948 research outputs found
The intermittent behavior and hierarchical clustering of the cosmic mass field
The hierarchical clustering model of the cosmic mass field is examined in the
context of intermittency. We show that the mass field satisfying the
correlation hierarchy is intermittent if , where is the dimension of the field, and is the power-law
index of the non-linear power spectrum in the discrete wavelet transform (DWT)
representation. We also find that a field with singular clustering can be
described by hierarchical clustering models with scale-dependent coefficients
and that this scale-dependence is completely determined by the
intermittent exponent and . Moreover, the singular exponents of a field
can be calculated by the asymptotic behavior of when is large.
Applying this result to the transmitted flux of HS1700 Ly forests, we
find that the underlying mass field of the Ly forests is significantly
intermittent. On physical scales less than about 2.0 h Mpc, the observed
intermittent behavior is qualitatively different from the prediction of the
hierarchical clustering with constant . The observations, however, do show
the existence of an asymptotic value for the singular exponents. Therefore, the
mass field can be described by the hierarchical clustering model with
scale-dependent . The singular exponent indicates that the cosmic mass
field at redshift is weakly singular at least on physical scales as
small as 10 h kpc.Comment: AAS Latex file, 33 pages,5 figures included, accepted for publication
in Ap
Exact Results for Hamiltonian Walks from the Solution of the Fully Packed Loop Model on the Honeycomb Lattice
We derive the nested Bethe Ansatz solution of the fully packed O() loop
model on the honeycomb lattice. From this solution we derive the bulk free
energy per site along with the central charge and geometric scaling dimensions
describing the critical behaviour. In the limit we obtain the exact
compact exponents and for Hamiltonian walks, along with
the exact value for the connective constant
(entropy). Although having sets of scaling dimensions in common, our results
indicate that Hamiltonian walks on the honeycomb and Manhattan lattices lie in
different universality classes.Comment: 12 pages, RevTeX, 3 figures supplied on request, ANU preprint
MRR-050-9
A note on graded Yang-Baxter solutions as braid-monoid invariants
We construct two solutions of the graded Yang-Baxter equation by
using the algebraic braid-monoid approach. The factorizable S-matrix
interpretation of these solutions is also discussed.Comment: 7 pages, UFSCARF-TH-94-1
Thermal and magnetic properties of integrable spin-1 and spin-3/2 chains with applications to real compounds
The ground state and thermodynamic properties of spin-1 and spin-3/2 chains
are investigated via exactly solved su(3) and su(4) models with physically
motivated chemical potential terms. The analysis involves the Thermodynamic
Bethe Ansatz and the High Temperature Expansion (HTE) methods. For the spin-1
chain with large single-ion anisotropy, a gapped phase occurs which is
significantly different from the valence-bond-solid Haldane phase. The
theoretical curves for the magnetization, susceptibility and specific heat are
favourably compared with experimental data for a number of spin-1 chain
compounds. For the spin-3/2 chain a degenerate gapped phase exists starting at
zero external magnetic field. A middle magnetization plateau can be triggered
by the single-ion anisotropy term. Overall, our results lend further weight to
the applicability of integrable models to the physics of low-dimensional
quantum spin systems. They also highlight the utility of the exact HTE method.Comment: 38 pages, 15 figure
Magnus and Iordanskii Forces in Superfluids
The total transverse force acting on a quantized vortex in a superfluid is a
problem that has eluded a complete understanding for more than three decades.
In this letter I propose a remarkably simple argument, somewhat reminiscent of
Laughlin's beautiful argument for the quantization of conductance in the
quantum Hall effect, to define the superfluid velocity part of the transverse
force. This term is found to be . Although
this result does not seem to be overly controversial, this thermodynamic
argument based only on macroscopic properties of the superfluid does offer a
robust derivation. A recent publication by Thouless, Ao and Niu has
demonstrated that the vortex velocity part of the transverse force in a
homogeneous neutral superfluid is given by the usual form . A combination of these two independent results and the required
Galilean invariance yields that there cannot be any transverse force
proportional to the normal fluid velocity, in apparent conflict with
Iordanskii's theory of the transverse force due to phonon scattering by the
vortex.Comment: RevTex, 1 Encapsulated Postscript figur
The Distribution of H2O Maser Emission in the Nucleus of NGC 4945
We present the first interferometer map of the water maser emission in the
active nucleus of NGC 4945. Although the declination of the galaxy is about -49
degrees, we were able to make the observations with the southernmost antennas
of the Very Long Baseline Array. Strong maser emission is present in three
velocity ranges, one near the systemic velocity and two shifted roughly
symmetrically by +/-(100-150) km/s. This is the first detection of highly
blue-shifted water emission in NGC 4945. We determined the position of the
maser to be RA(B1950)= 13 02 32.28 +/- 0.02 ; Dec(B1950)= -49 12 01.9 +/- 0.1.
