Physical Sciences and Mathematics Commons^™

Judy Reservoir Monitoring Project 2009–2010 Final Report, Robin A. Matthews, Joan Vandersypen

Judy Reservoir

The purpose of this study was to identify and count the phytoplankton in water samples collected from Judy Reservoir, and measure other standard biological and chemical parameters. Water quality data and algae counts have been collected on a weekly basis since October 2006; annual data summaries were sent to the Skagit Public Utility District No. 1 in 2007, 2008, and January 2010.

Lake Whatcom Bathymetry And Morphology, Robert J. Mitchell, Gerry Gabrisch, Robin A. Matthews

Lake Whatcom Bathymetry Report

Our objective for this study was to produce an accurate and usable bathymetric model and morphological data for Lake Whatcom to replace that produced by Lighthart et al. (1972). Herein, we summarize the techniques used to convert the 1999 the U. S. Bureau of Reclamation (BOR) hydrographic survey soundings and shoreline contours of Lake Whatcom into metric units and a Triangulated Irregular Network (TIN) bathymetry model. We also describe the procedures used to delineate the major lake basins and to calculate surface area, water volumes, and other morphometric parameters for each basin and the lake as a whole.

Stability Of Roots Of Polynomials Under Linear Combinations Of Derivatives, Branko Ćurgus, Vania Mascioni

Mathematics Faculty Publications

Let T=α ₀ I+α ₁ D+⋅⋅⋅+α _n D ⁿ , where D is the differentiation operator and α0≠0 , and let f be a square-free polynomial with large minimum root separation. We prove that the roots of Tf are close to the roots of f translated by −α ₁/α ₀.

Late Quaternary Slip Rate On The Kern Canyon Fault At Soda Spring, Tulare County, California, Colin B. Amos, Keith I. Kelson, Dylan H. Rood, David T. Simpson, Ronn S. Rose

Geology Faculty Publications

The Kern Canyon fault represents a major tectonic and physiographic boundary in the southern Sierra Nevada of east-central California. Previous investigations of the Kern Canyon fault underscore its importance as a Late Cretaceous and Neogene shear zone in the tectonic development of the southern Sierra Nevada. Study of the late Quaternary history of activity, however, has been confounded by the remote nature of the Kern Canyon fault and deep along-strike exhumation within the northern Kern River drainage, driven by focused fluvial and glacial erosion. Recent acquisition of airborne lidar (light detection and ranging) topography along the ∼140 km length of …

Gaussian Brunn-Minkowski Inequalities, Richard J. Gardner, Artem Zvavitch

Mathematics Faculty Publications

A detailed investigation is undertaken into Brunn-Minkowski-type inequalities for Gauss measure. A Gaussian dual Brunn-Minkowski inequality, the first of its type, is proved, together with precise equality conditions, and is shown to be the best possible from several points of view. A new Gaussian Brunn-Minkowski inequality is proposed and proved to be true in some significant special cases Throughout the study attention is paid to precise equality conditions and conditions on the coefficients of dilatation. Interesting links are found to the S-inequality and the (B) conjecture. An example is given to show that convexity is needed in the (B) conjecture.

The Planet, 2010, Fall, Mitch Olsen, Huxley College Of The Environment, Western Washington University

The Planet

No abstract provided.

Simulations Of Luminescent Solar Concentrators: Effects Of Polarization And Fluorophore Alignment, Stephen Mcdowall, Brad L. Johnson, David L. Patrick

Chemistry Faculty and Staff Publications

We model the effects of dye molecule alignment on the collection efficiency of luminescent solar concentrators (LSCs). A Monte Carlo model for photontransport in LSC’s is derived and utilized, which incorporates the effects of fluorescent-dye-molecular alignment and the subsequent control over absorption, emission, and propagation properties. We focus on the effects of molecular alignment statistics on photon absorption and subsequent emission, including polarization and propagation direction imparted by dipole direction, to model device light-capture efficiency, defined as the ratio of the amount of light reaching particular slab edges to that incident on a face. We find that modest control of …

Constructing Simultaneous Hecke Eigenforms, T. Shemanske, Stephanie Treneer, Lynne H. Walling

Mathematics Faculty Publications

It is well known that newforms of integral weight are simultaneous eigenforms for all the Hecke operators, and that the converse is not true. In this paper, we give a characterization of all simultaneous Hecke eigenforms associated to a given newform, and provide several applications. These include determining the number of linearly independent simultaneous eigenforms in a fixed space which correspond to a given newform, and characterizing several situations in which the full space of cusp forms is spanned by a basis consisting of such eigenforms. Part of our results can be seen as a generalization of results of Choie-Kohnen …

