36,749 research outputs found
Testing Higher-Order Lagrangian Perturbation Theory Against Numerical Simulations - 1. Pancake Models
We present results showing an improvement of the accuracy of perturbation
theory as applied to cosmological structure formation for a useful range of
quasilinear scales. The Lagrangian theory of gravitational instability of an
Einstein-de Sitter dust cosmogony investigated and solved up to the third order
in the series of papers by Buchert (1989, 1992, 1993a), Buchert \& Ehlers
(1993), Buchert (1993b), Ehlers \& Buchert (1993), is compared with numerical
simulations. In this paper we study the dynamics of pancake models as a first
step. In previous work (Coles \etal 1993, Melott \etal 1993, Melott 1993) the
accuracy of several analytical approximations for the modeling of large-scale
structure in the mildly non-linear regime was analyzed in the same way,
allowing for direct comparison of the accuracy of various approximations. In
particular, the ``Zel'dovich approximation'' (Zel'dovich 1970, 1973, hereafter
ZA) as a subclass of the first-order Lagrangian perturbation solutions was
found to provide an excellent approximation to the density field in the mildly
non-linear regime (i.e. up to a linear r.m.s. density contrast of ). The performance of ZA in hierarchical clustering models can be
greatly improved by truncating the initial power spectrum (smoothing the
initial data). We here explore whether this approximation can be further
improved with higher-order corrections in the displacement mapping from
homogeneity. We study a single pancake model (truncated power-spectrum with
power-index ) using cross-correlation statistics employed inComment: TeX, 18 pages excl.figures; contact [email protected] ;
[email protected] . submitted to Astron. & Astrophy
Realizing vector meson dominance with transverse charge densities
The transverse charge density in a fast-moving nucleon is represented as a
dispersion integral of the imaginary part of the Dirac form factor in the
timelike region (spectral function). At a given transverse distance b the
integration effectively extends over energies in a range sqrt{t} ~< 1/b, with
exponential suppression of larger values. The transverse charge density at
peripheral distances thus acts as a low-pass filter for the spectral function
and allows one to select energy regions dominated by specific t-channel states,
corresponding to definite exchange mechanisms in the spacelike form factor. We
show that distances b ~ 0.5 - 1.5 fm in the isovector density are maximally
sensitive to the rho meson region, with only a ~10% contribution from
higher-mass states. Soft-pion exchange governed by chiral dynamics becomes
relevant only at larger distances. In the isoscalar density higher-mass states
beyond the omega are comparatively more important. The dispersion approach
suggests that the positive transverse charge density in the neutron at b ~ 1
fm, found previously in a Fourier analysis of spacelike form factor data, could
serve as a sensitive test of the the isoscalar strength in the ~1 GeV mass
region. In terms of partonic structure, the transverse densities in the vector
meson region b ~ 1 fm support an approximate mean-field picture of the motion
of valence quarks in the nucleon.Comment: 14 pages, 12 figure
A stable range description of the space of link maps
We study the space of link maps, which are smooth maps from the disjoint
union of manifolds P and Q to a manifold N such that the images of P and Q are
disjoint. We give a range of dimensions, interpreted as the connectivity of a
certain map, in which the cobordism class of the "linking manifold" is enough
to distinguish the homotopy class of one link map from another.Comment: 10 page
Recommended from our members
Influence of street setbacks on solar reflection and air cooling by reflective streets in urban canyons
The ability of a climate model to accurately simulate the urban cooling effect of raising street albedo may be hampered by unrealistic representations of street geometry in the urban canyon. Even if the climate model is coupled to an urban canyon model (UCM), it is hard to define detailed urban geometries in UCMs. In this study, we relate simulated surface air temperature change to canyon albedo change. Using this relationship, we calculate scaling factors to adjust previously obtained surface air temperature changes that were simulated using generic canyon geometries. The adjusted temperature changes are obtained using a proposed multi-reflection urban canyon albedo model (UCAM), avoiding the need to rerun computationally expensive climate models. The adjusted temperature changes represent those that would be obtained from simulating with city-specific (local) geometries. Local urban geometries are estimated from details of the city's building stock and the city's street design guidelines. As a case study, we calculated average citywide seasonal scaling factors for realistic canyon geometries in Sacramento, California based on street design guidelines and building stock. The average scaling factors are multipliers used to adjust air temperature changes previously simulated by a Weather Research and Forecasting model coupled to an urban canyon model in which streets extended from wall to wall (omitting setbacks, such as sidewalks and yards). Sacramento's scaling factors ranged from 2.70 (summer) to 3.89 (winter), demonstrating the need to consider the actual urban geometry in urban climate studies
Continuum Limits of ``Induced QCD": Lessons of the Gaussian Model at d=1 and Beyond
We analyze the scalar field sector of the Kazakov--Migdal model of induced
QCD. We present a detailed description of the simplest one dimensional
{()} model which supports the hypothesis of wide applicability of the
mean--field approximation for the scalar fields and the existence of critical
behaviour in the model when the scalar action is Gaussian. Despite the
ocurrence of various non--trivial types of critical behaviour in the
model as , only the conventional large- limit is
relevant for its {\it continuum} limit. We also give a mean--field analysis of
the model in {\it any} and show that a saddle point always exists in
the region . In it exhibits critical behaviour as
. However when there is no critical
behaviour unless non--Gaussian terms are added to the scalar field action. We
argue that similar behaviour should occur for any finite thus providing a
simple explanation of a recent result of D. Gross. We show that critical
behaviour at and can be obtained by adding a
term to the scalar potential. This is equivalent to a local
modification of the integration measure in the original Kazakov--Migdal model.
Experience from previous studies of the Generalized Kontsevich Model implies
that, unlike the inclusion of higher powers in the potential, this minor
modification should not substantially alter the behaviour of the Gaussian
model.Comment: 31 page
Hopping conductivity in heavily doped n-type GaAs layers in the quantum Hall effect regime
We investigate the magnetoresistance of epitaxially grown, heavily doped
n-type GaAs layers with thickness (40-50 nm) larger than the electronic mean
free path (23 nm). The temperature dependence of the dissipative resistance
R_{xx} in the quantum Hall effect regime can be well described by a hopping law
(R_{xx} \propto exp{-(T_0/T)^p}) with p=0.6. We discuss this result in terms of
variable range hopping in a Coulomb gap together with a dependence of the
electron localization length on the energy in the gap. The value of the
exponent p>0.5 shows that electron-electron interactions have to be taken into
account in order to explain the occurrence of the quantum Hall effect in these
samples, which have a three-dimensional single electron density of states.Comment: 5 pages, 2 figures, 1 tabl
- …