Showing 1 - 50 of 96 Items

Date: 2016-10-01

Creator: Gil Yong Lee, Christopher Chong, Panayotis G. Kevrekidis, Jinkyu Yang

Access: Open access

We investigate wave mixing effects in a phononic crystal that couples the wave dynamics of two channels – primary and control ones – via a variable stiffness mechanism. We demonstrate analytically and numerically that the wave transmission in the primary channel can be manipulated by the control channel's signal. We show that the application of control waves allows the selection of a specific mode through the primary channel. We also demonstrate that the mixing of two wave modes is possible whereby a modulation effect is observed. A detailed study of the design parameters is also carried out to optimize the switching capabilities of the proposed system. Finally, we verify that the system can fulfill both switching and amplification functionalities, potentially enabling the realization of an acoustic transistor.

Date: 2010-01-13

Creator: Sean Cleary, Murray Elder, Andrew Rechnitzer, Jennifer Taback

Access: Open access

We consider random subgroups of Thompson's group F with respect to two natural stratifications of the set of all k-generator subgroups. We find that the isomorphism classes of subgroups which occur with positive density are not the same for the two stratifications. We give the first known examples of persistent subgroups, whose isomorphism classes occur with positive density within the set of k-generator subgroups, for all sufficiently large k. Additionally, Thompson's group provides the first example of a group without a generic isomorphism class of subgroup. Elements of F are represented uniquely by reduced pairs of finite rooted binary trees. We compute the asymptotic growth rate and a generating function for the number of reduced pairs of trees, which we show is D-finite (short for differentiably finite) and not algebraic. We then use the asymptotic growth to prove our density results. © European Mathematical Society.

Date: 2017-12-01

Creator: Alia Hamieh, Naomi Tanabe

Access: Open access

In this paper, we prove that a primitive Hilbert cusp form g is uniquely determined by the central values of the Rankin-Selberg L-functions (formula presented), where f runs through all primitive Hilbert cusp forms of level q for infinitely many prime ideals q. This result is a generalization of the work of Luo (1999) to the setting of totally real number fields.

Date: 2013-01-01

Creator: Alex H. Williams, Molly A. Kwiatkowski, Adam L. Mortimer, Eve Marder, Mary Lou, Zeeman, Patsy S. Dickinson

Access: Open access

The cardiac ganglion (CG) of Homarus americanus is a central pattern generator that consists of two oscillatory groups of neurons: "small cells" (SCs) and "large cells" (LCs). We have shown that SCs and LCs begin their bursts nearly simultaneously but end their bursts at variable phases. This variability contrasts with many other central pattern generator systems in which phase is well maintained. To determine both the consequences of this variability and how CG phasing is controlled, we modeled the CG as a pair of Morris-Lecar oscillators coupled by electrical and excitatory synapses and constructed a database of 15,000 simulated networks using random parameter sets. These simulations, like our experimental results, displayed variable phase relationships, with the bursts beginning together but ending at variable phases. The model suggests that the variable phasing of the pattern has important implications for the functional role of the excitatory synapses. In networks in which the two oscillators had similar duty cycles, the excitatory coupling functioned to increase cycle frequency. In networks with disparate duty cycles, it functioned to decrease network frequency. Overall, we suggest that the phasing of the CG may vary without compromising appropriate motor output and that this variability may critically determine how the network behaves in response to manipulations. © 2013 the American Physiological Society.

Date: 2018-09-13

Creator: E. G. Charalampidis, J. Lee, P. G. Kevrekidis, C. Chong

Access: Open access

We present a theoretical study of extreme events occurring in phononic lattices. In particular, we focus on the formation of rogue or freak waves, which are characterized by their localization in both spatial and temporal domains. We consider two examples. The first one is the prototypical nonlinear mass-spring system in the form of a homogeneous Fermi-Pasta-Ulam-Tsingou (FPUT) lattice with a polynomial potential. By deriving an approximation based on the nonlinear Schrödinger (NLS) equation, we are able to initialize the FPUT model using a suitably transformed Peregrine soliton solution of the NLS equation, obtaining dynamics that resembles a rogue wave on the FPUT lattice. We also show that Gaussian initial data can lead to dynamics featuring a rogue wave for sufficiently wide Gaussians. The second example is a diatomic granular crystal exhibiting rogue-wave-like dynamics, which we also obtain through an NLS reduction and numerical simulations. The granular crystal (a chain of particles that interact elastically) is a widely studied system that lends itself to experimental studies. This study serves to illustrate the potential of such dynamical lattices towards the experimental observation of acoustic rogue waves.

