Related papers: Oscillations on the Stretched Sierpinski Gasket
We use spectral decimation to provide formulae for computing the harmonic gradients of Laplacian eigenfunctions on the Sierpinski Gasket. These formulae are given in terms of special functions that are defined as infinite products.
The oscillations described by periodic functions play an important role in many areas. In the present paper, we study periodic functions which belong to the class of the $n$-member chains. The self-intersection and local singular points of…
The fluctuations of the work done by an external Gaussian random force on a harmonic oscillator that is also in contact with a thermal bath is studied. We have obtained the exact large deviation function as well as the complete asymptotic…
We first establish a sharp relation between the order of vanishing of a Dirichlet eigenfunction at a point and the leading term of the asymptotic expansion of the Dirichlet eigenvalue variation, as a removed compact set concentrates at that…
We calculate the mean and almost-sure leading order behaviour of the high frequency asymptotics of the eigenvalue counting function associated with the natural Dirichlet form on $\alpha$-stable trees, which lead in turn to short-time heat…
We present exact results on certain electronic properties of an anisotropic Sierpinski gasket fractal. We use a tight binding Hamiltonian and work within the formalism of a real space renormalization group (RSRG) method. The anisotropy is…
Using the isospectral partners of the Bessel functions derived by Reyes et al., we find, on one hand, that these functions show non-typical supersymmetric (SUSY) behavior and, on the other, that the isospectral partner of the classical wave…
We investigate the statistical properties of fluctuations in active systems that are governed by non-symmetric responses. Both an underdamped Langevin system with an odd resistance tensor and an overdamped Langevin system with an odd…
In recent years, the decay-less regime of standing transverse oscillations in coronal loops has been the topic of many observational and numerical studies, focusing on their physical characteristics, as well as their importance for coronal…
We investigate a qualitatively new regime of inflationary models with small and rapid oscillations in the potential-resonant non-Gaussianity. In contrast to the standard scenario, where most of the observable information is encoded in the…
Solar filament oscillations have been known for decades. Now thanks to the new capabilities of the new telescopes, these periodic motions are routinely observed. Oscillations in filaments show key aspects of their structure. A systematic…
The notion of spontaneous symmetry breaking has been well established to characterize classical and quantum phase transitions of matter, such as in condensation, crystallization or quantum magnetism. Generalizations of this paradigm to the…
In the Dirac theory for the motion of free relativistic electrons, highly oscillatory components appear in the time evolution of physical observables such as position, velocity, and spin angular momentum. This effect is known as…
We consider singularly perturbed second order elliptic system in the whole space with fast oscillating coefficients. We construct the complete asymptotic expansions for the eigenvalues converging to the isolated ones of the homogenized…
The oscillation of fluctuation with two state observables is investigated. Following the idea of Ohga, et al. [arXiv:2303.13116], we find that the fluctuation oscillation relative to their autocorrelations is bounded from above by the…
In a domain $\Omega\subset \mathbb{R}^{\mathbf{N}}$ we consider a selfadjoint operator $\mathbf{T}=\mathfrak{A}^*P\mathfrak{A} ,$ where $\mathfrak{A}$ is a pseudodifferential operator of order $-l=-\mathbf{N}/2$ and $P=V\mu_{\Sigma}$ is a…
In this paper, we establish an analogue of the classical mean value property for both the harmonic functions and some general functions in the domain of the Laplacian on the Sierpinski gasket. Furthermore, we extend the result to some other…
In the present paper we develop an approach to obtain sharp spectral asymptotics for Steklov type problems on planar domains with corners. Our main focus is on the two-dimensional sloshing problem, which is a mixed Steklov-Neumann boundary…
The relative configurational entropy per cell as a function of length scale is a sensitive detector of spatial self-similarity. For Sierpinski carpets the equally separated peaks of the above function appear at the length scales that depend…
We give an overview over the application of functional equations, namely the classical Poincar\'e and renewal equations, to the study of the spectrum of Laplace operators on self-similar fractals. We compare the techniques used to those…