Depth of focus and visual acuity with primary and secondary spherical aberration

It is known that the depth of focus (DOF) of the human eye can be affected by the higher order aberrations. We estimated the optimal combinations of primary and secondary Zernike spherical aberration to expand the DOF and evaluated their efficiency in real eyes using an adaptive optics system. The ratio between increased DOF and loss of visual acuity was used as the performance indicator. The results indicate that primary or secondary spherical aberration alone shows similar effectiveness in extending the DOF. However, combinations of primary and secondary spherical aberration with different signs provide better efficiency for expanding the DOF. This finding suggests that the optimal combinations of primary and secondary spherical aberration may be useful in the design of optical presbyopic corrections. © 2011 Elsevier Ltd. All rights reserved.

An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell

We develop a new analytical solution for a reactive transport model that describes the steady-state distribution of oxygen subject to diffusive transport and nonlinear uptake in a sphere. This model was originally reported by Lin (Journal of Theoretical Biology, 1976 v60, pp449–457) to represent the distribution of oxygen inside a cell and has since been studied extensively by both the numerical analysis and formal analysis communities. Here we extend these previous studies by deriving an analytical solution to a generalized reaction-diffusion equation that encompasses Lin’s model as a particular case. We evaluate the solution for the parameter combinations presented by Lin and show that the new solutions are identical to a grid-independent numerical approximation.

Rotorcraft collision avoidance using spherical image-based visual servoing and single point features

This paper presents a reactive collision avoidance method for small unmanned rotorcraft using spherical image-based visual servoing. Only a single point feature is used to guide the aircraft in a safe spiral like trajectory around the target, whilst a spherical camera model ensures the target always remains visible. A decision strategy to stop the avoidance control is derived based on the properties of spiral like motion, and the effect of accurate range measurements on the control scheme is discussed. We show that using a poor range estimate does not significantly degrade the collision avoidance performance, thus relaxing the need for accurate range measurements. We present simulated and experimental results using a small quad rotor to validate the approach.

Predicting the localized surface plasmon resonances of spherical nanoparticles on substrate : electrostatic eigenmode method

We present experimental results that demonstrate that the wavelength of the fundamental localised surface plasmon resonance for spherical gold nanoparticles on glass can be predicted using a simple, one line analytical formula derived from the electrostatic eigenmode method. This allows the role of the substrate in lifting mode degeneracies to be determined, and the role of local environment refractive indices on the plasmon resonance to be investigated. The effect of adding silica to the casting solution in minimizing nanopaticle agglomeration is also discussed.

Aircraft collision avoidance using spherical visual predictive control and single point features

This paper presents practical vision-based collision avoidance for objects approximating a single point feature. Using a spherical camera model, a visual predictive control scheme guides the aircraft around the object along a conical spiral trajectory. Visibility, state and control constraints are considered explicitly in the controller design by combining image and vehicle dynamics in the process model, and solving the nonlinear optimization problem over the resulting state space. Importantly, range is not required. Instead, the principles of conical spiral motion are used to design an objective function that simultaneously guides the aircraft along the avoidance trajectory, whilst providing an indication of the appropriate point to stop the spiral behaviour. Our approach is aimed at providing a potential solution to the See and Avoid problem for unmanned aircraft and is demonstrated through a series.

Validating SMPS-measured size distribution of double-mode spherical Silica nanoparticles by Transmission Electron Microscope (TEM)

A nanoparticles size is one of their key physical characteristics that can affect their fate in a human’s respiratory tract (in case of inhalation) and also in the environment. Hence, measuring the size distribution of nanoparticles is absolutely essential and contributes greatly to their characterization. For years, Scanning Mobility Particle Sizers (SMPS), which rely on measuring the electrical mobility diameter of particles, have been used as one of the most reliable real-time instruments for the size distribution measurement of nanoparticles. Despite its benefits, this instrument has some drawbacks, including equivalency problems for non-spherical particles (i.e. assuming a non-spherical particle is equal to a spherical particle of diameter d due to the same electrical mobility), as well as limitations in terms of its use in workplaces, because of its large size and the complexity of its operation...

An innovative method to obtain porous PLLA scaffolds with highly spherical and interconnected pores

Scaffolding is an essential issue in tissue engineering and scaffolds should answer certain essential criteria: biocompatibility, high porosity, and important pore interconnectivity to facilitate cell migration and fluid diffusion. In this work, a modified solvent castingparticulate leaching out method is presented to produce scaffolds with spherical and interconnected pores. Sugar particles (200–300 lm and 300–500 lm) were poured through a horizontal Meker burner flame and collected below the flame. While crossing the high temperature zone, the particles melted and adopted a spherical shape. Spherical particles were compressed in plastic mold. Then, poly-L-lactic acid solution was cast in the sugar assembly. After solvent evaporation, the sugar was removed by immersing the structure into distilled water for 3 days. The obtained scaffolds presented highly spherical interconnected pores, with interconnection pathways from 10 to 100 lm. Pore interconnection was obtained without any additional step. Compression tests were carried out to evaluate the scaffold mechanical performances. Moreover, rabbit bone marrow mesenchymal stem cells were found to adhere and to proliferate in vitro in the scaffold over 21 days. This technique produced scaffold with highly spherical and interconnected pores without the use of additional organic solvents to leach out the porogen.

