We propose a time dependent Eulerian model for sea surface entrainment, buoyancy transport and droplet dynamics of ocean oil. The model captures the microscale vertical oil mass exchanges in the neighborhood of the sea surface. This model is in turn part of an oil fate model designed to capture oil...
Humans move frequently and tend to carry parasites among areas with endemic malaria and into areas where local transmission is unsustainable. Human-mediated parasite mobility can thus sustain parasite populations in areas where they would otherwise be absent. Data describing human mobility and malaria epidemiology can help classify landscapes into parasite...
We study a class of two-generator two-relator groups, denoted J[subscript n](m, k), that arise in the study of relative asphericity as groups satisfying a transitional curvature condition. Particular instances of these groups occur in the literature as finite groups of intriguing orders. Here we find infinite families of non-elementary virtually...
The ability to evaluate the effective permeability of proppant packs is useful in predicting the efficiency of hydraulic fracture installations. In this paper we propose a computational approach combining microimaging data from X-ray computed microtomography, the simulations of flow at pore-scale, and an upscaling process which identifies the effective model...
Background:
Eastern equine encephalitis (EEE) virus (Togaviridae, Alphavirus) is a highly pathogenic mosquito-borne zoonosis that is responsible for occasional outbreaks of severe disease in humans and equines, resulting in high mortality and neurological impairment in most survivors. In the past, human disease outbreaks in the northeastern U.S. have occurred intermittently...
Motivation:
Estimation of bacterial community composition from high-throughput sequenced 16S rRNA gene amplicons is a key task in microbial ecology. Since the sequence data from each sample typically consist of a large number of reads and are adversely impacted by different levels of biological and technical noise, accurate analysis of...
Results are provided that highlight the effect of interfacial discontinuities in the
diffusion coefficient on the behavior of certain basic functionals of the diffusion, such
as local times and occupation times, extending previous results in [2, 3] on the behavior
of first passage times. The main goal is to obtain...
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.
Gene regulatory networks are commonly used for modeling biological processes and revealing underlying molecular mechanisms. The reconstruction of gene regulatory networks from observational data is a challenging task, especially considering the large number of players (e.g. genes) involved and the small number of biological replicates available for analysis. Herein, we...
The spectrum of the interior transmission problem is related to the unique determination of the acoustic properties of a body in thermoacoustic imaging. Under a non-trapping hypothesis, we show that sparsity of the interior transmission spectrum implies a range separation condition for the thermoacoustic operator. In odd dimensions greater than...
We consider computational modeling of flow with small and large velocities at
porescale and at corescale, and we address various challenges in simulation, upscaling, and modeling.
While our focus is on voxel-based data sets from real porous media imaging, our methodology is
verified first on synthetic geometries, and we analyze...
Abstract: We prove that for all ergodic extensions S-1 of a transformation by a locally compact second countable group G, and for all G-extensions S₂ of an aperiodic transformation, there is a relative speedup of S₁ that is relatively isomorphic to S₂. We apply this result to give necessary and...
We provide several examples of the use of geometric reasoning with three-dimensional spacetime diagrams, rather than algebraic manipulations using three-dimensional Lorentz transformations, to analyze problems in special relativity.
The process of complexification is used to classify Lie algebras and identify their Cartan subalgebras. However, this method does not distinguish between real forms of a complex Lie algebra, which can differ in signature. In this paper, we show how Cartan decompositions of a complexified Lie algebra can be combined...
We investigate a number of simple toy models to explore interesting relationships between dynamics and typicality. We start with an infinite model that has been proposed as an illustration of how nonergodic dynamics can produce interesting features that are suggestive for cosmological applications. We consider various attempts to define the...
The P1 discretization of the Laplace operator on a triangulated
polyhedral surface is related to geometric properties of the surface. This paper studies extremum problems for eigenvalues of the P1 discretization of the
Laplace operator. Among all triangles, an equilateral triangle has the maximal first positive eigenvalue. Among all cyclic...
We give explicit pseudo-Anosov homeomorphisms with vanishing
Sah–Arnoux–Fathi invariant. Any translation surface whose Veech group
is commensurable to any of a large class of triangle groups is shown to have
an affine pseudo-Anosov homeomorphism of this type. We also apply a reduction
to finite triangle groups and thereby show the...
We consider the well-posedness of a model for a flow-structure interaction. This model describes the dynamics of an elastic flexible plate with clamped boundary conditions immersed in a supersonic flow. A perturbed wave equation describes the flow potential. The plateʼs out-of-plane displacement can be modeled by various nonlinear plate equations...
We give continued fraction algorithms for each conjugacy class of triangle Fuchsian group of signature
(3, n, ∞), with n ≥ 4. In particular, we give an explicit form of the group that is a subgroup of the Hilbert
modular group of its trace field and provide an interval map...
