60,767 research outputs found
Lensing Properties of Cored Galaxy Models
A method is developed to evaluate the magnifications of the images of
galaxies with lensing potentials stratified on similar concentric ellipses. A
simple contour integral is provided which enables the sums of the
magnifications of even parity or odd parity or the central image to be easily
calculated. The sums for pairs of images vary considerably with source
position, while the signed sums can be remarkably uniform inside the tangential
caustic in the absence of naked cusps. For a family of models in which the
potential is a power-law of the elliptic radius, the number of visible images
is found as a function of flattening, external shear and core radius. The
magnification of the central image depends on the core radius and the slope of
the potential. For typical source and lens redshifts, the missing central image
leads to strong constraints; the mass distribution in the lensing galaxy must
be nearly cusped, and the cusp must be isothermal or stronger. This is in
accord with the cuspy cores seen in high resolution photometry of nearby,
massive, early-type galaxies, which typically have the surface density falling
like distance^{-1.3} outside a break radius of a few hundred parsecs. Cuspy
cores by themselves can provide an explanation of the missing central images.
Dark matter at large radii may alter the slope of the projected density;
provided the slope remains isothermal or steeper and the break radius remains
small, then the central image remains unobservable. The sensitivity of the
radio maps must be increased fifty-fold to find the central images in
abundance.Comment: 42 pages, 11 figures, ApJ in pres
Non-analytic curvature contributions to solvation free energies: influence of drying
We investigate the solvation of a hard spherical cavity, of radius ,
immersed in a fluid for which the interparticle forces are short ranged. For
thermodynamic states lying close to the liquid binodal, where the chemical
potential deviation is very small and
positive, complete wetting by gas (drying) occurs and two regimes of
interfacial behavior can be identified. These are characterized by the length
scale , where
is the planar gas-liquid surface tension and
is the difference in coexisting densities at temperature . For , the
interfacial free energy and the density profile of the fluid near the hard wall
can be expanded in powers of the curvature , in keeping with the
analysis of Stillinger and Cotter, J. Chem. Phys. {\bf 55}, 3449 (1971). In the
other regime, , the interfacial free energy and its derivatives acquire
terms depending on . Since can be made arbitrarily small this
implies non-analytic behavior, as , of the work of formation of a
hard spherical cavity and of the Gibbs adsorption and the fluid density at
contact with the wall. Our analysis, which is based on an effective interfacial
Hamiltonian combined with exact statistical mechanical sum rules, is confirmed
fully by the results of microscopic density functional calculations for a
square-well fluid.Comment: 17 pages, 3 figures; accepted for publication in J. Chem. Phy
Is there Ornstein-Zernike equation in the canonical ensemble?
A general density-functional formalism using an extended variable-space is
presented for classical fluids in the canonical ensemble (CE). An exact
equation is derived that plays the role of the Ornstein-Zernike (OZ) equation
in the grand canonical ensemble (GCE). When applied to the ideal gas we obtain
the exact result for the total correlation function h_N. For a homogeneous
fluid with N particles the new equation only differs from OZ by 1/N and it
allows to obtain an approximate expression for h_N in terms of its GCE
counterpart that agrees with the expansion of h_N in powers of 1/N.Comment: 5 pages, RevTeX. Submitted to Phys. Rev. Let
Pair-factorized steady states on arbitrary graphs
Stochastic mass transport models are usually described by specifying hopping
rates of particles between sites of a given lattice, and the goal is to predict
the existence and properties of the steady state. Here we ask the reverse
question: given a stationary state that factorizes over links (pairs of sites)
of an arbitrary connected graph, what are possible hopping rates that converge
to this state? We define a class of hopping functions which lead to the same
steady state and guarantee current conservation but may differ by the induced
current strength. For the special case of anisotropic hopping in two dimensions
we discuss some aspects of the phase structure. We also show how this case can
be traced back to an effective zero-range process in one dimension which is
solvable for a large class of hopping functions.Comment: IOP style, 9 pages, 1 figur