A variable diffusivity model for the drying of spherical food particulates

An investigation of the drying of spherical food particles was performed, using peas as the model material. In the development of a mathematical model for drying curves, moisture diffusion was modelled using Fick’s second law for mass transfer. The resulting partial differential equation was solved using a forward-time central-space finite difference approximation, with the assumption of variable effective diffusivity. In order to test the model, experimental data was collected for the drying of green peas in a fluidised bed at three drying temperatures. Through fitting three equation types for effective diffusivity to the data, it was found that a linear equation form, in which diffusivity increased with decreasing moisture content, was most appropriate. The final model accurately described the drying curves of the three experimental temperatures, with an R2 value greater than 98.6% for all temperatures.

Eight weeks of episodic visual navigation inside a non-stationary environment using adaptive spherical views

This paper presents a long-term experiment where a mobile robot uses adaptive spherical views to localize itself and navigate inside a non-stationary office environment. The office contains seven members of staff and experiences a continuous change in its appearance over time due to their daily activities. The experiment runs as an episodic navigation task in the office over a period of eight weeks. The spherical views are stored in the nodes of a pose graph and they are updated in response to the changes in the environment. The updating mechanism is inspired by the concepts of long- and short-term memories. The experimental evaluation is done using three performance metrics which evaluate the quality of both the adaptive spherical views and the navigation over time.

A variable diffusivity model for the drying of spherical food particulates

An investigation of the drying of spherical food particles was performed, using peas as the model material. In the development of a mathematical model for drying curves, moisture diffusion was modelled using Fick’s second law for mass transfer. The resulting partial differential equation was solved using a forward-time central-space finite difference approximation, with the assumption of variable effective diffusivity. In order to test the model, experimental data was collected for the drying of green peas in a fluidised bed at three drying temperatures. Through fitting three equation types for effective diffusivity to the data, it was found that a linear equation form, in which diffusivity increased with decreasing moisture content, was most appropriate. The final model accurately described the drying curves of the three experimental temperatures, with an R2 value greater than 98.6% for all temperatures.

Images inside a reflecting spherical surface with possible application in astronomy

This report studies an algebraic equation whose solution gives the image system of a source of light as seen by an observer inside a reflecting spherical surface. The equation is looked at numerically using GeoGebra. Under the hypothesis that our galaxy is enveloped by a reflecting interface this becomes a possible model for many mysterious extra galactic observations.

A comparison of stability and bifurcation criteria for inflated spherical elastic shells

The nonlinear stability analysis introduced by Chen and Haughton [1] is employed to study the full nonlinear stability of the non-homogeneous spherically symmetric deformation of an elastic thick-walled sphere. The shell is composed of an arbitrary homogeneous, incompressible elastic material. The stability criterion ultimately requires the solution of a third-order nonlinear ordinary differential equation. Numerical calculations performed for a wide variety of well-known incompressible materials are then compared with existing bifurcation results and are found to be identical. Further analysis and comparison between stability and bifurcation are conducted for the case of thin shells and we prove by direct calculation that the two criteria are identical for all modes and all materials.

Oscillating magnetic field current drive in a spherical plasma device

The continuous steady-state current drive in a spherical argon plasma by transverse oscillating magnetic field (OMF) is investigated. The experimental results reveal that a rotating magnetic field is generated, and its amplitude depends linearly on the external steady vertical magnetic field. It has been shown that steady toroidal currents of up to about 400 A can be driven by a 490 kHz OMF with an input power of 1.4 kW. The generation of steady toroidal magnetic fields directed oppositely in the upper and lower hemispheres have been recorded. The measurements of time-varying magnetic fields unveil a strong nonlinear effect of the frequency-doubled field harmonics generation. The electron number density and temperature of up to 6.2×1018 m-3 and 12 eV have been obtained. The observed effects validate the existing theory of the OMF current drive in spherical plasmas.

Series in vector spherical harmonics : an efficient tool for solution of nonlinear problems in spherical plasmas

The series expansion of the plasma fields and currents in vector spherical harmonics has been demonstrated to be an efficient technique for solution of nonlinear problems in spherically bounded plasmas. Using this technique, it is possible to describe the nonlinear plasma response to the rotating high-frequency magnetic field applied to the magnetically confined plasma sphere. The effect of the external magnetic field on the current drive and field configuration is studied. The results obtained are important for continuous current drive experiments in compact toruses. © 2000 American Institute of Physics.

An adaptive spherical view representation for navigation in changing environments

Real-world environments such as houses and offices change over time, meaning that a mobile robot’s map will become out of date. In previous work we introduced a method to update the reference views in a topological map so that a mobile robot could continue to localize itself in a changing environment using omni-directional vision. In this work we extend this longterm updating mechanism to incorporate a spherical metric representation of the observed visual features for each node in the topological map. Using multi-view geometry we are then able to estimate the heading of the robot, in order to enable navigation between the nodes of the map, and to simultaneously adapt the spherical view representation in response to environmental changes. The results demonstrate the persistent performance of the proposed system in a long-term experiment.