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The Minkowski functionals are a mathematical tool to quantify morphological features of patterns. Some applications to the matter distribution in galaxy catalogues and N-body simulations are reviewed, with an emphasis on the effects of…
The effect of space distribution of randomly-placed particles in a representative composite volume on the thermoelastic effective properties and local stress and strain distribution is analyzed. Quantitative assessment is performed using…
The lattice spin model, with nearest neighbor ferromagnetic exchange and long range dipolar interaction, is studied by the method of time series for observables based on cluster configurations and associated partitions, such as Shannon…
Second-order structured deformations of continua provide an extension of the multiscale geometry of first-order structured deformations by taking into account the effects of submacroscopic bending and curving. We derive here an integral…
Understanding and manipulating the relationship between intentionally introduced disorder and material properties necessitates efficient characterization techniques. For example, single crystal diffuse scattering experiments provide…
Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work…
Mutually repelling particles form spontaneously ordered clusters when forced into confinement. The clusters may adopt similar spatial arrangements even if the underlying particle interactions are contrastingly different. Here we demonstrate…
Multi-technique high resolution X-ray mapping enhanced by the recent advent of 4th generation synchrotron facilities can produce colossal datasets, challenging traditional analysis methods. Such difficulty is clearly materialized when…
Interfaces such as grain boundaries in polycrystalline as well as heterointerfaces in multiphase solids are ubiquitous in materials science and engineering. Far from being featureless dividing surfaces between neighboring crystals,…
We review theoretical results obtained recently in the framework of statistical mechanics to study systems with long range forces. This fundamental and methodological study leads us to consider the different domains of applications in a…
Field induced assembly of reconfigurable structures with complex hierarchical configurations has recently become an area of intense research with the promise for exciting applications in programmable self-assembly and nano/microstructure…
The paper continues a series of papers devoted to treatment of the crystalline state on the basis of the approach in equilibrium statistical mechanics proposed earlier by the author. This paper is concerned with elaboration of a…
It is demonstrated that power-laws which are modified by logarithmic corrections arise in supercorrelated systems. Their characteristic feature is the energy attributed to a state (or value of a general cost function) which depends…
In this paper we consider symmetric powers representation and exterior powers representation of finite groups, which generated by the representation which has finite dimension over the complex field. We calculate the multiplicity of…
A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. By rigorous asymptotic analysis we show that the sharp-interface limit of this model recovers the continuum model equations for the…
We review recent progress and future prospects of matter wave interferometry with complex organic molecules and inorganic clusters. Three variants of a near-field interference effect, based on diffraction by material nanostructures, at…
The properties of fluctuation induced interactions like van der Waals and Casimir-Lifshitz forces are of interest in a plethora of fields ranging from biophysics to nanotechnology. Here we describe a general approach to compute these…
Fluid-mediated interactions between particles in a vibrating fluid lead to both long range attraction and short range repulsion. The resulting patterns include hexagonally ordered micro-crystallites, time-periodic structures, and chaotic…
The form factors of integrable models in finite volume are studied. We construct the explicite representations for the form factors in terms of determinants.
A continuum density-field formulation with particle-scale resolution is constructed to simultaneously incorporate the orientation dependence of interparticle interactions and the rotational invariance of the system, a fundamental but…