Along-Strike Growth Of The Ostler Fault, New Zealand: Consequences For Drainage Deflection Above Active Thrust, Colin B. Amos, Douglas W. Burbank, Stuart A. L. Read

Geology Faculty Publications

Rarely are geologic records available to constrain the spatial and temporal evolution of thrust‐fault growth as slip accumulates during repeated earthquake events. Here, we utilize multiple generations of dated and deformed fluvial terraces to explore two key aspects of the along‐strike kinematic development of the Ostler fault zone in southern New Zealand over the past ∼100 k.y.: accumulation of fault slip through space and time and fixed‐length thrust growth that results in patterns of drainage diversion suggestive of laterally propagating faults. Along the Ostler fault, surface deformation patterns revealed by topographic surveying of terrace profiles in nine transverse drainages define …

Light Influences Feeding And Growth Of Echinoplutei., Lindsey Milonas, Bruno Pernet, Brian L. Bingham

Environmental Sciences Faculty and Staff Publications

Because planktonic invertebrate larvae may be food-limited, anything that increases feeding and digestive efficiency should increase the chances of larval survival to metamorphosis. As light directly enhances both feeding and digestion in some planktonic heterotrophic protists, we hypothesize that similar processes might occur in the larvae of marine invertebrates. We studied the direct effects of light on feeding and development in sea urchin larvae (Strongylocentrotus droebachiensis, S. franciscanus and sand dollar Dendraster excentricus). Larvae were placed in 12:12 h light:dark cycles or in complete darkness and ingestion rates were measured. We monitored larval morphology during the first …

The Planet, 2010, Spring, Kaylin Bettinger, Huxley College Of The Environment, Western Washington University

The Planet

No abstract provided.

Lake Samish Water Monitoring Project 2010 Final Report, Robin A. Matthews, Joan Vandersypen

Lake Samish

This report describes work done as a continuation of the Lake Samish monitoring project started in June 2005. Additional data and lake information is available in the 2006–2008 final reports (Matthews, et al., 2006; Matthews and Vandersypen, 2007; Matthews and Vandersypen, 2008).

Lake Samish is a valuable aquatic resource, providing public access for boating, fishing, swimming, picnicking, and other water and lakeshore activities. Residents around the lake enjoy outstanding views of both the lake and its surrounding watershed, and the lake serves as a water supply for many of the lakeshore residents.

Lake Samish is located in the Washington State …

Death Of A Cluster: The Destruction Of M67 As Seen By The Sloan Digital Sky Survey, James R. A. Davenport, Eric L. Sandquist

Physics & Astronomy

We probe the spatial and dynamical structure of the old open cluster M67 using photometric data from the Sloan Digital Sky Survey's sixth data release. Making use of an optimal contrast, or matched filter, algorithm, we map the distribution of high probability members of M67. We find an extended and elongated halo of likely members to a radius of nearly 60'. Our measured core radius of R _core = 824 ± 060 is somewhat larger than that of previous estimates. We attribute the larger core radius measurement to the SDSS probing lower mass main sequence stars than has been done …

Lake Whatcom Monitoring Project 2008/2009 Report, Robin A. Matthews, Michael Hilles, Joan Vandersypen, Robert J. Mitchell, Geoffrey B. Matthews

Lake Whatcom Annual Reports

This report is part of an on-going series of annual reports and special project reports that document the Lake Whatcom monitoring program. This work is conducted by the Institute for Watershed Studies and other departments at Western Washington University.

The major objective of this program is to provide long-term baseline water quality monitoring in Lake Whatcom and selected tributaries. Each section contains brief explanations about the water quality data, along with discussions of patterns observed in Lake Whatcom.

A Rigorous Analysis Using Optimal Transport Theory For A Two-Reflector Design Problem With A Point Source, Tilmann Glimm

Mathematics Faculty Publications

We consider the following geometric optics problem: construct a system of two reflectors which transforms a spherical wavefront generated by a point source into a beam of parallel rays. This beam has a prescribed intensity distribution. We give a rigorous analysis of this problem. The reflectors we construct are (parts of) the boundaries of convex sets. We prove existence of solutions for a large class of input data and give a uniqueness result. To the author’s knowledge, this is the first time that a rigorous mathematical analysis of this problem is given. The approach is based on optimal transportation theory. …

Judy Reservoir Monitoring Project 2010 Final Report, Robin A. Matthews, Joan Vandersypen, Rachael D. (Rachael Dawn) Gravon, Jessie Rosanbalm

Judy Reservoir

The purpose of this study was to identify and count the phytoplankton in water samples collected from Judy Reservoir, and measure other standard biological and chemical parameters. Water quality data and algae counts have been collected on a weekly basis since October 2006; annual data summaries were sent to the Skagit Public Utility District No. 1 in 2007 and 2008.

