Related papers: Classifying chemical elements and particles: from …
Logical proofs and definitions are developed to establish (i) the energy-level spacings, \xi for each chemical element (from the periodic table of chemical elements) can be converted to the ionization energies, (ii) both \xi and the…
The most successful "Standard Model" allows one to define the so-called "Elementary Particles". Now from another point of view, philosophical, how can we think of them? Which kind of a status can be attributed to Elementary Particles and…
Let $M$ be a cancellative and commutative monoid (written additively). The monoid $M$ is atomic if every non-invertible element can be written as a sum of irreducible elements (often called atoms in the literature). Weaker versions of…
A brief review, from basic atomic constants to "Mendeleev Table" of leptons, quarks, fundamental bosons, and then to superunification of all forces and particles.
The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and…
The spatial symmetry of matter - including finite objects like molecules or atomic clusters, and extended objects like periodic or aperiodic crystals - is described using point groups and space groups. Magnetic point groups and space groups…
An algebraic formalism for the study of interacting particle systems is developed. Particle processes are described in terms of the category theory. The problem for the unique description of these processes is discussed. Categories relevant…
Machine-learning of atomic-scale properties amounts to extracting correlations between structure, composition and the quantity that one wants to predict. Representing the input structure in a way that best reflects such correlations makes…
We review the progress in atomic structure theory with a focus on superheavy elements and the aim to predict their ground state configuration and element's placement in the periodic table. To understand the electronic structure and…
The concepts of alpha- and beta-packets of the periodic table of chemical elements and chemical compounds are defined. The first of the 47 minerals alpha-packets is composed. In it all minerals are arranged in increasing Iav index of…
The answers to many unsolved problems lie in the intractable chemical space of molecules and materials. Machine learning techniques are rapidly growing in popularity as a way to compress and explore chemical space efficiently. One of the…
Symmetry lies at the heart of todays theoretical study of particle physics. Our manuscript is a tutorial introducing foundational mathematics for understanding physical symmetries. We start from basic group theory and representation theory.…
We propose a computationally lean, two-stage approach that reliably predicts self-assembly behavior of complex charged molecules on a metallic surfaces under electrochemical conditions. Stage one uses ab initio simulations to provide…
Underlying any theory of physics is a layer of conceptual frames. They connect the mathematical structures used in theoretical models with physical phenomena, but they also constitute our fundamental assumptions about reality. Many of the…
We present an overview of the theory of finite groups, with regard to their application as flavour symmetries in particle physics. In a general part, we discuss useful theorems concerning group structure, conjugacy classes, representations…
We construct a two-class asymmetric interacting particle system with $U_q(so_6)$ or $U_q(so_8)$ symmetry, in which up to two particles may occupy a site if the two particles have different class. The particles exhibit a drift, but there is…
Decompositional theories describe the ways in which a global physical system can be split into subsystems, facilitating the study of how different possible partitions of a same system interplay, e.g. in terms of inclusions or signalling. In…
We define here the category of partial differential equations. Special cases of morphisms from an object (equation) are symmetries of the equation and reductions of the equation by a symmetry groups, but there are many other morphisms. We…
Group theory is used in many textbooks of contemporary physics. However, electromagnetic community often considers group theory as an "exotic" tool. Graduate and postgraduate textbooks on electromagnetics and electrodynamics usually do not…
All leptons, quarks, and gauge bosons can be placed in the periodic table of elementary particles. The periodic table is derived from dualities of string theory and a Kaluza-Klein substructure for the six extra spatial dimensions. As a…