Graphene-directed two-dimensional (2D) nitrogen-doped porous carbon frameworks (GPF) as the hosts for sulfur were constructed via the ionothermal polymerization of 1,4-dicyanobenzene directed by the polyacrylonitrile functionalized graphene nanosheets. As cathodes for lithium–sulfur (Li–S) batteries, the prepared GPF/sulfur nanocomposites exhibited a high capacity up to 962 mA h g⁻¹ after 120 cycles at 2 A g⁻¹. A high reversible capacity of 591 mA h g⁻¹ was still retained even at an extremely large current density of 20 A g⁻¹. Such impressive electrochemical performance of GPF should benefit from the 2D hierarchical porous architecture with an extremely high specific surface area, which could facilitate the efficient entrapment of sulfur and polysulfides and afford rapid charge transfer, fast electronic conduction as well as intimate contact between active materials and the electrolyte during cycling.

By the help of several examples the interactive work with the ClassPad330 is considered. The student can solve difficult exercises of practical applications step by step using the symbolic calculation and the graphic possibilities of the calculator. Sometimes several fields of mathematics are combined to solve a problem. Let us consider the ClassPad330 (with the actual operating system OS 03.03) and discuss on some new exercises in analysis, e.g. solving a linear differential equation by the help of the Laplace transformation and using the inverse Laplace transformation or considering the Fourier transformation in discrete time (the Fast Fourier Transformation FFT and the inverse FFT). We use the FFT- and IFFT-function to study periodic signals, if we only have a sequence generated by sampling the time signal. We know several ways to get a solution. The techniques for studying practical applications fall into the following three categories: analytic, graphic and numeric. We can use the Classpad software in the handheld or in the PC (ClassPad emulator version of the handheld).

The computation of the Coulomb potentials and forces in charged particle systems under 3d-periodic boundary conditions is possible in an efficient way by utilizing the Ewald summation formulas and applying the fast Fourier transform (FFT). In this paper we consider the particle-particle NFFT (P2NFFT) approach, which is based on the fast Fourier transform for nonequispaced data (NFFT) and compare the error behaviors regarding different window functions, which are used in order to approximate the given continuous charge distribution by a mesh based charge density. Typically B-splines are applied in the scope of particle mesh methods, as for instance within the well-known particle-particle particle-mesh (P3M) algorithm. The publicly available P2NFFT algorithm allows the application of an oversampled FFT as well as the usage of different window functions. We consider for the first time also an approximation by Bessel functions and show how the resulting root mean square errors in the forces can be predicted precisely and efficiently. The results show that, if the parameters are tuned appropriately, the Bessel window function is in many cases even the better choice in terms of computational costs. Moreover, the results indicate that it is often advantageous in terms of efficiency to spend some oversampling within the NFFT while using a window function with a smaller support.

A hybrid quantum-classical approach to the interaction of atomic clusters with intense laser fields in the vacuum ultra-violet (VUV) has been developed. Much emphasis is put on localized electrons, those quasi-free electrons which localize about the ions and screen them. These electrons set a time scale, which is used to interpolate between the quantum, rate based description of photon absorption by bound electrons and the classical, deterministic description of the cluster nano-plasma. Typical observables such as total energy absorption, electron and ion spectra are in very good agreement with the experimental findings. A scheme to probe the multi-electron motion in clusters with attosecond laser pulses is introduced. Conventional final state measurements in the energy domain cannot provide information about earlier states of the system due to the incoherent nature of the dynamics. Time-delayed attosecond pulses in the extreme ultra-violet (XUV) are used to probe the transient charging of the cluster ions during the interaction with the laser by measuring the kinetic energy of the electrons detached by the probe pulse. This information is otherwise lost at later times due to recombination. Knowledge about the transient charging would also shed more light on the still controversial subject of the energy absorption mechanisms in the VUV regime. Moving to shorter duration of the excitation, the characteristic time-scales for ionization and plasma equilibration are inversed. An attosecond laser pulse in the VUV regime creates a dense, warm nano-plasma far from equilibrium. Time-delayed attosecond pulses in the XUV probe then both the creation and the relaxation. The latter shows the breakup of the Bogoliubov hierarchy of characteristic times, indicating strongly-coupled plasma dynamics and drawing parallels to the relaxation of extended ultra-cold neutral plasmas with millions of particles.

