91,513 research outputs found
Reduced-order modeling and dynamics of nonlinear acoustic waves in a combustion chamber
For understanding the fundamental properties of unsteady motions in combustion chambers, and for applications of active feedback control, reduced-order models occupy a uniquely important position. A framework exists for transforming the representation of general behavior by a set of infinite-dimensional partial differential equations to a finite set of nonlinear second-order ordinary
differential equations in time. The procedure rests on an expansion of the pressure and velocity fields in modal or basis functions, followed by spatial averaging to give the set of second-order equations in time. Nonlinear gasdynamics
is accounted for explicitly, but all other contributing processes require modeling. Reduced-order models of the global behavior of the chamber dynamics, most importantly of the pressure, are obtained simply by truncating the
modal expansion to the desired number of terms. Central to the procedures is a criterion for deciding how many modes must be retained to give accurate results. Addressing that problem is the principal purpose of this paper. Our
analysis shows that, in case of longitudinal modes, a first mode instability problem requires a minimum of four modes in the modal truncation whereas, for a second mode instability, one needs to retain at least the first eight modes. A second important problem concerns the conditions under which a linearly stable system becomes unstable to sufficiently large disturbances. Previous work has given a partial answer, suggesting that nonlinear gasdynamics alone cannot produce pulsed or 'triggered' true nonlinear instabilities; that suggestion is now theoretically established. Also, a certain form of the nonlinear energy
addition by combustion processes is known to lead to stable limit cycles in a linearly stable system. A second form of nonlinear combustion dynamics with a new velocity coupling function that naturally displays a threshold character
is shown here also to produce triggered limit cycle behavior
Soliton dynamics in gas-filled hollow-core photonic crystal fibers
Gas-filled hollow-core photonic crystal fibers offer unprecedented
opportunities to observe novel nonlinear phenomena. The various properties of
gases that can be used to fill these fibers give additional degrees of freedom
for investigating nonlinear pulse propagation in a wide range of different
media. In this review, we will consider some of the the new nonlinear
interactions that have been discovered in recent years, in particular those
which are based on soliton dynamics
The Surface Topography of a Magnetic Fluid -- a Quantitative Comparison between Experiment and Numerical Simulation
The normal field instability in magnetic liquids is investigated
experimentally by means of a radioscopic technique which allows a precise
measurement of the surface topography. The dependence of the topography on the
magnetic field is compared to results obtained by numerical simulations via the
finite element method. Quantitative agreement has been found for the critical
field of the instability, the scaling of the pattern amplitude and the detailed
shape of the magnetic spikes. The fundamental Fourier mode approximates the
shape to within 10% accuracy for a range of up to 40% of the bifurcation
parameter of this subcritical bifurcation. The measured control parameter
dependence of the wavenumber differs qualitatively from analytical predictions
obtained by minimization of the free energy.Comment: 21 pages, 16 figures; corrected typos, added reference to Kuznetsov
and Spector(1976), S.J. Fortune(1995) and Harkins&Jordan (1930). Figures
revise
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