Experimental and Theoretical Description of Binary Mixtures Containing Monohydric Alcohols

The densities and speeds of sound in the pentan-1-ol + nonan-1-ol, pentan-1-ol + dekan-1-ol, propan-1-ol + hexan-1-ol, and propan-2-ol + hexan-1-ol binary systems have been measured within the whole composition range at 298.15 K. The quantities determined from the measurement data have been plotted as functions of composition. The excess molar volumes have been interpreted on the basis of results of the Symmetrical Extended Real Associated Solution Model (S-ERAS).     

Effizienz kommerziell erwerblicher Silikagele (dp=5 μm und 10 μm) in der Flüssigkeits-Chromatographie

Zusammenfassung 18 kommerziell erwerbliche Kieselgele mit Teilchengrößen (d _p) von 10 m und 5 m wurden systematisch untersucht. Die chromatographisch bestimmte mittlere Teilchengröße (d) ist etwa um 35% größer als die mit Hilfe des Coulter Counter bestimmte Größe (d _c). Die von den Herstellern angegebenend _p-Werte liegen meistens zwischend undd _c. Died-Werte streuten-für die mitd _p=10 m angegebenen Silikagele-zwischen 7,6 m und 12,2 m. Die Konstanten der vereinfachten (10 m Teilchen) bzw der vollständigen (5 m Teilchen) van Deemter Gleichung bei verschiedenen Kapazitäts verhältnissen (k=0–3) und die Asymmetriefaktoren (As) für die Inertsubstanzen wurden gemessen und tabelliert. Beiu=1 mm/s waren die reduzierten Bodenhöhen (h/d) kleiner als 3 für Substanzen mit 0k<3 fürd _p=10 m. Für sämtliche untersuchten Kieselgele waren die Kapazitätsverhältnisse der einzelnen Proben an einer gegebenen stationären Phase mit einer Genauigkeit von ±0.05 reproduzierbar. DieA, B undC Terme der van Deemter Gleichung (d _p=5 m) waren innerhalb von ±10% reproduzierbar, auch dann, wenn die Säule eine Woche trocken gelagert wurde. Die Abnahme vonU _min mit zunehmendenk-Werten hängt sowohl von der Qualität (z.B. geometrischer Form, Enge der Siebfraktion, etc.) der stationären Phase als auch von der Güte der Packungsmethode ab. Für kleinere Teilchen werden die reduzierten Bodenhöhen (h/d)_min größer. Da die Permeabilität der Säulen gemäß der Definition vond immer zud ² proportional ist, nimmt der Druckabfall an der Säule mit abnehmender Teilchengröße wesentlich zu. Die Lebensdauer von Säulen nimmt erfahrungsgemäß mit zunehmendem Druck ab. Die Bandenverbreiterung außerhalb der Säule ist oft bei kommerziell erwerblichen Geräten so groß, daß 10 cm lange Säule (i.D.=4 mm), die mit 5 m. Teichen gepackt wurden, identischen, jedoch mit 10 m Kieselgelen gepackten Säulen, in der Effizienz kaum überlegen sind. Obwohl die Definition vond sphärische Teilchen begünstigt, wenn reduzierte Bodenhöhen errechnet werden, ist die Effizienz von Säulen, die mit sphärischen und unregelmäßigen Teilchen gepackt sind, sehr ähnlich. die Bevorzugung der sphärischen Packungsmaterialien gegenüber den preiswerteren unregelmäßigen Silikagelen scheint experimentell nicht belegbar zu sein. DieA-Terme nehmen mit zunehmendenk-Werten immer zu, obwohl dies von der Theorie hier nicht zu erwarten ist. DieC Terme scheinen überwiegend von der Massentransportgeschwindigkeit in der Eluentenphase bestimmt zu sein. Diek-Abhängigkeit derC-Terme ist mit Hilfe des ausschließlichk-abhängigen Faktors derC _m-Terme der Golay-Gleichung gut zu beschreiben, fallsk>0,75 ist. Allerdings ist die Zunahme derC-Terme vonk=0 aufk=0,75 etwa um einen Faktor 3 kleiner als theoretisch errechenbar ist. Die Stabilität der Säulen wird demonstriert. Obwohl die 20 cm langen Säulen drei Monate lang trocken gelagert wurden, nahm die Effizienz nur vonn=17.000 aufn=15.000 ab. Mit 27 bar Druckabfall wurden 130 theoretische Böden pro Sekunde erreicht. Mittlerer Porendurchmesser, Porenvolumen und spezifische Oberfläche der kommerziell erwerblichen Kieselgele beeinflußten diek-Werte der Probesubstanzen. Obwohl die Variationsbreite dieser Faktoren bei den 18 untersuchten Kieselgelen nicht allzu eng war, beeinflußten diese Parameter die Effizienz der Säulenkaum.

