Further analysis of field effects on liquids and solidification

Numerical calculations of the magnitude of external field effects on liquids are presented to describe how external fields can influence the substructure of the field. Quantitative estimates of magnetic and gravitational effects are reported on melts of metals and semiconductors. The results are condensed in tables which contain the input data for calculation of the field effects on diffusion coefficient, solidification rate and for calculation of field forces on individual molecules in the melt

On the Fredholm property of bisingular pseudodifferential operators

For operators belonging either to a class of global bisingular pseudodifferential operators on $R^m \times R^n$ or to a class of bisingular pseudodifferential operators on a product $M \times N$ of two closed smooth manifolds, we show the equivalence of their ellipticity (defined by the invertibility of certain associated homogeneous principal symbols) and their Fredholm mapping property in associated scales of Sobolev spaces. We also prove the spectral invariance of these operator classes and then extend these results to the even larger classes of Toeplitz type operators.Comment: 21 pages. Expanded sections 3 and 4. Corrected typos. Added reference

Gauged O(n) spin models in one dimension

We consider a gauged O(n) spin model, n >= 2, in one dimension which contains both the pure O(n) and RP(n-1) models and which interpolates between them. We show that this model is equivalent to the non-interacting sum of the O(n) and Ising models. We derive the mass spectrum that scales in the continuum limit, and demonstrate that there are two universality classes, one of which contains the O(n) and RP(n-1) models and the other which has a tuneable parameter but which is degenerate in the sense that it arises from the direct sum of the O(n) and Ising models.Comment: 9 pages, no figures, LaTeX sourc

Further analysis of field effects on liquids and solidification. Study of the liquid-solid transition for materials processing in space

Expressions for diffusion coefficient, D, and solidification rate, Uc, from the free volume model of liquids developed by Turnbull and Cohen have been used to estimate the effects which microgravity and magnetic fields will have on these quantities. The mathematical formalism describing changes in D and Uc is the same for both the microgravity and magnetic field cases, but the difference between the magnitudes of the two effects is quite large. The change in D and Uc is found to be less than 0.0001% for the microgravity case and on the order of 0.1 to 1.1% for the magnetic field case for four representative materials. D and Uc are found to increase under the influence of an applied magnetic field, and this is in agreement with experimental observations

Spectroscopy of 19^{19}Ne for the thermonuclear 15^{15}O(α,γ\alpha,\gamma)19^{19}Ne and 18^{18}F(p,αp,\alpha)15^{15}O reaction rates

Uncertainties in the thermonuclear rates of the $^{15}$O($\alpha,\gamma$)$^{19}$Ne and $^{18}$F($p,\alpha$)$^{15}$O reactions affect model predictions of light curves from type I X-ray bursts and the amount of the observable radioisotope $^{18}$F produced in classical novae, respectively. To address these uncertainties, we have studied the nuclear structure of $^{19}$Ne over $E_{x} = 4.0 - 5.1$ MeV and $6.1 - 7.3$ MeV using the $^{19}$F($^{3}$He,t)$^{19}$Ne reaction. We find the $J^{\pi}$ values of the 4.14 and 4.20 MeV levels to be consistent with $9/2^{-}$ and $7/2^{-}$ respectively, in contrast to previous assumptions. We confirm the recently observed triplet of states around 6.4 MeV, and find evidence that the state at 6.29 MeV, just below the proton threshold, is either broad or a doublet. Our data also suggest that predicted but yet unobserved levels may exist near the 6.86 MeV state. Higher resolution experiments are urgently needed to further clarify the structure of $^{19}$Ne around the proton threshold before a reliable $^{18}$F($p,\alpha$)$^{15}$O rate for nova models can be determined.Comment: 5 pages, 3 figures, Phys. Rev. C (in press

Involution and Constrained Dynamics I: The Dirac Approach

We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an involutive system. We discuss the implications of this identification for field theories and argue that the involution analysis is more general and flexible than the Dirac approach. We also derive intrinsic expressions for the number of degrees of freedom.Comment: 28 pages, latex, no figure

On the General Analytical Solution of the Kinematic Cosserat Equations

Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.Comment: 14 pages, 3 figure

Is \gamma-ray emission from novae affected by interference effects in the 18F(p,\alpha)15O reaction?

The 18F(p,\alpha)15O reaction rate is crucial for constraining model predictions of the \gamma-ray observable radioisotope 18F produced in novae. The determination of this rate is challenging due to particular features of the level scheme of the compound nucleus, 19Ne, which result in interference effects potentially playing a significant role. The dominant uncertainty in this rate arises from interference between J\pi=3/2+ states near the proton threshold (Sp = 6.411 MeV) and a broad J\pi=3/2+ state at 665 keV above threshold. This unknown interference term results in up to a factor of 40 uncertainty in the astrophysical S-factor at nova temperatures. Here we report a new measurement of states in this energy region using the 19F(3He,t)19Ne reaction. In stark contrast with previous assumptions we find at least 3 resonances between the proton threshold and Ecm=50 keV, all with different angular distributions. None of these are consistent with J\pi= 3/2+ angular distributions. We find that the main uncertainty now arises from the unknown proton-width of the 48 keV resonance, not from possible interference effects. Hydrodynamic nova model calculations performed indicate that this unknown width affects 18F production by at least a factor of two in the model considered.Comment: 5 pages, 4 figures. Accepted for publication in Phys. Rev. Let