Colloquium at Tsinghua University, Tsinghua University, Beijing, China, October 23, 2014 2014
DOI: 10.2172/1989369
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Fundamental Structue of Matter and Interactions

Abstract: We study the Lane-Emden problemwhere Ω ⊂ R 2 is a smooth bounded domain and p > 1 is sufficiently large. We obtain sharp estimates and non-degeneracy of low energy nodal solutions u p (i.e. nodal solutions satisfying lim p→+∞ p Ω |u p | p+1 dx = 16πe). As applications, we prove that the comparable condition p( u 1) holds automatically for least energy nodal solutions, which confirms a conjecture raised by (Grossi-Grumiau-Pacella, Ann.

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Cited by 45 publications
(59 citation statements)
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“…where C is the contact coefficient between the crystallites (Shen and Hu, 2006). Superscripts 1 and 2 denote the series model and parallel model, respectively.…”
Section: Determination Of Model Parametersmentioning
confidence: 99%
“…where C is the contact coefficient between the crystallites (Shen and Hu, 2006). Superscripts 1 and 2 denote the series model and parallel model, respectively.…”
Section: Determination Of Model Parametersmentioning
confidence: 99%
“…Zhu et al [50,51] also proposed the "nanoparticle modulation" technique, which reduces the cohesion of fine particles and improves their flow and fluidization quality by applying ultrafine nanoparticles as fluidization additives. On the other hand, Huang et al [52] analyzed the influence of the surface roughness on interparticle forces, and the control over interparticle forces can improve the fluidization performance of particles. In the dry gas-solid reaction system, the fluidization characteristics of particles depend on the cohesive force (mainly the vdW force) and gravity, and the ratio of the cohesive force to gravity can reflect the relative strength of the cohesive force of particles, which can be defined by the dimensionless cohesive number C o .…”
Section: Fluidization Mechanism Of Nano Agglomerationsmentioning
confidence: 99%
“…The motion of the rigid body barycenter is decomposed into the translational motion of this point and the rotation around this point, which is described by 15 equations combined with 15 variables. The relevant equations can be expressed as follows [14]:…”
Section: Kinetic Equationsmentioning
confidence: 99%