Showing 31 - 40 of 94 Items
The spherical Bochner theorem on semisimple Lie groups
Date: 1975-01-01
Creator: William H. Barker
Access: Open access
- Let G be a connected semisimple Lie group with finite center and K a maximal compact subgroup. Denote (i) Harish-Chandra's Schwartz spaces by Cp(G)(0
Nonlinear localized modes in two-dimensional hexagonally-packed magnetic lattices
Date: 2021-04-01
Creator: Christopher Chong, Yifan Wang, Donovan Maréchal, Efstathios G. Charalampidis, Miguel, Molerón, Alejandro J. Martínez
Access: Open access
- We conduct an extensive study of nonlinear localized modes (NLMs), which are temporally periodic and spatially localized structures, in a two-dimensional array of repelling magnets. In our experiments, we arrange a lattice in a hexagonal configuration with a light-mass defect, and we harmonically drive the center of the chain with a tunable excitation frequency, amplitude, and angle. We use a damped, driven variant of a vector Fermi-Pasta-Ulam-Tsingou lattice to model our experimental setup. Despite the idealized nature of this model, we obtain good qualitative agreement between theory and experiments for a variety of dynamical behaviors. We find that the spatial decay is direction-dependent and that drive amplitudes along fundamental displacement axes lead to nonlinear resonant peaks in frequency continuations that are similar to those that occur in one-dimensional damped, driven lattices. However, we observe numerically that driving along other directions results in asymmetric NLMs that bifurcate from the main solution branch, which consists of symmetric NLMs. We also demonstrate both experimentally and numerically that solutions that appear to be time-quasiperiodic bifurcate from the branch of symmetric time-periodic NLMs.
Automorphisms of higher rank lamplighter groups
Date: 2015-12-01
Creator: Melanie Stein, Jennifer Taback, Peter Wong
Access: Open access
- Let τd(q) denote the group whose Cayley graph with respect to a particular generating set is the Diestel-Leader graph DLd(q), as described by Bartholdi, Neuhauser and Woess. We compute both Aut(τd(q)) and Out(τd(q)) for d ≥ 2, and apply our results to count twisted conjugacy classes in these groups when d ≥ 3. Specifically, we show that when d ≥ 3, the groups τd(q) have property R∞, that is, every automorphism has an infinite number of twisted conjugacy classes. In contrast, when d = 2 the lamplighter groups τ2(q) = Lq = Zq Z have property R∞ if and only if (q, 6)≠1.
Convergence of successive approximation methods with parameter target sets
Date: 2005-01-01
Creator: A.B. Levy
Access: Open access
Balancing Survival and Extinction in Nonautonomous Competitive Lotka-Volterra Systems
Date: 1995-06-01
Creator: F. Montes de Oca, M. L. Zeeman
Access: Open access
- We generalise and unify some recent results about extinction in nth-order nonautonomous competitive Lotka-Volterra systems. For each r ≤ n, we show that if the coefficients are continuous, bounded by strictly positive constants, and satisfy certain inequalities, then any solution with strictly positive initial values has the property that n - r of its components vanish, whilst the remaining r components asymptotically approach a canonical solution of an r-dimensional restricted system. In other words, r of the species being modeled survive whilst the remaining n - r are driven to extinction. © 1995 Academic Press, Inc.
Free limits of Thompson's group F
Date: 2011-12-01
Creator: Azer Akhmedov, Melanie Stein, Jennifer Taback
Access: Open access
- We produce a sequence of markings Sk of Thompson's group F within the space Gn of all marked n-generator groups so that the sequence (F, Sk) converges to the free group on n generators, for n ≥ 3. In addition, we give presentations for the limits of some other natural (convergent) sequences of markings to consider on F within G3, including (F, {x0, x1, xn}) and (F, {x0, x1, x0n}) © 2011 Springer Science+Business Media B.V.
Dead end words in lamplighter groups and other wreath products
Date: 2005-09-22
Creator: Sean Cleary, Jennifer Taback
Access: Open access
- We explore the geometry of the Cayley graphs of the lamplighter groups and a wide range of wreath products. We show that these groups have dead end elements of arbitrary depth with respect to their natural generating sets. An element w in a group G with finite generating set X is a dead end element if no geodesic ray from the identity to w in the Cayley graph Γ(G, X) can be extended past w. Additionally, we describe some non-convex behaviour of paths between elements in these Cayley graphs and seesaw words, which are potential obstructions to these graphs satisfying the k-fellow traveller property. © The Author 2005. Published by Oxford University Press. All rights reserved.
Breathers and other time-periodic solutions in an array of cantilevers decorated with magnetsy
Date: 2019-01-01
Creator: Christopher Chong, Andre Foehr, Efstathios G. Charalampidis, Panayotis G. Kevrekidis, Chiara, Daraio
Access: Open access
- In this article, the existence, stability and bifurcation structure of time-periodic solutions (including ones that also have the property of spatial localization, i.e., breathers) are studied in an array of cantilevers that have magnetic tips. The repelling magnetic tips are responsible for the intersite nonlinearity of the system, whereas the cantilevers are responsible for the onsite (potentially nonlinear) force. The relevant model is of the mixed Fermi-Pasta-Ulam-Tsingou and Klein-Gordon type with both damping and driving. In the case of base excitation, we provide experimental results to validate the model. In particular, we identify regions of bistability in the model and in the experiment, which agree with minimal tuning of the system parameters. We carry out additional numerical explorations in order to contrast the base excitation problem with the boundary excitation problem and the problem with a single mass defect. We find that the base excitation problem is more stable than the boundary excitation problem and that breathers are possible in the defect system. The effect of an onsite nonlinearity is also considered, where it is shown that bistability is possible for both softening and hardening cubic nonlinearities.
Bounding right-arm rotation distances
Date: 2007-03-01
Creator: Sean Cleary, Jennifer Taback
Access: Open access
- Rotation distance measures the difference in shape between binary trees of the same size by counting the minimum number of rotations needed to transform one tree to the other. We describe several types of rotation distance where restrictions are put on the locations where rotations are permitted, and provide upper bounds on distances between trees with a fixed number of nodes with respect to several families of these restrictions. These bounds are sharp in a certain asymptotic sense and are obtained by relating each restricted rotation distance to the word length of elements of Thompson's group F with respect to different generating sets, including both finite and infinite generating sets. © World Scientific Publishing Company.
Modeling Oyster Growth Dynamics in FLUPSY Systems to Develop a Decision Support Tool for Seed Management
Date: 2023-01-01
Creator: Gretchen Clauss
Access: Open access
- As the Gulf of Maine warms and lobsters move north to colder waters, Maine’s working water front has begun to diversify. There is a thriving new ecosystem of aquaculturists looking to keep Maine’s waterfront traditions alive in a lasting, sustainable way. One of the most popular aquaculture industries is oyster farming. With an increasing number of oyster farms developing in Midcoast Maine each year, we seek to develop a decision support tool to aid farmers in seed management. Oyster farmers can choose weather or not to use an upweller on their farm, and our goal is to provide guidance on this choice, as well as on upweller management. We begin by culminating and synthesizing data from previous literature and oyster farmers. We then use this data to first build a basic analytical model of a cohort of oysters based on an exponential growth model. We expand this model to include biological differences among oysters as well as management practices. Finally, we walk through a case study, illustrating how our tool could be used to make seed management decisions on an individual farm scale.