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Articles 16261 - 16290 of 26218

Full-Text Articles in Physical Sciences and Mathematics

Multiple Dark-Bright Solitons In Atomic Bose-Einstein Condensates, D. Yan, J. J. Chang, C. Hamner, Panos Kevrekidis, P. Engels, V. Achilleos, D. J. Frantzeskakis, R. Carretero-Gonz´Alez, P. Schmelcher Nov 2011

Multiple Dark-Bright Solitons In Atomic Bose-Einstein Condensates, D. Yan, J. J. Chang, C. Hamner, Panos Kevrekidis, P. Engels, V. Achilleos, D. J. Frantzeskakis, R. Carretero-Gonz´Alez, P. Schmelcher

Panos Kevrekidis

Motivated by recent experimental results, we present a systematic theoretical analysis of dark-bright-soliton interactions and multiple-dark-bright-soliton complexes in atomic two-component Bose-Einstein condensates. We study analytically the interactions between two dark-bright solitons in a homogeneous condensate and then extend our considerations to the presence of the trap. We illustrate the existence of robust stationary dark-bright-soliton “molecules,” composed of two or more solitons, which are formed due to the competition of the interaction forces between the dark- and bright-soliton components and the trap force. Our analysis is based on an effective equation of motion, derived for the distance between two dark-bright solitons. …

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The Schroedinger Equation With Potential In Random Motion, Marius Beceanu, Soffer Avy Nov 2011

The Schroedinger Equation With Potential In Random Motion, Marius Beceanu, Soffer Avy

Mathematics and Statistics Faculty Scholarship

We study Schroedinger's equation with a potential moving along a Brownian motion path. We prove a RAGE-type theorem and Strichartz estimates for the solution on average.

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Spatial Population Models In Spatiotemporally Structured Environments, David Hiebeler Nov 2011

Spatial Population Models In Spatiotemporally Structured Environments, David Hiebeler

University of Maine Office of Research Administration: Grant Reports

Spatial effects, such as habitat fragmentation and the location and size of disturbance events, play a key role in the dynamics of populations. This is true in natural populations (such as herbs living under a forest canopy) as well as human-dominated systems (for example, crop pests in agricultural landscapes). Focusing on the development of spatial population models, the project seeks to better understand how and why spatially autocorrelated disturbances affect the dynamics of populations with mixtures of short- and long-distance dispersal. A variety of disturbances are considered, including (1) static disturbance, representing habitat heterogeneity across a landscape; (2) short-term disturbance …

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Los Modelos De Equilibrio General: La Revisión De Chancelier Y Una Crítica A Debreu Y Mckenzie, Rodrigo Lopez-Pablos Nov 2011

Los Modelos De Equilibrio General: La Revisión De Chancelier Y Una Crítica A Debreu Y Mckenzie, Rodrigo Lopez-Pablos

Lopez-Pablos, Rodrigo

A revision on general equilibrium theory from an entropic perspective. JEL CLASSIFICATION: D50, O21, Z19

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Geometric Structures On Matrix-Valued Subdivision Schemes, James J. Smith Nov 2011

Geometric Structures On Matrix-Valued Subdivision Schemes, James J. Smith

Dissertations

Surface subdivision schemes are used in computer graphics to generate visually smooth surfaces of arbitrary topology. Applications in computer graphics utilize surface normals and curvature. In this paper, formulas are obtained for the first and second partial derivatives of limit surfaces formed using 1-ring subdivision schemes that have 2 by 2 matrix-valued masks. Consequently, surface normals, and Gaussian and mean curvatures can be derived. Both quadrilateral and triangular schemes are considered and for each scheme both interpolatory and approximating schemes are examined. In each case, we look at both extraordinary and regular vertices. Every 3-D vertex of the refinement polyhedrons …

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Extreme Math Makeover: Mathematics Assessment And Reporting In The Era Of The Common Core Standards, Glenn W. "Max" Mcgee Nov 2011

Extreme Math Makeover: Mathematics Assessment And Reporting In The Era Of The Common Core Standards, Glenn W. "Max" Mcgee

Publications & Research

This presentation discusses the need to develop high quality performance based assessments of the Common Core Mathematical Standards and Mathematical Practices. Several examples of performance assessments from high achieving countries as well as from the 2009 PISA test are included.

