Narrow Results

The aim of this work is to provide an overview on the recent advances in the selective area growth (SAG) of (In)GaN nanostructures by plasma assisted molecular beam epitaxy, focusing on their potential as building blocks for next generation LEDs.

The first three sections deal with the basic growth mechanisms of GaN SAG and the emission control in the entire ultraviolet to infrared range, including approaches for white light emission, using InGaN disks and thick segments on axial nanocolumns. SAG of axial nanostructures is developed on both GaN/sapphire templates and GaN-buffered Si(111).

As an alternative to axial nanocolumns, section 4 reports on the growth and characterization of InGaN/GaN core-shell structures on an ordered array of top-down patterned GaN microrods. Finally, section 5 reports on the SAG of GaN, with and without InGaN insertion, on semi-polar (11-22) and non-polar (11-20) templates. Upon SAG the high defect density present in the templates is strongly reduced as indicated by a dramatic improvement of the optical properties. In the case of SAG on non-polar (11-22) templates, the formation of nanostructures with a low aspect ratio took place allowing for the fabrication of high-quality, non-polar GaN pseudo-templates by coalescence of these nanostructures.

Molecular dynamics simulations technique is used to study the consolidation of two nanoparticles of Cu element. We have studied sintering processes of two nanoparticles at different temperatures. Two model systems with 4 and 10 nm diameter of particles are selected to study the sintering process of the two nanoparticles. Orientation effects on the physical properties of consolidation of two nanoparticles with respect to each other are investigated. Temperature effects on the consolidation of two nanoparticles are also studied. The order of the values obtained in the simulation for the constant volume heat capacity and latent heat of fusion is good agreement with the bulk results. Moreover, we have investigated the size effects on the consolidation of two different sizes of nanoparticles, that is, one particle of diameter with 10 nm is fixed while the other one is changing from 1 to 10 nm. Melting temperatures of the copper nanoparticles are found to be decreased as the size of the particle decreases. It is found that simulation results are compatible with the other theoretical calculations.

We present an application of the hybrid finite-difference Lattice-Boltzmann model, recently introduced by Lee and coworkers for the numerical simulation of complex multiphase flows.^1–4 Three typical test-case applications are discussed, namely Rayleigh–Taylor instability, liquid droplet break-up and coalescence. The numerical simulations of the Rayleigh–Taylor instability confirm the capability of Lee's method to reproduce literature results obtained with previous Lattice-Boltzmann models for non-ideal fluids. Simulations of two-dimensional droplet breakup reproduce the qualitative regimes observed in three-dimensional simulations, with mild quantitative deviations. Finally, the simulation of droplet coalescence highlights major departures from the three-dimensional picture.

Some properties: average multiplicity, average momentum and average transverse momentum of light nuclei (without identification), produced in ¹²CC collisions at 4.2A GeV/c are studied as a function of centrality. An unexpected change in the behavior of these properties is observed within the same region of centrality, where the multiplicity of the produced light nuclei is increased. These measurements are compared with models, Cascade and Fritiof predictions, which fail to account for the observed effect. It is suggested that the inclusion of nuclear coalescence effect may explain the difference between the measurements and the predictions.

A parallel three-dimensional lattice Boltzmann scheme for multicomponent immiscible fluids is proposed to simulate bubble rising and coalescence process in viscous flows. The lattice Boltzmann scheme is based on the free-energy model and is parallelized in the share-memory model by using the OpenMP. Bubble interface is described by a diffusion interface method solving the Cahn–Hilliard equation and both the surface tension force and the buoyancy are introduced in a form of discrete body force. To avoid the numerical instability caused by the interface deformation, the 18 point finite difference scheme is utilized to calculate the first- and second-order space derivative. The correction of the parallel scheme handling three-dimensional interfaces is verified by the Laplace law and the dynamic characteristics of an isolated bubble in stationary flows. Subsequently, effects of the initially relative position, accompanied by the size ratio on bubble–bubble interaction are studied. The results show that the present scheme can effectively describe the bubble interface dynamics, even if rupture and restructure occurs. In addition to the repulsion and coalescence phenomenon due to the relative position, the size ratio also plays an insignificant role in bubble deformation and trajectory.

