3D Ring Research Articles

Investigation of a 3-D hybrid finite-element/boundary-element method for electromagnetic launch applications and validation using semianalytical solutions

The hybrid finite element/boundary element (FE/BE) computational scheme is advantageous in that it satisfies boundary conditions at infinity while avoiding meshing and computations in the air regions. Of numerous hybrid schemes, one using the fundamental solution of Poisson's equation as the weighting function has been employed successfully in many fields. Analyses in electromagnetic (EM) launch usually involve strong coupling among EM, thermal, and structural equations. The hybrid method has the added benefit that it may be fashioned to incorporate the effect of structural deformations on EM fields. Here, a three-dimensional (3D) hybrid algorithm using the fundamental solution of Poisson's equation as the weighting function is investigated and implemented in the parallel version of the code electromechanical analysis program in 3D (EMAP3D). The method is validated using two examples with semianalytical solutions: a 3D ring conductor with rectangular cross section carrying uniform current, and a quadrupole configuration with four independent, closed-ring conductors excited by imposed potential differences. The solutions obtained using the hybrid method match the semianalytical solutions within approximately four percent deviations.

Synthesis of novel 6-enaminopurines.

Two different approaches have been used for the synthesis of 6-enaminopurines 6 from 5-amino-4-cyanoformimidoyl imidazoles. In the first approach imidazoles 1 were reacted with ethoxymethylenemalononitrile or ethoxymethylenecyanoacetate under mild experimental conditions and this led to 9-substituted-6-(1-amino-2,2-dicyanovinyl) purines 6a-f or 9-substituted-6-(1-amino-2-cyano-2-methoxycarbonylvinyl) purines 6g-k. These reactions are postulated to occur through an imidazo-pyrrolidine intermediate 7, which rapidly rearranges to the 6-enaminopurine 6. In the second approach 6-methoxyformimidoyl purines 3, prepared in two efficient steps from 5-amino-4-cyanoformimidoyl imidazoles 1, were reacted with malononitrile and methylcyanoacetate with a mild acid catalysis (ammonium acetate or piperidinium acetate) to give 6-enaminopurines 6a, 6d, 6f, 6g and 6k in very good yields. Only low yields were obtained for the 6-enaminopurine 6j, as competing nucleophilic attack on C-8 of either 3d or 6jcauses ring opening with formation of pyrimido-pyrimidines 11 and 10a respectively.

Nonlinear waves in a cylindrical Bose-Einstein condensate

We present a calculation of solitary waves propagating in a steady state with constant velocity $v$ along a cigar-shaped Bose-Einstein trap approximated as an infinitely elongated cylinder. For sufficiently weak couplings (densities), the main features of the calculated solitons could be captured by effective one-dimensional (1D) models. However, for stronger couplings of practical interest, the relevant solitary waves are found to be hybrids of quasi-1D solitons and 3D vortex rings. An interesting hierarchy of vortex rings occurs as the effective coupling constant is increased through a sequence of critical values. The energy-momentum dispersion of the above structures is shown to exhibit characteristics similar to a mode proposed sometime ago by Lieb within a strictly 1D model, as well as some rotonlike features.

Variations of Inner Magnetospheric Currents During the Magnetic Storm of May 1998

AbstractTransient variations of the geomagnetic field at low latitudes are mainly caused by the following current systems: the ionospheric dynamo current (IDC), the symmetrical ring current (SRC), and the 3D partial ring current system (PRFI). Meanwhile, the region I ield aligned current‐ionospheric current system (FACI) annot be ignored. In this paper, the ariations of these current systems during the large storm on May 1‐6, 1998 are discussed. The disturbances of the storm contains two events. One is during May 1‐3 and the other is during May 4‐5. The Sq‐field caused by IDC is calculated by using several station pairs. Then, the fields of other sources are separated by fitting data to their field models. Results show that: (1) PRFI and FACI do not develop significantly in the first event, while they develop strongly with substorms in the second event. (2) The variations of SRC‐field are similar to Dst index in the first event and delayed to Dst in the second event. (3) In the second event, PRFI develops before SRC, and SRC depresses associated with the recovery of PRFI and FACI. These results provide a clue to understand the formation of the ring current and field‐aligned currents and their relationship.

Shapes and sizes of arbitrary random walks at O(1/ d3) II. Asphericity and prolateness parameters

For arbitrary random walks in any d-dimensional space, expansions in powers of 1/ d of asphericity and prolateness parameters and moments of the inverse size ratio have been developed, which, at O(1/ d 3), yield very good approximations to exact values of the parameters for chains, rings, dumbbells and 3- and 5-arm regular stars. The 1/ d-expansions have also been used to obtain an estimate of these shape asymmetry parameters for 3D Edwards chains, rings, dumbbells and 3-arm stars and to give a mathematical proof that infinitely large random nets such as Bethe lattice or starburst and Mckay's net exhibit spherical symmetry. For arbitrary random walks at d = ∞, it is proved that these parameters coincide with their corresponding factors, while for an end-looped self-avoiding walk, it is found that its shape asymmetry is even larger than that of an open SAW. An 1/ f-expansion of the parameters for f-arm regular stars has also been obtained, and a comparison of the dimensionality dependence of the parameters with that of the corresponding factors has been made for the four types of random walks.