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## A perturbative approach to domain structure analysis in elastic cubic ferromagnetic crystals

### ARI - An International Journal for Physical and Engineering Sciences (1998-03-01) 51: 86-97 , March 01, 1998

A model of a continuum with an interface is adopted to describe domain structures in elastic ferromagnetic crystals at equilibrium. A perturbative method is applied to field equations and jump conditions in order to simplify their analysis, in the approximation of “infinitesimal” strains. In particular, a well-known domain structure for cubic ferromagnetic crystals in the absence of a magnetic field is studied.

## Geochemistry of subduction-related mafic to felsic volcanic rocks of the late Archean Wawa greenstone belts, Superior Province, Canada

### ARI - An International Journal for Physical and Engineering Sciences (1998-12-01) 51: 277-295 , December 01, 1998

The late Archean (2.7 Ga) Schreiber-Hemlo and White River-Dayohessarah greenstone belts are characterized by tectonically juxtaposed volcanic and siliciclastic sedimentary rocks, which were collectively intruded by the syn- to post-kinematic, high-Al, high La/Yb_{n} tonalite-trondhjemite-granodiorite (TTG) plutons. The volcanic rocks are composed of two distinct types of sequences: (1) komatiitic to tholeiitic basalts ocean plateau sequences and (2) mafic to felsic volcanic arc sequences. Based on major and trace element abundances, mafic to felsic, arcrelated volcanic rocks of the Schreiber-Hemlo and White River-Dayohessarah greenstone belts are divided into three major suites: (1) mafic to intermediate tholeiitic flows, (2) mafic to intermediate calc-alkaline flows, and (3) felsic calc-alkaline flows. All these suites share positively fractionated REE patterns, and negative anomalies of Nb and Ti. However, some intermediate and felsic volcanic rocks have positive Zr and Hf anomalies. Fractionated REE patterns, and negative Nb and Ti anomalies with respect to the neighbouring REE are all consistent with a juvenile oceanic island arc origins a metasomatized mantle wedge source for the tholeiitic suite. In comparison to tholeiites, the mafic to intermediate calc-alkaline suite is distinct in terms of: (1) enrichment in MgO, Th and LREE, Cr, and Ni; (2) higher Al_{2}O_{3}/TiO_{2} ratios; (3) more fractionated REE patterns; (4) more pronounced negative Nb and Ti anomalies; and (5) less fractionation between HREE and Sc-V, suggesting deeper and more primitive mantle source compositions for the calc-alkaline suite than the tholeiitic counterpart. Felsic rocks are defined by the enrichment of Zr and Hf, with respect to MREE, and correlate negatively with Sc abundances, suggesting garnet + amphibole ± clinopyroxene residual in the source. The inferred presence of garnet and clinopyroxene in the source is consistent with an independent argument for ecologitic residues in the slab. The existence of overlapping fields between mafic, intermediate, and felsic suites on trace element ratio diagrams suggest that processes controlling the production of these volcanic rocks were more complex than simple slab and/or wedge melting. This complexity may have resulted from a mixture of slab and wedge melts, second stage melting, magma mixing, fractional crystallization, partial equilibration with sub-arc wedge peridotite, crustal contamination, or some combination. Higher MgO, Ni, and Cr contents at a given Mg# in the basalts and andesites are consistent with higher geothermal gradients at Archean subduction zones than Phanerozoic counterparts.

## Shock waves by a kinetic model of van der Waals fluids

### ARI - An International Journal for Physical and Engineering Sciences (1999-03-01) 51: 203-215 , March 01, 1999

We present a four-velocity kinetic model of van der Waals fluids. Although, from the physical point of view this model is very simple, mathematically it is quite complicated. Due to this complexity we performed various simplifications, which are also presented. We look for traveling wave solutions for these simplified versions. A discussion of the types of the states of rest is presented. We pay some attention to the monotonicity of the density component of the traveling wave. Finally, we compare the model's kinetic and hydrodynamic shock wave structures. The new feature is that kinetic effects alone are unable to kill the artificial phenomenon of impending shock splitting.

## Equivalence transformations for one-dimensional wave equations of balance form

### ARI - An International Journal for Physical and Engineering Sciences (1998-03-01) 50: 151-160 , March 01, 1998

Equivalence transformations associated with the most general one-dimensional wave equation of balance form are investigated. Equivalence transformations considered here constitute a group and are thus much more general than symmetry groups, in the sense that they map equations involving arbitrary functions or parameters into equations of the same family. The formalism adopted in this work is based on exterior calculus, and the problem is simply reduced to determine isovector fields in the tangent space of an extended differentiable manifold dictated by the structure of the differential equation whose orbits induce transformations which leave an ideal of an exterior algebra over the manifold generated by certain contact and balance forms invariant. A general form of the isovector field is obtained. The components of the independent isovector fields are none other than the infinitesimal generators of the corresponding equivalence groups. Some special cases are also treated.

