Showing 21 - 30 of 94 Items
Effects of stochasticity on the length and behaviour of ecological transients
Date: 2021-07-01
Creator: Alan Hastings, Karen C. Abbott, Kim Cuddington, Tessa B. Francis, Ying Cheng, Lai, Andrew Morozov
Access: Open access
- There is a growing recognition that ecological systems can spend extended periods of time far away from an asymptotic state, and that ecological understanding will therefore require a deeper appreciation for how long ecological transients arise. Recent work has defined classes of deterministic mechanisms that can lead to long transients. Given the ubiquity of stochasticity in ecological systems, a similar systematic treatment of transients that includes the influence of stochasticity is important. Stochasticity can of course promote the appearance of transient dynamics by preventing systems from settling permanently near their asymptotic state, but stochasticity also interacts with deterministic features to create qualitatively new dynamics. As such, stochasticity may shorten, extend or fundamentally change a system's transient dynamics. Here, we describe a general framework that is developing for understanding the range of possible outcomes when random processes impact the dynamics of ecological systems over realistic time scales. We emphasize that we can understand the ways in which stochasticity can either extend or reduce the lifetime of transients by studying the interactions between the stochastic and deterministic processes present, and we summarize both the current state of knowledge and avenues for future advances.
Convexity Properties of the Diestel-Leader Group Γ_3(2)
Date: 2014-05-01
Creator: Peter J Davids
Access: Open access
- The Diestel-Leader groups are a family of groups first introduced in 2001 by Diestel and Leader in [7]. In this paper, we demonstrate that the Diestel-Leader group Γ3(2) is not almost convex with respect to a particular generating set S. Almost convexity is a geometric property that has been shown by Cannon [3] to guarantee a solvable word problem (that is, in any almost convex group there is a finite-step algorithm to determine if two strings of generators, or “words”, represent the same group element). Our proof relies on the word length formula given by Stein and Taback in [10], and we construct a family of group elements X that contradicts the almost convexity condition. We then go on to show that Γ3(2) is minimally almost convex with respect to S.
Instability in a Time-Modulated Lattice This record is embargoed.
- Embargo End Date: 2025-05-19
Date: 2022-01-01
Creator: Evelyn Wallace
Access: Embargoed
Mathematically Modeling a Nonlinear, Passive Acoustic Filter This record is embargoed.
- Embargo End Date: 2026-05-18
Date: 2023-01-01
Creator: Bjorn Ludwig
Access: Embargoed
On L-functions and the 1-Level Density
Date: 2023-01-01
Creator: Arav Agarwal
Access: Open access
- We begin with the classical study of the Riemann zeta function and Dirichlet L-functions. This includes a full exposition on one of the most useful ways of exploiting their connection with primes, namely, explicit formulae. We then proceed to introduce statistics of low-lying zeros of Dirichlet L-functions, discussing prior results of Fiorilli and Miller (2015) on the 1-level density of Dirichlet L-functions and their achievement in surpassing the prediction of the powerful Ratios Conjecture. Finally, we present our original work partially generalizing these results to the case of Hecke L-functions over imaginary quadratic fields.
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.
Mechanical Autonomous Stochastic Heat Engine
Date: 2016-06-28
Creator: Marc Serra-Garcia, André Foehr, Miguel Molerón, Joseph Lydon, Christopher, Chong, Chiara Daraio
Access: Open access
- Stochastic heat engines are devices that generate work from random thermal motion using a small number of highly fluctuating degrees of freedom. Proposals for such devices have existed for more than a century and include the Maxwell demon and the Feynman ratchet. Only recently have they been demonstrated experimentally, using, e.g., thermal cycles implemented in optical traps. However, recent experimental demonstrations of classical stochastic heat engines are nonautonomous, since they require an external control system that prescribes a heating and cooling cycle and consume more energy than they produce. We present a heat engine consisting of three coupled mechanical resonators (two ribbons and a cantilever) subject to a stochastic drive. The engine uses geometric nonlinearities in the resonating ribbons to autonomously convert a random excitation into a low-entropy, nonpassive oscillation of the cantilever. The engine presents the anomalous heat transport property of negative thermal conductivity, consisting in the ability to passively transfer energy from a cold reservoir to a hot reservoir.
Damped-driven granular chains: An ideal playground for dark breathers and multibreathers
Date: 2014-03-31
Creator: C. Chong, F. Li, J. Yang, M. O. Williams, I. G., Kevrekidis, P. G. Kevrekidis
Access: Open access
- By applying an out-of-phase actuation at the boundaries of a uniform chain of granular particles, we demonstrate experimentally that time-periodic and spatially localized structures with a nonzero background (so-called dark breathers) emerge for a wide range of parameter values and initial conditions. We demonstrate a remarkable control over the number of breathers within the multibreather pattern that can be "dialed in" by varying the frequency or amplitude of the actuation. The values of the frequency (or amplitude) where the transition between different multibreather states occurs are predicted accurately by the proposed theoretical model, which is numerically shown to support exact dark breather and multibreather solutions. Moreover, we visualize detailed temporal and spatial profiles of breathers and, especially, of multibreathers using a full-field probing technology and enable a systematic favorable comparison among theory, computation, and experiments. A detailed bifurcation analysis reveals that the dark and multibreather families are connected in a "snaking" pattern, providing a roadmap for the identification of such fundamental states and their bistability in the laboratory. © 2014 American Physical Society.
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.
Module structure of cells in unequal-parameter Hecke algebras
Date: 2010-09-06
Creator: Thomas Pietraho
Access: Open access
- A conjecture of Bonnafé, Geck, Iancu, and Lam parametrizes Kazhdan-Lusztig left cells for unequal-parameter Hecke algebras in type Bn by families of standard domino tableaux of arbitrary rank. Relying on a family of properties outlined by Lusztig and the recent work of Bonnafé, we verify the conjecture and describe the structure of each cell as a module for the underlying Weyl group. © 2010 by The Editorial Board of the Nagoya Mathematical Journal.