Physical Sciences and Mathematics Commons^™

Autonomous Estimates Of Horizontal Decorrelation Lengths For Digital Elevation Models, Andres Corrada-Emmanuel, Howard Schultz

Andrés Corrada-Emmanuel

The precision errors in a collection of digital elevation models (DEMs) can be estimated in the presence of large but sparse correlations even when no ground truth is known. We demonstrate this by considering the problem of how to estimate the horizontal decorrelation length of DEMs produced by an automatic photogrammetric process that relies on the epipolar constraint equations. The procedure is based on a set of autonomous elevation difference equations recently proposed by us. In this paper we show that these equations can only estimate the precision errors of DEMs. The accuracy errors are unknowable since there is no …

Autonomous Estimates Of Horizontal Decorrelation Lengths For Digital Elevation Models, Andres Corrada-Emmanuel, Howard Schultz

Computer Science Department Faculty Publication Series

The precision errors in a collection of digital elevation models (DEMs) can be estimated in the presence of large but sparse correlations even when no ground truth is known. We demonstrate this by considering the problem of how to estimate the horizontal decorrelation length of DEMs produced by an automatic photogrammetric process that relies on the epipolar constraint equations. The procedure is based on a set of autonomous elevation difference equations recently proposed by us. In this paper we show that these equations can only estimate the precision errors of DEMs. The accuracy errors are unknowable since there is no …

Inspiration (And Perspiration) From Biology, Vm Rotello

Vincent Rotello

The exquisite structures produced by biological systems provide inspiration for the fabrication of nanomaterials. We sometimes forget, however, that Nature can provide muscle while serving as a Muse--a wide array of nanosystems are produced biologically that can be used for the design of functional materials. At the 2007 Materials Research Society Fall Meeting in Boston, Symposium MM (Biomolecular and Biologically Inspired Interfaces and Assemblies) highlighted the synergy between researchers using biomaterials and those using nature as a model for synthetic and quasi-synthetic systems. The symposium was organized by Vincent Rotello, Paula Hammond, Molly Stevens, Jeffrey Tok, and Darrin Pochan, with …

Local Torsion On Elliptic Curves And The Deformation Theory Of Galois Representations, C David, T Weston

Mathematics and Statistics Department Faculty Publication Series

No abstract provided.

Dipole And Quadrupole Solitons In Optically-Induced Two-Dimensional Defocusing Photonic Lattices, H Susanto, Kjh Law, Pg Kevrekidis, L Tang, C Lou, X Wang, Z Chen

Mathematics and Statistics Department Faculty Publication Series

We demonstrate a possibility to generate localized states in effectively one-dimensional Bose-Einstein condensates with a negative scattering length in the form of a dark soliton in the presence of an optical lattice (OL) and/or a parabolic magnetic trap. We connect such structures with twisted localized modes (TLMs) that were previously found in the discrete nonlinear Schrödinger equation. Families of these structures are found as functions of the OL strength, tightness of the magnetic trap and chemical potential, and their stability regions are identified. Stable bound states of two TLMs are also found. In the case when the TLMs are unstable, …

Dark Solitons In External Potentials, De Pelinovsky, Pg Kevrekidis

Mathematics and Statistics Department Faculty Publication Series

We consider the persistence and stability of dark solitons in the Gross–Pitaevskii (GP) equation with a small decaying potential. We show that families of black solitons with zero speed originate from extremal points of an appropriately defined effective potential and persist for sufficiently small strength of the potential. We prove that families at the maximum points are generally unstable with exactly one real positive eigenvalue, while families at the minimum points are generally unstable with exactly two complex-conjugated eigenvalues with positive real part. This mechanism of destabilization of the black soliton is confirmed in numerical approximations of eigenvalues of the …

Rabi Switch Of Condensate Wave Functions In A Multicomponent Bose Gas, He Nistazakis, Z Rapti, Dj Frantzeskakis, Pg Kevrekidis, P Sodano, A Trombettoni

Mathematics and Statistics Department Faculty Publication Series

Using a time-dependent linear (Rabi) coupling between the components of a weakly interacting multicomponent Bose-Einstein condensate (BEC), we propose a protocol for transferring the wave function of one component to the other. This “Rabi switch” can be generated in a binary BEC mixture by an electromagnetic field between the two components, typically two hyperfine states. When the wave function to be transferred is, at a given time, a stationary state of the multicomponent Hamiltonian, then, after a time delay (depending on the Rabi frequency), it is possible to have the same wave function on the other condensate. The Rabi switch …