The coalescence, the initial stage of sintering, of two contacted Cu nanoparticles is investigated under different heating rates of 700, 350 and 233 K/ns. The nanoparticles coalesced rapidly at the initial stage when the temperature of the system is low. Then, the nanoparticles collided softly in an equilibrium period. After the system was increased to a high temperature, the shrinkage ratio, gyration radius and atoms’ diffusion started to change dramatically. The lower heating rate can result in smaller shrinkage ratio, larger gyration radius and diffusion of atoms. However, the growth of sintering neck is hardly influenced by the heating rate. The results provide a theoretical guidance for the fundamental understanding and potential application regarding nanoparticle sintering.

Molecular dynamic (MD) method is used to study the coalescence and fusing process of Au and Cu nanoclusters. The results show that shear deformation, surface and interface diffusion play important role in different stages of all simulation procedure. In most cases, shear deformation produces the twin boundary or/and stacking fault in particles by particle rotation and slide. The angle between the {111} of Au and Cu particles decrease with increasing temperature, which promotes the formation of the stable interface. Furthermore, the coalescence point and melting temperature increase as cluster diameter increases. For the other cases, there are no particle rotation and slide phenomenon in the elevating temperature process because the stable interface can be formed by forming twin boundaries once two particles contact.

The kinetics of the Ostwald ripening in a homogeneous supersaturated solution is studied both numerically and analytically. The time evolution of the grain-size distribution function in a new phase is theoretically described, taking into account the finite value of the maximal size of a grain. Two situations are considered: the kinetics of grain growth is controlled either by the grain-monomer reaction process (an early stage) or by the monomer diffusion process (a late stage). A transition to the final distribution is shown to take place through an intermediate-asymptotical mode of the Ostwald ripening kinetics, the crossover of the kinetic indices is demonstrated, and the duration of intermediate stage is evaluated.

The complex interactions of two and three spark-generated bubbles are studied using high speed photography. The corresponding simulations are performed using a 3D Boundary Element Method (BEM) code. The bubbles generated are between 3 to 5 mm in radius, and they are either in-phase or out-of-phase with one another. The possible interaction phenomena between two identically sized bubbles are summarized. Depending on their relative distances and phase differences, they can coalesce, jet towards or away from one another, split into smaller bubbles, or 'catapult' away from one another. The 'catapult' effect can be utilized to generated high speed jet in the absence of a solid boundary or shockwave. Also three bubble interactions are highlighted. Complicated phenomena such as bubble forming an elliptical shape and bubble splitting are observed. The BEM simulations provide insight into the physics of the phenomena by providing details such as detailed bubble shape changes (experimental observations are limited by the temporal and spatial resolution), and jet velocity. It is noted that the well-tested BEM code [1,2] utilized here is computationally very efficient as compared to other full-domain methods since only the bubble surface is meshed.

The droplet coalescence phenomenon extensively exists in the industrial production and application, as well as in nature, which is of great research significance. This paper adopted the molecular dynamics (MDs) simulation method to investigate the behavioral characteristics of water/water, ethanol/ethanol and water/ethanol nanodroplets coalescence. The results suggested that, in water and ethanol nanodroplet coalescence process within the water/ethanol system, ethanol was always wrapped on the outer layer of water droplets. The droplet shrinkage in the water/water system was greater than those in the other two systems; meanwhile, that in the water/ethanol system rapidly increased after the contact of droplets, and subsequently surpassed that in the ethanol/ethanol system.

The coalescence of particles extensively exists in the industrial production and nature, which is of great research significance. This paper examined the alloying process of Cu/Au nanoparticles with different sizes by molecular dynamics (MDs) simulations. The coalescence process presents three stages which can be divided by the contact and fusion. The alloying processes of Cu/Au nanoparticles with different sizes had contacted with each other before the heating at 300 K. The Au atoms diffused through the outer area of the sintering neck before the nanoparticles were fused into one particle. The coalescence had become severe after the systems reached the melting temperature. The different systems showed different sintering rate.

With the popularization of 3D printing technology, micro/nanoparticles sintering technology has drawn lots of attentions all over the world. Here, molecular dynamic simulation is employed to discuss the effects of different interfacial lattice structures, different diameter of nanoparticles, and different heating rates on the coalescence of metallic Cu nanoparticles. The results showed that the diameter of nanoparticles determine the melting point of the system. Besides, the interfacial lattice structure, diameter of nanoparticles, and heating rate have an influence on the initial sintering temperature. This is because the melting point is the inherent property of material which relies on the mass of substance. However, the initial sintering temperature is sensitive to many factors, including the temperature, interfacial, and intermolecular interactions.

