Materials Literature
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Symmetry is a cornerstone of modern mathematics and physics, yet conventional treatments typically regard symmetry as a static property of a single configuration or structure. This paper introduces a new perspective, Recursive Symmetry Theory, which treats symmetry as an operation that can be applied repeatedly to gen…
Liquid metals have emerged as promising heat transfer media across advanced energy systems. However, under off-normal conditions they may come into direct contact with water, triggering interfacial solidification—a critical yet largely unexplored phenomenon. Taking the steam generator tube rupture accident in lead-coo…
This manuscript introduces the concept of a Universal Invariant Space, a mathematical framework in which every mathematical object is assigned a unique invariant signature. The construction of the Universal Invariant Algebra follows from these signatures, providing a systematic means to compare and classify objects ac…
Abstract This review provides a comprehensive analysis of contemporary approaches to integrating machine learning with solid-state chemistry for the rational design and accelerated discovery of electrochemical materials for solid oxide fuel cells (SOFCs), solid oxide electrolysis cells (SOECs), and reversible solid ox…
Supplementary Material 1.
Supplementary Material 1.
FINDING: Fibonacci numbers appear in Mandelbrot set dynamics and can be generated via closed-form tree structures, linking recursion to fractal geometry. | MATH: Fibonacci recurrence \(F_n = F_{n-1} + F_{n-2}\); closed-form via Binet: \(F_n = \frac{\phi^n - \psi^n}{\sqrt{5}}\) where \(\phi = \frac{1+\sqrt{5}}{2} \appr…
Abstract Microdroplets provide highly dynamic interfacial environments capable of regulating chemical reactivity through the generation of localized electric fields (EFs) and reactive oxygen species, such as hydroxyl radicals (·OH), at their interfaces. However, direct nanoscale visualization of microdroplet-regulated…
Granular systems are common in nature and everyday life, but their behavior can be hard to predict, especially when they suddenly fail, as in an avalanche. To study this problem, we use a simple two-dimensional model of 19 particles inside a box. The particles can form stable jammed states or failure states where they…
This manuscript introduces the concept of Mathematical Structural Temperature (MST) as a quantitative measure of the exchangeability of legal configurations within a mathematical structure. MST is denoted by T_str(X) for a structure X and is defined through an axiomatic framework that captures the combinatorial richne…
The present work introduces Structural Minimality Theory, a framework for determining the smallest structural configuration that suffices to guarantee the validity of a given mathematical statement. By formalizing the notion of a Minimal Supporting Structure (MSS), the theory provides a systematic method to identify t…
In many complex systems, the underlying structure is not fully occupied by constituent elements; some positions that could logically host an element remain empty. These positions are not arbitrary omissions but are determined by the structure's intrinsic geometry, topology, and symmetry. This paper introduces a formal…
Nickel–titanium alloys produced through powder metallurgy were subjected to controlled aging treatments to examine how thermal exposure influences microstructural evolution, oxide formation, and corrosion performance. Aging at 600 °C for 1–3 h progressively reduced porosity and promoted the development of intermetalli…
Symmetry is a foundational concept in mathematics and physics, traditionally studied through group actions on spaces or objects. This paper proposes a unifying framework called the Universal Symmetry Hierarchy that extends the conventional notion of symmetry to multiple layers. We introduce the concept of Symmetry of…
In this study we have performed first principle calculations to study the electronic and its resulting thermoelectric properties of SnSb alloy within the framework of density functional theory (DFT). Generalized Gradient Approximation (GGA) is employed to model the exchange and correlation of KohnSham Eigen states. Th…
Revision Update V4: This manuscript has been extensively upgraded to formally introduce the TELOS (Twisted Encapsulated Layered Optimized Strain) Architecture. We have eliminated previous reliance on phenomenological "toy model" parameters by integrating large-scale, first-principles Density Functional Theory (DFT) an…
Machine-learning force fields provide a promising route for accelerating molecular simulation by replacing expensive quantum-chemical calculations with differentiable models of molecular energies and atomic forces. However, learning accurate and energy-conserving forces remains challenging, especially when the model m…
This paper develops a unified conceptual and analytical framework for the study of energy landscapes in mathematics. We show that a wide class of mathematical theories can be interpreted through the geometry of an associated scalar potential function, or "energy," defined on a suitable domain. By examining the critica…
Discovering materials with desirable properties often requires searching large candidate spaces while experimental or computational evaluations remain costly. Active learning addresses this challenge by using previous observations to select which candidate to evaluate next, typically through probabilistic surrogate mo…
A new series of difluoro-substituted analogues, 4-(((2,6-difluorophenyl)imino)methyl)phenyl 4-(x-alkyloxy)benzoates (DFPIMB-n), was synthesized to assess how lateral substitution and terminal alkoxy chain length affect mesomorphic behavior. Differential scanning calorimetry and polarized optical microscopy measurement…