Bright-Dark Soliton Complexes In Spinor Bose-Einstein Condensates, He Nistazakis, Dj Frantzeskakis, Pg Kevrekidis, Ba Malomed, R Carretero-Gonzalez

Mathematics and Statistics Department Faculty Publication Series

We consider vector solitons of mixed bright-dark types in quasi-one-dimensional spinor (F=1) Bose-Einstein condensates. Using a multiscale expansion technique, we reduce the corresponding nonintegrable system of three coupled Gross-Pitaevskii equations (GPEs) to an integrable Yajima-Oikawa system. In this way, we obtain approximate solutions for small-amplitude vector solitons of dark-dark-bright and bright-bright-dark types, in terms of the mF=+1,−1,0 spinor components, respectively. By means of numerical simulations of the full GPE system, we demonstrate that these states indeed feature soliton properties, i.e., they propagate undistorted and undergo quasielastic collisions. It is also shown that in the presence of a parabolic trap the …

Radially Symmetric Nonlinear States Of Harmonically Trapped Bose-Einstein Condensates, G Herring, Ld Carr, R Carretero-Gonzalez, Pg Kevrekidis, Dj Frantzeskakis

Mathematics and Statistics Department Faculty Publication Series

Starting from the spectrum of the radially symmetric quantum harmonic oscillator in two dimensions, we create a large set of nonlinear solutions. The relevant three principal branches, with nr=0,1, and 2 radial nodes, respectively, are systematically continued as a function of the chemical potential and their linear stability is analyzed in detail, in the absence as well as in the presence of topological charge m, i.e., vorticity. It is found that for repulsive interatomic interactions only the ground state is linearly stable throughout the parameter range examined. Furthermore, this is true for topological charges m=0 or 1; solutions with higher …

Lyapunov-Schmidt Reduction Algorithm For Three-Dimensional Discrete Vortices, M Lukas, D Pelinovsky, Pg Kevrekidis

Mathematics and Statistics Department Faculty Publication Series

We address the persistence and stability of three-dimensional vortex configurations in the discrete nonlinear Schrödinger equation and develop a symbolic package based on Wolfram’s MATHEMATICA for computations of the Lyapunov–Schmidt reduction method. The Lyapunov–Schmidt reduction method is a theoretical tool which enables us to study continuations and terminations of the discrete vortices for small coupling between lattice nodes as well as the spectral stability of the persistent configurations. The method was developed earlier in the context of the two-dimensional lattice and applied to the onsite and offsite configurations (called the vortex cross and the vortex cell) by using semianalytical computations …

Asymptotic Behavior Of The Magnetization Near Critical And Tricritical Points Via Ginzburg-Landau Polynomials, Rs Ellis, J Machta, Pth Otto

Mathematics and Statistics Department Faculty Publication Series

The purpose of this paper is to prove connections among the asymptotic behavior of the magnetization, the structure of the phase transitions, and a class of polynomials that we call the Ginzburg–Landau polynomials. The model under study is a mean-field version of a lattice spin model due to Blume and Capel. It is defined by a probability distribution that depends on the parameters β and K, which represent, respectively, the inverse temperature and the interaction strength. Our main focus is on the asymptotic behavior of the magnetization m(β _n ,K _n ) for appropriate sequences ( …

Cohomology Of Congruence Subgroups Of Sl(4, Z) Ii, A Ash, Pe Gunnells, M Mcconnell

Mathematics and Statistics Department Faculty Publication Series

In a previous paper [3] we computed cohomology groups H5(..0(N),C), where ..0(N) is a certain congruence subgroup of SL(4,Z), for a range of levels N. In this note we update this earlier work by extending the range of levels and describe cuspidal cohomology classes and additional boundary phenomena found since the publication of [3]. The cuspidal cohomology classes in this paper are the first cuspforms for GL(4) concretely constructed in terms of Betti cohomology.

Book Xii, Otto Vogl: Publications, 2001-2004, Jane C. Vogl

Emeritus Faculty Author Gallery

Books I-XII include citations to Otto Vogl's publications and patents. Printed versions of these twelve volumes are also available in the Integrated Sciences and Engineering Library of the University of Massachusetts in Amherst. MA, Lederle Graduate Research Center. The printed volumes include the full reprints of all cited publications.

