Imperfect Spheres Research Articles

Photoacoustic spectrum analysis for spherical target size and optical property determination: A feasibility study

The photoacoustic signal generated by an optically absorbing target is determined by the spatial profile of absorbed optical energy within the target. The analysis of the time profile and frequency content of the signal enables the recovery of the geometry of the object, as well as information about the optical properties. The photoacoustic response of spheres with a homogeneous absorbed optical energy profile is well described, and it is known that the width of the photoacoustic pulse is determined by the diameter of the sphere and its sound speed. In practice, the optical attenuation coefficients within the sphere will result in an inwardly decaying fluence profile leading to a similarly decaying absorbed optical energy profile. Further, the optical attenuation coefficients may be inhomogeneously distributed in the sphere. The implication for both cases is that the existing model for spheres does not fully apply. In this work, we developed analytical expressions for the photoacoustic time traces and amplitude spectra generated by a sphere with absorbed optical energy only in a spherical shell, and by a sphere with an inwardly decaying optical energy profile. Numerical simulations and experiments were conducted on these two imperfect sphere types. Fitting our model to the simulated or measured spectra allowed us to test our model’s ability to extract the sphere size and optical properties. We found that the radii can be recovered with high accuracy, even when the frequency response of the detector recording the photoacoustic pulse is not precisely known. The model was found to be less sensitive in recovering the optical attenuation coefficient, but it is feasible when the detector’s frequency response is well known.

Impact of Imperfect Artefacts and the Modus Operandi on Uncertainty Quantification Using Virtual Instruments

The usage of virtual instruments (VIs) to analyze measurements and calculate uncertainties is increasing. Well-known examples are virtual coordinate measurement machines (VCMMs) which are often used and even commercially offered to assess measurement uncertainties of CMMs. A more recent usage of the VI concept is posed by the modeling of scatterometers. These VIs can be used to assess the measurement uncertainty after the measurement has been performed based on the real measurement data or prior to the measurement to predict the measurement uncertainty using a type of simulated measurement data. The research question addressed in this paper is to assess if this predicted uncertainty will be similar in magnitude to the calculated uncertainty based on the measurement data. It turns out that this is not necessarily the case. The main observation of this paper was that the uncertainty predicted by a VI can be highly sensitive to the chosen way of operating the VI. To amend this situation, a simple procedure was proposed that can be used prior to performing the real measurement and that is believed to produce a conservative prediction of the measurement uncertainty in most cases. This was verified in a case study involving the measurement of the asphericity of an imperfect sphere using a CMM, with the uncertainty calculated by means of a VCMM.

A Convenient and High-Accuracy Multicamera Calibration Method Based on Imperfect Spherical Objects

Multicamera systems have important applications in industrial online measurement, attracting wide interest due to their encouraging performance. However, how to develop a convenient and high-accuracy multicamera calibration model is a big challenge. Traditional calibration methods based on 2-D objects require the preparation of high-precision and large-scale calibration objects and have poor adaptability to the spatial distribution of cameras. To address these issues, a convenient and accurate multicamera calibration method is proposed based on an imperfect spherical object. Specifically, a special calibration object, i.e., an imperfect sphere with many coded targets is designed for calibrating the multicamera system, where the optical axes of the cameras are different in orientations and converge into the measurement field. Then, a Euclidean reconstruction method is employed to calculate the camera poses and the spatial coordinates of feature points in the local coordinate system after the adaptive grouping of cameras is completed. Moreover, a graph theory-based optimal path transformation algorithm is developed to obtain the camera poses and spatial point coordinates in the global coordinate system (GCS), and a spherical projection optimization algorithm is designed to spheroidize the spatial coordinates of feature points. In the end, the camera poses and the spatial coordinates of feature points in the GCS are optimized by a bundle adjustment algorithm. We build a multicamera system and conduct extensive experiments to demonstrate the superiority of the proposed method.

Looking Beyond the Social: Religion as a Solution to Alienation in Xu Dishan’s, Bing Xin’s, and Su Xuelin’s Republican Era Literature

I argue that by participating in religious cultural phenomena, the protagonists of Xu Dishan’s and Su Xuelin’s fiction cultivate values that allow them to overcome their sense of social alienation by making them feel more confident about their ability to strengthen their relationships with others. These values include selflessness in the literature of both authors, as well as compassion in Su Xuelin’s literature. I further argue that these two authors’ literary narratives use the category of religion to label these values as existing outside of the space of human social interactions. This then allows protagonists to view the cultivation of these values as an ostensibly perfected resolution to their feeling of social alienation, which in the first place is caused by the imperfect sphere of human social interactions. The two case studies upon which this study draws to exemplify the argument include Yuguan from Xu Dishan’s Yuguan and Xingqiu from Su Xuelin’s Thorny Heart.

Various nanoparticle morphologies and surface properties of waterborne polyurethane controlled by water.

