Stress concentration and effective stiffness of aligned fiber reinforced composite with anisotropic constituents

The paper addresses the problem of calculation of the local stress field and effective elastic properties of a unidirectional fiber reinforced composite with anisotropic constituents. For this aim, the representative unit cell approach has been utilized. The micro geometry of the composite is modeled by a periodic structure with a unit cell containing multiple circular fibers. The number of fibers is sufficient to account for the micro structure statistics of composite. A new method based on the multipole expansion technique is developed to obtain the exact series solution for the micro stress field. The method combines the principle of superposition, technique of complex potentials and some new results in the theory of special functions. A proper choice of potentials and new results for their series expansions allow one to reduce the boundary-value problem for the multiple-connected domain to an ordinary, well-posed set of linear algebraic equations. This reduction provides high numerical efficiency of the developed method. Exact expressions for the components of the effective stiffness tensor have been obtained by analytical averaging of the strain and stress fields.     

Effective stability for generalized Hamiltonian systems

An effective stability result for generalized Hamiltonian systems is obtained by applying the simultaneous approximation technique due to Lochak. Among these systems, dimensions of action variables and angle variables might be distinct.     

A computational strategy for multiscale systems with applications to Lorenz 96 model

Numerical schemes for systems with multiple spatio-temporal scales are investigated. The multiscale schemes use asymptotic results for this type of systems which guarantee the existence of an effective dynamics for some suitably defined modes varying slowly on the largest scales. The multiscale schemes are analyzed in general, then illustrated on a specific example of a moderately large deterministic system displaying chaotic behavior due to Lorenz. Issues like consistency, accuracy, and efficiency are discussed in detail. The role of possible hidden slow variables as well as additional effects arising on the diffusive time-scale are also investigated. As a byproduct we obtain a rather complete characterization of the effective dynamics in Lorenz model.     

BRILL－NOETHER MATRIX FOR RANK TWO VECTOR BUNDLES

Lei X be an arbitrary smooth irreducible complex projective curve, E (?) X a rank two vector bundle generated by its sections. The author first represents E as a triple {D1,D2,f}, where D1 , D2 are two effective divisors with d = deg(D1) + deg(D2), and f ∈ H0(X, [D1] |D2) is a collection of polynomials. E is the extension of [D2] by [D1] which is determined by f. By using f and the Brill-Noether matrix of D1 + D2, the author constructs a 2g X d matrix WE whose zero space gives Im{H0(X,[D1]) (?) H0(X, [D1] |D1)}(?)Im{H0(X, E) (?) H0(X,[D2]) (?) H0(X,[D2] |D2)}. From this and H0(X,E) = H0(X, [D1]) (?) Im{H0(X, E) (?) H0(X, [D2])}, it is got in particular that dimH0(X, E) = deg(E) - rank(WE) + 2.     

The K–nucleus cross sections in relativistic non-linear models

The K⁺−nucleus cross sections have been calculated in relativistic non-linear models taking into account the in-medium modifications of nucleons and mesons properties. More precisely, we have taken into account both the dressing of the nucleon effective mass by the scalar nuclear field in the target and the coupling of the mesons exchanged between the K⁺ and the nucleons to the polarization of the medium. First, using the most recent relativistic non-linear models, the in-medium σ, ω and ρ meson masses have been obtained in the nuclear matter rest frame. The influence of the non-linear contributions on the K⁺−nucleus cross sections has then been studied. Finally, we have compared our results with the experimental data.     

Remarks on beyond leading order

In recent years a two-scale expansion was established to study reactions of the type NN→NNπ within chiral perturbation theory. Then the diagrams of some subclasses that are invariant under the choice of the pion field no longer appear at the same chiral order. In this Letter we show that the proposed expansion still leads to well defined results. We also discuss the appropriate choice of the heavy baryon propagator.     

g-factor anisotropy for donor-bound electrons at all magnetic fields

Summary A theory of theg-factor for electrons bound to donors in zincblende semiconductors is presented for all magnetic fields. Simple analytical expressions are obtained for weak, intermediate and high magnetic-field intensities. A comparison between theory and the experimental result in the case of InSb is made.     

Structure and properties of nonclassical polymers

Utilizing an extended Hubbard-type Hamiltonian which incorporates both nearest-neighbour Coulomb repulsion and exchange interactions, we have studied the energy dispersion of the lowest elementary excitation from the ferromagnetically aligned state of quasi one-dimensional alternant hydrocarbon networks. It was found that the main effect of the long range Coulomb interaction may be thought of as a renormalization (screening) of the on-site Hubbard integral. This implies an enhancement of the kinetic exchange term and impairs the stability of the ferromagnetic state towards single spin inversions. However, for physically relevant values of the parameters entering the model Hamiltonian, the collective spin excitation represents a magnon, whose energy band lies above the reference value pertaining to the magnetically saturated configuration.Dedicated to Prof. Dr. Adolf Neckel on the occasion of his 60th birthday     

A novel measurement method of Donnan potential at an interface between a charged membrane and mixed salt solution

We developed a novel measurement method of the Donnan potential difference at a charged membrane/salt solution interface. The method can measure the potential under the condition that the membrane charge density is much lower than the KCl concentration of the salt bridge. This method is very useful for obtaining the effective charge density of each layer of a bipolar membrane. The present experiments in a system of a negatively charged poly(vinyl alcohol) membrane and a single salt solution of KCl, NaCl, LiCl, CaCl₂ and LaC₃ revealed that the membrane effective charged density has the same value for all the ions. The experiments in mixed KCl and CaCl₂ solution revealed that the potential in the system is governed mainly by the concentration of the counterion having the highest valence in the system.     

Model studies of the chemisorption of hydrogen and oxygen on nickel surfaces

Atomic chemisorption of hydrogen and oxygen on the Ni(100) surface has been studied using an Effective Core Potential (ECP) approach described in a previous paper. Clusters of up to 50 nickel atoms have been used to model the surface. The computed chemisorption energies are 62 kcal/mol (exp. 63 kcal/mol) for hydrogen and 106 kcal/mol (exp. 115–130 kcal/mol) for oxygen. Correlating the adsorbate and the cluster-adsorbate bonds is extremely important for obtaining accceptable results, particularly for oxygen. Reasonable convergence of chemisorption energies is obtained with 40–50 cluster atoms for both hydrogen and oxygen. For hydrogen the addition of a third cluster layer stabilizes the results considerably. Both hydrogen and oxygen are adsorbed at (or close to) the four-fold hollow site. The calculated barriers for surface migration are also in good agreement with the experimental estimates. The calculated equilibrium heights above the surface are on the other hand too high compared with experiments. This disagreement is believed to be due to core-valence correlation effects, which are not incorporated in the present ECP. The cluster convergence for the height above the surface is much slower than for the chemisorption energy.