Related papers: Stochastic earthquake source model: the omega-squa…
Understanding the stability and long-time behavior of generative models is a fundamental problem in modern machine learning. This paper provides quantitative bounds on the sampling error of score-based generative models by leveraging…
Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its…
A stochastic wavevector approach is formulated to accurately represent compressible turbulence subject to rapid deformations. This approach is inspired by the incompressible particle representation model of Kassinos (1995) and preserves the…
The Swift-Hohenberg equation (SHE) is a partial differential equation that explains how patterns emerge from a spatially homogeneous state. It has been widely used in the theory of pattern formation. Following a recent study by Bramburger…
The elementary theory of relaxation of the source cooling down after the main shock of an earthquake is presented axiomatically. The names of the objects under study are given and the relationships between them are determined. A new basic…
Compositional observations are an increasingly prevalent data source in spatial statistics. Analysis of such data is typically done on log-ratio transformations or via Dirichlet regression. However, these approaches often make unnecessarily…
Over the last two decades, strain and GPS measurements have shown that slow slip on earthquake faults is a widespread phenomenon. Slow slip is also inferred from correlated small amplitude seismic signals known as nonvolcanic tremor and low…
This paper is concerned with the trends of stress fluctuations in dry granular materials as functions of the sample size D and of the grain diameter d. Results are obtained in the plateau regime of large axial deformation, during…
Statistical properties of the inhomogeneous version of the Olami-Feder-Christensen (OFC) model of earthquakes is investigated by numerical simulations. The spatial inhomogeneity is assumed to be dynamical. Critical features found in the…
We add the $\alpha-$ effect in the dynamo driven accretion disk model proposed by Tout & Pringle (1992), i.e., a dynamo model depends on the physical processes such as Parker instability, Balbus-Hawley instability, magnetic field…
Deep-focus earthquakes that occur at 350-660 km, where pressures 12-23 GPa and temperature 1800-2000 K, are generally assumed to be caused by olivine-spinel phase transformation (PT). However, there are many existing puzzles: (a) What are…
We propose a new physically-based ``multifractal stress activation'' model of earthquake interaction and triggering based on two simple ingredients: (i) a seismic rupture results from activated processes giving an exponential dependence on…
Existing theory of momentum assumes that gradients arrive at every parameter at a roughly constant rate, an assumption violated in practice by heavy-tailed data distributions and modern architectures. We theoretically analyze the dynamics…
We are interested in the question of stability in the field of shape optimization, with focus on the strategy using second order shape derivative. More precisely, we identify structural hypotheses on the hessian of the considered shape…
In Geosciences a class of phenomena that is widely studied given its real impact on human life are the tectonic faults slip. These landslides have different ways to manifest, ranging from aseismic events of slow displacement (slow slips) to…
In this work the data of the earthquake catalog of the NOAA, National Geophysical Data Center (NGDC) are processed in terms of global seismic energy release. The determined Global Cumulative Seismic Energy Release (GCSER) graph as a…
Accurate and economical modeling of near-surface transport processes is a standing challenge for various engineering and atmospheric boundary-layer flows. In this paper, we address this challenge by utilizing a stochastic one-dimensional…
Shubnikov-de Haas (SdH) oscillations have served as a paradigmatic experimental probe and tool for extracting key semiconductor parameters such as carrier density, effective mass, Zeeman splitting with g-factor $g^*$, quantum scattering…
Two approaches to incorporate heterogeneity in discrete models are compared. In the first, standard approach, the heterogeneity is dictated by geometrical structure of the discrete system. In the second approach, the heterogeneity is…
We present and analyze a simplified stochastic $\alpha \Omega -$dynamo model which is designed to assess the influence of additive and multiplicative noises, non-normality of dynamo equation, and nonlinearity of the $\alpha -$% effect and…