Probing the Structure, Pseudorotation, and Radial Vibrations of Cyclopentane by Femtosecond Rotational Raman Coherence Spectroscopy

Femtosecond time-resolved Raman rotational coherence spectroscopy (RCS) is employed to determine accurate rotational, vibration–rotation coupling constants, and centrifugal distortion constants of cyclopentane (C⁵H¹⁰). Its lowest-frequency vibration is a pseudorotating ring deformation that interconverts 10 permutationally distinct but energetically degenerate “twist” minima interspersed by 10 “bent” conformers. While the individual twist and bent structures are polar asymmetric tops, the pseudorotation is fast on the time scale of external rotation, rendering cyclopentane a fluxionally nonpolar symmetric top molecule. The pseudorotational level pattern corresponds to a one-dimensional internal rotor with a pseudorotation constant Bps ≈ 2.8 cm⁻¹. The pseudorotational levels are significantly populated up to l = ± 13 at 298 K; <10% of the molecules are in the l = 0 level. The next-higher vibration is the “radial” ν²³ ring deformation mode at 273 cm⁻¹, which is far above the pseudorotational fundamental. Femtosecond Raman RCS measurements were performed in a gas cell at T = 293 K and in a pulsed supersonic jet at T ≈ 90 K. The jet cooling reduces the pseudorotational distribution to l < ±8 and eliminates the population of ν²³, allowing one to determine the rotational constant as A0 = B0 = 6484.930(11) MHz. This value is ∼300 times more precise than the previous value. The fit of the RCS transients reveals that the rotation–pseudorotation coupling constant αe,psB = −0.00070(1) MHz is diminutive, implying that excitation of the pseudorotation has virtually no effect on the B0 rotational constant of cyclopentane. The smallness of αe,psB can be realized when comparing to the vibration–rotation coupling constant of the ν²³ vibration, αe,23B = −9.547(1) MHz, which is about 10⁴ times larger.

Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces

We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensions of sets by the maximum possible amount is a prevalent subset of the relevant function space. For foliations of a metric space X defined by a David–Semmes regular mapping Π : X → W, we quantitatively estimate, in terms of Hausdorff dimension in W, the size of the set of leaves of the foliation that are mapped onto sets of higher dimension. We discuss key examples of such foliations, including foliations of the Heisenberg group by left and right cosets of horizontal subgroups.

Frequency of Sobolev and quasiconformal dimension distortion

We study Hausdorff and Minkowski dimension distortion for images of generic affine subspaces of Euclidean space under Sobolev and quasiconformal maps. For a supercritical Sobolev map f defined on a domain in RnRn, we estimate from above the Hausdorff dimension of the set of affine subspaces parallel to a fixed m-dimensional linear subspace, whose image under f has positive HαHα measure for some fixed α>mα>m. As a consequence, we obtain new dimension distortion and absolute continuity statements valid for almost every affine subspace. Our results hold for mappings taking values in arbitrary metric spaces, yet are new even for quasiconformal maps of the plane. We illustrate our results with numerous examples.

Distortion-sensitive insight into the pretransitional behavior of 4- n -octyloxy-4′-cyanobiphenyl (8OCB)

Results of studies of the static and dynamic dielectric properties in rod-like 4-n-octyloxy-4'-cyanobiphenyl (8OCB) with isotropic (I)–nematic (N)–smectic A (SmA)–crystal (Cr) mesomorphism, combined with measurements of the low-frequency nonlinear dielectric effect and heat capacity are presented. The analysis is supported by the derivative-based and distortion-sensitive transformation of experimental data. Evidence for the I–N and N–SmA pretransitional anomalies, indicating the influence of tricritical behavior, is shown. It has also been found that neither the N phase nor the SmA phase are uniform and hallmarks of fluid–fluid crossovers can be detected. The dynamics, tested via the evolution of the primary relaxation time, is clearly non-Arrhenius and described via τ(T) = τc(T−TC)−phgr. In the immediate vicinity of the I–N transition a novel anomaly has been found: Δτ ∝ 1/(T − T*), where T* is the temperature of the virtual continuous transition and Δτ is the excess over the 'background behavior'. Experimental results are confronted with the comprehensive Landau–de Gennes theory based modeling.

