5,897 research outputs found
Generalized poisson brackets and nonlinear Liapunov stability application to reduces mhd
A method is presented for obtaining Liapunov
functionals (LF) and proving nonlinear stability. The method
uses the generalized Poisson bracket (GPB) formulation of
Hamiltonian dynamics. As an illustration, certain stationary
solutions of ideal reduced MHD (RMHD) are shown to be nonlinearly
stable. This includes Grad-Shafranov and Alfven
solutions
An Optimal Control Formulation for Inviscid Incompressible Ideal Fluid Flow
In this paper we consider the Hamiltonian formulation of the equations of
incompressible ideal fluid flow from the point of view of optimal control
theory. The equations are compared to the finite symmetric rigid body equations
analyzed earlier by the authors. We discuss various aspects of the Hamiltonian
structure of the Euler equations and show in particular that the optimal
control approach leads to a standard formulation of the Euler equations -- the
so-called impulse equations in their Lagrangian form. We discuss various other
aspects of the Euler equations from a pedagogical point of view. We show that
the Hamiltonian in the maximum principle is given by the pairing of the
Eulerian impulse density with the velocity. We provide a comparative discussion
of the flow equations in their Eulerian and Lagrangian form and describe how
these forms occur naturally in the context of optimal control. We demonstrate
that the extremal equations corresponding to the optimal control problem for
the flow have a natural canonical symplectic structure.Comment: 6 pages, no figures. To appear in Proceedings of the 39th IEEEE
Conference on Decision and Contro
Hamiltonian approach to hybrid plasma models
The Hamiltonian structures of several hybrid kinetic-fluid models are
identified explicitly, upon considering collisionless Vlasov dynamics for the
hot particles interacting with a bulk fluid. After presenting different
pressure-coupling schemes for an ordinary fluid interacting with a hot gas, the
paper extends the treatment to account for a fluid plasma interacting with an
energetic ion species. Both current-coupling and pressure-coupling MHD schemes
are treated extensively. In particular, pressure-coupling schemes are shown to
require a transport-like term in the Vlasov kinetic equation, in order for the
Hamiltonian structure to be preserved. The last part of the paper is devoted to
studying the more general case of an energetic ion species interacting with a
neutralizing electron background (hybrid Hall-MHD). Circulation laws and
Casimir functionals are presented explicitly in each case.Comment: 27 pages, no figures. To appear in J. Phys.
Altered muscarinic and nicotinic receptor densities in cortical and subcortical brain regions in Parkinson's disease
Muscarinic and nicotinic cholinergic receptors and choline acetyltransferase activity were studied in postmortem brain tissue from patients with histopathologically confirmed Parkinson's disease and matched control subjects. Using washed membrane homogenates from the frontal cortex, hippocampus, caudate nucleus, and putamen, saturation analysis of specific receptor binding was performed for the total number of muscarinic receptors with [3H]quinuclidinyl benzilate, for muscarinic M1 receptors with [3H]pirenzepine, for muscarinic M2 receptors with [3H]oxotremorine-M, and for nicotinic receptors with (-)-[3H]nicotine. In comparison with control tissues, choline acetyl-transferase activity was reduced in the frontal cortex and hippocampus and unchanged in the caudate nucleus and putamen of parkinsonian patients. In Parkinson's disease the maximal binding site density for [3H]quinuclidinyl benzilate was increased in the frontal cortex and unaltered in the hippocampus, caudate nucleus, and putamen. Specific [3H]pirenzepine binding was increased in the frontal cortex, unaltered in the hippocampus, and decreased in the caudate nucleus and putamen. In parkinsonian patients Bmax values for specific [3H]oxotremorine-M binding were reduced in the cortex and unchanged in the hippocampus and striatum compared with controls. Maximal (-)-[3H]nicotine binding was reduced in both the cortex and hippocampus and unaltered in both the caudate nucleus and putamen. Alterations of the equilibrium dissociation constant were not observed for any ligand in any of the brain areas examined. The present results suggest that both the innominatocortical and the septohippocampal cholinergic systems degenerate in Parkinson's disease.(ABSTRACT TRUNCATED AT 250 WORDS
Brain muscarinic cholinergic receptors in Huntington's disease
Muscarinic cholinergic receptors and choline acetyltransferase (ChAT) activity were studied in postmortem brain tissue from patients with Huntington's disease and matched control subjects. In comparison with controls, reductions in ChAT activity were found in the hippocampus, but not in the temporal cortex in Huntington's disease. Patients with Huntington's disease showed reduced densities of the total number of muscarinic receptors and of M-2 receptors in the hippocampus while the density of M-1 receptors was unaltered. Muscarinic receptor binding was unchanged in the temporal cortex. These results indicate a degeneration in Huntington's disease of the septo-hippocampal cholinergic pathway, but no impairment of the innominato-cortical cholinergic system
Terguride stimulates locomotor activity at 2 months but not 10 months after 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine treatment of common marmosets
