Three-dimensional pattern formation, multiple homogeneous soft modes, and nonlinear dielectric electroconvection

Patterns forming spontaneously in extended, three-dimensional, dissipative systems are likely to excite several homogeneous soft modes (approximate to hydrodynamic modes) of the underlying physical system, much more than quasi-one- (1D) and two-dimensional (2D) patterns are. The reason is the lack of damping boundaries. This paper compares two analytic techniques to derive the pattern dynamics from hydrodynamics, which are usually equivalent but lead to different results when applied to multiple homogeneous soft modes. Dielectric electroconvection in nematic liquid crystals is introduced as a model for 3D pattern formation. The 3D pattern dynamics including soft modes are derived. For slabs of large but finite thickness the description is reduced further to a 2D one. It is argued that the range of validity of 2D descriptions is limited to a very small region above threshold. The transition from 2D to 3D pattern dynamics is discussed. Experimentally testable predictions for the stable range of ideal patterns and the electric Nusselt numbers are made. For most results analytic approximations in terms of material parameters are given. [S1063-651X(00)09512-X].

Rigorous conditions for food-web intervality in high-dimensional trophic niche spaces

Food webs represent trophic (feeding) interactions in ecosystems. Since the late 1970s, it has been recognized that food-webs have a surprisingly close relationship to interval graphs. One interpretation of food-web intervality is that trophic niche space is low-dimensional, meaning that the trophic character of a species can be expressed by a single or at most a few quantitative traits. In a companion paper we demonstrated, by simulating a minimal food-web model, that food webs are also expected to be interval when niche-space is high-dimensional. Here we characterize the fundamental mechanisms underlying this phenomenon by proving a set of rigorous conditions for food-web intervality in high-dimensional niche spaces. Our results apply to a large class of food-web models, including the special case previously studied numerically.

Detailed analytical investigation of magnetic field line random walk in turbulent plasmas: I. Two-component slab/two-dimensional turbulence

The random displacement of magnetic field lines in the presence of magnetic turbulence in plasmas is investigated from first principles. A two-component (slab/two-dimensional composite) model for the turbulence spectrum is employes. An analytical investigation of the asymptotic behavior of the field-line mean square displacement (FL-MSD) is carried out. It is shown that the magnetic field lines behave superdifusively for every large values of the position variable z, since the FL-MSD sigma varies as sigma similar to z(4/3). An intermediate diffusive regime may also possible exist for finite values of z under conditions which are explicitly determined in terms of the intrinsic turbulent plasma parameters. The superdiffusie asymptotic result is confirmed numerically via an iterative algorithm. The relevance to previous resuslts is discussed.

Microcomputed tomography imaging in a rat model of delayed union/non-union fracture

We aimed to develop a clinically relevant delayed union/non-union fracture model to evaluate a cell therapy intervention repair strategy. Histology, three-dimensional (3D) micro-computed tomography (micro-CT) imaging and mechanical testing were utilized to develop an analytical protocol for qualitative and quantitative assessment of fracture repair. An open femoral diaphyseal osteotomy, combined with periosteal diathermy and endosteal excision, was held in compression by a four pin unilateral external fixator. Three delayed union/non-union fracture groups established at 6 weeks-(a) a control group, (b) a cell therapy group, and (c) a group receiving phosphate-buffered saline (PBS) injection alone-were examined subsequently at 8 and 14 weeks. The histological response was combined fibrous and cartilaginous non-unions in groups A and B with fibrous non-unions in group C. Mineralized callus volume/total volume percentage showed no statistically significant differences between groups. Endosteal calcified tissue volume/endosteal tissue volume, at the center of the fracture site, displayed statistically significant differences between 8 and 14 weeks for cell and PBS intervention groups but not for the control group. The percentage load to failure was significantly lower in the control and cell treatment groups than in the PBS alone group. High-resolution micro-CT imaging provides a powerful tool to augment characterization of repair in delayed union/non-union fractures together with outcomes such as histology and mechanical strength measurement. Accurate, nondestructive, 3D identification of mineralization progression in repairing fractures is enabled in the presence or absence of intervention strategies. (c) 2007 Orthopaedic Research Society.

