Permutative Zahlen

Mathematische Semesterberichte - Zur Untersuchung des 2017/18 von H. Hischer kommunizierten Vorkommens von 10-stelligen Dezimalzahlen, die sämtliche Ziffern $$1,2,\ldots, 9$$ enthalten...     

Magnetoelectric effect in cobalt ferrite-barium titanate composites and their electrical properties

CoFe₂O₄-BaTiO₃ composites were prepared using conventional ceramic double sintering process with various compositions. Presence of two phases in the composites was confirmed using X-ray diffraction. The dc resistivity and thermoemf as a function of temperature in the temperature range 300 K to 600 K were measured. Variation of dielectric constant (ɛ′) with frequency in the range 100 Hz to 1 MHz and also with temperature at a fixed frequency of 1 kHz was studied. The ac conductivity was derived from dielectric constant (ɛ′) and loss tangent (tan δ). The nature of conduction is discussed on the basis of small polaron hopping model. The static value of magnetoelectric conversion factor has been studied as a function of magnetic field.     

Development of injection-seeded, pulsed optical parametric generator/oscillator systems for high-resolution spectroscopy

We report the development and application of pulsed optical parametric generator (OPG) and optical parametric oscillator (OPO) systems that are injection seeded with near-infrared distributed feedback diode lasers. The OPG is injection seeded at the idler wavelength without the use of a resonant cavity. Two counter-rotating, beta-barium-borate (β-BBO) crystals are used in the OPG. These crystals are pumped by the third harmonic, 355-nm output of an injection-seeded Nd:YAG laser. An OPO version of the system has also been developed by placing two flat mirrors around the two β-BBO crystals to form a feedback cavity at the signal wavelength. The OPO cavity length is not actively controlled. The output signal beam from the OPG or OPO is amplified using an optical parametric amplifier (OPA) stage with four β-BBO crystals. The frequency bandwidths of the signal and idler laser radiation from OPG/OPA and OPO/OPA systems have been determined to be slightly greater than 200 MHz. The temporal pulses from each system are smooth and near-Gaussian. High-resolution optical absorption measurements of acetylene (C₂H₂) were performed as another check of the frequency spectrum of the idler beam. The frequency-doubled signal output of the OPO/OPA system was used to perform high-resolution, single-photon, laser-induced fluorescence (LIF) spectroscopic studies of the (0,0) vibrational band of the A ²Σ⁺−X ²Π electronic transition of nitric oxide (NO) at low pressure. Excellent agreement was obtained between the theory and the experiment. The signal output of the OPG/OPA system was also used for sub-Doppler, two-photon LIF spectroscopic studies of the same vibration–rotation manifold of NO.This revised version was published online in August 2005 with a corrected cover date.     

High-Performance Lithium Metal Batteries Enabled by a Fluorinated Cyclic Ether with a Low Reduction Potential

Electrolyte engineering is crucial for developing high-performance lithium metal batteries (LMB). Here, we synthesized two cosolvents methyl bis(fluorosulfonyl)imide (MFSI) and 3,3,4,4-tetrafluorotetrahydrofuran (TFF) with significantly different reduction potentials and add them into LiFSI-DME electrolytes. The LiFSI/TFF-DME electrolyte gave an average Li Coulombic efficiency (CE) of 99.41 % over 200 cycles, while the average Li CEs for MFSI-based electrolyte is only 98.62 %. Additionally, the TFF-based electrolytes exhibited a more reversible performance than the state-of-the-art fluorinated 1,4-dimethoxylbutane electrolyte in both Li||Cu half-cell and anode-free Cu||LiNi_0.8Mn_0.1Co_0.1O₂ full cell. More importantly, the decomposition product from bis(fluorosulfonyl)imide anion could react with ether solvent, which destroyed the SEI, thus decreasing cell performance. These key discoveries provide new insights into the rational design of electrolyte solvents and cosolvents for LMB.     

