We are concerned with the following density-suppressed motility model: ut = Δ(γ(v)u) + μu(1 − u); vt = Δv + u − v, in a bounded smooth domain Ω ⊂ R 2 with homogeneous Neumann boundary conditions, where the motility function γ(v) ∈ C 3 ([0, ∞)), γ(v) > 0, γ (v) < 0 for all v ≥ 0, limv→∞ γ(v) = 0, and limv→∞ γ (v) γ(v) exists. The model is proposed to advocate a new possible mechanism: density-suppressed motility can induce spatio-temporal pattern formation through self-trapping. The major technical difficulty in the analysis of above density-suppressed motility model is the possible degeneracy of diffusion from the condition limv→∞ γ(v) = 0. In this paper, by treating the motility function γ(v) as a weight function and employing the method of weighted energy estimates, we derive the a priori L ∞-bound of v to rule out the degeneracy and establish the global existence of classical solutions of the above problem with a uniform-in-time bound. Furthermore, we show if μ > K 0 16 with K 0 = max 0≤v≤∞ |γ (v)| 2 γ(v) , the constant steady state (1, 1) is globally asymptotically stable and, hence, pattern formation does not exist. For small μ > 0, we perform numerical simulations to illustrate aggregation patterns and wave propagation formed by the model.

No abstract

No abstract

Axial vector (J P C = 1 ++ ) charmonium and bottomonium hybrid masses are determined via QCD Laplace sum-rules. Previous sum-rule studies in this channel did not incorporate the dimension-six gluon condensate, which has been shown to be important for 1 −− and 0 −+ heavy quark hybrids. An updated analysis of axial vector charmonium and bottomonium hybrids is presented, including the effects of the dimension-six gluon condensate. The axial vector charmonium and bottomonium hybrid masses are predicted to be 5.13 GeV and 11.32 GeV, respectively. We discuss the implications of this result for the charmonium-like "XYZ" states and the charmonium hybrid multiplet structure observed in recent lattice calculations.

No abstract

No abstract

No abstract

No abstract