Corrections to Einstein's relation for Brownian motion in a tilted periodic potential

In this paper we revisit the problem of Brownian motion in a tilted periodic potential. We use homogenization theory to derive general formulas for the effective velocity and the effective diffusion tensor that are valid for arbitrary tilts. Furthermore, we obtain power series expansions for the velocity and the diffusion coefficient as functions of the external forcing. Thus, we provide systematic corrections to Einstein's formula and to linear response theory. Our theoretical results are supported by extensive numerical simulations. For our numerical experiments we use a novel spectral numerical method that leads to a very efficient and accurate calculation of the effective velocity and the effective diffusion tensor.Comment: 29 pages, 7 figures, submitted to the Journal of Statistical Physic

Centralisers of polynomially growing automorphisms of free groups

The main theorem of this thesis asserts that many centralisers in the automorphism groups Aut(F_n) and Out(F_n) of the free group F_n satisfy finiteness property VF, i.e. these centralisers have a finite index subgroup with a finite polyhedron as a classifying space. I first introduce higher graphs of groups and their automorphisms, which generalise the well-known graphs of groups. Important automorphisms are higher Dehn twists. I then use the structure of the automorphism group of the higher graph of groups to show that centralisers of higher Dehn twist automorphisms in Out(F_n) and Aut(F_n) are of type VF. This includes all polynomially growing automorphisms up to passing to powers. Finally, I compute explicit abelianisations of some centralisers, which give information on translation lengths in isometric CAT(0) actions

Combined optical and acoustical method for determination of thickness and porosity of transparent organic layers below the ultra-thin film limit

Analysis techniques are needed to determine the quantity and structure of materials composing an organic layer that is below an ultra-thin film limit and in a liquid environment. Neither optical nor acoustical techniques can independently distinguish between thickness and porosity of ultra-thin films due to parameter correlation. A combined optical and acoustical approach yields sufficient information to determine both thickness and porosity. We describe application of the combinatorial approach to measure single or multiple organic layers when the total layer thickness is small compared to the wavelength of the probing light. The instrumental setup allows for simultaneous in situ spectroscopic ellipsometry and quartz crystal microbalance dynamic measurements, and it is combined with a multiple-inlet fluid control system for different liquid solutions to be introduced during experiments. A virtual separation approach is implemented into our analysis scheme, differentiated by whether or not the organic adsorbate and liquid ambient densities are equal. The analysis scheme requires that the film be assumed transparent and rigid (non-viscoelastic). We present and discuss applications of our approach to studies of organic surfactant adsorption, self-assembled monolayer chemisorption, and multiple-layer target DNA sensor preparation and performance testing

Anisotropic contrast optical microscope

An optical microscope is described that reveals contrast in the Mueller matrix images of a thin, transparent, or semi-transparent specimen located within an anisotropic object plane (anisotropic filter). The specimen changes the anisotropy of the filter and thereby produces contrast within the Mueller matrix images. Here we use an anisotropic filter composed of a semi-transparent, nanostructured thin film with sub-wavelength thickness placed within the object plane. The sample is illuminated as in common optical microscopy but the light is modulated in its polarization using combinations of linear polarizers and phase plate (compensator) to control and analyze the state of polarization. Direct generalized ellipsometry data analysis approaches permit extraction of fundamental Mueller matrix object plane images dispensing with the need of Fourier expansion methods. Generalized ellipsometry model approaches are used for quantitative image analyses. These images are obtained from sets of multiple images obtained under various polarizer, analyzer, and compensator settings. Up to 16 independent Mueller matrix images can be obtained, while our current setup is limited to 11 images normalized by the unpolarized intensity. We demonstrate the anisotropic contrast optical microscope by measuring lithographically defined micro-patterned anisotropic filters, and we quantify the adsorption of an organic self-assembled monolayer film onto the anisotropic filter. Comparison with an isotropic glass slide demonstrates the image enhancement obtained by our method over microscopy without the use of an anisotropic filter. In our current instrument, we estimate the limit of detection for organic volumetric mass within the object plane of ≈49 fg within ≈7 × 7 μm2 object surface area. Compared to a quartz crystal microbalance with dissipation instrumentation, where contemporary limits require a total load of ≈500 pg for detection, the instrumentation demonstrated here improves sensitivity to a total mass required for detection by 4 orders of magnitude. We detail the design and operation principles of the anisotropic contrast optical microscope, and we present further applications to the detection of nanoparticles, to novel approaches for imaging chromatography and to new contrast modalities for observations on living cells

Anisotropic contrast optical microscope

An optical microscope is described that reveals contrast in the Mueller matrix images of a thin, transparent, or semi-transparent specimen located within an anisotropic object plane (anisotropic filter). The specimen changes the anisotropy of the filter and thereby produces contrast within the Mueller matrix images. Here we use an anisotropic filter composed of a semi-transparent, nanostructured thin film with sub-wavelength thickness placed within the object plane. The sample is illuminated as in common optical microscopy but the light is modulated in its polarization using combinations of linear polarizers and phase plate (compensator) to control and analyze the state of polarization. Direct generalized ellipsometry data analysis approaches permit extraction of fundamental Mueller matrix object plane images dispensing with the need of Fourier expansion methods. Generalized ellipsometry model approaches are used for quantitative image analyses. These images are obtained from sets of multiple images obtained under various polarizer, analyzer, and compensator settings. Up to 16 independent Mueller matrix images can be obtained, while our current setup is limited to 11 images normalized by the unpolarized intensity. We demonstrate the anisotropic contrast optical microscope by measuring lithographically defined micro-patterned anisotropic filters, and we quantify the adsorption of an organic self-assembled monolayer film onto the anisotropic filter. Comparison with an isotropic glass slide demonstrates the image enhancement obtained by our method over microscopy without the use of an anisotropic filter. In our current instrument, we estimate the limit of detection for organic volumetric mass within the object plane of ≈49 fg within ≈7 × 7 μm2 object surface area. Compared to a quartz crystal microbalance with dissipation instrumentation, where contemporary limits require a total load of ≈500 pg for detection, the instrumentation demonstrated here improves sensitivity to a total mass required for detection by 4 orders of magnitude. We detail the design and operation principles of the anisotropic contrast optical microscope, and we present further applications to the detection of nanoparticles, to novel approaches for imaging chromatography and to new contrast modalities for observations on living cells

BSA arrangement scenarios on various SAM surfaces.

<p>Left: Scenario 1 –Side-on; Right: Scenario 2: End-on.</p