393 research outputs found
The Square Root Depth Wave Equations
We introduce a set of coupled equations for multilayer water waves that
removes the ill-posedness of the multilayer Green-Naghdi (MGN) equations in the
presence of shear. The new well-posed equations are Hamiltonian and in the
absence of imposed background shear they retain the same travelling wave
solutions as MGN. We call the new model the Square Root Depth equations, from
the modified form of their kinetic energy of vertical motion. Our numerical
results show how the Square Root Depth equations model the effects of
multilayer wave propagation and interaction, with and without shear.Comment: 10 pages, 5 figure
An Euler Poincar\'e framework for the multilayer Green Nagdhi equations
The Green Nagdhi equations are frequently used as a model of the wave-like
behaviour of the free surface of a fluid, or the interface between two
homogeneous fluids of differing densities. Here we show that their multilayer
extension arises naturally from a framework based on the Euler Poincare theory
under an ansatz of columnar motion. The framework also extends to the
travelling wave solutions of the equations. We present numerical solutions of
the travelling wave problem in a number of flow regimes. We find that the free
surface and multilayer waves can exhibit intriguing differences compared to the
results of single layer or rigid lid models
Hydro-morphodynamics 2D modelling using a discontinuous Galerkin discretisation
The development of morphodynamic models to simulate sediment transport accurately is a challenging process that is becoming ever more important because of our increasing exploitation of the coastal zone, as well as sea-level rise and the potential increase in strength and frequency of storms due to a changing climate. Morphodynamic models are highly complex given the non-linear and coupled nature of the sediment transport problem. Here we implement a new depth-averaged coupled hydrodynamic and sediment transport model within the coastal ocean model Thetis, built using the code generating framework Firedrake which facilitates code flexibility and optimisation benefits. To the best of our knowledge, this represents the first full morphodynamic model including both bedload and suspended sediment transport which uses a discontinuous Galerkin based finite element discretisation. We implement new functionalities within Thetis extending its existing capacity to model scalar transport to modelling suspended sediment transport, incorporating within Thetis options to model bedload transport and bedlevel changes. We apply our model to problems with non-cohesive sediment and account for effects of gravity and helical flow by adding slope gradient terms and parametrising secondary currents. For validation purposes and in demonstrating model capability, we present results from test cases of a migrating trench and a meandering channel comparing against experimental data and the widely-used model Telemac-Mascaret
Type Ia supernova parameter estimation: a comparison of two approaches using current datasets
By using the Sloan Digital Sky Survey (SDSS) first year type Ia supernova (SN
Ia) compilation, we compare two different approaches (traditional \chi^2 and
complete likelihood) to determine parameter constraints when the magnitude
dispersion is to be estimated as well. We consider cosmological constant + Cold
Dark Matter (\Lambda CDM) and spatially flat, constant w Dark Energy + Cold
Dark Matter (FwCDM) cosmological models and show that, for current data, there
is a small difference in the best fit values and 30% difference in
confidence contour areas in case the MLCS2k2 light-curve fitter is adopted. For
the SALT2 light-curve fitter the differences are less significant (
13% difference in areas). In both cases the likelihood approach gives more
restrictive constraints. We argue for the importance of using the complete
likelihood instead of the \chi^2 approach when dealing with parameters in the
expression for the variance.Comment: 16 pages, 5 figures. More complete analysis by including peculiar
velocities and correlations among SALT2 parameters. Use of 2D contours
instead of 1D intervals for comparison. There can be now a significant
difference between the approaches, around 30% in contour area for MLCS2k2 and
up to 13% for SALT2. Generic streamlining of text and suppression of section
on model selectio
Baryon Acoustic Oscillations in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample
The spectroscopic Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) galaxy
sample represents the final set of galaxies observed using the original SDSS
target selection criteria. We analyse the clustering of galaxies within this
sample, including both the Luminous Red Galaxy (LRG) and Main samples, and also
include the 2-degree Field Galaxy Redshift Survey (2dFGRS) data. Baryon
Acoustic Oscillations are observed in power spectra measured for different
slices in redshift; this allows us to constrain the distance--redshift relation
at multiple epochs. We achieve a distance measure at redshift z=0.275, of
r_s(z_d)/D_V(0.275)=0.1390+/-0.0037 (2.7% accuracy), where r_s(z_d) is the
comoving sound horizon at the baryon drag epoch,
D_V(z)=[(1+z)^2D_A^2cz/H(z)]^(1/3), D_A(z) is the angular diameter distance and
H(z) is the Hubble parameter. We find an almost independent constraint on the
ratio of distances D_V(0.35)/D_V(0.2)=1.736+/-0.065, which is consistent at the
1.1sigma level with the best fit Lambda-CDM model obtained when combining our
z=0.275 distance constraint with the WMAP 5-year data. The offset is similar to
