9,903 research outputs found
Nematic liquid crystals : from Maier-Saupe to a continuum theory
We define a continuum energy functional in terms of the mean-field Maier-Saupe free energy, that describes both spatially homogeneous and inhomogeneous systems. The Maier-Saupe theory defines the main macroscopic variable, the Q-tensor order parameter, in terms of the second moment of a probability distribution function. This definition requires the eigenvalues of Q to be bounded both from below and above. We define a thermotropic bulk potential which blows up whenever the eigenvalues tend to these lower and upper bounds. This is in contrast to the Landau-de Gennes theory which has no such penalization. We study the asymptotics of this bulk potential in different regimes and discuss phase transitions predicted by this model
The hybrid SZ power spectrum: Combining cluster counts and SZ fluctuations to probe gas physics
Sunyaev-Zeldovich (SZ) effect from a cosmological distribution of clusters
carry information on the underlying cosmology as well as the cluster gas
physics. In order to study either cosmology or clusters one needs to break the
degeneracies between the two. We present a toy model showing how complementary
informations from SZ power spectrum and the SZ flux counts, both obtained from
upcoming SZ cluster surveys, can be used to mitigate the strong cosmological
influence (especially that of sigma_8) on the SZ fluctuations. Once the strong
dependence of the cluster SZ power spectrum on sigma_8 is diluted, the cluster
power spectrum can be used as a tool in studying cluster gas structure and
evolution. The method relies on the ability to write the Poisson contribution
to the SZ power spectrum in terms the observed SZ flux counts. We test the toy
model by applying the idea to simulations of SZ surveys.Comment: 12 pages. 11 plots. MNRAS submitte
Statistics of the first passage time of Brownian motion conditioned by maximum value or area
We derive the moments of the first passage time for Brownian motion
conditioned by either the maximum value or the area swept out by the motion.
These quantities are the natural counterparts to the moments of the maximum
value and area of Brownian excursions of fixed duration, which we also derive
for completeness within the same mathematical framework. Various applications
are indicated.Comment: 29 pages, 4 figures include
Maximum Distance Between the Leader and the Laggard for Three Brownian Walkers
We consider three independent Brownian walkers moving on a line. The process
terminates when the left-most walker (the `Leader') meets either of the other
two walkers. For arbitrary values of the diffusion constants D_1 (the Leader),
D_2 and D_3 of the three walkers, we compute the probability distribution
P(m|y_2,y_3) of the maximum distance m between the Leader and the current
right-most particle (the `Laggard') during the process, where y_2 and y_3 are
the initial distances between the leader and the other two walkers. The result
has, for large m, the form P(m|y_2,y_3) \sim A(y_2,y_3) m^{-\delta}, where
\delta = (2\pi-\theta)/(\pi-\theta) and \theta =
cos^{-1}(D_1/\sqrt{(D_1+D_2)(D_1+D_3)}. The amplitude A(y_2,y_3) is also
determined exactly
Universal Asymptotic Statistics of Maximal Relative Height in One-dimensional Solid-on-solid Models
We study the probability density function of the maximum relative
height in a wide class of one-dimensional solid-on-solid models of finite
size . For all these lattice models, in the large limit, a central limit
argument shows that, for periodic boundary conditions, takes a
universal scaling form , with the width of the fluctuating interface and the Airy
distribution function. For one instance of these models, corresponding to the
extremely anisotropic Ising model in two dimensions, this result is obtained by
an exact computation using transfer matrix technique, valid for any .
These arguments and exact analytical calculations are supported by numerical
simulations, which show in addition that the subleading scaling function is
also universal, up to a non universal amplitude, and simply given by the
derivative of the Airy distribution function .Comment: 13 pages, 4 figure
Antisite Domains in Double Perovskite Ferromagnets: Impact on Magnetotransport and Half-metallicity
Several double perovskite materials of the form A_2BB'O_6 exhibit high
ferromagnetic T_c, and significant low field magnetoresistance. They are also a
candidate source of spin polarized electrons. The potential usefulness of these
materials is, however, frustrated by mislocation of the B and B' ions, which do
not organise themselves in the ideal alternating structure. The result is a
strong dependence of physical properties on preparative conditions, reducing
the magnetization and destroying the half-metallicity. We provide the first
results on the impact of spatially correlated antisite disorder, as observed
experimentally, on the ferromagnetic double perovskites. The antisite domains
suppress magnetism and half-metallicity, as expected, but lead to a dramatic
enhancement of the low field magnetoresistance.Comment: 6 pages, pdflatex, EPL styl
- …