A simulation study of Sylvester's problem in three dimensions

1986 ◽  
Vol 23 (2) ◽  
pp. 509-513 ◽  
Author(s):  
Kim-Anh Do ◽  
Herbert Solomon
Keyword(s):  
Simulation Study ◽  
Higher Dimensions ◽  
Three Dimensions ◽  
Dimensional Sphere ◽  
Estimates Of Solutions ◽  
Sylvester’S Problem

This note gives estimates of solutions to the Sylvester problem in three dimensions. These results suggest that the solutions in four and higher dimensions are very close to the solution for the n -dimensional sphere which is known.

A simulation study of Sylvester's problem in three dimensions

1986 ◽  
Vol 23 (02) ◽  
pp. 509-513
Author(s):  
Kim-Anh Do ◽  
Herbert Solomon
Keyword(s):  
Simulation Study ◽  
Higher Dimensions ◽  
Three Dimensions ◽  
Dimensional Sphere ◽  
Estimates Of Solutions ◽  
Sylvester’S Problem

This note gives estimates of solutions to the Sylvester problem in three dimensions. These results suggest that the solutions in four and higher dimensions are very close to the solution for the n -dimensional sphere which is known.

scholarly journals Distributing coil elements in three dimensions enhances parallel transmission multiband RF performance: A simulation study in the human brain at 7 Tesla

2016 ◽  
Vol 75 (6) ◽  
pp. 2464-2472 ◽  
Author(s):  
Xiaoping Wu ◽  
Jinfeng Tian ◽  
Sebastian Schmitter ◽  
J. Tommy Vaughan ◽  
Kâmil Uğurbil ◽  
...  
Keyword(s):  
Human Brain ◽  
Simulation Study ◽  
Three Dimensions ◽  
7 Tesla ◽  
Parallel Transmission ◽  
Rf Performance

A Simulation Study on Welding Induced Distortion Control for Large Box Beam Structures

2004 ◽  
Author(s):  
Jun Xu ◽  
Wei Li
Keyword(s):  
Simulation Study ◽  
Welding Process ◽  
Three Dimensions ◽  
Beam Structures ◽  
Large Structures ◽  
Box Beam ◽  
Element Simulation ◽  
Distortion Control ◽  
Thermal Tensioning ◽  
Transient Thermal

Welding induced distortion in large structures is a major quality concern in industry. Many methods have been proposed in recent years to minimize the welding induced distortion. Among the available methods, transient thermal tensioning has been shown effective for minimizing the welding induced buckling distortion for T-joints. Due to the complexity of the welding process, different structures may require different strategies for distortion control. This paper presents a finite element simulation study on the distortion control for large box beam structures. The transient thermal tensioning method is applied through differential preheat on the two side plates of the beam. The effects of the preheating parameters including the average preheating temperature, temperature differential, and the preheating location are analyzed. It has been found that differential preheating control is effective in adjust the welding induced twist distortions. However, excessive differential preheating could generate bowing distortions. To determine an optimal preheating strategy, the distortions in all the three dimensions of a beam need to be considered simultaneously.

Structure of Liquid–Vapor Interfaces in the Ising Model

1997 ◽  
Vol 08 (03) ◽  
pp. 583-588 ◽  
Author(s):  
L. L. Moseley
Keyword(s):  
Computer Simulation ◽  
Asymptotic Behavior ◽  
Ising Model ◽  
Density Profile ◽  
Error Function ◽  
Higher Dimensions ◽  
Three Dimensions ◽  
Fluid Interface ◽  
Hyperbolic Tangent ◽  
Structure Of Liquid

The asymptotic behavior of the density profile of the fluid-fluid interface is investigated by computer simulation and is found to be better described by the error function than by the hyperbolic tangent in three dimensions. For higher dimensions the hyperbolic tangent is a better approximation.

YAMABE TYPE EQUATIONS ON THREE DIMENSIONAL RIEMANNIAN MANIFOLDS

1999 ◽  
Vol 01 (01) ◽  
pp. 1-50 ◽  
Author(s):  
YANYAN LI ◽  
MEIJUN ZHU
Keyword(s):  
Riemannian Manifolds ◽  
Compact Riemannian Manifold ◽  
Three Dimensional ◽  
Higher Dimensions ◽  
Dimensional Sphere ◽  
Compact Set ◽  
Curvature Function ◽  
Necessary And Sufficient Condition ◽  
All Solutions ◽  
Necessary And Sufficient

A theorem of Escobar and Schoen asserts that on a positive three dimensional smooth compact Riemannian manifold which is not conformally equivalent to the standard three dimensional sphere, a necessary and sufficient condition for a C2 function K to be the scalar curvature function of some conformal metric is that K is positive somewhere. We show that for any positive C2 function K, all such metrics stay in a compact set with respect to C3 norms and the total Leray-Schauder degree of all solutions is equal to -1. Such existence and compactness results no longer hold in such generality in higher dimensions or on manifolds conformally equivalent to standard three dimensional spheres. The results are also established for more general Yamabe type equations on three dimensional manifolds.

