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  • 1
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    Springer
    The European physical journal 25 (1976), S. 339-349 
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We have measured the thermal conductivitiesK s in the superconducting state andK n in the normal state of (La1−x REx) Al2 single crystals (RE: Gd, Ce;x≦0.005) between 0.4 and 8 K. The lattice conductivity is small in the superconducting state above 0.5T c and in the normal state and is independent of annealing. Annealing does, however, strongly depress the ratioK s e /K n e of the electronic thermal conductivities. We also report on a theory of the electronic thermal conductivity which describes the experimental results quantitatively. Interaction effects between impurities show up for the samples with the highest RE-concentration.
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  • 2
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    The European physical journal 25 (1976), S. 369-380 
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study the phase transitions induced by the Jahn-Teller effect ofE-doublet ions in a cubic crystal with antiferrodistortive interactions. AnS=1 pseudospin model is constructed which takes the three lowest vibronic levels of the Jahn-Teller complexes into account. We find a second-order phase transition to a tetragonal phase with two inequivalent sublattices. The transitions between the vibronic levels give rise to bands of collective vibronic excitations with strongly temperature-dependent frequencies. The nature of the various modes is analyzed in detail. We also study the coupling to the elastic displacement field of the crystal. For a sufficiently large coupling constant, this coupling stabilizes a different low-temperature tetragonal phase with two equivalent sublattices. In a certain region of coupling constants, a transition occurs between the two tetragonal phases by second-order transitions to an intermediate phase of lower symmetry. The influence of the coupling on the dynamic behaviour is discussed.
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  • 3
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    The European physical journal 25 (1976), S. 391-399 
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Exact series expansion data of Sykes et al. are used to calculate the average numberc n and perimeters n of clusters of sizen≦20 in the site percolation problem for the triangular, square, and honeycomb lattice. At the percolation thresholdp n we find a sharply peaked distribution of perimeterss n with mean 〈s n 〉=((1−p n )/p c )n+O(n σ ) and width 〈s n 2 〉−〈S n 〉2∝n 1.6 whereσ≃1/βδ=0.39. This “perimeter” 〈s n 〉 should not be interpreted as a cluster “surface” in the usual sense. Two tests confirm the universality hypothesis with reasonable accuracy. The asymptotic decay of the cluster numbersc n withn is consistent with the postulated asymmetry aboutp c : logc n ∝−n ζ forn→∞ withζ≃1 forp〈p c andζ≃1/2 forp〉p c .
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  • 4
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    The European physical journal 25 (1976), S. III 
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
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  • 5
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    The European physical journal 25 (1976), S. 211-218 
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Magnetic circular dichroism (MCD) of theA- andB-absorption band region has been obtained at 4.2 K and 50 kG in KI:Ga+, KI:In+, and KI:Sn2+. The MCD spectra indicate the complex nature of these bands more clearly than the absorption spectra themselves do. TheA-band MCD consists in all cases of a positive and a negative part reflecting the structure of the absorption band. TheB-band MCD shows three peaks, two positive peaks at 4.34 and 4.415 eV (4.09 and 4.175 eV) and a negative peak at 4.38 eV (4.125 eV) in KI:Ga+ (KI:In+). TheB-band in KI:Sn2+ consists of a shoulder (b 0) at 3.76 eV and a main band which has at least 5 sub-peaks (b 1~b 5) at 3.821, 3.841, 3.861, 3.880, and 3.895 eV; each of the subpeaks (b 1~b 5) gives a derivative-like MCD. The MCD shape functionΔf(ε) for the transitiona 1g 2 →a 1g t 1u has been obtained for one set of parameter values by using the classical Franck-Condon approximation and the Monte Carlo integration method. The result can explain the observed salient features of theB- as well asA-band MCD's, indicating the validity of the Franck-Condon approximation and the interaction mode coordinates.
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  • 6
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    The European physical journal 25 (1976), S. 237-246 
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The low temperature paraelectric alignment of substitutional NH 2 - dipole centres in alkali halide crystals is studied measuring the electric field induced variation of the UV absorption and the electro-birefringence (Kerr-effect). We obtain the magnitude of the electric dipole moment and of the anisotropy of the oscillator strength. The reorientation of the dipoles between their equilibrium orientations is investigated by measuring the time dependence of the electro-birefringence after rapid changes of the applied electric field. The results indicate the predominance of one-phonon assisted tunneling processes.
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  • 7
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    Rheologica acta 15 (1976), S. 658-664 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Ein ungewöhnliches Widerstandsverminderungs-Verhalten wird bei dem nicht-ionischen oberflächenaktiven Stoff Lubrol 17A10 in Anwesenheit des Elektrolyten K2SO4 beobachtet. Das System zeigt bei Zimmertemperatur ein normales Turbulenz-Verhalten, erlangt dagegen bei einer Temperatur in der Nähe des Trübungspunktes die Fähigkeit, die Reibung herabzusetzen. Die Konsequenzen eines derartigen Widerstandsverminderungs-Effekts bei erhöhter Temperatur werden unter dem Gesichtspunkt der Verwendbarkeit solcher Additive in Zentralheizungs-Systemen diskutiert.
    Notes: Summary An unusual drag reducing behaviour of the nonionic surfactant Lubrol 17 A 10 in the presence of the electrolyte K2SO4 has been observed. The system shows normal turbulent flow behaviour at room temperature, but depicts an ability to reduce friction when flowing at a temperature at and around its cloud point. The consequences of this elevated temperature drag reduction have been discussed from the viewpoint of using drag reducers in central heating systems.
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  • 8
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    Rheologica acta 15 (1976), S. 99-103 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Diese Arbeit beinhaltet eine Untersuchung des Spannungstensors in nicht-wärmeleitenden nematischen flüssigen Kristallen. Es wird vor allem gezeigt, daß die Theorie vonLee undEringen zwei nicht miteinander verträgliche Darstellungen des Spannungstensors enthält. Die erste scheint nicht imstande zu sein, die Strömungsverhältnisse bei nematischen flüssigen Kristallen richtig zu beschreiben. Von der zweiten wird dagegen gezeigt, daß sie einen ähnlichen Ausdruck für den Spannungstensor liefert wie die Theorie vonEricksen undLeslie.
    Notes: Summary This paper presents an analysis on the stress tensor in non-heat conducting nematic liquid crystals. Essentially it is shown that the Lee-Eringen theory possesses two inconsistent versions for the stress tensor. The first version appears to be incapable of describing the flow problems of nematic liquid crystals and the second version is shown to be similar to the stress tensor as proposed in the Ericksen-Leslie theory.
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  • 9
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    Rheologica acta 15 (1976), S. 120-129 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Es werden notwendige und hinreichende Kriterien dafür entwickelt, daß ein Geschwindigkeitsfeld eine Bewegung mit konstanter Deformationsvorgeschichte (MWCSH) erzeugt, und diese Kriterien werden an einer Anzahl von Beispielen veranschaulicht. Ebenso werden Erweiterungen angegeben, mit Hilfe derer man bestimmen kann, ob eine vorgegebene Deformationsvorgeschichte vom vorgenannten Typ ist.
    Notes: Summary Necessary and sufficient conditions to establish that a velocity field gives rise to a motion with constant stretch history are developed and illustrated with a number of examples. Extensions to determine whether a given strain history is of the above type is also made.
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  • 10
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Summary The viscous flow behaviour of polyacrylamides laboratory samples ofM = 5⋅105–5⋅106) dissolved in water, formamide and glycole in the concentration rangec p =0.1–5% has been investigated. Zero shear data of the aqueous solutions cannot be correlated usingBueche's (c · M) criterion; a good fit of all data is obtained, when the Simha parameterc · [η] is used. Comparison of the flow curves with variation of the solvent clearly shows a dependence on the thermodynamical properties of the polymer/solvent system. The combination of all results gives evidence for the fact, that specific energetic interactions — and not only simple geometric parameters — are a controlling factor in the structure formation (“entanglement”) of moderately concentrated solutions of polar polymers.
    Notes: Zusammenfassung Es wird über das Fließverhalten von Polyacrylamiden (Laborpräparate im MolekulargewichtsbereichM=5⋅105 bis 5⋅106) in Wasser. Formamid und Glykol im Konzentrationsbereichc p =0,1–5% berichtet. Die Viskositätsdaten der wäßrigen Lösungen im 1. newtonschen Bereich lassen sich in geschlossener Form nicht als Funktion von (c·M), sondern als Funktion des Simha-Parametersc·[η] darstellen. Der Vergleich der Fließkurven bei Variation des Lösungsmittels weist auf eine Korrelation mit den thermodynamischen Eigenschaften des Systems Polymer/Lösungsmittel hin. Die Summe der Befunde zeigt, daß spezifisch energetische Wechselwirkungen — und nicht nur rein geometrische Parameter — für die Strukturbildung („Entanglement“) in konzentrierteren Lösungen polarer Polymerer verantwortlich sein müssen.
