Related papers: Improved Conformal Mapping of the Borel Plane
Conformal mapping is an important mathematical tool in many physical and engineering fields, especially in electrostatics, fluid mechanics, classical mechanics, and transformation optics. However in the existing textbooks and literatures,…
Efficient topology optimization based on the adaptive auxiliary reduced model reanalysis (AARMR) is proposed to improve computational efficiency and scale. In this method, a projection auxiliary reduced model (PARM) is integrated into the…
In the article we consider the composite conformal map which maps annulus to infinite region with symmetric hole and nearly circular hole. It is shown that such transformation is good if the distance between centers of holes are large or…
Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…
Using schematic model potentials, we calculate exactly the virial coefficients of a classical gas up to sixth order and use them to assess the convergence properties of the virial expansion of basic thermodynamic quantities such as…
Consider discrete conformal maps defined on the basis of two conformally equivalent triangle meshes, that is edge lengths are related by scale factors associated to the vertices. Given a smooth conformal map $f$, we show that it can be…
A new Hardy space Hardy space approach of Dirichlet type problem based on Tikhonov regularization and Reproducing Hilbert kernel space is discussed in this paper, which turns out to be a typical extremal problem located on the upper…
The role of the conformal group in electrodynamics in four space-time dimensions is re-examined. As a pedagogic example we use the application of conformal transformations to find the electromagnetic field for a charged particle moving with…
Any subset of the plane can be approximated by a set of square pixels. This transition from a shape to its pixelation is rather brutal since it destroys geometric and topological information about the shape. Using a technique inspired by…
Conformal invariance plays a significant role in many areas of Physics, such as conformal field theory, renormalization theory, turbulence, general relativity. Naturally, it also plays an important role in geometry: theory of Riemannian…
Conformal field theories play a central role in modern theoretical physics with many applications to the understanding of phase transitions, gauge theories and even the quantum physics of gravity, through Maldacena's celebrated holographic…
The simplicity and the efficiency of a quasi-analytical method for solving nonlinear ordinary differential equations (ODE), is illustrated on the study of anharmonic oscillators (AO) with a potential $V(x) =\beta x^{2}+x^{2m}$ ($m>0$). The…
The bilocal expansion of Borel transform provides an efficient way of Borel resummation with low order perturbations in QCD. Its applications to the heavy quark pole mass, static potential, and lattice calculation are reviewed.
We reconsider in some detail a construction allowing (Borel) convergence of an alternative perturbative expansion, for specific physical quantities of asymptotically free models. The usual perturbative expansions (with an explicit mass…
We describe an explicit semi-algebraic partition for the complement of a real hyperplane arrangement such that each piece is contractible and so that the pieces form a basis of Borel-Moore homology. We also give an explicit correspondence…
This paper presents a new conformal method for generating simultaneous forecasting bands guaranteed to cover the entire path of a new random trajectory with sufficiently high probability. Prompted by the need for dependable uncertainty…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
We revise the use of 8-dimensional conformal, complex (Cartan) domains as a base for the construction of conformally invariant quantum (field) theory, either as phase or configuration spaces. We follow a gauge-invariant Lagrangian approach…
We study the conformal window of QCD using perturbation theory, starting from the perturbative upper edge and going down as much as we can towards the strongly coupled regime. We do so by exploiting the available five-loop computation of…
For lambda phi^4 problems, convergent perturbative series can be obtained by cutting off the large field configurations. The modified series converge to values exponentially close to the exact ones. For lambda larger than some critical…