Non-Abelian monopoles break color. II. Field theory and quantum mechanics

Many grand unified theories (GUT's) predict non-Abelian monopoles which are sources of non-Abelian (and Abelian) magnetic flux. In the preceding paper, we discussed in detail the topological obstructions to the global implementation of the action of the "unbroken symmetry group" H on a classical test particle in the field of such a monopole. In this paper, the existence of similar topological obstructions to the definition of H action on the fields in such a monopole sector, as well as on the states of a quantum-mechanical test particle in the presence of such fields, are shown in detail. Some subgroups of H which can be globally realized as groups of automorphisms are identified. We also discuss the application of our analysis to the SU(5) GUT and show in particular that the non-Abelian monopoles of that theory break color and electroweak symmetries.

An inhomogeneity problem in couple stress theory

Using Hilbert theory and Mindlin's couple stress theory, the problem of two-dimensional circular inhomogeneity (when the inserted material is of different size than the size of the cavity and having different elastic constants) is studiedin this paper. Stress could be bounded at infinity. The formulation is valid also for regions other then the circular ones when the matrix is finite has also been tackled. Numerical results are in conformity with the fact that the effect of couple stresses is negligible when the ratio of the smallest dimension of the body to the cahracteristic length is large.

Approximation of the perturbation equations of a quasi-linear hyperbolic system in the neighborhood of a bicharacteristic

In 1956 Whitham gave a nonlinear theory for computing the intensity of an acoustic pulse of an arbitrary shape. The theory has been used very successfully in computing the intensity of the sonic bang produced by a supersonic plane. [4.] derived an approximate quasi-linear equation for the propagation of a short wave in a compressible medium. These two methods are essentially nonlinear approximations of the perturbation equations of the system of gas-dynamic equations in the neighborhood of a bicharacteristic curve (or rays) for weak unsteady disturbances superimposed on a given steady solution. In this paper we have derived an approximate quasi-linear equation which is an approximation of perturbation equations in the neighborhood of a bicharacteristic curve for a weak pulse governed by a general system of first order quasi-linear partial differential equations in m + 1 independent variables (t, x1,…, xm) and derived Gubkin's result as a particular case when the system of equations consists of the equations of an unsteady motion of a compressible gas. We have also discussed the form of the approximate equation describing the waves propagating upsteam in an arbitrary multidimensional transonic flow.

An appendix to the paper "approximation of the perturbation equations of a quasi-linear hyperbolic system in the neighborhood of a bicharacteristic"

The theory of Varley and Cumberbatch [l] giving the intensity of discontinuities in the normal derivatives of the dependent variables at a wave front can be deduced from the more general results of Prasad which give the complete history of a disturbance not only at the wave front but also within a short distance behind the wave front. In what follows we omit the index M in Eq. (2.25) of Prasad [2].

A nonlinear theory of wake development

A simple new series, using an expansion of the velocity profile in parabolic cylinder functions, has been developed to describe the nonlinear evolution of a steady, laminar, incompressible wake from a given arbitrary initial profile. The first term in this series is itself found to provide a very satisfactory prediction of the decay of the maximum velocity defect in the wake behind a flat plate or aft of the recirculation zone behind a symmetric blunt body. A detailed analysis, including higher order terms, has been made of the flat plate wake with a Blasius profile at the trailing edge. The same method yields, as a special case, complete results for the development of linearized wakes with arbitrary initial profile under the influence of arbitrary pressure gradients. Finally, for purposes of comparison, a simple approximate solution is obtained using momentum integral methods, and found to predict satisfactorily the decay of the maximum velocity defect. © 1970 Wolters-Noordhoff Publishing.

Molecular theory of dielectric relaxation in a dense binary dipolar liquid

A molecular theory of dielectric relaxation in a dense binary dipolar liquid is presented. The theory takes into account the effects of intra- and interspecies intermolecular interactions. It is shown that the relaxation is, in general, nonexponential. In certain limits, we recover the biexponential form traditionally used to analyze the experimental data of dielectric relaxation in a binary mixture. However, the relaxation times are widely different from the prediction of the noninteracting rotational diffusion model of Debye for a binary system. Detailed numerical evaluation of the frequency-dependent dielectric function epsilon-(omega) is carried out by using the known analytic solution of the mean spherical approximation (MSA) model for the two-particle direct correlation function for a polar mixture. A microscopic expression for both wave vector (k) and frequency (omega) dependent dielectric function, epsilon-(k,omega), of a binary mixture is also presented. The theoretical predictions on epsilon-(omega) (= epsilon-(k = 0, omega)) have been compared with the available experimental results. In particular, the present theory offers a molecular explanation of the phenomenon of fusing of the two relaxation channels of the neat liquids, observed by Schallamach many years ago.

Perturbation of critical solution temperatures by impurity doping

An expression is developed for the variation of the critical solution temperature of a binary liquid system when a third component (dopant) is added, using an extension of the regular solution theory. The model can be used for UCST, LCST and for closed loop systems and has the correct features in the limiting cases.

New twelve node serendipity quadrilateral plate bending element based on Mindlin-Reissner theory using Integrated Force Method

The Integrated Force Method (IFM) is a novel matrix formulation developed for analyzing the civil, mechanical and aerospace engineering structures. In this method all independent/internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. This paper presents a new 12-node serendipity quadrilateral plate bending element MQP12 for the analysis of thin and thick plate problems using IFM. The Mindlin-Reissner plate theory has been employed in the formulation which accounts the effect of shear deformation. The performance of this new element with respect to accuracy and convergence is studied by analyzing many standard benchmark plate bending problems. The results of the new element MQP12 are compared with those of displacement-based 12-node plate bending elements available in the literature. The results are also compared with exact solutions. The new element MQP12 is free from shear locking and performs excellent for both thin and moderately thick plate bending situations.