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  • 11
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    Rheologica acta 15 (1976), S. 577-578 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Es ist bekannt, daß das Verschwinden der materiellen Ableitung des Geschwindigkeitsgradienten eine hinreichende Bedingung dafür darstellt, daß das Geschwindigkeitsfeld eine Bewegung mit konstanter Deformationsvorgeschichte beschreibt. Hier wird eine allgemeinere hinreichende Bedingung abgeleitet, und es wird gezeigt, daß diese zugleich auch eine notwendige Bedingung darstellt.
    Notes: Summary It is known that the vanishing of the material derivative of the velocity gradient is a sufficient condition for the velocity field to be that of a motion with constant stretch history. Here a sufficient condition, more general than this, is derived. It is shown that this is also necessary.
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  • 12
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 13
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    Rheologica acta 15 (1976), S. 585-586 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 14
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    Rheologica acta 15 (1976), S. 612-622 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Das Strömungsfeld einer linear-viskoelastischen Flüssigkeit im Képès-Rheometer wird unter Berücksichtigung der Flüssigkeitsträgheit theoretisch untersucht und eine exakte Lösung angegeben. Das Strömungsfeld einer newtonschen Flüssigkeit ergibt sich als ein Sonderfall dieser Lösung. Die auf die Halbkugeln ausgeübten Kräfte und Drehmomente lassen sich in einfacher Weise aus der Lösung ableiten.
    Notes: Summary The flow field of a linear viscoelastic fluid in the balance rheometer, taking fluid inertia into account, has been studied theoretically and an exact solution is given. The flow field of a Newtonian fluid is included in this solution as a special case. The forces and couples on the hemispheres are readily deduced from this solution.
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  • 15
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    Rheologica acta 15 (1976), S. 642-647 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Die Ergebnisse vonDenson und Mitarb. zur biaxialen Dehnung werden mit den Voraussagen eines nichtlinearen Modells der Viskoelastizität verglichen. Zur Erweiterung der Prüfung werden Meßergebnisse für die uniaxiale Dehnung am gleichen Material, einem kommerziellen Polyisobutylen, herangezogen. Das verwendete Modell scheint beide Dehnströmungstypen mit dem gleichen Wert des einzigen anpaßbaren Parameters in angemessener Weise zu beschreiben.
    Notes: Summary The biaxial extension results byDenson et al. are compared with the predictions of a model of non-linear viscoelasticity. Date of uniaxial extension on the same material (a commercial polyisobutylene) are taken for extending the comparison. The model used seems to adequately describe both types of elongational flow with the same value of the single adjustable parameter.
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  • 16
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    Rheologica acta 15 (1976), S. 654-657 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Mit Hilfe eines Schlitz-Düsen-Rheometers werden die Fließkurven und Viskositätsfunktionen eines sternförmigen Butadien-Styrol-Blockpolymerisats bei 160, 180, 200 und 220°C bestimmt. Bei einer kritischen Schubspannung tritt in den Fließkurven ein Übergang auf, der auf eine Modifikation der Schmelzstruktur hindeutet. Die Fließ-Aktivierungsenergie wird mit einer klassischen Schergeschwindigkeits-Temperatur-Superpositionsmethode abgeleitet; der erhaltene Wert macht für das Stern-Polymerisat das Vorhandensein eines Aggregat-Fließmechanismus wahrscheinlich. Austrittsdruck und Eintrittsdruckabfall werden gemessen und zeigen eine Abhängigkeit von der Schlitztiefe.
    Notes: Summary Flow curves and viscosity functions at 160, 180, 200 and 220 °C have been determined for a star-shaped butadiene-styrene block copolymer, by means of a slit die rheometer. At a critical shear stress, a transition occurs in flow curves, which suggests a modification in the melt structure. The flow activation energy is deduced by a classical shear rate—temperature superposition method, and the obtained value suggests an aggregates flow mechanism for the star-shaped product. Exit pressure and entrance pressure drop are obtained and show a dependence on the slit depth.
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  • 17
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    Rheologica acta 15 (1976), S. 648-653 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Für die Messung des komplexen Elastizitätsmoduls von Polymerfilmen wird eine Resonanzmethode ausgearbeitet und angewendet. Die Untersuchungen verwenden ein zusammengesetztes System, bestehend aus einem Metallblech, das an der einen Seite eingespannt und an der anderen Seite an einen senkrecht dazu angeordneten Polymerfilm angeklebt ist, der seinerseits an seiner andern Seite eingespannt wird. Dieses System liefert bei Anregung durch eine harmonische Kraft mit variabler Frequenz eine Resonanzkurve. Der Ausdruck für die Schwingungsamplitude am Ende des Blechs wird berechnet und ergibt sich als eine Funktion der geometrischen und mechanischen Kenngrößen, wobei das viskoelastische Polymer durchE′1 und tgδ 1 charakterisiert wird. Diese Parameter werden mittels einer iterativen Optimierungs-Methode ausgerechnet. Es wird die Möglichkeit ausgenützt, zur Erhöhung der Meßgenauigkeit sowohl Länge und Dicke der Systemkomponenten als auch den Typ des Blechs zu ändern. Als Anwendungsbeispiel wird ein 50 µm dicker Film von Nylon 6 untersucht.
    Notes: Summary A resonance method was studied and set up for measuring the complex elastic modulus of polymeric films. Investigations were concerned with a composite system consisting of a metal sheet clamped at one end and glued at the other to a polymeric film orthogonal to it, which on its turn was clamped to the other end. The system excited by a variable frequency harmonic force supplied a resonance curve. After an analytical study, the expression is given of the vibration amplitude at the sheet end. It is a function of the geometric and mechanical characteristics of the components: the viscoelastic polymer is characterized byE′1 and tgδ 1. Such parameters are calculated by iterative optimization method. The opportunity is evaluated of operating by conveniently choosing the components length and thickness as well as the sheet type, in order to improve measurement accuracy. An applicative example is given by using a film of nylon 6, 50 µm thick.
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  • 18
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    Rheologica acta 15 (1976), S. 85-98 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Mit Hilfe der Methoden der Thermodynamik irreversibler Prozesse werden nichtlineare rheologische Stoffgleichungen für viskoelastische Polymere abgeleitet. Diese Gleichungen enthalten nur wenige Konstanten, die eine klare physikalische Bedeutung haben. Die Untersuchung ist auf die Hypothese gegründet, daß der hochelastische Zustand, der durch große elastische Dehnungen gekennzeichnet ist, der Zustand des lokalen thermodynamischen Gleichgewichts dieser Stoffe ist. Es wird eine theoretische Erklärung des kinetischen Übergangs von flüssigen Polymeren in den hochelastischen Zustand bei Temperaturen oberhalb der Fließtemperatur gegeben.
    Notes: Summary Nonlinear constitutive equations for viscoelastic polymer media have been derived with the help of irreversible thermodynamical methods. These equations contain a small number of constants which have obvious physical meaning. The work is based on the hypothesis that the high-elasticity state characterized by large elastic strains is the local equilibrium thermodynamical state of these media. A theoretical description is given to explain the kinetic transition of fluid polymer media into high-elasticity state at temperatures above the flow temperature.
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  • 19
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    Rheologica acta 15 (1976), S. 104-119 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Ein System, bestehend aus einer inkompressiblen newtonschen Flüssigkeit mit darin suspendierten starren kugelförmigen Teilchen wird untersucht. Mit Hilfe irreduzibler kartesischer Tensoren erhält man eine explizite Lösung des Stokesschen Problems einer Kugel in einem beliebigen Strömungsfeld. Diese Lösung behält ihre Gültigkeit sogar dann, wenn die Kugeln so klein sind, daß die Haftbedingung der Flüssigkeit nicht länger gültig zu sein braucht (Richardson). Da dann die Brownsche Bewegung nicht länger vernach-lässigt werden kann, wird der Einfluß der thermischen Bewegung untersucht. Während kein Einfluß in einer Couette-Strömung feststellbar ist, ändern sich die Resultate für eine Poiseuille-Strömung drastisch: In einer vertikalen Kapillarströmung stellt sich eine ungleichförmige radiale Verteilung von Teilchen ein, und in einer horizontalen Poiseuille-Strömung wird die scheinbare Viskosität eine Funktion des Kugelradius. Sie nimmt nicht nur mit größer werdendem Radius zu, sondern ist auch immer größer als im Fall auftriebloser Kugeln. Diese Resultate werden über die Bewegungsgleichungen einer Kugelsuspension gewonnen, wobei die Gleichungen mit Hilfe von Ensemble-Mittelwerten hergeleitet werden. Der Vorteil solcher Mittelwerte über Volumenmittelwerte wird aufgezeigt.
    Notes: Summary A system consisting of an incompressible Newtonian fluid in which solid particles of spherical shape are suspended is investiged. Employing irreducibleCartesian tensors an explicit solution to the Stokes problem for a sphere in an arbitrary flow field is obtained, valid even under conditions that the sphere is so small that the customary no-slip assumption need no longer be valid (Richardson). Since in that case Brownian motion cannot be neglected the effect of thermal agitation is studied. While no influence is found for a Couette flow the results for Poiseuille flow are markedly effected: In a vertical tube flow a nonuniform radial distribution of spheres results while for horizontal Poiseuille flow the effective viscosity becomes dependent upon the sphere radius. It increases with increasing sphere radius and is always larger than the corresponding result for truly neutrally buoyant spheres. These results are obtained from the equations governing the mechanical behavior of such a suspension, equations which are derived by means of ensemble averages. The advantage of these averages over the volume averages is demonstrated.