Who Is Who In Polymer Science: A, Otto Vogl

Emeritus Faculty Author Gallery

Aklonis, John

Albertsson, Ann Christine

Ando, Isao

Selected Photographs Of Otto Vogl Museum Exhibit, His University Office And Home Office, Otto Vogl

Emeritus Faculty Author Gallery

Selected Photographs of a special exhibit on Dr. Otto Vogl at the Stadtmuseum in Traiskirchen, Austria. Also includes photographs depicting the life Otto Vogl in his home office and his office at the University of Massachusetts in Amherst in his early retirement, as an Emeritus Member of the Department of Polymer Science and Engineering.

Who Is Who In Polymer Science: B, Otto Vogl

Emeritus Faculty Author Gallery

Blum, Frank

Brittain, William J.

Brown, R. Malcolm Jr

Who Is Who In Polymer Science: D, Otto Vogl

Emeritus Faculty Author Gallery

Daly, William H.

DeSimone, Joseph M.

Who Is Who In Polymer Science: H, Otto Vogl

Emeritus Faculty Author Gallery

Hadjichristidis, Nikos

Hashimoto,Takeji

Higgins, Julia

Horie, Kazayuki

Hult, Andres

Who Is Who In Polymer Science: C, Otto Vogl

Emeritus Faculty Author Gallery

Carraher, James

Cheradame, Herve

Chodak, Ivan

Chujo, Yoshiki

Ciardelli, Francesco

Crivello, James V.

Who Is Who In Polymer Science: E, Otto Vogl

Emeritus Faculty Author Gallery

Eder, Erich

Eisenbach, Claus

Endo, Masayuki

Who Is Who In Polymer Science: J, Otto Vogl

Emeritus Faculty Author Gallery

Jaycox, Gary D.

Who Is Who In Polymer Science: K, Otto Vogl

Emeritus Faculty Author Gallery

Kajiyama, Tisoro

Kaminsky, Walter

Kawaguchi, Haruma

Kimura, Yoshiharu

Kirshenbaum, Gerald S.

Kitayama, Tatsuki

Klemm, Elisabeth

Klemm, Dieter

Koetz, Joachim

Kohjiya, Shinzo

Koide, Naohuki

Korshak, Yuri

Kratky, Christoph

Kricheldorf, Hans R.

Kubisa, Przemislaw

Who Is Who In Polymer Science: L, Otto Vogl

Emeritus Faculty Author Gallery

Lederer, Klaus

Ledwith, Anthony

Lehn. Jean-Marie

Levon, Kalle

Lovinger, Andrew

Who Is Who In Polymer Science: M, Otto Vogl

Emeritus Faculty Author Gallery

Matyjaszewski, Kristof

McCormick, Charles

Mencer, Helena Jasna

Mitchell, John D. I.

Muehlhaupt, Rolf

Mueller, Axel H.E.

Muthukumar, Murugappan

Who Is Who In Polymer Science: O, Otto Vogl

Emeritus Faculty Author Gallery

Ohno Hideyuki

Okamoto, Yoshiyuki

Ottenbrite, Raffael

Ouchi, Tatsuro

Who Is Who In Polymer Science: N, Otto Vogl

Emeritus Faculty Author Gallery

Negulescu, Ioan

Nishide, Hiroyuki

Nuyken, Oskar

Who Is Who In Polymer Science: P, Otto Vogl

Emeritus Faculty Author Gallery

Percec, Virgil

Puskas, Judit

Who Is Who In Polymer Science: R, Otto Vogl

Emeritus Faculty Author Gallery

Roder, Helga

Russell, Thomas Paul

Rychla, Lyda

Rychly, Jozef

Who Is Who In Polymer Science: S, Otto Vogl

Emeritus Faculty Author Gallery

Salamone, Ann Beal

Sanchez, Isaac

Sawamoto, Mitsuo

Simonsick, William J. Jr.

Shanks, Robert

Shen, Zhiquan

Shirota, Yasuhiko

Shoda, Shin-ichiro

Slomkovski, Stanislaw

Who Is Who In Polymer Science: T, Otto Vogl

Emeritus Faculty Author Gallery

Tantayanon, Supawan

Tirrell, David A

Tirrell, Matthew

Tsuji, Masaki

Tsvetanov, Christo