Isotropy

About: Isotropy is a research topic. Over the lifetime, 30050 publications have been published within this topic receiving 663626 citations.

Ground state energy of a many fermion system. 2.

Abstract: The perturbation series for the ground-state energy of a many-fermion system is investigated to arbitrary order for the "isotropic" case. This is the case of over-all spherical symmetry, both in the interaction and in the unperturbed single particle energies. It is shown that for spin one-half fermions the Brueckner-Goldstone perturbation series is valid to all orders in the perturbation. For spins greater than one-half it is in general incorrect even in the isotropic case, unless the interactions are spin independent. The discussion to arbitrary order in the interaction is carried out by means of a Feynman-like propagator formalism, which is developed in detail.

Large Elastic Deformations of Isotropic Materials. VII. Experiments on the Deformation of Rubber

Abstract: It is shown in this part how the theory of large elastic deformations of incompressible isotropic materials, developed in previous parts, can be used to interpret the load-deformation curves obtained for certain simple types of deformation of vulcanized rubber test-pieces in terms of a single stored-energy function. The types of experiment described are: (i) the pure homogeneous deformation of a thin sheet of rubber in which the deformation is varied in such a manner that one of the invariants of the strain, I 1 or I 2 , is maintained constant; (ii) pure shear of a thin sheet of rubber (i.e. pure homogeneous deformation in which one of the extension ratios in the plane of the sheet is maintained at unity, while the other is varied); (iii) simultaneous simple extension and pure shear of a thin sheet (i.e. pure homogeneous deformation in which one of the extension ratios in the plane of the sheet is maintained constant at a value less than unity, while the other is varied); (iv) simple extension of a strip of rubber; (v) simple compression (i.e. simple extension in which the extension ratio is less than unity); (vi) simple torsion of a right-circular cylinder; (vii) superposed axial extension and torsion of a right-circular cylindrical rod. It is shown that the load-deformation curves in all these cases can be interpreted on the basis of the theory in terms of a stored-energy function W which is such that δ W /δ I 1 is independent of I 1 and I 2 and the ratio (δ W /δ I 2 ) (δ W /δ I 1 ) is independent of I 1 and falls, as I 2 increases, from about 0*25 at I 2 = 3.

Shear Deformation in Heterogeneous Anisotropic Plates

Abstract: : A bending theory for anisotropic laminated plates developed by Yang, Norris,and Stavsky is investigated. The theory includes shear deformation and rotary inertia in the same manner as Mindlin's theory for isotropic homogeneous plates. The governing equations reveal that unsymmetrically laminated plates display the same bending-extensional coupling phenomenon found in classical laminated plate theory based on the Kirchhoff assumptions. Solutions are presented for bending under transverse load and for flexural vibration frequencies of symmetrical and nonsymmetrical laminates. Good agreement is observed in numerical results for plate bending as compared to exact solutions obtained from classical elasticity theory. For certain fiber reinforced composite materials, radical departure from classical laminated plate theory is indicated. (Author-PL)

Valence Bond Ground States in Isotropic Quantum Antiferromagnets

Abstract: Haldane predicted that the isotropic quantum Heisenberg spin chain is in a “massive” phase if the spin is integral. The first rigorous example of an isotropic model in such a phase is presented. The Hamiltonian has an exactSO(3) symmetry and is translationally invariant, but we prove the model has a unique ground state, a gap in the spectrum of the Hamiltonian immediately above the ground state and exponential decay of the correlation functions in the ground state. Models in two and higher dimension which are expected to have the same properties are also presented. For these models we construct an exact ground state, and for some of them we prove that the two-point function decays exponentially in this ground state. In all these models exact ground states are constructed by using valence bonds.

Elastic wave behavior across linear slip interfaces

Abstract: A model for an imperfectly bonded interface between two elastic media is proposed. Displacement across this surface is not required to be continuous. The displacement discontinuity, or slip, is taken to be linearly related to the stress traction which is continuous across the interface. For isotropic interface behavior, there are two complex frequency dependent interface compliances, ηN and ηT, where the component of the slip normal to the interface is given by ηN times the normal stress and the component tangential to the interface is given by ηT times the shear stress and is in the same direction. Reflection and transmission coefficients for harmonic plane waves incident at arbitrary angles upon a plane linear slip interface are computed in terms of the interface compliances. These coefficients are frequency dependent even when the compliances are real and frequency independent. Examples of the effects of buried slip interfaces on reflection coefficient spectra and on Love‐wave dispersion relations are ...