The spectral problem for the dispersionless Camassa-Holm equation

We present a spectral and inverse spectral theory for the zero dispersion spectral problem associated with the Camassa-Holm equation. This is an alternative approach to that in [10] by Eckhardt and Teschl

Observation of individual molecules trapped on a nanostructured insulator

For the first time, ordered polar molecules confined in monolayer-deep rectangular pits produced on an alkali halide surface by electron irradiation have been resolved at room temperature by non-contact atomic force microscopy. Molecules self-assemble in a specific fashion inside pits of width smaller than 15 nm. By contrast no ordered aggregates of molecules are observed on flat terraces. Conclusions regarding nucleation and ordering mechanisms are drawn. Trapping in pits as small as 2 nm opens a route to address single molecules

Single layer graphene induces load-bearing molecular layering at the hexadecane-steel interface

The influence of a single layer graphene on the interface between a polished steel surface and the model lubricant hexadecane is explored by high-resolution force microscopy. Nanometer-scale friction is reduced by a factor of three on graphene compared to the steel substrate, with an ordered layer of hexadecane adsorbed on the graphene. Graphene furthermore induces a molecular ordering in the confined lubricant with an average range of 4-5 layers and with a strongly increased load-bearing capacity compared to the lubricant on the bare steel substrate. © 2019 IOP Publishing Ltd

Distance dependence of force and dissipation in non-contact atomic force microscopy on Cu(100) and Al(111)

The dynamic characteristics of a tip oscillating in the nc-AFM mode in close vicinity to a Cu(100)-surface are investigated by means of phase variation experiments in the constant amplitude mode. The change of the quality factor upon approaching the surface deduced from both frequency shift and excitation versus phase curves yield to consistent values. The optimum phase is found to be independent of distance. The dependence of the quality factor on distance is related to 'true' damping, because artefacts related to phase misadjustment can be excluded. The experimental results, as well as on-resonance measurements at different bias voltages on an Al(111) surface, are compared to Joule dissipation and to a model of dissipation in which long-range forces lead to viscoelastic deformations

Revealing the Meissner Corpuscles in Human Glabrous Skin Using In Vivo Non-Invasive Imaging Techniques

The presence of mechanoreceptors in glabrous skin allows humans to discriminate textures by touch. The amount and distribution of these receptors defines our tactile sensitivity and can be affected by diseases such as diabetes, HIV-related pathologies, and hereditary neuropathies. The quantification of mechanoreceptors as clinical markers by biopsy is an invasive method of diagnosis. We report the localization and quantification of Meissner corpuscles in glabrous skin using in vivo, non-invasive optical microscopy techniques. Our approach is supported by the discovery of epidermal protrusions which are co-localized with Meissner corpuscles. Index fingers, small fingers, and tenar palm regions of ten participants were imaged by optical coherence tomography (OCT) and laser scan microscopy (LSM) to determine the thickness of the stratum corneum and epidermis and to count the Meissner corpuscles. We discovered that regions containing Meissner corpuscles could be easily identified by LSM with an enhanced optical reflectance above the corpuscles, caused by a protrusion of the strongly reflecting epidermis into the stratum corneum with its weak reflectance. We suggest that this local morphology above Meissner corpuscles has a function in tactile perception

Null sets of harmonic measure on NTA domains: Lipschitz approximation revisited

We show the David-Jerison construction of big pieces of Lipschitz graphs inside a corkscrew domain does not require its surface measure be upper Ahlfors regular. Thus we can study absolute continuity of harmonic measure and surface measure on NTA domains of locally finite perimeter using Lipschitz approximations. A partial analogue of the F. and M. Riesz Theorem for simply connected planar domains is obtained for NTA domains in space. As a consequence every Wolff snowflake has infinite surface measure.Comment: 22 pages, 6 figure

Human glabrous skin contains crystallized urea dendriform structures in the stratum corneum which affect the hydration levels

Glabrous skin is hair-free skin with a high density of sweat glands, which is found on the palms, and soles of mammalians, covered with a thick stratum corneum. Dry hands are often an occupational problem which deserves attention from dermatologists. Urea is found in the skin as a component of the natural moisturizing factor and of sweat. We report the discovery of dendrimer structures of crystalized urea in the stratum corneum of palmar glabrous skin using laser scanning microscopy. The chemical and structural nature of the urea crystallites was investigated in vivo by non-invasive techniques. The relation of crystallization to skin hydration was explored. We analysed the index finger, small finger and tenar palmar area of 18 study participants using noninvasive optical methods, such as laser scanning microscopy, Raman microspectroscopy and two-photon tomography. Skin hydration was measured using corneometry. Crystalline urea structures were found in the stratum corneum of about two-thirds of the participants. Participants with a higher density of crystallized urea structures exhibited a lower skin hydration. The chemical nature and the crystalline structure of the urea were confirmed by Raman microspectroscopy and by second harmonic generated signals in two-photon tomography. The presence of urea dendrimer crystals in the glabrous skin seems to reduce the water binding capacity leading to dry hands. These findings highlight a new direction in understanding the mechanisms leading to dry hands and open opportunities for the development of better moisturizers and hand disinfection products and for diagnostic of dry skin

Role of friction-induced torque in stick-slip motion

We present a minimal quasistatic 1D model describing the kinematics of the transition from static friction to stick-slip motion of a linear elastic block on a rigid plane. We show how the kinematics of both the precursors to frictional sliding and the periodic stick-slip motion are controlled by the amount of friction-induced torque at the interface. Our model provides a general framework to understand and relate a series of recent experimental observations, in particular the nucleation location of micro-slip instabilities and the build up of an asymmetric field of real contact area.Comment: 6 pages, 5 figure

Atomic Scale Memory at a Silicon Surface

The limits of pushing storage density to the atomic scale are explored with a memory that stores a bit by the presence or absence of one silicon atom. These atoms are positioned at lattice sites along self-assembled tracks with a pitch of 5 atom rows. The writing process involves removal of Si atoms with the tip of a scanning tunneling microscope. The memory can be reformatted by controlled deposition of silicon. The constraints on speed and reliability are compared with data storage in magnetic hard disks and DNA.Comment: 13 pages, 5 figures, accepted by Nanotechnolog