3,044 research outputs found
Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth
In the present contribution we review basic mathematical results for three
physical systems involving self-organising solid or liquid films at solid
surfaces. The films may undergo a structuring process by dewetting,
evaporation/condensation or epitaxial growth, respectively. We highlight
similarities and differences of the three systems based on the observation that
in certain limits all of them may be described using models of similar form,
i.e., time evolution equations for the film thickness profile. Those equations
represent gradient dynamics characterized by mobility functions and an
underlying energy functional.
Two basic steps of mathematical analysis are used to compare the different
system. First, we discuss the linear stability of homogeneous steady states,
i.e., flat films; and second the systematics of non-trivial steady states,
i.e., drop/hole states for dewetting films and quantum dot states in epitaxial
growth, respectively. Our aim is to illustrate that the underlying solution
structure might be very complex as in the case of epitaxial growth but can be
better understood when comparing to the much simpler results for the dewetting
liquid film. We furthermore show that the numerical continuation techniques
employed can shed some light on this structure in a more convenient way than
time-stepping methods.
Finally we discuss that the usage of the employed general formulation does
not only relate seemingly not related physical systems mathematically, but does
as well allow to discuss model extensions in a more unified way
Demonstration of a state-insensitive, compensated nanofiber trap
We report the experimental realization of an optical trap that localizes single Cs atoms ≃ 215
nm from surface of a dielectric nanober. By operating at magic wavelengths for pairs of counterpropagating
red- and blue-detuned trapping beams, dierential scalar light shifts are eliminated, and
vector shifts are suppressed by ≈ 250. We thereby measure an absorption linewidth Γ/2π = 5.7 ± 0.1
MHz for the Cs 6S_(1/2), F = 4 → 6P_(3/2), F' = 5 transition, where Γ_0/2π = 5.2 MHz in free space.
Optical depth d ≃ 66 is observed, corresponding to an optical depth per atom d_1 ≃ 0.08. These
advances provide an important capability for the implementation of functional quantum optical
networks and precision atomic spectroscopy near dielectric surfaces
Raman spectroscopy - A powerful tool for in situ planetary science
This paper introduces Raman spectroscopy and discusses various scenarios where it might be applied to in situ planetary missions. We demonstrate the extensive capabilities of Raman spectroscopy for planetary investigations and argue that this technique is essential for future planetary missions
PNIPAAm microgels with defined network architecture as temperature sensors in optical stretchers
Stretching individual living cells with light is a standard method to assess their mechanical properties. Yet, heat introduced by the laser light of optical stretchers may unwittingly change the mechanical properties of cells therein. To estimate the temperature induced by an optical trap, we introduce cell-sized, elastic poly(N-isopropylacrylamide) (PNIPAAm) microgels that relate temperature changes to hydrogel swelling. For their usage as a standardized calibration tool, we analyze the effect of free-radical chain-growth gelation (FCG) and polymer-analogous photogelation (PAG) on hydrogel network heterogeneity, micromechanics, and temperature response by Brillouin microscopy and optical diffraction tomography. Using a combination of tailor-made PNIPAAm macromers, PAG, and microfluidic processing, we obtain microgels with homogeneous network architecture. With that, we expand the capability of standardized microgels in calibrating and validating cell mechanics analysis, not only considering cell and microgel elasticity but also providing stimuli-responsiveness to consider dynamic changes that cells may undergo during characterization
Spatial Light Modulators for the Manipulation of Individual Atoms
We propose a novel dipole trapping scheme using spatial light modulators
(SLM) for the manipulation of individual atoms. The scheme uses a high
numerical aperture microscope to map the intensity distribution of a SLM onto a
cloud of cold atoms. The regions of high intensity act as optical dipole force
traps. With a SLM fast enough to modify the trapping potential in real time,
this technique is well suited for the controlled addressing and manipulation of
arbitrarily selected atoms.Comment: 9 pages, 5 figure
Cumulants and the moment algebra: tools for analysing weak measurements
Recently it has been shown that cumulants significantly simplify the analysis
of multipartite weak measurements. Here we consider the mathematical structure
that underlies this, and find that it can be formulated in terms of what we
call the moment algebra. Apart from resulting in simpler proofs, the
flexibility of this structure allows generalizations of the original results to
a number of weak measurement scenarios, including one where the weakly
interacting pointers reach thermal equilibrium with the probed system.Comment: Journal reference added, minor correction
Stratified spatiotemporal chaos in anisotropic reaction-diffusion systems
Numerical simulations of two dimensional pattern formation in an anisotropic
bistable reaction-diffusion medium reveal a new dynamical state, stratified
spatiotemporal chaos, characterized by strong correlations along one of the
principal axes. Equations that describe the dependence of front motion on the
angle illustrate the mechanism leading to stratified chaos
Continuation for thin film hydrodynamics and related scalar problems
This chapter illustrates how to apply continuation techniques in the analysis
of a particular class of nonlinear kinetic equations that describe the time
evolution through transport equations for a single scalar field like a
densities or interface profiles of various types. We first systematically
introduce these equations as gradient dynamics combining mass-conserving and
nonmass-conserving fluxes followed by a discussion of nonvariational amendmends
and a brief introduction to their analysis by numerical continuation. The
approach is first applied to a number of common examples of variational
equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including
certain thin-film equations for partially wetting liquids on homogeneous and
heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal
equations. Second we consider nonvariational examples as the
Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard
equations and thin-film equations describing stationary sliding drops and a
transversal front instability in a dip-coating. Through the different examples
we illustrate how to employ the numerical tools provided by the packages
auto07p and pde2path to determine steady, stationary and time-periodic
solutions in one and two dimensions and the resulting bifurcation diagrams. The
incorporation of boundary conditions and integral side conditions is also
discussed as well as problem-specific implementation issues
Front instabilities in evaporatively dewetting nanofluids
Various experimental settings that involve drying solutions or suspensions of
nanoparticles -- often called nanofluids -- have recently been used to produce
structured nanoparticle layers. In addition to the formation of polygonal
networks and spinodal-like patterns, the occurrence of branched structures has
been reported. After reviewing the experimental results we use a modified
version of the Monte Carlo model first introduced by Rabani et al. [Nature 426,
271 (2003)] to study structure formation in evaporating films of nanoparticle
solutions for the case that all structuring is driven by the interplay of
evaporating solvent and diffusing nanoparticles.
After introducing the model and its general behavior we focus on receding
dewetting fronts which are initially straight but develop a transverse
fingering instability. We analyze the dependence of the characteristics of the
resulting branching patterns on the driving chemical potential, the mobility
and concentration of the nanoparticles, and the interaction strength between
liquid and nanoparticles. This allows us to understand the underlying
instability mechanism.Comment: 35 pages, 28 figure
- …