On the statistical mechanics of the traveling salesman problem

We consider the statistical mechanics of the traveling salesman problem (TSP) and develop some representations to study it. In one representation the mean field theory has a simple form and brings out some of the essential features of the problem. It shows that the system has spontaneous symmetry breaking at any nonzero temperature. In general the phase progressively changes as one decreases the temperature. At low temperatures the mean field theory solution is very sensitive to any small perturbations, due to the divergence of some local susceptibilities. This critical region extends down to zero temperature. We perform the quenched average for a nonmetric TSP in the second representation and the resulting problem is more complicated than the infinite-range spin-glass problem, suggesting that the free energy landscape may be more complex. The role played by frustration in this problem appears explicitly through the localization property of a random matrix, which resembles the tight binding matrix of an electron in a random lattice.     

Das Düsenschwellphänomen beim Austritt einer wandhaftenden anorganischen Glasschmelze aus Strangpreßwerkzeugen mit nichtkreisförmigem Öffnungsquerschnitt

Zusammenfassung Eine ausgeprägte Strangaufweitung tritt bei anorganischen Glasschmelzen dann auf, wenn bei schleichender Strömung eine Haftung zwischen der Wand des Matrizenkanals und dem strömenden Medium gegeben ist. Sie rührt dabei von der Umorientierung der Geschwindigkeitsverteilung von einem parabelförmigen zu einem kastenförmigen Profil her.In den experimentellen Untersuchungen konnte festgestellt werden, daß oberhalb einer bestimmten Kanallänge, d. h. bei ausgeprägten Strömungsverhältnissen im Preßwerkzeug die flächenbezogene Strangaufweitung konstant und dabei insbesondere unabhängig von der Profilform etwa 29% beträgt. Daraus wird gefolgert, daß dieser Betrag dem linearen Wert für den zweidimensionalen Fall des unendlich ausgedehnten Spaltes entsprechen muß.In einer theoretischen Analyse wurde die Berechnung dieses Falles ausgehend von der Stokes-Gleichung mit Hilfe der Methode der finiten Elemente durchgeführt. Aus der sich daraus ergebenden Druck- und Geschwindigkeitsverteilung konnte schließlich die Kontur des austretenden Stranges sowie dessen Endhöhe ermittelt werden.Ein Vergleich der experimentell und rechnerisch ermittelten Werte für die Strangaufweitung zeigt dabei eine recht gute Übereinstimmung und bestätigt dadurch auch die weitgehende Unabhängigkeit der flächenbezogenen Aufweitung von der Querschnittsform des Stranges.

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Inorganic glass melts are showing a characteristic die swell, when in the case of slow motion a strong adhesion between the streaming fluid and the wall of the die channel exists. The reason for this phenomenon is the rearrangement of the velocity profile from a parabolic to a box-type design form.The experimental investigations have demonstrated, that above a certain channel length, this means at distinct flow conditions inside the die channel, the value for the extension of the cross-sectional area is constant of about 29%. Particularly it is independent of the shape of the used die profiles. From this result, it is to deduce that this value must correspond to that of the two-dimensional case of the infinite extended slit.In a theoretical analysis the computation of this case was performed, starting from the Stokes-equation by the finite element method. By means of the resulting pressure and velocity distribution, the contour of the emerging rod and its final thickness could be determined.A comparison between experimental and computational results shows good agreement. So the appreciable independence of the magnitude of the die swell from the profile of the extruded rod is confirmed.

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A Fläche - a ^p ,a ^u Knotenpunktsvariablen für Druck bzw. Geschwindigkeit - a, b Seitenlängen des Rechteckprofils - B =L · N ^u Matrix - D Viskositätsmatrix - f Kräftematrix - K Schwerkraftvektor - K ^p ,K ^u Elementdruckmatrix, Elementgeschwindigkeitsmatrix - L Transformationsmatrix für den ebenen Fall - m Kronecker-Symbol für den zweidimensionalen Strömungszustand - N ^p ,N ^u Ansatzfunktionsmatrizen für Druck bzw. Geschwindigkeit - p Preßdruck - R Radius - T Preßtemperatur - t Lastvektor - u = (w, v) Geschwindigkeitsvektor - _A flächenbezogene Strangaufweitung - _R Aufweitung einer linearen QuerschnittsabmessungR - dynamische Viskosität - Dichte - D u/Dt Substantielle Ableitung der Geschwindigkeit nach der Zeit - T Transponierte einer Matrix (oberer Index) Vorgetragen auf der Jahrestagung der Deutschen Rheologischen Gesellschaft in Berlin vom 13.–15. Mai 1985     

