The initial-value problem is studied for evolution equations in Hilbert space of the general form d/dt A(u) + B(u) ϶ f, where and are maximal monotone operators. Existence of a solution is proved when A is a subgradient and either is strongly monotone or B is coercive; existence is established...
A mixed initial and boundary value problem is considered for
a partial differential equation of the form Muₜ(x, t)+Lu(x, t)=0,
where M and L are elliptic differential operators of orders 2 m
and 2l, respectively, with m ≤ l. The existence and uniqueness
of a strong solution of this equation...
Advective skew dispersion is a natural Markov process defined ned
by a di ffusion with drift across an interface of jump discontinuity in
a piecewise constant diff usion coeffcient. In the absence of drift this
process may be represented as a function of -skew Brownian motion
for a uniquely determined...
We consider solutions to the two-dimensional incompressible Navier-Stokes and Euler equations for which velocity and vorticity are bounded in the plane. We show that for every T > 0, the Navier-Stokes velocity converges in L∞([0,T]; L∞(R²)) as viscosity approaches 0 to the Euler velocity generated from the same initial data....
This article concerns a systemic manifestation of small scale interfacial heterogeneities in large scale quantities of interest to a variety of diverse applications spanning the earth, biological and ecological sciences. Beginning with formulations in terms of partial differential equations governing the conservative, advective-dispersive transport of mass concentrations in divergence form,...
Average annual losses caused by geologic hazards in Oregon are difficult to determine, owing to incomplete and scattered data. Preliminary considerations, however, indicate that losses to landslides may total between $4 million and $40 million per year. As many as nine persons have been killed by one landslide in Oregon...
We consider flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are treated with Neumann type flow conditions, and a novel treatment of the so called Kutta-Joukowsky flow conditions are given in the subsonic case. The...
The purpose of this note is to provide a coupling of weak limits in distribution of sequence of (normalized) multiplicative cascade measures under strong disorder in terms of the extremes of an associated branching random walk, assuming i.i.d positive, non-lattice bond weights and a second moment condition. The solution is...
The convolution inequality h ∗ h(ξ) ≤ B|ξ|θh(ξ) defined on Rⁿ
arises from a probabilistic representation of solutions of the n-dimensional
Navier-Stokes equations, n ≥ 2. Using a chaining argument, we establish
in all dimensions n ≥ 1 the nonexistence of strictly positive fully supported
solutions of this inequality for...
In this paper we extend the results of the research started by the first author in which Karlin-McGregor diagonalization of certain reversible Markov chains over countably infinite general state spaces by orthogonal polynomials was used to estimate the rate of convergence to a stationary distribution. We use a method of...
A mathematical model of a differential thermal analysis (DTA)
system was formulated so that influence of the various physical parameters
on the DTA peak could be determined. The specific DTA apparatus
simulated had cylindrical sample holes drilled into a nickel
block considered to have a negligible thermal resistance, and the...
The surgery technique of Gromov and Lawson may be used to construct families of positive scalar curvature metrics which are parameterised by Morse functions. This has played an important role in the study of the space of metrics of positive scalar curvature on a smooth manifold and its corresponding moduli...
For each Cantor set C in R³, all points of which have bounded local genus, we show that there are infinitely many inequivalent Cantor sets in R³ with the complement having the same fundamental group as the complement of C. This answers a question from Open Problems in Topology and...
Given two rational maps φ and ψ on Ρ¹ of degree at least two, we study a symmetric, nonnegative real-valued pairing〈φ, ψ〉which is closely related to the canonical height functions hφ and hψ associated to these maps. Our main results show a strong connection between the value of〈φ, ψ〉and the...
Extensions of the fractional Brownian fields are constructed over
a complete Riemannian manifold. This construction is carried out for the full
range of the Hurst parameter α ∈ (0, 1). In particular, we establish existence,
distributional scaling (self-similiarity), stationarity of the increments, and almost
sure H¨older continuity of sample paths....
Let X and Y be a pair of smooth manifolds, each obtainable
from the other by surgery in codimension at least three. We show that the
corresponding spaces Riem⁺(X) and Riem⁺(Y), respectively consisting of
Riemannian metrics of positive scalar curvature on X and Y, are homotopy
equivalent. This result is...
For every finitely generated abelian group G, we construct an irreducible
open 3-manifold M[subscript G] whose end set is homeomorphic to a Cantor set and
whose homogeneity group is isomorphic to G. The end homogeneity group
is the group of self-homeomorphisms of the end set that extend to homeomorphisms
of...
Importance sampling algorithms are discussed in detail, with an emphasis on implicit sampling, and applied to data assimilation via particle filters. Implicit sampling makes it possible to use the data to find high-probability samples at relatively low cost, making the assimilation more efficient. A new analysis of the feasibility of...
We derive the fundamental solution of the linearized problem of the motion of a viscous uid around a rotating body when the axis of rotation of the body is not parallel to the velocity of the uid at infinity.