Das Institut für Kern- und Teilchenphysik (IKTP) der Technischen Universität Dresden (TUD) hat im Forschungszentrum Dresden-Rossendorf (FZD) ein Labor zur Untersuchung von neutroneninduzierten kernphysikalischen Prozessen in Materialien, die für die Fusionsforschung relevant sind, aufgebaut. Das Labor ist ausgestattet mit drei intensiven Neutronenquellen: einer 14 MeV-Neutronenquelle, einer weißen kontinuierlichen Photoneutronen-Quelle, die näher in dieser Arbeit beschrieben wird, und einer gepulsten Photoneutronen-Quelle, die vom FZD inKooperation mit der TUD aufgebaut wurde. Die kontinuierliche Photoneutronen-Quelle basiert auf einem Radiator aus Wolfram (engl. Tungsten Photoneutron Source (TPNS)). TPNS nutzt die im ELBE-Beschleuniger (Elektronen Linearbeschleuniger für Strahlen hoher Brillianz und niedriger Emittanz (ELBE)) beschleunigten Elektronen zur Neutronenerzeugung. Der Prozess läuft über Zwischenschritte ab, indem bei der Abbremsung der Elektronen im Radiator Bremsstrahlungsphotonen entstehen, die anschließend Neutronen durch (γ,xn)-Reaktionen erzeugen. Das Neutronenspektrum der TPNS kann mittels Moderatoren so modifiziert werden, dass es dem in der ersten Wand im Fusionsreaktor entspricht. Dies ermöglicht Untersuchungen mit einem für einen Fusionsreaktor typischen Neutronenspektrum. Die technische Verwirklichung des Projektes, die Inbetriebnahme der Anlage sowie die Durchführung der ersten Experimente zur Neutronenerzeugung ist Inhalt dieser Arbeit. Die Neutronenquelle ist insbesondere für qualitative Untersuchungen in der Fusionsneutronik bestimmt. Der Fusionsreaktor produziert, im Vergleich zu einem Spaltungsreaktor, keine langlebigen Isotope als Abfall. Die wesentliche Aktivität des Reaktors ist in Konstruktionsmaterialien akkumuliert. Durch sorgfältige Auswahl der Materialien kann man die Aktivierung minimieren und damit künftig wesentlich weniger radioaktives Inventar produzieren als in Spaltreaktoren. Ziel der kernphysikalischen Untersuchungen ist, solche Materialien für den Aufbau eines Fusionsreaktors zu erforschen, die niedrigaktivierbar sind, das heißt wenig Aktivität akkumulieren können, und eine Halbwertzeit von einigen Jahren haben. Es ist das Ziel, alle Konstruktionsmaterialien nach 100 Jahren wiederverwenden zu können. Die Neutronenflussdichte einer Photoneutronenquelle ist einige Größenordnungen höher als die, die mittels eines DT-Neutronengenerators mit anschließender Moderation erreicht werden kann. Die gesamte Arbeit ist in drei Teile geteilt. Der erste Teil leitet in die Problematik der Energieversorgung ein und zeigt die Kernfusion als eine vielversprechende Energiequelle der naher Zukunft auf. Das Neutronenlabor der TUD, in dem die TPNS aufgebaut ist, wird ebenfalls kurz vorgestellt. Der zweite Teil befasst sich mit der TPNS selbst, mit ihrem physikalischen Entwurf, der Konstruktion und dem Aufbau bis zu der Inbetriebnahme sowie dem ersten Experiment an der TPNS. Der letzte, dritte Teil ist die Zusammenfassung der vorhandenen Ergebnisse und gibt einen Ausblick auf die zukünftige Vorhaben. / The Institute for Nuclear and Particle Physics at the Technische Universität Dresden (TUD) has build a neutron physics laboratory at Forschungszentrum Dresden-Rossendorf (FZD) to investigate nuclear processes in materials. The experiments are focused on materials relevant to nuclear fusion. The laboratory is equipped with three intensive neutron sources. The first is a 14 MeV monochromatic neutron source based on the DT reaction (owned by TUD); the other two are continuous and pulsed white photoneutron sources based on (γ,xn) reactions. One pulsed photoneutron source is realized by FZD in cooperation with the TUD. The continuous photoneutron source utilises a tungsten radiator (Tungsten Photoneutron Source) to produce neutrons with a wide energy spectra. The TPNS uses the ELBE-accelerator as a source of electrons for neutron production. This process involves an intermediate step, where slowed down electrons produce bremsstrahlung (γ -rays) absorbed by tungsten nuclei. Consecutively, the excited nuclei emit neutrons. The neutron flux of the photoneutron source is five orders of magnitude higher than the flux of the DT neutron sources with appropriate moderation. The neutron spectrum of TPNS can be modified by moderators, in such a way that the spectrum is comparable to that in the first wall of a Tokamak-Reactor. That allows investigations with the typical neutron spectrum of the fusion reactor. The technical solution, initial operation and the first experiment are described in this work. The neutron source is, in particular, dedicated to quantitative investigations in fusion neutronics. A fusion reactor produces radioactive isotopes as a nuclear waste. The main activity is accumulated in the structural materials. Carefully selected structural materials can significantly minimize the activity and thereby the amount of nuclear waste. The purpose of this project is to find constructional materials with half-lives shorter than several years, which can be recycled after about 100 years. The work is divided into three parts. The first part is dedicated to the energy supply problem and nuclear fusion is addressed as a promising solution of the near future. The neutron laboratory housing the TPNS is also briefly described. The second part deals with the tungsten photoneutron source, the design, construction, operation and the first experiments for neutron production. The third part summarises results and presents an outlook for future experiments with the TPNS.

