Convergence of Calabi–Yau manifolds

In this paper, we study the convergence of Calabi–Yau manifolds under Kähler degeneration to orbifold singularities and complex degeneration to canonical singularities (including the conifold singularities), and the collapsing of a family of Calabi–Yau manifolds.     

Accuracy and complexity evaluation of defuzzification strategies for the discretised interval type-2 fuzzy set

The work reported in this paper addresses the challenge of the efficient and accurate defuzzification of discretised interval type-2 fuzzy sets. The exhaustive method of defuzzification for type-2 fuzzy sets is extremely slow, owing to its enormous computational complexity. Several approximate methods have been devised in response to this bottleneck. In this paper we survey four alternative strategies for defuzzifying an interval type-2 fuzzy set: (1) The Karnik–Mendel Iterative Procedure, (2) the Wu–Mendel Approximation, (3) the Greenfield–Chiclana Collapsing Defuzzifier, and (4) the Nie–Tan Method.We evaluated the different methods experimentally for accuracy, by means of a comparative study using six representative test sets with varied characteristics, using the exhaustive method as the standard. A preliminary ranking of the methods was achieved using a multi-criteria decision making methodology based on the assignment of weights according to performance. The ranking produced, in order of decreasing accuracy, is (1) the Collapsing Defuzzifier, (2) the Nie–Tan Method, (3) the Karnik–Mendel Iterative Procedure, and (4) the Wu–Mendel Approximation.Following that, a more rigorous analysis was undertaken by means of the Wilcoxon Nonparametric Test, in order to validate the preliminary test conclusions. It was found that there was no evidence of a significant difference between the accuracy of the Collapsing and Nie–Tan Methods, and between that of the Karnik–Mendel Iterative Procedure and the Wu–Mendel Approximation. However, there was evidence to suggest that the collapsing and Nie–Tan Methods are more accurate than the Karnik–Mendel Iterative Procedure and the Wu–Mendel Approximation.In relation to efficiency, each method’s computational complexity was analysed, resulting in a ranking (from least computationally complex to most computationally complex) as follows: (1) the Nie–Tan Method, (2) the Karnik–Mendel Iterative Procedure (lowest complexity possible), (3) the Greenfield–Chiclana Collapsing Defuzzifier, (4) the Karnik–Mendel Iterative Procedure (highest complexity possible), and (5) the Wu–Mendel Approximation.     

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基于多光子非线性Compton散射模型,研究了Compton散射下等离子体中强朗缪尔湍动对调制不稳定性的影响。将入射光和Compton散射光作为形成强朗缪尔湍动和调制不稳定性的新机制,给出了强朗缪尔湍动、色散和调制不稳定性时间增长率所满足的修正方程,并进行了数值模拟。结果表明,与Compton散射前相比,Compton散射使等离子体内产生了更为剧烈的坍塌,坍塌后期形成的强朗缪尔湍动,使等离子体界面附近的调制不稳定性的时间增长率显著增大,调制不稳定性发展得更快,光场峰值增加得更强,并使整体激光场出现明显的成丝现象。     

Collapsed 5-manifolds with pinched positive sectional curvature

Let M be a closed 5-manifold of pinched curvature 0<δ?secM?1. We prove that M is homeomorphic to a spherical space form if one of the following conditions holds:

(i)

The center of the fundamental group has index ?w(δ), a constant depending on δ;

(ii)

and the fundamental group is a non-cyclic group of order ?C, a constant;

(iii)

The volume is less than ?(δ) and the fundamental group is either isomorphic to a spherical 5-space group or has an odd order, and it has a center of index ?w, a constant.

     

Vortex dynamics of collapsing bubbles: Impact on the boundary layer measured by chronoamperometry

Cavitation bubbles collapsing in the vicinity to a solid substrate induce intense micro-convection at the solid. Here we study the transient near-wall flows generated by single collapsing bubbles by chronoamperometric measurements synchronously coupled with high-speed imaging. The individual bubbles are created at confined positions by a focused laser pulse. They reach a maximum expansion radius of approximately 425 μm. Several stand-off distances to the flat solid boundary are investigated and all distances are chosen sufficiently large that no gas phase of the expanding and collapsing bubble touches the solid directly. With a microelectrode embedded into the substrate, the time-resolved perturbations in the liquid shear layer are probed by means of a chronoamperometric technique. The measurements of electric current are synchronized with high-speed imaging of the bubble dynamics. The perturbations of the near-wall layer are found to result mainly from ring vortices created by the jetting bubble. Other bubble induced flows, such as the jet and flows following the radial bubble oscillations are perceptible with this technique, but show a minor influence at the stand-off distances investigated.     

超声清洗过程环境压力对声空化效应的影响*

在不同深度条件下的水下构建物超声清洗中,声空化是重要的源动力之一。为探明水下环境压力对声空化的影响,本文基于数值计算的方法,通过对超声波作用下气泡动力学的研究,讨论了环境压力对空化泡溃灭时的气泡最大半径、释放能量以及溃灭功率等因素的影响。结果表明：空化泡最大半径与环境压力在一定范围内呈近似线性关系;随着环境压力增大,空化泡释放能量和溃灭功率均显著减小,且两者在变化趋势和变化幅度上几乎一致;当环境压力大于声压幅值时,空化泡的最大半径、内部压强、内部温度与释放能量均远低于空化发生在环境压力小于声压幅值时的情形。     

Phase Transition of Meshwork Models for Spherical Membranes

We have studied two types of meshwork models by using the canonical Monte Carlo simulation technique. The first meshwork model has elastic junctions, which are composed of vertices, bonds, and triangles, while the second model has rigid junctions, which are hexagonal (or pentagonal) rigid plates. Two-dimensional elasticity is assumed only at the elastic junctions in the first model, and no two-dimensional bending elasticity is assumed in the second model. Both of the meshworks are of spherical topology. We find that both models undergo a first-order collapsing transition between the smooth spherical phase and the collapsed phase. The Hausdorff dimension of the smooth phase is H≃2 in both models as expected. It is also found that H≃2 in the collapsed phase of the second model, and that H is relatively larger than 2 in the collapsed phase of the first model, but it remains in the physical bound, i.e., H<3. Moreover, the first model undergoes a discontinuous surface fluctuations transition at the same transition point as that of the collapsing transition, while the second model undergoes a continuous transition of surface fluctuation. This indicates that the phase structure of the meshwork model is weakly dependent on the elasticity at the junctions. This work was supported in part by a Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science.     

A generalized π2-diffeomorphism finiteness theorem

The π₂-diffeomorphism finiteness result of F. Fang-X. Rong and A. Petrunin-W. Tuschmann (independently) asserts that the diffeomorphic types of compact n-manifolds M with vanishing first and second homotopy groups can be bounded above in terms of n; and upper bounds on the absolute value of sectional curvature and diameter of M: In this paper, we will generalize this π₂-diffeomorphism finiteness by removing the condition that π₁(M) = 0 and asserting the diffeomorphism finiteness on the Riemannian universal cover of M:     

Changing cofinalities and collapsing cardinals in models of set theory

If a˜cardinal κ₁, regular in the ground model M, is collapsed in the extension N to a˜cardinal κ₀ and its new cofinality, ρ, is less than κ₀, then, under some additional assumptions, each cardinal λ>κ₁ less than cc(P(κ₁)/[κ₁]^<κ₁) is collapsed to κ₀ as well. If in addition N=M[f], where f : ρ→κ₁ is an unbounded mapping, then N is a˜|λ|=κ₀-minimal extension. This and similar results are applied to generalized forcing notions of Bukovský and Namba.