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  • 20
    ISSN: 1435-1528
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  • 21
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Ausgehend von der vonLodge vorgeschlagenen „gummiartigen“ Flüssigkeit wird ein Stoffgesetz in Integralform angegeben, das eine Beschreibung des nicht-linearen Scher- und Dehnungsverhaltens eines Polyäthylens niederer Dichte bei konstanter Deformationsgeschwindigkeit erlaubt, wie es vonMeissner beobachtet wurde. Die Gedächtnisfunktion der „gummiartigen“ Flüssigkeit wird durch eine Dämpfungsfunktionh = exp [ —n $$h = \exp [ - n\sqrt {I_2 - 3} ]$$ ] modifiziert, wobeiI 2 die zweite Invariante des Fingerschen Deformationstensors ist. Die Voraussagen dieses Stoffgesetzes für den zeitlichen Verlauf von Schubspannung, erster Normalspannungsdifferenz und Dehnspannung und für die Schergeschwindigkeitsabhängigkeit von Viskosität und erster Normalspannungsfunktion werden mit experimentellen Ergebnissen verglichen. Für die Beschreibung des nicht-linearen Verhaltens sind drei Stoffkonstanten notwendig: Die Scherviskosität im newtonschen Grenzfall und eine charakteristische Zeitkonstante, die sich aus Experimenten im linear-viskoelastischen Bereich bestimmen lassen, und eine Dämpfungskonstanten = 1/γ s = 1/γ n ,wobei γ s bzw.γ n die Scherdeformation ist, bei der die Schubspannung bzw. die erste Normalspannungsdifferenz ihr Maximum erreicht.
    Notes: Summary A single integral constitutive equation is presented, which gives a reasonable description of the non-linear shear and elongational behavior of a low-density branched polyethylene melt at constant strain rate observed byMeissner. The memory function of this integral equation is a product of the memory function of Lodge's rubber like-liquid theory and a damping functionh = exp [ —n $$h = \exp [ - n\sqrt {I_2 - 3} ]$$ ], whereI 2 is the second invariant of the Finger tensor. Stress- and normal stress overshoot are described as well as shear rate dependence of the transient shear viscosity and the first normal stress coefficient. Tensil stress overshoot and a finite, rate-dependent steady-state elongational viscosity is predicted in simple elongational flow. Three material constants are necessary for this description: a steady-state zero shear viscosity and a characteristic time constant, which both can be determined from data in the linear viscoelastic region, and a damping constantn = 1/γ s = 2/γ n , whereγ s andγ n are the shear strains, which correspond to maximum shear stress and maximum first normal stress difference respectively.
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  • 22
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    Rheologica acta 15 (1976), S. 156-162 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Zu der in Teil I formulierten Bedingung der statistischen Invarianz wird hier noch eine die Geschwindigkeit der Energiedissipation in einem veränderlichen Netzwerk betreffende Annahme (energetic assumption) hinzugefügt. Das einfachste Netzwerk-Modell, das diesen beiden Bedingungen genügt, wird mit einiger Ausführlichkeit untersucht. Dieses sagt nicht-newtonsche Viskosität, Überschießen beim Spannversuch, ausgeprägte Instabilitäten beim Kriechversuch („katastrophisches Kriechverhalten“) und ein mit den experimentellen Beobachtungen gut übereinstimmendes Verhältnis der zweiten zur ersten Normalspannungsdifferenz (von — 1/6 bei kleinen Schergeschwindigkeiten) voraus. Anschließend wird gezeigt, daß das Ergebnis betreffend das Verhältnis der Normalspannungsdifferenzen bei kleinen Schergeschwindigkeiten für die gesamte Klasse von Netzwerk-Flüssigkeiten gilt, welche die beiden oben genannten Bedingungen erfüllen.
    Notes: Summary A general “energetic assumption” concerning the rate of dissipation of the energy in an impermanent network is added to the condition of statistical invariance formulated in part I. The simplest network model obeying both conditions is analysed in some detail. Non-Newtonian viscosity, overshoot effects, gross instability effects in creep experiments (catastrophic creep behaviour) and a correct ratio (= −1/6 at small shear rates) of the secondary — to the primary normal stress difference in steady shear are predicted by this model. The result concerning the normal stress ratio at small velocity gradients is shown to apply to the general class of network fluids obeying both the condition of statistical invariance and the energetic assumption.
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  • 23
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    Rheologica acta 15 (1976), S. 179-188 
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Es wird das Phänomen des Überschießens der Spannung (beim Spannversuch) theoretisch und experimentell untersucht mit dem Ziel, zwischen einem (scheinbaren) Überschießen infolge instrumenteller Gegebenheiten und einem (wirklichen) Überschießen infolge von Stoffeigenschaften zu unterscheiden. Die Experimente werden mit einem Weissenberg-Rheogoniometer ausgeführt, und es wird dem Einfluß der Eigenfrequenz des Drehmoment-Meßsystems sowie den Randeffekten besondere Aufmerksamkeit geschenkt. Die experimentellen Ergebnisse für newtonsche Flüssigkeiten zeigen eine ausgezeichnete Übereinstimmung mit den theoretischen Voraussagen. Im Falle der elastischen Flüssigkeiten sind die experimentellen Ergebnisse in qualitativer Übereinstimmung mit den Voraussagen für eine einfache viskoelastische Modellflüssigkeit. Es werden keine signifikanten Abweichungen infolge von Randeffekten gefunden. Man kommt zu dem Schluß, daß es sich trotz der Möglichkeit einer deutlichen Beeinflussung durch instrumentelle Faktoren beim Überschießen der Spannung dennoch primär um die Auswirkung einer Stoffeigenschaft handelt.
    Notes: Summary We give theoretical and experimental consideration to the stress overshoot phenomenon and attempt to distinguish between (apparent) overshoot arising frominstrument effects and (real) overshoot which can be regarded as a property of the material. The experiments are performed on a Weissenberg Rheogoniometer and particular attention is paid to the effect of the natural frequency of the torquemeasuring system and also to edge effects. The experimental results for Newtonian liquids are found to be in excellent quantitative agreement with the theoretical predictions. In the case of elastic liquids, the experimental results are in qualitative agreement with the predictions for a simple elastico-viscous model. We do not find any significant evidence of aberrations due to edge effects. It is concluded that although stress overshoot can be significantly affected by instrument factors, it is nevertheless a true material property.
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    Rheologica acta 15 (1976), S. 207-208 
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    Rheologica acta 15 (1976), S. 199-205 
    ISSN: 1435-1528
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    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Summary Some polymer melts do not stick to solid surfaces but exhibit wall slipping properties (e. g. PVC). In spite of its influence on the flow in general and on the processing conditions in particular there is little and contradicting information available on such polymers. This may be connected with certain inferiorities of the known methods for obtaining slip properties. The present paper deals with the application of a certain method for this purpose. After various preliminary tests HDPE as a wall sticking and rigid PVC as a wall slipping model fluid has been studied. For the PVC dimensionless slip values up to 95% have been found (443 K). That leads to the conclusion that the presented method may be applied for studying slip properties of polymer melts.
    Notes: Zusammenfassung Neben wandhaftenden Polymerschmelzen sind auch solche bekannt, die an festen Wänden gleiten. Insbesondere gilt das für das wirtschaftlich wichtige PVC. Trotz der Auswirkungen des Gleitverhaltens auf die Fließ- bzw. Verarbeitungsprozesse liegen hierzu nicht genügend und häufig widersprüchliche Ergebnisse vor. Da dies mit den Unzulänglichkeiten der aus der Literatur bekannten Meßmethoden zusammenhängt, wird in der vorliegenden Arbeit eine für einen anderen Zweck bekannte visuelle Meßmethode hinsichtlich ihrer Brauchbarkeit für die Ermittlung des Gleitverhaltens untersucht. Nach umfangreichen Vorversuchen, die zu wichtigen Korrekturgrößen für die eigentlichen Meßwerte führten, sind vergleichende Messungen an Niederdruckpolyäthylen als wandhaftender Substanz und an Hart-PVC als wandgleitender Substanz durchgeführt worden. Die für das PVC bei 443 K gefundenen dimensionslosen Gleitanteile von ca. 95% zeigen, daß das beschriebene Meßverfahren prinzipiell für den gedachten Zweck verwendbar ist.