No description available.

We consider multivariate trigonometric polynomials with frequencies supported on a fixed but arbitrary frequency index set I, which is a finite set of integer vectors of length d. Naturally, one is interested in spatial discretizations in the d-dimensional torus such that - the sampling values of the trigonometric polynomial at the nodes of this spatial discretization uniquely determines the trigonometric polynomial, - the corresponding discrete Fourier transform is fast realizable, and - the corresponding fast Fourier transform is stable. An algorithm that computes the discrete Fourier transform and that needs a computational complexity that is bounded from above by terms that are linear in the maximum of the number of input and output data up to some logarithmic factors is called fast Fourier transform. We call the fast Fourier transform stable if the Fourier matrix of the discrete Fourier transform has a condition number near one and the fast algorithm does not corrupt this theoretical stability. We suggest to use rank-1 lattices and a generalization as spatial discretizations in order to sample multivariate trigonometric polynomials and we develop construction methods in order to determine reconstructing sampling sets, i.e., sets of sampling nodes that allow for the unique, fast, and stable reconstruction of trigonometric polynomials. The methods for determining reconstructing rank-1 lattices are component{by{component constructions, similar to the seminal methods that are developed in the field of numerical integration. During this thesis we identify a component{by{component construction of reconstructing rank-1 lattices that allows for an estimate of the number of sampling nodes M |I|\le M\le \max\left(\frac{2}{3}|I|^2,\max\{3\|\mathbf{k}\|_\infty\colon\mathbf{k}\in I\}\right) that is sufficient in order to uniquely reconstruct each multivariate trigonometric polynomial with frequencies supported on the frequency index set I. We observe that the bounds on the number M only depends on the number of frequency indices contained in I and the expansion of I, but not on the spatial dimension d. Hence, rank-1 lattices are suitable spatial discretizations in arbitrarily high dimensional problems. Furthermore, we consider a generalization of the concept of rank-1 lattices, which we call generated sets. We use a quite different approach in order to determine suitable reconstructing generated sets. The corresponding construction method is based on a continuous optimization method. Besides the theoretical considerations, we focus on the practicability of the presented algorithms and illustrate the theoretical findings by means of several examples. In addition, we investigate the approximation properties of the considered sampling schemes. We apply the results to the most important structures of frequency indices in higher dimensions, so-called hyperbolic crosses and demonstrate the approximation properties by the means of several examples that include the solution of Poisson's equation as one representative of partial differential equations.

We consider multivariate trigonometric polynomials with frequencies supported on a fixed but arbitrary frequency index set I, which is a finite set of integer vectors of length d. Naturally, one is interested in spatial discretizations in the d-dimensional torus such that - the sampling values of the trigonometric polynomial at the nodes of this spatial discretization uniquely determines the trigonometric polynomial, - the corresponding discrete Fourier transform is fast realizable, and - the corresponding fast Fourier transform is stable. An algorithm that computes the discrete Fourier transform and that needs a computational complexity that is bounded from above by terms that are linear in the maximum of the number of input and output data up to some logarithmic factors is called fast Fourier transform. We call the fast Fourier transform stable if the Fourier matrix of the discrete Fourier transform has a condition number near one and the fast algorithm does not corrupt this theoretical stability. We suggest to use rank-1 lattices and a generalization as spatial discretizations in order to sample multivariate trigonometric polynomials and we develop construction methods in order to determine reconstructing sampling sets, i.e., sets of sampling nodes that allow for the unique, fast, and stable reconstruction of trigonometric polynomials. The methods for determining reconstructing rank-1 lattices are component{by{component constructions, similar to the seminal methods that are developed in the field of numerical integration. During this thesis we identify a component{by{component construction of reconstructing rank-1 lattices that allows for an estimate of the number of sampling nodes M |I|\le M\le \max\left(\frac{2}{3}|I|^2,\max\{3\|\mathbf{k}\|_\infty\colon\mathbf{k}\in I\}\right) that is sufficient in order to uniquely reconstruct each multivariate trigonometric polynomial with frequencies supported on the frequency index set I. We observe that the bounds on the number M only depends on the number of frequency indices contained in I and the expansion of I, but not on the spatial dimension d. Hence, rank-1 lattices are suitable spatial discretizations in arbitrarily high dimensional problems. Furthermore, we consider a generalization of the concept of rank-1 lattices, which we call generated sets. We use a quite different approach in order to determine suitable reconstructing generated sets. The corresponding construction method is based on a continuous optimization method. Besides the theoretical considerations, we focus on the practicability of the presented algorithms and illustrate the theoretical findings by means of several examples. In addition, we investigate the approximation properties of the considered sampling schemes. We apply the results to the most important structures of frequency indices in higher dimensions, so-called hyperbolic crosses and demonstrate the approximation properties by the means of several examples that include the solution of Poisson's equation as one representative of partial differential equations.

No description available.

No description available.