Steady state three-dimensional mathematical model for cupola

A three-dimensional mathematical model has been developed to simulate the gas flow, composition, and temperature profiles inside a cupola. Comparison of the model with the reported experimental data shows the presence of a zone with low combustion rate at the tuyere level. For a 24 in (610 mm) cupola with four rows of tuyeres, the combustion zones from each tuyere overlap each other, forming an overall combustion zone of cylindrical shape of height similar to 0.2 m. Using the model, it is found that the spout temperature initially increases with increasing blast velocity and attains a maximum. Further increase in blast velocity does not change the spout temperature. This suggests that smaller size tuyeres and higher permeability of the bed can give superior cupola performance. (C) 1997 The Institute of Materials.

The physics and technology of gallium antimonide: An emerging optoelectronic material

Recent advances in nonsilica fiber technology have prompted the development of suitable materials for devices operating beyond 1.55 mu m. The III-V ternaries and quaternaries (AlGaIn)(AsSb) lattice matched to GaSb seem to be the obvious choice and have turned out to be promising candidates for high speed electronic and long wavelength photonic devices. Consequently, there has been tremendous upthrust in research activities of GaSb-based systems. As a matter of fact, this compound has proved to be an interesting material for both basic and applied research. At present, GaSb technology is in its infancy and considerable research has to be carried out before it can be employed for large scale device fabrication. This article presents an up to date comprehensive account of research carried out hitherto. It explores in detail the material aspects of GaSb starting from crystal growth in bulk and epitaxial form, post growth material processing to device feasibility. An overview of the lattice, electronic, transport, optical and device related properties is presented. Some of the current areas of research and development have been critically reviewed and their significance for both understanding the basic physics as well as for device applications are addressed. These include the role of defects and impurities on the structural, optical and electrical properties of the material, various techniques employed for surface and bulk defect passivation and their effect on the device characteristics, development of novel device structures, etc. Several avenues where further work is required in order to upgrade this III-V compound for optoelectronic devices are listed. It is concluded that the present day knowledge in this material system is sufficient to understand the basic properties and what should be more vigorously pursued is their implementation for device fabrication. (C) 1997 American Institute of Physics.

Coherent states on Hilbert modules

We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over C*-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert C*-modules which have a natural left action from another C*-algebra, say A. The coherent states are well defined in this case and they behave well with respect to the left action by A. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive definite kernel between two C*-algebras, in complete analogy to the Hilbert space situation. Related to this, there is a dilation result for positive operator-valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory. Some possible physical applications are also mentioned.

Superconductivity from repulsion: a variational view

This letter presents a new class of variational wavefunctions for Fermi systems in any dimension. These wavefunctions introduce correlations between Cooper pairs in different momentum states and the relevant correlations can be computed analytically. At half filling we have a ground state with critical superconducting correlations, that causes negligible increase of the kinetic energy. We find large enhancements in a Cooper-pair correlation function caused purely by the interplay between the uncertainty principle, repulsion and the proximity of half filling. This is surprising since there is no accompanying signature in usual charge and spin response functions, and typifies a novel kind of many-body cooperative behaviour.

The 2D Coulomb gas on a 1D lattice

The statistical mechanics of a two-dimensional Coulomb gas confined to one dimension is studied, wherein hard core particles move on a ring. Exact self-duality is shown for a version of the sine-Gordon model arising in this context, thereby locating the transition temperature exactly. We present asymptotically exact results for the correlations in the model and characterize the low- and high-temperature phases. Numerical simulations provide support to these renormalization group calculations. Connections with other interesting problems, such as the quantum Brownian motion of a panicle in a periodic potential and impurity problems, are pointed out.

Physics based basis function for vibration analysis of high speed rotating beams

The natural frequencies of continuous systems depend on the governing partial differential equation and can be numerically estimated using the finite element method. The accuracy and convergence of the finite element method depends on the choice of basis functions. A basis function will generally perform better if it is closely linked to the problem physics. The stiffness matrix is the same for either static or dynamic loading, hence the basis function can be chosen such that it satisfies the static part of the governing differential equation. However, in the case of a rotating beam, an exact closed form solution for the static part of the governing differential equation is not known. In this paper, we try to find an approximate solution for the static part of the governing differential equation for an uniform rotating beam. The error resulting from the approximation is minimized to generate relations between the constants assumed in the solution. This new function is used as a basis function which gives rise to shape functions which depend on position of the element in the beam, material, geometric properties and rotational speed of the beam. The results of finite element analysis with the new basis functions are verified with published literature for uniform and tapered rotating beams under different boundary conditions. Numerical results clearly show the advantage of the current approach at high rotation speeds with a reduction of 10 to 33% in the degrees of freedom required for convergence of the first five modes to four decimal places for an uniform rotating cantilever beam.

The origin of degeneracies and crossings in the 1d Hubbard model

The paper is devoted to the connection between integrability of a finite quantum system and degeneracies of its energy levels. In particular, we analyse in detail the energy spectra of finite Hubbard chains. Heilmann and Lieb demonstrated that in these systems there are crossings of levels of the same parameter-independent symmetry. We show that this apparent violation of the Wigner-von Neumann noncrossing rule follows directly from the existence of nontrivial conservation laws and is a characteristic signature of quantum integrability. The energy spectra of Hubbard chains display many instances of permanent (at all values of the coupling) twofold degeneracies that cannot be explained by parameter-independent symmetries. We relate these degeneracies to the different transformation properties of the conserved currents under spatial reflections and the particle-hole transformation and estimate the fraction of doubly degenerate states. We also discuss multiply degenerate eigenstates of the Hubbard Hamiltonian. The wavefunctions of many of these states do not depend on the coupling, which suggests the existence of an additional parameter-independent symmetry.