Date: 2018-09-07

Creator: Alan Hastings, Karen C. Abbott, Kim Cuddington, Tessa Francis, Gabriel, Gellner, Ying Cheng Lai

Access: Open access

The importance of transient dynamics in ecological systems and in the models that describe them has become increasingly recognized. However, previous work has typically treated each instance of these dynamics separately. We review both empirical examples and model systems, and outline a classification of transient dynamics based on ideas and concepts from dynamical systems theory. This classification provides ways to understand the likelihood of transients for particular systems, and to guide investigations to determine the timing of sudden switches in dynamics and other characteristics of transients. Implications for both management and underlying ecological theories emerge.

Date: 2015-05-01

Creator: Daniel C Byrnes

Access: Open access

In order to identify potentially profitable investment strategies, hedge funds and asset managers can use historical market data to simulate a strategy's performance, a process known as backtesting. While the abundance of historical stock price data and powerful computing technologies has made it feasible to run millions of simulations in a short period of time, this process may produce statistically insignificant results in the form of false positives. As the number of configurations of a strategy increases, it becomes more likely that some of the configurations will perform well by chance alone. The phenomenon of backtest overfitting occurs when a model interprets market idiosyncrasies as signal rather than noise, and is often not taken into account in the strategy selection process. As a result, the finance industry and academic literature are rife with skill-less strategies that have no capability of beating the market. This paper explores the development of a minimum criterion that managers and investors can use during the backtesting process in order to increase confidence that a strategy's performance is not the result of pure chance. To do this we will use extreme value theory to determine the probability of observing a specific result, or something more extreme than this result, given that multiple configurations of a strategy were tested.

Date: 2021-01-01

Creator: Max Thrush Hukill

Access: Open access

The standard statistical methodology for analyzing complex case-control studies in ethology is often limited by approaches that force researchers to model distinct aspects of biological processes in a piecemeal, disjointed fashion. By developing a hierarchical Bayesian model, this work demonstrates that statistical inference in this context can be done using a single coherent framework. To do this, we construct a continuous-time Markov chain (CTMC) to model bumblebee foraging behavior. To connect the experimental design with the CTMC, we employ a mixture model controlled by a logistic regression on the two-factor design matrix. We then show how to infer these model parameters from experimental data using Markov chain Monte Carlo and interpret the results from a motivating experiment.

Date: 2006-04-01

Creator: R. Carretero-González, J. D. Talley, C. Chong, B. A. Malomed

Access: Open access

We analyze the existence and stability of localized solutions in the one-dimensional discrete nonlinear Schrödinger (DNLS) equation with a combination of competing self-focusing cubic and defocusing quintic onsite nonlinearities. We produce a stability diagram for different families of soliton solutions that suggests the (co)existence of infinitely many branches of stable localized solutions. Bifurcations that occur with an increase in the coupling constant are studied in a numerical form. A variational approximation is developed for accurate prediction of the most fundamental and next-order solitons, together with their bifurcations. Salient properties of the model, which distinguish it from the well-known cubic DNLS equation, are the existence of two different types of symmetric solitons and stable asymmetric soliton solutions that are found in narrow regions of the parameter space. The asymmetric solutions appear from and disappear back into the symmetric ones via loops of forward and backward pitchfork bifurcations. © 2006 Elsevier Ltd. All rights reserved.

Date: 2010-01-01

Creator: Thomas Pietraho

Access: Open access

We describe a map relating hyperoctahedral Robinson-Schensted algorithms on standard domino tableaux of unequal rank. Iteration of this map relates the algorithms defined by Garfinkle and Stanton-White and when restricted to involutions, this construction answers a question posed by van Leeuwen. The principal technique is derived from operations defined on standard domino tableaux by Garfinkle which must be extended to this more general setting. © Birkhäuser Verlag Basel/Switzerland 2009.

