Related papers: Statistical theory of structures with extended def…
Heterogeneity is classified in five categories---topologic, geometric, kinematic, static, and constitutive---and the first four categories are investigated in a numerical DEM simulation of biaxial compression. The simulation experiments…
Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the…
Lattice structures have great potential for several application fields ranging from medical and tissue engineering to aeronautical one. Their development is further speeded up by the continuing advances in additive manufacturing…
It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the…
We discuss the relevance of methods of graph theory for the study of damage in simple model materials described by the random fuse model. While such methods are not commonly used when dealing with regular random lattices, which mimic…
Disorder and long-range interactions are two of the key components that make material failure an interesting playfield for the application of statistical mechanics. The cornerstone in this respect has been lattice models of the fracture in…
A homogeneous mass-fragmentation, as it has been defined in \cite{RFC}, describes the evolution of the collection of masses of fragments of an object which breaks down into pieces as time passes. Here, we show that this model can be…
In this paper the characteristic matrix method is used to study the propagation of electromagnetic waves through one-dimensional lossy photonic crystals composed of negative and positive refractive index material layers with symmetric and…
Disorder is more the rule than the exception in natural and synthetic materials. Nonetheless, wave propagation within inhomogeneously disordered materials has received scant attention. We combine microwave experiments and theory to find the…
This chapter covers methodological issues related to estimation, testing and computation for models involving structural changes. Our aim is to review developments as they relate to econometric applications based on linear models.…
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…
Homogeneous fragmentations describe the evolution of a unit mass that breaks down randomly into pieces as time passes. They can be thought of as continuous time analogs of a certain type of branching random walks, which suggests the use of…
The situation of the metastable phase decay on the several types of heterogeneous centers is considered. This publication directly continues " [email protected] get 0001104 ". Here we give the results of numerical modeling for the total…
The emergence of scanning probe and electron beam imaging techniques have allowed quantitative studies of atomic structure and minute details of electronic and vibrational structure on the level of individual atomic units. These microscopic…
The situation of the decay of the metastable phase on the several types of heterogeneous centers is described analytically. The total number of heterogeneous centers is supposed to be equal for different types. This description decomposes…
Traditional Statistical Process Control methodologies face several challenges when monitoring defects in complex geometries, such as those of products obtained via Additive Manufacturing techniques. Many approaches cannot be applied in…
Inference for statistics of a stationary time series often involve nuisance parameters and sampling distributions that are difficult to estimate. In this paper, we propose the method of orthogonal samples, which can be used to address some…
Previously reported crystalline structures obtained by an iterative phase retrieval reconstruction of their diffraction patterns seem to be free from displaying any irregularities or defects in the lattice, which appears to be unrealistic.…
Micro and nanoscale materials have remarkable mechanical properties, such as enhanced strength and toughness, but usually display sample-to-sample fluctuations and non-trivial size effects, a nuisance for engineering applications and an…
An algorithm is developed for structure identification of amorphous carbonaceous nanomaterials with a joint x-ray and neutron diffraction data analysis, using the data on the chemical composition of the sample from other diagnostics. The…