The Static Maxwell System in Three Dimensional Axially Symmetric Inhomogeneous Media and Axially Symmetric Generalization of the Cauchy–Riemann System

We have studied the behaviour of a charged particle in an axially symmetric magnetic field having a neutral point, so as to find a possibility of confining a charged particle in a thermonuclear device. In order to study the motion we have reduced a three-dimensional motion to a two-dimensional one by introducing a fictitious potential. Following Schmidt we have classified the motion, as an ‘off-axis motion’ and ‘encircling motion’ depending on the behaviour of this potential. We see that the particle performs a hybrid type of motion in the negative z-axis, i.e. at some instant it is in ‘off-axis motion’ while at another instant it is in ‘encircling motion’. We have also solved the equation of motion numerically and the graphs of the particle trajectory verify our analysis. We find that in most of the cases the particle is contained. The magnetic moment is found to be moderately adiabatic.

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On dynamic ray tracing in three dimensional inhomogeneous media

Studia Geophysica et Geodaetica ◽

10.1007/bf01634140 ◽

1980 ◽

Vol 24 (3) ◽

pp. 317-318

Author(s):

Peter Hubral ◽

I. Pšenčík

Keyword(s):

Ray Tracing ◽

Three Dimensional ◽

Inhomogeneous Media ◽

Dynamic Ray Tracing

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LOW- TO MID-FREQUENCY SCATTERING FROM ELASTIC OBJECTS ON A SAND SEA FLOOR: SIMULATION OF FREQUENCY AND ASPECT DEPENDENT STRUCTURAL ECHOES

Journal of Computational Acoustics ◽

10.1142/s0218396x12400073 ◽

2012 ◽

Vol 20 (02) ◽

pp. 1240007 ◽

Cited By ~ 13

Author(s):

MARIO ZAMPOLLI ◽

AUBREY L. ESPANA ◽

KEVIN L. WILLIAMS ◽

STEVEN G. KARGL ◽

ERIC I. THORSOS ◽

...

Keyword(s):

Scattering Problem ◽

Three Dimensional ◽

Element Model ◽

Propagation Model ◽

Target Strength ◽

Unexploded Ordnance ◽

Two Dimensional ◽

Axially Symmetric ◽

Sea Floor ◽

Spectral Integral

The scattering from roughly meter-sized targets, such as pipes, cylinders and unexploded ordnance shells in the 1–30 kHz frequency band is studied by numerical simulations and compared to experimental results. The numerical tool used to compute the frequency and aspect-dependent target strength is a hybrid model, consisting of a local finite-element model for the vicinity of the target, based on the decomposition of the three-dimensional scattering problem for axially symmetric objects into a series of independent two-dimensional problems, and a propagation model based on the wavenumber spectral integral representation of the Green's functions for layered media.

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A PARALLEL SOLVER FOR REACTION–DIFFUSION SYSTEMS IN COMPUTATIONAL ELECTROCARDIOLOGY

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202504003489 ◽

2004 ◽

Vol 14 (06) ◽

pp. 883-911 ◽

Cited By ~ 121

Author(s):

PIERO COLLI FRANZONE ◽

LUCA F. PAVARINO

Keyword(s):

Large Scale ◽

Three Dimensional ◽

Reaction Diffusion ◽

Ionic Currents ◽

Reaction Diffusion Equations ◽

Reaction Diffusion Equation ◽

Fiber Direction ◽

Axially Symmetric ◽

Reaction Diffusion Systems ◽

Cardiac Model

In this work, a parallel three-dimensional solver for numerical simulations in computational electrocardiology is introduced and studied. The solver is based on the anisotropic Bidomain cardiac model, consisting of a system of two degenerate parabolic reaction–diffusion equations describing the intra and extracellular potentials of the myocardial tissue. This model includes intramural fiber rotation and anisotropic conductivity coefficients that can be fully orthotropic or axially symmetric around the fiber direction. The solver also includes the simpler anisotropic Monodomain model, consisting of only one reaction–diffusion equation. These cardiac models are coupled with a membrane model for the ionic currents, consisting of a system of ordinary differential equations that can vary from the simple FitzHugh–Nagumo (FHN) model to the more complex phase-I Luo–Rudy model (LR1). The solver employs structured isoparametric Q1finite elements in space and a semi-implicit adaptive method in time. Parallelization and portability are based on the PETSc parallel library. Large-scale computations with up to O(107) unknowns have been run on parallel computers, simulating excitation and repolarization phenomena in three-dimensional domains.

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Finite-element modeling of three-dimensional electromagnetic fields in inhomogeneous media

Radio Science ◽

10.1029/90rs00932 ◽

1991 ◽

Vol 26 (1) ◽

pp. 275-280 ◽

Cited By ~ 9

Author(s):

Gerrit Mur

Keyword(s):

Finite Element ◽

Finite Element Modeling ◽

Electromagnetic Fields ◽

Three Dimensional ◽

Inhomogeneous Media ◽

Element Modeling

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Axisymmetric three-dimensional gravity currents generated by lock exchange

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.500 ◽

2018 ◽

Vol 851 ◽

pp. 507-544 ◽

Cited By ~ 15

Author(s):

Roberto Inghilesi ◽

Claudia Adduce ◽

Valentina Lombardi ◽

Federico Roman ◽

Vincenzo Armenio

Keyword(s):

Froude Number ◽

Flow Rate ◽

Rapid Development ◽

Three Dimensional ◽

Gravity Currents ◽

Constant Flow ◽

Axially Symmetric ◽

Grashof Number ◽

Constant Flow Rate ◽

Dimensional Gravity

Unconfined three-dimensional gravity currents generated by lock exchange using a small dividing gate in a sufficiently large tank are investigated by means of large eddy simulations under the Boussinesq approximation, with Grashof numbers varying over five orders of magnitudes. The study shows that, after an initial transient, the flow can be separated into an axisymmetric expansion and a globally translating motion. In particular, the circular frontline spreads like a constant-flow-rate, axially symmetric gravity current about a virtual source translating along the symmetry axis. The flow is characterised by the presence of lobe and cleft instabilities and hydrodynamic shocks. Depending on the Grashof number, the shocks can either be isolated or produced continuously. In the latter case a typical ring structure is visible in the density and velocity fields. The analysis of the frontal spreading of the axisymmetric part of the current indicates the presence of three regimes, namely, a slumping phase, an inertial–buoyancy equilibrium regime and a viscous–buoyancy equilibrium regime. The viscous–buoyancy phase is in good agreement with the model of Huppert (J. Fluid Mech., vol. 121, 1982, pp. 43–58), while the inertial phase is consistent with the experiments of Britter (Atmos. Environ., vol. 13, 1979, pp. 1241–1247), conducted for purely axially symmetric, constant inflow, gravity currents. The adoption of the slumping model of Huppert & Simpson (J. Fluid Mech., vol. 99 (04), 1980, pp. 785–799), which is here extended to the case of constant-flow-rate cylindrical currents, allows reconciling of the different theories about the initial radial spreading in the context of different asymptotic regimes. As expected, the slumping phase is governed by the Froude number at the lock’s gate, whereas the transition to the viscous phase depends on both the Froude number at the gate and the Grashof number. The identification of the inertial–buoyancy regime in the presence of hydrodynamic shocks for this class of flows is important, due to the lack of analytical solutions for the similarity problem in the framework of shallow water theory. This fact has considerably slowed the research on variable-flow-rate axisymmetric gravity currents, as opposed to the rapid development of the knowledge about cylindrical constant-volume and planar gravity currents, despite their own environmental relevance.

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