Date: 2016-11-01

Creator: Aba Mbirika, Thomas Pietraho, William Silver

Access: Open access

We present a formula for the values of the sign representations of a complex reflection group G(r, p, n) in terms of its image under a generalized Robinson–Schensted algorithm.

Date: 2013-04-08

Creator: C. Chong, P. G. Kevrekidis, G. Theocharis, Chiara Daraio

Access: Open access

We present a study of the existence, stability, and bifurcation structure of families of dark breathers in a one-dimensional uniform chain of spherical beads under static load. A defocusing nonlinear Schrödinger equation (NLS) is derived for frequencies that are close to the edge of the phonon band and is used to construct targeted initial conditions for numerical computations. Salient features of the system include the existence of large amplitude solutions that emerge from the small amplitude solutions described by the NLS equation, and the presence of a nonlinear instability that, to the best of the authors' knowledge, has not been observed in classical Fermi-Pasta-Ulam lattices. Finally, it is also demonstrated that these dark breathers can be detected in a physically realistic experimental settings by merely actuating the ends of an initially at rest chain of beads and inducing destructive interference between their signals. © 2013 American Physical Society.

Date: 2015-11-01

Creator: Jennifer Taback, Sharif Younes

Access: Open access

The definition of graph automatic groups by Kharlampovich, Khoussainov and Miasnikov and its extension to C-graph automatic by Elder and the first author raise the question of whether Thompson's group F is graph automatic. We define a language of normal forms based on the combinatorial "caret types", which arise when elements of F are considered as pairs of finite rooted binary trees. The language is accepted by a finite state machine with two counters, and forms the basis of a 3-counter graph automatic structure for the group.

• Embargo End Date: 2026-05-18

Date: 2023-01-01

Creator: Ari Geisler

Access: Embargoed

Date: 2022-01-01

Creator: Yucheng Hua

Access: Open access

The theory of functional approximation has numerous applications in sciences and industry. This thesis focuses on the possible approaches to approximate a continuous function on a compact subset of R2 using a variety of constructions. The results are presented from the following four general topics: polynomials, Fourier series, wavelets, and neural networks. Approximation with polynomials on subsets of R leads to the discussion of the Stone-Weierstrass theorem. Convergence of Fourier series is characterized on the unit circle. Wavelets are introduced following the Fourier transform, and their construction as well as ability to approximate functions in L2(R) is discussed. At the end, the universal approximation theorem for artificial neural networks is presented, and the function representation and approximation with single- and multilayer neural networks on R2 is constructed.

Date: 2023-01-01

Creator: Ethan Winters

Access: Open access

This work builds up the theory surrounding a recent result of Erlandsson, Leininger, and Sadanand: the Current Support Theorem. This theorem states precisely when a hyperbolic cone metric on a surface is determined by the support of its Liouville current. To provide background for this theorem, we will cover hyperbolic geometry and hyperbolic surfaces more generally, cone surfaces, covering spaces of surfaces, the notion of an orbifold, and geodesic currents. A corollary to this theorem found in the original paper is discussed which asserts that a surface with more than $32(g-1)$ cone points must be rigid. We extend this result to the case that there are more than $3(g-1)$ cone points. An infinite family of cone surfaces which are not rigid and which have precisely $3(g-1)$ cone points is also provided, hence demonstrating tightness.

Date: 1991-01-01

Creator: M. Alfaro, M. Conger, K. Hodges, A. Levy, R., Kochar, L. Kuklinski

Access: Open access

Date: 2008-10-13

Creator: Thomas Pietraho

Access: Open access

We examine the partition of a finite Coxeter group of type B into cells determined by a weight function L. The main objective of these notes is to reconcile Lusztig's description of constructible representations in this setting with conjectured combinatorial descriptions of cells.

Date: 2003-01-01

Creator: Jennifer Taback, Kevin Whyte

Access: Open access

Date: 2011-12-01

Creator: Sean Cleary, Susan Hermiller, Melanie Stein, Jennifer Taback

Access: Open access

We give the first examples of groups which admit a tame combing with linear radial tameness function with respect to any choice of finite presentation, but which are not minimally almost convex on a standard generating set. Namely, we explicitly construct such combings for Thompson's group F and the Baumslag-Solitar groups BS(1, p) with p ≥ 3. In order to make this construction for Thompson's group F, we significantly expand the understanding of the Cayley complex of this group with respect to the standard finite presentation. In particular we describe a quasigeodesic set of normal forms and combinatorially classify the arrangements of 2-cells adjacent to edges that do not lie on normal form paths. © 2010 Springer-Verlag.