We address the long-time behavior of a non-rotational von Karman plate in an inviscid potential flow. The model arises in aeroelasticity and models the interaction between a thin, nonlinear panel and a flow of gas in which it is immersed [6, 21, 23]. Recent results in [16, 18] show that...
The purpose of this study was to detail mathematical knowledge that supports the work of teaching proof and to investigate how such knowledge is evidenced in professional development (PD). To advance the construct of mathematical knowledge for teaching (MKT) in the context of proof, I developed a framework of MKT...
A mathematical model of Limiting Dilution Analysis for two limiting
parameters is presented and investigated. Limiting Dilution Analysis is a microbiological
cell assay developed for immunological application. In the given
case we deal with the interaction between B lymphocytes, macrophage derived
factor and T-independent antigens. The state of the art...
The sublimation of snow and evaporation of melted snow is contrasted between brush, grass and bare ground sites using eddy-correlation data. Averaged over the entire winter season, the evaporation/sublimation is about 20% greater over the brush site than the bare ground site, apparently due to greater supply of snow. Blowing...
In a simulator-defined MDP, the Markovian dynamics and rewards are provided in the form of a simulator from which samples can be drawn. This paper studies MDP planning algorithms that attempt to minimize the number of simulator calls before terminating and outputting a policy that is approximately optimal with high...
In this dissertation we develop mathematical treatment for two important applications: (i) evolution of methane in coalbeds with the associated phenomena of adsorption, and (ii) formation of methane hydrates in seabed. We use simplified models for (i) and (ii) since we are more interested in qualitative properties of the solutions...
The long-term evolution of Gaussian eddies is studied in an equivalent barotropic model using both linear and nonlinear quasi-geostrophic theory in an attempt to understand westward propagating satellite altimetry tracked mesoscale eddies. By examining both individual eddies and a large basin seeded with eddies, it is shown that long term...
Each chapter in this expository paper considers a mathematical model of an aspect of animal behavior, and how it affects the patterns of movement across and within a landscape. These models are all directly or indirectly related to questions in either Behavioral Ecology or Landscape Ecology, or both. I first...
This article describes the motivation, design, and progress of the Journal of Open Source Software (JOSS). JOSS is a free and open-access journal that publishes articles describing research software. It has the dual goals of improving the quality of the software submitted and providing a mechanism for research software developers...
Published November 1985. Facts and recommendations in this publication may no longer be valid. Please look for up-to-date information in the OSU Extension Catalog: http://extension.oregonstate.edu/catalog
While the locomotion performance of legged robots over flat terrain or known obstacles has improved over the past few decades, they have yet to equal the performance of their animal counterparts over variable terrain. This work analyzes a multi-legged reduced order model of cockroach locomotion on variable slopes which will...
In the study of gas chromatography a model is presented to simulate
a capillary gas chromatographic system. The model was developed
to study the concentrations of sample gas as a function of time and
space as it travels through the capillary column. The molecular migration
was approximated by elementary diffusion...
In this thesis, we investigate the problem of simulating Maxwell's equations in dispersive dielectric media. We begin by explaining the relevance of Maxwell's equations to
21st century problems. We also discuss the previous work on the numerical simulations of
Maxwell's equations. Introductions to Maxwell's equations and the Yee finite difference...
A new second order accurate nonuniform grid spacing technique which does not
depend on supraconvergence is developed for Finite Difference Time Domain (FDTD)
simulation of general three dimensional structures. The technique is useful for FDTD
simulations of systems which require finer details in small regions of the simulation space by...
Published March 1972. Facts and recommendations in this publication may no longer be valid. Please look for up-to-date information in the OSU Extension Catalog: http://extension.oregonstate.edu/catalog
Occurrence of human error in highly complex systems, such as a cockpit, can be disastrous and/or overwhelmingly costly. Mismanagement of multiple concurrent tasks has been observed by researchers to be a type of repetitive human error in previous studies of accidents and incidents. This error may occur in the form...
Although the Dunns’ learning styles and Gardner’s multiple intelligences theories are two distinct areas of research, they do not oppose each other and can be used together to improve learning. The design of this tutorial is an attempt to integrate students’ learning styles and their unique blend of intelligences in...
Many Gram-negative bacteria use a type III secretion system (T3SS) to establish associations with their hosts. The T3SS is a conduit for direct injection of type-III effector proteins into host cells, where they manipulate the host for the benefit of the infecting bacterium. For plant-associated pathogens, the variations in number...
Changes in the global climate and forest management practices have given rise to increasing numbers and severity of wildfires. More than five million acres burned in the United States in 2017, while in Canada 7.4 million acres burned. In particular, an increasing amount of dead woody biomass is a key...
The problem of analyzing the general linear, time-varying
system is investigated. The approach starts with four different
system representations: the differential equation, transform representations,
signal flow graphs, or block diagrams. Given one of
these system describing representations, it is shown what the
engineer can find out about the system and...