Cubic and ultimate groups of complete symmetry

It is shown that the systems of definite actions described by polar and axial tensors of the second rank and their combinations during the superposition of their elements of complete symmetry with the elements of complete symmetry of the "grey" cube, result in 11 cubic crystallographical groups of complete symmetry. There are 35 ultimate groups (i.e., the groups having the axes of symmetry of infinite order) in complete symmetry of finite figures. 14 out of these groups are ultimate groups of symmetry of polar and axial tensors of the second rank and 24 are new groups. All these 24 ultimate groups are conventional groups since they cannot be presented by certain finite figures possessing the axes of symmetry {Mathematical expression}. Geometrical interpretation for some of the groups of complete symmetry is given. The connection between complete symmetry and physical properties of the crystals (electrical, magnetic and optical) is shown.

The change of complete symmetry of the crystals during the phase transitions in ferroelectrics and ferromagnetics

The extension of the superposition principle of the symmetries (P. Curie principle of symmetry) for the case of complete symmetry is given. The enumeration of all crystallographical groups of complete symmetry is presented, the number of elements having complete symmetry for each class of the crystals being indicated. The change of complete symmetry of the crystals under the phase transitions is obtained by superimposing the elements of complete symmetry of polar or axial vectors on the one hand, and the elements of complete symmetry of the crystals on the other. The tables of complete symmetry changes for the cubic, rhombic, monoclinic and triclinic crystals during the ferroelectric and ferromagnetic phase transitions are given.

Symmetry and shape issues in nanostructure growth

Symmetry plays a key role in dictating the equilibrium morphology of crystals. However, several growth morphologies that deviate from the point group symmetry are routinely observed under several different growth conditions. In this article, we present a summary of symmetry-breaking mechanisms that are operative for crystals grown from the vapour phase as well as those formed as a result of wet chemical synthesis. This understanding is crucial for rationalizing the variety of morphologies observed during nanocrystal synthesis and also providesa rational framework for the synthesis of anisotropic nanostructures.

Active vibration suppression of beams with discrete actuators using optimal dynamic inversion

Most of the structural elements like beams, cables etc. are flexible and should be modeled as distributed parameter systems (DPS) to represent the reality better. For large structures, the usual approach of 'modal representation' is not an accurate representation. Moreover, for excessive vibrations (possibly due to strong wind, earthquake etc.), external power source (controller) is needed to suppress it, as the natural damping of these structures is usually small. In this paper, we propose to use a recently developed optinial dynamic inversion technique to design a set of discrete controllers for this purpose. We assume that the control force to the structure is applied through finite number of actuators, which are located at predefined locations in the spatial domain. The method used in this paper determines control forces directly from the partial differential equation (PDE) model of the system. The formulation has better practical significance, both because it leads to a closed form solution of the controller (hence avoids computational issues) as well as because a set of discrete actuators along the spatial domain can be implemented with relative ease (as compared to a continuous actuator).

A neuro-adaptive augmented optimal dynamic inversion approach for effective and efficient treatment of chronic myelogenous leukemia

Combining the advanced techniques of optimal dynamic inversion and model-following neuro-adaptive control design, an efficient technique is presented for effective treatment of chronic myelogenous leukemia (CML). A recently developed nonlinear mathematical model for cell dynamics is used for the control (medication) synthesis. First, taking a set of nominal parameters, a nominal controller is designed based on the principle of optimal dynamic inversion. This controller can treat nominal patients (patients having same nominal parameters as used for the control design) effectively. However, since the parameters of an actual patient can be different from that of the ideal patient, to make the treatment strategy more effective and efficient, a model-following neuro-adaptive controller is augmented to the nominal controller. In this approach, a neural network trained online (based on Lyapunov stability theory) facilitates a new adaptive controller, computed online. From the simulation studies, this adaptive control design approach (treatment strategy) is found to be very effective to treat the CML disease for actual patients. Sufficient generality is retained in the theoretical developments in this paper, so that the techniques presented can be applied to other similar problem as well. Note that the technique presented is computationally non-intensive and all computations can be carried out online.

Experimental investigation of the dependence of barrier height on metal work function for metal---SiO2---p---Si (MIS) Schottky-barrier diodes in the presence of inversion

The dependence of barrier height on the metal work function of metal-SiO2-p-Si Schottky barrier diodes was investigated and nonlinearity was found. This is explained by the theoretical model proposed recently by Chattopadhyay and Daw. The values of interface trap density and fixed charge density of the insulating layer of the diodes were calculated using this model and found to be appreciably different from those estimated by the usual method.

The structure of ammonium oxalohydroxamate - a monopropellant

Abstract. NHn+.C2H3NzO4, Mr= 137.1, triclinic, Pi, a=3-952(1), b=6.772(1), c=9.993(1)A, a= 98.06 (1), fl= 89.96 (1), ~= 106.96 (1) °. V=253.06 A 3, z = 2, 2(Cu Ka) = 1.5418 A, g =15.29 cm -~, D m = 1.805, D x = 1.798 g cm -3, F(000)= 144, T= 293 K, R = 0.048 for 795 observed reflections. The unit cell contains two independent centrosymmetric molecules, one centred at (0,0,0) and the other at (0.5, 0.0, 0.5). The presence of experimentally determined~N-H groups and the -C=O bond lengths of 1.248 (4) and 1.247 (4)A indicate that the compound exists in the oxamic rather than the oximic form. Only one hydroxyl hydrogen is associated with each molecule. They are located at centres of inversion (0,0.5,0 and 0,0.5,0.5) and are shared between symmetry-related molecules via short symmetric H bonds with O...O=2.454(4), 2.457(4) and all O-H = 1.23 A

X-ray diffraction from single Al6CuLi3 grains showing five-fold symmetry

We present here the detailed results of X-ray diffraction from single quasicrystals of Al6CuLi3. X-ray precession photographs taken down the two-, three- and five-fold axes along with rotation and zero-level Weissenberg photographs are shown. Preliminary analysis of the diffraction data rules out the twin hypothesis.

