117,452 research outputs found
Symplectic reduction and topology for applications in classical molecular dynamics
This paper aims to introduce readers with backgrounds in classical molecular dynamics to some ideas in geometric mechanics that may be useful. This is done through some simple but specific examples: (i) the separation of the rotational and internal energies in an arbitrarily floppy N-body system and (ii) the reduction of the phase space accompanying the change from the laboratory coordinate system to the center of mass coordinate system relevant to molecular collision dynamics. For the case of two-body molecular systems constrained to a plane, symplectic reduction is employed to demonstrate explicitly the separation of translational, rotational, and internal energies and the corresponding reductions of the phase space describing the dynamics for Hamiltonian systems with symmetry. Further, by examining the topology of the energy-momentum map, a unified treatment is presented of the reduction results for the description of (i) the classical dynamics of rotating and vibrating diatomic molecules, which correspond to bound trajectories and (ii) the classical dynamics of atom–atom collisions, which correspond to scattering trajectories. This provides a framework for the treatment of the dynamics of larger N-body systems, including the dynamics of larger rotating and vibrating polyatomic molecular systems and the dynamics of molecule–molecule collisions
Well-posedness of the Ericksen-Leslie system
In this paper, we prove the local well-posedness of the Ericksen-Leslie
system, and the global well-posednss for small initial data under the physical
constrain condition on the Leslie coefficients, which ensures that the energy
of the system is dissipated. Instead of the Ginzburg-Landau approximation, we
construct an approximate system with the dissipated energy based on a new
formulation of the system.Comment: 16 page
Saturation of dephasing time in mesoscopic devices produced by a ferromagnetic state
We consider an exchange model of itinerant electrons in a Heisenberg
ferromagnet and we assume that the ferromagnet is in a fully polarized state.
Using the Holstein-Primakoff transformation we are able to obtain a
boson-fermion Hamiltonian that is well-known in the interaction between light
and matter. This model describes the spontaneous emission in two-level atoms
that is the proper decoherence mechanism when the number of modes of the
radiation field is taken increasingly large, the vacuum acting as a reservoir.
In the same way one can see that the interaction between the bosonic modes of
spin waves and an itinerant electron produces decoherence by spin flipping with
a rate proportional to the size of the system. In this way we are able to show
that the experiments on quantum dots, described in D. K. Ferry et al. [Phys.
Rev. Lett. {\bf 82}, 4687 (1999)], and nanowires, described in D. Natelson et
al. [Phys. Rev. Lett. {\bf 86}, 1821 (2001)], can be understood as the
interaction of itinerant electrons and an electron gas in a fully polarized
state.Comment: 10 pages, no figure. Changed title. Revised version accepted for
publication in Physical Review
Jet vortex generators for turbulent flow separation control
A parametric study was performed with jet vortex generators to determine their effectiveness in controlling flow separation associated with low speed turbulent flow over a two dimensional rearward-facing ramp. Results indicate that flow separation control can be accomplished with the level of control achieved being a function of jet speed, jet orientation (with respect to the free stream direction), and orifice pattern (double row of jets vs. single row). Compared to slot blowing, jet vortex generators can provide an equivalent level of flow control over a larger spanwise region (for constant jet flow area and speed)
Thermodynamical Consistent Modeling and Analysis of Nematic Liquid Crystal Flows
The general Ericksen-Leslie system for the flow of nematic liquid crystals is
reconsidered in the non-isothermal case aiming for thermodynamically consistent
models. The non-isothermal model is then investigated analytically. A fairly
complete dynamic theory is developed by analyzing these systems as quasilinear
parabolic evolution equations in an -setting. First, the existence of
a unique, local strong solution is proved. It is then shown that this solution
extends to a global strong solution provided the initial data are close to an
equilibrium or the solution is eventually bounded in the natural norm of the
underlying state space. In these cases, the solution converges exponentially to
an equilibrium in the natural state manifold
K to pi and K to 0 in 2+1 Flavor Partially Quenched Chiral Perturbation Theory
We calculate results for K to pi and K to 0 matrix elements to
next-to-leading order in 2+1 flavor partially quenched chiral perturbation
theory. Results are presented for both the Delta I=1/2 and 3/2 channels, for
chiral operators corresponding to current-current, gluonic penguin, and
electroweak penguin 4-quark operators. These formulas are useful for studying
the chiral behavior of currently available 2+1 flavor lattice QCD results, from
which the low energy constants of the chiral effective theory can be
determined. The low energy constants of these matrix elements are necessary for
an understanding of the Delta I=1/2 rule, and for calculations of
epsilon'/epsilon using current lattice QCD simulations.Comment: 43 pages, 2 figures, uses RevTeX, added and updated reference
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