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    Rheologica acta 15 (1976), S. 209-214 
    ISSN: 1435-1528
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    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Es wird die Lösung des stationären Grenzschichtproblems inkompressibler mikropolarer Flüssigkeiten für den Fall der Nichtähnlichkeit bei zweidimensionalen und achsensymmetrischen Körpern vorgelegt. Die dem Problem zugrunde liegenden partiellen Differentialgleichungen werden durch Einführung neuer Koordinaten auf ein endliches Gebiet transformiert. Die so erhaltenen Gleichungen werden mit Hilfe eines impliziten Differenzenverfahrens numerisch gelöst. Die Rechnung wird für den Zylinder und die Kugel durchgeführt. Die Ergebnisse zeigen, daß die Grenzschichtablösung früher erfolgt als bei vergleichbaren newtonschen Flüssigkeiten. Wandreibung und Geschwindigkeitsprofile hängen von der Gestalt des Körpers ab und sind nahezu unempfindlich gegen Mikrorotation und Kopplungsparameter, vorausgesetzt, daß der letztere klein ist. Dagegen hängen das Profil und der Gradient der Mikrorotation vom Parameter der Mikrorotation ab und sind ebenfalls unempfindlich gegen die Kopplungsparameter.
    Notes: Summary The solution of the steady laminar incompressible nonsimilar boundary-layer problem for micropolar fluids over two-dimensional and axisymmetric bodies has been presented. The partial differential equations governing the flow have been transformed into new co-ordinates having finite range. The resulting equations have been solved numerically using implicit finite-difference scheme. The computations have been carried out for a cylinder and a sphere. The results indicate that the separation in micropolar fluids occurs at earlier streamwise locations as compared to Newtonian fluids. The skin friction and velocity profiles depend on the shape of the body and are almost insensitive to microrotation or coupling parameter, provided the coupling parameter is small. On the other hand, the microrotation profiles and microrotation gradient depend on the microrotation parameter and they are insensitive to the coupling parameter.
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    Rheologica acta 15 (1976), S. 223-230 
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    Description / Table of Contents: Zusammenfassung Es gibt keine Rechtfertigung für die Behauptung, daß viskoelastische Modelle, die eine schergeschwindigkeitsabhängige Memory-Funktion haben, nicht zulässig sind. Veröffentlichte Behauptungen entgegengesetzten Inhalts werden als unbegründet bewiesen. Es wird gezeigt, daß zwar die experimentellen Tatsachen die Unzulässigkeit von konstituierenden Gleichungen mit Schergeschwindigkeitsabhängigkeit nicht beweisen, wohl aber auf notwendige Kennzeichen für die Zulässigkeit einer größeren Klasse solcher Modelle hinweisen. Das Vorhandensein eines Spektrums der Viskosität (oder des Elastizitätsmoduls) und von charakteristischen Zeiten in der Memory-Funktion, sowie auch die Abhängigkeit der Memory-Funktion von der Schergeschwindigkeitsvorgeschichte (von der „Anregungszeit“ bis zur „Beobachtungszeit“), erweisen sich als zwei solcher Kennzeichen der allgemeinen viskoelastischen konstituierenden Gleichung vonCarreau (1), die sich auf die Theorie der Gaußschen Netzwerke vonLodge(2) stützt. Dies ist das wohl bekannteste und am meisten abgehandelte Beispiel eines annehmbaren Modells mit Schergeschwindigkeitsabhängigkeit.
    Notes: Summary There is no justification for the claim that viscoelastic models having deformation rate dependent memory functions are inadmissible. Published statements to the contrary are shown to be unfounded. It is shown that while the experimental evidence does not establish the inadmissibility of rate-dependent constitutive equations, it does indicate necessary characteristics for acceptability of one broad class of these models. The existence of a spectrum of viscosities (or elastic moduli) and characteristic times in the memory function and the dependence of the memory function on the history of the rate of deformation from the time of “excitation” to the time of “observation” are shown to be two such characteristics for the general viscoelastic constitutive equation ofCarreau (1) which is based on the Gaussian network theory ofLodge (2). This is perhaps the best known and most extensively evaluated example of an acceptable rate-dependent model.
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    Rheologica acta 15 (1976), S. 238-241 
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    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Ein vonBradley entwickeltes Modell für die Zerstäubung von Flüssigkeiten durch Gase, die mit hoher Geschwindigkeit strömen, wird auf elastische Flüssigkeiten ausgedehnt. Es werden numerische Ergebnisse über die Abhängigkeit der am häufigsten vorkommenden Tropfengröße von der Elastizität mitgeteilt. Dabei wird gezeigt, daß Elastizität der betrachteten Art eine Verringerung der Tropfengröße bewirkt.
    Notes: Summary The mathematical model of high velocity gas atomization developed byBradley is extended to include liquids which possess elasticity. Numerical results exhibiting the dependence of the most frefrently occurring drop size upon elasticity are presented. It is shown that elasticity of the type considered has the effect of reducing the predicted drop size.
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    ISSN: 1435-1528
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    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Ein modifizierter Kegel-Platte-Apparat wird beschrieben, der entworfen wurde, um die Strömungsdoppelbrechung polymerer Schmelzen in einem großen Bereich von Schergeschwindigkeiten zu messen. Meßergebnisse an Proben von Polyäthylen hoher und niedriger Dichte, sowie von Polystyrol, werden wiedergegeben. Anomalien, die an den Auslöschungswinkelkurven in der Nähe der Ordnungen, bei denen der Phasenunterschied Vielfache von 2π beträgt, gefunden wurden, weisen auf ausgeprägte Randeffekte hin, die offenkundig von der Natur des Polymeren abhängen. Die Messungen an der Probe des Polyäthylens hoher Dichte wurden dazu verwendet, die Gültigkeit des spannungsoptischen Gesetzes zu prüfen. Die Messungen an der Probe des Polyäthylens niedriger Dichte zeigen mechanische Degradierung an. Einige typische Übergangsmessungen an der Polystyrolprobe werden beschrieben. Die erhaltenen Ergebnisse werden mit entsprechenden Ergebnissen mechanischer Messungen, die mit Hilfe des Weissenberg-Rheogoniometers erhalten wurden, verglichen, wobei die erwartete Übereinstimmung gefunden wurde.
    Notes: Summary A description is given of a modified cone-and-plate apparatus designed for the measurement of the flow birefringence of polymer melts in a wide range of shear rates. Results are given of measurements on samples of high and low density polyethylene and polystyrene. Anomalies, as found in the extinction angle curves near the fringes, where the phase differences become equal to multiples of 2π, point to pronounced edge effects which appear to depend on the type of polymer. The measurements on the high density polyethylene were used to check the validity of the stress-optical law. The measurements on the low density polyethylene sample show mechanical degradation of this polymer. Some typical transient measurements on the polystyrene sample are presented and successfully related to the corresponding mechanical measurements, as obtained with the aid of a cone-and-plate Weissenberg rheogoniometer.
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    Description / Table of Contents: Zusammenfassung In der vorliegenden Arbeit wird die Scherströmung analysiert, die in einem zur Messung der Strömungsdoppelbrechung polymerer Schmelzen dienenden geschlossenen Kegel-Platte-Rheometer auftritt. Die Abhängigkeit der Viskosität von der Schergeschwindigkeit und der Temperatur wird mit Hilfe einer Beziehung berücksichtigt, die das Modell der unelastischen Ostwald-De Waele-Flüssigkeit mit einer exponentiellen Temperatur-Abhängigkeit verbindet. Geschwindigkeits-und Temperaturprofile werden berechnet. Unter anderem wird gezeigt, wie die viskose Dissipation das Geschwindigkeitsfeld stören kann.
    Notes: Summary In this paper an analysis is given of the shear flow which occurs in a closed cone-and-plate rheometer, as is used for the measurement of the flow birefringence of polymer melts. The influences of shear rate and temperature on the fluid viscosity are taken into account by the use of a relation which combines the concept of the inelastic “power law fluid” with that of an exponential temperature dependence. Velocity and temperature profiles are calculated. Among other things it is shown, how viscous dissipation can disturb the flow field.
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    Rheologica acta 15 (1976), S. 516-516 
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    ISSN: 1435-1528
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    Description / Table of Contents: Zusammenfassung Ein koaxialer Zylinderapparat für die Messung der Strömungsdoppelbrechung von polymeren Schmelzen wird beschrieben. Der Meßbereich des Apparates beschränkt sich auf extrem kleine Schergeschwindigkeiten (~10−3 s−1). Die Eignung für Messungen unter zeitlich veränderlichen Spannungszuständen ist von Bedeutung. Veränderliche Schub- und Normalspannungen, die beim Einschalten einer konstanten Schergeschwindigkeit wachsen und beim Ausschalten wieder relaxieren, werden mit Hilfe der Strömungsdoppelbrechung untersucht. Zu diesem Zweck wird die Gültigkeit der spannungsoptischen Regel einer genauen Prüfung unterzogen. Das Modell der „rubberlike liquid“, wie es vonLodge vorgeschlagen wurde, wird zur Beschreibung des Fließverhaltens polymerer Schmelzen herangezogen. Die Wahl dieses Modelles erfolgte in erster Linie deshalb, weilLodges Gleichungen sich für die Anwendung einer Methode eignen, die ursprünglich vonSchwarzl undStruik für die praktische Berechnung von Relationen zwischen linear-viskoelastischen Funktionen entwickelt wurde. Auf diese Weise konnten quantitative Kriterien für die Gültigkeit desLodgeschen Flüssigkeitsmodelles erstellt werden. Im speziellen Fall wurden die dynamischen Speicher- und Verlustmoduln als Referenzfunktionen für die Interpretation der Strömungsdoppelbrechung verwendet. Das „rubberlike-liquid“-Modell erweist für polymere Schmelzen Brauchbarkeit für extrem kleine Schergeschwindigkeiten und, bei beliebigen Schergeschwindigkeiten, für totale Schubdeformationen kleiner als eins.
