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 $R$, 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 $\delta \mu\equiv \mu - \mu_{co}(T)$ 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 $R_c=2 \gamma_{gl}^\infty/(\Delta \rho \delta \mu)$, where $\gamma_{gl}^\infty$ is the planar gas-liquid surface tension and $\Delta \rho$ is the difference in coexisting densities at temperature $T$. For $R>R_c$, the interfacial free energy and the density profile of the fluid near the hard wall can be expanded in powers of the curvature $R^{-1}$, in keeping with the analysis of Stillinger and Cotter, J. Chem. Phys. {\bf 55}, 3449 (1971). In the other regime, $R<R_c$, the interfacial free energy and its derivatives acquire terms depending on $\ln R$. Since $R_c^{-1}$ can be made arbitrarily small this implies non-analytic behavior, as $R^{-1}\to 0$, 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

Boundary layer integral matrix procedure: Verification of models

The three turbulent models currently available in the JANNAF version of the Aerotherm Boundary Layer Integral Matrix Procedure (BLIMP-J) code were studied. The BLIMP-J program is the standard prediction method for boundary layer effects in liquid rocket engine thrust chambers. Experimental data from flow fields with large edge-to-wall temperature ratios are compared to the predictions of the three turbulence models contained in BLIMP-J. In addition, test conditions necessary to generate additional data on a flat plate or in a nozzle are given. It is concluded that the Cebeci-Smith turbulence model be the recommended model for the prediction of boundary layer effects in liquid rocket engines. In addition, the effects of homogeneous chemical reaction kinetics were examined for a hydrogen/oxygen system. Results show that for most flows, kinetics are probably only significant for stoichiometric mixture ratios

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

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

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

Effective anisotropies and energy barriers of magnetic nanoparticles with Néel surface anisotropy

Magnetic nanoparticles with Néel surface anisotropy, different internal structures, surface arrangements, and elongation are modeled as many-spin systems. The results suggest that the energy of many-spin nanoparticles cut from cubic lattices can be represented by an effective one-spin potential containing uniaxial and cubic anisotropies. It is shown that the values and signs of the corresponding constants depend strongly on the particle's surface arrangement, internal structure, and shape. Particles cut from a simple cubic lattice have the opposite sign of the effective cubic term, as compared to particles cut from the face-centered cubic lattice. Furthermore, other remarkable phenomena are observed in nanoparticles with relatively strong surface effects. (i) In elongated particles surface effects can change the sign of the uniaxial anisotropy. (ii) In symmetric particles (spherical and truncated octahedral) with cubic core anisotropy surface effects can change the sing of the latter. We also show that the competition between the core and surface anisotropies leads to a new energy that contributes to both the second- and fourth-order effective anisotropies. We evaluate energy barriers ΔE as functions of the strength of the surface anisotropy and the particle size. The results are analyzed with the help of the effective one-spin potential, which allows us to assess the consistency of the widely used formula ΔE/V= K∞ +6 Ks /D, where K∞ is the core anisotropy constant, Ks is a phenomenological constant related to surface anisotropy, and D is the particle's diameter. We show that the energy barriers are consistent with this formula only for elongated particles for which the surface contribution to the effective uniaxial anisotropy scales with the surface and is linear in the constant of the Néel surface anisotropy. © 2007 The American Physical Society

The Age-Specific Force of Natural Selection and Walls of Death

W. D. Hamilton's celebrated formula for the age-specific force of natural selection furnishes predictions for senescent mortality due to mutation accumulation, at the price of reliance on a linear approximation. Applying to Hamilton's setting the full non-linear demographic model for mutation accumulation of Evans et al. (2007), we find surprising differences. Non-linear interactions cause the collapse of Hamilton-style predictions in the most commonly studied case, refine predictions in other cases, and allow Walls of Death at ages before the end of reproduction. Haldane's Principle for genetic load has an exact but unfamiliar generalization.Comment: 27 page

The Tilt of the Local Velocity Ellipsoid as Seen by Gaia

The Gaia Radial Velocity Spectrometer (RVS) provides a sample of 7,224,631 stars with full six-dimensional phase space information. Bayesian distances of these stars are available from the catalogue of Sch\"onrich et al. (2019). We exploit this to map out the behaviour of the velocity ellipsoid within 5 kpc of the Sun. We find that the tilt of the disc-dominated RVS sample is accurately described by the relation $\alpha = (0.952 \pm 0.007)\arctan (|z|/R)$, where ($R,z$) are cylindrical polar coordinates. This corresponds to velocity ellipsoids close to spherical alignment (for which the normalising constant would be unity) and pointing towards the Galactic centre. Flattening of the tilt of the velocity ellipsoids is enhanced close to the plane and Galactic centre, whilst at high elevations far from the Galactic center the population is consistent with exact spherical alignment. Using the LAMOST catalogue cross-matched with Gaia DR2, we construct thin disc and halo samples of reasonable purity based on metallicity. We find that the tilt of thin disc stars straddles $\alpha = (0.909-1.038)\arctan (|z|/R)$, and of halo stars straddles $\alpha = (0.927-1.063)\arctan (|z|/R)$. We caution against the use of reciprocal parallax for distances in studies of the tilt, as this can lead to serious artefacts.Comment: MNRAS, revised version contains additional checks on the integrity of the distance