Resolving Scale Ambiguity Via XSlit Aspect Ratio Analysis

In perspective cameras, images of a frontal-parallel 3D object preserve its aspect ratio invariant to its depth. Such an invariance is useful in photography but is unique to perspective projection. In this paper, we show that alternative non-perspective cameras such as the crossed-slit or XSlit cameras exhibit a different depth-dependent aspect ratio (DDAR) property that can be used to 3D recovery. We first conduct a comprehensive analysis to characterize DDAR, infer object depth from its AR, and model recoverable depth range, sensitivity, and error. We show that repeated shape patterns in real Manhattan World scenes can be used for 3D reconstruction using a single XSlit image. We also extend our analysis to model slopes of lines. Specifically, parallel 3D lines exhibit depth-dependent slopes (DDS) on their images which can also be used to infer their depths. We validate our analyses using real XSlit cameras, XSlit panoramas, and catadioptric mirrors. Experiments show that DDAR and DDS provide important depth cues and enable effective single-image scene reconstruction

Dual equilibrium in a finite aspect ratio tokamak

A new approach to high pressure magnetically-confined plasmas is necessary to design efficient fusion devices. This paper presents an equilibrium combining two solutions of the Grad-Shafranov equation, which describes the magnetohydrodynamic equilibrium in toroidal geometry. The outer equilibrium is paramagnetic and confines the inner equilibrium, whose strong diamagnetism permits to balance large pressure gradients. The existence of both equilibria in the same volume yields a dual equilibrium structure. Their combination also improves free-boundary mode stability

Rayleigh-Benard Convection in Large-Aspect-Ratio Domains

The coarsening and wavenumber selection of striped states growing from random initial conditions are studied in a non-relaxational, spatially extended, and far-from-equilibrium system by performing large-scale numerical simulations of Rayleigh-B\'{e}nard convection in a large-aspect-ratio cylindrical domain with experimentally realistic boundaries. We find evidence that various measures of the coarsening dynamics scale in time with different power-law exponents, indicating that multiple length scales are required in describing the time dependent pattern evolution. The translational correlation length scales with time as $t^{0.12}$, the orientational correlation length scales as $t^{0.54}$, and the density of defects scale as $t^{-0.45}$. The final pattern evolves toward the wavenumber where isolated dislocations become motionless, suggesting a possible wavenumber selection mechanism for large-aspect-ratio convection.Comment: 5 pages, 6 figure

Planar Detonation Wave Initiation in Large-Aspect-Ratio Channels

In this study, two initiator designs are presented that are able to form planar detonations with low input energy in large-aspect-ratio channels over distances corresponding to only a few channel heights. The initiators use a single spark and an array of small channels to shape the detonation wave. The first design, referred to as the static initiator, is simple to construct as it consists of straight channels which connect at right angles. However, it is only able to create planar waves using mixtures that can reliably detonate in its small-width channels. An improved design, referred to as the dynamic initiator, is capable of detonating insensitive mixtures using an oxyacetylene gas slug injected into the initiator shortly before ignition, but is more complex to construct. The two versions are presented next, including an overview of their design and operation. Design drawings of each initiator are available elsewhere [7]. Finally, photographs and pressure traces of the resulting planar waves generated by each device are shown

Aspect-ratio-dependent charging in high-density plasmas

The effect of aspect ratio (depth/width) on charge buildup in trenches during plasma etching of polysilicon-on-insulator structures is studied by Monte Carlo simulations. Increased electron shadowing at larger aspect ratios reduces the electron current to the trench bottom. To reach a new charging steady state, the bottom potential must increase, significantly perturbing the local ion dynamics in the trench: the deflected ions bombard the sidewall with larger energies resulting in severe notching. The results capture reported experimental trends and reveal why the increase in aspect ratio that follows the reduction in critical device dimensions will cause more problems unless the geometry is scaled to maintain a constant aspect ratio

Effect of microchannel aspect ratio on residence time distributions and the axial dispersion coefficient

The effect of microchannel aspect ratio (channel depth/channel width) on residence time distributions and the axial dispersion coefficient have been investigated for Newtonian and shear thinning non-Newtonian flow using computational fluid dynamics. The results reveal that for a fixed cross sectional area and throughput, there is a narrowing of the residence time distribution as the aspect ratio decreases. This is quantified by an axial dispersion coefficient that increases rapidly for aspect ratios less than 0.3 and then tends towards an asymptote as the aspect ratio goes to 1. The results also show that the axial dispersion coefficient is related linearly to the Reynolds number when either the aspect ratio or the mean fluid velocity is varied. However, the fluid Péclet number is a linear function of the Reynolds number only when the aspect ratio (and therefore hydraulic diameter) is varied. Globally, the results indicate that microchannels should be designed with low aspect ratios (≤ 0.3) for reduced axial dispersion

Optimization of low aspect ratio, iron dominated dipole magnets

A study of the optimization of iron dominated dipole magnets with pole face widths comparable or less than the gap size, i.e., low aspect ratio (AR), is conducted using both theoretical and computational approaches. This regime of magnet design is particularly relevant in the context of laser plasma accelerators (LPA) due to unique beam parameters and geometric constraints, namely large energy spreads and the requirement for large apertures to accommodate drive laser passage. The breakdown of commonly employed approximations and rules of thumb in typical AR1 magnet design is examined. A library of generalized, optimized pole face geometries is provided to expedite optimization of future magnets. Finally, this methodology is used to design an electromagnetic chicane which has been fabricated, validated, and is currently in use in an x-ray free electron laser driven LPA experiment at LBNL

Theory of small aspect ratio waves in deep water

In the limit of small values of the aspect ratio parameter (or wave steepness) which measures the amplitude of a surface wave in units of its wave-length, a model equation is derived from the Euler system in infinite depth (deep water) without potential flow assumption. The resulting equation is shown to sustain periodic waves which on the one side tend to the proper linear limit at small amplitudes, on the other side possess a threshold amplitude where wave crest peaking is achieved. An explicit expression of the crest angle at wave breaking is found in terms of the wave velocity. By numerical simulations, stable soliton-like solutions (experiencing elastic interactions) propagate in a given velocities range on the edge of which they tend to the peakon solution.Comment: LaTex file, 16 pages, 4 figure