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Full-Text Articles in Physics
Nonlinear Dynamics In Combinatorial Games: Renormalizing Chomp, Eric J. Friedman, Adam S. Landsberg
Nonlinear Dynamics In Combinatorial Games: Renormalizing Chomp, Eric J. Friedman, Adam S. Landsberg
WM Keck Science Faculty Papers
We develop a new approach to combinatorial games that reveals connections between such games and some of the central ideas of nonlinear dynamics: scaling behaviors, complex dynamics and chaos, universality, and aggregation processes. We take as our model system the combinatorial game Chomp, which is one of the simplest in a class of "unsolved" combinatorial games that includes Chess, Checkers, and Go. We discover that the game possesses an underlying geometric structure that "grows" (reminiscent of crystal growth), and show how this growth can be analyzed using a renormalization procedure adapted from physics. In effect, this methodology allows one to …
Behavior Of Coupled Automata, Reuben Gann, Jessica Venable, Eric J. Friedman, Adam S. Landsberg
Behavior Of Coupled Automata, Reuben Gann, Jessica Venable, Eric J. Friedman, Adam S. Landsberg
WM Keck Science Faculty Papers
We study the nature of statistical correlations that develop between systems of interacting self-organized critical automata (sandpiles). Numerical and analytical findings are presented describing the emergence of "synchronization" between sandpiles and the dependency of this synchronization on factors such as variations in coupling strength, toppling rule probabilities, symmetric versus asymmetric coupling rules, and numbers of sandpiles.
Large-Scale Synchrony In Weakly Interacting Automata, Eric J. Friedman, Adam S. Landsberg
Large-Scale Synchrony In Weakly Interacting Automata, Eric J. Friedman, Adam S. Landsberg
WM Keck Science Faculty Papers
We study the behavior of two spatially distributed (sandpile) models which are weakly linked with one another. Using a Monte Carlo implementation of the renormalization-group and algebraic methods, we describe how large-scale correlations emerge between the two systems, leading to synchronized behavior.
Spectral Equivalence Of Bosons And Fermions In One-Dimensional Harmonic Potentials, Michael Crescimanno, Adam S. Landsberg
Spectral Equivalence Of Bosons And Fermions In One-Dimensional Harmonic Potentials, Michael Crescimanno, Adam S. Landsberg
WM Keck Science Faculty Papers
Recently, Schmidt and Schnack [Physica A 260, 479 (1998)], following earlier references, reiterate that the specific heat of N noninteracting bosons in a one-dimensional harmonic well equals that of N noninteracting fermions in the same potential. We show that this peculiar relationship between heat capacities results from a more dramatic equivalence between Bose and Fermi systems. Namely, we prove that the excitations of such Bose and Fermi systems are spectrally equivalent. Two complementary proofs of this equivalence are provided; one based on a combinatoric argument, the other from analysis of the underlying dynamical symmetry group.
Disorder-Induced Desynchronization In A 2x2 Circular Josephson Junction Array, Adam S. Landsberg
Disorder-Induced Desynchronization In A 2x2 Circular Josephson Junction Array, Adam S. Landsberg
WM Keck Science Faculty Papers
Analytical results are presented which characterize the behavior of a dc-biased, two-dimensional circular array of overdamped Josephson junctions subject to increasing levels of disorder. It is shown that high levels of disorder can abruptly destroy the synchronous functioning of the array. We identify the transition boundary between synchronized and desynchronized behavior, along with the mechanism responsible for the loss of frequency locking. Comparisons with recent results for arrays with rectangular lattice geometries are described.
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 …
Effect Of Disorder On Synchronization In Prototype 2-Dimensional Josephson Arrays, Adam S. Landsberg, Yuri Braiman, Kurt Wiesenfeld
Effect Of Disorder On Synchronization In Prototype 2-Dimensional Josephson Arrays, Adam S. Landsberg, Yuri Braiman, Kurt Wiesenfeld
WM Keck Science Faculty Papers
We study the effects of quenched disorder on the dynamics of two-dimensional arrays of overdamped Josephson junctions. Disorder in both the junction critical currents and resistances is considered. Analytical results for small arrays are used to identify a physical mechanism which promotes frequency locking across each row of the array, and to show that no such locking mechanism exists between rows. The intrarow locking mechanism is surprisingly strong, so that a row can tolerate large amounts of disorder before frequency locking is destroyed.
Disorder And Synchronization In A Josephson Junction Plaquette, Adam S. Landsberg, Yuri Braiman, Kurt Wiesenfeld
Disorder And Synchronization In A Josephson Junction Plaquette, Adam S. Landsberg, Yuri Braiman, Kurt Wiesenfeld
WM Keck Science Faculty Papers
We describe the effects of disorder on the coherence properties of a 2 x 2 array of Josephson junctions (a "plaquette"). The disorder is introduced through variations in the junction characteristics. We show that the array will remain one-to-one frequency locked despite large amounts of the disorder, and determine analytically the maximum disorder that can be tolerated before a transition to a desynchronized state occurs. Connections with larger N x M arrays are also drawn.
Geometrical Phases And Symmetries In Dissipative Systems, Adam S. Landsberg
Geometrical Phases And Symmetries In Dissipative Systems, Adam S. Landsberg
WM Keck Science Faculty Papers
A geometrical phase is constructed for dissipative dynamical systems possessing continuous symmetries. It emerges as the natural analog of the holonomy associated with the adiabatic variation of parameters in quantum-mechanical and classical Hamiltonian systems. In continuous media, the physical manifestation of this phase is a spatial shift of a wave pattern, typically a translation or rotation. An illustration associated with pattern formation in fluids is provided.