1,817 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
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
Lubricated friction between incommensurate substrates
This paper is part of a study of the frictional dynamics of a confined solid
lubricant film - modelled as a one-dimensional chain of interacting particles
confined between two ideally incommensurate substrates, one of which is driven
relative to the other through an attached spring moving at constant velocity.
This model system is characterized by three inherent length scales; depending
on the precise choice of incommensurability among them it displays a strikingly
different tribological behavior. Contrary to two length-scale systems such as
the standard Frenkel-Kontorova (FK) model, for large chain stiffness one finds
that here the most favorable (lowest friction) sliding regime is achieved by
chain-substrate incommensurabilities belonging to the class of non-quadratic
irrational numbers (e.g., the spiral mean). The well-known golden mean
(quadratic) incommensurability which slides best in the standard FK model shows
instead higher kinetic-friction values. The underlying reason lies in the
pinning properties of the lattice of solitons formed by the chain with the
substrate having the closest periodicity, with the other slider.Comment: 14 pagine latex - elsart, including 4 figures, submitted to Tribology
Internationa
Oscillatory Instabilities of Standing Waves in One-Dimensional Nonlinear Lattices
In one-dimensional anharmonic lattices, we construct nonlinear standing waves
(SWs) reducing to harmonic SWs at small amplitude. For SWs with spatial
periodicity incommensurate with the lattice period, a transition by breaking of
analyticity versus wave amplitude is observed. As a consequence of the
discreteness, oscillatory linear instabilities, persisting for arbitrarily
small amplitude in infinite lattices, appear for all wave numbers Q not equal
to zero or \pi. Incommensurate analytic SWs with |Q|>\pi/2 may however appear
as 'quasi-stable', as their instability growth rate is of higher order.Comment: 4 pages, 6 figures, to appear in Phys. Rev. Let
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.
Phases of Josephson Junction Ladders
We study a Josephson junction ladder in a magnetic field in the absence of
charging effects via a transfer matrix formalism. The eigenvalues of the
transfer matrix are found numerically, giving a determination of the different
phases of the ladder. The spatial periodicity of the ground state exhibits a
devil's staircase as a function of the magnetic flux filling factor . If the
transverse Josephson coupling is varied a continuous superconducting-normal
transition in the transverse direction is observed, analogous to the breakdown
of the KAM trajectories in dynamical systems.Comment: 12 pages with 3 figures, REVTE
Controlled engineering of extended states in disordered systems
We describe how to engineer wavefunction delocalization in disordered systems
modelled by tight-binding Hamiltonians in d>1 dimensions. We show analytically
that a simple product structure for the random onsite potential energies,
together with suitably chosen hopping strengths, allows a resonant scattering
process leading to ballistic transport along one direction, and a controlled
coexistence of extended Bloch states and anisotropically localized states in
the spectrum. We demonstrate that these features persist in the thermodynamic
limit for a continuous range of the system parameters. Numerical results
support these findings and highlight the robustness of the extended regime with
respect to deviations from the exact resonance condition for finite systems.
The localization and transport properties of the system can be engineered
almost at will and independently in each direction. This study gives rise to
the possibility of designing disordered potentials that work as switching
devices and band-pass filters for quantum waves, such as matter waves in
optical lattices.Comment: 14 pages, 11 figure
Surface spin-flop and discommensuration transitions in antiferromagnets
Phase diagrams as a function of anisotropy and magnetic field are
obtained for discommensurations and surface states for an antiferromagnet in
which is parallel to the easy axis, by modeling it using the ground states
of a one-dimensional chain of classical XY spins. A surface spin-flop phase
exists for all , but the interval in over which it is stable becomes
extremely small as goes to zero. First-order transitions, separating
different surface states and ending in critical points, exist inside the
surface spin-flop region. They accumulate at a field (depending on )
significantly less than the value for a bulk spin-flop transition. For
there is no surface spin-flop phase in the strict sense;
instead, the surface restructures by, in effect, producing a discommensuration
infinitely far away in the bulk. The results are used to explain in detail the
phase transitions occurring in systems consisting of a finite, even number of
layers.Comment: Revtex 17 pages, 15 figure
- …