Water plays important roles in organic reactions such as polyurethane synthesis, and the aqueous solution environment affects polymer morphology and other properties. This paper focuses on the morphology and surface properties of waterborne polyurethane resulting from the organic reaction in water involving different forms (solid and liquid), temperatures and aqueous solutions. We provide evidence from TEM observations that the appearance of polyurethane nanoparticles in aqueous solutions presents diverse forms, including imperfect spheres, perfect spheres, perfect and homogenous spheres and tubes. Based on the results on FTIR, GPC, AFM and XRD experiments, we suggest that the shape of the nanoparticles may be decided by the crimp degree (i.e., the degree of polyurethane chains intertangling in the water environment) and order degree, which are determined by the molecular weight (Mn) and hydrogen bonds. Meanwhile, solid water and high-temperature water can both reduce hard segments that gather on the polyurethane film surface to reduce hydrophilic groups and produce a soft surface. Our findings show that water may play key roles in aqueous polymer formation and bring order to molecular chains.

Methylviologen Mediated Electrosynthesis of Palladium Nanoparticles Stabilized with CTAC

Efficient electrosynthesis of ultrasmall palladium nanoparticles stabilized with CTA+ cetyltrimethylammonium cations (Pd@CTA+) was carried out in an aqueous medium by methylviologen mediated electroreduction of poorly soluble aggregates ([PdCl4]2−·2CTA+)n of [PdCl4]2− anionic complex with CTA+ cations on a glassy carbon electrode at potentials of the MV2+/MV•+ redox couple. ([PdCl4]2−·2CTA+)n aggregates are reduced directly on the electrode at a low rate and the generated metal is deposited on the electrode. In the case of mediated reduction, the metal is not deposited on the cathode, and after passing of Q = 2 F quantitative conversion from [PdCl4]2− to Pd@CTA+ nanoparticles occurs in the solution bulk. These particles are positively charged (zeta-potential is 66.8 mV) and their hydrodynamic diameter is 18 nm. Separated Pd@CTAC nanoparticles are combined into larger aggregates due to coalescence of the organic shell. The predominant shape of metal nanoparticles is an imperfect sphere with a diameter of 5 ± 3 nm, and the average size of the metal crystallites is 4.66 nm.

Evaluation of radial voidage profiles in packed beds of low‐aspect ratios

AbstractThe relationship between the radial voidage profile, ϵ(r), and the radial distribution of centres of mono‐sized spherical particles, f(r), is revised. A close expression is given for the section S(r1, rc), the area of the segment of a cylindrical surface of radius r intersected by a particle centred at rC. From this expression, ϵ(r) can be evaluated straightforwardly from the knowledge of f(r). The range 1≥ a ≥ 2 of aspect ratios (a = dT/dp is then analysed specifically. For this range, the distribution of spherical particles has been characterized theoretically (Govindarao et al., 1992) and a simple expression allows the evaluation of ϵ(r). The use of this expression for actual catalyst particles, imperfect spheres showing a distribution of sizes, in finally analyzed.

Survey and Review

Science, and applied mathematics, proceeds by recognizing quantities that can be viewed as infinite or infinitesimal. We treat an iron bar as a continuum, ignoring the fact that it is made of molecules. We treat the planets as point masses, ignoring the fact that they are imperfect spheres. And so on. The article by Chapman in this issue represents an exceptionally highly developed example of this art. His problem is the behavior of type-II superconductors, a booming technological topic since the discovery of high-temperature superconductivity in 1986. In a magnetic field, a type-II superconducting material may divide between superconducting regions and nonsuperconducting ``vortices.' As a certain Ginzburg--Landau parameter increases, the number of vortices approaches infinity---should we model this as a continuum of vortices? But that is just the beginning. Further parameters describe the distance between impurities in the material, the rate of change of the applied magnetic field, and the magnetic penetration depth, any or all of which may approach zero. A whole hierarchy of mathematical models is appropriate to handle the different combinations that may arise, and all of them have potential relevance to technology. Chapman attempts to shed light on each member of this hierarchy. It will probably be decades before we see which of his equations prove to be important. Our second article, by Hethcote, also describes a hierarchy of mathematical models---now ODEs as well as PDEs. The scientific application could not be more different, or more urgent: Hethcote's subject is infectious diseases such as smallpox, polio, measles, and AIDS. He begins with the continuum approximation that populations are infinite. The hierarchy comes from many other effects that are important for some diseases but near enough to infinitesimal for others, such as transference of temporary passive immunity from mothers to newborns, latency between exposure and infectivity, dependence on age, spatial heterogeneity, and variation among subpopulations. Since smallpox has been eradicated worldwide, why is there little hope for eradication of measles? Why don't China and India vaccinate against rubella? Hethcote gives quantitative answers to such questions, focusing his discussion around parameter \textit{R}$_{\mbox{\sffamily\scriptsize 0}}$, the "basic reproduction number." His epidemiological models with age dependence lead to computer simulations for comparing vaccination programs for measles in Africa and whooping cough in the United States. Pick up this fascinating article and start reading! It will enrich your view of our world and your appreciation of applied mathematics.