In this paper dynamic von Karman equations with localized interior damping supported in a boundary collar are considered. Hadamard well-posedness for von Karman plates with various types of nonlinear damping are well known, and the long-time behavior of nonlinear plates has been a topic of recent interest. Since the von...
We consider a renewal jump diffusion process, more specifically a renewal insurance risk model with investments in a stock whose price is modeled by a geometric Brownian motion. Using Laplace transforms and regular variation theory, we introduce a transparent and unifying analytic method for investigating the asymptotic behavior of ruin...
Given a number field K, we consider families of critically separable rational maps of degree d over K possessing a certain fixed-point and multiplier structure. With suitable notions of isomorphism and good reduction between rational maps in these families, we prove a finiteness theorem which is analogous to Shafarevich’s theorem...
We explore two characteristic features of x-ray computed tomography inversion formulas in two and
three dimensions that are dependent on π-lines. In such formulas the data from a given source
position contribute only to the reconstruction of ƒ(x) for x in a certain region, called the region
of backprojection. The...
A mathematical evidence-in a statistically significant sense-of a geometric scenario leading to criticality of the Navier-Stokes problem is presented. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4752170]
In [BH], a chain complex was constructed in a combinatorial way
which conjecturally is a resolution of the (dual of the) integral Specht
module for the symmetric group in terms of permutation modules.
In this paper we extend the definition of the chain complex to the
integral Iwahori Hecke algebra...
The Laplace-Beltrami operator of a smooth Riemannian manifold is determined by the Riemannian metric. Conversely, the heat kernel constructed from the eigenvalues and eigenfunctions of the Laplace-Beltrami operator determines the Riemannian metric. This work proves the analogy on Euclidean polyhedral surfaces (triangle meshes), that the discrete heat kernel and the...
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...
We extend the idea of bilateral determinism of a free Z-action by D. Ornstein and B. Weiss to a free Z²-action. We show that we have a 'stronger' spatial determinism for Z²-actions: to determine the complete Z²-name of a point, it is enough to know the name of a fraction...
Let K be a cyclic number field of prime degree ℓ. Heilbronn showed that for a given ℓ there are only finitely many such fields that are norm-Euclidean. In the case of ℓ = 2 all such norm-Euclidean fields have been identified, but for ℓ ≠ 2, little else is...
Double-diffusion model is used to simulate slightly compressible fluid flow in periodic porous media as a macro-model in place of the original highly heterogeneous micro-model. In this paper, we formulate an adaptive two-grid numerical finite element discretization of the double-diffusion system and perform a comparison between the micro- and macro-model....
The degenerate nature of the metric on null hypersurfaces makes it difficult to define a covariant derivative on null submanifolds. Recent approaches using decomposition to define a covariant derivative on null hypersurfaces are investigated, with examples demonstrating the limitations of the methods. Motivated by Geroch’s work on asymptotically flat spacetimes,...
We develop the theory of degenerate and nonlinear evolution systems in mixed formulation.
It will be shown that many of the well-known results for the stationary problem extend to
the nonlinear case and that the dynamics of a degenerate Cauchy problem is governed by a nonlinear
semigroup. The results are...
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...
A definition is suggested for affine symmetry tensors, which generalize the notion of affine vectors in the same way that (conformal) Killing tensors generalize (conformal) Killing vectors. An identity for these tensors is proven, which gives the second derivative of the tensor in terms of the curvature tensor, generalizing a...
We study the stability properties of, and the phase error present in, a finite element scheme for Maxwell’s
equations coupled with a Debye or Lorentz polarization model. In one dimension we consider a second order
formulation for the electric field with an ordinary differential equation for the electric polarization added...
This paper is included in the Proceedings, Part 1, of the International Conference on Computational Science 2009 (ICCS 2009) held in Baton Rouge, LA, USA, May 25-27, 2009.
An upscaled elliptic-parabolic system of partial differential equations
describing the multiscale flow of a single-phase incompressible fluid and
transport of a dissolved chemical by advection and diffusion through a heterogeneous
porous medium is developed without the usual assumptions of scale
separation. After a review of homogenization results for the traditional...
The authors of this paper met at a summer institute sponsored by the Oregon Collaborative for Excellence in the Preparation of Teachers (OCEPT). Edwards is a researcher in undergraduate mathematics education. Ward, a pure mathematician teaching at an undergraduate institution, had had little exposure to mathematics education research prior to...
The distributed-microstructure model for the flow of single phase
fluid in a partially fissured composite medium due to Douglas-Peszyńska-Showalter [12] is extended to a quasi-linear version. This model contains the
geometry of the local cells distributed throughout the medium, the flux exchange
across their intricate interface with the imbedded fissure...