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.

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.

• Embargo End Date: 2025-05-19

Date: 2022-01-01

Creator: Evelyn Wallace

Access: Embargoed

• Embargo End Date: 2026-05-18

Date: 2023-01-01

Creator: Bjorn Ludwig

Access: Embargoed

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.

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.

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.

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.

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.

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.

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

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.

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.

Date: 2005-01-01

Creator: A.B. Levy

Access: Open access

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.

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.

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.

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.

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.

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.

Date: 2016-04-15

Creator: H. Yasuda, C. Chong, E. G. Charalampidis, P. G. Kevrekidis, J., Yang

Access: Open access

We investigate the nonlinear wave dynamics of origami-based metamaterials composed of Tachi-Miura polyhedron (TMP) unit cells. These cells exhibit strain softening behavior under compression, which can be tuned by modifying their geometrical configurations or initial folded conditions. We assemble these TMP cells into a cluster of origami-based metamaterials, and we theoretically model and numerically analyze their wave transmission mechanism under external impact. Numerical simulations show that origami-based metamaterials can provide a prototypical platform for the formation of nonlinear coherent structures in the form of rarefaction waves, which feature a tensile wavefront upon the application of compression to the system. We also demonstrate the existence of numerically exact traveling rarefaction waves in an effective lumped-mass model. Origami-based metamaterials can be highly useful for mitigating shock waves, potentially enabling a wide variety of engineering applications.

Date: 2015-01-01

Creator: E. G. Charalampidis, F. Li, C. Chong, J. Yang, P. G., Kevrekidis

Access: Open access

We consider time-periodic structures of granular crystals consisting of alternate chrome steel (S) and tungsten carbide (W) spherical particles where each unit cell follows the pattern of a 2: 1 trimer: S-W-S. The configuration at the left boundary is driven by a harmonic in-time actuation with given amplitude and frequency while the right one is a fixed wall. Similar to the case of a dimer chain, the combination of dissipation, driving of the boundary, and intrinsic nonlinearity leads to complex dynamics. For fixed driving frequencies in each of the spectral gaps, we find that the nonlinear surface modes and the states dictated by the linear drive collide in a saddle-node bifurcation as the driving amplitude is increased, beyond which the dynamics of the system becomes chaotic. While the bifurcation structure is similar for solutions within the first and second gap, those in the first gap appear to be less robust. We also conduct a continuation in driving frequency, where it is apparent that the nonlinearity of the system results in a complex bifurcation diagram, involving an intricate set of loops of branches, especially within the spectral gap. The theoretical findings are qualitatively corroborated by the experimental full-field visualization of the time-periodic structures.

Date: 2017-02-22

Creator: S. P. Wallen, J. Lee, D. Mei, C. Chong, P. G., Kevrekidis, N. Boechler

Access: Open access

We report on the existence of discrete breathers in a one-dimensional, mass-in-mass chain with linear intersite coupling and nonlinear, precompressed Hertzian local resonators, which is motivated by recent studies of the dynamics of microspheres adhered to elastic substrates. After predicting theoretically the existence of discrete breathers in the continuum and anticontinuum limits of intersite coupling, we use numerical continuation to compute a family of breathers interpolating between the two regimes in a finite chain, where the displacement profiles of the breathers are localized around one lattice site. We then analyze the frequency-amplitude dependence of the breathers by performing numerical continuation on a linear eigenmode (vanishing amplitude) solution of the system near the upper band gap edge. Finally, we use direct numerical integration of the equations of motion to demonstrate the formation and evolution of the identified localized modes in energy-conserving and dissipative scenarios, including within settings that may be relevant to future experimental studies.

Date: 2001-01-01

Creator: M. Farkas, P. Van Den Driessche, M. L. Zeeman

Access: Open access

Criteria are given under which the boundary of an oriented surface does not consist entirely of trajectories of the C1 differential equation ẋ = f(x) in Rn. The special case of an annulus is further considered, and the criteria are used to deduce sufficient conditions for the differential equation to have at most one cycle. A bound on the number of cycles on surfaces of higher connectivity is given by similar conditions. ©2000 American Mathematical Society.

