Materials Literature
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This paper introduces a novel framework called Mathematical Phase Alignment Theory (MPAT) that formalizes the intuition that diverse mathematical domains can exhibit coherent phase relationships when appropriately mapped. Central to this framework is the Alignment Operator, a construct that aligns the intrinsic phase…
Hybrid composites are increasingly attractive due to their lightweight nature and enhanced flame-retardant properties. This study investigated flame-retardant hybrid laminates by using carbon fibers and multiwalled carbon nanotubes (MWCNT) coated hemp fibers embedded in a novolac phenolic resin. Ammonium polyphosphate…
Quaternary mixed-metal chalcohalides offer a compositionally versatile platform for developing lead-free semiconductor nanomaterials, yet colloidal access to Cu–Bi–S–Cl compositions remains unexplored. Here, we report the first solution-phase synthesis of CuBiSCl₂ nanocrystals (NCs) through a hot-co-injection strategy…
تحلیل بنیادین، بازنویسی تانسوری و اثبات جامع معمای شماره ۱ از ۳۰ (سری جدید: نیروی هستهای ضعیف): «مسئله سلسلهمراتب (The Hierarchy Problem) و پارادوکس تنظیم ظریف و سیستم هماهنگسازی مقیاس انرژی در منیفولد ۱۱۵۵ بعدی»؛ مبنی بر اینکه «اختلاف نجومی ۱۴ مرتبه بزرگی میان مقیاس الکتروضعیف ($\sim 100 \text{ GeV}$) و مقیاس پلان…
FINDING: No new mathematical tablet discovery is reported; the search results are dominated by sensationalist YouTube titles and a single arXiv paper on AI metadata classification, not mathematical content. MATH: No equations, constants, or ratios are extractable from the provided sources. The arXiv paper (2603.03892v…
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…
Functionalities of ferroelectric materials are governed by the spatial organization and coupling of polarization, strain, lattice rotation, and structural order accessible via atomically resolved scanning transmission electron microscopy (STEM) images. Quantitative interpretation of atomic-resolution STEM data has con…
This paper introduces the Algorithmic Coarse-Graining Theory, a framework for understanding and predicting the preservation of key properties during the process of coarse-graining. Coarse-graining is a computational technique used to simplify complex systems by reducing the level of detail in the representation. The c…
AbstractSimulating electronic transport properties and scattering networks within continuous condensed matter physicspresents an intractable computational barrier due to the factorial scaling of infinite continuum path permutations.This paper introduces a unified framework that utilizes Ewin Tang’s dequantization matr…
The phase field method provides a unified framework for modeling a wide range of interfacial phenomena without explicit tracking of interfaces. In this paper we develop a comprehensive mathematical formulation of phase field theory, starting from the variational principle that defines a diffuse interface free energy f…
The concept of symmetry has long served as a cornerstone in the formulation of physical laws and mathematical structures. Classical symmetry refers to transformations that leave a system's observable configuration unchanged. In this work we introduce a complementary notion, which we call deep symmetry, defined as the…
This capstone project is sponsored by Northrop Grumman (NGC). The goal of the project is to redesign an ablation torch testing system to improve usability, safety, and versatility. Northrop Grumman relies on their ablation torch testing system to conduct quantitative evaluations of materials and high stress and high t…
The concept of repetition is a cornerstone of mathematics, appearing in combinatorics, group theory, fractal geometry, and category theory. Traditional studies focus on periodicity, yet many structures exhibit repetition without strict periodicity. This paper introduces a formal framework for measuring how a single re…
FINDING: Fibonacci numbers appear in Mandelbrot set dynamics and can be generated via closed-form tree structures without recursion. MATH: - Fibonacci recurrence: \( F_n = F_{n-1} + F_{n-2} \), with \( F_0 = 0, F_1 = 1 \). - Closed-form (Binet): \( F_n = \frac{\phi^n - \psi^n}{\sqrt{5}} \), where \( \phi = \frac{1+\sq…
This paper introduces Algorithmic Chemical Theory (ACT), a novel approach to chemical understanding and prediction. Instead of viewing algorithms as discrete modules, ACT proposes that algorithms are fundamental, irreducible elements analogous to those found in the periodic table. These algorithmic elements can intera…
Research article: Multimodal AI in Scientific Discovery: 2025 Benchmarks in Drug Discovery and Materials Science
In this study, an innovative approach combining semi-analytical modeling with machine learning-based prediction methods is proposed to analyze the dynamic behavior of short fiber-reinforced viscoelastic microbeams. Developed based on the modified couple stress theory, the model examined the vibration characteristics o…
Quaternary mixed-metal chalcohalides offer a compositionally versatile platform for developing lead-free semiconductor nanomaterials, yet colloidal access to Cu–Bi–S–Cl compositions remains unexplored. Here, we report the first solution-phase synthesis of CuBiSCl₂ nanocrystals (NCs) through a hot-co-injection strategy…
Meissner polyhedra are constant-width bodies obtained from extremal finite sets of unit diameter. Such a generating set may contain dangling points, namely points having exactly two diametric neighbors. This article studies whether these points can play an essential role in surface-area minimization. Given an extremal…