Tactile Recognition Based on Repetition of Grasping of an Object with a Robot Hand. Calculation Method for Increasing Probability Levels Using Fuzzy Relations.

A new robotic tactile recognition method wherein repetitions of grasping of an object enhanced recognition certainty was presented. To evaluate the certainty, probability levels of recognition were calculated by a fuzzy relational matrix defining similarities between objects. Calculations using various kinds of fuzzy compositions and binary operations required for the iterative evaluation process were compared. Arithmetic sum and product were found to be most suitable, being able to reflect the increase in probability levels. By applying the arithmetic calculations, a new program module for increasing probability levels was implemented. The module was incorporated into the fuzzy production system which was composed of a calculation module for characteristic parameters and an inference module using fuzzy production rules. Three modules were cyclically processed through repetitions of grasping of an object. A series of tactile recognition experiments using a robot hand equipped with three-axis tactile sensors were performed. Consequently, the present system succeeded in recognizing three-dimensional shapes of unknown objects such as an icosahedron and an imperfect sphere, which could not be recognized through only a single grasping.

Dynamic buckling of imperfection-sensitive shell structures

Structural buckling under loads may occur at load levels that are less than the corresponding static loads. Presence of local geometric imperfections may induce an early buckling for both static and loadings. The phenomenon of dynamic weakening is studied for a general class of shell structures under a general class of time-dependent loadings. A doubly curved quadrilateral Love-Kirchhoff shell finite element is used. Geometric deviations of the shell middle surface are included within the element formulation by suitably modifying the strain-displacement relations. This is accomplished by retaining additional terms that are quadratic in spatial derivatives of imperfections and displacement components. The nonlinear equations of motion are written in the Lagrangian system and are solved by using an incremental algorithm based on Newmark's generalized operator. The responses up to buckling are obtained for a perfect spherical cap and an imperfect spherical cap both under external pressure, as well as a complete imperfect sphere under external pressure. Numerical results include the effects of amplitude of imperfection and thickness of shell on the buckling loads. The formulation is general and can be applied to obtain the buckling responses of a wide variety of shell structures.

The Functions and Limits of Autobiography in Augustine's "Confessions"

The topic of this issue, structure of in fiction, will require certain refinements if I am to deal with it either as a serious theoretical problem or as a possible pragmatic approach to the specific question concerning the functions and limits of autobiographical discourse in St. Augustine's autobiography, the Confessions. I shall not try to remake the topic all at once, but will hope, rather, that its transformation will occur during the analysis that follows. One preliminary remark should be made about the ability of language to express reality in the first place, at least in Augustine's eyes. While Augustine believes that the grammatical structure of language does to a certain extent correspond to the ontological structure of reality, language as a signifying process is not immanent in the that is known, but in the cognitive activity of the knowing mind. Hence, the capacity of language to express truth belonging to the objective world is at best limited. The language of the mind is truest when the mind itself becomes an object of knowledge, for then the knower and the known are one and the same. But even then, this correspondence of language to is finite, subject to error, weak, and unstable at least when it is compared with the Word of as Son and expression of the of the Father: God the Son is substantially similar to the Father in all things (De trin. XV:xi 20).1 Rhetorician that he was, Augustine was aware that in the limited and imperfect sphere of human speech, there are multiple alternatives in the choice of that one wishes to understand, and multiple alternatives in the mode of expressing a reality. Moreover,

Reflection of circularly polarized waves from imperfect spheres

Calculations have been made of the radar cross sections of imperfect spheres to circularly polarized radiation. The matrix method of Waterman was used and only imperfections having axial symmetry were considered. Some results for spheres with an equatorial cylindrical section are given for spheres up to six wavelengths in diameter.

On the Formation of Hailstones, Raindrops, and Snowflakes 1

THE author commences by recapitulating some of the leading points in a paper which he read before the same Society on October 31, 1876, “On the Manner in which Raindrops and Hailstones are Formed.” In this paper, which was published in NATURE (vol. xvi. p. 163), he had shown that the aggregation of the small cloud particles into raindrops or hailstones is sufficiently accounted for by the fact that the larger pirticles descend faster than the others, and consequently overtake those immediately beneath them, and, combining with these, form still larger particles, which move with greater velocity, and more quickly overtaking the particles in front of them, add to their size at an increasing rate. He also showed that the shape and structure of ordinary hailstones was exactly such as would result from this manner of formation. For he had observed that the shape of hailstones was not as it at first sight appeared, that of more or less imperfect spheres, but that of more or less imperfect cones or pyramids with rounded bases, the conical surfaces being striated, the striæ radiating from the vertex; the texture being that of an aggregation of a number of small ice particles without crystalline form, being packed more closely together toward the base or rounded face of the stone. In this paper the author had reverted to the possibility of making artificial hailstones by blowing a stream of frozen fog against a small object, making, as it were, the cloud to rise up and meet the stone, instead of the stone falling through the cloud.