We discuss the contribution to the characteristic lensing quantities, i.e. the deflection angle and Einstein radius, due to the higher order terms (e.g. the gravitomagnetic terms) considered in the lens potential. The cases we analyze are the singular isothermal sphere and the disk of spiral galaxies. It is possible to see that the perturbative effects could be of the order 10−3 with respect to...

We construct a model for black hole formation in galactic bulges. The initial state is a slowly rotating isothermal sphere, with an effective transport speed and rotation rate Q. The black hole mass is determined when the aeff centrifugal radius of the collapse flow exceeds the capture radius of the central black hole. This model reproduces the observed correlation between black hole masses and...

Certain models with purely repulsive pair interactions can form cluster crystals with multiply-occupied lattice sites. Simulating these models' equilibrium properties is, however, quite challenging. Here, we develop an expanded isothermal-isobaric [N]pT ensemble that surmounts this problem by allowing both particle number and lattice spacing to fluctuate. It is particularly efficient at high T,...

Nested Sampling (NS) is a powerful athermal statistical mechanical sampling technique that directly calculates the partition function, and hence gives access to all thermodynamic quantities in absolute terms, including absolute free energies and absolute entropies. NS has been used predominately to compute the canonical (NVT) partition function. Although NS has recently been used to obtain the ...

I report on recent measurements of two scaling relations of spheroids in the distant universe: the Fundamental Plane, and the relation between lensing velocity dispersion and stellar velocity dispersion. The joint analysis of the two scaling relations indicates that the most massive (above ∼ 1011.5M⊙) spheroids are consistent with no evolution since z ∼ 1 both in terms of star formation and int...

The dark matter in the galaxy cluster Abell 1689 is modelled as an isothermal sphere of neutrinos. New data on the 2d mass density allow an accurate description of its core and halo. The model has no “missing baryon problem” and beyond 2.1 Mpc the baryons have the cosmic mass abundance. Combination of cluster data with the cosmic dark matter fraction – here supposed to stem from the neutrinos –...

We examine the microscopic structure of a hard-sphere fluid confined to a small cylindrical pore by means of Monte Carlo simulation. In order to analyze finite-size effects, the simulations are carried out in the framework of different statistical mechanics ensembles. We find that the size effects are specially relevant in the canonical ensemble where noticeable differences are found with the r...

A semi-empirical equation of state was developed for square-well chain fluids on the basis of Monte Carlo (MC) simulation data. The equation was formed by combining terms describing non-bonded square-well segments, hard-sphere chain formation, and a perturbation term describing the square-well contribution to chain formation. The functional dependence on the chain length is the same as that der...

To date, the study of high-magniication gravitational lensing eeects of galaxy clusters has focused upon the grossly distorted, luminous arc-like features formed in massive, centrally condensed clusters. We investigate the formation of a diierent type of image , highly magniied yet undistorted, in two widely employed cluster mass density prooles; an isothermal sphere with a core, and a universa...

Transformation thermodynamics, as one of the important branches among the extensions of transformation optics, has attracted plentiful attentions and interests recently. The result of transformation thermodynamics, or called as "thermal cloak", can realize isothermal region and hide objects from heat. In this paper, we presented the concept of "reverse thermal cloak" to correspond to the therma...