Cosmic Clowns : Convention, Invention, and Inversion in the Yaqui Easter Ritual

Cosmic Clowns: Convention, Invention, and Inversion in the Yaqui Easter Ritual is an ethnographic study of masked clown figures called Chapayekas. They represent Judas and the Roman soldiers in the Passion play that forms the narrative core of the Easter ritual of the Yaquis, an indigenous group in Sonora, Mexico. The study looks at how the Chapayeka is created as a ritual figure, how their performance is constructed, and what the part of the clown is in the dynamics of the ritual. The material was gathered over three periods of anthropological fieldwork in Cócorit, Sonora during Easter in 2004, 2006 and 2007. The Chapayeka masks portray foreigners, animals, mythological figures, and even figures from television and movies. They combine two kinds of performance: they perform set, conventional actions, and improvise and invent new ones. This creates dialectics of invention and convention that allow the figure to mediate between the ritual and its context and different kinds of beings within the Yaqui cosmology. The conventional side of their performance is a cycle of death and rebirth that is an inversion of the cycle of Jesus. Through invention, they separate themselves from the other performers and make themselves powerful. Alternation between the two modes enhances that power and brings it into the conventions of the ritual; ultimately the Chapayekas revitalize the entire ritual. The study finds that the clowns are extremely important to the continuity of both ritual and culture, as the combination of continuity and change, convention and invention, is what makes it possible to recreate the conventions of Yaqui culture as powerful and compelling in various contexts. Another factor is the prevalence of dialectical mediation, which relates concepts by defining them against each other as opposites, and makes it possible to cross a boundary while keeping it intact. Clowns embody and create dialectics to mediate boundaries while guarding against relativization, the disappearance of distinctions. The Chapayekas create and constitute boundaries between the self and other, microcosm and macrocosm, sacred and profane. The study argues that all clown and trickster figures are characterized by constantly alternating between invention and convention; this is what connects them to the collective and moral aspect of culture and, at the same time, makes them unpredictable and powerful. It is possible to do justice to the opposed aspects of these ambiguous and paradoxical figures by taking into account the different foundations and contextual effects of the different modes of symbolization.

Symmetry preservation during radiation damage

An examination of radiation-damage processes consequent to high-energy irradiation in certain ammonium salts studied using ESR of free radical together with the structural information available from neutron diffraction studies shows that, other factors being equal/nearly equal, symmetry-related bonds are preserved in preference to those unrelated to one another by any symmetry.

Artificial commutation for inversion into a weak AC system in a multiterminal HVDC system

This paper deals with the application of artificial commutation for a normally rated inverter connecting a weak AC system in a multiterminal HVDC (MTDC) system. Artificial commutation is achieved using series capacitors. A modular digital simulation technique is developed to study the dynamic performance of the system. It is shown that by a proper selection of the value of the capacitor it is possible to limit the valve stresses and the DC harmonics to acceptable levels and achieve an improved performance during severe transient conditions. The determination of the value of the series capacitor is based on a parametric study.

Symmetry adaptation of correlated states in the valence bond basis

Symmetry?adapted linear combinations of valence?bond (VB) diagrams are constructed for arbitrary point groups and total spin S using diagrammatic VB methods. VB diagrams are related uniquely to invariant subspaces whose size reflects the number of group elements; their nonorthogonality leads to sparser matrices and is fully incorporated into a binary integer representation. Symmetry?adapated linear combinations of VB diagrams are constructed for the 1764 singlets of a half?filled cube of eight sites, the 2.8 million ??electron singlets of anthracene, and for illustrative S?0 systems.

E. C. G. Sudarshan and Symmetry in Classical Dynamics, Optics and Quantum Mechanics

We review work initiated and inspired by Sudarshan in relativistic dynamics, beam optics, partial coherence theory, Wigner distribution methods, multimode quantum optical squeezing, and geometric phases. The 1963 No Interaction Theorem using Dirac's instant form and particle World Line Conditions is recalled. Later attempts to overcome this result exploiting constrained Hamiltonian theory, reformulation of the World Line Conditions and extending Dirac's formalism, are reviewed. Dirac's front form leads to a formulation of Fourier Optics for the Maxwell field, determining the actions of First Order Systems (corresponding to matrices of Sp(2,R) and Sp(4,R)) on polarization in a consistent manner. These groups also help characterize properties and propagation of partially coherent Gaussian Schell Model beams, leading to invariant quality parameters and the new Twist phase. The higher dimensional groups Sp(2n,R) appear in the theory of Wigner distributions and in quantum optics. Elegant criteria for a Gaussian phase space function to be a Wigner distribution, expressions for multimode uncertainty principles and squeezing are described. In geometric phase theory we highlight the use of invariance properties that lead to a kinematical formulation and the important role of Bargmann invariants. Special features of these phases arising from unitary Lie group representations, and a new formulation based on the idea of Null Phase Curves, are presented.