Eric Lord

Indian Institute of Science, Metallurgy, Department Member

Followers

Following

Co-authors

Public Views

Theoretical physicist

less

Uploads

Papers by Eric Lord

Gravitational theory in the presence of spinors

Errata: "Role of f-gravity in cosmological models" [Nature, Vol. 249, p. 640 - 641 (1974)]

Nature

Hadron dilation, shear and spin as components of the intrinsic hypermomentum current and metric-affine theory of gravitation

Physics Letters B, 1977

The infinite unitary irreducible spinor representations of the SL(3, R) algebra of hadron excitat... more The infinite unitary irreducible spinor representations of the SL(3, R) algebra of hadron excitations are embedded in a global GA(4, R) with intrinsic dilation, shear and spin pieces in its hypermomentum current (i.e. the affine generalization of angular momentum). When gauged over a spacetime with a local Minkowski metric, GA(4, R) reproduces the metric-affine theory of gravity, in which the hypermomentum is coupled to the connection and the energy-momentum to the tetrad. The SL (3, R)algebra of hadron excitations and the affine group. It was suggested by Dothan et al. [1] (which we refer to as DGN) that the observed sequences of angular momentum excitations of hadrons could be described by unitary infinite-dimensional representations of a non-compact group. One possibility put forward was the group SL(3, R) generated by an angular momentum and by a tensor operator which generates shearlike deformations of hadronic matter. In the DGN model, the angular momentum involved was the quasi-orbital quark angular momentum L, discussed by Gell-Mann [2], and the tensor operator was the time derivative of the energy quadmpole moment. Two representations ~0(l = 0,2,4...) and Q)l(l = 1,3,5...) were constructed by the "ladder operator" methodsthus reproducing the observed"Aj = +2 rule". At the suggestion of one of the authors, the possibility that the excitations could be excitations of total angular momentum (i.e. the spin of the hadron) was investigated by Joseph [3], who constructed the 1 Alexander von Humboldt Fellow.

Download

The prediction of the behaviour of building—environment systems

Building and Environment, 1983

Abstract A generalized model of building-environment interactions is presented, based on concepts... more Abstract A generalized model of building-environment interactions is presented, based on concepts of systems theory and transport theory. The model establishes a framework within which the general principles underlying the formulation of methods of performance prediction can be identified. Several well known examples of predictive methods are discussed from the viewpoint established by the model.

A symmetrical indexing scheme for decagonal quasicrystals analogous to Miller–Bravais indexing of hexagonal crystals

Acta Crystallographica Section A Foundations of Crystallography, 2006

The problems of redundancy and superfluous indices in indexing the planes and axes in a decagonal... more The problems of redundancy and superfluous indices in indexing the planes and axes in a decagonal quasicrystal are considered, using a scheme of five coplanar vectors in the quasiperiodic plane and one perpendicular vector. Of all the indexing schemes in use, this scheme offers the maximum advantage. An analogy is drawn to the hexagonal system using Miller-Bravais indices. Based on this, a symmetry-based indexing system for decagonal phases is devised that follows a simplified approximate zone law analogous to the exact zone law for the hexagonal case. The indices based on this scheme will be designated as 'Frank indices'. High-symmetry electron diffraction zone-axis patterns as well as powder X-ray diffraction patterns are indexed using Frank indices and compared with those of other indexing schemes.

Download

Atomic size factor criterion in designing Bulk Metallic Glasses

Geometrical Interpretation of Ini~nii-Wigner Contractions

The In/bnii-Wigner contractions which interrelate the Lie algebras of the isometry groups of metr... more The In/bnii-Wigner contractions which interrelate the Lie algebras of the isometry groups of metric spaces are discussed with reference to deformations of the absolutes of the spaces. A general formula is derived for the Lie algebra commutation relations of the isometry group for any N-dimensional metric space. These ideas are illustrated by a discussion of important particular cases, which interrelate the four-dimensional de Sitter, Poincar6, and Galilean groups.

Geometrical Interpretation of Ini~nii-Wigner Contractions

Parallelohedra and topological transitions in cellular structures

Philosophical Magazine Letters, 2008

In 1891, Fedorov showed that tilings of three-dimensional space by congruent convex polyhedra, in... more In 1891, Fedorov showed that tilings of three-dimensional space by congruent convex polyhedra, in which all the tiles are in the same orientation, belong to just five topological classes. In 1953, Cyril Stanley Smith generalized Fedorov's result by dispensing with the convexity requirement. In this and the later work of Ferro and Fortes, solutions were obtained by applying topological transitions, of the kind that occur during grain growth, to the well-known space-filling by Kelvin 14-hedra. We demonstrate an anomalous solution to the generalized Fedorov problem that is not derivable by this method, and which provides a counter example to some conjectures suggested by O'Keeffe. Finally, a further generalization is proposed, that has relevance in the study of periodic networks. We conclude with a few examples to indicate some interesting directions for possible future developments of the idea that Fedorov and Smith had initiated.