We discuss Einstein’s field equations in the presence of signature change using variational methods, obtaining a generalization of the Lanczos equation relating the distributional term in the stress tensor to the discontinuity of the extrinsic curvature. In particular, there is no distributional term in the stress tensor, and hence no...
We examine some of the subtleties inherent in formulating a theory of spinors on a manifold with a smooth degenerate metric. We concentrate on the case where the metric is singular on a hypersurface that partitions the manifold into Lorentzian and Euclidean domains. We introduce the notion of a complex...
We derive conditions for rotating particle detectors to respond in a variety of bounded spacetimes and
compare the results with the folklore that particle detectors do not respond in the vacuum state appropriate to
their motion. Applications involving possible violations of the second law of thermodynamics are briefly
addressed.
We contrast the two approaches to ‘‘classical’’ signature change used by Hayward with the one used by us (Hellaby and Dray). There is (as yet) no rigorous derivation of appropriate distributional field equations. Hayward’s distributional approach is based on a postulated modified form of the field equations. We make an...
A general porous-medium equation is uniquely solved subject to a pair of boundary conditions for the trace of the solution and a second function on the boundary. The use of maximal monotone graphs for the three nonlinearities permits not only the inclusion of the usual boundary conditions of Dirichlet, Neumann,...
A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifold is equivalent to the one‐parameter family of hypersurfaces orthogonal to the curves, each of which inherits...
A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) one‐form field. Such a manifold admits natural generalizations of Lie differentiation, exterior differentiation, and covariant differentiation, all based on a nonstandard action...
The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegant...
The divergence theorem as usually stated cannot be applied across a change of signature unless it is reexpressed to allow for a finite source term on the signature change surface. Consequently all conservation laws must also be ‘‘modified,’’ and therefore insistence on conservation of matter across such a surface cannot...
We consider the (massless) scalar field on a two-dimensional manifold with metric that changes signature from Lorentzian to Euclidean. Requiring a conserved momentum in the spatially homogeneous case leads to a particular choice of propagation rule. The resulting mix of positive and negative frequencies depends only on the total (conformal)...
A system of quasilinear degenerate parabolic equations arising in the modeling of diffusion in a fissured medium is studied. There is one such equation in the local cell coordinates at each point of the medium, and these are coupled through a similar equation in the global coordinates. It is shown...
In four dimensions, two metrics that are conformally related define the same Hodge dual operator on the space of two‐forms. The converse, namely, that two metrics that have the same Hodge dual are conformally related, is established. This is true for metrics of arbitrary (nondegenerate) signature. For Euclidean signature a...
Anderson and DeWitt considered the quantization of a massless scalar field in a spacetime whose spacelike hypersurfaces change topology and concluded that the topology change gives rise to infinite particle and energy production. We show here that their calculations are insufficient and that their propagation rule is unphysical. However, our...
A unified, self‐contained treatment of Wigner D functions, spin‐weighted spherical harmonics, and monopole harmonics is given, both in coordinate‐free language and for a particular choice of coordinates.
Diffusion in a fissured medium with absorption or partial saturation effects leads to a pseudoparabolic equation nonlinear in both the enthalpy and the permeability. The corresponding initial-boundary value problem is shown to have a solution in various Sobolev-Besov spaces, and sufficient conditions are given for the problem to be well-posed.
We compare two independent generalizations of the usual spherical harmonics, namely monopole harmonics and spin‐weighted spherical harmonics, and make precise the sense in which they can be considered to be the same. By analogy with the spin‐gauge language, raising and lowering operators for the monopole index of the monopole harmonics...
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...
We give a nonstandard method of integrating the equation Bu" + Cu’ + Au = f in Hilbert space by reducing it to a first order system in which the differentiated term corresponds to energy. Semigroup theory gives existence for hyperbolic and for parabolic cases. When C = εA, ε...
The L²-error estimates are established for the continuous time Faedo-Galerkin approximation to solutions of a linear parabolic initial boundary value problem that has elliptic part of order 2m. Properties of analytic semigroups are used to obtain these estimates directly from the L²-estimates for the corresponding steady state elliptic problem under...
The Cauchy problem for the evolution equation Mu’(t) + N(t,u(t)) = 0 is studied, where M and N(t,•) are, respectively, possibly degenerate and nonlinear monotone operators from a vector space to its dual. Sufficient conditions for existence and for uniqueness of solutions are obtained by reducing the problem to an...
An existence theory is developed for a semilinear evolution equation in Banach space which is modeled on boundary value problems for partial differential equations of Sobolev type. The operators are assumed to be measurable and to satisfy coercive estimates which are not necessarily uniform in their time dependence, and to...
We are concerned here with well-posed problems for the partial differential equation uₜ(x, t) + yMuₜ(x, t) + Lu(x, t) = f(x, t) containing the elliptic differential operator M of order 2m and the differential operator L of order ≤2m. Hilbert space methods are used to formulate and solve an...
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...