cosmology, a difference equation for the wave function
describes the evolution of a universe model. This is different from the
differential equations that arise in Wheeler-DeWitt quantizations, and some
aspects of general properties of solutions can appear differently. Properties
of particular interest are boundedness and the presence of small-scale
oscillations. Continued fraction techniques are used to show in different
matter models the presence of special initial conditions leading to bounded
solutions, and an explicit expression for these initial values is derived.Comment: 27 pages, 2 figure
- …