Schlieren visualization of shock wave phenomena over a missile-shaped body at hypersonic Mach numbers

The flow over a missile-shaped configuration is investigated by means of Schlieren visualization in short-duration facility producing free stream Mach numbers of 5.75 and 8. This visualization technique is demonstrated with a 41 degrees full apex angle blunt cone missile-shaped body mounted with and without cavity. Experiments are carried out with air as the test gas to visualize the flow field. The experimental results show a strong intensity variation in the deflection of light in a flow field, due to the flow compressibility. Shock stand-off distance measured with the Schlieren method is in good agreement with theory and computational fluid dynamic study for both the configurations. Magnitude of the shock oscillation for a cavity model may be greater than the case of a model without cavity. The picture of visualization shows that there is an outgoing and incoming flow closer to the cavity. Cavity flow oscillation was found to subside to steady flow with a decrease in the free stream Mach number.

A Microscopic Theory of the f.c.c.-b.c.c. Interface .

We present a first-principles theory of the equilibrium b.c.c.-f.c.c. interface at coexistence using the density functional method. We assume that the interfacial region has local body-centred tetragonal (b.c.t.) symmetry and predict typical interfacial widths to be of order 2 to 3 lattice spacings with typical energies close to 0.05 J/m2. These quantities are in good agreement with laboratory measurements on coherent interfaces.

Rudiments of complexity theory for scientists and engineers

Complexity theory is an important and growing area in computer science that has caught the imagination of many researchers in mathematics, physics and biology. In order to reach out to a large section of scientists and engineers, the paper introduces elementary concepts in complexity theory in a informal manner, motivating the reader with many examples.

Unified approach to the constraint counting theory of glasses

An approach to the constraint counting theory of glasses is applied to many glass systems which include an oxide, chalcohalide, and chalcogenides. In this, shifting of the percolation threshold due to noncovalent bonding interactions in a basically covalent network and other recent extensions of the theory appear natural. This is particularly insightful and reveals that the chemical threshold signifies another structural transition along with the rigidity percolation threshold, thus unifying these two seemingly disparate toplogical concepts. [S0163-1829(99)11441-3].

Non-resonant perturbation formula for interaction impedance measurement for a folded-waveguide SWS

The non-resonant perturbation formula for the measurement of interaction impedance of a folded-waveguide slow-wave structure was derived for the relevant electromagnetic field configuration at the axis of the beam-hole of the structure. Efficacy of the theory was benchmarked through virtual measurement using 3D electromagnetic modeling in CST-studio.

Non-Fermi-liquid theory for disordered metals near two dimensions

We consider the Finkelstein action describing a system of spin-polarized or spinless electrons in 2+2epsilon dimensions, in the presence of disorder as well as the Coulomb interactions. We extend the renormalization-group analysis of our previous work and evaluate the metal-insulator transition of the electron gas to second order in an epsilon expansion. We obtain the complete scaling behavior of physical observables like the conductivity and the specific heat with varying frequency, temperature, and/or electron density. We extend the results for the interacting electron gas in 2+2epsilon dimensions to include the quantum critical behavior of the plateau transitions in the quantum Hall regime. Although these transitions have a very different microscopic origin and are controlled by a topological term in the action (theta term), the quantum critical behavior is in many ways the same in both cases. We show that the two independent critical exponents of the quantum Hall plateau transitions, previously denoted as nu and p, control not only the scaling behavior of the conductances sigma(xx) and sigma(xy) at finite temperatures T, but also the non-Fermi-liquid behavior of the specific heat (c(v)proportional toT(p)). To extract the numerical values of nu and p it is necessary to extend the experiments on transport to include the specific heat of the electron gas.

Fully Comprehensive Geometrically Non-Linear Dynamic Analysis of Multi-Body Beam Systems with Elastic Couplings

This paper is concerned with the dynamic analysis of flexible,non-linear multi-body beam systems. The focus is on problems where the strains within each elastic body (beam) remain small. Based on geometrically non-linear elasticity theory, the non-linear 3-D beam problem splits into either a linear or non-linear 2-D analysis of the beam cross-section and a non-linear 1-D analysis along the beam reference line. The splitting of the three-dimensional beam problem into two- and one-dimensional parts, called dimensional reduction,results in a tremendous savings of computational effort relative to the cost of three-dimensional finite element analysis,the only alternative for realistic beams. The analysis of beam-like structures made of laminated composite materials requires a much more complicated methodology. Hence, the analysis procedure based on Variational Asymptotic Method (VAM), a tool to carry out the dimensional reduction, is used here.The analysis methodology can be viewed as a 3-step procedure. First, the sectional properties of beams made of composite materials are determined either based on an asymptotic procedure that involves a 2-D finite element nonlinear analysis of the beam cross-section to capture trapeze effect or using strip-like beam analysis, starting from Classical Laminated Shell Theory (CLST). Second, the dynamic response of non-linear, flexible multi-body beam systems is simulated within the framework of energy-preserving and energy-decaying time integration schemes that provide unconditional stability for non-linear beam systems. Finally,local 3-D responses in the beams are recovered, based on the 1-D responses predicted in the second step. Numerical examples are presented and results from this analysis are compared with those available in the literature.