Article
Engineering, Aerospace
John A. Schaefer, Andrew W. Cary, Mori Mani, Thomas A. Grandine, Christopher J. Roy, Heng Xiao
Summary: In recent years, there has been a substantial increase in demand for stochastic engineering results, with advancements in computing technology and statistical methods making uncertainty quantification studies feasible. While uncertainty can be quantified at specific locations, the challenge remains to interpolate or extrapolate this information to predict uncertainty at untested locations.
Article
Thermodynamics
Benedikt Sterr, Ehsan Mahravan, Daegyoum Kim
Summary: In this study, polynomial chaos expansions are used to investigate the stochastic heat transfer performance of a microchannel heat sink. It is found that an increase in surface roughness enhances heat transfer, and local surface height alone is insufficient to explain changes in the local Nusselt number, with sensitivity increasing with the absolute value of the local surface height. Probability density functions are estimated from the polynomial chaos expansions to identify peaks and ridges of the surface where Nusselt number and velocity magnitude are more sensitive to local surface roughness.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2021)
Article
Computer Science, Interdisciplinary Applications
Kyriakos D. Kantarakias, George Papadakis
Summary: This article introduces the method of least squares regression for uncertainty quantification, and improves the linear system by adding the gradient of the quantity of interest (QoI) with respect to stochastic variables. The gradient is efficiently computed from the adjoint system of equations. An effective sampling strategy is required to minimize the condition number of the augmented LSQ system. Two strategies are compared, and the first one is found to be more efficient in terms of accuracy vs number of evaluations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Engineering, Multidisciplinary
Nick Pepper, Francesco Montomoli, Sanjiv Sharma
Summary: This work introduces a framework for updating probability distribution estimates with scarce experimental data, using the Maximum Entropy Principle and Polynomial Chaos Expansion. By minimizing KL divergence and taking into account experimental constraints, the method improves the accuracy of the estimates.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Metallurgy & Metallurgical Engineering
Marks Legkovskis, Peter J. Thomas, Michael Auinger
Summary: Uncertainty quantification is crucial in steel reheating simulations due to input uncertainties in defining surface properties and furnace conditions. The study uses polynomial chaos expansion to reduce computational effort and presents a comprehensive uncertainty quantification analysis of a walking-beam reheat furnace. The analysis reveals the significant influence of parameters related to emissivity and oxide scale growth on slab temperature and identifies the transition in importance of oxide scale growth inputs.
STEEL RESEARCH INTERNATIONAL
(2023)
Article
Computer Science, Interdisciplinary Applications
G. Ninos, V Bartzis, N. Merlemis, I. E. Sarris
Summary: This study analyzes recent research efforts and directions in implementing Uncertainty Quantification (UQ) in human hemodynamic flows, emphasizing the importance of finding the best statistical methods and parameters to represent uncertainties and achieve good interpretation of input-output interactions.
COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE
(2021)
Article
Engineering, Marine
Ming Chen, Xinhu Zhang, Kechun Shen, Guang Pan
Summary: This study investigates the high-dimensional uncertainty quantification of critical buckling pressure for a composite cylindrical shell with geometric and material uncertainties using sparse polynomial chaos expansion (PCE). The results show that the uncertainty of the longitudinal modulus has a massive influence on the critical buckling pressure, while the uncertainties of other parameters have a weak influence.
JOURNAL OF MARINE SCIENCE AND ENGINEERING
(2022)
Article
Ecology
Jody R. Reimer, Frederick R. Adler, Kenneth M. Golden, Akil Narayan
Summary: Uncertainty in parameters in ecological models can be incorporated by treating parameters as random variables with distributions. Recent advances in uncertainty quantification methods provide new approaches for analyzing models with random parameters. Modelling key parameters as random variables changes the characteristics of the model. The computational efficiency of polynomial chaos methods helps in better predicting and synthesizing models with data.
