Gauge theory of a group of diffeomorphisms. III. The fiber bundle description

A new fiber bundle approach to the gauge theory of a group G that involves space‐time symmetries as well as internal symmetries is presented. The ungauged group G is regarded as the group of left translations on a fiber bundle G(G/H,H), where H is a closed subgroup and G/H is space‐time. The Yang–Mills potential is the pullback of the Maurer–Cartan form and the Yang–Mills fields are zero. More general diffeomorphisms on the bundle space are then identified as the appropriate gauged generalizations of the left translations, and the Yang–Mills potential is identified as the pullback of the dual of a certain kind of vielbein on the group manifold. The Yang–Mills fields include a torsion on space‐time.

On Application Of The Method Of Kinetic Invariants To The Description Of Dissolution Accompanied By A Chemical Reaction

The dissolution, accompanied by chemical reaction, of monodisperse solid particles has been analysed. The resulting model, which accounts for the variation of mass transfer coefficient with the size of the dissolving particles, yields an approximate analytical form of a kinetic function. Rigorous numerical and approximate analytical solutions have been obtained for the governing system of nonlinear ordinary differential equations. The transient nature of the dissolution process as well as the accuracy of the analytical solution is brought out by the rigorous numerical solution. The analytical solution is fairly accurate for the major part of the range of operational times encountered in practice.

The role of larval nutrition in pre-imaginal biasing of caste in the primitively eusocial wasp Ropalidia marginata (Hymenoptera: Vespidae)

1. When freshly eclosed females of the primitively eusocial wasp Ropalidia marginata (Lep.) are isolated, only about 50% of them build nests and lay eggs thereby suggesting a pre-imaginal biasing of caste. 2. Wasps that lay eggs take a very variable amount of time after eclosion to start doing so. 3. Females eclosing from nests where larvae are fed at a relatively higher rate are more likely to become egg-layers and are likely to take less time after eclosion to begin to lay eggs. 4. Thus, both forms of pre-imaginal biasing of caste, namely, differences in egg laying capacity and differences in the time taken to attain reproductive maturity, appear to be influenced by larval nutrition.

A standard reference frame for the description of Nucleic Acid Base-Pair Geometry

A common point of reference is needed to describe the three-dimensional arrangements of bases and base-pairs in nucleic acid structures. The different standards used in computer programs created for this purpose give rise to con¯icting interpretations of the same structure.1 For example, parts of a structure that appear ``normal'' according to one computational scheme may be highly unusual according to another and vice versa. It is thus dif®cult to carry out comprehensive comparisons of nucleic acid structures and to pinpoint unique conformational features in individual structures

Molecular theory of ion solvation dynamics in water, acetonitrile and methanol: A unified microscopic description of collective dynamics in dipolar liquids

A recently developed microscopic theory of solvation dynamics in real dipolar liquids is used to calculate, for the first time, the solvation time correlation function in liquid acetonitrile, water and methanol. The calculated results are in excellent agreement with known experimental and computer simulation studies.

Path integral description of polymers using fractional Brownian walks

The statistical properties of fractional Brownian walks are used to construct a path integral representation of the conformations of polymers with different degrees of bond correlation. We specifically derive an expression for the distribution function of the chains’ end‐to‐end distance, and evaluate it by several independent methods, including direct evaluation of the discrete limit of the path integral, decomposition into normal modes, and solution of a partial differential equation. The distribution function is found to be Gaussian in the spatial coordinates of the monomer positions, as in the random walk description of the chain, but the contour variables, which specify the location of the monomer along the chain backbone, now depend on an index h, the degree of correlation of the fractional Brownian walk. The special case of h=1/2 corresponds to the random walk. In constructing the normal mode picture of the chain, we conjecture the existence of a theorem regarding the zeros of the Bessel function.

Formation and propagation of bands in jerky flow:a coupled lattice map description

There has been revival of interest in Jerky flow from the point of view of dynamical systems. The earliest attempt in this direction was from our group. One of the predictions of the theory is that Jerky flow could be chaotic. This has been recently verified by us. We have recently extended the earlier model to account for the spatial aspect as well. Both these models are in the form of coupled set of nonlinear differential equations and hence, they are complicated in their structure. For this reason we wish to devise a model based on the results of these two theories in the form of coupled lattice map for the description of the formation and propagation of dislocation bands. We report here one such model and its results.

