Minimising wave drag for free surface flow past a two-dimensional stern

Free surface flow past a two-dimensional semi-infinite curved plate is considered, with emphasis given to solving for the shape of the resulting wave train that appears downstream on the surface of the fluid. This flow configuration can be interpreted as applying near the stern of a wide blunt ship. For steady flow in a fluid of finite depth, we apply the Wiener-Hopf technique to solve a linearised problem, valid for small perturbations of the uniform stream. Weakly nonlinear results found using a forced KdV equation are also presented, as are numerical solutions to the fully nonlinear problem, computed using a conformal mapping and a boundary integral technique. By considering different families of shapes for the semi-infinite plate, it is shown how the amplitude of the waves can be minimised. For plates that increase in height as a function of the direction of flow, reach a local maximum, and then point slightly downwards at the point at which the free surface detaches, it appears the downstream wavetrain can be eliminated entirely.

Effective shear modulus approach for two dimensional solids and plate bending problems by meshless point collocation method

For the analysis of material nonlinearity, an effective shear modulus approach based on the strain control method is proposed in this paper by using point collocation method. Hencky’s total deformation theory is used to evaluate the effective shear modulus, Young’s modulus and Poisson’s ratio, which are treated as spatial field variables. These effective properties are obtained by the strain controlled projection method in an iterative manner. To evaluate the second order derivatives of shape function at the field point, the radial basis function (RBF) in the local support domain is used. Several numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method and comparisons have been made with analytical solutions and the finite element method (ABAQUS).

Two-dimensional simulation of nanoparticle deposition from high-density plasmas on microstructured surfaces

Selective and controlled deposition of plasma-grown nanoparticles is one of the pressing problems of plasma-aided nanofabrication. The results of advanced numerical simulations of motion of charge-variable nanoparticles in the plasma presheath and sheath areas and in localized microscopic electric fields created by surface microstructures are reported. Conditions for site-selective deposition of such nanoparticles onto individual microstructures and open surface areas within a periodic micropattern are formulated. The effects of plasma parameters, surface potential, and micropattern features on nanoparticle deposition are investigated and explained using particle charging and plasma force arguments. The results are generic and applicable to a broad range of nanoparticle-generating plasmas and practical problems ranging from management of nanoparticle contamination in microelectronics to site-selective nanoparticle deposition into specified device locations, and synthesis of advanced microporous materials and nanoparticle superlattices. © 2007 American Institute of Physics.

Evaluation of two-dimensional quantizers for Fourier transform binary holograms

Quantization formats of four digital holographic codes (Lohmann,Lee, Burckhardt and Hsueh-Sawchuk) are evaluated. A quantitative assessment is made from errors in both the Fourier transform and image domains. In general, small errors in the Fourier amplitude or phase alone do not guarantee high image fidelity. From quantization considerations, the Lee hologram is shown to be the best choice for randomly phase coded objects. When phase coding is not feasible, the Lohmann hologram is preferable as it is easier to plot.

Jumping numbers of a simple complete ideal in a two-dimensional regular local ring

The multiplier ideals of an ideal in a regular local ring form a family of ideals parametrized by non-negative rational numbers. As the rational number increases the corresponding multiplier ideal remains unchanged until at some point it gets strictly smaller. A rational number where this kind of diminishing occurs is called a jumping number of the ideal. In this manuscript we shall give an explicit formula for the jumping numbers of a simple complete ideal in a two dimensional regular local ring. In particular, we obtain a formula for the jumping numbers of an analytically irreducible plane curve. We then show that the jumping numbers determine the equisingularity class of the curve.

On the computation of two-dimensional compressible flow fields by the modified local stability scheme

The modified local stability scheme is applied to several two-dimensional problems—blunt body flow, regular reflection of a shock and lambda shock. The resolution of the flow features obtained by the modified local stability scheme is found to be better than that achieved by the other first order schemes and almost identical to that achieved by the second order schemes incorporating artificial viscosity. The scheme is easy for coding, consumes moderate amount of computer storage and time. The scheme can be advantageously used in place of second order schemes.

