Related papers: Analytic Materials
Materials with nanoscale phase separation are considered. These materials are formed by a mixture of several phases, so that inside one phase there exist nanosize inclusions of other phases, with random shapes and random spatial locations.…
Studies on time and memory costs of products in geometric algebra have been limited to cases where multivectors with multiple grades have only non-zero elements. This allows to design efficient algorithms for a generic purpose; however, it…
Novel optical elements containing semitransparent wavelike films embedded into the bulk of transparent material, which form a reflection image without transmitted light distortion, are studied. The dynamic theory of light diffraction by a…
An extension of the ambient metric construction of Fefferman-Graham to infinite order in even dimensions is described. The main ingredients are the introduction of "inhomogeneous ambient metrics" with asymptotic expansions involving the…
Successful materials innovations can transform society. However, materials research often involves long timelines and low success probabilities, dissuading investors who have expectations of shorter times from bench to business. A…
We present a multimodal deep learning (MDL) framework for predicting physical properties of a 10-dimensional acrylic polymer composite material by merging physical attributes and chemical data. Our MDL model comprises four modules,…
Here, we present an overview of recent developments in the characterization of electromagnetic and quantum metamaterials using effective medium methods. It is highlighted that both electromagnetic and electronic systems can be homogenized…
We obtain analytical solutions for positive-to-negative transition materials with a smooth transition profile "$\tanh$". The fields are expressed in terms of hypergeometric functions. The final expressions for reflection and transmission…
The approach based on selected set of samples and selected set of analytical tools occurred quite efficient when applying to amorphous carbons thus leading to a transformation of the current representation of the issue based on particulars…
The notions of uniformity and homogeneity of elastic materials are reviewed in terms of Lie groupoids and frame bundles. This framework is also extended to consider the case Functionally Graded Media, which allows us to obtain some…
Theoretical frameworks used to qualitatively and quantitatively describe nuclear dynamics in solids are often based on the harmonic approximation. However, this approximation is known to become inaccurate or to break down completely in many…
The methods of Information geometry have been glowing up to develop various subjects of theoretical physics, including quantum information systems. The present article has two purposes. The first one is to develop general theory of…
Consider a graphed holomorphic surface $u=F(x,y)$ in $\mathbb{C}^3_{x,y,u}$ under the action of the affine transformation group $A(3)$. In 1999, Eastwood and Ezhov obtained a list of homogeneous models by determining possible tangential…
The four types of homogeneity -- additive, multiplicative, exponential, and logarithmic -- are generalized as transformations describing how a function $f$ changes under scaling or shifting of its arguments. These generalized homogeneity…
We provide an introduction to complex photonic media, that is, composite materials with spatial inhomogeneities that are distributed over length scales comparable to or smaller than the wavelength of light. This blossoming field is firmly…
We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It…
The "Workshop on Machine learning in heterogeneous porous materials" brought together international scientific communities of applied mathematics, porous media, and material sciences with experts in the areas of heterogeneous materials,…
Heterogeneous materials exhibit anisotropy which is influenced by factors such as individual phase properties and microstructural configuration that form crucial descriptors of heterogeneity. A review of anisotropy indices proposed in the…
In this mini-review we summarize the progress of modeling, simulation and analysis of shock responses of heterogeneous materials in our group in recent years. The basic methodology is as below. We first decompose the problem into different…
Segregation is a popular phenomenon. It has considerable effects on material performance. To the author's knowledge, there is still no automated objective quantitative indicator for segregation. In order to full fill this task, segregation…