A multi-purpose method for analysis of spur gear tooth loading
A large digitized approach was developed for the static and dynamic load analysis of spur gearing. An iterative procedure was used to calculate directly the "variable-variable" gear mesh stiffness as a function of transmitted load, gear tooth profile errors, gear tooth deflections and gear hub torsional deformation, and position of contacting profile points. The developed approach can be used to analyze the loads, Hertz stresses, and PV for the normal and high contrast ratio gearing, presently the modeling is limited to the condition that for a given gear all teeth have identical spacing and profiles (with or without surface imperfections). Certain types of simulated sinusoidal profile errors and pitting can cause interruptions of the gear mesh stiffness function and, thus, increase the dynamic loads in spur gearing. In addition, a finite element stress and mesh subprogram was developed for future introduction into the main program for calculating the gear tooth bending stresses under dynamic loads
Measuring snow cover using satellite imagery during 1973 and 1974 melt season: North Santiam, Boise, and Upper Snake Basins, phase 1
Measurements are examined of snow coverage during the snow-melt season in 1973 and 1974 from LANDSAT imagery for the three Columbia River Subbasins. Satellite derived snow cover inventories for the three test basins were obtained as an alternative to inventories performed with the current operational practice of using small aircraft flights over selected snow fields. The accuracy and precision versus cost for several different interactive image analysis procedures was investigated using a display device, the Electronic Satellite Image Analysis Console. Single-band radiance thresholding was the principal technique employed in the snow detection, although this technique was supplemented by an editing procedure involving reference to hand-generated elevation contours. For each data and view measured, a binary thematic map or "mask" depicting the snow cover was generated by a combination of objective and subjective procedures. Photographs of data analysis equipment (displays) are shown
Kinetic pathways of multi-phase surfactant systems
The relaxation following a temperature quench of two-phase (lamellar and
sponge phase) and three-phase (lamellar, sponge and micellar phase) samples,
has been studied in an SDS/octanol/brine system. In the three-phase case we
have observed samples that are initially mainly sponge phase with lamellar and
micellar phase on the top and bottom respectively. Upon decreasing temperature
most of the volume of the sponge phase is replaced by lamellar phase. During
the equilibriation we have observed three regimes of behaviour within the
sponge phase: (i) disruption in the sponge texture, then (ii) after the sponge
phase homogenises there is a lamellar nucleation regime and finally (iii) a
bizarre plume connects the lamellar phase with the micellar phase. The
relaxation of the two-phase sample proceeds instead in two stages. First
lamellar drops nucleate in the sponge phase forming a onion `gel' structure.
Over time the lamellar structure compacts while equilibriating into a two phase
lamellar/sponge phase sample. We offer possible explanatioins for some of these
observations in the context of a general theory for phase kinetics in systems
with one fast and one slow variable.Comment: 1 textfile, 20 figures (jpg), to appear in PR
Correlation function algebra for inhomogeneous fluids
We consider variational (density functional) models of fluids confined in
parallel-plate geometries (with walls situated in the planes z=0 and z=L
respectively) and focus on the structure of the pair correlation function
G(r_1,r_2). We show that for local variational models there exist two
non-trivial identities relating both the transverse Fourier transform G(z_\mu,
z_\nu;q) and the zeroth moment G_0(z_\mu,z_\nu) at different positions z_1, z_2
and z_3. These relations form an algebra which severely restricts the possible
form of the function G_0(z_\mu,z_\nu). For the common situations in which the
equilibrium one-body (magnetization/number density) profile m_0(z) exhibits an
odd or even reflection symmetry in the z=L/2 plane the algebra simplifies
considerably and is used to relate the correlation function to the finite-size
excess free-energy \gamma(L). We rederive non-trivial scaling expressions for
the finite-size contribution to the free-energy at bulk criticality and for
systems where large scale interfacial fluctuations are present. Extensions to
non-planar geometries are also considered.Comment: 15 pages, RevTex, 4 eps figures. To appear in J.Phys.Condens.Matte
- …