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Efficiency of commerically available silicas in HPLC

Summary Eighteen commercially available silicas having nominal particle sizes (d _p) of 10 m and 5 m, have been systematically studied. The chromatographically determined average particle size (d) is about 35% greater than the average particle size as estimated using a Coulter Counter (d _c). The particle sizes quoted by the manufacturers mostly lie betweend andd _c. Thed values for the silicas with a quotedd _p of 10 m lay between 7.6 m and 12.2 m. The constants of the simplified (for 10 m particles) or the complete (for 5 m particles) van Deemter equation were measured and tabulated for varying capacity ratios (k=0–3) as were the asymmetry factorsAs for an inert substance. When u=1 mm/s the reduced plate height (h/d) was less than 3 for substances with 0k<3 whend _p=10 m. The capacity ratios of individual samples on a given stationary phase were reproducible with an accuracy of ±0.05 for all the silicas studied. TheA, B andC terms of the van Deemter equation (d _p=5 m) were reproducible to within ±10%, even when the column was stored dry for a week. The decrease inu _min with increasingk value depended both on the quality of the stationary phase (e.g., its geometrical form, the narrowness of the sieve fraction) and on the packing method. The reduced plate heights (h/d)_min were bigger for smaller particles. In consequence of the definition ofd, the permeability of a column is always proportional tod ² and the pressure drop in columns with smaller size particles increased substantially. It is a matter of experience that the column life decreases with increasing pressure drop. The extracolumn band broadening of commercial instruments is often so large that 10 cm long columns (i.d.=4 mm) packed with 5 m particles are scarcely more efficient than identical columns packed with 10 m particles. Although the definition ofd favours spherical particles if reduced plate heights are to be calculated, the efficiencies of columns packed with spherical particles are very similar to those packed with irregular particles. The preference for spherical packing material over the cheaper irregular silica does not seems to be supported by experiment. TheA term always increases with increasingk values, although this is theoretically unexpected. TheC terms seems to be overwhelmingly determined by the speed of mass transport in the mobile phase. The dependence of theC term onk is, whenk is >0.75, well described using the exclusivelyk dependent factions of theC _m term of the Golay equation. However, the increase in theC term whenk is increased from 0 to 0.75 is about a factor three less than the theoretically calculated value. The stability of the columns has been demonstrated. Although columns (20 cm long in length) were stored dry for three months the efficiency only decreased slightly. With a 26 bar pressure drop 130 theoretical plates per second were obtained. The average pore diameters, pore volumes and specific surface areas of the commerical silicas influenced thek values of the sample substances. These factors however scarcely affected the column efficiencies even though their range of variation was not very narrow in the 18 silicas studied.

     

An investigation into natural vibrations of fluid–structure interaction systems subject to Sommerfeld radiation condition

A fluid-structure interaction system subject to Sommerfeld＇s condition is defined as a Sommerfeld system which is divided into three categories： Fluid Sommerfeld （FS） System, Solid Sommerfeld （SS） System and Fluid Solid Sommerfeld （FSS） System of which Sommerfeld conditions are imposed on a fluid boundary only, a solid boundary only and both fluid and solid boundaries, respectively. This paper follows the previous initial results claimed by simple examples to further mathematically investigate the natural vibrations of generalized Sommerfeld systems. A new parameter representing the speed of radiation wave for generalized 3-D problems with more complicated boundary conditions is introduced into the Sommerfeld condition which allows investigation of the natural vibrations of a Sommerfeld system involving both free surface and compressible waves. The mathematical demonstrations and selected examples confirm and reveal the natural behaviour of generalized Sommerfeld systems defined above. These generalized conclusions can be used in theoretical or engineering analysis of the vibrations of various Sommerfeld systems in engineering.     

