Related papers: Percolation theory
In this editorial survey we introduce the special issue of the journal Communications in Mathematics on the topic in the title of the article. Our main goal is to briefly outline some of the main aspects of this important area at the…
This technical note provides a high-level overview of the present state of basic field electron emission (FE) theory, as suitable for use in the context of technological applications of FE theory. At present there is much theoretical…
The purpose of this article is to discuss recent advances in the growing field of phase retrieval, and to publicize open problems that we believe will be of interest to mathematicians in general, and algebraists in particular.
For Encyclopedia of Complexist and System Science No abstract given I. Definition and Introduction II. Ising Model III. Fractals IV. Diffusion on Fractals V. Ising Model on Fractals VI. Other Subjects ? VII. Networks VIII. Future Directions
In a recent paper, we have reported a universal power law for both site and bond percolation thresholds for any lattice of cubic symmetry. Extension to anisotropic lattices is discussed.
The paper is withdrawn by the author. This was an embryon of the book which has now been published with World Scientific under the title "Lectures on Quantum Chromodynamics". See http://www.wspc.com.sg/books/physics/4443.html, where the…
This is an account of the theory of inverse semigroups, assuming only that the reader knows the basics of semigroup theory.
This article was published as Sec.4 of the "Roadmap on Structured Light" in Journal of Optics 19 (2017) 013001. Section 4 describes the essential elements of the classical theory of electromagnetic force and momentum.
We formulate conjectures regarding percolation on planar triangulations suggested by assuming (quasi) invariance under coarse conformal uniformization.
Transformation equations for physical quantities that characterize plane electromagnetic wave propagation in transparent optical media are presented. The Doppler effect, and measurements performed by an observer moving with the wave are…
Convection-diffusion equation is used to describe particle migration process in many fields, while it is proposed based on the empirical Fick's law. In this paper, with the help of the percolation model, we theoretically investigate the…
This is an entry for Physics Today's recent essay contest, written as a "Search and Discovery" news story, imagining what major breakthroughs might be shaking the physics world one hundred years from now.
1. Introduction - 2. Astrophysics and Cosmology - 3. Neutrino Oscillations - 4. Higgs and New Physics Searches - 5. Flavour Physics and CP Violation - 6. QCD - 7. Heavy Ion Collisions - 8. Outlook
This is a narrative of the basic theoretical ideas of axisymmetric two-dimensional solitons and of their connection to basic experiments on magnetic compounds. A shortened and edited version appeared in Physics Today.
We will provide detailed arguments showing that the set of Maxwell equations, and the corresponding wave equations, do not properly describe the evolution of electromagnetic wave-fronts. We propose a nonlinear corrected version that is…
This expository article written for the Notices of the American Mathematical Society provides an overview of transcendental functions arising as solutions of the discrete Painlev\'e equations, for which the developments of the last two…
An outline of J\"org Eschmeier's main mathematical contributions is organized both on a historical perspective, as well as on a few distinct topics. The reader can grasp from our essay the dynamics of spectral theory of commutative tuples…
We give a brief survey of some of the geometry of mirror symmetry, written in 2004 for the "Encyclopaedia of Mathematical Physics". Probably a little bit out of date now in a few places, but hey.
The paper shows how the diffusive movement of ions through a channel protein can be described as a chemical reaction over an arbitrary shaped potential barrier. The result is simple and intuitive but without approximation beyond the…
We take some first steps in providing a synthetic theory of distributions. In particular, we are interested in the use of distribution theory as foundation, not just as tool, in the study of the wave equation.