Related papers: Wrapping and unwrapping multifractal fields
Multifractal analysis is one of the important approaches that enables us to measure the complexity of various data via the scaling properties. We compare the most common techniques used for multifractal exponents estimation from both…
This work outlines a diffuse interface method for the study of fracture and fragmentation in ductile metals at high strain-rates in Eulerian finite volume simulations. The work is based on an existing diffuse interface method capable of…
In this paper we propose a new approach for constructing \emph{multivariate} Gaussian random fields (GRFs) with oscillating covariance functions through systems of stochastic partial differential equations (SPDEs). We discuss how to build…
A method is proposed for generating compact fractal disordered media, by generalizing the random midpoint displacement algorithm. The obtained structures are invasive stochastic fractals, with the Hurst exponent varying as a continuous…
Topography is the expression of both internal and external processes of a planetary body. Thus hypsometry (the study of topography) is a way to decipher the dynamic of a planet. For that purpose, the statistics of height and slopes may be…
We introduce regular series expansion for weakly- and moderately-correlated fermionic systems, based on Fluctuating Local Field approach. The method relies on the explicit account of leading fluctuating mode(s) and is therefore suitable for…
A new type of elasticity of random (multifractal) structures is suggested. A closed system of constitutive equations is obtained on the basis of two proposed phenomenological laws of reversible deformations of multifractal structures. The…
We introduce a novel framework that integrates Neural Radiance Fields (NeRF) with Material Point Method (MPM) simulation to infer granular material properties from visual observations. Our approach begins by generating synthetic…
The mean-field theory (MFT) of simple glasses, which is exact in the limit of infinite spatial dimensions, $d\rightarrow\infty$, offers theoretical insight as well as quantitative predictions about certain features of $d=3$ systems. In…
Some types of medical and topographic imaging device produce images in which the pixel values are "phase-wrapped", i.e. measured modulus a known scalar. Phase unwrapping can be viewed as the problem of inferring the number of shifts between…
We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…
This paper is devoted to the asymptotic analysis of the reinforced elephant random walk (RERW) using a martingale approach. In the diffusive and critical regimes, we establish the almost sure convergence, the law of iterated logarithm and…
Novel view synthesis has recently been revolutionized by 3D Gaussian Splatting (3DGS), which enables real-time rendering through explicit primitive rasterization. However, existing methods tie visual fidelity strictly to the number of…
Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of multifractality in the time series. Series fluctuating according to a qGaussian…
This article presents GRFsaw, an open-source software for generating two-phase (binary) microstructures with user-defined structural properties. Unlike most standard software for microstructure generation, GRFsaw is based on the concept of…
A multifractal analysis is performed on a three-dimensional grayscale image associated with a complex system. First, a procedure for generating 3D synthetic images (2D image stacks) of a complex structure exhibiting multifractal behaviour…
Many models of fractal growth patterns (like Diffusion Limited Aggregation and Dielectric Breakdown Models) combine complex geometry with randomness; this double difficulty is a stumbling block to their elucidation. In this paper we…
Continuous wavelet transform (CWT) based time-scale and multi-fractal analyses have been carried out on the anode glow related nonlinear floating potential fluctuations in a hollow cathode glow discharge plasma. CWT has been used to obtain…
We study the multifractal temporal scaling properties of river discharge and precipitation records. We compare the results for the multifractal detrended fluctuation analysis method with the results for the wavelet transform modulus maxima…
We present a learning-based method for synthesizing novel views of complex scenes using only unstructured collections of in-the-wild photographs. We build on Neural Radiance Fields (NeRF), which uses the weights of a multilayer perceptron…