2,990 research outputs found
Parametric forcing approach to rough-wall turbulent channel flow
The effects of rough surfaces on turbulent channel flow are modelled by an extra force term in the Navier–Stokes equations. This force term contains two parameters, related to the density and the height of the roughness elements, and a shape function, which regulates the influence of the force term with respect to the distance from the channel wall. This permits a more flexible specification of a rough surface than a single parameter such as the equivalent sand grain roughness. The effects of the roughness force term on turbulent channel flow have been investigated for a large number of parameter combinations and several shape functions by direct numerical simulations. It is possible to cover the full spectrum of rough flows ranging from hydraulically smooth through transitionally rough to fully rough cases. By using different parameter combinations and shape functions, it is possible to match the effects of different types of rough surfaces. Mean flow and standard turbulence statistics have been used to compare the results to recent experimental and numerical studies and a good qualitative agreement has been found. Outer scaling is preserved for the streamwise velocity for both the mean profile as well as its mean square fluctuations in all but extremely rough cases. The structure of the turbulent flow shows a trend towards more isotropic turbulent states within the roughness layer. In extremely rough cases, spanwise structures emerge near the wall and the turbulent state resembles a mixing layer. A direct comparison with the study of Ashrafian, Andersson & Manhart (Intl J. Heat Fluid Flow, vol. 25, 2004, pp. 373–383) shows a good quantitative agreement of the mean flow and Reynolds stresses everywhere except in the immediate vicinity of the rough wall. The proposed roughness force term may be of benefit as a wall model for direct and large-eddy numerical simulations in cases where the exact details of the flow over a rough wall can be neglecte
The 1D interacting Bose gas in a hard wall box
We consider the integrable one-dimensional delta-function interacting Bose
gas in a hard wall box which is exactly solved via the coordinate Bethe Ansatz.
The ground state energy, including the surface energy, is derived from the
Lieb-Liniger type integral equations. The leading and correction terms are
obtained in the weak coupling and strong coupling regimes from both the
discrete Bethe equations and the integral equations. This allows the
investigation of both finite-size and boundary effects in the integrable model.
We also study the Luttinger liquid behaviour by calculating Luttinger
parameters and correlations. The hard wall boundary conditions are seen to have
a strong effect on the ground state energy and phase correlations in the weak
coupling regime. Enhancement of the local two-body correlations is shown by
application of the Hellmann-Feynman theorem.Comment: 23 pages, 7 figures. Improved version. Extra figure added for the
weak coupling regime. New expression for the interaction-dependent cloud size
and additional reference
Collective dispersion relations for the 1D interacting two-component Bose and Fermi gases
We investigate the elementary excitations of charge and spin degrees for the
1D interacting two-component Bose and Fermi gases by means of the discrete
Bethe ansatz equations. Analytic results in the limiting cases of strong and
weak interactions are derived, where the Bosons are treated in the repulsive
and the fermions in the strongly attractive regime. We confirm and complement
results obtained previously from the Bethe ansatz equations in the
thermodynamic limit.Comment: 12 pages, 1 figur
Evolving turbulence and magnetic fields in galaxy clusters
We discuss, using simple analytical models and MHD simulations, the origin
and parameters of turbulence and magnetic fields in galaxy clusters. Three
physically distinct regimes can be identified in the evolution of cluster
turbulence and magnetic fields. Firstly, the fluctuation dynamo will produce
microgauss-strong, random magnetic fields during cluster formation and major
mergers. Turbulent velocity of about 300 km/s can be maintained at scales
100-200 kpc. The magnetic field is intermittent, has a smaller scale of 20-30
kpc and average strength of 2 microgauss. Secondly, when major mergers end,
turbulent speed and magnetic field undergo a power-law decay, decreasing in
strength but increasing in scale by a factor of about two. Thirdly,
smaller-mass subclusters and cluster galaxies produce turbulent wakes, with
turbulent speeds and magnetic field strengths similar to those quoted above.
