Results 1 - 9 of 9
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[en] A finite element method is introduced for solving the neutron transport equations. Our method falls into the category of Petrov-Galerkin solution, since the trial space differs from the test space. The close relationship between this method and the discrete ordinate method is discussed, and the methods are compared for simple test problems
[en] The problem of optical design is stated as follows: Given a principal surface r(α), and a maximum focal angle α/sub m/, find the pair of optical surfaces for which diffraction limited focusing is achieved. It is shown that specification of r(α) and α/sub m/ uniquely determines the lens design to within a scale factor, given the refractive index of the lens. It is further shown that one straightforward Runge-Kutta integration routine generates both surfaces for either a lens or a pair of mirror surfaces. The complete family of aplanatic lenses is described. Deviation from sphericity is discussed, as well as the possibility of realizing the specified lens designs. The family of lenses which map uniform incident intensity into uniform illumination about the focus is also described. Extension of the method to off-axis aberrations is considered. (auth)
[en] In this paper, we prove that the numerical solution of the mono-directional neutron transport equation by the Petrov-Galerkin method converges to the true solution in the L2 norm at the rate of h2. Since consistency has been shown elsewhere, the focus here is on stability. We prove that the system of Petrov-Galerkin equations is stable by showing that the 2-norm of the inverse of the matrix for the system of equations is bounded by a number that is independent of the order of the matrix. This bound is equal to the length of the longest path that it takes a neutron to cross the domain in a straight line. A consequence of this bound is that the global error of the Petrov-Galerkin approximation is of the same order of h as the local truncation error. We use this result to explain the widely held observation that the solution of the Petrov-Galerkin method is second accurate for one class of problems, but is only first order accurate for another class of problems
[en] A general class of iterative methods is introduced for solving symmetric, positive definite linear systems. These methods use two different approximations to the inverse of the matrix of the problem, one of which involves the inverse of a smaller matrix. It is shown that the methods of this class reduce the error by a constant factor at each step and that under ideal circumstances this constant is equal to (k' - 1)/(k' + 1), where k' is the ratio of the largest eigenvalue to the (J + 1)st eigenvalue of the matrix, J being the dimension of the smaller matrix involved. A multigrid method is presented as an example of a method of this class, and it is shown that while the multigrid method does not quite achieve this optimal rate of convergence, it does reduce the error at each step by a constant factor independent of the mesh spacing h. The size of this constant factor and properties of the differential equation and the discretization that affect it are also discussed. 5 references, 1 table
[en] 1 - Description of program or function: ITMETH is a collection of iterative routines for solving large, sparse linear systems. 2 - Method of solution: ITMETH solves general linear systems of the form AX=B using a variety of methods: Jacobi iteration; Gauss-Seidel iteration; incomplete LU decomposition or matrix splitting with iterative refinement; diagonal scaling, matrix splitting, or incomplete LU decomposition with the conjugate gradient method for the problem AA'Y=B, X=A'Y; bi-conjugate gradient method with diagonal scaling, matrix splitting, or incomplete LU decomposition; and ortho-min method with diagonal scaling, matrix splitting, or incomplete LU decomposition. ITMETH also solves symmetric positive definite linear systems AX=B using the conjugate gradient method with diagonal scaling or matrix splitting, or the incomplete Cholesky conjugate gradient method
[en] A finite element using different trial and test spaces in introduced for solving the neutron transport equation in spherical geometry. It is shown that the widely used discrete ordinates method can also be thought of as such a finite element technique, in which integrals appearing in the difference equations are replaced by one-point Gauss quadrature formulas (midpoint rule). Comparison of accuracy between the new method and the discrete ordinates method is discussed, and numerical examples are given to illustrate the greater accuracy of the new technique
