1,690 research outputs found
Automation of The Guiding Center Expansion
We report on the use of the recently-developed Mathematica package
\emph{VEST} (Vector Einstein Summation Tools) to automatically derive the
guiding center transformation. Our Mathematica code employs a recursive
procedure to derive the transformation order-by-order. This procedure has
several novel features. (1) It is designed to allow the user to easily explore
the guiding center transformation's numerous non-unique forms or
representations. (2) The procedure proceeds entirely in cartesian position and
velocity coordinates, thereby producing manifestly gyrogauge invariant results;
the commonly-used perpendicular unit vector fields are never even
introduced. (3) It is easy to apply in the derivation of higher-order
contributions to the guiding center transformation without fear of human error.
Our code therefore stands as a useful tool for exploring subtle issues related
to the physics of toroidal momentum conservation in tokamaks.Comment: 34 page
An investigation of combustion instability in aircraft-engine reheat systems
The principal objective of this study was to examine experimentally
the effects of upstream temperature, velocity, gutter blockage, tailpipe
length, and main and pilot fuel flows, on the form of combustion instability
encountered in aircraft reheat systems which is sometimes referred to as 'buzz'.
Tests were carried out at atmospheric pressure for upstream temperatures of
between 200 and 500°C, and upstream velocities ranging from 140 to 200 ft/sec.
Three values of stabilizer blockage were employed, namely 25, 30 and 35%.
The tailpipe length was varied between 9 and 45 inches. Auto-correlation
techniques were used in the frequency analysis of the buzz waveforms.
It was found that a certain minimum tailpipe length is necessary in
order to produce buzz which is then strengthened as the tailpipe length is
increased. Buzz also becomes more pronounced with an increase in gas velocity
but stabilizer blockage appears to have no discernible effect … [cont.]
When You Come Home
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A Lagrangian kinetic model for collisionless magnetic reconnection
A new fully kinetic system is proposed for modeling collisionless magnetic
reconnection. The formulation relies on fundamental principles in Lagrangian
dynamics, in which the inertia of the electron mean flow is neglected in the
expression of the Lagrangian, rather then enforcing a zero electron mass in the
equations of motion. This is done upon splitting the electron velocity into its
mean and fluctuating parts, so that the latter naturally produce the
corresponding pressure tensor. The model exhibits a new Coriolis force term,
which emerges from a change of frame in the electron dynamics. Then, if the
electron heat flux is neglected, the strong electron magnetization limit yields
a hybrid model, in which the electron pressure tensor is frozen into the
electron mean velocity.Comment: 15 pages, no figures. To Appear in Plasma Phys. Control. Fusio
A simple interpretation of quantum mirages
In an interesting new experiment the electronic structure of a magnetic atom
adsorbed on the surface of Cu(111), observed by STM, was projected into a
remote location on the same surface. The purpose of the present paper is to
interpret this experiment with a model Hamiltonian, using ellipses of the size
of the experimental ones, containing about 2300 atoms. The charge distribution
for the different wavefunctions is analyzed, in particular, for those with
energy close to the Fermi energy of copper Ef. Some of them show two symmetric
maxima located on the principal axis of the ellipse but not necessarily at the
foci. If a Co atom is adsorbed at the site where the wavefunction with energy
has a maximum and the interaction is small, the main effect of the
adsorbed atom will be to split this particular wavefunction in two. The total
charge density will remain the same but the local density of states will
present a dip at Ef at any site where the charge density is large enough. We
relate the presence of this dip to the observation of quantum mirages. Our
interpretation suggests that other sites, apart from the foci of the ellipses,
can be used for projecting atomic images and also indicates the conditions for
other non magnetic adsorbates to produce mirages.Comment: 3 pages, 3 Fig
The Hamiltonian structure and Euler-Poincar\'{e} formulation of the Vlasov-Maxwell and gyrokinetic systems
We present a new variational principle for the gyrokinetic system, similar to
the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in
the Eulerian frame and based on constrained variations of the phase space fluid
velocity and particle distribution function. Using a Legendre transform, we
explicitly derive the field theoretic Hamiltonian structure of the system. This
is carried out with a modified Dirac theory of constraints, which is used to
construct meaningful brackets from those obtained directly from
Euler-Poincar\'{e} theory. Possible applications of these formulations include
continuum geometric integration techniques, large-eddy simulation models and
Casimir type stability methods.
[1] H. Cendra et. al., Journal of Mathematical Physics 39, 3138 (1998)Comment: 36 pages, 1 figur
Multiscale Modeling of Ultra High Temperature Ceramics (UHTC) ZrB2 and HfB2: Application to Lattice Thermal Conductivity
We are developing a multiscale framework in computational modeling for the ultra high temperature ceramics (UHTC) ZrB2 and HfB2. These materials are characterized by high melting point, good strength, and reasonable oxidation resistance. They are candidate materials for a number of applications in extreme environments including sharp leading edges of hypersonic aircraft. In particular, we used a combination of ab initio methods, atomistic simulations and continuum computations to obtain insights into fundamental properties of these materials. Ab initio methods were used to compute basic structural, mechanical and thermal properties. From these results, a database was constructed to fit a Tersoff style interatomic potential suitable for atomistic simulations. These potentials were used to evaluate the lattice thermal conductivity of single crystals and the thermal resistance of simple grain boundaries. Finite element method (FEM) computations using atomistic results as inputs were performed with meshes constructed on SEM images thereby modeling the realistic microstructure. These continuum computations showed the reduction in thermal conductivity due to the grain boundary network
Multiscale Modeling of Grain Boundaries in ZrB2: Structure, Energetics, and Thermal Resistance
A combination of ab initio, atomistic and finite element methods (FEM) were used to investigate the structures, energetics and lattice thermal conductance of grain boundaries for the ultra high temperature ceramic ZrB2. Atomic models of idealized boundaries were relaxed using density functional theory. Information about bonding across the interfaces was determined from the electron localization function. The Kapitza conductance of larger scale versions of the boundary models were computed using non-equilibrium molecular dynamics. The interfacial thermal parameters together with single crystal thermal conductivities were used as parameters in microstructural computations. FEM meshes were constructed on top of microstructural images. From these computations, the effective thermal conductivity of the polycrystalline structure was determined
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