    Notes: Summary A description is given of a coaxial cylinder apparatus, suitable for the measurement of the flow birefringence of polymer melts at extremely low shear rates (~10−3 s−1) and, in particular, under transient conditions. Transient stresses including normal stresses, which grow after a suddenly imposed constant rate of shear and relax after a sudden cessation of a steady shear flow, are investigated with the aid of the flow birefringence technique. For this purpose use is made of the stress-optical law, which is carefully checked. Lodge's rubberlike liquid model is chosen for the description of the flow behaviour of polymer melts. One of the primary reasons for this choice lies in the fact thatLodge's equations are suitable for the application of a method which was originally designed bySchwarzl andStruik for the practical calculation of interrelations between linear viscoelastic functions. In this way it was possible to find quantitative criteria for the limits of validity of the rubberlike liquid model. In particular, the dynamic storage and loss moduli were used as reference functions for the interpretation of the flow birefringence data. The rubberlike liquid model appears to be valid for polymer melts at extremely low rates of shear and, for any rate of shear, when the total shear applied, does not exceed unity.
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    Rheologica acta 15 (1976), S. 329-355 
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    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Summary After a short review of the relations between drag reduction and flow laminarization in dilute solutions of long chain polymers in pipe flow the present status of research of the stability of such solutions in Couette flow is outlined. Existing discrepancies and contradictions are pointed out. Then the Couette apparatus used for the measurements is described together with the methods for temperature control and flow visualization. The test solutions — polyacrylamide (Separan AP 30)-solutions in water and various glycerol-water mixtures in concentrations from 5 to 1000 ppm — are investigated with respect to pH-value effects and for biological and mechanical degradation. A standard procedure for the preparation of the solutions is developed. The flow curves of these solutions are measured in a range of about 6 decades of the rate of shear. The reduced viscosity (Staudinger function) is calculated therefrom. These solutions show four different types of instabilities: spiral-type, oscillatory, steady instabilities and turbulence. The critical Reynolds-number for each type is determined as a function of polymer concentration and the age of the solution. Normally one observes first an increase and then a decrease in the stabilization effect. Increasing the concentration further a destabilization is sometimes found. Spiral-type instabilities always show destabilization. For instabilities of the cellular type with increasing solution concentration an increasing length of the cells is measured. An attempt is made to explain these effects by the structural properties of the polymer solutions. These phenomena are related to phenomena observed in pipe flow experiments and compared with earlier observations.
    Notes: Zusammenfassung Nach einem kurzen Überblick über die Beziehungen zwischen Widerstandsverminderung (drag reduction) und Laminarisierung bei verdünnten Lösungen sehr langkettiger Polymerer in einer Rohrströmung · wird auf die bisherigen Untersuchungen der Stabilität solcher Lösungen in der Couette-Strömung eingegangen, und es werden die noch bestehenden Unklarheiten und Widersprüche aufgezeigt. Anschließend werden die zur Durchführung der eigenen Untersuchungen konstruierte Couette-Apparatur sowie die Methoden der Temperierung und der Sichtbarmachung der Strömung beschrieben. Die Versuchsflüssigkeiten — Polyacrylamid (Separan AP 30)-Lösungen in Wasser und verschiedenen Glycerin-Wasser-Mischungen mit Konzentrationen zwischen 5 und 1000 ppm — werden auf den Einfluß des pH-Werts, des biologischen und mechanischen Abbaus und der Alterungseinflüsse untersucht, und es wird eine Standard-Ansatzmethode entwickelt. Die Fließkurven dieser Lösungen werden über ca. 6 Zehnerpotenzen der Schergeschwindigkeit bestimmt und daraus die Staudinger-Funktion (reduced viscosity) abgeleitet. Bei diesen Lösungen werden vier verschiedene Typen von Instabilitäten beobachtet: spiralartige, schwingende, stationäre Instabilitäten und Turbulenz. Die zugeordneten kritischen Reynolds-Zahlen werden in Abhängigkeit von der Polymerkonzentration und vom Alter der Lösungen bestimmt. Man beobachtet zumeist eine mit wachsender Polymerkonzentration erst zunehmende, dann aber wieder abnehmende Stabilisierung, die schließlich sogar in eine Destabilisierung übergeht; bei den spiralartigen Instabilitäten wird von Anfang an Destabilisierung gefunden. Für die stationären Instabilitäten vom Zellular-Typ werden außerdem die Längen der Zellen gemessen und dabei eine mit steigender Konzentration zunehmende Länge festgestellt. Diese Effekte werden aus der Struktur der Polymerlösungen zu deuten versucht, mit den in der Rohrströmung beobachteten Phänomenen in Zusammenhang gebracht und mit den Ergebnissen der früheren Untersuchungen verglichen.
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    Rheologica acta 15 (1976), S. 367-378 
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    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Unter der Beschränkung auf Deformationen, für welche Invarianz gegen Verschiebungen in der Zeit vorliegt, wird eine Reihe von Modellen zur Voraussage des viskoelastischen Verhaltens isotroper weicher Polymerer entwickelt. Diese Modelle beschreiben die zeitabhängige Spannung durch ein Boltzmannsches Superpositionsintegral, in das ein geeignet gewähltes nicht-lineares Dehnungsmaß eingeführt wird. Die Theorie wird in der allgemeinen drei-dimensionalen Form dargestellt. Sie verwendet eine einzige Zeitfunktion, nämlich den Relaxationsmodul der linearen Theorie der Viskoelastizität. In der einfachsten Form enthält das Dehnungsmaß nur einen Stoffparameter.
    Notes: Summary Restricting consideration to deformations in which time shift invariance is preserved, a series of models was developed for the prediction of the viscoelastic behavior of isotropic soft polymers. The models describe the time dependent stress through the Boltzmann superposition integral incorporating into it an appropriately chosen nonlinear measure of strain. The theory was developed in its most general threedimensional form. It requires a single time function, the relaxation modulus of linear viscoelastic theory. In its simplest form the strain measure contains a single material parameter.
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    Rheologica acta 15 (1976), S. 508-515 
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    Description / Table of Contents: Zusammenfassung Die Zahl der Veröffentlichungen pro Jahr nimmt auf dem Gebiet der Rheologie ebenso wie auf anderen Gebieten stetig zu. Es erscheint daher an der Zeit, auf eine stärkere Nutzung vorhandener Dokumentationsdienste hinzuwirken. Die Deutsche Rheologische Gesellschaft, 1 Berlin 45, Unter den Eichen 87, gibt gemeinsam mit der Bundesanstalt für Materialprüfung in regelmäßiger Folge einen international verwendbaren Dokumentationsdienst Rheologie heraus, der einen weitgehend vollständigen und nach Sachgebieten geordneten Nachweis der einschlägigen Weltliteratur enthält. Die erfaßten Arbeiten betreffen die allgemeinen Grundlagen der Rheologie, die Rheometrie, das rheologische Verhalten von Polymerschmelzen und -lösungen, Kunststoffe und Kautschuk, Metalle, Pasten, Kolloide und Suspensionen, Böden, Keramik, Beton, pharmazeutische Präparate und Kosmetika, Lebensmittel, Verfahrenstechnik, Formungsvorgänge, Strömungs- und Fließvorgänge, Mischvorgänge usw. Der Dokumentationsdienst steht allen Interessenten gegen einen Unkostenbeitrag zur Verfügung. Seine Herausgabe wurde dadurch veranlaßt, daß die in der systematischen Erfassung, Ordnung, Auswertung und Anwendung der bereits erzielten und veröffentlichten Forschungs- und Untersuchungsergebnisse noch liegenden Möglichkeiten längst nicht ausreichend genutzt werden. Sowohl eine gezieltere und intensivierte Forschung und Entwicklung einerseits als auch eine weitere Rationalisierung und Kostensenkung im Bereich der Praxis andererseits setzen eine bessere Anwendung bisher erzielter Ergebnisse voraus. Die Dokumentation Rheologie bezieht sich daher sowohl auf die Grundlagenforschung als auch auf die Belange der betrieblichen Praxis. Mit Hilfe dieser Dokumentation werden Recherchen zu allgemeinen und speziellen Fragestellungen aus Forschung und Praxis der Rheologie wesentlich erleichtert. Solche Recherchen bieten die Gewähr, daß zu beginnende Forschungsvorhaben vom Stand des Wissens ausgehen und Hinweise für die Lösung praktischer Probleme gefunden werden. Darüber hinaus wird eine planmäßige und systematische Auswertung der vorhandenen umfangreichen Literatur durch Erstellung und Veröffentlichung von Literaturberichten angeregt.
