Global Existence for a Parabolic-hyperbolic Free Boundary Problem Modelling Tumor Growth

In this paper we study a free boundary problem modelling tumor growth, proposed by A. Friedman in 2004. This free boundary problem involves a nonlinear second-order parabolic equation describing the diffusion of nutrient in the tumor, and three nonlinear first-order hyperbolic equations describing the evolution of proliferative cells, quiescent cells and dead cells, respectively. By applying Lp theory of parabolic equations, the characteristic theory of hyperbolic equations, and the Banach fixed point theorem, we prove that this problem has a unique global classical solution.     

A three-dimensional steady-state tumor system

The growth of tumors can be modeled as a free boundary problem involving partial differential equations. We consider one such model and compute steady-state solutions for this model. These solutions include radially symmetric solutions where the free boundary is a sphere and nonradially symmetric solutions. Linear and nonlinear stability for these solutions are determined numerically.     

化学气相沉积法制备大面积二维材料薄膜:方法与机制

近年来,二维层状材料由于其丰富的材料体系和独特的物理化学性质而受到人们的广泛关注.后摩尔时代要求器件高度集成化,大面积、高质量的二维材料可以保证器件中结构和电子性能的连续性.要实现二维材料工业级别的规模化生产,样品的可控制备是其前提.化学气相沉积是满足上述要求的一种强有力的方法,已广泛应用于二维材料及其复合结构的生长制...     

Heterogeneous nucleation and depletion effect in nanowire growth

Recent experiments by Ross and co-workers proved the possibility of a mononuclear regime with heterogeneous nucleation as well as jerky growth in the vapor–liquid–solid (VLS) process for silicon nanowires. In this work, a theoretical model is presented which incorporates the effects of (i) a mononuclear regime with layer by layer growth, (i) heterogeneous nucleation of each new layer at the edge of a Au–Si droplet, (iii) drop of supersaturation after each successful nucleation and respective fast layer growth, (iv) time-dependent nucleation barrier during each new waiting period and (v) correlation between subsequent waiting periods (non-Markovian sequence of waiting periods).     

Bifurcation and disaggregation in urban/regional spatial modelling: A technical note

Using the Lowry-Garin model as an example, we illustrate the complexity of bifurcation and aggregation issues in urban/regional spatial systems. As a first step, a disaggregate version of the Lowry-Garin model is formulated. Then the general conditions for bifurcation are identified in terms of disaggregate labor-force participation rate, population-serving ratio and accessibility indices. Physical interpretation of these conditions is also given.     

Multiple domain dynamics simulated with coupled level sets

We adapt the level-set method to simulate epitaxial growth of thin films on a surface that consists of different reconstruction domains. Both the island boundaries and the boundaries of the reconstruction domains are described by different level-set functions. A formalism of coupled level-set functions that describe entirely different physical properties is introduced, where the velocity of each level-set function is determined by the value of the other level-set functions.     

Tangential Limits of Potentials on Homogeneous Trees

Let T be a homogeneous tree of homogeneity q+1. Let denote the boundary of T, consisting of all infinite geodesics b=[b ₀,b ₁,b ₂,] beginning at the root, 0. For each b, 1, and a0 we define the approach region _,a (b) to be the set of all vertices t such that, for some j, t is a descendant of b _j and the geodesic distance of t to b _j is at most (–1)j+a. If >1, we view these as tangential approach regions to b with degree of tangency . We consider potentials Gf on T for which the Riesz mass f satisfies the growth condition _T f ^p (t)q ^–|t|<, where p>1 and 0<<1, or p=1 and 0<1. For 11/, we show that Gf(s) has limit zero as s approaches a boundary point b within _,a (b) except for a subset E of of -dimensional Hausdorff measure 0, where H (E)=sup_>0inf _i q ^{–|t i|}:E a subset of the boundary points passing through t _i for some i,|t _i |>log _q (1/).     

Flying qubits and entangled photons

Efficient generation of polarized single photons or entangled photon pairs is crucial for the implementation of quantum key distribution (QKD) systems. Self organized semiconductor quantum dots (QDs) are capable of emitting on demand one polarized photon or an entangled photon pair upon current injection. Highly efficient single‐photon sources consist of a pin structure inserted into a microcavity where single electrons and holes are funneled into an InAs QD via a submicron AlOx aperture, leading to emission of single polarized photons with record purity of the spectrum and non‐classicality of the photons. A new QD site‐control technique is based on using the surface strain field of an AlO_x current aperture below the QD. GaN/AlN QD based devices are promising to operate at room temperature and reveal a fine‐structure splitting (FSS) depending inversely on the QD size. Large GaN/AlN QDs show disappearance of the FSS. Theory also suggests QDs grown on (111)‐oriented GaAs substrates as source of entangled photon pairs.