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Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...
Current geomechanical applications imply non-isothermal processes of unsaturated geomaterials, in most cases following stress paths different than the classical triaxial compression often used in laboratory testing. Though the effects of temperature, sucti ...
The core structures of < c + a > edge and screw dislocations in Mg are computed using density functional theory (DFT). Both types dissociate into two 1/2 < c + a > partials on the second-order pyramidal planes. These DFT results are then allowed to relax w ...
Network information theory studies the communication of information in a network and considers its fundamental limits. Motivating from the extensive presence of the networks in the daily life, the thesis studies the fundamental limits of particular network ...
A graph G is a diameter graph in R-d if its vertex set is a finite subset in R-d of diameter 1 and edges join pairs of vertices a unit distance apart. It is shown that if a diameter graph G in R-4 contains the complete subgraph K on five vertices, then any ...
Bloch theorem is useful for analyzing wave propagation in periodic systems. It has been widely used to determine the energy bands of various translationally-periodic crystals and with the advent of nanoscale structures like nanotubes, it has been extended ...
Chirality is present as a trend of research in biological and chemical communities for it has a significant effect on physiological properties and pharmacological effects. Further, manipulating specific morphological chirality recently has emerged as a pro ...
We present a high-throughput microfluidic platform capable of quantitating up to 384 biomarkers in 4 distinct samples by immunoassay. The microfluidic device contains 384 unit cells, which can be individually programmed with pairs of capture and detection ...
We prove a quantitative estimate on the number of certain singularities in almost minimizing clusters. In particular, we consider the singular points belonging to the lowest stratum of the Federer-Almgren stratification (namely, where each tangent cone doe ...
We study the approximation properties of a wide class of finite element differential forms on curvilinear cubic meshes in n dimensions. Specifically, we consider meshes in which each element is the image of a cubical reference element under a diffeomorphis ...
