3,789 research outputs found
Thermal fluctuations and boundary conditions in the lattice Boltzmann method
The lattice Boltzmann method is a popular approach for simulating hydrodynamic interactions in soft matter and complex fluids. The solvent is represented on a discrete lattice whose nodes are populated by particle distributions that propagate on the discrete links between the nodes and undergo local collisions. On large length and time scales, the microdynamics leads to a hydrodynamic flow field that satisfies the Navier-Stokes equation. In this thesis, several extensions to the lattice Boltzmann method are developed. In complex fluids, for example suspensions, Brownian motion of the solutes is of paramount importance. However, it can not be simulated with the original lattice Boltzmann method because the dynamics is completely deterministic. It is possible, though, to introduce thermal fluctuations in order to reproduce the equations of fluctuating hydrodynamics. In this work, a generalized lattice gas model is used to systematically derive the fluctuating lattice Boltzmann equation from statistical mechanics principles. The stochastic part of the dynamics is interpreted as a Monte Carlo process, which is then required to satisfy the condition of detailed balance. This leads to an expression for the thermal fluctuations which implies that it is essential to thermalize all degrees of freedom of the system, including the kinetic modes. The new formalism guarantees that the fluctuating lattice Boltzmann equation is simultaneously consistent with both fluctuating hydrodynamics and statistical mechanics. This establishes a foundation for future extensions, such as the treatment of multi-phase and thermal flows. An important range of applications for the lattice Boltzmann method is formed by microfluidics. Fostered by the “lab-on-a-chip” paradigm, there is an increasing need for computer simulations which are able to complement the achievements of theory and experiment. Microfluidic systems are characterized by a large surface-to-volume ratio and, therefore, boundary conditions are of special relevance. On the microscale, the standard no-slip boundary condition used in hydrodynamics has to be replaced by a slip boundary condition. In this work, a boundary condition for lattice Boltzmann is constructed that allows the slip length to be tuned by a single model parameter. Furthermore, a conceptually new approach for constructing boundary conditions is explored, where the reduced symmetry at the boundary is explicitly incorporated into the lattice model. The lattice Boltzmann method is systematically extended to the reduced symmetry model. In the case of a Poiseuille flow in a plane channel, it is shown that a special choice of the collision operator is required to reproduce the correct flow profile. This systematic approach sheds light on the consequences of the reduced symmetry at the boundary and leads to a deeper understanding of boundary conditions in the lattice Boltzmann method. This can help to develop improved boundary conditions that lead to more accurate simulation results
Ellipsoidal Coulomb Crystals in a Linear Radiofrequency Trap
A static quadrupole potential breaks the cylindrical symmetry of the
effective potential of a linear rf trap. For a one-component fluid plasma at
low temperature, the resulting equilibrium charge distribution is predicted to
be an ellipsoid. We have produced laser-cooled Be ellipsoidal ion crystals
and found good agreement between their shapes and the cold fluid prediction. In
two-species mixtures, containing Be and sympathetically cooled ions of
lower mass, a sufficiently strong static quadrupole potential produces a
spatial separation of the species.Comment: 4 pages, 3 figure
Precision spectroscopy of the molecular ion HD+: control of Zeeman shifts
Precision spectroscopy on cold molecules can potentially enable novel tests
of fundamental laws of physics and alternative determination of some
fundamental constants. Realizing this potential requires a thorough
understanding of the systematic effects that shift the energy levels of
molecules. We have performed a complete ab initio calculation of the magnetic
field effects for a particular system, the heteronuclear molecular hydrogen ion
HD+. Different spectroscopic schemes have been considered, and numerous
transitions, all accessible by modern radiation sources and exhibiting well
controllable or negligible Zeeman shift, have been found to exist. Thus, HD+ is
a perspective candidate for determination of the ratio of electron-to-nuclear
reduced mass, and for tests of its time-independence.Comment: A Table added, references and figures update
Sympathetic cooling of He ions in a radiofrequency trap
We have generated Coulomb crystals of ultracold He ions in a linear
radiofrequency trap, by sympathetic cooling via laser--cooled Be.