## A recurrent perceptron learning algorithm for cellular neural networks

### ARI - An International Journal for Physical and Engineering Sciences (1998-12-01) 51: 296-309 , December 01, 1998

A supervised learning algorithm for obtaining the template coefficients in completely stable Cellular Neural Networks (CNNs) is analysed in the paper. The considered algorithm resembles the well-known perceptron learning algorithm and hence called as Recurrent Perceptron Learning Algorithm (RPLA) when applied to a dynamical network. The RPLA learns pointwise defined algebraic mappings from initial-state and input spaces into steady-state output space; despite learning whole trajectories through desired equilibrium points. The RPLA has been used for training CNNs to perform some image processing tasks and found to be successful in binary image processing. The edge detection templates found by RPLA have performances comparable to those of Canny’s edge detector for binary images.

## Electrodynamics of microstretch and micropolar fluids

### ARI - An International Journal for Physical and Engineering Sciences (1998-03-01) 50: 169-179 , March 01, 1998

A continuum theory is developed for anisotropic microstretch and micropolar fluids subject to electormagnetic interactions. Balance laws and thermodynamically admissible constitutive equations are obtained. Material and thermodynamic stability restrictions on the material moduli are determined. Field equations are obtained for both anisotropic microstretch and micropolar fluids. The general theory is specialized to formulate field equations for micropolar magneto and electro-hydrodynamics.

## On asymptotic equipartition of energy in linear elastodynamics for exterior domains

### ARI - An International Journal for Physical and Engineering Sciences (1999-03-01) 51: 191-195 , March 01, 1999

This paper deals with the problem of equipartition of the total energy in linear elastodynamics for exterior domains. Suitable hypotheses on the initial data and on the acoustic tensor allow us to prove that Cesaro's means of the kinetic and strain energies tend to one-half of the total energy asymptotically in time.

## Selective excitation of parabolic Stark states in ion-atom collisions via the Paul-trap mechanism

### ARI - An International Journal for Physical and Engineering Sciences (1998-03-01) 51: 48-55 , March 01, 1998

Excitation of atoms by ion impact is analyzed for such collisions where only the Coulomb field of the ion affects the excitation process. At intermediate energies, electrons bound to the atom are promoted on the saddle of a two-center Coulomb field, where they are dynamically stabilized by a Paul-trap-like mechanism. These excitation processes lead to transient atomic states with large electric dipole moments. By measuring the intensity of HeI spectral lines induced by 10–500-keV protonhelium and 65-MeV Ar^{q +}-helium (*q* = 6 and 13) collisions as a function of an electric field *F*_{z} applied to the collision volume, the electric dipole moments predicted by the Paul-trap model were detected.

## A unified continuum theory of liquid crystals

### ARI - An International Journal for Physical and Engineering Sciences (1997-02-01) 50: 73-84 , February 01, 1997

A unified continuum theory is proposed governing physical behavior of all liquid crystals whose molecules are modelled with rigid directors. Balance laws and constitutive equations are given and thermodynamic restrictions are obtained. Chiral and nonchiral liquid crystals are shown to differ only in their symmetry groups and smectic liquid crystals in a constraint on twist elasticities. Dynamic constitutive equations include translation and gyration viscosities coupled with heat conduction. The theory is shown to give the director (Oseen-Frank) theory under special conditions valid for that theory.

## A new Trefftz method for solving boundary value problems

### ARI - An International Journal for Physical and Engineering Sciences (1997-02-01) 50: 85-95 , February 01, 1997

We describe a new Quasi Trefftz Spectral Method (QTSM) for solving elliptic boundary value problems in some domain Ω with the governing equation *Lu* = *f*. QTSM combines the properties of the boundary methods with the spectral approach. The special feature of QTSM is that we use trial functions which satisfy the corresponding homogeneous equation *Lu* = 0 only approximately. We expand these trial functions with respect to eigenfunctions of the operator *L* in some domain Ω*0* ⊃ Ω with appropriate simple boundary conditions. The method has been found to work well for different inhomogeneous problems with the Laplace and the Helmholtz operators, axisymmetric and periodic problems, problems with infinitely long boundaries. The possibilities of further development of QTSM are also discussed.