| Title | : | Tensor-Valued Random Fields for Continuum Physics |
| Author | : | Anatoliy Malyarenko |
| Language | : | en |
| Rating | : | 4.90 out of 5 stars |
| Type | : | PDF, ePub, Kindle |
| Uploaded | : | Apr 10, 2021 |
Download Tensor-Valued Random Fields for Continuum Physics - Anatoliy Malyarenko | ePub
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On this basis, a statistical description of second-order (statistically) homogeneous and isotropic rank-3 tensor-valued random fields is given. With a group-theoretic foundation, correlation functions and their spectral counterparts are obtained in terms of stochastic integrals with respect to certain random measures for the fields that belong.
The corresponding random fields are known as χ 2 fields with d degrees of freedom, the t field with d − 1 degrees of freedom, and the f field with n and m degrees of freedom. These three random fields all have very different spatial behaviour, and each is as fundamental to the statistical applications of random field theory.
Tensor-valued random fields for meso-scale stochastic model of anisotropic elastic microstructure and probabilistic analysis of representative volume element size. Probabilistic engineering mechanics 23(2–3):307–323, 2008a.
In particular, the construction of tensor-valued random eld representations modeling the coecients of stochastic elliptic operators is of great importance and nds applications in a broad range of engineering or scientic elds (such as biomedical engineering, geophysics or wave propagation through random media for instance).
The probability model used for the stiffness tensor-valued random field of the random anisotropic elastic microstructure is an extension of the model recently introduced by the author for elliptic stochastic partial differential operators. The stochastic boundary value problem is numerically solved by using the stochastic finite element method.
We construct classes of homogeneous random fields on a three-dimensional euclidean space that take values in linear spaces of tensors of a fixed rank and are isotropic with respect to a fixed orthogonal representation of the group of \ (3\times 3\) orthogonal matrices. The constructed classes depend on finitely many isotropic spectral densities.
Ostoja-starzewski, spectral expansions of homogeneous and isotropic tensor-valued random fields, arxiv:1402. 1648, journal of applied mathematics and physics (zamp) 67(3), paper 59, 2016.
The stress fields responsible for deep-seated earthquake sources cannot be measured directly, but they can be inferred from models of earthquake systems that obey the laws of physics and conform to the relationships between stress and deformation (rheology) observed in the laboratory.
May 24, 2018 we consider a real-valued random field z on s2 and assume that the the support of g ⊗ g includes that of fn, where ⊗ denotes the tensor.
The tf package provides many functions for creating random-valued tensors and the following table lists five of them.
Abstract this paper deals with the identification of probabilistic models of the random coefficients in stochastic boundary value problems (sbvp).
Ble 1 ), namely turning bands method, spectral method, matrix decomposition a general complex-valued random field k() can be expressed as a fourier-.
Reduced chaos decomposition with random coefficients of vector-valued random variables and random fields.
Random fields, stochastic models and stochastic researchgate, the probabilistic description of both scalar random variables and matrix-valued random.
Gaussian tensor-valued random field adapted to the algebraic properties of the 3d-elasticity field and to the corresponding stochastic elliptic boundary value problem. The hyperparameters of the prior stochastic model of the apparent elas-ticity random field at mesoscale, are its statistical mean va lue, its spatial corre-.
When dealing with tensor-valued data, traditional approaches for filtering, registration or segmentation have been adapted in order to account for the special properties of this data modality. In this paper, we introduce mixtures of gaussians on tensor fields as a new statistical model for the segmentation of tensor valued images.
178--206 daniel smith and michael smith estimation of binary markov random fields using markov chain monte carlo 207--227 guosheng yin and donglin zeng efficient algorithm for computing maximum likelihood estimates in linear transformation models.
The interface between random field theory and stochastic geometry has been at the centre of this relating to tensor, rather than scalar-valued, random fields.
This paper is concerned with the construction of a new class of generalized nonparametric probabilistic models for matrix-valued non-gaussian random fields.
Feb 23, 2021 used in the notebooks transformer model for language understanding customization basics: tensors and operations deepdream pix2pix.
Conditional random fields, which model the distribution of a multivariate response be natural for continuous, skewed continuous or count-valued random variables.
Tensor-valued random fields in continuum physics malyarenko, anatoliy mälardalen university, school of education, culture and communication, educational sciences and mathematics.
Diffusion tensor imaging in multiple sclerosis at different final outcomes.
Dec 25, 2015 kriging prediction for manifold-valued random fields as shape analysis, diffusion tensor imaging and the analysis of covariance matrices.
Abstract tensor valued images, for instance originating from diffusion tensor magnetic resonance imaging (dt-mri), have become more and more important over the last couple of years. Due to the nonlinear structure of such data it is nontrivial to adapt well-established image processing techniques to them.
Before a complete random field theory of tensor-valued signals can be developed, further work is required to extend the concept of roughness and smoothness to tensor-valued data, as these tensors arise in the statistical flattening and omnibus significance testing for signal detection in scalar-valued random fields.