Perturbative theory and modeling of electronic-resonance-enhanced coherent anti-Stokes Raman scattering spectroscopy of nitric oxide

A theory is developed for three-laser electronic-resonance-enhanced (ERE) coherent anti-Stokes Raman scattering (CARS) spectroscopy of nitric oxide (NO). A vibrational Q-branch Raman polarization is excited in the NO molecule by the frequency difference between visible Raman pump and Stokes beams. An ultraviolet probe beam is scattered from the induced Raman polarization to produce an ultraviolet ERE-CARS signal. The frequency of the ultraviolet probe beam is selected to be in electronic resonance with rotational transitions in the A (2)Sigma(+)<--X (2)Pi (1,0) band of NO. This choice results in a resonance between the frequency of the ERE-CARS signal and transitions in the (0,0) band. The theoretical model for ERE-CARS NO spectra has been developed in the perturbative limit. Comparisons to experimental spectra are presented where either the probe laser was scanned with fixed Stokes frequency or the Stokes laser was scanned with fixed probe frequency. At atmospheric pressure and an NO concentration of 100 ppm, good agreement is found between theoretical and experimental spectral peak locations and relative intensities for both types of spectra. Factors relating to saturation in the experiments are discussed, including implications for the theoretical predictions.     

Detection of acetylene by electronic resonance-enhanced coherent anti-Stokes Raman scattering

We report the detection of acetylene (C₂H₂) at low concentrations by electronic resonance-enhanced coherent anti-Stokes Raman scattering (ERE-CARS). Visible pump and Stokes beams are tuned into resonance with Q-branch transitions in the v₂ Raman band of acetylene. An ultraviolet probe beam is tuned into resonance with the – electronic transition of C₂H₂, resulting in significant electronic resonance enhancement of the CARS signal. The signal is found to increase significantly with rising pressure for the pressure range 0.1–8 bar at 300 K. Collisional narrowing of the spectra appears to be important at 2 bar and above. A detection limit of approximately 25 ppm at 300 K and 1 bar is achieved for our experimental conditions. The signal magnitudes and the shape of the C₂H₂ spectrum are essentially constant for UV probe wavelengths from 233.0 to 238.5 nm, thus indicating that significant resonant enhancement is achieved even without tuning the probe beam into resonance with a specific electronic resonance transition. PACS 42.65.Dr; 42.62.Fi; 42.65.-k     

Measurement of nitric oxide concentrations in flames by using electronic-resonance-enhanced coherent anti-Stokes Raman scattering

We have measured nitric oxide (NO) concentrations in flames by using electronic-resonance-enhanced coherent anti-Stokes Raman spectroscopy (ERE-CARS). Visible pump and Stokes beams were tuned to a Q-branch vibrational Raman resonance of NO. A UV probe beam was tuned into resonance with specific rotational transitions in the (v"=1,v'=0) vibrational band in the A(2)Sigma(+)-X(2)Pi electronic transition, thus providing a substantial electronic-resonance enhancement of the resulting CARS signal. NO concentrations were measured at levels down to 50 parts in 10(6) in H(2)/air flames at atmospheric pressure. NO was also detected in heavily sooting C(2)H(2)/air flames at atmospheric pressure with minimal background interference.     

Structure and mixing of a transient flow of helium injected into an established flow of nitrogen: two dimensional measurement and simulation

The transient injection and mixing between nitrogen and helium in a confined chamber at atmospheric pressure is studied experimentally. The 2D injector and mixing chamber contained a middle injection slot for nitrogen flanked by a pair of outer slots for helium. Experiments were conducted by introducing the helium streams into a previously established quasi-steady flow of nitrogen. The nitrogen stream was seeded with nitric oxide (NO) that served as a source for quantitative, planar laser-induced fluorescence (PLIF) imaging of the transient mixing process. PLIF images were acquired by triggering an Nd:YAG laser system at selected times following helium valve actuation. The observed flow structures and extent of mixing between the two streams proved to be highly unsteady and irregular with the helium/nitrogen jets frequently deviating from the centerline toward the confining walls. Representative unsteady CFD solutions also show this same absence of symmetry and the same general flow structures as the measurements, however, they predict somewhat higher helium concentration in recirculation regions than were observed in the measurements.