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Highly Connected Multicoloured Subgraphs Of Multicoloured Graphs, H. Liu, R. Morris, N. Prince Nov 2011

Highly Connected Multicoloured Subgraphs Of Multicoloured Graphs, H. Liu, R. Morris, N. Prince

Hua Kun Liu

Suppose the edges of the complete graph on n vertices, E(Kn), are coloured using r colours; how large a k-connected subgraph are we guaranteed to find, which uses only at most s of the colours? This question is due to Bollobás, and the case s=1 was considered in Liu et al. [Highly connected monochromatic subgraphs of multicoloured graphs, J. Graph Theory, to appear]. Here we shall consider the case s is greater than or equal to 2, proving in particular that when s=2 and r+1 is a power of 2 then the answer lies between 4n/(r+1)-17kr(r+2k+1) and 4n/(r+1)+4 and that …

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Topological Properties Of Invariant Sets For Anosov Maps With Holes, Skyler C. Simmons Nov 2011

Topological Properties Of Invariant Sets For Anosov Maps With Holes, Skyler C. Simmons

Theses and Dissertations

We begin by studying various topological properties of invariant sets of hyperbolic toral automorphisms in the linear case. Results related to cardinality, local maximality, entropy, and dimension are presented. Where possible, we extend the results to the case of hyperbolic toral automorphisms in higher dimensions, and further to general Anosov maps.

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Breathers In Oscillator Chains With Hertzian Interactions, Guillaume James, Panos Kevrekidis, Jesus Cuevas Nov 2011

Breathers In Oscillator Chains With Hertzian Interactions, Guillaume James, Panos Kevrekidis, Jesus Cuevas

Panos Kevrekidis

We prove nonexistence of breathers (spatially localized and time-periodic oscillations) for a class of Fermi-Pasta-Ulam lattices representing an uncompressed chain of beads interacting via Hertz's contact forces. We then consider the setting in which an additional on-site potential is present, motivated by the Newton's cradle under the effect of gravity. Using both direct numerical computations and a simplified asymptotic model of the oscillator chain, the so-called discrete p-Schr\"odinger (DpS) equation, we show the existence of discrete breathers and study their spectral properties and mobility. Due to the fully nonlinear character of Hertzian interactions, breathers are found to be much more …

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Defeating The Kalka–Teicher–Tsaban Linear Algebra Attack On The Algebraic Eraser, Dorian Goldfeld, Paul E. Gunnells Nov 2011

Defeating The Kalka–Teicher–Tsaban Linear Algebra Attack On The Algebraic Eraser, Dorian Goldfeld, Paul E. Gunnells

Paul Gunnells

The Algebraic Eraser (AE) is a public key protocol for shar- ing information over an insecure channel using commutative and non- commutative groups; a concrete realization is given by Colored Burau Key Agreement Protocol (CBKAP). In this paper, we describe how to choose data in CBKAP to thwart an attack by Kalka–Teicher–Tsaban.

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Biomimetic Broadband Antireflection Gratings On Solar-Grade Multicrystalline Silicon Wafers, Blayne M. Phillips, Peng Jiang, Bin Jiang Nov 2011

Biomimetic Broadband Antireflection Gratings On Solar-Grade Multicrystalline Silicon Wafers, Blayne M. Phillips, Peng Jiang, Bin Jiang

Mathematics and Statistics Faculty Publications and Presentations

The authors report a simple and scalable bottom-up technique for fabricating broadband antireflection gratings on solar-grade multicrystalline silicon (mc-Si) wafers. A Langmuir-Blodgett process is developed to assemble close-packed silica microspheres on rough mc-Si substrates. Subwavelength moth-eye pillars can then be patterned on mc-Si by using the silica microspheres as structural template. Hemispherical reflectance measurements show that the resulting mc-Si gratings exhibit near zero reflection for a wide range of wavelengths. Both experimental results and theoretical prediction using a rigorous coupled-wave analysis model show that close-packed moth-eye arrays exhibit better antireflection performance than non-close-packed arrays due to a smoother refractive index …

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Rabi Flopping Induces Spatial Demixing Dynamics, E. Nicklas, H. Strobel, T. Zibold, C. Gross, B. A. Malomed, Panos Kevrekidis, M. K. Oberthaler Nov 2011

Rabi Flopping Induces Spatial Demixing Dynamics, E. Nicklas, H. Strobel, T. Zibold, C. Gross, B. A. Malomed, Panos Kevrekidis, M. K. Oberthaler

Panos Kevrekidis

We experimentally investigate the mixing and demixing dynamics of Bose-Einstein condensates in the presence of a linear coupling between two internal states. The observed amplitude reduction of the Rabi oscillations can be understood as a result of demixing dynamics of dressed states as experimentally confirmed by reconstructing the spatial profile of dressed state amplitudes. The observations are in quantitative agreement with numerical integration of coupled Gross-Pitaevskii equations without free parameters, which also reveals the criticality of the dynamics on the symmetry of the system. Our observations demonstrate new possibilities for changing effective atomic interactions and studying critical phenomena.

