All-optical measurement of elastic constants in nematic liquid crystals

In this article we present a new all-optical method to measure elastic constants connected with twist and bend deformations. The method is based on the optical Freedericksz threshold effect induced by the linearly polarized electro-magnetic wave. In the experiment elastic constants are measured of commonly used liquid crystals 6CHBT and E7 and two new nematic mixtures with low birefringence. The proposed method is neither very sensitive on the variation of cell thickness, beam waist or the power of a light beam nor does it need any special design of a liquid crystal cell. The experimental results are in good agreement with the values obtain by other methods based on an electro-optical effect

Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces

Reproducing kernel Hilbert spaces (RKHSs) play an important role in many statistics and machine learning applications ranging from support vector machines to Gaussian processes and kernel embeddings of distributions. Operators acting on such spaces are, for instance, required to embed conditional probability distributions in order to implement the kernel Bayes rule and build sequential data models. It was recently shown that transfer operators such as the Perron-Frobenius or Koopman operator can also be approximated in a similar fashion using covariance and cross-covariance operators and that eigenfunctions of these operators can be obtained by solving associated matrix eigenvalue problems. The goal of this paper is to provide a solid functional analytic foundation for the eigenvalue decomposition of RKHS operators and to extend the approach to the singular value decomposition. The results are illustrated with simple guiding examples

A weak characterization of slow variables in stochastic dynamical systems

We present a novel characterization of slow variables for continuous Markov processes that provably preserve the slow timescales. These slow variables are known as reaction coordinates in molecular dynamical applications, where they play a key role in system analysis and coarse graining. The defining characteristics of these slow variables is that they parametrize a so-called transition manifold, a low-dimensional manifold in a certain density function space that emerges with progressive equilibration of the system's fast variables. The existence of said manifold was previously predicted for certain classes of metastable and slow-fast systems. However, in the original work, the existence of the manifold hinges on the pointwise convergence of the system's transition density functions towards it. We show in this work that a convergence in average with respect to the system's stationary measure is sufficient to yield reaction coordinates with the same key qualities. This allows one to accurately predict the timescale preservation in systems where the old theory is not applicable or would give overly pessimistic results. Moreover, the new characterization is still constructive, in that it allows for the algorithmic identification of a good slow variable. The improved characterization, the error prediction and the variable construction are demonstrated by a small metastable system

Resonances in a chaotic attractor crisis of the Lorenz Flow

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as tools for supporting the understanding of critical transitions in chaotic dynamical systems. However, it is in general not clear how the statistical properties of dynamical systems change across a boundary crisis during which a chaotic attractor collides with a saddle. This behavior is investigated here for a boundary crisis in the Lorenz flow, for which neither the Lyapunov exponents nor the covariant Lyapunov vectors provide a criterion for the crisis. Instead, the convergence of the time evolution of probability densities to the invariant measure, governed by the semigroup of transfer operators, is expected to slow down at the approach of the crisis. Such convergence is described by the eigenvalues of the generator of this semigroup, which can be divided into two families, referred to as the stable and unstable Ruelle--Pollicott resonances, respectively. The former describes the convergence of densities to the attractor (or escape from a repeller) and is estimated from many short time series sampling the state space. The latter is responsible for the decay of correlations, or mixing, and can be estimated from a long times series, invoking ergodicity. It is found numerically for the Lorenz flow that the stable resonances do approach the imaginary axis during the crisis, as is indicative of the loss of global stability of the attractor. On the other hand, the unstable resonances, and a fortiori the decay of correlations, do not flag the proximity of the crisis, thus questioning the usual design of early warning indicators of boundary crises of chaotic attractors and the applicability of response theory close to such crises

Eigenschaften der Ca(2+)-Transport-ATPase der Humanerythrozyten nach gezielter Spaltung mit einigen Proteasen

SIGLEAvailable from: Zentralstelle fuer Agrardokumentation und -information (ZADI), Villichgasse 17, D-53177 Bonn / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Kernel-based approximation of the koopman generator and schrodinger operator

Many dimensionality and model reduction techniques rely on estimating dominant eigenfunctions of associated dynamical operators from data. Important examples include the Koopman operator and its generator, but also the Schrödinger operator. We propose a kernel-based method for the approximation of differential operators in reproducing kernel Hilbert spaces and show how eigenfunctions can be estimated by solving auxiliary matrix eigenvalue problems. The resulting algorithms are applied to molecular dynamics and quantum chemistry examples. Furthermore, we exploit that, under certain conditions, the Schrödinger operator can be transformed into a Kolmogorov backward operator corresponding to a drift-diffusion process and vice versa. This allows us to apply methods developed for the analysis of high-dimensional stochastic differential equations to quantum mechanical systems

Interplay of thermo-optic and reorientational responses in nematicon generation

Employing several nematic liquid crystal mixtures, we investigate how the thermo-optic response of nonlinear birefringent soft-matter affects the propagation of light beams and the features of self-induced waveguides. We address the formation of optical spatial solitons and the control of their trajectories versus temperature, comparing the measurements with the expectations based on a simplified model, showing an excellent agreement. Moreover, in a guest⁻host mixture with an absorbing dye dopant, we study the competition between reorientational and thermal nonlinearities, demonstrating that the two processes can be adjusted independently in order to tune the soliton properties, i.e., trajectory and confinement strength. Our results are an important contribution to better comprehend the role played by material properties on linear and nonlinear beam propagation, as well as their exploitation for signal processing and addressing

Experimental verification of hematite ingot mould heat capacity and its direct utilisation in simulation of casting process

Heat capacity of alloys (metals) is one of the crucial thermophysical parameters used for process behaviour prediction in many applications. Heat capacity is an input variable for many thermodynamical (e.g. Thermocalc, Pandat, MTData, …) and kinetic programs (e.g. IDS-Solidification analysis package, …). The dependences of heat capacity on common variables (temperature, pressure, ...) are also commonly used as the input data in software packages (e.g. ProCast, Magmasoft, ANSYS Fluent, …) that are applicable in the field of applied research for simulations of technological processes. It follows from the above that the heat capacities of materials, alloys in our case, play a very important role in the field of basic and applied research. Generally speaking, experimental data can be found in the literature, but corresponding (needed) data for the given alloy can very seldom be found or can differ from the tabulated ones. The knowledge of proper values of heat capacities of alloys at the corresponding temperature can be substantially used for addition to and thus towards the precision of the existing database and simulation software. This study presents the values of C p measured for the hematite ingot mould and comparison of the measured data with the C p values obtained using the software CompuTherm with respect to simulation of technological casting process.Web of Science112148047