Download

Coincidence sites for rational lattices

Zeitschrift für Kristallographie, 2006

The problem of identifying the coincidence site lattices produced by the disorientations of any r... more The problem of identifying the coincidence site lattices produced by the disorientations of any rational lattice is investigated. A very simple new procedure for computing the CSLs is presented, based on Grimmer's reciprocity theorem and application of the reduction algorithm introduced by Buerger for finding reduced cells. The point symmetries of a lattice imply that any orientation relationship that produces a CSL can be alternatively expressed by a variety of different rotations. Two simple numerical methods (one based on integral matrix operations and one based on quaternions) are demonstrated for finding all the equivalent rotations that produce the same CSL and for obtaining a single “canonical” rotation as a representative of an equivalence class.

Download

A unified approach to the gauging of space-time and internal symmetries

General Relativity and Gravitation, 1987

The properties of the manifold of a Lie groupG, fibered by the cosets of a sub-groupH, are exploi... more The properties of the manifold of a Lie groupG, fibered by the cosets of a sub-groupH, are exploited to obtain a geometrical description of gauge theories in space-timeG/H. Gauge potentials and matter fields are pullbacks of equivariant fields onG. Our concept of a connection is more restricted than that in the similar scheme of Ne'eman and Regge, so that its degrees of freedom are just those of a set of gauge potentials forG, onG/H, with no redundant components. The ``translational'' gauge potentials give rise in a natural way to a nonsingular tetrad onG/H. The underlying groupG to be gauged is the groupG of left translations on the manifoldG and is associated with a ``trivial'' connection, namely the Maurer-Cartan form. Gauge transformations are all those diffeomorphisms onG that preserve the fiber-bundle structure.

Science, Mind and Paranormal Experience

. ...

Download

Coincidence-site lattices as rational approximants to irrational twins

Journal of Materials Science, 2006

It is well known that sequences of crystals with Mackay icosahedral motif and increasing lattice ... more It is well known that sequences of crystals with Mackay icosahedral motif and increasing lattice parameters exist converging to the icosahedral quasicrystal in the limit. They are known as rational approximants. It has also been demonstrated that it is possible to create icosahedral symmetry by irrational twins involving five variants by 72°rotations around an irrational axis [s 1 0] or an irrational angle of 44.48°a round a rotation axis [1 1 1]. These twinned crystals do not share a coincidence site lattice. In this paper, it is demonstrated that the above twinning relationship arises in the limit of a sequence of coincidence site lattices starting with the cubic twins with S = 3 and extending through S = 7, 19, 49, 129, 337, …, ¥ created by rotation around [1 1 1] axis. It is also noted that the boundaries of higher CSL values (S > 7) are composed of a combination of structural units from S = 3 and S = 7 boundaries.

Download

Role of F-gravity in cosmological models

The role of "cosmological constant" and f-gravity in removing gravitational singularities

Current Science, 1974

The general principles underlying the interaction between buildings and their environments

Building and Environment, 1980

Abstract In all mathematical approaches to the solution of problems involving the prediction of i... more Abstract In all mathematical approaches to the solution of problems involving the prediction of interaction between objects and energy-carrying fields, one encounters a problem of description. For example, the prediction of building performance, and the establishment of criteria for adequate building performance, require at the outset criteria for setting up efficient methods of describing environmental fields and building forms. A conceptual framework is presented which can serve as a basis for a rational approach to the problem of description. It consists of an elucidation of the general principles underlying the description of energy transport and energy conversion, and of the mediation of these processes by the geometrical and physical properties of objects.

Description and prediction in the environmental design of buildings

Building and Environment, 1982

Abstract The problem of predicting building performance is analysed in order to reveal the struct... more Abstract The problem of predicting building performance is analysed in order to reveal the structure of the problem and the basic principles that underly any specific attempt at prediction. The problem of formulating appropriate modes of description for a predictive procedure is identified and discussed. A formal language for expressing the properties of description and prediction, which might form the basis of a more comprehensive theory of description and prediction, is presented.

Tensors: Relativity and Cosmology

Periodic minimal surfaces of cubic symmetry

A survey of cubic minimal surfaces is presented, based on the concept of fundamental surface patc... more A survey of cubic minimal surfaces is presented, based on the concept of fundamental surface patches and their relation to the asymmetric units of the space groups. The software Surface Evolver has been used to test for stability and to produce graphic displays. Particular emphasis is given to those surfaces that can be generated by a finite piece bounded by straight lines. Some new varieties have been found and a systematic nomenclature is introduced, which provides a symbol (a 'gene') for each triply-periodic minimal surface that specifies the surface unambiguously.

Download

Analytic continuation of Moyal and operator algebras

International Journal of Theoretical Physics, 1973

We consider the ana|ytic continuat~ot~ rrf flz~ecemm_~or [q~"~r?] t'or vahms ofm, n ~ pos~ tire i... more

Download

Eric Lord

Uploads

Papers by Eric Lord

Log In