The velocity scales are about 200 kpc and 10 kpc respectively, and the magnetic
field scale is about 6 times smaller. Although these wakes may fill only a
small fraction of the cluster volume, their area covering factor can be close
to unity. So one can potentially reconcile observations that indicate the
coexistence of turbulence with ordered filamentary gas structures, as in the
Perseus cluster. Random Faraday rotation measure is estimated to be typically
100-200 rad/m^2, in agreement with observations. We predict detectable
synchrotron polarization from cluster radio halos at wavelengths 3-6 cm, if
observed at sufficiently high resolution (abridged).Comment: 20 pages, 9 figures, Replaced to match version accepted by MNRA
Quantum phase diagram of an exactly solved mixed spin ladder
We investigate the quantum phase diagram of the exactly solved mixed
spin-(1/2,1) ladder via the thermodynamic Bethe ansatz (TBA). In the absence of
a magnetic field the model exhibits three quantum phases associated with su(2),
su(4) and su(6) symmetries. In the presence of a strong magnetic field, there
is a third and full saturation magnetization plateaux within the strong
antiferromagnetic rung coupling regime. Gapless and gapped phases appear in
turn as the magnetic field increases. For weak rung coupling, the fractional
magnetization plateau vanishs and exhibits new quantum phase transitions.
However, in the ferromagnetic coupling regime, the system does not have a third
saturation magnetization plat eau. The critical behaviour in the vicinity of
the critical points is also derived systematically using the TBA.Comment: 20 pages, 2 figure
Random walks on finite lattice tubes
Exact results are obtained for random walks on finite lattice tubes with a
single source and absorbing lattice sites at the ends. Explicit formulae are
derived for the absorption probabilities at the ends and for the expectations
that a random walk will visit a particular lattice site before being absorbed.
Results are obtained for lattice tubes of arbitrary size and each of the
regular lattice types; square, triangular and honeycomb. The results include an
adjustable parameter to model the effects of strain, such as surface curvature,
on the surface diffusion. Results for the triangular lattice tubes and the
honeycomb lattice tubes model diffusion of adatoms on single walled zig-zag
carbon nano-tubes with open ends.Comment: 22 pages, 4 figure
Exactly solvable quantum spin ladders associated with the orthogonal and symplectic Lie algebras
We extend the results of spin ladder models associated with the Lie algebras
to the case of the orthogonal and symplectic algebras $o(2^n),\
sp(2^n)$ where n is the number of legs for the system. Two classes of models
are found whose symmetry, either orthogonal or symplectic, has an explicit n
dependence. Integrability of these models is shown for an arbitrary coupling of
XX type rung interactions and applied magnetic field term.Comment: 7 pages, Late
On the von Karman-Howarth equations for Hall MHD flows
The von Karman-Howarth equations are derived for three-dimensional (3D) Hall
magnetohydrodynamics (MHD) in the case of an homogeneous and isotropic
turbulence. From these equations, we derive exact scaling laws for the
third-order correlation tensors. We show how these relations are compatible
with previous heuristic and numerical results. These multi-scale laws provide a
relevant tool to investigate the non-linear nature of the high frequency
magnetic field fluctuations in the solar wind or, more generally, in any plasma
where the Hall effect is important.Comment: 11 page
Exactly solvable models and ultracold Fermi gases
Exactly solvable models of ultracold Fermi gases are reviewed via their
thermodynamic Bethe Ansatz solution. Analytical and numerical results are
obtained for the thermodynamics and ground state properties of two- and
three-component one-dimensional attractive fermions with population imbalance.
New results for the universal finite temperature corrections are given for the
two-component model. For the three-component model, numerical solution of the
dressed energy equations confirm that the analytical expressions for the
critical fields and the resulting phase diagrams at zero temperature are highly
accurate in the strong coupling regime. The results provide a precise
description of the quantum phases and universal thermodynamics which are
applicable to experiments with cold fermionic atoms confined to one-dimensional
tubes.Comment: based on an invited talk at Statphys24, Cairns (Australia) 2010. 16
pages, 6 figure
Evidence for the super Tonks-Girardeau gas
We provide evidence in support of a recent proposal by Astrakharchik at al.
for the existence of a super Tonks-Girardeau gas-like state in the attractive
interaction regime of quasi-one-dimensional Bose gases. We show that the super
Tonks-Giradeau gas-like state corresponds to a highly-excited Bethe state in
the integrable interacting Bose gas for which the bosons acquire hard-core
behaviour. The gas-like state properties vary smoothly throughout a wide range
from strong repulsion to strong attraction. There is an additional stable
gas-like phase in this regime in which the bosons form two-body bound states
behaving like hard-core bosons.Comment: 10 pages, 1 figure, 2 tables, additional text on the stability of the
super T-G gas-like stat
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