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Sensitivity Analysis For Two-Level Value Functions With Applications To Bilevel Programming, S Dempe, Boris S. Mordukhovich, B Zemkoho Nov 2011

Sensitivity Analysis For Two-Level Value Functions With Applications To Bilevel Programming, S Dempe, Boris S. Mordukhovich, B Zemkoho

Mathematics Research Reports

This paper contributes to a deeper understanding of the link between a now conventional framework in hierarchical optimization spread under the name of the optimistic bilevel problem and its initial more difficult formulation that we call here the original optimistic bilevel optimization problem. It follows from this research that, although the process of deriving necessary optimality conditions for the latter problem is more involved, the conditions themselves do not to a large extent differ from those known for the conventional problem. It has been already well recognized in the literature that for optimality conditions of the usual optimistic bilevel program …

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Combinatorics Of Two-Toned Tilings, Arthur T. Benjamin, Phyllis Chinn, Jacob N. Scott '11, Greg Simay Nov 2011

Combinatorics Of Two-Toned Tilings, Arthur T. Benjamin, Phyllis Chinn, Jacob N. Scott '11, Greg Simay

All HMC Faculty Publications and Research

We introduce the function a(r, n) which counts tilings of length n + r that utilize white tiles (whose lengths can vary between 1 and n) and r identical red squares. These tilings are called two-toned tilings. We provide combinatorial proofs of several identities satisfied by a(r, n) and its generalizations, including one that produces kth order Fibonacci numbers. Applications to integer partitions are also provided.

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An Analysis Of The Effect Of Stress Diffusion On The Dynamics Of Creeping Viscoelastic Flow, Becca Thomases Nov 2011

An Analysis Of The Effect Of Stress Diffusion On The Dynamics Of Creeping Viscoelastic Flow, Becca Thomases

Mathematics Sciences: Faculty Publications

The effect of stress diffusivity is examined in both the Oldroyd-B and FENE-P models of a viscoelastic fluid in the low Reynolds (Stokes) limit for a 2D periodic time-dependent flow. A local analytic solution can be obtained when assuming a flow of the form u=Wi-1(x,-y), where Wi is the Weissenberg number. In this case the width of the birefringent strand of the polymer stress scales with the added viscosity as ν1/2, and is independent of the Weissenberg number. Also, the " expected" maximum extension of the polymer coils remains finite with any stress diffusion and scales as Wi·ν-1/2. These predictions …

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Compositions, Partitions, And Fibonacci Numbers, Andrew Sills Nov 2011

Compositions, Partitions, And Fibonacci Numbers, Andrew Sills

Department of Mathematical Sciences Faculty Publications

A bijective proof is given for the following theorem: the number of compositions of n into odd parts equals the number of compositions of n+ 1 into parts greater than one. Some commentary about the history of partitions and compositions is provided.

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Cagan Type Rational Expectations Model On Time Scales With Their Applications To Economics, Funda Ekiz Nov 2011

Cagan Type Rational Expectations Model On Time Scales With Their Applications To Economics, Funda Ekiz

Masters Theses & Specialist Projects

Rational expectations provide people or economic agents making future decision with available information and past experiences. The first approach to the idea of rational expectations was given approximately fifty years ago by John F. Muth. Many models in economics have been studied using the rational expectations idea. The most familiar one among them is the rational expectations version of the Cagans hyperination model where the expectation for tomorrow is formed using all the information available today. This model was reinterpreted by Thomas J. Sargent and Neil Wallace in 1973. After that time, many solution techniques were suggested to solve the …

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Support Varieties And Representation Type Of Self-Injective Algebras, Jorg Feldvoss, Sarah Witherspoon Nov 2011

Support Varieties And Representation Type Of Self-Injective Algebras, Jorg Feldvoss, Sarah Witherspoon

University Faculty and Staff Publications

We use the theory of varieties for modules arising from Hochschild cohomology to give an alternative version of the wildness criterion of Bergh and Solberg [7]: If a finite dimensional self-injective algebra has a module of complexity at least 3 and satisfies some finiteness assumptions on Hochschild cohomology, then the algebra is wild. We show directly how this is related to the analogous theory for Hopf algebras that we developed in [23]. We give applications to many different types of algebras: Hecke algebras, reduced universal enveloping algebras, small half- quantum groups, and Nichols (quantum symmetric) algebras.