The mixed dopamine (DA) agonist/antagonist terguride acts as a DA antagonist on normosensitive receptors but shows DA agonistic properties at supersensitive DA receptors. Such a compound could offer an alternative to the treatment of Parkinson's disease with indirect or direct DA agonists. The present study compares the actions of terguride, 4-12 mg/kg i.p., in naive common marmosets with its effects in animals rendered parkinsonian by administration of 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP), 2 months or 10 months previously, in order to test its antiparkinsonian efficacy. Terguride reduced locomotor activity in naive common marmosets, similar to its effects in rodents and in line with the DA antagonistic activity of the compound. In marmosets treated with MPTP 2 months previously and exhibiting pronounced behavioural motor deficits, terguride stimulated locomotor activity, showing DA agonistic properties under these conditions. In contrast, the locomotor activity of animals that had recovered from MPTP treatment 10 months previously was not altered by terguride. It is concluded that terguride has anti-akinetic efficacy in this primate model of Parkinson's disease. In addition, terguride offers a unique opportunity to differentiate, pharmacologically, the extent of dopaminergic recovery from MPTP treatment in this primate species
Chiral Anomalies via Classical and Quantum Functional Methods
In the quantum path integral formulation of a field theory model an anomaly
arises when the functional measure is not invariant under a symmetry
transformation of the Lagrangian. In this paper, generalizing previous work
done on the point particle, we show that even at the classical level we can
give a path integral formulation for any field theory model. Since classical
mechanics cannot be affected by anomalies, the measure of the classical path
integral of a field theory must be invariant under the symmetry. The classical
path integral measure contains the fields of the quantum one plus some extra
auxiliary ones. So, at the classical level, there must be a sort of
"cancellation" of the quantum anomaly between the original fields and the
auxiliary ones. In this paper we prove in detail how this occurs for the chiral
anomaly.Comment: 26 pages, Latex, misprint fixed, a dedication include
Averaged Template Matching Equations
By exploiting an analogy with averaging procedures in fluid
dynamics, we present a set of averaged template matching equations.
These equations are analogs of the exact template matching equations
that retain all the geometric properties associated with the diffeomorphismgrou
p, and which are expected to average out small scale features
and so should, as in hydrodynamics, be more computationally efficient
for resolving the larger scale features. Froma geometric point of view,
the new equations may be viewed as coming from a change in norm that
is used to measure the distance between images. The results in this paper
represent first steps in a longer termpro gram: what is here is only
for binary images and an algorithm for numerical computation is not
yet operational. Some suggestions for further steps to develop the results
given in this paper are suggested
Discrete Routh Reduction
This paper develops the theory of abelian Routh reduction for discrete
mechanical systems and applies it to the variational integration of mechanical
systems with abelian symmetry. The reduction of variational Runge-Kutta
discretizations is considered, as well as the extent to which symmetry
reduction and discretization commute. These reduced methods allow the direct
simulation of dynamical features such as relative equilibria and relative
periodic orbits that can be obscured or difficult to identify in the unreduced
dynamics. The methods are demonstrated for the dynamics of an Earth orbiting
satellite with a non-spherical correction, as well as the double
spherical pendulum. The problem is interesting because in the unreduced
picture, geometric phases inherent in the model and those due to numerical
discretization can be hard to distinguish, but this issue does not appear in
the reduced algorithm, where one can directly observe interesting dynamical
structures in the reduced phase space (the cotangent bundle of shape space), in
which the geometric phases have been removed. The main feature of the double
spherical pendulum example is that it has a nontrivial magnetic term in its
reduced symplectic form. Our method is still efficient as it can directly
handle the essential non-canonical nature of the symplectic structure. In
contrast, a traditional symplectic method for canonical systems could require
repeated coordinate changes if one is evoking Darboux' theorem to transform the
symplectic structure into canonical form, thereby incurring additional
computational cost. Our method allows one to design reduced symplectic
integrators in a natural way, despite the noncanonical nature of the symplectic
structure.Comment: 24 pages, 7 figures, numerous minor improvements, references added,
fixed typo
Discrete Lie Advection of Differential Forms
In this paper, we present a numerical technique for performing Lie advection
of arbitrary differential forms. Leveraging advances in high-resolution finite
volume methods for scalar hyperbolic conservation laws, we first discretize the
interior product (also called contraction) through integrals over Eulerian
approximations of extrusions. This, along with Cartan's homotopy formula and a
discrete exterior derivative, can then be used to derive a discrete Lie
derivative. The usefulness of this operator is demonstrated through the
numerical advection of scalar fields and 1-forms on regular grids.Comment: Accepted version; to be published in J. FoC
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