(rev. Feb 18, 2010)

Domains Of Water Molecules Provide Mechanisms Of Potentization In Homeopathy, George Czerlinski, Tjalling Ypma

Mathematics Faculty Publications

In homeopathy, high potentization means such high dilution that there is no longer even one molecule of the original active agent per gram of the mixture. Nevertheless such high dilutions apparently remain effective. We develop a possible mechanism for homeopathic potentization to explain this phenomenon. This mechanism consists of three consecutive processes: initiation, multiplication, and amplification. Initiation is the mechano-chemical generation, by strong shaking following each dilution step, of radicals which remain in existence by mutual stabilization in simultaneously formed electronic domains. Multiplication transfers electronic excitation level structures from the original homeopathic agent to these radical-containing domains, stabilizing them further. …

The Linus Sequence, Paul Balister, Steven Kalikow, Amites Sarkar

Mathematics Faculty Publications

Define the Linus sequence L_n for n ≥ 1 as a 0–1 sequence with L₁ = 0, and L_n chosen so as to minimize the length of the longest immediately repeated block L_n−2r+1 L_n−r = L_n−r+1 L_n. Define the Sally sequence S_n as the length r of the longest repeated block that was avoided by the choice of L_n. We prove several results about these sequences, such as exponential decay of the frequency of highly periodic subwords of the Linus sequence, zero entropy of any …

Gauge Equivalence In Stationary Radiative Transport Through Media With Varying Index Of Refraction, Stephen R. Mcdowall, Plamen Stefanov, Alexandru Tamasan

Mathematics Faculty Publications

Three dimensional anisotropic attenuating and scattering media sharing the same albedo operator have been shown to be related via a gauge transformation. Such transformations define an equivalence relation. We show that the gauge equivalence is also valid in media with non-constant index of refraction, modeled by a Riemannian metric. The two dimensional model is also investigated.

Anisotropic Classes Of Homogeneous Pseudodifferential Symbols, Árpád Bényi, Marcin Bownik

Mathematics Faculty Publications

We define homogeneous classes of x-dependent anisotropic symbols S˙mγ,δ(A) in the framework determined by an expansive dilation A, thus extending the existing theory for diagonal dilations. We revisit anisotropic analogues of Hörmander–Mikhlin multipliers introduced by Rivière [Ark. Mat. 9 (1971)] and provide direct proofs of their boundedness on Lebesgue and Hardy spaces by making use of the well-established Calderón–Zygmund theory on spaces of homogeneous type. We then show that x-dependent symbols in S˙01,1(A) yield Calderón–Zygmund kernels, yet their L2 boundedness fails. Finally, we prove boundedness results …

On The Hörmander Classes Of Bilinear Pseudodifferential Operators, Árpád Bényi, Diego Maldonado, Virginia Naibo, Rodolfo H. (Rodolfo Humberto) Torres

Mathematics Faculty Publications

Bilinear pseudodifferential operators with symbols in the bilinear analog of all the Hörmander classes are considered and the possibility of a symbolic calculus for the transposes of the operators in such classes is investigated. Precise results about which classes are closed under transposition and can be characterized in terms of asymptotic expansions are presented. This work extends the results for more limited classes studied before in the literature and, hence, allows the use of the symbolic calculus (when it exists) as an alternative way to recover the boundedness on products of Lebesgue spaces for the classes that yield operators with …

Sentry Selection In Wireless Networks, Paul Balister, Béla Bollobás, Amites Sarkar, Mark Walters

Mathematics Faculty Publications

Let P be a Poisson process of intensity one in the infinite plane R². We surround each point x of P by the open disc of radius r centred at x. Now let S_n be a fixed disc of area n, and let C_r(S_n) be the set of discs which intersect S_n. Write E_r^k for the event that C_r(S_n) is a k-cover of S_n, and F_r^k for the event that C_r(S_n) …

Secrecy Coverage (Conference Proceeding), Amites Sarkar, Martin Haenggi

Mathematics Faculty Publications

Motivated by information-theoretic secrecy, geometric models for secrecy in wireless networks have begun to receive increased attention. The general question is how the presence of eavesdroppers affects the properties and performance of the network. Previously the focus has been mostly on connectivity. Here we study the impact of eavesdroppers on the coverage of a network of base stations. The problem we address is the following. Let base stations and eavesdroppers be distributed as stationary Poisson point processes in a disk of area n. If the coverage of each base station is limited by the distance to the nearest eavesdropper, …

Bifurcation Of Solutions Of Separable Parameterized Equations Into Lines, Tjalling Ypma, Yun-Qiu Shen