    Notes: Summary As the number of rheological and other scientific publications increases considerably year by year, documentation services should be used more extensively. The Deutsche Rheologische Gesellschaft (German Society of Rheology), 1 Berlin 45, Unter den Eichen 87, jointly with the Federal Institute for Materials Testing publishes at regular intervals an internationally useable and applicable “Documentation Rheology”, which contains a fairly complete collection of relevant literature subdivided into subject groups. The papers listed cover fundamentals of rheology, rheometry, rheological behaviour of polymer melts and solutions, plastics and rubber, metals, pastes, colloids and suspensions, solids, ceramics, concrete, pharmaceutical products and cosmetics, food stuffs, chemical engineering, forming processes, flow processes, mixing processes and so on. The documentation is available at a small charge. It has been published to make better use of the possibilities that lie in a systematic collection, arrangement, exploitation and application of findings achieved and published so far. Methodical and intensified research and development, as well as further rationalization and cost-saving measures in the field of practical application depend on a better utilization of existing findings. The above-mentioned documentation service covers basic research as well as technical application. With the aid of it literature search on general or more specific problems of research and practice can be done quicker and carried out much more easily. Literature search done this way guarantees that a research project will start from the current state of knowledge and that sufficient hints to solutions of practical problems are at hand. Moreover, the preparation and publication of literature reports will initiate a systematic evaluation of the numerous existing publications.
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    Optical and quantum electronics 8 (1976), S. 323-327 
    ISSN: 1572-817X
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    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract Results are presented of surface roughness measurements obtained by applying Beckmann's theory on the scattering of electromagnetic waves from rough surfaces to the scattering of laser light from ground glass surfaces. Measurements of the variance of surface height obtained in several scattering geometries and also from stylus measurements are presented and shown to agree closely for each surface. Also results are presented which show that the usual assumption of a Gaussian form for the autocorrelation function of surface height does not apply to the surfaces being studied here.
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    Optical and quantum electronics 8 (1976), S. 355-365 
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    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract A theory of film nonlinearities relating to amplitude holograms and bleached phase holograms is developed which is adapted to the problem of the holographic storage of digital data. The amplitude transmittance characteristics are for this purpose expanded in power series. The odd higher-order terms of the expansion yield expressions defining ghost spots that impair image quality.
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    Optical and quantum electronics 8 (1976), S. 367-370 
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    Optical and quantum electronics 8 (1976), S. 371-372 
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    Optical and quantum electronics 8 (1976), S. 373-373 
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    Optical and quantum electronics 8 (1976), S. 373-381 
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    Notes: Abstract Solutions to charge transport equations are used to illustrate the variation of the active region refractive index of the double-heterostructure GaAs laser. It is shown that a marked asymmetry can arise in the refractive index. In this paper, a suitable waveguide theory is developed to take account of this effect. The necessity for such a waveguide theory is demonstrated by comparing threshold current densities and far-field patterns calculated with this model to those calculated using a simpler waveguide model.
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    Optical and quantum electronics 8 (1976), S. 393-398 
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    Notes: Abstract The propagation of the electromagnetic wave field in a nonlinear medium is discussed in the framework of generalized nonlinear geometrical optics. In this approach the nonlinearity of the medium and the angles between the rays and the general orientation of the wave's beam are not assumed to be small. The exact analytical solutions of the equations of this generalized nonlinear geometrical optics are constructed. These solutions show the possibility of a peculiar mechanism of space stratification of the field.
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    Optical and quantum electronics 8 (1976), S. 383-391 
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    Notes: Abstract Self-consistent calculations of the electrical and optical properties of the double-heterostructure laser have been made. Theoretical studies of both aspects of the device performance have been utilized in this work which describes the behaviour of the laser both below and at threshold. The interdependence of the electrical and optical properties of the device has been established and incorporated into a self-consistency scheme. A computer program has been developed to perform the calculations given the specification of device parameters. Within the program the transport equations are solved, the active region refractive index calculated and then used in the waveguide theory. From the solution to the waveguide equations a lasing frequency and threshold current for the specified cavity mode are obtained. A consistency criterion is applied between the transport and waveguide parts of the theory. The program allows the performance of the laser to be monitored providing such information asI–V characteristics, near and far field patterns for various cavity modes with their threshold currents and lasing frequencies.
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    Optical and quantum electronics 8 (1976), S. 409-423 
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    Notes: Abstract A very powerful, fixed zenith laser radar system, based upon a liquid dye laser, is described in detail. The laser is a linear flashlamp pumped dye system capable of an average power output of 6W at a prf of 3 s−1 using rhodamine 6G dye and about 3W with the same prf using esculin monohydrate dye. The use of this laser as a transmitting source in the lidar system has permitted the detection of Stokes shifted vibration/rotation Raman back-scattered light from neutral nitrogen in the stratosphere and from these measurements, stratospheric temperature profiles have been derived. The lidar has also been used to study elastic backscattering from the stratosphere at two wavelengths and preliminary results of a new technique for studying stratospheric aerosol are presented.
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    Optical and quantum electronics 8 (1976), S. 399-407 
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    Notes: Abstract We have studied the effect of weakz-dependence of the dielectric constant on the propagation of modes in SELFOC fibres. We have also used the Green's function technique to study mode conversion due to weak irregularities in a waveguide.
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    Optical and quantum electronics 8 (1976), S. 425-431 
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    Notes: Abstract New theoretical results connected with the stability of multiple pulsing in a passively mode-locked quasicontinuous laser in the rate equation approximation are presented. Together with earlier results, these allow the number of pulses per cavity transit to be predicted and a qualitative estimate made of the pulse duration for any combination of parameters. The results are illustrated by computer evolutions.
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    Optical and quantum electronics 8 (1976), S. 513-522 
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    Notes: Abstract Most single photon coherent propagation effects are shown to have their two-photon analogue. The case of zero-area pulse propagation (90° phase shifted in the two-photon situation), frequency shift with distance, and selective optical excitation for isotope separation are considered. Selective two-photon pumping is shown to occur even when the pulse spectrum overlaps the various isotope shifted lines. An application to radiation pressure isotope separation is proposed.
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    Optical and quantum electronics 8 (1976), S. 523-529 
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    Notes: Abstract The relation between the velocity of a moving diffuse object and the mean number of integrated speckles in the certain time interval at the far-field plane of the object is obtained. By using this relation based on the first order statistics of integrated speckles, a new method of measuring the velocity of the diffuse object is proposed and experimentally verified. The first order probability density function of time-integrated speckles is also studied from which the validity of the present method is verified.
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    Optical and quantum electronics 8 (1976), S. 531-535 
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    Notes: Abstract The Gloge model for mode-coupled pulse propagation in a step index fibre has been re-examined and a dynamic model proposed to explain the significance of the pulse-broadening regime in which the pulse widthτ varies as√L. This leads to the conclusion that the critical factor controlling such propagation is the existence of a particular distribution of power which is a function of space, time and angle.
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    Optical and quantum electronics 8 (1976), S. 537-544 
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    Notes: Abstract A technique is described for improving the propagation characteristics of high order laser beam modes. A thin phase plate inserted in the beam forces all portions of the wave front to oscillate in phase and yields a substantial improvement in the far field intensity distribution. Depending on the mode order, the peak intensity at a distant target may be readily increased by more than a factor of ten.
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    Optical and quantum electronics 8 (1976), S. 207-211 
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    Notes: Abstract The transformation of a Gaussian beam by a lens has often been described in terms of geometrical optics by the formal application of the ABCD-matrix law of the lens to the complex beam parameter. In this paper we present as a wave optical method the scalar diffraction approach to the same problem. It is shown that the fresnel approximation yields results which are analytically identical to those obtained by the ABCD-law, if truncation effects of the lens can be neglected.
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    Optical and quantum electronics 8 (1976), S. 213-217 
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    Notes: Abstract Nonlinear absorption has been observed in proustite at 694 nm; however at 1.06μm, in contrast to previous results, no nonlinear absorption could be detected at intensities up to the damage threshold. Measurements on CdSe at 1.06μm and 1.32μm show that the nonlinear absorption mechanism is two photon absorption followed by absorption by the photo-induced carriers. The implications of this for nonlinear mixing applications are discussed.
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    Optical and quantum electronics 8 (1976), S. 231-235 
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    Notes: Abstract A simultaneously Q-switched and acousto-optic mode-locked high-pressure iodine photodissociation (λ=1.315μm) oscillator system, capable of generating pulse-widths as short as 160 ps is described. Good agreement is found between theory and experiment for the pressure-dependence of the modelocked pulse-width. The results indicate that pulse-widths approaching 100ps should be obtainable with this type of system.
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    Optical and quantum electronics 8 (1976), S. 219-229 
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    Notes: Abstract Pulse propagation in a photochemical iodine laser amplifier is investigated both experimentally and by solving the Maxwell-Schrödinger equations by computer. Pulse shortening and pulse reshaping are observed in agreement with theory. For pulse durations approaching the dephasing time, it is found that a further decrease in duration by gain saturation is hard to obtain and requires high power levels or high initial inversion. The numerical analysis includes reservoir effects due to tightly coupled hyperfine levels in the iodine groundstate and phase modulation (chirping) of the input pulse. Comparison of the iodine parameters with those of Nd and CO2 lasers shows that for nanosecond pulses pulse shortening occurs more readily in the latter two systems in agreement with experiments.
