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 $A$ 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