Fractal Structure in Ionization Dynamics

Chaotic dynamics in open systems produces fractals. This can be seen, for example, in the ionization of an electron from a hydrogen atom in applied parallel electric and magnetic fields. We summarize some of our recent work on the order that can be found in these fractals.     

Monopole charge quantization or why electromagnetism is a U(1)-gauge theory

We obtain Dirac’s classic monopole charge quantization from the point of view of geometric quantization and demonstrate how this leads to the conclusion that the electromagnetic field is a U(1)-gauge field.     

圆形区域内香枞芽虫的分布模型

本文讨论圆形区域内芽虫分布模型,特别研究了芽虫与天敌接触时产生与避免outbreak状态的可能性。     

Rheological and diffusion properties of a dextran-con A polymer in the presence of Insulin and Magnesium

Previous work carried out in our laboratories has focused on the formation and investigation of a dextran and concanavalin A (con A) based gel, which has the ability to alter its conformational structure in the presence and absence of free and terminal glucoses such that a gel–sol phase transition occurs. Here we report the diffusion and rheological investigations in to the effects of the addition of insulin and varyingconcentrations of magnesium chloride hexahydrate (Mg₂Cl₂6H₂O) at 20 and 37 °C. Rheological examination of glucose-sensitive (dextran-con A) gels were conducted using a cone and plate viscometer used in continual rotation and oscillatory modes. The results are interpreted in terms of the structure of the gel network and suggest rheological assessment provides an effective method of assessing the properties of gel systems. The subsequent testing of such formulations in in-vitro diffusion experiments revealed a reduction in the rate of diffusivity in the insulin marker, poly R-478 dye. The performance of this self-regulating drug delivery system has been examined and the addition of insulin and magnesium chloride may alter the way in which the gel operates as a drug delivery device and in the delivery of insulin. This may have implications for other ligands.     

Parity violation at neutron p-wave resonances of238U and232Th and related questions

Parity violation effects have been studied at 40 neutron p-wave resonances of the even-even nuclei²³⁸U and²³²Th. Of these 11 show parity violation effects larger than 2 standard deviations, making parity violation a rather common phenomenon. Parity mixing up to 10% has been found. The root-mean squared matrix elements for parity violation derived from these resonances are M=0.58 (+0.50/-0.25) meV for²³⁸U, respectively 1.39 (+0.35/-0.38) meV for²³²Th.     

Approximation of a laminated microstructure for a rotationally invariant,double well energy density

Summary. We give error estimates for the approximation of a laminated microstructure which minimizes the energy for a rotationally invariant, double well energy density . We present error estimates for the convergence of the deformation in the convergence of directional derivatives of the deformation in the “twin planes,” the weak convergence of the deformation gradient, the convergence of the microstructure (or Young measure) of the deformation gradients, and the convergence of nonlinear integrals of the deformation gradient. Received July 25, 1995 / Revised version received November 20, 1995     

Variable flip angle imaging and fat suppression in combined gradient and spin-echo (GREASE) techniques

Conventional "proton density" and "T2-weighted" spin-echo images are susceptible to motion induced artifact, which is exacerbated by lipid signals. Gradient moment nulling can reduce motion artifact but lengthens the minimum TE, degrading the "proton density" contrast. We designed a pulse sequence capable of optimizing proton density and T2-weighted contrast while suppressing lipid signals and motion induced artifacts. Proton density weighting was obtained by rapid readout gradient reversal immediately after the excitation RF pulse, within a conventional spin-echo sequence. By analyzing the behavior of the macroscopic magnetization and optimizing excitation flip angle, we suppressed T1 contribution to the image, thereby enhancing proton density and T2-weighted contrast with a two- to four-fold reduction of repetition time. This permitted an increased number of averages to be used, reducing motion induced artifacts. Fat suppression in the presence of motion was investigated in two groups of 8 volunteers each by (i) modified Dixon technique, (ii) selective excitation, and (iii) hybrid of both. Elimination of fat signal by the first technique was relatively uniform across the field of view, but it did not fully suppress the ghosts originating from fat motion. Selective excitation, while sensitive to the main field inhomogeneity, largely eliminated the ghosts (0.21 +/- 0.05 vs. 0.29 +/- 0.06, p less than 0.01). The hybrid of both techniques combined with bandwidth optimization, however, showed the best results (0.17 +/- 0.04, p less than 0.001). Variable flip-angle imaging allows optimization of image contrast which, along with averaging and effective fat suppression, significantly improves gradient- and spin-echo imaging, particularly in the presence of motion.