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Fluctuating And Dissipative Dynamics Of Dark Solitons In Quasicondensates S., S. P. Cockburn, H. E. Nistazakis, T. P. Horikis, Panos Kevrekidis, N. P. Proukakis, D. J. Frantzeskakis Oct 2011

Fluctuating And Dissipative Dynamics Of Dark Solitons In Quasicondensates S., S. P. Cockburn, H. E. Nistazakis, T. P. Horikis, Panos Kevrekidis, N. P. Proukakis, D. J. Frantzeskakis

Panos Kevrekidis

The fluctuating and dissipative dynamics of matter-wave dark solitons within harmonically trapped, partially condensed Bose gases is studied both numerically and analytically. A study of the stochastic Gross-Pitaevskii equation, which correctly accounts for density and phase fluctuations at finite temperatures, reveals dark-soliton decay times to be lognormally distributed at each temperature, thereby characterizing the previously predicted long-lived soliton trajectories within each ensemble of numerical realizations [ S. P. Cockburn et al. Phys. Rev. Lett. 104 174101 (2010)]. Expectation values for the average soliton lifetimes extracted from these distributions are found to agree well with both numerical and analytic predictions based …

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Counter-Propagating Two-Soliton Solutions In The Fermi–Pasta–Ulam Lattice, Aaron Hoffman, C.E. Wayne Oct 2011

Counter-Propagating Two-Soliton Solutions In The Fermi–Pasta–Ulam Lattice, Aaron Hoffman, C.E. Wayne

Aaron Hoffman

We study the interaction of small amplitude, long-wavelength solitary wavesin the Fermi–Pasta–Ulam model with general nearest-neighbour interactionpotential. We establish global-in-time existence and stability of counterpropagatingsolitary wave solutions. These solutions are close to the linearsuperposition of two solitary waves for large positive and negative values oftime; for intermediate values of time these solutions describe the interactionof two counter-propagating pulses. These solutions are stable with respectto perturbations in L2 and asymptotically stable with respect to perturbationswhich decay exponentially at spatial ±∞.

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Resolutions Of The Steinberg Module For Gl(N), Avner Ash, Paul E. Gunnells, Mark Mcconnell Oct 2011

Resolutions Of The Steinberg Module For Gl(N), Avner Ash, Paul E. Gunnells, Mark Mcconnell

Paul Gunnells

We give several resolutions of the Steinberg representation St_n for the general linear group over a principal ideal domain, in particular over Z. We compare them, and use these results to prove that the computations in [AGM4] are definitive. In particular, in [AGM4] we use two complexes to compute certain cohomology groups of congruence subgroups of SL(4,Z). One complex is based on Voronoi's polyhedral decomposition of the symmetric space for SL(n,R), whereas the other is a larger complex that has an action of the Hecke operators. We prove that both complexes allow us to compute the relevant cohomology groups, and …

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Boundary Effects In Large-Aspect-Ratio Lasers, G.K. Harkness, W.J. Firth, John B. Geddes, J.V Moloney, E.M. Wright Oct 2011

Boundary Effects In Large-Aspect-Ratio Lasers, G.K. Harkness, W.J. Firth, John B. Geddes, J.V Moloney, E.M. Wright

John B. Geddes

We study theoretically the effect of transverse boundary conditions on the traveling waves foundin infinitely extended and positively detuned laser systems. We find that for large-aspect-ratiosystems, well above threshold and away from the boundaries, the traveling waves persist. Sourceand sink defects are observed on the boundaries, and in very-large-aspect-ratio systems these defectscan also exist away from the boundaries. The transverse size of the sink defect, relative to the sizeof the transverse domain, is important in determining the final pattern observed, and so, close tothreshold, standing waves are always observed.

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Why Probability Appears In Quantum Mechaincs, Jerome Blackman, Wu Teh Hsiang Oct 2011

Why Probability Appears In Quantum Mechaincs, Jerome Blackman, Wu Teh Hsiang

Mathematics - All Scholarship

Early in the development of quantum theory Bohr introduced what came to be called the Copenhagen interpretation. Specifically, the square of the absolute value of the wave function was to be used as a probability density. There followed lengthy arguments about this ranging from alternative universes to Schrodinger's cat. Einstein famously remarked "I am convinced that He (God) does not play dice." The purpose of this paper is to present a mathematical model of the measuring process that shows that the Copenhagen interpretation can actually follow from the fact that the time development of quantum systems is governed by the …

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Constructing Large Numbers With Cheap Computers, Andrew Shallue, Steven Hayman Oct 2011

Constructing Large Numbers With Cheap Computers, Andrew Shallue, Steven Hayman

Scholarship

No abstract provided.

