Related papers: G\"ursey, Groups & Fluids
These lecture notes want to illustrate the close connection between statistical mechanics and field theory not only on the formal level, i.e. that many concepts of one area can easily be taken over to the other one, but also on the level of…
This is an extended version of summary of the talk at the International Conference on Group Theory in honor of Victor Mazurov on the occasion of his 80th birthday. The concise version of this report can be found in the talks and…
Gauge invariance in discrete dynamical systems and its connection with quantization are considered. For a complete description of gauge symmetries of a system we construct explicitly a class of groups unifying in a natural way the space and…
In this paper, the analog of Maxwell electromagnetism for hydrodynamic turbulence, the metafluid dynamics, is extended in order to reformulate the metafluid dynamics as a gauge field theory. That analogy opens up the possibility to…
Hydrodynamics, a term apparently introduced by Daniel Bernoulli (1700-1783) to comprise hydrostatic and hydraulics, has a long history with several theoretical approaches. Here, after a descriptive introduction, we present so-called…
This is a short review in honor of B. Mandelbrot's 80st birthday, to appear in W ilmott magazine. We discuss how multiplicative cascades and related multifractal ideas might be relevant to model the main statistical features of financial…
"There are several interpretations and approaches to relativity. All of them are characterized by the fact that none of them is accepted by physicists without doubts, even the Einsteinian General Relativity! Only those theories can get into…
The fluctuation theorem is a pivotal result of statistical physics. It quantifies the probability of observing fluctuations which are in violation of the second law of thermodynamics. More specifically, it quantifies the ratio of the…
This is the English version of my inaugural lecture at Coll\`ege de France in 2021, available at https://www.youtube.com/watch?v=bxktplKMhKU. I reflect on the difficulty of multi-disciplinary research, which often hinges of unexpected…
This article is a slightly expanded version of the talk I delivered at the Special Plenary Session of the 46-th Annual Meeting of the Israel Physical Society (Technion, Haifa, May 11, 2000) dedicated to Misha Marinov. In the first part I…
This is the Preface to the special issue of 'International Journal of Geometric Methods in Modern Physics', v.3, N.1 (2006) dedicated to the 50th aniversary of gauge gravitation theory. It addresses the geometry underlying gauge gravitation…
In this course, I talk about the source of mathematical constructivism and its role in the future development of theoretical physics. I describe what physical constructivism is and why it is necessary for the penetration of exact methods of…
Many features of real granular fluids under rapid flow are exhibited as well by a system of smooth hard spheres with inelastic collisions. For such a system, it is tempting to apply standard methods of kinetic theory and hydrodynamics to…
In this paper, we study the long-time behavior of a fluid particle immersed in a turbulent fluid driven by a diffusion with jumps, that is, a Feller process associated with a non-local operator. We derive the law of large numbers and…
The concept of gyrogroups is a generalization of groups which do not explicitly have associativity. In this paper, the notion of fuzzy gyronorms on gyrogroups is introduced. The relations of fuzzy metrics (in the sense of George and…
Professor Chen Ning Yang has made seminal and influential contributions in many different areas in theoretical physics. This talk focuses on his contributions in statistical mechanics, a field in which Professor Yang has held a continual…
Liquids flow, making them remarkably distinct from solids and close to gases. At the same time, interactions in liquids are strong as in solids. The combination of these two properties is believed to be the ultimate obstacle to constructing…
Starting from Greg Moore's description about Physical Mathematics, a framework is proposed in order to understand it, based on Gilles Ch\^atelet's philosophy. It will be argued that Ch\^atelet's ideas of inverting, splitting, augmenting and…
The aim of this article is to give a survey of combination theorems occurring in hyperbolic geometry, geometric group theory and complex dynamics, with a particular focus on Thurston's contribution and influence in the field.
When an ensemble of particles interact hydrodynamically, they generically display large-scale transient structures such as swirls in sedimenting particles [1], or colloidal strings in sheared suspensions [2]. Understanding these…