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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some special cases of the three dimensional Kakeya conjecture and their application to the restriction conjecture
三维Kakeya猜想 特殊情况 限制猜想
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2023/5/9
We will discuss two special cases of the three-dimensional Kakeya conjecture: SL_2 Kakeya and a refined Wolff's hairbrush result. As an application of the refined Wolff's hairbrush result, we will dis...
QUASIHOMOGENEOUS THREE-DIMENSIONAL REAL ANALYTIC LORENTZ METRICS DO NOT EXIST
THREE-DIMENSIONAL LORENTZ METRICS
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2015/10/14
We show that a germ of a real analytic Lorentz metric on R
3 which is locally homogeneous on an
open set containing the origin in its closure is necessarily locally homogeneous. We classifiy L...
Those groups r which act properly discontinuously and aillnely on II?’ with
compact fundamental domain are classified. First it is shown that such a group f
contains a solvable subgroup of finite ...
Fast X-Ray and Beamlet Transforms for Three-Dimensional Data
Three-Dimensional Data 3-D Volumetric (Raster-Scan) Dat
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2015/8/21
Three-dimensional volumetric data are becoming increasingly available
in a wide range of scientific and technical disciplines. With the right tools,
we can expect such data to yield valuable i...
Nonoverlapping Domain Decomposition Methods with Simplified Coarse Spaces for Solving Three-dimensional Elliptic Problems
domain decomposition coarse subspace substructuring preconditioner inexact solver condition number
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2012/8/8
In this paper we propose a substructuring preconditioner for solving three-dimensional
elliptic equations with strongly discontinuous coe±cients. The new preconditioner
can be viewed as a variant of...
Bounds on the volume fractions of two materials in a three dimensional body from boundary measurements by the translation method
inverse problems size estimation electrical impedance tomography
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2012/6/19
Using the translation method of Tartar, Murat, Lurie, and Cherkaev bounds are derived on the volume occupied by an inclusion in a three-dimensional conducting body. They assume electrical impedance to...
A New Fourth Order Difference Approximation for the Solution of Three-dimensional Non-linear Biharmonic Equations Using Coupled Approach
Three-Dimensional Non-Linear Biharmonic Equation Finite Differences Fourth Order Accuracy Compact Discretization Block-Block-Tridiagonal Tangential Derivatives Laplacian Stream Function Reynolds Number
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2013/1/30
This paper deals with a new higher order compact difference scheme, which is, O(h4) using coupled approach on the 19-point 3D stencil for the solution of three dimensional nonlinear biharmonic equatio...
An Efficient Direct Method to Solve the Three Dimensional Poisson’s Equation
Poisson’s Equation Finite Difference Method Tri-diagonal Matrix Hockney’s Method Thomas Algorithm
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2013/1/30
In this work, the three dimensional Poisson’s equation in Cartesian coordinates with the Dirichlet’s boundary conditions in a cube is solved directly, by extending the method of Hockney. The Poisson e...
On the existence of weak solutions to the three-dimensional steady compressible Navier-Stokes equations in bounded domains
Steady compressible Navier-Stokes equations existence for any γ > 1 weighted estimate bounded domains
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2011/9/22
Abstract: We prove the existence of a weak solution to the three-dimensional steady compressible isentropic Navier-Stokes equations in bounded domains for any specific heat ratio \gamma > 1. Generally...
Stretching and folding diagnostics in solutions of the three-dimensional Euler and Navier-Stokes equations
diagnostics three-dimensional Euler Navier-Stokes equations
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2011/3/3
Two possible diagnostics of stretching and folding (S&F) in fluid flows are discussed, based on the dynamics of the gradient of potential vor-ticity (q = ω · ∇) associated with solutions of the...
A hierarchy of length scales for solutions of the three-dimensional Navier-Stokes equations
hierarchy of length scales for solutions three-dimensional Navier-Stokes equations
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2010/12/28
Moments of the vorticity are used to define and estimate a hierarchy of time-averaged inverse length scales λ−1 m for the three-dimensional Navier-Stokes equations on a periodic
box [0, L]3.
Stretching and folding diagnostics in solutions of the three-dimensional Euler and Navier-Stokes equations
Stretching folding diagnostics three-dimensional Euler Navier-Stokes equations
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2010/12/28
Two possible diagnostics of stretching and folding (S&F) in fluid flows are discussed, based on the dynamics of the gradient of potential vor-ticity (q = ω · ∇) associated with solutions of the...
Three-dimensional Couette flow in a composite channel partially filled with a porous medium
Couette flow composite channel Brinkman porous medium
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2010/11/1
The couette flow of a viscous fluid in a channel, partially filled with a porous medium has been analyzed. The lower part of the channel is occupied by a porous medium, while the upper part is occupie...
Study of three-dimensional crack fronts under plane stress using a phase field model
Materials Science (cond-mat.mtrl-sci) Other Condensed Matter (cond-mat.other) Pattern Formation and Solitons (nlin.PS)
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2010/11/11
The shape of a crack front propagating through a thin sample is studied using a phase field model. The model is shown to have a well defined sharp interface limit. The crack front is found to be an el...
Three-Dimensional Lattice Boltzmann Model for High-Speed Compressible Flows
Statistical Mechanics (cond-mat.stat-mech) Soft Condensed Matter (cond-mat.soft) Cellular Automata and Lattice Gases (nlin.CG) Computational Physics (physics.comp-ph) Plasma Physics (physics.plasm-ph)
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2010/11/10
A highly efficient three-dimensional (3D) Lattice Boltzmann (LB) model for high speed compressible flows is proposed. This model is developed from the original one by Kataoka and Tsutahara[Phys. Rev. ...