J. A. Krumhansl

Hysteresis and hierarchies: Dynamics of disorder-driven first-order phase transformations

We use the zero-temperature random-field Ising model to study hysteretic behavior at first-order phase transitions. Sweeping the external field through zero, the model exhibits hysteresis, the return-point memory effect, and avalanche fluctuations. There is a critical value of disorder at which a jump in the magnetization (corresponding to an infinite avalanche) first occurs. We study the universal behavior at this critical point using mean-field theory, and also present results of numerical simulations in three dimensions.

Formal aspects of the theory of the scattering of ultrasound by flaws in elastic materials

An integral equation is used to derive formal expressions for the scattering of a plane wave from a single homogeneous flaw embedded in an isotropic elastic medium. Expressions are found for the scattered amplitudes and differential cross sections. An optical theorem is also derived.

The Born approximation in the theory of the scattering of elastic waves by flaws

We used the integral equation formulation of the scattering of elastic waves to generate an approximate solution analogous to the Born approximation in quantum mechanics. This solution is attractive because of the ease with which it may be applied to scatterers of complicated shapes. We investigated the validity of the approximation by comparing it with exact results for spherical scatterers. Our conclusion for voids in elastic media is that the approximation describes well the scattering when the wavelength of the incident wave is approximately an order of magnitude larger than the scatterer and when the scattering is viewed in the backscattered directions. For many applications this range of validity is experimentally accessible. For elastic inclusions, however, where the properties of defect and host differed by 20–40%, the Born approximation is surprisingly good for all angles and even at short wavelengths.

Weakly-pinned Froehlich-charge-density-wave condensates: a new, nonlinear, current-carrying elementary excitation

New, nonlinear, charged elementary excitations are predicted to occur for weakly-pinned Froehlich-charge-density-wave condensates at low temperatures.

DISORDER-DRIVEN PRETRANSITIONAL TWEED PATTERN IN MARTENSITIC TRANSFORMATIONS

Defying the conventional wisdom regarding first-order transitions, {ital solid{minus}solid} {ital displacive} {ital transformations} are often accompanied by pronounced pretransitional phenomena. Generally, these phenomena are indicative of some mesoscopic lattice deformation that ``anticipates`` the upcoming phase transition. Among these precursive effects is the observation of the so-called ``tweed`` pattern in transmission electron microscopy in a wide variety of materials. We have investigated the tweed deformation in a two-dimensional model system, and found that it arises because the compositional disorder intrinsic to any alloy conspires with the natural geometric constraints of the lattice to produce a frustrated, glassy phase. The predicted phase diagram and glassy behavior have been verified by numerical simulations, and diffraction patterns of simulated systems are found to compare well with experimental data. Analytically comparing to alternative models of strain-disorder coupling, we show that the present model best accounts for experimental observations.

Macroscopic engineering properties of polycrystalline materials: Elastic properties

We outline the formal application of integral equation methods (Green’s function techniques) to the systematic computation of the effective elastic properties of polycrystalline materials from the specification of the statistical distribution of elastic properties of the constituent grains (or pores). These methods are not entirely new, but by the use of recent developments in theory of the physics of the electronic porperties and lattice dynamics of disordered solids, we can place various methods on a common footing and indicate their limitations. Some details for the computational application of these methods are also presented.

Solitons in condensed matter: A paradigm

Abstract For this new journal dealing with nonlinear phenomena we review the setting of several important current problems in the physics of condensed matter (solids, liquids). We show how the concepts embodied in the mathematical analysis of solitons provide systematic new insight (i.e., a paradigm) into a central question: what are the important physical configurations in nonlinear condensed systems? Following these general issues we summarize the analysis of the dynamics and equilibrium thermodynamics (i.e., statistical mechanics) of non-linear one-dimensional model systems, and we indicate how the solitonic configurational phenomenology provides a basis for dynamic effects which are seen both experimentally and in molecular dynamics computer simulations. Many problems in condensed matter differ from the more familiar nonlinear mechanical or hydrodynamic applications in that finite temperature thermal fluctuations must be considered along with systematic dynamics.

The Lattice Vibration Specific Heat of Graphite

Recent experiments have shown that the specific heat of graphite varies as T2 instead of T3 between 15°K and 80°K. In this paper such a behavior is shown to be a consequence of the elastic anisotropy of graphite, and therefore an intrinsic property, rather than a particle size effect as suggested by Gurney, or a plate‐like behavior as suggested by Komatsu and Nagamiya. The Gurney treatment is shown to be in error both as to the enumeration of modes, and as to the temperature range over which the particle size effect might be of significance. The Komatsu and Nagamiya treatment is shown to be inconsistent with elasticity theory. The present treatment employs a semirigorous analysis of the normal mode problem for the transverse vibrations, approximated for long wavelengths. It is found that experimental data from 15–1000°K can be well fitted by dividing the lattice vibrations into two types: (a) modes with atom displacements normal to the layer planes with a Debye temperature of 900°K, and (b) modes with ato...

Determination of flaw characteristics from ultrasonic scattering data

We report an approximate technique (and some test results) for determining the characteristics of flaws in elastic media from a knowledge of the ultrasonic scattering amplitudes. The technique is rigorously valid in the weak‐scattering limit. Good results have been obtained for strongly scattering spherical flaws such as a void in stainless steel. The technique is insensitive to random noise in the scattering amplitudes.

Triplet Correlation in Liquid Argon by Monte Carlo Method: Low Densities

The triplet correlation function for low density fluid argon was obtained by the Monte Carlo method for three different temperatures, assuming a Lennard‐Jones‐type potential. At low densities the agreement with the prediction of the Kirkwood superposition assumption (SA) was found to be better than 10% for most values. Significant differences between the two were found at small distances, where the SA gives unreliable estimates, and at the peaks of the triplet function, where the SA predicts too large a value.