Applications of chalcogenide glass optical fibers

Chalcogenide-glass fibers based on sulfide, selenide, telluride and their rare-earth-doped compositions are being actively pursued worldwide. Great strides have been made in reducing optical losses using improved chemical purification techniques, but further improvements are needed in both purification and fiberization technology to attain the theoretical optical losses. Despite this, chalcogenide-glass fibers are enabling numerous applications that include laser power delivery, chemical sensing, and imaging, scanning near field microscopy/spectroscopy, IR sources/lasers, amplifiers and optical switches.     

Photocatalytic Oxidation of Aniline in the Gas Phase Using Porous TiO2 Thin Films

The gas-phase photocatalytic oxidation of aniline on a new kind of porous nano-TiO₂ composite films is investigated. The composite film was prepared on glass fiber with the water glass as binders and dilute H₂SO₄ solution as solidifying reagent. The surface characters were observed by scanning electron microscope. The photocatalytic degradation of aniline on the composite films was carried out in a TiO₂/UV system. Some important factors affecting the photodegradation, such as the concentration of TiO₂, the initial concentration of aniline, and the existing water vapor, are also studied. The product of photocatalytic oxidation was detected by Fourier transform-Infrared. The partial intermediate products were absorbed on TiO₂ surface, which resulted in catalyst deactivation. But when it was irradiated under UV illumination or solar irradiation for some time, the catalyst could be reused without loss of catalytic activity. Translated from the Journal of Wuhan University (Natural Science Edition), 2005, 51(2) (in Chinese)     

Chiral molecular glass: synthesis and characterization of enantiomerically pure thiophene-based [7]helicene

Synthesis of thiophene-based [7]helicenes, which are functionalized for both design of organic chiral glasses with strong chiroptical properties and for further homologation to higher [n]helicenes, is reported. The key synthetic transformations are kinetic resolution of the intermediate diketone and the annelation step forming the center benzene ring by means of an intramolecular McMurry reaction. Based upon X-ray crystallographic determinations of the absolute configurations for (+)-enantiomers of the diketone and the [7]helicene, stereochemical correlation between the (R) axial chirality of the diketone and the (M) helical chirality of the [7]helicene is established. One such enantiopure trimethylsilyl-substituted [7]helicene possesses enchanced chiroptical properties and forms a chiral molecular glass.     

A novel phosphoramidite method for automated synthesis of oligonucleotides on glass supports for biosensor development

Two protocols for functionalization of glass supports with hexaethylene glycol (HEG)-linked oligonucleotides were developed. The first method (standard amidite protocol) made use of the 2-cyanoethyl-phosphoramidite derivative of 4,4′-dimethoxytrityl-protected HEG. This was first coupled to the support by standard solid-phase phosphoramidite chemistry followed by extension with a thymidylic acid icosanucleotide. Stepwise addition of the linker phosphoramidite graduated at 1% (relative to the total sites available) perstep at 50°C resulted in an optimal yield of immobilized oligonucleotides at a density of 2.24 × 10¹⁰ strands/mm². This observed loading maximum lies well below the theoretical maximum loading owing to nonspecific adsorption of HEG on the glass and subsequent blocking of reactive sites. Surface loadings as high as 3.73 × 10¹⁰/mm² and of excellent sequence quality were achieved with a reverse amidite protocol. The support was first modified into a 2-cyanoethyl-N,N-diisopropylphosphoramidite analog followed by coupling with 4,4′-dimethoxytrityl-protected HEG. This protocol is conveniently available when using a conventional DNA synthesizer. The reverse amidite protocol allowed for control of the surface loading at values suitable for subsequent analytical applications that make use of immobilized oligonucleotides as probes for selective hybridization of sample nucleic acids of unknown sequence and concentration.     