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Constructing Large Numbers With Cheap Computers, Andrew Shallue, Steven Hayman Oct 2011

Constructing Large Numbers With Cheap Computers, Andrew Shallue, Steven Hayman

Andrew Shallue

No abstract provided.

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A Generalization Of The Fujisawa–Kuh Global Inversion Theorem, M. Radulescu, S. Radulescu, Eduardo C. Balreira Oct 2011

A Generalization Of The Fujisawa–Kuh Global Inversion Theorem, M. Radulescu, S. Radulescu, Eduardo C. Balreira

Mathematics Faculty Research

We discuss the problem of global invertibility of nonlinear maps defined on the finitedimensional Euclidean space via differential tests. We provide a generalization of theFujisawa-Kuh global inversion theorem and introduce a generalized ratio conditionwhich detects when the pre-image of a certain class of linear manifolds is non-emptyand connected. In particular, we provide conditions that also detect global injectivity.

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On The N-Wave Equations And Soliton Interactions In Two And Three Dimensions, Vladimir S. Gerdjikov, Rossen Ivanov, Assen V. Kyuldjiev Oct 2011

On The N-Wave Equations And Soliton Interactions In Two And Three Dimensions, Vladimir S. Gerdjikov, Rossen Ivanov, Assen V. Kyuldjiev

Articles

Several important examples of the N-wave equations are studied. These integrable equations can be linearized by formulation of the inverse scattering as a local Riemann–Hilbert problem (RHP). Several nontrivial reductions are presented. Such reductions can be applied to the generic N-wave equations but mainly the 3- and 4-wave interactions are presented as examples. Their one and two-soliton solutions are derived and their soliton interactions are analyzed. It is shown that additional reductions may lead to new types of soliton solutions. In particular the 4-wave equations with Z2xZ2 reduction group allow breather-like solitons. Finally it is demonstrated that …

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Small And Large Time Stability Of The Time Taken For A Lévy Process To Cross Curved Boundaries, Philip S. Griffin, Ross A. Maller Oct 2011

Small And Large Time Stability Of The Time Taken For A Lévy Process To Cross Curved Boundaries, Philip S. Griffin, Ross A. Maller

Mathematics - All Scholarship

This paper is concerned with the small time behaviour of a Levy process X. In particular, we investigate the stabilities of the times, Tb(r) and Tb*(r), at which X, started with X0 = 0, first leaves the space-time regions {(t, y) ∈ R2 : y ≤ rtb, t ≥ 0} (one-sided exit), or {(t, y) in R2 :|y| ≤ rtb, t ≥ 0} (two-sided exit), 0 ≤ b < 1, as r -> 0. Thus essentially we determine whether or not these passage times behave like deterministic functions in the sense of different modes of convergence; specifically convergence …

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Small And Large Time Stability Of The Time Taken For A Lévy Process To Cross Curved Boundaries, Philip S. Griffin, Ross A. Maller Oct 2011

Small And Large Time Stability Of The Time Taken For A Lévy Process To Cross Curved Boundaries, Philip S. Griffin, Ross A. Maller

Mathematics - All Scholarship

This paper is concerned with the small time behaviour of a Levy process X. In particular, we investigate the stabilities of the times, Tb(r) and T*b (r), at which X, started with X0 = 0, first leaves the space-time regions {(t, y) in R2 : y ≤ rtb, t ≥ 0} (one-sided exit), or {(t, y) in R2 :|y| ≤ rtb, t ≥ 0} (two-sided exit), 0 ≤ b < 1, as r ↓ 0. Thus essentially we determine whether or not these passage times behave like deterministic functions in the sense of different modes of convergence; specifically convergence in probability, almost surely and in Lp. In many instances these are seen to be equivalent to relative stability of the process X itself. The …

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Warped Product Rigidity, Chenxu He, Peter Petersen, William Wylie Oct 2011

Warped Product Rigidity, Chenxu He, Peter Petersen, William Wylie

Mathematics - All Scholarship

In this paper we study the space of solutions to an overdetermined linear system involving the Hessian of functions. We show that if the solution space has dimension greater than one, then the underlying manifold has a very rigid warped product structure. This warped product structure will be used to study warped product Einstein structures in our paper "The space of virtual solutions to the warped product Einstein equation".

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