Spontaneous generation of optical activity in urea inclusion compounds vis-a-vis current theories

A novel test of recent theories of the origin of optical activity has been designed based on the inclusion of certain alkyl 2-methylhexanoates into urea channels.

Different phenomenological theories and their abilities to describe the interdiffusion process in a binary system during multiphase growth

There are essentially two different phenomenological models available to describe the interdiffusion process in binary systems in the olid state. The first of these, which is used more frequently, is based on the theory of flux partitioning. The second model, developed much more recently, uses the theory of dissociation and reaction. Although the theory of flux partitioning has been widely used, we found that this theory does not account for the mobility of both species and therefore is not suitable for use in most interdiffusion systems. We have first modified this theory to take into account the mobility of both species and then further extended it to develop relations or the integrated diffusion coefficient and the ratio of diffusivities of the species. The versatility of these two different models is examined in the Co-Si system with respect to different end-member compositions. From our analysis, we found that the applicability of the theory of flux partitioning is rather limited but the theory of dissociation and reaction can be used in any binary system.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Determination of stress-intensity factors for cracks in tubes under torsion

An experimental investigation by two-dimensional photoelastic technique is carried out to study the stress distribution and to determine the stress-intensity factors for arbitrarily oriented cracks in thin cylindrical shells subjected to torsion. A new method is employed to evaluate the pure and mixed-mode SIF's.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Renormalisation of the Fayet-Illiopoulos term in supersymmetric spontaneously broken U( 1) gauge theories

It is shown that the Fayet-Illiopoulos D term in N= 1 supersymmetric spontaneously broken U( 1) gauge theories may get one-loop corrections, even when trace U( 1) charges are zero. However, these corrections are only logarithmically divergent and hence do not affect the naturalness of the theory.

Spontaneous symmetry breaking in twisted noncommutative quantum theories

We analyze aspects of symmetry breaking for Moyal spacetimes within a quantization scheme which preserves the twisted Poincare´ symmetry. Towards this purpose, we develop the Lehmann-Symanzik- Zimmermann (LSZ) approach for Moyal spacetimes. The latter gives a formula for scattering amplitudes on these spacetimes which can be obtained from the corresponding ones on the commutative spacetime. This formula applies in the presence of spontaneous breakdown of symmetries as well. We also derive Goldstone’s theorem on Moyal spacetime. The formalism developed here can be directly applied to the twisted standard model.

Testing approximate theories of first-order phase transitions on the two-dimensional Potts model

The two-dimensional,q-state (q>4) Potts model is used as a testing ground for approximate theories of first-order phase transitions. In particular, the predictions of a theory analogous to the Ramakrishnan-Yussouff theory of freezing are compared with those of ordinary mean-field (Curie-Wiess) theory. It is found that the Curie-Weiss theory is a better approximation than the Ramakrishnan-Yussouff theory, even though the former neglects all fluctuations. It is shown that the Ramakrishnan-Yussouff theory overestimates the effects of fluctuations in this system. The reasons behind the failure of the Ramakrishnan-Yussouff approximation and the suitability of using the two-dimensional Potts model as a testing ground for these theories are discussed.

Application of various viscosity theories to the viscosity data of methyl methacrylate-acrylonitrile random copolymersstar

Values of Ko, Flory constant related to unperturbed dimensions, are evaluated for methyl methacrylate-acrylonitrile random copolymers using Flory-Fox, Kurata-Stockmayer and Inagaki-Ptitsyn methods and compared with the Ko values obtained by Stockmayer-Fixman method. Ko values are seen to be less in solvents which have large a (Mark-Houwink exponent) values. A correlation between Ko and a is developed to arrive at a more reliable estimate of Ko for this copolymer system.

Renormalisation of the Fayet-Illiopoulos term in supersymmetric spontaneously broken U( 1) gauge theories

It is shown that the Fayet-Illiopoulos D term in N= 1 supersymmetric spontaneously broken U( 1) gauge theories may get one-loop corrections, even when trace U( 1) charges are zero. However, these corrections are only logarithmically divergent and hence do not affect the naturalness of the theory.

Comparison of Elasticity, Shell Core, and Sandwich Shell Theories

The problem of an infinite circular sandwich shell subjected to an a\isymmetric radial line load is investigated using three-dimensional elasticity theory, shell core method, and sandwich shell theory due to Fulton and Schmidt. A comparison of the stresses and displacements with an exact elasticity solution is carried out for various shell parameters in order to clearly bring out the limitations of sandwich shell theories of Fulton and Schmidt as well as the shell core solution.

Cancellation of quadratically divergent mass corrections in globally supersymmetric spontaneously broken gauge theories

The one-loop quadratically divergent mass corrections in globally supersymmetric gauge theories with spontaneously broken abelian and non-abelian gauge symmetry are studied. Quadratically divergent mass corrections are found to persist in an abelian model with an ABJ anomaly. However, additional supermultiplets necessary to cancel the ABJ anomaly, turn out to be sufficient to eliminate the quadratic divergences as well, rendering the theory natural. Quadratic divergences are shown to vanish also in the case of an anomaly free model with spontaneously broken non-abelian gauge symmetry.

Influence of electroslag refining on the hot ductility of AISI 4340 steel in torsion

Electroslag refining is a useful remelting process by which clean steels can be produced for sophisticated applications. In this investigation, AISI 4340 steel has been electroslag refined and the improvement in its hot ductility has been assessed using hot torsion tests; electroslag refining has improved the hot ductility considerably. The temperature at which peak ductility is obtained has also increased — from 1473 K in the unrefined steel to 1573 K in ESR steel. Results indicate that it should be possible to subject the ESR ingot to much higher strains per unit operation during industrial hot working processes such as forging, which would result in a considerable saving of power. The improvement in hot ductility in ESR steel has been attributed primarily to the removal of non-metallic inclusions and the reduction in sulphur content. From the apparent activation energy estimated from the hot torsion data, the dynamic recrystallization process is identified as the mechanism controlling the rate of hot deformation.