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Full-Text Articles in Physical Sciences and Mathematics
Dynamical Effects Of Partial Orderings In Physical Systems, Adam S. Landsberg, Eric J. Friedman
Dynamical Effects Of Partial Orderings In Physical Systems, Adam S. Landsberg, Eric J. Friedman
WM Keck Science Faculty Papers
We demonstrate that many physical systems possess an often overlooked property known as a partial-ordering structure. The detection and analysis of this special geometric property can be crucial for understanding a system's dynamical behavior. We review here the fundamental dynamical features common to all such systems, and describe how the partial ordering imposes interesting restrictions on their possible behavior. We show, for instance, that though such systems are capable of displaying highly complex and even chaotic behaviors, most of their experimentally observable behaviors will be simple. Partial orderings are illustrated with examples drawn from many branches of physics, including solid …
Oscillatory Doubly Diffusive Convection In A Finite Container, Adam S. Landsberg, Edgar Knobloch
Oscillatory Doubly Diffusive Convection In A Finite Container, Adam S. Landsberg, Edgar Knobloch
WM Keck Science Faculty Papers
Oscillatory doubly diffusive convection in a large aspect ratio Hele-Shaw cell is considered. The partial differential equations are reduced via center-unstable manifold reduction to the normal form equations describing the interaction of even and odd parity standing waves near onset. These equations take the form of the equations for a Hopf bifurcation with approximate D4 symmetry, verifying the conclusions of the preceding paper [A.S. Landsberg and E. Knobloch, Phys. Rev. E 53, 3579 (1996)]. In particular, the amplitude equations differ in the limit of large aspect ratios from the usual Ginzburg-Landau description in having additional nonlinear terms with O(1) coefficients. …
Oscillatory Bifurcation With Broken Translation Symmetry, Adam S. Landsberg, Edgar Knobloch
Oscillatory Bifurcation With Broken Translation Symmetry, Adam S. Landsberg, Edgar Knobloch
WM Keck Science Faculty Papers
The effect of distant endwalls on the bifurcation to traveling waves is considered. Previous approaches have treated the problem by assuming that it is a weak perturbation of the translation invariant problem. When the problem is formulated instead in a finite box of length L and the limit L--> [infinity] is taken, one obtains amplitude equations that differ from the usual Ginzburg-Landau description by the presence of an additional nonlinear term. This formulation leads to a description in terms of the amplitudes of the primary box modes, which are odd and even parity standing waves. For large L, the equations …