that found in previous analyses of the SDSS DR5 sample, but the discrepancy is
now of lower significance, a change caused by a revised error analysis and a
change in the methodology adopted, as well as the addition of more data. Using
WMAP5 constraints on Omega_bh^2 and Omega_ch^2, and combining our BAO distance
measurements with those from the Union Supernova sample, places a tight
constraint on Omega_m=0.286+/-0.018 and H_0 = 68.2+/-2.2km/s/Mpc that is robust
to allowing curvature and non-Lambda dark energy. This result is independent of
the behaviour of dark energy at redshifts greater than those probed by the BAO
and supernova measurements. (abridged)Comment: 22 pages, 16 figures, minor changes to match version published in
MNRA
Cosmological Constraints from the Clustering of the Sloan Digital Sky Survey DR7 Luminous Red Galaxies
We present the power spectrum of the reconstructed halo density field derived
from a sample of Luminous Red Galaxies (LRGs) from the Sloan Digital Sky Survey
Seventh Data Release (DR7). The halo power spectrum has a direct connection to
the underlying dark matter power for k <= 0.2 h/Mpc, well into the quasi-linear
regime. This enables us to use a factor of ~8 more modes in the cosmological
analysis than an analysis with kmax = 0.1 h/Mpc, as was adopted in the SDSS
team analysis of the DR4 LRG sample (Tegmark et al. 2006). The observed halo
power spectrum for 0.02 < k < 0.2 h/Mpc is well-fit by our model: chi^2 = 39.6
for 40 degrees of freedom for the best fit LCDM model. We find \Omega_m h^2 *
(n_s/0.96)^0.13 = 0.141^{+0.009}_{-0.012} for a power law primordial power
spectrum with spectral index n_s and \Omega_b h^2 = 0.02265 fixed, consistent
with CMB measurements. The halo power spectrum also constrains the ratio of the
comoving sound horizon at the baryon-drag epoch to an effective distance to
z=0.35: r_s/D_V(0.35) = 0.1097^{+0.0039}_{-0.0042}. Combining the halo power
spectrum measurement with the WMAP 5 year results, for the flat LCDM model we
find \Omega_m = 0.289 +/- 0.019 and H_0 = 69.4 +/- 1.6 km/s/Mpc. Allowing for
massive neutrinos in LCDM, we find \sum m_{\nu} < 0.62 eV at the 95% confidence
level. If we instead consider the effective number of relativistic species Neff
as a free parameter, we find Neff = 4.8^{+1.8}_{-1.7}. Combining also with the
Kowalski et al. (2008) supernova sample, we find \Omega_{tot} = 1.011 +/- 0.009
and w = -0.99 +/- 0.11 for an open cosmology with constant dark energy equation
of state w.Comment: 26 pages, 19 figures, submitted to MNRAS. The power spectrum and a
module to calculate the likelihoods is publicly available at
http://lambda.gsfc.nasa.gov/toolbox/lrgdr/ . v2 fixes abstract formatting
issu
-Strands
A -strand is a map for a Lie
group that follows from Hamilton's principle for a certain class of
-invariant Lagrangians. The SO(3)-strand is the -strand version of the
rigid body equation and it may be regarded physically as a continuous spin
chain. Here, -strand dynamics for ellipsoidal rotations is derived as
an Euler-Poincar\'e system for a certain class of variations and recast as a
Lie-Poisson system for coadjoint flow with the same Hamiltonian structure as
for a perfect complex fluid. For a special Hamiltonian, the -strand is
mapped into a completely integrable generalization of the classical chiral
model for the SO(3)-strand. Analogous results are obtained for the
-strand. The -strand is the -strand version of the
Bloch-Iserles ordinary differential equation, whose solutions exhibit dynamical
sorting. Numerical solutions show nonlinear interactions of coherent wave-like
solutions in both cases. -strand equations on the
diffeomorphism group are also introduced and shown
to admit solutions with singular support (e.g., peakons).Comment: 35 pages, 5 figures, 3rd version. To appear in J Nonlin Sc
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: measurements of the growth of structure and expansion rate at z=0.57 from anisotropic clustering
We analyze the anisotropic clustering of massive galaxies from the Sloan
Digital Sky Survey III Baryon Oscillation Spectroscopic Survey (BOSS) Data
Release 9 (DR9) sample, which consists of 264,283 galaxies in the redshift
range 0.43 < z < 0.7 spanning 3,275 square degrees. Both peculiar velocities
and errors in the assumed redshift-distance relation ("Alcock-Paczynski
effect") generate correlations between clustering amplitude and orientation
with respect to the line-of-sight. Together with the sharp baryon acoustic
oscillation (BAO) standard ruler, our measurements of the broadband shape of
the monopole and quadrupole correlation functions simultaneously constrain the
comoving angular diameter distance (2190 +/- 61 Mpc) to z=0.57, the Hubble
expansion rate at z=0.57 (92.4 +/- 4.5 km/s/Mpc), and the growth rate of
structure at that same redshift (d sigma8/d ln a = 0.43 +/- 0.069). Our
analysis provides the best current direct determination of both DA and H in
galaxy clustering data using this technique. If we further assume a LCDM
expansion history, our growth constraint tightens to d sigma8/d ln a = 0.415
+/- 0.034. In combination with the cosmic microwave background, our
measurements of DA, H, and growth all separately require dark energy at z >
0.57, and when combined imply \Omega_{\Lambda} = 0.74 +/- 0.016, independent of
the Universe's evolution at z<0.57. In our companion paper (Samushia et al.
prep), we explore further cosmological implications of these observations.Comment: 19 pages, 11 figures, submitted to MNRAS, comments welcom
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