A Fredholm-type theory for third-kind linear integral equations

The third-kind linear integral equation Image where g(t) vanishes at a finite number of points in (a, b), is considered. In general, the Fredholm Alternative theory [[5.]] does not hold good for this type of integral equation. However, imposing certain conditions on g(t) and K(t, t′), the above integral equation was shown [[1.], 49–57] to obey a Fredholm-type theory, except for a certain class of kernels for which the question was left open. In this note a theory is presented for the equation under consideration with some additional assumptions on such kernels.

A semi-empirical theory of molten salts

A semi-empirical model is presented for describing the interionic interactions in molten salts using the experimentally available structure data. An extension of Bertaut's method of non-overlapping charges is used to estimate the electrostatic interaction energy in ionic melts. It is shown, in agreement with earlier computer simulation studies, that this energy increases when an ionic salt melts. The repulsion between ions is described using a compressible ion theory which uses structure-independent parameters. The van der Waals interactions and the thermal free energy are also included in the total energy, which is minimised with respect to isostructural volume variations to calculate the equilibrium density. Detailed results are presented for three molten systems, NaCl, CaCl2 and ZnCl2, and are shown to be in satisfactory agreement with experiments. With reliable structural data now being reported for several other molten salts, the present study gains relevance.

Vibrations of laminated beams

Governing equations in the form of simultaneous ordinary differential equations have been derived for natural vibration analysis of isotropic laminated beams. This formulation includes significant secondary effects such as transverse shear and rotatory inetia. Through a numerical example, the influence of these secondary effects has been studied.

A phase space approach to generalized Hamilton–Jacobi theory

Generalizations of H–J theory have been discussed before in the literature. The present approach differs from others in that it employs geometrical ideas on phase space and classical transformation theory to derive the basic equations. The relation between constants of motion and symmetries of the generalized H–J equations is then clarified. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

A note on the effective medium theory of random resistive-reactive medium

The effective medium theory for a system with randomly distributed point conductivity and polarisability is reformulated, with attention to cross-terms involving the two disorder parameters. The treatment reveals a certain inconsistency of the conventional theory owing to the neglect of the Maxwell-Wagner effect. The results are significant for the critical resistivity and dielectric anomalies of a binary liquid mixture at the phase separation point.

The non-planar peptide unit II. Comparison of theory with crystal structure datastar, open

The theoretical results derived in Part I (Ramachandran, G.N., Lakshminarayan, A.V. and Kolaskar, A.S. (1973) Biochim. Biophys. Acta 303, 8–13) that the three bonds of the peptide unit meeting at N can have a pyramidal structure is confirmed by an analysis of 14 published crystal structures of small peptides. It is shown that the dihedral angles θN and Δω are correlated, while θC, is small and is uncorrelated with Δω, showing that the non-planar distortion at C′ is generally small.

A theory of the upper critical field in antiferromagnetic superconductors

A generalized Ginzburg-Landau approach is used to study the nonmonotonic temperature dependence of the upper critical field H c 2(T) in antiferromagnetic superconductors RE(Mo)6S8; RE = Dy, Tb, Gd. It is found that electrodynamic effects incorporated through screening and indirect coupling between the staggered magnetization M Q (T) and superconducting order parameter psgr cannot explain the observed nonmonotonicity. This suggests that the direct coupling between the two order parameters should be considered to understand the experimental results, a finding which is consistent with recent microscopic calculations.

Theory of the non-planar peptide unitstar, open

By means of CNDO/2 calculations on N-methyl acetamide, it is shown that the state of minimum energy of the trans-peptide unit is a non-planar conformation, with the NH and NC2α bonds being significantly out of the plane formed by the atoms C1α, C′, O and N.

On a finite element model for the analysis of through cracks in laminated anisotropic cylindrical shells

A finite element model for the analysis of laminated composite cylindrical shells with through cracks is presented. The analysis takes into account anisotropic elastic behaviour, bending-extensional coupling and transverse shear deformation effects. The proposed finite element model is based on the approach of dividing a cracked configuration into triangular shaped singular elements around the crack tip with adjoining quadrilateral shaped regular elements. The parabolic isoparametric cylindrical shell elements (both singular and regular) used in this model employ independent displacement and rotation interpolation in the shell middle surface. The numerical comparisons show the evidence to the conclusion that the proposed model will yield accurate stress intensity factors from a relatively coarse mesh. Through the analysis of a pressurised fibre composite cylindrical shell with an axial crack, the effect of material orthotropy on the crack tip stress intensity factors is shown to be quite significant.

Einstein relation in n-i-p-i and microstructures of nonlinear optical, optoelectronic and related materials: Simplified theory, relative comparison and suggestions for an experimental determination

We investigate the Einstein relation for the diffusivity-mobility ratio (DMR) for n-i-p-i and the microstructures of nonlinear optical compounds on the basis of a newly formulated electron dispersion law. The corresponding results for III-V, ternary and quaternary materials form a special case of our generalized analysis. The respective DMRs for II-VI, IV-VI and stressed materials have been studied. It has been found that taking CdGeAs2, Cd3As2, InAs, InSb, Hg1−xCdxTe, In1−xGaxAsyP1−y lattices matched to InP, CdS, PbTe, PbSnTe and Pb1−xSnxSe and stressed InSb as examples that the DMR increases with increasing electron concentration in various manners with different numerical magnitudes which reflect the different signatures of the n-i-p-i systems and the corresponding microstructures. We have suggested an experimental method of determining the DMR in this case and the present simplified analysis is in agreement with the suggested relationship. In addition, our results find three applications in the field of quantum effect devices.

Finite element analysis of curved anisotropic laminated hollow bars

Curved hollow bars of laminated anisotropic construction are used as structural members in many industries. They are used in order to save weight without loss of stiffness in comparison with solid sections. In this paper are presented the details of the development of the stiffness matrices of laminated anisotropic curved hollow bars under line member assumptions for two typical sections, circular and square. They are 16dof elements which make use of one-dimensional first-order Hermite interpolation polynomials for the description of assumed displacement state. Problems for which analytical or other solutions are available are first solved using these elements. Good agreement was found between the results. In order to show the capability of the element, application is made to carbon fibre reinforced plastic layered anisotropic curved hollow bars.

Finite element analysis of laminated anisotropic beams of bimodulus materials

This paper presents finite element analysis of laminated anisotropic beams of bimodulus materials. The finite element has 16 d.o.f. and uses the displacement field in terms of first order Hermite interpolation polynomials. As the neutral axis position may change from point to point along the length of the beam, an iterative procedure is employed to determine the location of zero strain points along the length. Using this element some problems of laminated beams of bimodulus materials are solved for concentrated loads/moments perpendicular and parallel to the layering planes as well as combined loads.

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.

Self-consistent theory of localization in weakly disordered systems

An analytic treatment of localization in a weakly disordered system is presented for the case where the real lattice is approximated by a Cayley tree. Contrary to a recent assertion we find that the mobility edge moves inwards into the band as disorder increases from zero.