Stable crystals containing up to 150 localized He ions at 20 mK were
obtained. Ensembles or single ultracold He ions open up interesting
perspectives for performing precision tests of QED and measurements of nuclear
radii. The present work also indicates the feasibility of cooling and
crystallizing highly charged atomic ions using Be as coolant.Comment: 4 pages, 2 figure
Reply on the ``Comment on `Loss-error compensation in quantum- state measurements' ''
The authors of the Comment [G. M. D'Ariano and C. Macchiavello to be
published in Phys. Rev. A, quant-ph/9701009] tried to reestablish a 0.5
efficiency bound for loss compensation in optical homodyne tomography. In our
reply we demonstrate that neither does such a rigorous bound exist nor is the
bound required for ruling out the state reconstruction of an individual system
[G. M. D'Ariano and H. P. Yuen, Phys. Rev. Lett. 76, 2832 (1996)].Comment: LaTex, 2 pages, 1 Figure; to be published in Physical Review
Observation of twin beam correlations and quadrature entanglement by frequency doubling in a two-port resonator
We demonstrate production of quantum correlated and entangled beams by second
harmonic generation in a nonlinear resonator with two output ports. The output
beams at wavelength 428.5 nm exhibit 0.9 dB of nonclassical intensity
correlations and 0.3 dB of entanglement.Comment: 5 pages, 7 figure
Demonstration of a Transportable 1 Hz-Linewidth Laser
We present the setup and test of a transportable clock laser at 698 nm for a
strontium lattice clock. A master-slave diode laser system is stabilized to a
rigidly mounted optical reference cavity. The setup was transported by truck
over 400 km from Braunschweig to D\"usseldorf, where the cavity-stabilized
laser was compared to a stationary clock laser for the interrogation of
ytterbium (578 nm). Only minor realignments were necessary after the transport.
The lasers were compared by a Ti:Sapphire frequency comb used as a transfer
oscillator. The thus generated virtual beat showed a combined linewidth below 1
Hz (at 1156 nm). The transport back to Braunschweig did not degrade the laser
performance, as was shown by interrogating the strontium clock transition.Comment: 3 pages, 4 figure
The electric dipole moment of the neutron from 2+1 flavor lattice QCD
We compute the electric dipole moment d_n of the neutron from a fully
dynamical simulation of lattice QCD with 2+1 flavors of clover fermions and
nonvanishing theta term. The latter is rotated into the pseudoscalar density in
the fermionic action using the axial anomaly. To make the action real, the
vacuum angle theta is taken to be purely imaginary. The physical value of d_n
is obtained by analytic continuation. We find d_n = -3.8(2)(9) x 10^{-16}
[theta e cm], which, when combined with the experimental limit on d_n, leads to
the upper bound theta < 7.6 x 10^{-11}.Comment: 12 pages, 8 figures, matches PRL published versio
Implementation of on-site velocity boundary conditions for D3Q19 lattice Boltzmann
On-site boundary conditions are often desired for lattice Boltzmann
simulations of fluid flow in complex geometries such as porous media or
microfluidic devices. The possibility to specify the exact position of the
boundary, independent of other simulation parameters, simplifies the analysis
of the system. For practical applications it should allow to freely specify the
direction of the flux, and it should be straight forward to implement in three
dimensions. Furthermore, especially for parallelized solvers it is of great
advantage if the boundary condition can be applied locally, involving only
information available on the current lattice site. We meet this need by
describing in detail how to transfer the approach suggested by Zou and He to a
D3Q19 lattice. The boundary condition acts locally, is independent of the
details of the relaxation process during collision and contains no artificial
slip. In particular, the case of an on-site no-slip boundary condition is
naturally included. We test the boundary condition in several setups and
confirm that it is capable to accurately model the velocity field up to second
order and does not contain any numerical slip.Comment: 13 pages, 4 figures, revised versio
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