Direct comparison between potential landscape and local density of states in a disordered two-dimensional electron system

The local density of states (LDOS) of the adsorbate induced two-dimensional electron system (2DES) on n-InAs(110) is studied by low-temperature scanning tunneling spectroscopy. The LDOS exhibits irregular structures with fluctuation lengths decreasing with increasing energy. Fourier transformation reveals that the k-values of the unperturbed 2DES dominate the LDOS, but additional lower k-values contribute significantly. To clarify the origin of the additional k-space intensity, we measure the potential landscape of the same 2DES area with the help of the tip induced quantum dot. This allows to calculate the expected LDOS from the single particle Schroedinger equation and to directly compare it with the measured one. Reasonable correspondance between calculated and measured LDOS is found.Comment: 7 pages, 4 figures, submitted to PR

Reactive SINDy: Discovering governing reactions from concentration data

The inner workings of a biological cell or a chemical reaction can be rationalized by the network of reactions, whose structure reveals the most important functional mechanisms. For complex systems, these reaction networks are not known a priori and cannot be efficiently computed with ab initio methods, therefore an important approach goal is to estimate effective reaction networks from observations, such as time series of the main species. Reaction networks estimated with standard machine learning techniques such as least-squares regression may fit the observations, but will typically contain spurious reactions. Here we extend the sparse identification of nonlinear dynamics (SINDy) method to vector-valued ansatz functions, each describing a particular reaction process. The resulting sparse tensor regression method “reactive SINDy” is able to estimate a parsimonious reaction network. We illustrate that a gene regulation network can be correctly estimated from observed time series

A Kohn-Sham system at zero temperature

An one-dimensional Kohn-Sham system for spin particles is considered which effectively describes semiconductor {nano}structures and which is investigated at zero temperature. We prove the existence of solutions and derive a priori estimates. For this purpose we find estimates for eigenvalues of the Schr\"odinger operator with effective Kohn-Sham potential and obtain $W^{1,2}$-bounds of the associated particle density operator. Afterwards, compactness and continuity results allow to apply Schauder's fixed point theorem. In case of vanishing exchange-correlation potential uniqueness is shown by monotonicity arguments. Finally, we investigate the behavior of the system if the temperature approaches zero.Comment: 27 page

Elastic properties of grafted microtubules

We use single-particle tracking to study the elastic properties of single microtubules grafted to a substrate. Thermal fluctuations of the free microtubule's end are recorded, in order to measure position distribution functions from which we calculate the persistence length of microtubules with contour lengths between 2.6 and 48 micrometers. We find the persistence length to vary by more than a factor of 20 over the total range of contour lengths. Our results support the hypothesis that shearing between protofilaments contributes significantly to the mechanics of microtubules.Comment: 9 pages, 3 figure

On the rationality of the moduli space of L\"uroth quartics

We prove that the moduli space M_L of L"uroth quartics in P^2, i.e. the space of quartics which can be circumscribed around a complete pentagon of lines modulo the action of PGL_3(CC) is rational, as is the related moduli space of Bateman seven-tuples of points in P^2.Comment: 7 page

The MIPAS balloon borne trace constitutent experiment

A novel cryogenic Fourier transform spectrometer (FTS) has been developed for limb emission measurements in the mid IR-region from balloon-borne platforms. The FTS is a rapid scanning interferometer using a modified Michelson arrangement which allows a spectral resolution of 0.04 cm(exp -1) to be achieved. Solid carbon-dioxide cooling of the spectrometer and liquid-helium cooling of the detectors provide adequate sensitivity. The line of sight can be stabilized in terms of azimuth and elevation. A three-mirror off-axis telescope provides good vertical resolution and straylight rejection. Calibration is performed by high elevation and internal blackbody measurements. Four balloon flights were performed, two of them during spring turn-around 1989 and 1990 over mid-latitudes (Aire sur L'Adour, France, 44 deg N) and two near the northern polar circle in winter 1992 (Esrange, Sweden, 68 deg N). Limb emission spectra were collected from 32 km to 39 km floating altitudes covering tangent heights between the lower troposphere and the floating altitude. The trace gases CO2, H2O, O3, CH4, N2O, HNO3, N2O5, ClONO2, CF2Cl2, CFCl3, CHF2Cl, CCl4, and C2H6 have been identified in the measured spectra. The 1989 data have been analyzed to retrieve profiles of O3, HNO3, CFCl3 and CF2Cl2. The flights over Kiruna have provided the first ever reported profile measurements of the key reservoir species ClONO2 and N2O5 inside the polar vortex

Atomic clocks with suppressed blackbody radiation shift

We develop a nonstandard concept of atomic clocks where the blackbody radiation shift (BBRS) and its temperature fluctuations can be dramatically suppressed (by one to three orders of magnitude) independent of the environmental temperature. The suppression is based on the fact that in a system with two accessible clock transitions (with frequencies v1 and v2) which are exposed to the same thermal environment, there exists a "synthetic" frequency v_{syn} (v1-e12 v2) largely immune to the BBRS. As an example, it is shown that in the case of ion 171Yb+ it is possible to create a clock in which the BBRS can be suppressed to the fractional level of 10^{-18} in a broad interval near room temperature (300\pm 15 K). We also propose a realization of our method with the use of an optical frequency comb generator stabilized to both frequencies v1 and v2. Here the frequency v_{syn} is generated as one of the components of the comb spectrum and can be used as an atomic standard.Comment: 5 pages, 2 figure