Phase diagram of spin-1 bosons on one-dimensional lattices

Spinor Bose condensates loaded in optical lattices have a rich phase diagram characterized by different magnetic order. Here we apply the density matrix renormalization group to accurately determine the phase diagram for spin-1 bosons loaded on a one-dimensional lattice. The Mott lobes present an even or odd asymmetry associated to the boson filling. We show that for odd fillings the insulating phase is always in a dimerized state. The results obtained in this work are also relevant for the determination of the ground state phase diagram of the S=1 Heisenberg model with biquadratic interaction.

ON THE UNIVERSALITY OF 2-DIMENSIONAL DIFFUSION-LIMITED DEPOSITION

A history dependent stick probability is introduced to the diffusion-limited deposition model. The exponents in the scaling laws are calculated. The universality class is also discussed.

A technique for mapping three-dimensional number densities of species in laser produced plumes

The potential of a diagnostic technique to provide quantitative three-dimensional (3D) density distributions of species in a low temperature laser-produced plume is shown. An expanded, short pulse, tunable dye laser is used to probe the plume at a set time during the expansion. Simultaneous recording of two-dimensional in-line absorbance maps and orthogonal recording of laser induced fluorescence permits the 3D density mapping by scanning the dye laser frequency. Preliminary data, supported by a simple model, is presented for the case of Ba II ions in a YBCO plume heated by a KrF laser. (C) 1996 American Institute of Physics.

Asymptotic layer-type model of high pressure direct current glow discharge in electronegative gases

Here a self-consistent one-dimensional continuum model is presented for a narrow gap plane-parallel dc glow discharge. The governing equations consist of continuity and momentum equations for positive and negative ions and electrons coupled with Poisson's equation. A singular perturbation method is developed for the analysis of high pressure dc glow discharge. The kinetic processes of the ionization, electron attachment, and ion-ion recombination are included in the model. Explicit results are obtained for the asymptotic limits: delta=(r(D)/L)(2)--> 0, omega=(r(S)/L)(2)--> 0, where r(D) is the Debye radius, r(S) is recombination length, and L is the gap length. The discharge gap divides naturally into four layers with multiple space scales: anode fall region, positive column, transitional region, cathode fall region and diffusion layer adjacent to the cathode surface, its formation is discussed. The effects of the gas pressure, gap spacing and dc voltage on the electrical properties of the layers and its dimension are investigated. (C) 2000 American Institute of Physics. [S0021-8979(00)00813-6].

Dynamical scattering models in optomechanics: Going beyond the 'coupled cavities' model

Recently [A. Xuereb, et al., Phys. Rev. Lett. 105, 013602 (2010)], we calculated the radiation field and the optical forces acting on a moving object inside a general one-dimensional configuration of immobile optical elements. In this article we analyse the forces acting on a semi-transparent mirror in the 'membrane-in-the-middle' configuration and compare the results obtained from solving scattering model to those from the coupled cavities model that is often used in cavity optomechanical system. We highlight the departure of this model from the more exact scattering theory when the reflectivity of the moving element drops below about 50%.

Kinematic Analysis and Dimensional Synthesis of Exechon Parallel Kinematic Machine for Large Volume Machining

A parallel kinematic machine (PKM) topology can only give its best performance when its geometrical parameters are optimized. In this paper, dimensional synthesis of a newly developed PKM is presented for the first time. An optimization method is developed with the objective to maximize both workspace volume and global dexterity of the PKM. Results show that the method can effectively identify design parameter changes under different weighted objectives. The PKM with optimized dimensions has a large workspace to footprint ratio and a large well-conditioned workspace, hence justifies its suitability for large volume machining.

Two-dimensional Monte Carlo simulations of H i line formation in massive young stellar object disc winds

Massive young stellar objects (YSOs) are powerful infrared Hi line emitters. It has been suggested that these lines form in an outflow from a disc surrounding the YSO. Here, new two-dimensional Monte Carlo radiative transfer calculations are described which test this hypothesis. Infrared spectra are synthesized for a YSO disc wind model based on earlier hydrodynamical calculations. The model spectra are in qualitative agreement with the observed spectra from massive YSOs, and therefore provide support for a disc wind explanation for the Hi lines. However, there are some significant differences: the models tend to overpredict the Bra/Br? ratio of equivalent widths and produce line profiles which are slightly too broad and, in contrast to typical observations, are double-peaked. The interpretation of these differences within the context of the disc wind picture and suggestions for their resolution via modifications to the assumed disc and outflow structure are discussed. © 2005 RAS.

