Related papers: Group analysis approach for finding reciprocal tra…
The functional renormalisation group is employed to study the non-linear regime of late-time cosmic structure formation. This framework naturally allows for non-perturbative approximation schemes, usually guided by underlying symmetries or…
This study presents a novel analytical framework for modeling unsteady gas dynamics in parallel pipeline systems under leakage conditions. The proposed method introduces a time-dependent leakage mass flow rate function, which dynamically…
In this paper, we propose a unified convergence analysis for a class of generic shuffling-type gradient methods for solving finite-sum optimization problems. Our analysis works with any sampling without replacement strategy and covers many…
We derive generic relativistic hydrodynamical equations with dissipative effects from the underlying Boltzmann equation in a mechanical and systematic way on the basis of so called the renormalization-group (RG) method. A macroscopic frame…
Classical dimensional analysis is one of the cornerstones of qualitative physics and is also used in the analysis of engineering systems, for example in engineering design. The basic power product relationship in dimensional analysis is…
For many finite groups, the Inverse Galois Problem can be approached through modular/automorphic Galois representations. This is a report explaining the basic strategy, ideas and methods behind some recent results. It focusses mostly on the…
Group-based reinforcement can induce discontinuous transitions from inactive to active phases in higher-order contagion models. However, these results are typically obtained on static interaction structures or within mean-field…
In the modeling of complex biological systems, the use of power-law models (such as S-systems and GMA systems) often provides a remarkable accuracy over several orders of magnitude in concentrations, an unusually broad range not fully…
We present a generalization of Lie's method for finding the group invariant solutions to a system of partial differential equations. Our generalization relaxes the standard transversality assumption and encompasses the common situation…
Our goal is to find classes of convolution semigroups on Lie groups $G$ that give rise to interesting processes in symmetric spaces $G/K$. The $K$-bi-invariant convolution semigroups are a well-studied example. An appealing direction for…
This paper introduces a position-space renormalization-group approach for nonequilibrium systems and applies the method to a driven stochastic one-dimensional gas with open boundaries. The dynamics are characterized by three parameters: the…
This is the second part of the series of papers on symmetry properties of a class of variable coefficient (1+1)-dimensional nonlinear diffusion-convection equations of general form $f(x)u_t=(g(x)A(u)u_x)_x+h(x)B(u)u_x$. At first, we review…
We carry out the complete group classification of the class of (1+1)-dimensional linear Schr\"odinger equations with complex-valued potentials. After introducing the notion of uniformly semi-normalized classes of differential equations, we…
The requirement that duality and renormalization group transformations commute as motions in the space of a theory has recently been explored to extract information about the renormalization flows in different statistical and field…
The complexity of biological systems, and the increasingly large amount of associated experimental data, necessitates that we develop mathematical models to further our understanding of these systems. As biological systems are generally not…
It is explained how field-theoretic methods and the dynamic renormalisation group (RG) can be applied to study the universal scaling properties of systems that either undergo a continuous phase transition or display generic scale…
Convolution is conventionally defined as a linear operation on functions of one or more variables which commutes with shifts. Group convolution generalizes the concept to linear operations on functions of group elements representing more…
Using Klein's approach, geometry can be studied in terms of a space of points and a group of transformations of that space. This allows us to apply algebraic tools in studying geometry of mathematical structures. In this article, we follow…
We use group representation theory to give algebraic formulae to compute complete transversals of singularities of vector fields, either in the nonsymmetric or in the reversible equivariant contexts. This computation produces normal forms…
This paper argues that the ideas underlying the renormalization group technique used to characterize phase transitions in condensed matter systems could be useful for distinguishing computational complexity classes. The paper presents a…