In the present paper, the smoothness of a Coalescence Hidden-variable Fractal Interpolation Surface (CHFIS), as described by its Lipschitz exponent, is investigated. This is achieved by considering the simulation of a generally uneven surface using CHFIS. The influence of free variables and Lipschitz exponent on the smoothness of CHFIS is demonstrated by considering interpolation data generated from a sample surface.

A two-component analysis of spectra to p_t = 12 GeV/c for identified pions and protons from 200 GeV Au–Au collisions is presented. The method is similar to an analysis of the n_ch dependence of p_t spectra from p–p collisions at 200 GeV, but applied to Au–Au centrality dependence. The soft-component reference is a Lévy distribution on transverse mass m_t. The hard-component reference is a Gaussian on transverse rapidity y_t with exponential (p_t power-law) tail. Deviations of data from the reference are described by hard-component ratio r_AA, which generalizes nuclear modification factor R_AA. The analysis suggests that centrality evolution of pion and proton spectra is dominated by changes in parton fragmentation. The structure of r_AA suggests that parton energy loss produces a negative boost Δy_t of a large fraction (but not all) of the minimum-bias fragment distribution, and that lower-energy partons suffer relatively less energy loss, possibly due to color screening. The analysis also suggests that the anomalous p/π ratio may be due to differences in the parton energy-loss process experienced by the two hadron species. This analysis provides no evidence for radial flow.

This paper generalizes the classical cubic spline with the construction of the cubic spline coalescence hidden variable fractal interpolation function (CHFIF) through its moments, i.e. its second derivative at the mesh points. The second derivative of a cubic spline CHFIF is a typical fractal function that is self-affine or non-self-affine depending on the parameters of the generalized iterated function system. The convergence results and effects of hidden variables are discussed for cubic spline CHFIFs.

Riemann–Liouville fractional calculus of Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) is studied in this paper. It is shown in this paper that fractional integral of order $\nu$ of a CHFIF defined on any interval $[a,b]$ is also a CHFIF albeit passing through different interpolation points. Further, conditions for fractional derivative of order $\nu$ of a CHFIF is derived in this paper. It is shown that under these conditions on free parameters, fractional derivative of order $\nu$ of a CHFIF defined on any interval $[a,b]$ is also a CHFIF.

In this paper, a new notion of super coalescence hidden-variable fractal interpolation function (SCHFIF) is introduced. The construction of SCHFIF involves choosing an IFS from a pool of several non-diagonal IFS at each level of iteration. Further, the integral of a SCHFIF is studied and shown to be a SCHFIF passing through a different set of interpolation data.

In this paper we study the structure of square integrable functionals measurable with respect to coalescing stochastic flows. The case of the Wiener process stopped at the moment of hitting an irregular continuous level is considered. Relying on the change of measure technique, we present a new construction of multiple stochastic integrals with respect to stopped Wiener process. An intrinsic analogue of the Itô–Wiener expansion for the space of square integrable functionals measurable with respect to the stopped Wiener process is constructed.

An infection spreads in a binary tree of height n as follows: initially, each leaf is either infected by one of k states or it is not infected at all. The infection state of each leaf is independently distributed according to a probability vector p = (p₁, …, p_k+1). The remaining nodes become infected or not via annihilation and coalescence: nodes whose two children have the same state (infected or not) are infected (or not) by this state; nodes whose two children have different states are not infected; nodes such that only one of the children is infected are infected by this state. In this paper we characterize, for every p, the limiting distribution at the root node of as n goes to infinity.

We also consider a variant of the model when k = 2 and a mutation can happen, with a fixed probability q, at each infection step. We characterize, in terms of p and q, the limiting distribution at the root node of as n goes to infinity.

The distribution at the root node is driven by a dynamical system, and the proofs rely on the analysis of this dynamics.

Existence of random dynamical systems for a class of coalescing stochastic flows on $ℝ$ is proved. A new state space for coalescing flows is built. As particular cases coalescing flows of solutions to stochastic differential equations and coalescing Harris flows are considered.