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Carl Schorlemmer" Leuna-Merseburg, Sektion Physik, DDR -42 MerseburgIn einer abersicht werden statistisch-mechanische Theorien polymerer Netzwerke diskutiert und ihre Leistungsfahigkeit zur Erklarung der mechanischen Eigenschaften der Netzwerke untersueht. Es zeigt sich, daB ein tieferes Verstandnis der Struktur-Eigenschafts-Korrelation polymerer Netzwerke im kautschukelastischen Zustand moglich ist, wenn bei der Formulierung einer statistischen Mechanik der Netzwerke die Undurchdringbarkeit der Netzwerkketten berucksichtigt wird. Illone~~~~pno-cmamucmu~ecicue meopuu nonuMepimx cemoic. 0630p. B B n A e o63opa 0 6 c y~~a m -r~~ cTaTkIcTL1qecKkI-MexaHL19eCKYle Teopvrvr n o n u r M e p H M x c e T o H K H c c a e A y e T c H npmemMOCTb 3TIIX TeOpII& ,lT,Jlfi 065RCHeHIIfi MeXaHKqeCKIIX CBOaCTB CeTOK. YqIITbIBaFl npII (POPMYJIHpOBKe CTaTACTHqeCKO& MeXaHIIKH CeTOK HelIPOHIlKHOBeHIIe q e I I e & nOJIHMepHO& CeTKH, B 0 3 M O X H O 6onee m y 6 o~o e IIOHHMaHHe B3aAMOC-B R 3 e f i Me?KAY CTPYKTYPOfi K CBOPCTBaMH IIOJIAMepHbIX CeTOK B BbICOK03JIaCTII9eCKOM COCTOHHIIII. Molecular statistical theories of polymer networks. Review The current statistical theories of polymer networks and their success in explaining the mechanical network properties are reviewed. A more exhaustive elucidation of the structure-property relationship of networks in polymers relating to the rubber-elastic state can be achieved by considering topological constraints in the description of the statistical mechanics of networks.

Inhal tsii bersic h tMit der in Teil 12) angegebenen Methode zur Ermittlung der Wahrscheinlichkeit optischer ubergange wird auch die Wahrscheinlichkeit strahlungsloser ubergange zwischen zwei Eigenzustanden eines in einer Storstelle gebundenen Elektrons berechnet, wobei die Abhangigkeit der Gleichgewichtslage und der Frequenzen der Gitterbausteine vom Elektronenzustand berucksichtigt wird. Der Storterm folgt nach einer unitaren Transformation des Gesamthamiltonoperators in die Form K + AK. Eine spezielle Transformation entspricht der B o r n -0 p p e n h c: im e r -Naherung. Im Rahmen dieser Naherung und unter der Voraussetzung, da13 nur die Gleichgewichtslage der Gitterbausteine vom Elektronenzustand abhangig ist und alle mit dem Elektron wechselwirkenden Gitteroszillatoren die gleiche Frequenz haben, ergibt sich genau das H u a n g -1) Gekiirzte Wiedergabe eines Teils der Dissertation (Jena, Sommer 1955).

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Calculations carried out on a simple model (a gyroscope with a triaxial but nearly sphero-symmetrical inertia ellipsoid having weak isotropic frictional coupling with a surrounding hollow sphere which rotates with constant angular velocity) show that each disturbance of the gyroscope causes a gradually decreasing rotation of the gyroscope in relation to the sphere, the rotation axis falling exactly into the equatorial plane and rotating within the latter. Transferring this concept to the Earth's solid core permits one to set up a hypothesis for the explanation of the declination, drift, and reversals of the Earth's magnetic field.The declination of the Earth's magnetic dipole field from the north-south direction, the drift, and reversals, may be indicative of the presence of possibly small, but wideranging systematic variations from rotational symmetry in the structure of the Earth's interior, although the character of these variations is largely unknown. The above-mentioned phenomena would be understandable if, within the fluid zone, the Earth's solid core would rotate relatively to the Earth's mantle, the axis of rotation falling into the equatorial plane and rotating within the latter. The Earth's solid core and the mantle are not rigidly coupled, so different rotations are in fact possible and have been discussed (e.g. Malkus 1968). If, rotating in the manner stated above, an electrically conducting core should in part carry along a penetrating magnetic field it would thus cause an inclination of the Earth's magnetic field and a drift; indeed a very slow rotation is sufficient to effect these phenomena. For these effects it is of minor importance how the magnetic field is generated by flow within the fluid zone; therefore, this question is not considered at all here. This paper merely shows that, according to the theory of the gyroscope, such a rotation of the Earth's solid core can and possibly even must occur (Steenbeck & Helmis 1969).For this purpose a rather simplified model is set up. A rigid body of arbitrary shape with three different principal moments of inertia rotates initially in any way within a hollow sphere which rotates with a constant angular velocity Go. The rigid body and the sphere are coupled only by isotropic friction. Which rotational states will then develop for the rigid body?If rotating freely, a gyroscope having three different principal moments of inertia, 0, < O2 < e3, generally passes through a sequence of different states of motion, where the instantaneous axis of rotation is fixed neither in space nor in the gyroscope. We first of all describe this behaviour, which had been shown already by Euler, in a way *