Generalized transformation design: Metrics,speeds, and diffusion

We show that a unified and maximally generalized approach to spatial transformation design is possible, one that encompasses all second order waves, rays, and diffusion processes in anisotropic media. Until the final step, it is unnecessary to specify the physical process for which a specific transformation design is to be implemented. The principal approximation is the neglect of wave impedance, an attribute that plays no role in ray propagation, and is therefore irrelevant for pure ray devices; another constraint is that for waves the spatial variation in material parameters needs to be sufficiently small compared with the wavelength. The key link between our general formulation and a specific implementation is how the spatial metric relates to the speed of disturbance in a given medium, whether it is electromagnetic, acoustic, or diffusive. Notably, we show that our generalized ray theory, in allowing for anisotropic indexes (speeds), generates the same predictions as does a wave theory, and the results are closely related to those for diffusion processes.     

Measurement of speed of sound in poly(lactic acid)-clay composite

We measured longitudinal speed of sound for matrix[poly(lactic acid)]-additive(clay particles) composite rectangular-solid specimen prepared by injection molding. It was found that the speed of sound measured in the direction along the longer side of the specimen was the highest at the middle of the specimen. This trend corresponded with that for crystallinity determined through differential scanning calorimetry (DSC). A cross section view of the specimen parallel to its longer side showed that there was a transverse flow trace of resin in the vicinity of the injection gate while the flow trace along the direction of the longer side spread wider as getting far from the gate toward the middle of the specimen. The high crystallinity appeared in the middle of the specimen was inferred to come from the promotion of crystallization by molecular orientation induced with the above flow trace parallel to the direction along the longer side of the specimen.     

Dimensions and units in electrodynamics

We sketch the foundations of classical electrodynamics, in particular the transition that took place when Einstein, in 1915, succeeded to formulate general relativity. In 1916 Einstein demonstrated that, with a choice of suitable variables for the electromagnetic field, it is possible to put Maxwells equation into a form that is covariant under general coordinate transformations. This unfolded, by basic contributions of Kottler, Cartan, van Dantzig, Schouten & Dorgelo, Toupin & Truesdell, and Post, to what one may call premetric classical electrodynamics. This framework will be described shortly. An analysis is given of the physical dimensions involved in electrodynamics and subsequently the question of units addressed. It will be pointed out that these results are untouched by the generalization of classical to quantum electrodynamics (QED). We compare critically our results with those of L.B. Okun which he had presented at a recent conference.     

Comments on ‘the group velocity of some numerical schemes’

The proper phase and group speeds when quadratic finite elements are applied to the one-dimensional pure advection equation are presented and the myth of a spurious computational mode is dispelled.     

Dynamics of neuronal waves

First of all, by studying the existence and stability of traveling wave fronts of the following nonlinear nonlocal model equation

Almost all triple systems with independent neighborhoods are semi-bipartite

The neighborhood of a pair of vertices u, v in a triple system is the set of vertices w such that uvw is an edge. A triple system H is semi-bipartite if its vertex set contains a vertex subset X such that every edge of H intersects X in exactly two points. It is easy to see that if H is semi-bipartite, then the neighborhood of every pair of vertices in H is an independent set. We show a partial converse of this statement by proving that almost all triple systems with vertex sets [n] and independent neighborhoods are semi-bipartite. Our result can be viewed as an extension of the Erd?s-Kleitman-Rothschild theorem to triple systems.The proof uses the Frankl-Rödl hypergraph regularity lemma, and stability theorems. Similar results have recently been proved for hypergraphs with various other local constraints.