Mathematics Faculty Publications

Many applications give rise to separable parameterized equations of the form A(y,µ)z + b(y, µ) = 0, where y ∈ Rⁿ, z ∈ R^N and the parameter µ ∈ R; here A(y,µ) is an (N + n) × N matrix and b(y, µ) ∈ R^{N +n}. Under the assumption that A(y, µ) has full rank we showed in [21] that bifurcation points can be located by solving a reduced equation of the form f ( …

Zeros Of Some Level 2 Eisenstein Series, Sharon Garthwaite, Ling Long, Holly Swisher, Stephanie Treneer

Mathematics Faculty Publications

The zeros of classical Eisenstein series satisfy many intriguing properties. Work of F. Rankin and Swinnerton-Dyer pinpoints their location to a certain arc of the fundamental domain, and recent work by Nozaki explores their interlacing property. In this paper we extend these distribution properties to a particular family of Eisenstein series on Γ(2) because of its elegant connection to a classical Jacobi elliptic function cn(u) which satisfies a differential equation (see formula (1.2)). As part of this study we recursively define a sequence of polynomials from the differential equation mentioned above that allow us to calculate zeros …

The Planet, 2010, Winter, Kaylin Bettinger, Huxley College Of The Environment, Western Washington University

The Planet

No abstract provided.

Chemical Structure Of Vanadium-Based Contact Formation On N-Ain, S. Pookpanratana, R. France, M. Blum, Sean R. Mulcahy, A. Bell, M. Bär, L. Weinhardt, Y. Zhang, T. Hofmann, O. Fuchs, W. Yang, J. D. Denlinger, T. D. Moustakas, C. Heske

Geology Faculty Publications

We have investigated the chemical interaction between a Au/V/Al/V layer structure and n-type AlN epilayers using soft x-ray photoemission, x-ray emission spectroscopy, and atomic force microscopy. To understand the complex processes involved in this multicomponent system, we have studied the interface before and after a rapid thermal annealing step. We find the formation of a number of chemical phases at the interface, including VN, metallic vanadium, aluminum oxide, and metallic gold. An interaction mechanism for metal contact formation on the entire n-Al,GaN system is proposed. ©

Expression, Purification, And Analysis Of Unknown Translation Factors From Escherichia Coli: A Synthesis Approach, Justin D. Walter, Peter Littlefield, Scott P. Delbecq, Gerry Prody, P. Clint Spiegel

Chemistry Faculty and Staff Publications

New approaches are currently being developed to expose biochemistry and molecular biology undergraduates to a more interactive learning environment. Here, we propose a unique project-based laboratory module, which incorporates exposure to biophysical chemistry approaches to address problems in protein chemistry. Each of the experiments described herein contributes to the stepwise process of isolating, identifying, and analyzing a protein involved in a central biological process, prokaryotic translation. Students are provided with expression plasmids that harbor an unknown translation factor, and it is their charge to complete a series of experiments that will allow them to develop hypotheses for discovering the identity …

Recent And Future Warm Extreme Events And High-Mountain Slope Stability, C. Huggel, N. Salzmann, S. Allen, Jacqueline Caplan-Auerbach, L. Fischer, W. Haeberli, C. Larsen, D. Schneider, R. Wessels

Geology Faculty Publications

The number of large slope failures in some high-mountain regions such as the European Alps has increased during the past two to three decades. There is concern that recent climate change is driving this increase in slope failures, thus possibly further exacerbating the hazard in the future. Although the effects of a gradual temperature rise on glaciers and permafrost have been extensively studied, the impacts of short-term, unusually warm temperature increases on slope stability in high mountains remain largely unexplored. We describe several large slope failures in rock and ice in recent years in Alaska, New Zealand and the European …

Insights Into Rock-Ice Avalanche Dynamics By Combined Analysis Of Seismic Recordings And A Numerical Avalanche Mode, Demian Schneider, Perry Bartelt, Jacqueline Caplan-Auerbach, Marc Christen, Christian Huggel, Brian W. Mcardell

Geology Faculty Publications

Rock‐ice avalanches larger than 1 × 10⁶ m³ are high‐magnitude, low‐frequency events that may occur in all ice‐covered, high mountain areas around the world and can cause extensive damage if they reach populated regions. The temporal and spatial evolution of the seismic signature from two events was analyzed, and recordings at selected stations were compared to numerical model results of avalanche propagation. The first event is a rock‐ice avalanche from Iliamna volcano in Alaska which serves as a “natural laboratory” with simple geometric conditions. The second one originated on Aoraki/Mt. Cook, New Zealand Southern Alps, and is characterized …