Article
Mathematics, Applied
Jonas Kusch, Louisa Schlachter
Summary: This article investigates intrusive uncertainty quantification schemes for systems of conservation laws with uncertainty, addressing the challenges through two different strategies. The first strategy involves combining filters with the multi-element approach for hyperbolicity-preserving stochastic Galerkin scheme, while the second strategy introduces a multi-element approach for intrusive polynomial moment method to reduce computational costs. The proposed approaches are extended to adaptivity, allowing for adjusting the number of basis functions in each multi-element to the smoothness of the solution.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Engineering, Civil
Vinh Ngoc Tran, Jongho Kim
Summary: This study introduces the strengths of polynomial chaos-kriging (PCK), a new surrogate model that combines polynomial chaos extension (PCE) and Gaussian process with kriging variance. The results show that PCK outperforms PCE and ordinary kriging (OK) in mimicking predictive and sensitive behaviors of the original model with a smaller-sized training dataset. Additionally, PCK accurately predicts hydrographs and flood peaks for extreme events that differ significantly from the training set.
JOURNAL OF HYDROLOGY
(2022)
Article
Engineering, Mechanical
Premjit Saha, Tarunraj Singh, Gary Dargush
Summary: This paper focuses on the utilization of polynomial chaos (PC) to develop surrogate models for differential algebraic equations (DAEs), with emphasis on both intrusive and nonintrusive approaches. The use of Lagrange interpolation polynomials as basis functions is discussed, with examples of a benchmark RLC circuit and a simple pendulum illustrating the effectiveness of the proposed approach. Validation of PC models using Monte Carlo (MC) simulations and estimation of evolving probably density functions (PDFs) are also carried out.
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS
(2021)
Article
Engineering, Civil
Z. P. Xu, Y. P. Li, G. H. Huang, Z. Y. Shen
Summary: In this study, a PCE-ANOVA-RF method is developed to analyze the effects of multiple uncertain parameters in the SWAT model and generate probabilistic forecasts of daily streamflow. The proposed method not only reveals the impact of parameter uncertainty and saves computation time, but also expands PCE's ability to predict future streamflow processes. The feasibility and applicability of the method are verified in the Amu Darya River Basin in Central Asia.
JOURNAL OF HYDROLOGY
(2023)
Article
Engineering, Multidisciplinary
Arash Mohammadi, Koji Shimoyama, Mohamad Sadeq Karimi, Mehrdad Raisee
Summary: An efficient surrogate model based on POD and compressed sensing is developed for affordable representation of high-dimensional stochastic fields, showing potential in engineering applications.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Mathematics, Applied
Xiang Sun, Jung-Il Choi
Summary: The proposed method utilizes POD and PCE to model spacetime-dependent parameterized problems, effectively estimating low-order moments and accuracy loss under uncorrelated or correlated input parameters.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Brian Turnquist, Mark Owkes
Summary: multiUQ is a novel tool for simulating gas-liquid multiphase flows and quantifying uncertainty in results by considering variability in fluid properties and initial/boundary conditions. It utilizes polynomial chaos and stochastic variables to include uncertainty in simulation solutions, and employs an intrusive uncertainty quantification method to provide distribution of solutions and desired statistics in a cost-effective manner.
