Related papers: Multifractal tubes
Metric regularity has emerged during last 2-3 decades as one of the central concepts of variational analysis. The roots of this concept go back to a circle of fundamental regularity ideas of classical analysis embodied in such results as…
The theoretical framework for higher-order correlation functions involving multiple times and multiple points in a classical, many-body system developed by Van Zon and Schofield [Phys. Rev. E 65, 011106 (2002)] is extended here to include…
The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a…
Processes occurring in real open systems are far from equilibrium state and they can lead to synergetic effects, which are caused by coordinated behavior of system units. Traditional methods of analysis often just establish such behavior,…
We investigate stochastic processes possessing scale invariance properties which we refer to as multifractal processes. The examples of such processes known so far do not go much beyond the original cascade construction of Mandelbrot. We…
The permeability of a porous medium is strongly affected by its local geometry and connectivity, the size distribution of the solid inclusions and the pores available for flow. Since direct measurements of the permeability are time…
Cavitation in tubes is a common occurrence in nature and engineering applications. Previous studies of cavitation bubble dynamics mainly consider bubbles in stagnant-water tubes, but the dynamics of cavitation bubbles in tubes with flow is…
The emergence of nonequilibrium phenomena in individual complex wave systems has long been of fundamental interests. Its analytic studies remain notoriously difficult. Using the mathematical tool of the concentration of measure (CM), we…
This paper proposes a unified framework for designing robustness in optimization under uncertainty using gauge sets, convex sets that generalize distance and capture how distributions may deviate from a nominal reference. Representing…
We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A…
Kusuoka's measure on fractals is a Gibbs measure of a very special kind, because its potential is discontinuous, while the standard theory of Gibbs measures requires continuous (actuallly, H\"older) potentials. In this paper, we shall see…
In this paper, we introduce the concept of the $\alpha$-fractal function and fractal approximation for a set-valued continuous map defined on a closed and bounded interval of real numbers. Also, we study some properties of such fractal…
We develop a replicated liquid theory for structural glasses which exhibit spatial variation of physical quantities along one axis, say $z$-axis. The theory becomes exact with infinite transverse dimension $d-1 \to \infty$. It provides an…
This paper deals with properties of filtrations on vector spaces indexed by partially ordered finitely generated abelian groups, which we call multifiltrations. We discuss the usual properties of filtrations, like exhaustivity and…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
We give a generalization of Lagarias' formula for diffraction by ideal crystals, and we apply it to the lattice case, in preparation for addressing the problem of quasicrystals and complex dimensions posed by Lapidus and van Frankenhuijsen…
In this paper, we analyze the question of replica symmetry in the bulk for multi-partite entanglement measures in the vacuum state of two dimensional holographic CFTs. We first define a class of multi-partite local unitary invariants,…
Fractals and multifractals and their associated scaling laws provide a quantification of the complexity of a variety of scale invariant complex systems. Here, we focus on lattice multifractals which exhibit complex exponents associated with…
In the first part of this doctoral thesis we develop a regularity theory for a polyconvex functional in compressible elasticity. In the second part, we will concentrate on uniqueness questions in various situations of finite elasticity.…
Global and local regularities of functions are analyzed in anisotropic function spaces, under a common framework, that of hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities…