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.
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.
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...
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....