Time-dependent three-dimensional spectrum synthesis for Type Ia supernovae

A Monte Carlo code (artis) for modelling time-dependent three-dimensional spectral synthesis in chemically inhomogeneous models of Type Ia supernova ejecta is presented. Following the propagation of ?-ray photons, emitted by the radioactive decay of the nucleosynthesis products, energy is deposited in the supernova ejecta and the radiative transfer problem is solved self-consistently, enforcing the constraint of energy conservation in the comoving frame. Assuming a photoionization-dominated plasma, the equations of ionization equilibrium are solved together with the thermal balance equation adopting an approximate treatment of excitation. Since we implement a fully general treatment of line formation, there are no free parameters to adjust. Thus, a direct comparison between synthetic spectra and light curves, calculated from hydrodynamic explosion models, and observations is feasible. The code is applied to the well-known W7 explosion model and the results tested against other studies. Finally, the effect of asymmetric ejecta on broad-band light curves and spectra is illustrated using an elliptical toy model. © 2009 RAS.

Three-dimensional delayed-detonation models with nucleosynthesis for type ia supernovae

We present results for a suite of 14 three-dimensional, high-resolution hydrodynamical simulations of delayed-detonation models of Type Ia supernova (SN Ia) explosions. This model suite comprises the first set of three-dimensional SN Ia simulations with detailed isotopic yield information. As such, it may serve as a data base for Chandrasekhar-mass delayed-detonation model nucleosynthetic yields and for deriving synthetic observables such as spectra and light curves. We employ aphysically motivated, stochastic model based on turbulent velocity fluctuations and fuel density to calculate in situ the deflagration-to-detonation transition probabilities. To obtain different strengths of the deflagration phase and thereby different degrees of pre-expansion, we have chosen a sequence of initial models with 1, 3, 5, 10, 20, 40, 100, 150, 200, 300 and 1600 (two different realizations) ignition kernels in a hydrostatic white dwarf with a central density of 2.9 × 10 g cm, as well as one high central density (5.5 × 10 g cm) and one low central density (1.0 × 10 g cm) rendition of the 100 ignition kernel configuration. For each simulation, we determined detailed nucleosynthetic yields by postprocessing10 tracer particles with a 384 nuclide reaction network. All delayed-detonation models result in explosions unbinding thewhite dwarf, producing a range of 56Ni masses from 0.32 to 1.11M. As a general trend, the models predict that the stableneutron-rich iron-group isotopes are not found at the lowest velocities, but rather at intermediate velocities (~3000×10 000 km s) in a shell surrounding a Ni-rich core. The models further predict relatively low-velocity oxygen and carbon, with typical minimum velocities around 4000 and 10 000 km s, respectively. © 2012 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society.

Automatic dimensional reduction and meshing of stiffened thin-wall structures

The creation of idealised, dimensionally reduced meshes for preliminary design and optimisation remains a time-consuming, manual task. A dimensionally reduced model is ideal for assessing design changes through modification of element properties without the need to create a new geometry or mesh. In this paper, a novel approach for automating the creation of mixed dimensional meshes is presented. The input to the process is a solid model which has been decomposed into a non-manifold assembly of smaller volumes with different meshing significance. Associativity between the original solid model and the dimensionally reduced equivalent is maintained. The approach is validated by means of a free-free modal analysis on an output mesh of a gas turbine engine component of industrial complexity. Extensions and enhancements to this work are also discussed.

Human pose tracking in low dimensional space enhanced by limb correction

This paper proposes a two-level 3D human pose tracking method for a specific action captured by several cameras. The generation of pose estimates relies on fitting a 3D articulated model on a Visual Hull generated from the input images. First, an initial pose estimate is constrained by a low dimensional manifold learnt by Temporal Laplacian Eigenmaps. Then, an improved global pose is calculated by refining individual limb poses. The validation of our method uses a public standard dataset and demonstrates its accurate and computational efficiency. © 2011 IEEE.