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    Optical and quantum electronics 8 (1976), S. 237-240 
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    Notes: Abstract Properties of the Fabry-Perot resonator as a part of an optical imaging system are discussed from the point of view of optical information theory. Information capacity of the system is derived and expressed in terms of the number of degrees of freedom of the optical wave field at the output. It is pointed out that the Fabry-Perot resonator is well suited for processing of image signals having a periodic structure.
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    Optical and quantum electronics 8 (1976), S. 255-257 
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    Optical and quantum electronics 8 (1976), S. 259-260 
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    Optical and quantum electronics 8 (1976), S. 261-262 
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    Optical and quantum electronics 8 (1976), S. 241-253 
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    Notes: Abstract An asymmetrical four-layered metal-clad dielectric optical waveguide can support the TEN and TMN modes forN⩾0 with the same phase-velocity if the core thickness,t 3, and the buffer layer thickness,t 2, are suitably chosen. Only metals that have a negative real part ∈′1 of their complex permittivity $$\hat \in _{\text{1}} = \in '_1 - j \in ''_1 $$ at optical frequencies are considered as the cladding material. It is shown that the application of a lossless approximation which set ∈″1=0 enables the development of a real expression which may be solved directly for the values oft 2 andt 3 that are required to achieve the equal-phase-velocity characteristic. Parametric plots for the guide dimensions are presented for representative waveguides and it is shown that an appropriate choice oft 2 andt 3 will reduce the absorption losses of the TE and TM modes to negligible levels. This property of the waveguide will find application in thin film optical devices such as polarization rotation modulators that require the simultaneous propagation of TE and TM polarized waves.
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    Optical and quantum electronics 8 (1976), S. 263-266 
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    Optical and quantum electronics 8 (1976), S. 267-267 
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    Optical and quantum electronics 8 (1976), S. ii 
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    Optical and quantum electronics 8 (1976), S. 335-341 
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    Notes: Abstract The field distribution and polarization state of waveguide modes propagating around a curved dielectric optical fibre are investigated analytically by using a first-order perturbation theory. It is shown that the polarization direction of all modes except the HE1m modes changes due to bending. Field distributions are also deformed and the shift in the field maximum, which takes place in the plane of curvature, is clarified for the dominant HE11 mode.
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    Optical and quantum electronics 8 (1976), S. 343-353 
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    Notes: Abstract The problem of baseband equalization in optical p.c.m. fibre systems is considered. Zero-forcing, minimum-mean-square error, and Kaiman equalizers are briefly reviewed and their relative merits discussed. The performance of the overall communication system is the average probability of error, which can be computed by means of the proposed method with high accuracy. A final section presents some diagrams that may be useful in designing the equalizer and in evaluating the degradation affecting the error probability with respect to ideal conditions. A presentation ofadaptive equalization results concludes the paper.
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    Optical and quantum electronics 8 (1976), S. 509-512 
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    Notes: Abstract Ray theory has been proved to work in Part I and is now applied to general graded fibres. A new approach to the time problem is described and a hidden effect of random distortion is analysed. It is concluded that the bandwidth of very well graded fibres may not be improved by random mode coupling.
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    Optical and quantum electronics 8 (1976), S. 565-566 
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    Optical and quantum electronics 8 (1976), S. ii 
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    Optical and quantum electronics 8 (1976), S. 433-452 
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    Notes: Abstract If the metal cladding of a dielectric optical waveguide is sufficiently thin to be only partially reflecting, then the waveguide modes differ from those of the conventional metal-clad waveguide. The TE modes are little affected by a variation in the metal thickness but the TM modes change considerably due to a coupling between the waveguide modes and the surface plasma waves supported by both the metal: dielectric interfaces and the metal film. It is the refractive index of the dielectric cladding which is remote from the guiding core that determines whether the lowest order TM mode is the TM0 or TM1 mode. This dielectric cladding also strongly influences the attenuation of the TM modes and, if the guide supports a TM0 mode, then the attenuation of the TM modes far from cut-off are an order of magnitude higher than that of the corresponding modes when the guide cannot support a TM0 mode. If the guide can support a TM0 mode then its dimensions can be chosen such that it will support the TEN and TMN modes with equal phase velocities. A lossless approximation is used to develop an expression which will specify the required guide dimensions directly and parametric plots of these dimensions are discussed.
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    Optical and quantum electronics 8 (1976), S. 453-458 
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    Notes: Abstract Thermal damage of silicon photodiodes exposed to intense optical radiation is investigated. Damage thresholds of Si photodiodes irradiated by 1.06μm laser pulses are reported for values of irradiation time,τ, ranging from 10−8 to 1s. Threshold laser irradiation produces visible microscopic damage and a permanent degradation in photoresponse. The loss of responsivity is associated with degradation of the detector diode characteristics due to laser-induced heating. The time and wavelength dependence agree with the predictions of a thermal model which treats a semi-infinite material irradiated by a Gaussian laser beam. The energy density thresholds are independent ofτ for short irradiation times and asymptotically approach a limiting behaviour which increases asτ for long times. They are given by the empirical relationE 0=65[1+217τ/tan−1(258τ)1/2] J cm−2 for 1.06μm radiation. The thresholds at short irradiation times of detectors damaged by 1.06μm radiation are about 25 times larger than those of detectors exposed to 0.6943μm radiation. The greater susceptibility at 0.6943μm is attributed to a larger optical absorption coefficient.
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    Optical and quantum electronics 8 (1976), S. 1-14 
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    Notes: Abstract Early determinations of the speed of light, based on astronomical observations or terrestrial time-of-flight experiments, were largely superseded in the 1940's by measurements of the frequency and wavelength of microwave radiation. The results were limited by the uncertainty in the wavelength measurements, and it was apparent that greater accuracy could be achieved by using radiation of shorter wavelength. It was, however, not until the development of lasers, and the nonlinear optical techniques made possible by their high output intensities, that frequency measurements could be extended towards the visible region of the spectrum. Stimulated by a demand for a more precise knowledge of the speed of light for application in space research, geodesy, and metrology, a new series of determinations has recently taken place. The measurements were made upon the radiations from a number of different stabilized-laser systems operating in the near infrared and visible spectral regions. Several different interferometric techniques were developed for the wavelength measurements. The results have led to a new recommended value for the speed of light, 299 792 458±1.2 m s−1, and to the possibility of re-defining the unit of length.
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    Optical and quantum electronics 8 (1976), S. 15-22 
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    Notes: Abstract The effects of Cu-doping, oxygen and dopant on the fast neutron radiation damage of silicon solar cells are studied in this paper. The diffusion length damage coefficientK L is defined as KL= (1/L i 2 − 1/L o 2 )φ−1= Δ(1/L2)φ−1. The Δ(1/L2) values of n/p-type cells, measured at 300 and 80K, are smaller by about one order in magnitude than those of p/n-type cells. Characteristic curves of Δ(1/L 2) values versus total neutron flux of p/n, n/p and copper-doped n/p-type cells begin to deviate from a 45° straight line around a total neutron flux of 1012 to 1013 n cm−2. The effect of copper-doping on the radiation resistant property is observed with high resistivity bulk n/p-type (20 to 40 Ω-cm) cells, but not with low resistivity bulk n/p-type (10 Ω-cm) cells at 300K. Values of Δ(1/L 2) versus neutron flux, measured at 80K, are not affected by copper-doping, bulk dopant and oxygen concentration in the bulk region of n/p-type cells. The isochronal annealing of silicon solar cells depends on the total neutron flux, copper-doping and carrier injection during the annealing process. Namely, copper-doping and carrier injection enhance the annealing process of the neutron-induced defect clusters in n/p-type cells.
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    Optical and quantum electronics 8 (1976), S. 23-30 
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    Notes: Abstract Properties of the solutions of the coupled equations describing the flow of average mode power in optical waveguides are investigated. All of the important properties and their theoretical foundations are first reviewed for systems with arbitrary coupling and loss coefficients. It is then shown that, for the special class of systems with nearest-neighbour coupling, the solutions are expressible in terms of orthogonal polynomials. In particular, for systems obeying a quasi-uniform loss model and having coupling coefficients with simple dependence on mode number (uniform or linear), the solutions are associated with the classical polynomials. As illustrations of this analysis, the characteristics of optical power flow in three such systems are studied in detail. These include a slab-waveguide with uniform coupling, the corresponding cylindrical waveguide with uniform coupling, and a parabolic-index fibre with linear coupling dependence.
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    Optical and quantum electronics 8 (1976), S. 31-37 
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    Notes: Abstract Optimization techniques for lens design require that some criterion, or figure of merit, is chosen to describe the performance of the optical system. This study is concerned with systems where the true criterion is the diffraction optical transfer function (OTF). Recent investigations [1] have shown that the geometrical approximation to the diffraction OTF is a valid criterion for OTF optimization for all practical ranges of aberration size and spatial frequency. This paper gives details of these investigations, and compares the geometric criterion with other optimization criteria. It will be shown that in most cases the geometric criterion is markedly superior.