COMPUTER PHYSICS COMMUNICATIONS
(2021)
Article
Mathematics, Applied
Geunsu Choi, Mingu Jung, Sun Kwang Kim, Miguel Martin
Summary: This paper studies weak-star quasi norm attaining operators and proves that the set of such operators is dense in the space of bounded linear operators regardless of the choice of Banach spaces. It is also shown that weak-star quasi norm attaining operators have distinct properties from other types of norm attaining operators, although they may share some equivalent properties under certain conditions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maria Lorente, Francisco J. Martin-Reyes, Israel P. Rivera-Rios
Summary: In this paper, we provide quantitative one-sided estimates that recover the dependences in the classical setting. We estimate the one-sided maximal function in Lorentz spaces and demonstrate the applicability of the conjugation method for commutators in this context.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Fernando Cobos, Luz M. Fernandez-Cabrera
Summary: We provide a necessary and sufficient condition for the weak compactness of bilinear operators interpolated using the real method. However, this characterization does not hold for interpolated operators using the complex method.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ovgue Gurel Yilmaz, Sofiya Ostrovska, Mehmet Turan
Summary: The Lupas q-analogue Rn,q, the first q-version of the Bernstein polynomials, was originally proposed by A. Lupas in 1987 but gained popularity 20 years later when q-analogues of classical operators in approximation theory became a focus of intensive research. This work investigates the continuity of operators Rn,q with respect to the parameter q in both the strong operator topology and the uniform operator topology, considering both fixed and infinite n.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
M. Agranovsky, A. Koldobsky, D. Ryabogin, V. Yaskin
Summary: This article modifies the concept of polynomial integrability for even dimensions and proves that ellipsoids are the only convex infinitely smooth bodies satisfying this property.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Abel Komalovics, Lajos Molnar
Summary: In this paper, a parametric family of two-variable maps on positive cones of C*-algebras is defined and studied from various perspectives. The square roots of the values of these maps under a faithful tracial positive linear functional are considered as a family of potential distance measures. The study explores the problem of well-definedness and whether these distance measures are true metrics, and also provides some related trace characterizations. Several difficult open questions are formulated.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Frederic Bayart
Summary: The passage describes the construction of an operator on a separable Hilbert space that is 5-hypercyclic for all δ in the range (ε, 1) and is not 5-hypercyclic for all δ in the range (0, ε).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Helene Frankowska, Nikolai P. Osmolovskii
Summary: This paper investigates second-order optimality conditions for the minimization problem of a C2 function f on a general set K in a Banach space X. Both necessary and sufficient conditions are discussed, with the sufficiency condition requiring additional assumptions. The paper demonstrates the validity of these assumptions for the case when the set K is an intersection of sets described by smooth inequalities and equalities, such as in mathematical programming problems. The novelty of the approach lies in the arbitrary nature of the set K and the straightforward proofs.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ole Fredrik Brevig, Kristian Seip
Summary: This paper studies the Hankel operator on the Hardy space and discusses its minimal and maximal norms, as well as the relationship between the maximal norm and the properties of the function.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Alexander Meskhi
Summary: Rubio de Francia's extrapolation theorem is established for new weighted grand Morrey spaces Mp),lambda,theta w (X) with weights w beyond the Muckenhoupt Ap classes. This result implies the one-weight inequality for operators of Harmonic Analysis in these spaces for appropriate weights. The necessary conditions for the boundedness of the Hardy-Littlewood maximal operator and the Hilbert transform in these spaces are also obtained. Some structural properties of new weighted grand Morrey spaces are investigated. Problems are studied in the case when operators and spaces are defined on spaces of homogeneous type.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maud Szusterman
Summary: In this work, the necessary conditions on the structure of the boundary of a convex body K to satisfy all inequalities are investigated. A new solution for the 3-dimensional case is obtained in particular.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Rami Ayoush, Michal Wojciechowski
Summary: In this article, lower bounds for the lower Hausdorff dimension of finite measures are provided under certain restrictions on their quaternionic spherical harmonics expansions. This estimate is analogous to a result previously obtained by the authors for complex spheres.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
F. G. Abdullayev, V. V. Savchuk
Summary: This paper investigates the convergence and theorem proof of the Takenaka-Malmquist system and Fejer-type operator on the unit circle, and provides relevant results on the class of holomorphic functions representable by Cauchy-type integrals with bounded densities.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Sofiya Ostrovska, Mikhail I. Ostrovskii
Summary: This work aims to establish new results on the structure of transportation cost spaces. The main outcome of this paper states that if a metric space X contains an isometric copy of L1 in its transportation cost space, then it also contains a 1-complemented isometric copy of $1.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Pilar Rueda, Enrique A. Sanchez Perez
Summary: We prove a factorization theorem for Lipschitz operators acting on certain subsets of metric spaces of measurable functions and with values on general metric spaces. Our results show how a Lipschitz operator can be extended to a subset of other metric space of measurable functions that satisfies the following optimality condition: it is the biggest metric space, formed by measurable functions, to which the operator can be extended preserving the Lipschitz constant. Also, we demonstrate the coarsest metric that can be given for a metric space in which an order bounded lattice-valued-Lipschitz map is defined, and provide concrete examples involving the relevant space L0(mu).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
