Thermodynamic scaling theory for impurities in metals

A perturbative scaling theory for calculating static thermodynamic properties of arbitrary local impurity degrees of freedom interacting with the conduction electrons of a metal is presented. The basic features are developments of the ideas of Anderson and Wilson, but the precise formulation is new and is capable of taking into account band-edge effects which cannot be neglected in certain problems. Recursion relations are derived for arbitrary interaction Hamiltonians up to third order in perturbation theory. A generalized impurity Hamiltonian is defined and its scaling equations are derived up to third order. The strategy of using such perturbative scaling equations is delineated and the renormalization-group aspects are discussed. The method is illustrated by applying it to the single-impurity Kondo problem whose static properties are well understood.

Binary decompositions and acyclic schemes

It is well known that the notions of normal forms and acyclicity capture many practical desirable properties for database schemes. The basic schema design problem is to develop design methodologies that strive toward these ideals. The usual approach is to first normalize the database scheme as far as possible. If the resulting scheme is cyclic, then one tries to transform it into an acyclic scheme. In this paper, we argue in favor of carrying out these two phases of design concurrently. In order to do this efficiently, we need to be able to incrementally analyze the acyclicity status of a database scheme as it is being designed. To this end, we propose the formalism of "binary decompositions". Using this, we characterize design sequences that exactly generate theta-acyclic schemes, for theta = agr,beta. We then show how our results can be put to use in database design. Finally, we also show that our formalism above can be effectively used as a proof tool in dependency theory. We demonstrate its power by showing that it leads to a significant simplification of the proofs of some previous results connecting sets of multivalued dependencies and acyclic join dependencies.

Note on the one-parameter scaling theory of localisation

The necessary and sufficient condition for the existence of the one-parameter scale function, the /Munction, is obtained exactly. The analysis reveals certain inconsistency inherent in the scaling theory, and tends to support Motts’ idea of minimum metallic conductivity.

Three-dimensional elastic analysis of cracked thick plates under bending fields

A three-dimensional analysis is presented for the bending problem of finite thick plates with through-the-thickness cracks. A general solution is obtained for Navier's equations of the theory of elasticity. It is found that the in-plane stresses and the transverse normal stress at the crack front are singular with an inverse square root singularity, while the transverse shear stresses are of the order of unity. Results from a numerical study indicate that the stress intensity factor, which varies across the thickness, is influenced by the thickness ratio in a significant manner. Results from a parametric study and those from a comparative study with existing finite element values are presented.

Information theory and resistance fluctuations in one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. For the probability distribution of the transfer matrix R of the conductor we propose a distribution of maximum information entropy, constrained by the following physical requirements: (1) flux conservation, (2) time-reversal invariance, and (3) scaling with the length of the conductor of the two lowest cumulants of ω, where R=exp(iω→⋅Jbhat). The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.

Theory of freezing in simple systems

The transition parameters for the freezing of two one-component liquids into crystalline solids are evaluated by two theoretical approaches. The first system considered is liquid sodium which crystallizes into a body-centered-cubic (bcc) lattice; the second system is the freezing of adhesive hard spheres into a face-centered-cubic (fcc) lattice. Two related theoretical techniques are used in this evaluation: One is based upon a recently developed bifurcation analysis; the other is based upon the theory of freezing developed by Ramakrishnan and Yussouff. For liquid sodium, where experimental information is available, the predictions of the two theories agree well with experiment and each other. The adhesive-hard-sphere system, which displays a triple point and can be used to fit some liquids accurately, shows a temperature dependence of the freezing parameters which is similar to Lennard-Jones systems. At very low temperature, the fractional density change on freezing shows a dramatic increase as a function of temperature indicating the importance of all the contributions due to the triplet direction correlation function. Also, we consider the freezing of a one-component liquid into a simple-cubic (sc) lattice by bifurcation analysis and show that this transition is highly unfavorable, independent of interatomic potential choice. The bifurcation diagrams for the three lattices considered are compared and found to be strikingly different. Finally, a new stability analysis of the bifurcation diagrams is presented.

Spectral analysis of finite section normal integral operators

Some continuity and differentiability properties of the eigenvalues and eigenfunctions of finite section normal integral operators are proved. These are the extension of corresponding results for symmetric operators ([4.], 554–566; K. B. Athreya and R. Vittal Rao, to appear; [10.], 463–471.

