2,713 research outputs found
A low dimensional dynamical system for the wall layer
Low dimensional dynamical systems which model a fully developed turbulent wall layer were derived.The model is based on the optimally fast convergent proper orthogonal decomposition, or Karhunen-Loeve expansion. This decomposition provides a set of eigenfunctions which are derived from the autocorrelation tensor at zero time lag. Via Galerkin projection, low dimensional sets of ordinary differential equations in time, for the coefficients of the expansion, were derived from the Navier-Stokes equations. The energy loss to the unresolved modes was modeled by an eddy viscosity representation, analogous to Heisenberg's spectral model. A set of eigenfunctions and eigenvalues were obtained from direct numerical simulation of a plane channel at a Reynolds number of 6600, based on the mean centerline velocity and the channel width flow and compared with previous work done by Herzog. Using the new eigenvalues and eigenfunctions, a new ten dimensional set of ordinary differential equations were derived using five non-zero cross-stream Fourier modes with a periodic length of 377 wall units. The dynamical system was integrated for a range of the eddy viscosity prameter alpha. This work is encouraging
Aubry transition studied by direct evaluation of the modulation functions of infinite incommensurate systems
Incommensurate structures can be described by the Frenkel Kontorova model.
Aubry has shown that, at a critical value K_c of the coupling of the harmonic
chain to an incommensurate periodic potential, the system displays the
analyticity breaking transition between a sliding and pinned state. The ground
state equations coincide with the standard map in non-linear dynamics, with
smooth or chaotic orbits below and above K_c respectively. For the standard
map, Greene and MacKay have calculated the value K_c=.971635. Conversely,
evaluations based on the analyticity breaking of the modulation function have
been performed for high commensurate approximants. Here we show how the
modulation function of the infinite system can be calculated without using
approximants but by Taylor expansions of increasing order. This approach leads
to a value K_c'=.97978, implying the existence of a golden invariant circle up
to K_c' > K_c.Comment: 7 pages, 5 figures, file 'epl.cls' necessary for compilation
provided; Revised version, accepted for publication in Europhysics Letter
Magnetotail changes in relation to the solar wind magnetic field and magnetospheric substorms
An attempt is made to understand some of the magnetotail dynamics by using simultaneous observations from several satellites: Explorers 33 and 35 in the solar wind, IMP 4 in the near magnetotail (30 RE), ATS 1, and OGO 5 in the magnetosphere. It was observed that in the main lobes of the tail the magnetic field increases slowly when the interplanetary magnetic field turns southward, and can decrease slowly after a substorm. The plasma sheet changes indicate a thinning when the interplanetary magnetic field turns southward and an expansion when it turns northward. When combined with the plasma sheet expansion, which has been observed to follow a substorm, these results allow a schematic view of the relations between the changes in the orientation of the solar wind magnetic field, the substorms, and the changes in the tail parameters to be developed
The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results
The problem of finding the exact energies and configurations for the
Frenkel-Kontorova model consisting of particles in one dimension connected to
their nearest-neighbors by springs and placed in a periodic potential
consisting of segments from parabolas of identical (positive) curvature but
arbitrary height and spacing, is reduced to that of minimizing a certain convex
function defined on a finite simplex.Comment: 12 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 6
Postscript figures, accepted by Phys. Rev.
Renormalization and Quantum Scaling of Frenkel-Kontorova Models
We generalise the classical Transition by Breaking of Analyticity for the
class of Frenkel-Kontorova models studied by Aubry and others to non-zero
Planck's constant and temperature. This analysis is based on the study of a
renormalization operator for the case of irrational mean spacing using
Feynman's functional integral approach. We show how existing classical results
extend to the quantum regime. In particular we extend MacKay's renormalization
approach for the classical statistical mechanics to deduce scaling of low
frequency effects and quantum effects. Our approach extends the phenomenon of
hierarchical melting studied by Vallet, Schilling and Aubry to the quantum
regime.Comment: 14 pages, 1 figure, submitted to J.Stat.Phy
Mode solutions for a Klein-Gordon field in anti-de Sitter spacetime with dynamical boundary conditions of Wentzell type
We study a real, massive Klein-Gordon field in the Poincar\'e fundamental
domain of the -dimensional anti-de Sitter (AdS) spacetime, subject to a
particular choice of dynamical boundary conditions of generalized Wentzell
type, whereby the boundary data solves a non-homogeneous, boundary Klein-Gordon
equation, with the source term fixed by the normal derivative of the scalar
field at the boundary. This naturally defines a field in the conformal boundary
of the Poincar\'e fundamental domain of AdS. We completely solve the equations
for the bulk and boundary fields and investigate the existence of bound state
solutions, motivated by the analogous problem with Robin boundary conditions,
which are recovered as a limiting case. Finally, we argue that both Robin and
generalized Wentzell boundary conditions are distinguished in the sense that
they are invariant under the action of the isometry group of the AdS conformal
boundary, a condition which ensures in addition that the total flux of energy
across the boundary vanishes.Comment: 12 pages, 1 figure. In V3: refs. added, introduction and conclusions
expande
Controlling Mixing Inside a Droplet by Time Dependent Rigid-body Rotation
The use of microscopic discrete fluid volumes (i.e., droplets) as
microreactors for digital microfluidic applications often requires mixing
enhancement and control within droplets. In this work, we consider a
translating spherical liquid droplet to which we impose a time periodic
rigid-body rotation which we model using the superposition of a Hill vortex and
an unsteady rigid body rotation. This perturbation in the form of a rotation
not only creates a three-dimensional chaotic mixing region, which operates
through the stretching and folding of material lines, but also offers the
possibility of controlling both the size and the location of the mixing. Such a
control is achieved by judiciously adjusting the three parameters that
characterize the rotation, i.e., the rotation amplitude, frequency and
orientation of the rotation. As the size of the mixing region is increased,
complete mixing within the drop is obtained.Comment: 6 pages, 6 figure
Employers and Employees: A Call for Oklahoma\u27s Adoption of the Whistle-Blower Exception to the Employment-at-Will Doctrine
Discrete Nonlinear Schr{\"o}dinger Breathers in a Phonon Bath
We study the dynamics of the discrete nonlinear Schr{\"o}dinger lattice
initialized such that a very long transitory period of time in which standard
Boltzmann statistics is insufficient is reached. Our study of the nonlinear
system locked in this {\em non-Gibbsian} state focuses on the dynamics of
discrete breathers (also called intrinsic localized modes). It is found that
part of the energy spontaneously condenses into several discrete breathers.
Although these discrete breathers are extremely long lived, their total number
is found to decrease as the evolution progresses. Even though the total number
of discrete breathers decreases we report the surprising observation that the
energy content in the discrete breather population increases. We interpret
these observations in the perspective of discrete breather creation and
annihilation and find that the death of a discrete breather cause effective
energy transfer to a spatially nearby discrete breather. It is found that the
concepts of a multi-frequency discrete breather and of internal modes is
crucial for this process. Finally, we find that the existence of a discrete
breather tends to soften the lattice in its immediate neighborhood, resulting
in high amplitude thermal fluctuation close to an existing discrete breather.
This in turn nucleates discrete breather creation close to a already existing
discrete breather
An analytical law for size effects on thermal conductivity of nanostructures
The thermal conductivity of a nanostructure is sensitive to its dimensions. A
simple analytical scaling law that predicts how conductivity changes with the
dimensions of the structure, however, has not been developed. The lack of such
a law is a hurdle in "phonon engineering" of many important applications. Here,
we report an analytical scaling law for thermal conductivity of nanostructures
as a function of their dimensions. We have verified the law using very large
molecular dynamics simulations
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