Related papers: Constructing and Understanding New and Old Scales …
Polymer materials have the characteristic feature that they are multiscale systems by definition. Already the description of a single molecules involves a multitude of different scales, and cooperative processes in polymer assemblies are…
This paper explores the issues around the construction of large-scale complex systems which are built as 'systems of systems' and suggests that there are fundamental reasons, derived from the inherent complexity in these systems, why our…
We describe some scaling issues that arise when using lattice Boltzmann methods to simulate binary fluid mixtures -- both in the presence and in the absence of colloidal particles. Two types of scaling problem arise: physical and…
I discuss some of the difficulties with formulating chiral symmetry on the lattice and review a recently proposed scheme for a fully finite and exactly gauge invariant lattice regularization of the standard model.
Simulations of large-scale structure in the universe have played a vital role in observational cosmology since 1980's in particular. Their important role will definitely continue to be true in the 21st century. Rather the requirements for…
We think about what the subscheme of the formal scheme is. Differently form the ordinary scheme, the formal scheme has different notions of ``subscheme''. We lay a foundation for these notions and compare them. We also relate them to…
In this work we introduce new scalar field models and study the defect solutions they may engender. The investigation is based on the deformation procedure, which greatly simplify the calculations, leading us to new models together with the…
In this paper we present the status of the physics of Planck scale black holes with particular reference to their conjectured production in particle accelerator experiments at the terascale. After reviewing some open issues of fundamental…
In this paper we will relate hyperstructures and the general $\mathscr{H}$-principle to known mathematical structures, and also discuss how they may give rise to new mathematical structures. The main purpose is to point out new ideas and…
In this work, I briefly report on constraints that can be obtained on new physics models that extend the scalar sector of the Standard Model (SM) of particle physics at the LHC. I concentrate on a few simple examples which serve to…
In the first part of this article, we consider ruled surfaces defined over a finite field; we introduce invariants for them, and describe some explicit contructions that illustrate possible behaviour of these invariants. In the second part,…
An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This…
Given a tiling of a 2D grid with several types of tiles, we can count for every row and column how many tiles of each type it intersects. These numbers are called the_projections_. We are interested in the problem of reconstructing a tiling…
This chapter describes interrelations between: (1) algebraic structure on sets of scalars, (2) properties of monads associated with such sets of scalars, and (3) structure in categories (esp. Lawvere theories) associated with these monads.…
We apply an old method for constructing points-and-lines configurations in the plane to study some recent questions in incidence geometry.
Questions of set-theoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made…
Scaling laws arise and are eulogized across disciplines from natural to social sciences for providing pithy, quantitative, `scale-free', and `universal' power law relationships between two variables. On a log-log plot, the power laws…
Multiscale modeling of material properties has emerged as one of the grand challenges in material science and engineering. We provide a comprehensive, though not exhaustive, overview of the current status of multiscale simulations of…
Positive experience of agile development methods in smaller projects has created interest in the applicability of such methods in larger scale projects. However, there is a lack of conceptual clarity regarding what large-scale agile…
Conceptual Scaling is a useful standard tool in Formal Concept Analysis and beyond. Its mathematical theory, as elaborated in the last chapter of the FCA monograph, still has room for improvement. As it stands, even some of the basic…