Kac-Akhiezer formula for normal integral operators

The Kac-Akhiezer formula for finite section normal Wiener-Hopf integral operators is proved. This is an extension of the corresponding result for symmetric operator [2, 3, 4, 5, 6, 7].

Aspects of tautomerism 9-solvolysis of normal and pseudo phthaloyl chlorides

Solvolysis of normal and pseudo phthaloyl chlorides in aqueous acetone and in aqueous dioxane has revealed that the former solvolyses about hundred-fold faster than the latter. Contrary to the accepted belief, there is no evidence for equilibrium between the normal and the pseudo forms of phthaloyl chloride, under a variety of conditions.

Transient pulse evolution of active-mode locking in an intra-cavity frequency-doubled laser

The theory of transient mode locking for an active modulator in an intracavity frequency-doubled laser is presented. The theory is applied to mode-locked and intracavity frequency-doubled Nd:YAG laser and the mode-locked pulse width is plotted as a function of number of round trips inside the cavity. It is found that the pulse compression is faster and the system takes a very short time to approach the steady state in the presence of a second harmonic generating crystal inside the laser cavity. The effect of modulation depth and the second harmonic conversion efficiency on the temporal behavior of the pulse width is discussed.

Critical-point Properties of Liquids and the Born-Green Theory

Recent work of Jones et al. giving the long-range behaviour of the pair correlation function is used to confirm that the critical ratio Pc/nckBTc = 1/2 in the Born-Green theory. This deviates from experimental results on simple insulating liquids by more than the predictions of the van der Waals equation of state. A brief discussion of conditions for thermodynamic consistency, which the Born-Green theory violates, is then given. Finally, the approach of the Ornstein-Zernike correlation function to its critical point behaviour is discussed within the Born-Green theory.

Role of conformational dynamics in kinetics of an enzymatic cycle in a nonequilibrium steady state

Enzyme is a dynamic entity with diverse time scales, ranging from picoseconds to seconds or even longer. Here we develop a rate theory for enzyme catalysis that includes conformational dynamics as cycling on a two-dimensional (2D) reaction free energy surface involving an intrinsic reaction coordinate (X) and an enzyme conformational coordinate (Q). The validity of Michaelis-Menten (MM) equation, i.e., substrate concentration dependence of enzymatic velocity, is examined under a nonequilibrium steady state. Under certain conditions, the classic MM equation holds but with generalized microscopic interpretations of kinetic parameters. However, under other conditions, our rate theory predicts either positive (sigmoidal-like) or negative (biphasic-like) kinetic cooperativity due to the modified effective 2D reaction pathway on X-Q surface, which can explain non-MM dependence previously observed on many monomeric enzymes that involve slow or hysteretic conformational transitions. Furthermore, we find that a slow conformational relaxation during product release could retain the enzyme in a favorable configuration, such that enzymatic turnover is dynamically accelerated at high substrate concentrations. The effect of such conformation retainment in a nonequilibrium steady state is evaluated.

Conformational Analysis and Electronic Structure of Monothiodiacetamide: Normal Coordinate Analysis and Molecular Orbital Study

The infrared spectra of monothiodiacetamide (MTDA, CHaCONHCSCH3) and its N-deuterated compound in solution, solid state and at low temperature are measured. Normal coordinate analysis for the planar vibrations of MTDAd o and -dl have been performed for the two most probable cis-trans-CONHCSor -CSNHCO-conformers using a simple Urey-Bradley force function. The conformation of MTDA derived from the vibrational spectra is supported by the all valence CNDO/2 molecular orbital method. The vibrational assignments and the electronic structure of MTDA are also given.

On the propagation of a weak shock front: Theory and application

In this paper the kinematics of a weak shock front governed by a hyperbolic system of conservation laws is studied. This is used to develop a method for solving problems, involving the propagation of nonlinear unimodal waves. It consists of first solving the nonlinear wave problem by moving along the bicharacteristics of the system and then fitting the shock into this solution field, so that it satisfies the necessary jump conditions. The kinematics of the shock leads in a natural way to the definition of ldquoshock-raysrdquo, which play the same role as the ldquoraysrdquo in a continuous flow. A special case of a circular cylinder introduced suddenly in a constant streaming flow is studied in detail. The shock fitted in the upstream region propagates with a velocity which is the mean of the velocities of the linear and the nonlinear wave fronts. In the downstream the solution is given by an expansion wave.

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.