A study of double-variable-curvature microlenses (DVCM) for promoting coupling efficiency between the high-power 980-nm pumping laser diodes and the single-mode fibers has been proposed. In comparison with the previous works on asymmetric fiber microlenses fabricated by the multi-step processes with complicated fabrication, the advantages of the DVCM structure for achieving high coupling are a single-step fabrication, a reproducible process, and a high-yield output. In the fusing procedure, the slight arc fusion was mainly applied for fine polishing merely instead of reshaping for the reason that the fabricated double-variable-curvature fiber endface (DVCFE) was very close to the ideal shape. Hence, the fabrication time was reduced and the yield was promoted due to the withdrawn step of tip elimination. In this study, the geometric center of the fiber was defined through, the cladding diameter and the core diameter, for comparison to measure the offset. The offset measured by the core diameter was more accurate and coincidence with the coupling efficiency in the experiment. In the fabricated 45 DVCMs, to achieve the average coupling efficiencies higher than 84%, the offsets were ought to be controlled in merely less than 0.6£gm with the curvature radii in the minor axis ranged from 2.4 to 2.9£gm (with tolerance of 0.5£gm). Alternatively, the offsets were ought to be controlled in less than 0.3£gm though the curvature radii in the minor axis ranged from 2.4 to 3.7£gm (with larger tolerance of 1.3£gm). However, it was more difficult to control over the offsets than the curvature radii in the minor axis while fabricating the DVCMs. In conclusion, to achieve higher yield, it was relatively practical to control the offsets of fiber microlenses to be less than 0.6£gm with 2.4 to 2.9£gm curvature radius. As a result, the coupling efficiencies were all higher than 80%.

Variation of the center of gravity of a golf club head will influence the initial velocity and rotation of speed of a ball after the golf ball is struck by golf club head. After fixing the weight of 200g of a golf head, the researcher changes the volume of golf head and the horizontal curvature of radius. He also distribute counterpoise to investigates the effect of launching of a golf ball. This thesis summarizes the ball of three-dimensional flight trajectory and offset distance. For the volume of the golf head is 400 cc, the best level of the radius of horizontal curvature is 11 in, in the 430 cc should use a radius of horizontal curvature of 12 in, and the 460 cc head club can chose a radius of horizontal curvature of 13 in. The distribution of counterpoise can effectively improve the play¡¦s habits, so the trajectory of a golf ball can be appropriately adjusted. By finite element method, the physical behavior of a series of the lunching ball can be predicted. The trajectory of golf ball can be measured by substituting the inertial value of ball into the three-dimension equations of motion. According to the trajectory of golf ball flight by this study, this study provides the characteristics for designing a golf club head.

In this thesis, a pursuit-evasion game, in which the pursuer moves with simple motion whereas the evader moves at a fixed speed but with a curvature constraint, is investigated. The game is the inverse of the usual homicidal chauffeur game. Square of the distance between the pursuer and the evader when the game is terminated is selected as the cost function. To solve such a zero-sum game, the variational approach will be employed to solve the problem. An algorithm will be proposed to determine a saddle point and the value of the game under consideration

To find a relationship between moment versus curvature in a traction-free ovine artery, a pure moment was applied to a radially cut ovine artery (length 50.23 mm). The curvature of the segment opposite the cut was calculated and used to calculate the pre-stresses using a Fung type model. The pre-stresses were then used to calculate the moment. The moment applied during the experiment was calculated by recording the twist applied and the stiffness of the wire applying the moment. The artery was sutured symmetrically with a custom jig, and then sutured to two blocks, one fixed and one subject to the pure moment. The axial strain was assumed unity. The Fung model yielded a linear moment versus curvature relationship, as well as the moment versus curvature relationship for the experiment. Despite both small and large stretches, the strains felt by the artery were not influential enough to display a non-linear correlation for moment vs curvature.

A strategy was proposed to make machining rate stable and the machining precision achieved by properly tool dwelling time when surface still has form error after previously machining. Using computer simulation to plan tool dwelling time and to estimate practicability of this strategy. As a result of curvatures are different on the every points of the work piece surface. Normal vectors that between tool and work pieces surface are not stable in polishing process.HDP conditions and film thickness will be changed by curvature radius of work pieces.So HDP conditions must be controlled when the planning of tool motion. Analyzing all of different aspheric surfaces to make sure this strategy can be used. The different thing that between axially symmetric and axially non-symmetric is tool dwelling time should be a linear function the product of the depth function of profile and the radius for symmetric work pieces, but that of axially non-symmetric work pieces only should be linearly proportional to the depth function of profile.

Thèse : Analyse : Faculté des sciences de Paris : 1856. Thèse : Astronomie : Faculté des sciences de Paris : 1856. / Titre provenant de l'écran-titre.

Thesis (doctoral)--Westfälischen Wilhelms-Universität zu Münster, 1911. / Cover title. Vita. Includes bibliographical references.

Classical field curvature theory emphasizes the Petzval theorem, which models field curvature aberration to the 4th order. However, modern lens designs use aspheric surfaces. These surfaces strongly induce higher order field curvature aberration which is not accounted for Petzval field curvature. This dissertation focuses on developing higher order field curvature theories that are applied to highly aspheric designs. Three new theories to control field curvature aberration are discussed. Theory 1: an aspheric surface that is close to the image and has two aspheric terms sharply reduces field curvature by 85%. Theory 2: an aspheric surface that is farther from the image plane induces astigmatism to balance Petzval field curvature. Theory 3: oblique spherical aberration can be induced to balance Petzval field curvature. All three theories are applied to real design examples including the following lenses: cellular phone, wide angle, fast photographic, and zoom lenses. All of the analyses results are consistent with the theories. Moreover, two types of novel aspheric surfaces are proposed to control field curvature. Neither of the surfaces are polynomial-type surfaces. Examples show that the novel aspheric surfaces are equivalent to even aspheric surfaces with two aspheric coefficients in terms of field curvature correction. The study on field curvature correction using aspheric surfaces provides an alternative method to use when aspheres are accessible. Overall, this dissertation advances the theory of field curvature aberration, and it is particularly valuable to evaluate highly aspheric designs when Petzval theory is inapplicable.

In this thesis we study singularity formation in two basic nonlinear equations in $n$ dimensions: nonlinear heat equation (also known as reaction-diffusion equation) and mean curvature flow equation. For the nonlinear heat equation, we show that for an important or natural open set of initial conditions the solution will blowup in finite time. We also characterize the blowup profile near blowup time. For the mean curvature flow we show that for an initial surface sufficiently close, in the Sobolev norm with the index greater than $\frac{n}{2} + 1$, to the standard n-dimensional sphere, the solution collapses in a finite time $t_*$, to a point. We also show that as $t\rightarrow t_*$, it looks like a sphere of radius $\sqrt{2n(t_*-t)}$.

In this thesis we study singularity formation in two basic nonlinear equations in $n$ dimensions: nonlinear heat equation (also known as reaction-diffusion equation) and mean curvature flow equation. For the nonlinear heat equation, we show that for an important or natural open set of initial conditions the solution will blowup in finite time. We also characterize the blowup profile near blowup time. For the mean curvature flow we show that for an initial surface sufficiently close, in the Sobolev norm with the index greater than $\frac{n}{2} + 1$, to the standard n-dimensional sphere, the solution collapses in a finite time $t_*$, to a point. We also show that as $t\rightarrow t_*$, it looks like a sphere of radius $\sqrt{2n(t_*-t)}$.