Date: 2004-07-01

Creator: Sean Cleary, Jennifer Taback

Access: Open access

We study some combinatorial consequences of Blake Fordham's theorems on the word metric of Thompson's group F in the standard two generator presentation. We explore connections between the tree pair diagram representing an element w of F, its normal form in the infinite presentation, its word length, and minimal length representatives of it. We estimate word length in terms of the number and type of carets in the tree pair diagram and show sharpness of those estimates. In addition we explore some properties of the Cayley graph of F with respect to the two generator finite presentation. Namely, we exhibit the form of "dead end" elements in this Cayley graph, and show that it has no "deep pockets". Finally, we discuss a simple method for constructing minimal length representatives for strictly positive or negative words.

Date: 2007-05-01

Creator: Murad Özaydin, Charlotte Simmons, Jennifer Taback

Access: Open access

We classify, up to conjugacy, all orientation-preserving actions of PSL2(p) on closed connected orientable surfaces with spherical quotients. This classification is valid in the topological, PL, smooth, conformal, geometric and algebraic categories and is related to the Inverse Galois Problem. © 2006 American Mathematical Society.

Date: 2014-09-01

Creator: Murray Elder, Jennifer Taback

Access: Open access

We generalize the notion of a graph automatic group introduced by Kharlampovich, Khoussainov and Miasnikov by replacing the regular languages in their definition with more powerful language classes. For a fixed language class C, we call the resulting groups C-graph automatic. We prove that the class of C-graph automatic groups is closed under change of generating set, direct and free product for certain classes C. We show that for quasi-realtime counter-graph automatic groups where normal forms have length that is linear in the geodesic length, there is an algorithm to compute normal forms (and therefore solve the word problem) in polynomial time. The class of quasi-realtime counter-graph automatic groups includes all Baumslag-Solitar groups, and the free group of countably infinite rank. Context-sensitive-graph automatic groups are shown to be a very large class, which encompasses, for example, groups with unsolvable conjugacy problem, the Grigorchuk group, and Thompson's groups F, T and V. © 2014 Elsevier Inc.

Date: 2016-05-01

Creator: Murray Elder, Jennifer Taback

Access: Open access

It is not known whether Thompson's group F is automatic. With the recent extensions of the notion of an automatic group to graph automatic by Kharlampovich, Khoussainov and Miasnikov and then to C-graph automatic by the authors, a compelling question is whether F is graph automatic or C-graph automatic for an appropriate language class C. The extended definitions allow the use of a symbol alphabet for the normal form language, replacing the dependence on generating set. In this paper we construct a 1-counter graph automatic structure for F based on the standard infinite normal form for group elements.

Date: 2008-11-01

Creator: Martina Chirilus-Bruckner, Christopher Chong, Guido Schneider, Hannes Uecker

Access: Open access

We give a detailed analysis of the interaction of two NLS-described wave packets with different carrier waves for a nonlinear wave equation. By separating the internal dynamics of each wave packet from the dynamics caused by the interaction we prove that there is almost no interaction of such wave packets. We also prove the validity of a formula for the envelope shift caused by the interaction of the wave packets. © 2008 Elsevier Inc. All rights reserved.

Date: 2019-01-01

Creator: Hiromi Yasuda, Yasuhiro Miyazawa, Efstathios G. Charalampidis, Christopher Chong, Panayotis G., Kevrekidis, Jinkyu Yang

Access: Open access

The principles underlying the art of origami paper folding can be applied to design sophisticated metamaterials with unique mechanical properties. By exploiting the flat crease patterns that determine the dynamic folding and unfolding motion of origami, we are able to design an origami-based metamaterial that can form rarefaction solitary waves. Our analytical, numerical, and experimental results demonstrate that this rarefaction solitary wave overtakes initial compressive strain waves, thereby causing the latter part of the origami structure to feel tension first instead of compression under impact. This counterintuitive dynamic mechanism can be used to create a highly efficient-yet reusable-impact mitigating system without relying on material damping, plasticity, or fracture.