Critical intensities of Boolean models with different underlying convex shapes

2002 ◽  
Vol 34 (01) ◽  
pp. 48-57
Author(s):  
Rahul Roy ◽  
Hideki Tanemura
Keyword(s):  
Unit Area ◽  
Higher Dimensions ◽  
Boolean Model ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Boolean Models ◽  
Regular Polytope ◽  
Minimum Value ◽  
Critical Intensity ◽  
Poisson Boolean Model

We consider the Poisson Boolean model of percolation where the percolating shapes are convex regions. By an enhancement argument we strengthen a result of Jonasson (2000) to show that the critical intensity of percolation in two dimensions is minimized among the class of convex shapes of unit area when the percolating shapes are triangles, and, for any other shape, the critical intensity is strictly larger than this minimum value. We also obtain a partial generalization to higher dimensions. In particular, for three dimensions, the critical intensity of percolation is minimized among the class of regular polytopes of unit volume when the percolating shapes are tetrahedrons. Moreover, for any other regular polytope, the critical intensity is strictly larger than this minimum value.

Asymptotic properties of the equilibrium probability of identity in a geographically structured population

1977 ◽  
Vol 9 (2) ◽  
pp. 268-282 ◽  
Author(s):  
Stanley Sawyer
Keyword(s):  
Nearest Neighbor ◽  
Asymptotic Properties ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Three Dimensions ◽  
One Dimension ◽  
Order Zero ◽  
Structured Population ◽  
Equilibrium Probability ◽  
Migration Law

Let I(x, u) be the probability that two genes found a vector distance x apart are the same type in an infinite-allele selectively-neutral migration model with mutation rate u. The creatures involved inhabit an infinite of colonies, are diploid and are held at N per colony. Set in one dimension and in higher dimensions, where σ2 is the covariance matrix of the migration law (which is assumed to have finite fifth moments). Then in one dimension, in two dimensions, and in three dimensions uniformly for Here C0 is a constant depending on the migration law, K0(y) is the Bessel function of the second kind of order zero, and are the eigenvalues of σ2. For symmetric nearest-neighbor migrations, in one dimension and log mi in two. For is known in one dimension and C0 does not appear. In two dimensions, These results extend and make more precise earlier work of Malécot, Weiss and Kimura and Nagylaki.

The Osculatory Packing of a Three Dimensional Sphere

1973 ◽  
Vol 25 (2) ◽  
pp. 303-322 ◽  
Author(s):  
David W. Boyd
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Higher Dimensions ◽  
Dimensional Euclidean Space ◽  
Dimensional Sphere ◽  
Specific Knowledge ◽  
Precise Information ◽  
Practical Applications ◽  
Physical Problems ◽  
Three Dimensional Space

Packings by unequal spheres in three dimensional space have interested many authors. This is to some extent due to the practical applications of such investigations to engineering and physical problems (see, for example, [16; 17; 31]). There are a few general results known concerning complete packings by spheres in N-dimensional Euclidean space, due mainly to Larman [20; 21]. For osculatory packings, although there is a great deal of specific knowledge about the two-dimensional situation, the results for higher dimensions, such as [4], rely on general methods which do not give particularly precise information.

scholarly journals Heegaard splittings and Morse-Smale flows

2003 ◽  
Vol 2003 (56) ◽  
pp. 3539-3572 ◽  
Author(s):  
Ralf Gautschi ◽  
Joel W. Robbin ◽  
Dietmar A. Salamon
Keyword(s):  
Floer Homology ◽  
Higher Dimensions ◽  
Three Dimensions ◽  
Heegaard Splittings ◽  
Higher Dimensional ◽  
Poincare Conjecture ◽  
Smale Flows ◽  
Connecting Orbit

We describe three theorems which summarize what survives in three dimensions of Smale's proof of the higher-dimensional Poincaré conjecture. The proofs require Smale's cancellation lemma and a lemma asserting the existence of a2-gon. Such2-gons are the analogues in dimension two of Whitney disks in higher dimensions. They are also embedded lunes; an (immersed) lune is an index-one connecting orbit in the Lagrangian Floer homology determined by two embedded loops in a2-manifold.

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