First-principle description of magnonic PdnFem multilayers

Ab-initio calculations are used to determine the parameters that determine magnonic band structure of PdnFem multilayers (n = 2, m <= 8). We obtain the layer-resolved magnetization, the exchange coupling, and the magnetic anisotropy of the Pd-Fe structures. The Fe moment is 3.0 mu(B) close to the Pd layers and 2.2 mu(B) in the middle of the Fe layers. An intriguing but not usually considered aspect is that the elemental Pd is nonmagnetic, similar to Cu spacer layers in other multilayer systems. This leads to a pre-asymptotic ferromagnetic coupling through the Pd (about 40 mJ/m(2)). Furthermore, the Pd acquires a small moment due to spin polarization by neighboring Fe atoms, which translates into magnetic anisotropy. The anisotropies are large, in the range typical for L1(0) structures, which is beneficial for high-frequency applications. (C) 2011 American Institute of Physics. doi:10.1063/1.3556763]

The diatom genus Gomphonema Ehrenberg in India: Checklist and description of three new species

We have compiled a checklist of Gomphonema Ehrenberg taxa reported previously from India. From forty-nine references, over 100 Gomphonema taxa have been reported, including 39 new taxon descriptions. In addition to these previous reports of Gomphonema taxa, we describe three new species. G. gandhii Karthick & Kociolek, sp. nov., G. difformum Karthick & Kociolek, sp. nov. and G. diminutum Karthick & Kociolek, sp. nov., all from hill streams of Western Ghats, India. Frustule morphology, as studied in light and scanning electron microscopy, is compared with that of other recently described Gomphonema species from Africa and Asia. All three Indian species have distinctly dilated proximal raphe ends, in addition to differentiated apical pore fields, septa, pseudosepta and a round external stigma! opening. Gomphonema gandhii is linear-lanceolate-clavate, has a wide axial area, and is 19-51 mu m long, 3-7 mu m broad. Gomphonema difformum is smaller than G. gandhii, and has a hyaline area around the headpole. Gomphonema diminuta is much smaller and narrower than the other two species. These species are distinct from their closest congeners by their sizes, shape and structure of the head pole, and striae densities. All these species were described from low nutrient, neutral, low ionic content streams of Western Ghats. As most other species described from tropical region these three species appear to be endemic to India. Moreover, within India they have hitherto only been found in Western Ghats, one of the twelve biodiversity hotspots of the World.

Insulating State and Breakdown of Fermi Liquid Description in Molecular-Scale Single-Crystalline Wires of Gold

Electrical transport measurements on ultrathin single-crystalline Au nanowires, synthesized via a wet chemical route, show an unexpected insulating behavior. The linear response electrical resistance exhibits a power-law dependence on temperature. In addition, the variation of current over a wide range of temperature and voltage obeys a universal scaling relation that provides compelling evidence for a non-Fermi liquid behavior. Our results demonstrate that the quantum ground state In ultrathin nanowires of simple metallic systems can be radically different from their bulk counterparts and can be described In terms of a Tomonaga-Luttinger liquid (TLL), in the presence of remarkably strong electron-electron interactions.

Simulating grasping behavior of people using the relational description scheme

This paper presents an enhanced relational description for the prescription of the grasp requirement and evolution of the posture of a digital human hand towards satisfaction of this requirement. Precise relational description needs anatomical segmentation of the hand geometry into palmar, dorsal and lateral patches using the palm-plane and joint locations information, and operational segmentation of the object geometry into pull,push and lateral patches with due consideration to the effect of friction. Relational description identifies appropriate patches for a desired grasp condition. Satisfaction of this requirement occurs in two discrete stages,namely,contact establishment and post-contact force exertion for object capturing. Contact establishment occurs in four potentially overlapping phases,namely,re-orientation,transfer,pre- shaping,and closing-in. The novel h and re-orientation phase,enables the palm to face the object in a task sequence scenario, transfer takes the wrist to the ball park ; pre-shaping and close-in finally achieves the contact. In this paper, an anatomically pertinent closed-form formulation is presented for the closing-in phase for identification of the point of contact on the patches ,prescribed by the relational description. Since mere contact does not ensure grasp and slip phenomenon at the point of contact on application of force is a common occurrence, the effect of slip in presence of friction has been studied for 2D and 3D object grasping endeavours and a computational generation of the slip locus is presented.A general slip locus is found to be a non-linear curve even on planar faces.Two varieties of slip phenomena,namely,stabilizing and non-stabilizing slips, and their local characteristics have been identified.Study of the evolution of this slip characteristic over the slip locus exhibited diverse grasping behaviour possibilities. Thus, the relational description paradigm not only makes the requirement specification easy and meaningful but also enables high fidelity hand object interaction studies possible.

Theoretical description of coherent doublon creation via lattice modulation spectroscopy

Using a recently developed strong-coupling method, we present a comprehensive theory for doublon production processes in modulation spectroscopy of a three-dimensional system of ultracold fermionic atoms in an optical lattice with a trap. The theoretical predictions compare well to the experimental time traces of doublon production. For experimentally feasible conditions, we provide a quantitative prediction for the presence of a nonlinear ``two-photon'' excitation at strong modulation amplitudes.