Showing 61 - 70 of 94 Items
Metric properties of diestel-leader groups
Date: 2013-06-01
Creator: Melanie Stein, Jennifer Taback
Access: Open access
Equivalence classes in the Weyl groups of type Bn
Date: 2008-04-01
Creator: Thomas Pietraho
Access: Open access
- We consider two families of equivalence classes in the Weyl groups of type B n which are suggested by the study of left cells in unequal parameter Iwahori-Hecke algebras. Both families are indexed by a non-negative integer r. It has been shown that the first family coincides with left cells corresponding to the equal parameter Iwahori-Hecke algebra when r=0; the equivalence classes in the second family agree with left cells corresponding to a special class of choices of unequal parameters when r is sufficiently large. Our main result shows that the two families of equivalence classes coincide, suggesting the structure of left cells for remaining choices of the Iwahori-Hecke algebra parameters. © 2007 Springer Science+Business Media, LLC.
Convergence of successive approximation methods with parameter target sets
Date: 2005-01-01
Creator: A.B. Levy
Access: Open access
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.
Emergence of dispersive shocks and rarefaction waves in power-law contact models
Date: 2017-06-16
Creator: H. Yasuda, C. Chong, J. Yang, P. G. Kevrekidis
Access: Open access
- In the present work, motivated by generalized forms of the Hertzian dynamics associated with granular crystals, we consider the possibility of such models to give rise to both dispersive shock and rarefaction waves. Depending on the value p of the nonlinearity exponent, we find that both of these possibilities are realizable. We use a quasicontinuum approximation of a generalized inviscid Burgers model in order to predict the solution profile up to times near the formation of the dispersive shock, as well as to estimate when it will occur. Beyond that time threshold, oscillations associated with the highly dispersive nature of the underlying model emerge, which cannot be captured by the quasicontinuum approximation. Our analytical characterization of the above features is complemented by systematic numerical computations.
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.
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
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.
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.
Highly nonlinear wave propagation in elastic woodpile periodic structures
Date: 2015-03-17
Creator: E. Kim, F. Li, C. Chong, G. Theocharis, J., Yang, P. G. Kevrekidis
Access: Open access
- In the present work, we experimentally implement, numerically compute with, and theoretically analyze a configuration in the form of a single column woodpile periodic structure. Our main finding is that a Hertzian, locally resonant, woodpile lattice offers a test bed for the formation of genuinely traveling waves composed of a strongly localized solitary wave on top of a small amplitude oscillatory tail. This type of wave, called a nanopteron, is not only motivated theoretically and numerically, but is also visualized experimentally by means of a laser Doppler vibrometer. This system can also be useful for manipulating stress waves at will, for example, to achieve strong attenuation and modulation of high-amplitude impacts without relying on damping in the system.