Related papers: Group analysis of the membrane shape equation
We reproduce the symmetric and asymmetric ``rippled'' $P_{\beta'}$ states of lipid membranes by Monte Carlo simulations of a coarse-grained molecular model for lipid-solvent mixtures. The structure and properties compare favorably with…
Using the classical S.Lie method we obtain a complete description of infinitesimal symmetries of a holomorphic PDE system defining the Segre family of a real analytic hypersurface. This gives a new proof of some well known results of CR…
Lie symmetry analysis is one of the powerful tools to analyze nonlinear ordinary differential equations. We review the effectiveness of this method in terms of various symmetries. We present the method of deriving Lie point symmetries,…
This paper is concerned with investigating the asymptotic behavior of the gradients of solutions to a class of elliptic systems with general boundary data, especially covering the Lam\'{e} systems, in a narrow region. The novelty of this…
Noncommutative harmonic analysis is used to solve a nonparametric estimation problem stated in terms of compound Poisson processes on compact Lie groups. This problem of decompounding is a generalization of a similar classical problem. The…
Using methods from algebraic topology and group cohomology, I pursue Grothendieck's question on equality of geometric and cohomological Brauer groups in the context of complex-analytic spaces. The main result is that equality holds under…
We describe arbitrary multiplicative differential forms on Lie groupoids infinitesimally, i.e., in terms of Lie algebroid data. This description is based on the study of linear differential forms on Lie algebroids and encompasses many known…
We study the symmetry groups and winding numbers of planar curves obtained as images of weighted sums of exponentials. More generally, we study the image of the complex unit circle under a finite or infinite Laurent series using a…
We present the package SADE (Symmetry Analysis of Differential Equations) for the determination of symmetries and related properties of systems of differential equations. The main methods implemented are: Lie, nonclassical, Lie-B\"acklund…
We discuss existence of mixed state of multicomponent system with given spectrum and given reduced density matrices. We give a complete solution of the problem in terms of linear inequalities on the spectra, accompanied with extensive…
A class of the Benjamin-Bona-Mahony-Burgers (BBMB) equations with time-dependent coefficients is investigated with the Lie symmetry point of view. The set of admissible transformations of the class is described exhaustively. The complete…
Every linear system of partial differential equations (PDEs) admits a scaling symmetry in its dependent variables. In conjunction with other admitted symmetries of linear type, the associated invariant solution condition poses a linear…
Lie symmetry analysis is an established method for generating symmetries of differential equations. We apply this method together the generalized fundamental theorem of double reduction. In particular, Noether symmetries and some associated…
The descent algebra of the symmetric group, over a field of non-zero characteristic p, is studied. A homomorphism into the algebra of generalised p-modular characters of the symmetric group is defined. This is then used to determine the…
We present a simple and computationally efficient coarse-grained and solvent-free model for simulating lipid bilayer membranes. In order to be used in concert with particle-based reaction-diffusion simulations, the model is purely based on…
A renormalization group method with the Lie symmetry is presented for the singular perturbation problems. Asymptotic solutions are obtained as group-invariant solutions under approximate Lie group admitted by perturbed differential…
We explore to what extent the underlying variety of a connected algebraic group or the underlying manifold of a real Lie group determines its group structure.
Heterogeneities in the cell membrane due to coexisting lipid phases have been conjectured to play a major functional role in cell signaling and membrane trafficking. Thereby the material properties of multiphase systems, such as the line…
We study a mechanism of symmetry reduction in a higher-dimensional field theory upon orbifold compactification. Split multiplets appear unless all components in a multiplet of a symmetry group have a common parity on an orbifold. A gauge…
The aim of this paper is to explain, mostly through examples, what groupoids are and how they describe symmetry. We will begin with elementary examples, with discrete symmetry, and end with examples in the differentiable setting which…