Chemically Programmed Ultrahigh Density Two-Dimensional Semiconductor Superlattice Array

Designing an ultrahigh density linear superlattice array consisting of periodic blocks of different semiconductors in the strong confinement regime via a direct synthetic route remains an unachieved challenge in nanotechnology. We report a general synthesis route for the formulation of a large-area ultrahigh density superlattice array that involves adjoining multiple units of ZnS rods by prolate US particles at the tips. A single one-dimensional wire is 300-500 nm long and consists of periodic quantum wells with a barrier width of 5 nm provided by ZnS and a well width of 1-2 nm provided by CdS, defining a superlattice structure. The synthesis route allows for tailoring of ultranarrow laserlike emissions (fwhm approximate to 125 meV) originating from strong interwell energy dispersion along with control of the width, pitch, and registry of the superlattice assembly. Such an exceptional high-density superlattice array could form the basis of ultrahigh density memories in addition to offering opportunities for technological advancement in conventional heterojunction-based device applications.

Solid-solid collapse transition in a two dimensional model molecular system

Solid-solid collapse transition in open framework structures is ubiquitous in nature. The real difficulty in understanding detailed microscopic aspects of such transitions in molecular systems arises from the interplay between different energy and length scales involved in molecular systems, often mediated through a solvent. In this work we employ Monte-Carlo simulation to study the collapse transition in a model molecular system interacting via both isotropic as well as anisotropic interactions having different length and energy scales. The model we use is known as Mercedes-Benz (MB), which, for a specific set of parameters, sustains two solid phases: honeycomb and oblique. In order to study the temperature induced collapse transition, we start with a metastable honeycomb solid and induce transition by increasing temperature. High density oblique solid so formed has two characteristic length scales corresponding to isotropic and anisotropic parts of interaction potential. Contrary to the common belief and classical nucleation theory, interestingly, we find linear strip-like nucleating clusters having significantly different order and average coordination number than the bulk stable phase. In the early stage of growth, the cluster grows as a linear strip, followed by branched and ring-like strips. The geometry of growing cluster is a consequence of the delicate balance between two types of interactions, which enables the dominance of stabilizing energy over destabilizing surface energy. The nucleus of stable oblique phase is wetted by intermediate order particles, which minimizes the surface free energy. In the case of pressure induced transition at low temperature the collapsed state is a disordered solid. The disordered solid phase has diverse local quasi-stable structures along with oblique-solid like domains. (C) 2013 AIP Publishing LLC.

Low-density three-dimensional foam using self-reinforced hybrid two-dimensional atomic layers

Low-density nanostructured foams are often limited in applications due to their low mechanical and thermal stabilities. Here we report an approach of building the structural units of three-dimensional (3D) foams using hybrid two-dimensional (2D) atomic layers made of stacked graphene oxide layers reinforced with conformal hexagonal boron nitride (h-BN) platelets. The ultra-low density (1/400 times density of graphite) 3D porous structures are scalably synthesized using solution processing method. A layered 3D foam structure forms due to presence of h-BN and significant improvements in the mechanical properties are observed for the hybrid foam structures, over a range of temperatures, compared with pristine graphene oxide or reduced graphene oxide foams. It is found that domains of h-BN layers on the graphene oxide framework help to reinforce the 2D structural units, providing the observed improvement in mechanical integrity of the 3D foam structure.

Asymptotic scaling in the two-dimensional O(3) Nonlinear sigma model: a Monte Carlo study on parallel computers

We investigate the 2d O(3) model with the standard action by Monte Carlo simulation at couplings β up to 2.05. We measure the energy density, mass gap and susceptibility of the model, and gather high statistics on lattices of size L ≤ 1024 using the Floating Point Systems T-series vector hypercube and the Thinking Machines Corp.'s Connection Machine 2. Asymptotic scaling does not appear to set in for this action, even at β = 2.10, where the correlation length is 420. We observe a 20% difference between our estimate m/Λ^─_(Ms) = 3.52(6) at this β and the recent exact analytical result . We use the overrelaxation algorithm interleaved with Metropolis updates and show that decorrelation time scales with the correlation length and the number of overrelaxation steps per sweep. We determine its effective dynamical critical exponent to be z' = 1.079(10); thus critical slowing down is reduced significantly for this local algorithm that is vectorizable and parallelizable.

We also use the cluster Monte Carlo algorithms, which are non-local Monte Carlo update schemes which can greatly increase the efficiency of computer simulations of spin models. The major computational task in these algorithms is connected component labeling, to identify clusters of connected sites on a lattice. We have devised some new SIMD component labeling algorithms, and implemented them on the Connection Machine. We investigate their performance when applied to the cluster update of the two dimensional Ising spin model.