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    Optical and quantum electronics 8 (1976), S. 39-42 
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    Notes: Abstract We describe measurements in which the radiative losses from a multimode fibre have been resolved into three components. These are the Rayleigh Scatter component from the material, the loss by tunnelling from the modes closest to cut-off into the surrounding material, and the forward scatter loss caused by imperfections in the fibre that are large compared to a wavelength.
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    Optical and quantum electronics 8 (1976), S. 43-47 
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    Notes: Abstract Approximate and much simplified dispersion relations are obtained for the problem of optical wave propagation within weakly guiding elliptical fibres. The refractive index difference between the core and its cladding of weakly guiding optical fibres that are contenders for use as practical optical communication lines is very small; i.e., (n 1/n0−1) ≪1 wheren 1 is the core index andn 0 is the cladding index. These greatly simplified dispersion relations are then used to calculate the propagation constants for several higher order modes on an elliptical optical fibre.
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    Optical and quantum electronics 8 (1976), S. 61-67 
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    Notes: Abstract Expressions are derived for the first and second order statistical properties of speckle formed in the image of a diffuse object when the illumination is both temporally and spatially partially coherent. Sunlight falls into this illumination category, and we are therefore able to deduce conditions under which sunlight speckle will show best contrast.
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    Optical and quantum electronics 8 (1976), S. 49-60 
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    Notes: Abstract An investigation of the low order modes supported by an asymmetrical four-layered metal-clad optical waveguide is presented showing the attenuation characteristics and the field profiles. The attenuation and phase constants are examined as functions of both the thickness and refractive index of the buffer layer as well as the mode order. The results for small and large buffer layer thicknesses are discussed in terms of the modes supported by simpler asymmetrical three-layered metal-clad and dielectric-clad waveguides respectively. It is shown that the coupling of the TM polarized modes to the lossy surface plasma wave depends upon the buffer layer thickness, the refractive indices of the buffer layer and dielectric cladding and the mode order. This coupling is very dependent upon the mode order with the TM0 mode exhibiting far weaker coupling than the higher order TM modes. Methods of controlling the amount of coupling and hence the attenuation of the TM modes are discussed.
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    Optical and quantum electronics 8 (1976), S. 73-75 
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    Optical and quantum electronics 8 (1976), S. 69-72 
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    Notes: Abstract Interband phototransitions and photoionization of coulombic centres allow linear detection of light intensity in Al/ZnS/Au photocells. The opposite spectral variations of photoconduction and apparent internal electric field lead to a maximum of spectral sensitivity of about 15μA mW−1 in the u.v. region for 500 Å sulphide thickness. Adequate simplified band models are proposed.
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    Optical and quantum electronics 8 (1976), S. 76-77 
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    Optical and quantum electronics 8 (1976), S. 78-79 
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    Optical and quantum electronics 8 (1976), S. 80-82 
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    Optical and quantum electronics 8 (1976), S. 83-84 
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    Optical and quantum electronics 8 (1976), S. II 
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    Optical and quantum electronics 8 (1976), S. 85-85 
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    Optical and quantum electronics 8 (1976), S. 95-104 
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    Notes: Abstract This paper is concerned with the properties of the atmosphere that limit the effectiveness of laser probing. We analyse the fluctuations in amplitude and phase of a laser signal that are induced by propagation through the irregular refractive-index structure of the atmosphere.
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    Optical and quantum electronics 8 (1976), S. 105-115 
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    Notes: Abstract A brief review is given of the various motion systems in the atmosphere, with emphasis on those which are judged most important for transport of airborne material.
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    Optical and quantum electronics 8 (1976), S. 87-93 
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    Notes: Abstract Two applications of optical methods to the measurement of atmospheric pollutants are discussed. The combination of Fourier Transform Spectrometer and long path infrared absorption cell has been used to measure many compounds simultaneously in polluted air samples at Pasadena, California. The detection limit for most pollutants has been about 10−8 atmospheres partial pressure. A 4 km cell is being developed for use in 1976 with the objective of further lowering the detection limit by a factor of ten. Nondispersive spectral correlation techniques are also being applied in the ambient air. In this case a selected pollutant is measured by passing the infrared radiation from a thermal source through a train of passive components, including the atmospheric sample cell and a gas-filled filter cell. These spectral correlation methods show great sensitivity and selectivity and have a promising future for further application.
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    Optical and quantum electronics 8 (1976), S. 117-144 
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    Notes: Abstract This paper discusses the information available concerning atmospheric molecular absorption of radiation in the 1 to 25μm range. Particular attention is given to the high spectral resolution requirements for predicting laser transmittance. The following subjects are reviewed: the content and variability of the atmosphere, calculations of transmittance and the data on which they are based, and laser measurements of molecular absorption.
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    Optical and quantum electronics 8 (1976), S. 145-154 
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    Notes: Abstract Measurements of temporal variation of stratospheric NO are important in validating its postulated role in catalytic destruction of stratospheric ozone. This paper reviews the results of NO measurements obtained from the two recent balloon-borne spin-flip Raman laser opto-acoustic spectroscopy experiments. The temporal variation of NO reported here strongly supports the role of NO in the stratospheric O3 balance. The paper compares the results obtained here with those obtained using different techniques. Also are compared the relative merits of the various techniques. Future improvements in the present technique as well as other possible experimental stratospheric studies are considered.
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    Optical and quantum electronics 8 (1976), S. 169-183 
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    Notes: Abstract The problem of pattern recognition is introduced and several major techniques in statistical pattern recognition are described. Data analysis in atmospheric laser spectroscopy could be viewed as a pattern recognition problem when the exact functional relationships between various atmospheric situations and spectral measurements are unknown. This paper tries to illustrate the use of pattern recognition as a potential tool to solve this class of data analysis problems.
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    Optical and quantum electronics 8 (1976), S. 155-167 
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    Notes: Abstract Tunable laser spectroscopy has necessitated the introduction of new measurement techniques, particularly with regard to the wavelength calibration. This paper highlights some of these requirements and surveys laser spectroscopic measurements which have already been performed in the infrared. The rather unique properties of tunable infrared lasers also make them useful for air pollution monitoring. In particular, several tunable laser techniques have been used for long-path monitoring of ambient gases in the atmosphere by resonance absorption. The results of these measurements and prospects for the future will be discussed.
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    Optical and quantum electronics 8 (1976), S. 191-194 
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    Optical and quantum electronics 8 (1976), S. 197-201 
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    Notes: Abstract A total internal reflection diffraction device has been constructed using a quadratic electro-optic material (KTN). This device exhibits a best zero order extinction voltage of 40 V, and a capacitance of 630 pf at room temperature (20° C above Curie temperature). Useful modulation is achieved with coarse gratings (0.4 mm pitch at 0.63μm) and mildly striated material can often be used.
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    Notes: Summary Limitations of present laser techniques (1) Availability of suitable lasers. Most important factors are (a) tunability over the atmospheric window regions, (b) stability and (c) long-term operating characteristics. (2) Atmospheric turbulence, which limits detection sensitivity. (3) Interferences, which limit selectivity. (4) Portability and costs, which severely limit utilization. Implications for instrumentation technology (1) Improved sensitivity of the detection/analysis system is required, including use of optical enhancement techniques, where applicable, by longer (or multiple) optical paths. (2) Elimination or minimization of interference effects by better spectral selection, primarily by use of multiple lines. (3) Tunable lasers which can be tuned over wider spectral regions, covering all windows are essential. (4) More information is needed to better characterize atmospheric turbulence in order that instrumentation may be designed to overcome the limitations it imposes.
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    Optical and quantum electronics 8 (1976), S. 203-206 
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    Notes: Abstract The polarization parameters of optical radar signals, which are characterized by parameters resulting from entropy of partially polarized light waves, are discussed. It is shown that the properties of the signal can be represented by a factor which is a ratio of entropies, and by two parameters of the polarization ellipse. The proposed method using quasilinearly polarized signals of He-Ne laser at 632.8 nm was applied to the investigations of a number of typical materials.
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    Optical and quantum electronics 8 (1976), S. 269-278 
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    Notes: Abstract As a first stage in self-consistent calculations of the optical and electrical properties of the double heterostructure laser, a numerical integration procedure has been developed for the solution of the charge transport equations. The procedure is capable of integrating the equations for a range of device parameters without excessive demands upon computing facilities. The calculated distributions of electrons and holes across the device reveal the inadequacies of analytical solutions to approximate forms of the equations. It is found to be essential to a proper treatment of the transport problem to include the variation of the electric field by way of Poisson's equations. The retention of Poisson's equation in the scheme of transport equations introduces difficulties in an integration routine. It is these difficulties that are successfully overcome by the procedure described in this paper.
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    Optical and quantum electronics 8 (1976), S. 295-300 
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    Notes: Abstract The method of electro-optical tuning is theoretically investigated using a four 45°X ADP crystal system. High tuning rates of ∂λ/∂V=0.266 Å V−1 are obtained by placing the crystals optically in series and electrically in parallel. Experimental results show agreement with theoretical expectations.
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