Related papers: Old but Not Obsolete: Dimensional Analysis in Nond…
A numerical bifurcation analysis of the electrically driven plane sheet pinch is presented. The electrical conductivity varies across the sheet such as to allow instability of the quiescent basic state at some critical Hartmann number. The…
The fractal dimension is a central quantity in nonlinear dynamics and can be estimated via several different numerical techniques. In this review paper we present a self-contained and comprehensive introduction to the fractal dimension. We…
Inclusion of redundant fundamental quantities in SI system has resulted in lot of ambiguities and confusion in modern theories. The incompatibilities between the existing theories can possibly be due to incorrect assumption of fundamental…
Deriving macroscopic phenomenological laws of irreversible thermodynamics from simple microscopic models is one of the tasks of non-equilibrium statistical mechanics. We consider stationary energy transport in crystals with reference to…
Nonlinear bending phenomena of thin elastic structures arise in various modern and classical applications. Characterizing low energy states of elastic rods has been investigated by Bernoulli in 1738 and related models are used to determine…
Density functional theory (DFT) is used in thousands of papers each year, yet lack of universality reduces DFT's predictive capacity, and functionals may produce energy-density imbalances. The absolute electronegativity (\chi) and hardness…
A central problem of materials science is to determine whether a hypothetical material is stable without being synthesized, which is mathematically equivalent to a global optimization problem on a highly non-linear and multi-modal potential…
This paper introduces a novel variational Bayesian method that integrates Tucker decomposition for efficient high-dimensional inverse problem solving. The method reduces computational complexity by transforming variational inference from a…
Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time…
Dimensional analysis provides a universal framework for reducing physical complexity and reveal inherent laws. However, its application to high-dimensional systems still generates redundant dimensionless parameters, making it challenging to…
Three-dimensional electron diffraction (3D ED) has emerged as a powerful method for solving the structures of sub-micron-sized particles down to nanoparticles. However, it faces technical challenges when applied to beam-sensitive samples or…
This thesis synthesizes probability and entropic inference with Quantum Mechanics (QM) and quantum measurement [1-6]. It is shown that the standard and quantum relative entropies are tools designed for the purpose of updating probability…
This paper derives a finite-strain plate theory consistent with the principle of stationary three-dimensional (3-D) potential energy under general loadings with a third-order error. Staring from the 3-D nonlinear elasticity (with both…
The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…
Correcting for detector effects in experimental data, particularly through unfolding, is critical for enabling precision measurements in high-energy physics. However, traditional unfolding methods face challenges in scalability,…
Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…
This paper presents a novel theoretical framework for reducing the computational complexity of multi-model adaptive control/estimation systems through systematic transformation to controllable canonical form. While traditional multi-model…
This paper proposes a tool for dimension reduction where the dimension of the original space is reduced: a Principal Loading Analysis (PLA). PLA is a tool to reduce dimensions by discarding variables. The intuition is that variables are…
Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…
Purpose: Biophysical tissue models are increasingly used in the interpretation of diffusion MRI (dMRI) data, with the potential to provide specific biomarkers of brain microstructural changes. However, the general Standard Model has…