Finally we use a Monte Carlo Renormalization Group method to directly measure the couplings of block Hamiltonians at different blocking levels. For the usual averaging block transformation we confirm the renormalized trajectory (RT) observed by Okawa. For another improved probabilistic block transformation we find the RT, showing that it is much closer to the Standard Action. We then use this block transformation to obtain the discrete β-function of the model which we compare to the perturbative result. We do not see convergence, except when using a rescaled coupling β_E to effectively resum the series. For the latter case we see agreement for m/ Λ^─_(Ms) at , β = 2.14, 2.26, 2.38 and 2.50. To three loops m/Λ^─_(Ms) = 3.047(35) at β = 2.50, which is very close to the exact value m/ Λ^─_(Ms) = 2.943. Our last point at β = 2.62 disagrees with this estimate however.

STUDY ON MICROWAVE CYCLOTRON RESONANCE OF HIGH-MOBILITY GaAs/Al-0.35 Ga-0.65 As TWO-DIMENSIONAL ELECTRON GAS

The properties of electron states in the presence of microwave irradiation play a key role in understanding the oscillations of longitudinal resistance and the zero-resistance states in a high-mobility two-dimensional electron gas(2DEG) in low magnetic field. The properties of electron states in a high-mobility and low-density GaAs/Al0.35Ga0.65As 2DEG in the presence of Ka-band microwave irradiation were studied by reflectance-based optically detected cyclotron resonance(RODCR). The influences of the direction of microwave alternating electronic field, wavelength of the laser, and temperature on RODCR results were discussed. The results show that RODCR measurements provide a convenient and powerful method for studying electron states in 2DEG.

Effect of electron-electron scattering on spin dephasing in a high-mobility low-density two-dimensional electron gas

By utilizing time-resolved Kerr rotation techniques, we have investigated the spin dynamics of a high-mobility low density two-dimensional electron gas in a GaAs/Al0.35Ga0.65As heterostructure in the dependence on temperature from 1.5 to 30 K. It is found that the spin relaxation/dephasing time under a magnetic field of 0.5 T exhibits a maximum of 3.12 ns around 14 K, which is superimposed on an increasing background with rising temperature. The appearance of the maximum is ascribed to that at the temperature where the crossover from the degenerate to the nondegenerate regime takes place, electron-electron Coulomb scattering becomes strongest, and thus inhomogeneous precession broadening due to the D'yakonov-Perel' mechanism becomes weakest. These results agree with the recent theoretical predictions [J. Zhou et al., Phys. Rev. B 15, 045305 (2007)], which verify the importance of electron-electron Coulomb scattering to electron spin relaxation/dephasing.

Spin dynamics of electrons in the first excited subband of a high-mobility low-density two-dimensional electron system

We report on time-resolved Kerr rotation measurements of spin coherence of electrons in the first excited subband of a high-mobility low-density two-dimensional electron system in a GaAs/Al0.35Ga0.65As heterostructure. While the transverse spin lifetime (T-2(*)) of electrons decreases monotonically with increasing magnetic field, it has a nonmonotonic dependence on the temperature and reaches a peak value of 596 ps at 36 K, indicating the effect of intersubband electron-electron scattering on the electron-spin relaxation.

Spin-polarized transport of two-dimensional electron gas embedded in a diluted magnetic semiconductor

The spin-polarized transport property of a diluted magnetic semiconductor two-dimensional electron gas is investigated theoretically at low temperature. A large current polarization can be found in this system even at small magnetic fields and oscillates with increasing magnetic field while the carrier polarization is vanishingly small. The magnitude as well as the sign of the current polarization can be tuned by varying magnetic field, the electron density and the Mn concentration. (c) 2005 American Institute of Physics.

Mode softening in charge-density excitations of a two-dimensional electron gas driven by Rashba spin-orbit interaction

The electron density response of a uniform two-dimensional (2D) electron gas is investigated in the presence of a perpendicular magnetic field and Rashba spin-orbit interaction (SOI). It is found that, within the Hartree-Fock approximation, a charge density excitation mode below the cyclotron resonance frequency shows a mode softening behavior, when the spin-orbit coupling strength falls into a certain interval. This mode softening indicates that the ground state of an interacting uniform 2D electron gas may be driven by the Rashba SOI to undergo a phase transition to a nonuniform charge density wave state.