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The BIRD digital repository system captures, stores, indexes, preserves, and distributes digital research material.Thu, 20 Sep 2018 12:55:34 GMT2018-09-20T12:55:34ZOn the geometry of strongly flat semigroups and their generalizations
http://hdl.handle.net/20.500.11824/855
On the geometry of strongly flat semigroups and their generalizations
László T.; Némethi A.
Our goal is to convince the readers that the theory of complex normal surface singularities can be a powerful tool in the study of numerical semigroups, and, in the same time, a very rich source of interesting affine and numerical semigroups. More precisely, we prove that the strongly flat semigroups, which satisfy the maximality property with respect to the Diophantine Frobenius problem, are exactly the numerical semigroups associated with negative de nite Seifert homology spheres via the possible `weights' of the generic $S^1$-orbit. Furthermore, we consider their generalization to the Seifert rational homology sphere case and prove an explicit (up to a Laufer computation sequence) formula for their Frobenius number. The singularities behind are
the weighted homogeneous ones, whose several topological and analytical properties are exploited.
Tue, 18 Sep 2018 00:00:00 GMThttp://hdl.handle.net/20.500.11824/8552018-09-18T00:00:00ZA Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements
http://hdl.handle.net/20.500.11824/854
A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements
Shahriari M.; Rojas S.; Pardo D.; Rodríguez-Rozas A.; Bakr S.A.; Calo V.M.; Muga I.
In some geological formations, borehole resistivity measurements can be simulated using a sequence of 1D models. By considering a 1D layered media, we can reduce the dimensionality of the problem from 3D to 1.5D via a Hankel transform. The resulting formulation is often solved via a semi-analytic method, mainly due to its high performance. However, semi-analytic methods have important limitations such as, for example, their inability to model piecewise linear variations on the resistivity. Herein, we develop a multi-scale finite element method (FEM) to solve the secondary field formulation. This numerical scheme overcomes the limitations of semi-analytic methods while still delivering high performance. We illustrate the performance of the method with numerical synthetic examples based on two symmetric logging-while-drilling (LWD) induction devices operating at 2 MHz and 500 KHz, respectively.
Thu, 14 Jun 2018 00:00:00 GMThttp://hdl.handle.net/20.500.11824/8542018-06-14T00:00:00ZOn the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids
http://hdl.handle.net/20.500.11824/853
On the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids
Scrobogna S.
We study a class of 2D solutions of a Bloch-Torrey regularization of the Rosensweig system in the whole space, which arise when the initial data and the external magnetic field are 2D. We prove that such solutions are globally defined if the initial data is in $ H^k\pare{\bR^2}, k\geqslant 1 $.
Sat, 01 Sep 2018 00:00:00 GMThttp://hdl.handle.net/20.500.11824/8532018-09-01T00:00:00ZNumerical simulation of the von Kármán sodium dynamo experiment
http://hdl.handle.net/20.500.11824/852
Numerical simulation of the von Kármán sodium dynamo experiment
Nore C.; Castanon Quiroz D.; Cappanera L.; Guermond, L.J.
We present hydrodynamic and magnetohydrodynamic (MHD) simulations of liquid sodium flows in the von Kármán sodium (VKS) set-up. The counter-rotating impellers made of soft iron that were used in the successful 2006 experiment are represented by means of a pseudo-penalty method. Hydrodynamic simulations are performed at high kinetic Reynolds numbers using a large eddy simulation technique. The results compare well with the experimental data: the flow is laminar and steady or slightly fluctuating at small angular frequencies; small scales fill the bulk and a Kolmogorov-like spectrum is obtained at large angular frequencies. Near the tips of the blades the flow is expelled and takes the form of intense helical vortices. The equatorial shear layer acquires a wavy shape due to three coherent co-rotating radial vortices as observed in hydrodynamic experiments. MHD computations are performed: at fixed kinetic Reynolds number, increasing the magnetic permeability of the impellers reduces the critical magnetic Reynolds number for dynamo action; at fixed magnetic permeability, increasing the kinetic Reynolds number also decreases the dynamo threshold. Our results support the conjecture that the critical magnetic Reynolds number tends to a constant as the kinetic Reynolds number tends to infinity. The resulting dynamo is a mostly axisymmetric axial dipole with an azimuthal component concentrated near the impellers as observed in the VKS experiment. A speculative mechanism for dynamo action in the VKS experiment is proposed.
Mon, 03 Sep 2018 00:00:00 GMThttp://hdl.handle.net/20.500.11824/8522018-09-03T00:00:00Z