6,070 research outputs found
Asymptotic Stability, Instability and Stabilization of Relative Equilibria
In this paper we analyze asymptotic stability, instability and stabilization for the relative equilibria, i.e. equilibria modulo a group action, of natural mechanical systems. The practical applications of these results are to rotating mechanical systems where the group is the rotation group. We use a modification of the Energy-Casimir and Energy-Momentum methods for Hamiltonian systems to analyze systems with dissipation. Our work couples the modern theory of block diagonalization to the classical work of Chetaev
Kinetic energy functional for Fermi vapors in spherical harmonic confinement
Two equations are constructed which reflect, for fermions moving
independently in a spherical harmonic potential, a differential virial theorem
and a relation between the turning points of kinetic energy and particle
densities. These equations are used to derive a differential equation for the
particle density and a non-local kinetic energy functional.Comment: 8 pages, 2 figure
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
The relation between stellar magnetic field geometry and chromospheric activity cycles - I. The highly variable field of ɛ Eridani at activity minimum
The young and magnetically active K dwarf Epsilon Eridani exhibits a chromospheric activity cycle of about 3 years. Previous reconstructions of its large-scale magnetic field show strong variations at yearly epochs. To understand how Epsilon Eridani's large-scale magnetic field geometry evolves over its activity cycle we focus on high cadence observations spanning 5 months at its activity minimum. Over this timespan we reconstruct 3 maps of Epsilon Eridani's large-scale magnetic field using the tomographic technique of Zeeman Doppler Imaging. The results show that at the minimum of its cycle, Epsilon Eridani's large-scale field is more complex than the simple dipolar structure of the Sun and 61 Cyg A at minimum. Additionally we observe a surprisingly rapid regeneration of a strong axisymmetric toroidal field as Epsilon Eridani emerges from its S-index activity minimum. Our results show that all stars do not exhibit the same field geometry as the Sun and this will be an important constraint for the dynamo models of active solar-type stars
Mapping of serotype-specific, immunodominant epitopes in the NS-4 region of hepatitis C virus (HCV):use of type-specific peptides to serologically differentiate infections with HCV types 1, 2, and 3
The effect of sequence variability between different types of hepatitis C virus (HCV) on the antigenicity of the NS-4 protein was investigated by epitope mapping and by enzyme-linked immunosorbent assay with branched oligopeptides. Epitope mapping of the region between amino acid residues 1679 and 1768 in the HCV polyprotein revealed two major antigenic regions (1961 to 1708 and 1710 to 1728) that were recognized by antibody elicited upon natural infection of HCV. The antigenic regions were highly variable between variants of HCV, with only 50 to 60% amino acid sequence similarity between types 1, 2, and 3. Although limited serological cross-reactivity between HCV types was detected between peptides, particularly in the first antigenic region of NS-4, type-specific reactivity formed the principal component of the natural humoral immune response to NS-4. Type-specific antibody to particular HCV types was detected in 89% of the samples from anti-HCV-positive blood donors and correlated almost exactly with genotypic analysis of HCV sequences amplified from the samples by polymerase chain reaction. Whereas almost all blood donors appeared to be infected with a single virus type (97%), a higher proportion of samples (40%) from hemophiliacs infected from transfusion of non-heat-inactivated clotting factor contained antibody to two or even all three HCV types, providing evidence that long-term exposure may lead to multiple infection with different variants of HCV
The Dynamics of Two Coupled Rigid Bodies
In this paper we derive a Poisson bracket on the phase space so(3)^*x so(3)^*x SO(3) such that the dynamics of two three- dimensional rigid bodies coupled by a ball and socket joint can be written as a Hamiltonian system
Dirac method and symplectic submanifolds in the cotangent bundle of a factorizable Lie group
In this work we study some symplectic submanifolds in the cotangent bundle of
a factorizable Lie group defined by second class constraints. By applying the
Dirac method, we study many issues of these spaces as fundamental Dirac
brackets, symmetries, and collective dynamics. This last item allows to study
integrability as inherited from a system on the whole cotangent bundle, leading
in a natural way to the AKS theory for integrable systems
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