Generation of non-gaussian tensor-valued random fields using an isde-based algorithm. In safety, reliability, risk and life cycle performance of structures and infrastructures proceedings of the 11th international conference on structural safety and reliability, icossar 2013, 2793-2798.
Tensor-valued random fields for meso-scale stochastic model of anisotropic elastic microstructure and probabilistic analysis of representative volume element size. On the homogenization and the simulation of random materials.
International audiencethis paper is devoted to the identification of bayesian posteriors for the random coefficients of the high-dimension polynomial chaos expansions of non-gaussian tensor-valued random fields using partial and limited experimental data.
Sun j and xu z (2010) scale selection for anisotropic diffusion filter by markov random field model, pattern recognition, 43:8, (2630-2645), online publication date: 1-aug-2010.
Abstract: this work is concerned with the construction of a random generator for non-gaussian tensor-valued random fields. Specifically, it focuses on the generation of the class of prior algebraic stochastic models associated with elliptic operators, for which the family of first-order marginal probability distributions is con-structed using the maxent principle.
As mentioned in the introduction, we decompose the velocity field: unlike the reynolds decomposition, the filtered component is a random field and in general, the filtered residual is non-zero. The filtering operation commutes with differentiating with respect to time and it commutes with taking the mean.
This leads to tensor-valued random fields in which the key role is played by a statistical volume element (sve); when the sve becomes sufficiently large, its properties become deterministic and one recovers the representative volume element (rve) of deterministic continuum physics.
Programme le workshop débutera lundi 5 à 14h30 et s'achèvera mercredi 7 à 16h30.
5: seqeval: pip install keras implementation of conditional random field. Contribute to bojone/crf development by creating an account on github. Pre-trained models and datasets built by google and the community.
Citeseerx - document details (isaac councill, lee giles, pradeep teregowda): in this presentation, we will present and discuss some of the most recent contributions to the construction of prior algebraic stochastic models (pasm) for non-gaussian tensor-valued random fields.
These issues and better (scale dependent) bounds (plus models of random microstructures, tensor-valued random fields, classical versus non-classical continuum mechanics, static versus dynamic responses, elastic versus inelastic, and much more) are discussed at length in [microstructural randomness and scaling in mechanics of materials by ostoja.
Request pdf tensor-valued random fields in continuum physics this article reports progress on homogeneous isotropic tensor random fields (trfs) for continuum mechanics.
Russell: we introduce a new approximation for large-scale gaussian processes, the gaussian process random field (gprf), in which local gps are coupled via pairwise potentials. 375: m-statistic for kernel change-point detection: shuang li, yao xie, hanjun dai, le song.
This paper is devoted to the identification of high-dimension polynomial chaos expansions with random coefficients for non-gaussian tensor-valued random fields using partial and limited experimental data. The experimental data sets correspond to partial experimental data made up of an observation vector which is the response of a stochastic boundary value problem depending on the tensor-valued.
For linear elastic isotropic solids, the random vector p(x) (x be- ing fixed) can be taken as p(x) is a normalized rq-valued gaussian random field with indepen-.
This study presents a numerical analysis of the topology of a set of cosmologically interesting three-dimensional gaussian random fields in terms of their betti numbers $\\beta_0$, $\\beta_1$ and $\\beta_2$. We show that betti numbers entail a considerably richer characterization of the topology of the primordial density field.
Apr 28, 2011 non‐gaussian positive‐definite matrix‐valued random fields with constrained eigenvalues: application to random elasticity tensors with.
Tensor-valued random fields describing the piezoelectric effect. 13th world congress in computational mechanics, new york, usa, july 25, 2018. Emerging trends in applied mathematics and mechanics etamm2018, kraków, poland, june 20, 2018.
Motivationtensor fields (tfs) appear throughout continuum physics, while random fields (rfs) are the subject of much research in probability theory and stochastic processes. Whenever there is randomness in loadings (surface or body type) and/or microstructure, the tfs become random and we have tensor-valued random fields or, simply, tensor.
Oct 23, 2007 section we consider various generalizations to the vector-valued random fields.
Itô sde-based generator for a class of non-gaussian vector-valued random fields in uncertainty quantification.
The new stochastic representation builds upon a walpole tensor decomposition, which strategy involves both matrix-valued and scalar-valued random fields.
Tensor-valued random fields random fields are of great use in studying natural processes by the monte carlo method in which the random fields correspond to naturally spatially varying properties.
We generalize the translation invariant tensor-valued minkowski functionals which are defined on two-dimensional flat space to the unit sphere. The contours enclosing boundaries of level sets of random fields give a spatial distribution of random smooth closed curves. We outline a method to compute the tensor-valued minkowski functionals.
These fields are an extension of markov random fields for tensor-valued random variables. By extending the results of dobruschin, hammersley and clifford to such tensor valued fields, we proved that tensor markov fields are indeed gibbs fields, whenever strictly positive probability measures are considered.
Nov 23, 2010 partial sum of a hilbert-space valued strictly stationary random field x can be thought of as represented by the n× n “covariance matrix”.
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