2,234 research outputs found

    Energy and volume of vector fields on spherical domains

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    We present in this paper a \boundary version" for theorems about minimality of volume and energy functionals on a spherical domain of threedimensional Euclidean sphere

    The utility of surface magnetic field measurements in the MAGSAT program

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    To take full advantage of the global, vector, survey by the Magsat satellite, and international program of augmented surface measurements was proposed. For secular variation and upper mantle conductivity the proposed measurements are global. The repeat station measurements for secular variation should be occupied at 2-3 year intervals. A special observing period in November and December of 1979 is proposed during which simultaneous, continuous, global measurements for upper mantle conductivity studies are to be gathered. Finally, it is recommended that the networks in operation during the IMS extend their operation through the Fall of 1980 to provide correlative data useful for high latitude disturbance studies and for crustal conductivity studies

    On the 2D Dirac oscillator in the presence of vector and scalar potentials in the cosmic string spacetime in the context of spin and pseudospin symmetries

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    The Dirac equation with both scalar and vector couplings describing the dynamics of a two-dimensional Dirac oscillator in the cosmic string spacetime is considered. We derive the Dirac-Pauli equation and solve it in the limit of the spin and the pseudo-spin symmetries. We analyze the presence of cylindrical symmetric scalar potentials which allows us to provide analytic solutions for the resultant field equation. By using an appropriate ansatz, we find that the radial equation is a biconfluent Heun-like differential equation. The solution of this equation provides us with more than one expression for the energy eigenvalues of the oscillator. We investigate these energies and find that there is a quantum condition between them. We study this condition in detail and find that it requires the fixation of one of the physical parameters involved in the problem. Expressions for the energy of the oscillator are obtained for some values of the quantum number nn. Some particular cases which lead to known physical systems are also addressed.Comment: 15 pages, 8 figures, matches published versio

    A stochastic approach to the closure of accessible sets of control systems with application on homogeneous spaces

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    Given a control system on a compact manifold M, we study conditions for the foliation defined by the accessible sets to be dense in M. For this, we relate the control system to a stochastic differential equation and, by the support theorem, we give a characterization of the density in terms of the infinitesimal generator of the diffusion and its invariant measures.33351953

    Decomposition of stochastic flows with automorphism of subbundles component

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    We show that given a GG-structure PP on a differentiable manifold MM, if the group G(M)G(M) of automorphisms of PP is big enough, then there exists the quotient of an stochastic flows phitphi_t by G(M)G(M), in the sense that ϕt=ξtρt\phi_t = \xi_t \circ \rho_t where ξtG(M)\xi_t \in G(M), the remainder ρt\rho_t has derivative which is vertical but transversal to the fibre of PP. This geometrical context generalizes previous results where MM is a Riemannian manifold and ϕt\phi_t is decomposed with an isometric component, see Liao \cite{Liao1} and Ruffino \cite{Ruffino}, which in our context corresponds to the particular case of an SO(n)-structure on MM.Comment: To appear in Stochastics and Dynamics, 201

    Initial geomagnetic field model from MAGSAT

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    Magsat data from magnetically quiet days were used to derive a thirteenth degree and order spherical harmonic geomagnetic field model, MGST(3/80). The model utilized both scalar and vector data and fit that data with standard deviations of 8, 52, 55 and 97 nT for the scalar magnitude, B sub r, B sub theta and B sub phi respectively. When compared with earlier models, the Earth's dipole moment continues to decrease at a rate of about 26 nT/year. Evaluation of earlier models with Magsat data shows that the scalar field at the Magsat epoch is best predicted by the POGO(2/72) model but that the AWC/75 and IGS/75 are better for predicting vector fields
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