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A Posteriori Validation of Generalized Polynomial Chaos Expansions
SIAM Journal on Applied Dynamical Systems, 2023 Generalized polynomial chaos expansions are a powerful tool to study differential equations with random coefficients, allowing in particular to efficiently approximate random invariant sets associated to such equations. In this work, we use ideas from validated numerics in order to obtain rigorous a posteriori error estimates together with existence ...
Maxime Breden
exaly +5 more sources
A Generalized Polynomial Chaos-Based Approach to Analyze the Impacts of Process Deviations on MEMS Beams [PDF]
Sensors, 2017 A microstructure beam is one of the fundamental elements in MEMS devices like cantilever sensors, RF/optical switches, varactors, resonators, etc.
Lili Gao, Zai-Fa Zhou, Qing-An Huang
doaj +2 more sources
Full-cycle prediction of crack healing in self-healing concrete using generalized polynomial chaos expansion [PDF]
Communications EngineeringThe crack healing capacity of self-healing concrete is crucial for enhancing structural durability, especially in aggressive environments where the dynamic progression of healing depth directly influences service life.
Changhao Fu +6 more
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Generalized Polynomial Chaos Expansion for Fast and Accurate Uncertainty Quantification in Geomechanical Modelling [PDF]
Algorithms, 2020 Geomechanical modelling of the processes associated to the exploitation of subsurface resources, such as land subsidence or triggered/induced seismicity, is a common practice of major interest.
Claudia Zoccarato +3 more
doaj +2 more sources
Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures [PDF]
SIAM Journal of Scientific Computing, 2006 We develop a multi-element generalized polynomial chaos (ME-gPC) method for arbitrary probability measures and apply it to solve ordinary and partial differential equations with stochastic inputs. Given a stochastic input with an arbitrary probability measure, its random space is decomposed into smaller elements.
Xiaoliang Wan, George Em Karniadakis
exaly +2 more sources
Modeling of fractional order DPG model insight global warming and pollution effect on desertification for control mechanism [PDF]
Scientific ReportsThis study presents a novel fractional-order mathematical model that investigates the dynamic interplay between dust pollutants, plant biomass, and global warming, referred to as the DPG system.
Muhammad Farman +6 more
doaj +2 more sources
Results in Physics, 2023 The paper mainly studies the traveling wave solutions, phase portrait and chaotic pattern of the generalized fractional stochastic Schrödinger equations forced by multiplicative Brownian motion. By using the polynomial complete discrimination method, the
Da Shi, Zhao Li, Tianyong Han
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Polynomials and General Degree-Based Topological Indices of Generalized Sierpinski Networks
Complexity, 2021 Sierpinski networks are networks of fractal nature having several applications in computer science, music, chemistry, and mathematics. These networks are commonly used in chaos, fractals, recursive sequences, and complex systems.
Chengmei Fan +4 more
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Topics in Cognitive Science, EarlyView., 2023 Abstract Fractal fluctuations are a core concept for inquiries into human behavior and cognition from a dynamic systems perspective. Here, we present a generalized variance method for multivariate detrended fluctuation analysis (mvDFA). The advantage of this extension is that it can be applied to multivariate time series and considers intercorrelation ...
Sebastian Wallot +5 more
wiley +1 more source
Uncertainty Quantification of GEKO Model Coefficients on Compressible Flows
International Journal of Aerospace Engineering, 2021 In the present work, supersonic flows over an axisymmetric base and a 24-deg compression ramp are investigated using the generalized k-ω (GEKO) model implemented in the commercial software, ANSYS FLUENT.
Yeong-Ki Jung +2 more
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