In many cases, structural measurements on heterogeneous materials do not directly yield real-space images, but intensities in reciprocal space. This is notably true for all scattering methods, but also for certain NMR imaging experiments. As is well known, this reciprocal space information can be expressed in the form of spatial correlation functions. Determination of real-space structures that can then be used to model material properties from spatial correlation functions is a computationally demanding task. We have developed a novel algorithm for this, which is several orders of magnitude more efficient than prior art. In addition, we study the restoration of multiphase microstructures, conditions imposed on truly representable correlation functions, and the uniqueness of the restoration process.
Interfacial friction is one of the oldest problems in physics and chemistry and certainly one of the most important from a practical point of view. Due to its practical importance and the relevance to basic scientific questions there has been major increase in activity in the study of interfacial friction on the microscopic level during the last decade. New experimental tools have been developed that allow for detailed investigations of friction at nanometer length scales, a range over which the related processes have been termed nanotribology. Intriguing structural and dynamical features have been observed experimentally in nanoscale molecular systems confined between two atomically smooth solid surfaces. These include for example, stick-slip motion, intermittent stick-slip motion characterized by force fluctuations, transition to sliding above the critical velocity, and a dependence of friction on the history of the system. These and other observations have motivated theoretical efforts, both numerical and analytical, but most issues are still subject to controversy. In spite of the recently growing efforts many aspects of friction are still not well understood. We investigate in detail a minimalistic model which includes most of the relevant microscopic parameters needed to obtain the above experimental observables. We also establish relationships between the properties of the embedded system and the frictional forces. Our aim is therefore to better understand the origins of friction and to learn how to control its nature. Our approach leads to a new look at this old problem and to predictions amenable to experimental tests.
Composite materials are engineered materials made from two or more constituents that remain separate and distinct on a microscopic level while forming a single macroscopic component. A classical problem in materials science is to determine the effective elastic properties of a composite material made up of a random distribution of elastic inclusions embedded in a continuous matrix. We have numerically studied the transverse elastic behavior of a unidirectional composite comprising non-overlapping silica fibers dispersed in a rubber matrix. Some composite morphologies that provided an ultra high transverse shear modulus at rather moderate silica loadings were identified. For these morphologies, predicted elastic stiffening levels were in agreement with those measured at low strains in carbon black and silica filled rubbers, leading one to surmise that such elastic stiffening may also play an important role in the low strain mechanical responses of actual carbon black or silica filled rubbers.
In another cycle of publications we have calculated numerically the concentration dependence of the transverse Poisson's ratios of packed arrays of nonoverlapping identical parallel cylindrical voids dispersed in an aluminum matrix. It was shown that the transverse Poisson's ratio of the hexagonal and random packed arrays approached 1 upon increasing the concentration of voids while the ratio of the square packed array along the principal continuation directions approached 0. Experimental measurements were carried out on rectangular aluminum bricks with identical cylindrical holes drilled in square and hexagonal packed arrays. Experimental results were in good agreement with numerical predictions. We then demonstrated, based on the numerical and experimental results, that by varying the spatial arrangement of the holes and their volume fraction, one can design and manufacture voided materials with a tailored Poisson's ratio between 0 and 1. In practice, those with a high Poisson's ratio, i.e., close to 1, can be used to amplify the lateral responses of the structures while those with a low one, i.e., close to 0, can largely attenuate the lateral responses and can therefore be used in situations where stringent lateral stability is needed.