Similarity solutions for slender rivulets with thermocapillarity

We use the lubrication approximation to investigate the steady flow of slender non-uniform rivulets of a viscous fluid on an inclined plane that is either heated or cooled relative to the surrounding atmosphere. Four non-isothermal situations in which thermocapillary effects play a significant role are considered. We derive the general equations for a slender rivulet subject to gravity, surface tension, thermocapillarity and a constant surface shear stress. Similarity solutions describing a thermocapillary-driven rivulet widening or narrowing due to either gravitational or surface-tension effects on a non-uniformly heated or cooled substrate are obtained, and we present examples of these solutions when the substrate temperature gradient depends on the longitudinal coordinate according to a general power law. When gravitational effects are strong there is a unique solution representing both a narrowing pendent rivulet and a widening sessile rivulet whose transverse profile always has a single global maximum. When surface-tension effects are strong there is a one-parameter family of solutions representing both a narrowing and a widening rivulet whose transverse profile has either a single global maximum or two equal global maxima and a local minimum. Unique similarity solutions whose transverse profiles always have a single global maximum are also obtained for both a gravity-driven and a constant-surface-shear-stress-driven rivulet widening or narrowing due to thermocapillarity on a uniformly heated or cooled substrate. The solutions in both cases represent both a narrowing rivulet on a heated substrate and a widening rivulet on a cooled substrate (albeit with infinite width in the gravity-driven case)

Interpreting interpolation: the pattern of interpolation errors in digital surface models derived from laser scanning data

Errors within height models have, in the past, been communicated in terms of global measures ofaccuracy for the model. Such quantification ignores the spatial structure of errors across thesurface, hindering subsequent analysis. This paper demonstrates the importance ofunderstanding the spatial structure of error using, as an example, the creation of a DigitalSurface Model (DSM) from laser scanner data

Similarity solutions for slender dry patches with thermocapillarity

We use the lubrication approximation to investigate slender dry patches in an infinitely wide film of viscous fluid flowing steadily on an inclined plane that is either heated or cooled relative to the surrounding atmosphere. Four non-isothermal situations in which thermocapillary effects play a significant role are considered. Similarity solutions describing a thermocapillary-driven flow with a dry patch that is widening or narrowing due to either gravitational or surface-tension effects on a non-uniformly heated or cooled substrate are obtained, and we present examples of these solutions when the substrate temperature gradient depends on the longitudinal coordinate according to a general power law. When gravitational effects are strong the solution contains a free parameter, and for each value of this parameter there is a unique solution representing both a narrowing pendent dry patch and a widening sessile dry patch, whose transverse profile has a monotonically increasing shape. When surface tension effects are strong the solution also contains a free parameter, and for each value of this parameter there is both a unique solution representing a narrowing dry patch, whose transverse profile has a monotonically increasing shape, and a one-parameter family of solutions representing a widening dry patch, whose transverse profile has a capillary ridge near the contact line and decays in an oscillatory manner far from it. Similarity solutions are also obtained for both a gravity-driven and a constant surface- shear-stress-driven flow with a dry patch that is widening or narrowing due to thermocapillarity on a uniformly heated or cooled substrate. The solutions in both cases contain a free parameter, and for each value of this parameter there is a unique solution representing both a narrowing dry patch on a heated substrate and a widening dry patch on a cooled substrate, whose transverse profile has a monotonically increasing shape

Electron Multiplying Low-Voltage CCD With Increased Gain

Novel designs for the gain elements in electron multiplying (EM) CCDs have been implemented in a device manufactured in a low voltage CMOS process. Derived with help from TCAD simulations, the designs employ modified gate geometries in order to significantly increase the EM gain over traditional structures. Two new EM elements have been demonstrated with an order of magnitude higher gain than the typical rectangular gate designs, achieved over 100 amplifying stages and without an increase in the electric field. The principles presented in this work can be used in CMOS and CCD imagers employing electron multiplication in order to boost the gain and reduce undesirable effects such as clock-induced charge generation and gain ageing

Entangled-state cryptographic protocol that remains secure even if nonlocal hidden variables exist and can be measured with arbitrary precision

Standard quantum cryptographic protocols are not secure if one assumes that nonlocal hidden variables exist and can be measured with arbitrary precision. The security can be restored if one of the communicating parties randomly switches between two standard protocols.Comment: Shortened version, accepted in Phys. Rev.

Quasi-steady spreading of a thin ridge of fluid with temperature-dependent surface tension on a heated or cooled substrate

We investigate theoretically the problem of the quasi-steady spreading or contraction of a thin two-dimensional sessile or pendent ridge of viscous fluid with temperature-dependent surface tension on a planar horizontal substrate that is uniformly heated or cooled relative to the atmosphere. We derive an implicit solution of the leading-order thin-film equation for the free-surface profile of the ridge and use this to examine the quasi-steady evolution of the ridge, the dynamics of the moving contact lines being modelled by a 'Tanner law' relating the velocity of the contact line to the contact angle; in particular, we obtain a complete description of the possible forms that the evolution may take. In both the case of a (sessile or pendent) ridge on a heated substrate and the case of a pendent ridge on a cooled substrate when gravitational effects are relatively weak, there is one stable final state to which the ridge may evolve. In the case of a pendent ridge on a cooled substrate when gravitational effects are stronger, there may be one or two stable final states; moreover, the contact angles may vary non-monotonically with time during the evolution to one of these states. In the case of a pendent ridge on a cooled substrate when gravitational effects are even stronger, there may be up to three stable final states with qualitatively different solutions; moreover, the ridge may evolve via an intermediate state from which quasi-steady motion cannot persist, and so there will be a transient non-quasi-steady adjustment (in which the contact angles change rapidly, with the positions of the contact lines unaffected), after which quasi-steady motion is resumed. Lastly, we consider the behaviour of the ridge in the asymptotic limits of strong heating or cooling of the substrate and of strong or weak gravitational effects