6,881 research outputs found
A new approach to stochastic evolution equations with adapted drift
In this paper we develop a new approach to stochastic evolution equations
with an unbounded drift which is dependent on time and the underlying
probability space in an adapted way. It is well-known that the semigroup
approach to equations with random drift leads to adaptedness problems for the
stochastic convolution term. In this paper we give a new representation formula
for the stochastic convolution which avoids integration of nonadapted
processes. Here we mainly consider the parabolic setting. We establish
connections with other solution concepts such as weak solutions. The usual
parabolic regularity properties are derived and we show that the new approach
can be applied in the study of semilinear problems with random drift. At the
end of the paper the results are illustrated with two examples of stochastic
heat equations with random drift.Comment: Minor revision. Accepted for publication in Journal of Differential
Equation
Co-evaporation of Co-Cr at intermediate oblique incidence
The Co-evaPoration technique has been used for deposition of Co-Cr layers. Deposition has been done under intermediate angle of incidence of opposing vapour streams. The layers showed a single Phase hcP poly-crystalline structure. The (002) plane turned out to be tilted towards the direction of the CO source. The layers showed good perpendicular magnetic behaviour although the magnetic anisotropy axis was also inclined towards the Co-source. Because of the opposing angle of incidence for Co and Cr atoms, a process-induced segregation takes place which causes a relative high coercivity also at low Process temFeratures. A simple model for the segregation effect can explain the relation between the existance of a non-magnetic region and an increased coercivity of th Co-Cr film
Large difference in the elastic properties of fcc and hcp hard-sphere crystals
We report a numerical calculation of the elastic constants of the fcc and hcp
crystal phases of monodisperse hard-sphere colloids. Surprisingly, some of
these elastic constants are very different (up to 20%), even though the free
energy, pressure and bulk compressibility of the two crystal structures are
very nearly equal. As a consequence, a moderate deformation of a hard-sphere
crystal may make the hcp phase more stable than the fcc phase. This finding has
implications for the design of patterned templates to grow colloidal hcp
crystals. We also find that, below close packing, there is a small, but
significant, difference between the distances between hexagonal layers (c/a
ratios) of fcc and hcp crystals.Comment: 4 pages, 4 figures, accepted for publication in Physical Review
Letter
Large effect of polydispersity on defect concentrations in colloidal crystals
We compute the equilibrium concentration of stacking faults and point defects
in polydisperse hard-sphere crystals. We find that, while the concentration of
stacking faults remains similar to that of monodisperse hard sphere crystals,
the concentration of vacancies decreases by about a factor two. Most
strikingly, the concentration of interstitials in the maximally polydisperse
crystal may be some six orders of magnitude larger than in a monodisperse
crystal. We show that this dramatic increase in interstitial concentration is
due to the increased probability of finding small particles and that the
small-particle tail of the particle size distribution is crucial for the
interstitial concentration in a colloidal crystal.Comment: 6 pages, 4 figure
Systematic uncertainties in gravitational lensing models: a semi-analytical study of PG1115+080
While the Hubble constant can be derived from observable time delays between
images of lensed quasars, the result is often highly sensitive to assumptions
and systematic uncertainties in the lensing model. Unlike most previous authors
we explore a broad class of models with non-parametric lens radial profile and
allow for non-elliptical lens potentials. The axis ratio and position angle of
the lens can be determined from the image positions of quadruple gravitational
lensed systems by solving the lens equation semi-analytically, independent of
the radial profile. We give simple equations for estimating the power-law slope
of the lens density directly from the image positions and for estimating the
time delay ratios. Our method greatly simplifies the numerics for fitting
observations and is fast in exploring the model parameter space. As an
illustration we apply the model to PG1115+080. We show that the measured image
positions and time delays do not uniquely determine the Hubble constant. The
mass-to-light ratio of the lens galaxy increases with radius, higher at image C
than at image B.Comment: Some small corrections and clarifications added. 20 pages, 11
figures, accepted by MNRA
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