[en] 1 - Description of program or function: SLAP is a set of routines for solving large sparse systems of linear equations. One need not store the entire matrix - only the nonzero elements and their row and column numbers. Any nonzero structure is acceptable, so the linear system solver need not be modified when the structure of the matrix changes. Auxiliary storage space is acquired and released within the routines themselves by use of the LRLTRAN POINTER statement. 2 - Method of solution: SLAP contains one direct solver, a band matrix factorization and solution routine, BAND, and several interactive solvers. The iterative routines are as follows: JACOBI, Jacobi iteration; GS, Gauss-Seidel Iteration; ILUIR, incomplete LU decomposition with iterative refinement; DSCG and ICCG, diagonal scaling and incomplete Cholesky decomposition with conjugate gradient iteration (for symmetric positive definite matrices only); DSCGN and ILUGGN, diagonal scaling and incomplete LU decomposition with conjugate gradient interaction on the normal equations; DSBCG and ILUBCG, diagonal scaling and incomplete LU decomposition with bi-conjugate gradient iteration; and DSOMN and ILUOMN, diagonal scaling and incomplete LU decomposition with ORTHOMIN iteration
[en] The Gemini Planet Imager (GPI) is an extreme AO coronagraphic integral field unit YJHK spectrograph destined for first light on the 8m Gemini South telescope in 2011. GPI fields a 1500 channel AO system feeding an apodized pupil Lyot coronagraph, and a nIR non-common-path slow wavefront sensor. It targets detection and characterizion of relatively young (<2GYr), self luminous planets up to 10 million times as faint as their primary star. We present the coronagraph subsystem's in-lab performance, and describe the studies required to specify and fabricate the coronagraph. Coronagraphic pupil apodization is implemented with metallic half-tone screens on glass, and the focal plane occulters are deep reactive ion etched holes in optically polished silicon mirrors. Our JH testbed achieves H-band contrast below a million at separations above 5 resolution elements, without using an AO system. We present an overview of the coronagraphic masks and our testbed coronagraphic data. We also demonstrate the performance of an astrometric and photometric grid that enables coronagraphic astrometry relative to the primary star in every exposure, a proven technique that has yielded on-sky precision of the order of a milliarsecond.
[en] Highlights: ► Ordering of polymer electrolytes under applied magnetic field. ► Positive effect of nanosize ferromagnetic filler. ► Structure-ion conductivity interrelationship. - Abstract: We recently presented a procedure for orienting the polyethylene-oxide (PEO) helices in a direction perpendicular to the film plane by casting the polymer electrolytes (PE) under a magnetic field (MF). Here we study the influence of magnetic fields of different strengths and configurations on the structural properties and ionic conductivity of concentrated LiCF3SO3 (LiTf) and LiAsF6:P(EO) pristine and composite polymer electrolytes containing γ-Fe2O3 nanoparticles. Some data of LiI:P(EO) system are shown for comparison. We suggest that the effect of type of salt (LiI, LiTf and LiAsF6) on the structure–conductivity relationship of the polymer electrolytes cast under magnetic field is closely connected to the crystallinity of the PEO–LiX system. It was found that the higher the content of the crystalline phase and the size of spherulites in the typically cast salt-polymer system, the stronger the influence of the magnetic field on the conductivity enhancement when the electrolyte is cast and dried under MF. Casting of the PE from a high-dielectric-constant solvent results in disentanglement of the PEO chains, which facilitates even more the perpendicular orientation of helices under applied MF. The enhancement of ionic conductivity was appreciably higher in the PEs cast under strong NdFeB magnets than under SmCo. Both bulk (intrachain) and grain-boundary conductivities increase when a MF is applied, but the improvement in the grain-boundary conductivity – associated with ion-hopping between polymer chains – is more pronounced. For LiAsF6:(PEO)3 at 65 °C, the interchain conductivity increased by a factor of 75, while the intrachain conductivity increased by a factor of 11–14. At room temperature, the SEI resistance of these PEs, cast under NdFeB HMF, decreased by a factor of up to 7, as compared to the typically cast polymer electrolytes. The effect of MF on orientation is observed directly down to the molecular level by 7Li nuclear magnetic resonance measurements.