3,651 research outputs found
Shock-resolved Navier–Stokes simulation of the Richtmyer–Meshkov instability start-up at a light–heavy interface
The single-mode Richtmyer–Meshkov instability is investigated using a first-order perturbation of the two-dimensional Navier–Stokes equations about a one-dimensional unsteady shock-resolved base flow. A feature-tracking local refinement scheme is used to fully resolve the viscous internal structure of the shock. This method captures perturbations on the shocks and their influence on the interface growth throughout the simulation, to accurately examine the start-up and early linear growth phases of the instability. Results are compared to analytic models of the instability, showing some agreement with predicted asymptotic growth rates towards the inviscid limit, but significant discrepancies are noted in the transient growth phase. Viscous effects are found to be inadequately predicted by existing models
A study of planar Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state
We present a numerical comparison study of planar Richtmyer-Meshkov instability with the intention of exposing the role of the equation of state. Results for Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state derived from a linear shock-particle speed Hugoniot relationship (Jeanloz, J. Geophys. Res. 94, 5873, 1989; McQueen et al., High Velocity Impact Phenomena (1970), pp. 294–417; Menikoff and Plohr, Rev. Mod. Phys. 61(1), 75 1989) are compared to those from perfect gases under nondimensionally matched initial conditions at room temperature and pressure. The study was performed using Caltech’s Adaptive Mesh Refinement, Object-oriented C++ (AMROC) (Deiterding, Adaptive Mesh Refinement: Theory and Applications (2005), Vol. 41, pp. 361–372; Deiterding, “Parallel adaptive simulation of multi-dimensional detonation structures,” Ph.D. thesis (Brandenburgische Technische Universität Cottbus, September 2003)) framework with a low-dissipation, hybrid, center-difference, limiter patch solver (Ward and Pullin, J. Comput. Phys. 229, 2999 (2010)). Results for single and triple mode planar Richtmyer-Meshkov instability when a reflected shock wave occurs are first examined for mid-ocean ridge basalt (MORB) and molybdenum modeled by Mie-Grüneisen equations of state. The single mode case is examined for incident shock Mach numbers of 1.5 and 2.5. The planar triple mode case is studied using a single incident Mach number of 2.5 with initial corrugation wavenumbers related by k_1 = k_2+k_3. Comparison is then drawn to Richtmyer-Meshkov instability in perfect gases with matched nondimensional pressure jump across the incident shock, post-shock Atwood ratio, post-shock amplitude-to-wavelength ratio, and time nondimensionalized by Richtmyer’s linear growth time constant prediction. Differences in start-up time and growth rate oscillations are observed across equations of state. Growth rate oscillation frequency is seen to correlate directly to the oscillation frequency for the transmitted and reflected shocks. For the single mode cases, further comparison is given for vorticity distribution and corrugation centerline shortly after shock interaction. Additionally, we examine single mode Richtmyer-Meshkov instability when a reflected expansion wave is present for incident Mach numbers of 1.5 and 2.5. Comparison to perfect gas solutions in such cases yields a higher degree of similarity in start-up time and growth rate oscillations. The formation of incipient weak waves in the heavy fluid driven by waves emanating from the perturbed transmitted shock is observed when an expansion wave is reflected
Numerical investigation of unsteady laminar incompressible co-axial boundary layer flows
Finite difference method for analysis of laminar incompressible boundary layer flows at jet exi
Moving constraints as stabilizing controls in classical mechanics
The paper analyzes a Lagrangian system which is controlled by directly
assigning some of the coordinates as functions of time, by means of
frictionless constraints. In a natural system of coordinates, the equations of
motions contain terms which are linear or quadratic w.r.t.time derivatives of
the control functions. After reviewing the basic equations, we explain the
significance of the quadratic terms, related to geodesics orthogonal to a given
foliation. We then study the problem of stabilization of the system to a given
point, by means of oscillating controls. This problem is first reduced to the
weak stability for a related convex-valued differential inclusion, then studied
by Lyapunov functions methods. In the last sections, we illustrate the results
by means of various mechanical examples.Comment: 52 pages, 4 figure
Formation Flight of Earth Satellites on Low-Eccentricity KAM Tori
The problem of Earth satellite constellation and formation flight is investigated in the context of Kolmogorov-Arnold-Moser (KAM) theory. KAM tori are constructed utilizing Wiesel’s Low-Eccentricity Earth Satellite Theory, allowing numerical representation of the perturbed tori describing Earth orbits acted upon by geopotential perturbations as sets of Fourier series. A maneuvering strategy using the local linearization of the KAM tangent space is developed and applied, demonstrating the ability to maneuver onto and within desired torus surfaces. Constellation and formation design and maintenance on KAM tori are discussed, along with stability and maneuver error concerns. It is shown that placement of satellites on KAM tori results in virtually no secular relative motion in the full geopotential to within computational precision. The effects of maneuver magnitude errors are quantified in terms of a singular value decomposition of the modal system for several orbits of interest, introducing a statistical distribution in terms of torus angle drift rates due to mismatched energies. This distribution is then used to create expectations of the steady-state station-keeping costs, showing that these costs are driven by operational and spacecraft limitations, and not by limitations of the dynamics formulation. A non-optimal continuous control strategy for formations based on Control Lyapunov Functions is also outlined and demonstrated in the context of formation reconfiguration
Sensitivity analysis of circadian entrainment in the space of phase response curves
Sensitivity analysis is a classical and fundamental tool to evaluate the role
of a given parameter in a given system characteristic. Because the phase
response curve is a fundamental input--output characteristic of oscillators, we
developed a sensitivity analysis for oscillator models in the space of phase
response curves. The proposed tool can be applied to high-dimensional
oscillator models without facing the curse of dimensionality obstacle
associated with numerical exploration of the parameter space. Application of
this tool to a state-of-the-art model of circadian rhythms suggests that it can
be useful and instrumental to biological investigations.Comment: 22 pages, 8 figures. Correction of a mistake in Definition 2.1. arXiv
admin note: text overlap with arXiv:1206.414
Phase reduction approach to synchronization of spatiotemporal rhythms in reaction-diffusion systems
Reaction-diffusion systems can describe a wide class of rhythmic
spatiotemporal patterns observed in chemical and biological systems, such as
circulating pulses on a ring, oscillating spots, target waves, and rotating
spirals. These rhythmic dynamics can be considered limit cycles of
reaction-diffusion systems. However, the conventional phase-reduction theory,
which provides a simple unified framework for analyzing synchronization
properties of limit-cycle oscillators subjected to weak forcing, has mostly
been restricted to low-dimensional dynamical systems. Here, we develop a
phase-reduction theory for stable limit-cycle solutions of infinite-dimensional
reaction-diffusion systems. By generalizing the notion of isochrons to
functional space, the phase sensitivity function - a fundamental quantity for
phase reduction - is derived. For illustration, several rhythmic dynamics of
the FitzHugh-Nagumo model of excitable media are considered. Nontrivial phase
response properties and synchronization dynamics are revealed, reflecting their
complex spatiotemporal organization. Our theory will provide a general basis
for the analysis and control of spatiotemporal rhythms in various
reaction-diffusion systems.Comment: 19 pages, 6 figures, see the journal for a full versio
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