Nanoporous Materials Can Tune the Critical Point of a Pure Substance

Molecular simulations and NMR relaxometry experiments demonstrate that pure benzene or xylene confined in isoreticular metal–organic frameworks (IRMOFs) exhibit true vapor–liquid phase equilibria where the effective critical point may be reduced by tuning the structure of the MOF. Our results are consistent with vapor and liquid phases extending over many MOF unit cells. These results are counterintuitive since the MOF pore diameters are approximately the same length scale as the adsorbate molecules. As applications of these materials in catalysis, separations, and gas storage rely on the ability to tune the properties of adsorbed molecules, we anticipate that the ability to systematically control the critical point, thereby preparing spatially inhomogeneous local adsorbate densities, could add a new design tool for MOF applications.     

Higher regularity of the free boundary in the parabolic Signorini problem

We show that the quotient of two caloric functions which vanish on a portion of an \(H^{k+ \alpha }\) regular slit is \(H^{k+ \alpha }\) at the slit, for \(k \ge 2\). In the case \(k=1\), we show that the quotient is in \(H^{1+\alpha }\) if the slit is assumed to be space-time \(C^{1, \alpha }\) regular. This can be thought of as a parabolic analogue of a recent important result in De Silva and Savin (Boundary Harnack estimates in slit domains and applications to thin free boundary problems, 2014), whose ideas inspired us. As an application, we show that the free boundary near a regular point of the parabolic thin obstacle problem studied in Danielli et al. (Optimal regularity and the free boundary in the parabolic Signorini problem. Mem. Am. Math. Soc., 2013) with zero obstacle is \(C^{\infty }\) regular in space and time.     

Measurements on a molecular beam apparatus for mass spectrometric study of reactions in flames

Summary The formation of a molecular beam in sampling 1 torr to 1 atm. gases (Ar or H₂) is studied for three diameters of the sampling orifice. To modulate the beam, use is made of a mechanical chopper placed very near the sampling orifice. This enables us to measure the scattering of the beam by collisions between beam molecules. From our measurements it follows that these collisions are very important for >0.020 mm at an initial pressure of 1 atm. We discuss the consequences of our results for mass spectrometric studies of flames.     

Validation of an extractive, airborne, compact TDL spectrometer for atmospheric humidity sensing by blind intercomparison

Accuracy, precision, repeatability and long-term stability, are the most important requirements to enable reliable airborne humidity measurements, which are needed for climate models or to validate e.g. remote sensing instrumentation like satellites. However, various hygrometer artifacts which depend on the individual sensor principle and the application profile frequently cause problems and significantly complicate the hygrometer choice. Sensor intercomparisons are one way of providing the information for an optimal choice. In this paper we present the first part of a blind, static, laboratory-based intercomparison of a new, calibration-free, 1.4 μm diode laser-based, optical hygrometer (SEALDH) with the two most important measurement principles for airborne hygrometry (frost-point hygrometers, FPH, and Lyman-alpha fluorescence hygrometers, LAFH). During three days of measurement, the TDL-hygrometer achieved a H₂O resolution of up to 0.5 ppmv (Δt=2 sec) at tropospheric pressure and H₂O concentration levels (100–800 hPa, 10 to 8000 ppmv H₂O). Its absolute accuracy was investigated via blind intercomparison with two reference FPHs and a LAFH. Without any calibration of SEALDH, i.e. without a comparison to a water vapor standard, we achieve an excellent agreement with the reference sensors, with an average systematic offset (over all three days) of ?3.9 %±1.5 %, which is fully consistent with the sensor’s uncertainty bounds. Further we also reevaluated the SEALDH data of day 2 and 3 in a calibrated mode using an independent set of FPH data from the first day and found an 8-fold accuracy improvement, yielding an excellent overall relative deviation of only 0.52 %±1.5 % with respect to a LAFH and a D/FH sensor.     

Isospectral surfaces with distinct covering spectra via Cayley graphs

The covering spectrum is a geometric invariant of a Riemannian manifold, more generally of a metric space, that measures the size of its one-dimensional holes by isolating a portion of the length spectrum. In a previous paper we demonstrated that the covering spectrum is not a spectral invariant of a manifold in dimensions three and higher. In this article we give an example of two isospectral Cayley graphs that admit length space structures with distinct covering spectra. From this we deduce the existence of infinitely many pairs of Sunada-isospectral surfaces with unequal covering spectra.