On-column injection onto capillary columns. Part 2: Study of sampling conditions; practical recommendations

During one year continuous use of on-column injection, the typical advantages described in our first report have fully been confirmed. In addition the analysis of large sample volumes has proved promising. Only minor modifications have been applied to the on-column injector device. Broad evidence has been gathered showing that full separation efficiency of the capillary columns after on-column injection is attained only when cold trapping or the solvent effect, as band shortening mechanisms, are working- While, under the conditions of on-column injection, cold trapping is less efficient than with other injection techniques, the opposite holds true for the solvent effect. Compared with splitless injection, the danger of excessive solvent condensation on the column is increased. A working rule is presented for establishing the optimal chromatographic conditions for handling large sample volumes while ensuring full separation efficiency yet avoiding harm to the column.     

Boson peak and fast relaxation process near the glass transition in polystyrene

Atactic polystyrene, both side group and main chain deuterated, was investigated by inelastic neutron scattering in a wide temperature range around the glass transition from 2 to 450 K. In the glass the Boson peak position is only very weakly influenced by the deuteration of the phenyl group. In the neighborhood of the glass transition temperatureT _g we find a fast relaxation process similar to other glasses. The onset of the fast relaxation in polystyrene, however, is observed already at temperaturesT _g — 200 K. Results from partially deuterated polystyrene suggest a change of the phenyl ring dynamics already far belowT _g.     

Measurement of attachment force of microbial cells

A parallel-plate flow chamber consisting of two transparent electro-conductive glass plates was constructed. The two glass plates were set parallel to each other and connected to a potentiostat apparatus to regulate the strength of the electric field between the plates. A microbial cell suspension was flowed through the chamber. This system enabled the application of an electrostatic force to suspend charged particles, e.g. microbial cells, existing between the two plates. The time course of the cell attachment of Pseudomonas syringae pv. atropurpurea NIAES 1309 suspended in 10 mM phosphate buffer solution (pH 7.0) to the glass plate was investigated at various electric field strengths ranging from −4.2 to +4.1 V cm⁻¹. The attachment rate and the maximum number of attached cells increased linearly with the increase in the strength of the positive electric field. In contrast, the rate and the number of cells decreased linearly with the decrease in the strength of the negative electric field. These linear relations gave a specific value for the strength of the electric field (−5.9 ± 0.7 V cm⁻¹) where the electrostatic repulsion and the microbial attachment force were thought to be equal, resulting in no cell attachment. From this value, the electrostatic repulsion, i.e. the microbial attachment force, was calculated to be 5.0 × 10⁻¹¹ N cell⁻¹ for cells of average size.     

Dielectric relaxation of polystyrene with side-chain- and chain-end-labels

Polystyrenes with different concentrations of side groups with cyano groups were prepared and complex dielectric constants were measured in the range of the glass transition temperature and the frequency range of 10^–2–10⁷ Hz.The GPC and DSC measurements showed that the molecular weight of these polystyrenes was about 10500 g/mole and the glass transition temperatures were 89.5°C for all samples.The dielectric relaxation spectra obtained for the side group polystyrene labels and also the chain-end polystyrene labels prepared before [9] were analyzed to find out the degree of coupling of the chain-end and side-group labels with the cooperative reorientation of the polymeric matrix. The analysis of the spectra was carried out using the analysis method developed by Mansour and Stoll [6].The results obtained showed that both end- and side-group labels are strongly coupled with the segmental reorientation and relax with relaxation times longer than that of the segments.The value of logf _m = (logf _m(label)) – logf _m(matrix)) was obtained from the recently designed comparison diagram suggested by Mansour and Stoll [6, 14]. The value of logf _m depends on the label length in the case of chain-end labels.It was surprising to find that the side groups relax slower than the segments by only 0.9 decades. These results obtained implied that the label relaxes through a multistep relaxation mechanism of the side and end groups and not through a diffusion mechanism of the whole chain. In addition, the effective lengths of the relaxing units were determined using the empirical equation obtained before in the case of rodlike molecules in polyisoprene [7].