A centrifugal ice microtome for measurements of atmospheric CO₂ on air trapped in polar ice cores

For atmospheric CO2 reconstructions using ice cores, the technique to release the trapped air from the ice samples is essential for the precision and accuracy of the measurements. We present here a new dry extraction technique in combination with a new gas analytical system that together show significant improvements with respect to current systems. Ice samples (3–15 g) are pulverised using a novel centrifugal ice microtome (CIM) by shaving the ice in a cooled vacuum chamber (−27 °C) in which no friction occurs due to the use of magnetic bearings. Both, the shaving principle of the CIM and the use of magnetic bearings have not been applied so far in this field. Shaving the ice samples produces finer ice powder and releases a minimum of 90% of the trapped air compared to 50%–70% when needle crushing is employed. In addition, the friction-free motion with an optimized design to reduce contaminations of the inner surfaces of the device result in a reduced system offset of about 2.0 ppmv compared to 4.9 ppmv. The gas analytical part shows a higher precision than the corresponding part of our previous system by a factor of two, and all processes except the loading and cleaning of the CIM now run automatically. Compared to our previous system, the complete system shows a 3 times better measurement reproducibility of about 1.1 ppmv (1 σ) which is similar to the best reproducibility of other systems applied in this field. With this high reproducibility, no replicate measurements are required anymore for most future measurement campaigns resulting in a possible output of 12–20 measurements per day compared to a maximum of 6 with other systems.

Distortion-free enhancement of terahertz signals measured by electro-optic sampling. I. Theory

We present three methods for the distortion-free enhancement of THz signals measured by electro-optic sampling in zinc blende-type detector crystals, e.g., ZnTe or GaP. A technique commonly used in optically heterodyne-detected optical Kerr effect spectroscopy is introduced, which is based on two measurements at opposite optical biases near the zero transmission point in a crossed polarizer detection geometry. In contrast to other techniques for an undistorted THz signal enhancement, it also works in a balanced detection scheme and does not require an elaborate procedure for the reconstruction of the true signal as the two measured waveforms are simply subtracted to remove distortions. We study three different approaches for setting an optical bias using the Jones matrix formalism and discuss them also in the framework of optical heterodyne detection. We show that there is an optimal bias point in realistic situations where a small fraction of the probe light is scattered by optical components. The experimental demonstration will be given in the second part of this two-paper series [J. Opt. Soc. Am. B, doc. ID 204877 (2014, posted online)].

Distortion-free enhancement of terahertz signals measured by electro-optic sampling. II. Experiment

Three methods for distortion-free enhancement of electro-optic sampling measurements of terahertz signals are tested. In the first part of this two-paper series [J. Opt. Soc. Am B 31, 904–910 (2014)], the theoretical framework for describing the signal enhancement was presented and discussed. As the applied optical bias is decreased, individual signal traces become enhanced but distorted. Here we experimentally show that nonlinear signal components that distort the terahertz electric field measurement can be removed by subtracting traces recorded with opposite optical bias values. In all three methods tested, we observe up to an order of magnitude increase in distortion-free signal enhancement, in agreement with the theory, making possible measurements of small terahertz-induced transient birefringence signals with increased signal-to-noise ratio.

Color polymorphism and sex ratio distortion in a cichlid fish as an incipient stage in sympatric speciation by sexual selection

We investigated a Lake Victoria cichlid with a complex colour polymorphism that apparently represents one original species and two incipient species, all of which are sympatric. In laboratory breeding experiments we observed sex ratio distortion in certain matings between original and incipient species. Mate choice experiments show that males of the incipient species exhibit mating preferences against the original species, and males and females of the original species exhibit strong mating preferences against the incipient species. Mating preferences might evolve by sex ratio selection to avoid matings with distorted progeny sex ratios. Phenotype frequencies in nature suggest that mating preferences translate into mating frequencies, thus restricting gene flow and exerting disruptive sexual selection between the original and incipient species. The incipient species do not differ in morphology or ecology from the original species, implying that colour polymorphism, associated with sex ratio distortion, can be an incipient stage in sympatric speciation, and that disruption of gene flow can precede ecological differentiation