Roy equation analysis of ππ scattering

We analyse the Roy equations for the lowest partial waves of elastic ππ scattering. In the first part of the paper, we review the mathematical properties of these equations as well as their phenomenological applications. In particular, the experimental situation concerning the contributions from intermediate energies and the evaluation of the driving terms are discussed in detail. We then demonstrate that the two S-wave scattering lengths a00 and a02 are the essential parameters in the low energy region: Once these are known, the available experimental information determines the behaviour near threshold to within remarkably small uncertainties. An explicit numerical representation for the energy dependence of the S- and P-waves is given and it is shown that the threshold parameters of the D- and F-waves are also fixed very sharply in terms of a00 and a20. In agreement with earlier work, which is reviewed in some detail, we find that the Roy equations admit physically acceptable solutions only within a band of the (a00,a02) plane. We show that the data on the reactions e+e−→ππ and τ→ππν reduce the width of this band quite significantly. Furthermore, we discuss the relevance of the decay K→ππeν in restricting the allowed range of a00, preparing the grounds for an analysis of the forthcoming precision data on this decay and on pionic atoms. We expect these to reduce the uncertainties in the two basic low energy parameters very substantially, so that a meaningful test of the chiral perturbation theory predictions will become possible.

The physics of active membranes

We review recent work on the physical properties of model fluid membranes in nonequilibrium situations resembling those encountered in the living cell and contrast their properties with those of the more familiar membranes at thermal equilibrium. We survey models for the effect of (i) active pumps and (ii) active fission–fusion processes encountered in intracellular trafficking on the stability and fluctuations of fluid membranes. Our purpose is twofold: to highlight the exciting nonequilibrium phenomena that arise in biological systems, and to show how some crucial features of living systems, namely dissipative energy uptake and directed motion, can fruitfully be incorporated into physical models of biological interest.

Top polarization, forward-backward asymmetry, and new physics

We consider how the measurement of top polarization at the Tevatron can be used to characterize and discriminate among different new physics models that have been suggested to explain the anomalous top forward-backward asymmetry reported at the Tevatron. This has the advantage of catching the essence of the parity-violating effect characteristic to the different suggested new physics models. Other observables constructed from these asymmetries are shown to be useful in discriminating between the models, even after taking into account the statistical errors. Finally, we discuss some signals at the 7 TeV LHC.

A nonlinear spectral finite element model for analysis of wave propagation in solid with internal friction and dissipation

A geometrically non-linear Spectral Finite Flement Model (SFEM) including hysteresis, internal friction and viscous dissipation in the material is developed and is used to study non-linear dissipative wave propagation in elementary rod under high amplitude pulse loading. The solution to non-linear dispersive dissipative equation constitutes one of the most difficult problems in contemporary mathematical physics. Although intensive research towards analytical developments are on, a general purpose cumputational discretization technique for complex applications, such as finite element, but with all the features of travelling wave (TW) solutions is not available. The present effort is aimed towards development of such computational framework. Fast Fourier Transform (FFT) is used for transformation between temporal and frequency domain. SFEM for the associated linear system is used as initial state for vector iteration. General purpose procedure involving matrix computation and frequency domain convolution operators are used and implemented in a finite element code. Convergnence of the spectral residual force vector ensures the solution accuracy. Important conclusions are drawn from the numerical simulations. Future course of developments are highlighted.

Two-channel Kondo physics in odd impurity chains

We study odd-membered chains of spin-1/2 impurities, with each end connected to its own metallic lead. For antiferromagnetic exchange coupling, universal two-channel Kondo (2CK) physics is shown to arise at low energies. Two overscreening mechanisms are found to occur depending on coupling strength, with distinct signatures in physical properties. For strong interimpurity coupling, a residual chain spin-1/2 moment experiences a renormalized effective coupling to the leads, while in the weak-coupling regime, Kondo coupling is mediated via incipient single-channel Kondo singlet formation. We also investigate models in which the leads are tunnel-coupled to the impurity chain, permitting variable dot filling under applied gate voltages. Effective low-energy models for each regime of filling are derived, and for even fillings where the chain ground state is a spin singlet, an orbital 2CK effect is found to be operative. Provided mirror symmetry is preserved, 2CK physics is shown to be wholly robust to variable dot filling; in particular, the single-particle spectrum at the Fermi level, and hence the low-temperature zero-bias conductance, is always pinned to half-unitarity. We derive a Friedel-Luttinger sum rule and from it show that, in contrast to a Fermi liquid, the Luttinger integral is nonzero and determined solely by the ``excess'' dot charge as controlled by gate voltage. The relevance of the work to real quantum dot devices, where interlead charge-transfer processes fatal to 2CK physics are present, is also discussed. Physical arguments and numerical renormalization-group techniques are used to obtain a detailed understanding of these problems.