The uncertainties in earlier estimates are at least several arcseconds. The
maser lies within 2'' (36 pc at a distance of 3.7 Mpc) of the peaks in 1.4 GHz
continuum and 1.6 micron emission from the nucleus. The mappable maser emission
is distributed roughly linearly over about 40 milliarcseconds (0.7 pc) at a
position angle of about 45 degrees, which is close to the 43 +/- 2 degree
position angle of the galactic disk. The red and blue-shifted emission
symmetrically stradle the systemic emission on the sky, which suggests material
in edge-on circular motion around a central object. The position-velocity
structure indicates a binding mass of about one million Suns, within a volume
of radius about 0.3 pc. This implies that the central engine radiates on the
order of 10% of its Eddington luminosity.Comment: 18 pages, including 5 Postscript figures. Accepted for publication in
ApJ Letter
One-Dimensional Impenetrable Anyons in Thermal Equilibrium. II. Determinant Representation for the Dynamic Correlation Functions
We have obtained a determinant representation for the time- and
temperature-dependent field-field correlation function of the impenetrable
Lieb-Liniger gas of anyons through direct summation of the form factors. In the
static case, the obtained results are shown to be equivalent to those that
follow from the anyonic generalization of Lenard's formula.Comment: 16 pages, RevTeX
Thermodynamics, spin-charge separation and correlation functions of spin-1/2 fermions with repulsive interaction
We investigate the low temperature thermodynamics and correlation functions
of one-dimensional spin-1/2 fermions with strong repulsion in an external
magnetic field via the thermodynamic Bethe ansatz method. The exact
thermodynamics of the model in a weak magnetic field is derived with the help
of Wiener-Hopf techniques. It turns out that the low energy physics can be
described by spin-charge separated conformal field theories of an effective
Tomonaga-Luttinger liquid and an antiferromagnetic SU(2) Heisenberg spin chain.
However, these two types of conformally invariant low-lying excitations may
break down as excitations take place far away from the Fermi points. The long
distance asymptotics of the correlation functions and the critical exponents
for the model in the presence of a magnetic field at zero temperature are
derived in detail by solving dressed charge equations and by conformal mapping.
Furthermore, we calculate the conformal dimensions for particular cases of
correlation functions. The leading terms of these correlation functions are
given explicitly for a weak magnetic field and for a magnetic field
close to the critical field . Our analytical results
provide insights into universal thermodynamics and criticality in
one-dimensional many-body physics.Comment: revised version, 47 pages, 4 figures, additional tex
Magnetic Field Amplification by Small-Scale Dynamo Action: Dependence on Turbulence Models and Reynolds and Prandtl Numbers
The small-scale dynamo is a process by which turbulent kinetic energy is
converted into magnetic energy, and thus is expected to depend crucially on the
nature of turbulence. In this work, we present a model for the small-scale
dynamo that takes into account the slope of the turbulent velocity spectrum
v(l) ~ l^theta, where l and v(l) are the size of a turbulent fluctuation and
the typical velocity on that scale. The time evolution of the fluctuation
component of the magnetic field, i.e., the small-scale field, is described by
the Kazantsev equation. We solve this linear differential equation for its
eigenvalues with the quantum-mechanical WKB-approximation. The validity of this
method is estimated as a function of the magnetic Prandtl number Pm. We
calculate the minimal magnetic Reynolds number for dynamo action, Rm_crit,
using our model of the turbulent velocity correlation function. For Kolmogorov
turbulence (theta=1/3), we find that the critical magnetic Reynolds number is
approximately 110 and for Burgers turbulence (theta=1/2) approximately 2700.
Furthermore, we derive that the growth rate of the small-scale magnetic field
for a general type of turbulence is Gamma ~ Re^((1-theta)/(1+theta)) in the
limit of infinite magnetic Prandtl numbers. For decreasing magnetic Prandtl
number (down to Pm approximately larger than 10), the growth rate of the
small-scale dynamo decreases. The details of this drop depend on the
WKB-approximation, which becomes invalid for a magnetic Prandtl number of about
unity.Comment: 13 pages, 8 figures; published in Phys. Rev. E 201
Tangling clustering of inertial particles in stably stratified turbulence
We have predicted theoretically and detected in laboratory experiments a new
type of particle clustering (tangling clustering of inertial particles) in a
stably stratified turbulence with imposed mean vertical temperature gradient.
In this stratified turbulence a spatial distribution of the mean particle
number density is nonuniform due to the phenomenon of turbulent thermal
diffusion, that results in formation of a gradient of the mean particle number
density, \nabla N, and generation of fluctuations of the particle number
density by tangling of the gradient, \nabla N, by velocity fluctuations. The
mean temperature gradient, \nabla T, produces the temperature fluctuations by
tangling of the gradient, \nabla T, by velocity fluctuations. These
fluctuations increase the rate of formation of the particle clusters in small
scales. In the laboratory stratified turbulence this tangling clustering is
much more effective than a pure inertial clustering that has been observed in
isothermal turbulence. In particular, in our experiments in oscillating grid
isothermal turbulence in air without imposed mean temperature gradient, the
inertial clustering is very weak for solid particles with the diameter 10
microns and Reynolds numbers Re =250. Our theoretical predictions are in a good
agreement with the obtained experimental results.Comment: 16 pages, 4 figures, REVTEX4, revised versio
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