Article
Automation & Control Systems
Anna Kirpichnikova, Jussi Korpela, Matti J. Lassas, Lauri Oksanen
Summary: In this study, by analyzing the hyperbolic Neumann-to-Dirichlet map, a sequence of boundary values can be constructed so that the waves converge to zero at time T and the time derivative of the waves converges to a delta distribution. The limit of these waves can be considered as waves produced by an artificial point source.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2021)
Article
Mathematics
Yanjun Ma
Summary: In this paper, we study a zeroth-order perturbation q(x) of the buckling operator delta(2)-kappa delta, and show that it can be uniquely determined by measuring the Dirichlet-to-Neumann data on the boundary. We extend the conclusion of the biharmonic operator to the buckling operator, and the Dirichlet-to-Neumann map provided in this study is more meaningful and general.
Article
Chemistry, Physical
Thomas M. Koller, Manuel Kerscher, Andreas P. Froeba
Summary: This article discusses the application of surface light scattering near the critical damping of surface fluctuations and introduces a new evaluation method that accurately determines viscosity and surface tension.
JOURNAL OF COLLOID AND INTERFACE SCIENCE
(2022)
Article
Mathematics
Sagrario Lantaron, Susana Merchan
Summary: In this study, we examined the Schrodinger operator with a potential q on a disk and the corresponding Dirichlet-to-Neumann (DtN) map. Numerical and analytical results were provided on the map's range and stability for a specific class of one-step radial potentials.
Article
Mechanics
Daniel B. Shaw, Luc Deike
Summary: An experimental study was conducted on bubble coalescence at an air-water interface, examining the evolution of underwater neck and surface bridge. The research explored a wide range of Bond numbers to compare gravity and capillary forces, finding different behaviors for nearly spherical bubbles with Bo << 1 and non-spherical bubbles with Bo > 1. By observing inertial-capillary growth and using a simple oscillatory model, the study characterized the dynamics of both the bubble neck and upper surface in various Bond number scenarios.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Engineering, Mechanical
Feng-Lian Li, Chuanzeng Zhang, Yue-Sheng Wang
Summary: The study investigates the effects of viscosity on band-gaps of 2D viscoelastic phononic crystals using the DIN map method. The results show that viscosity influences the location and width of the band-gaps, providing an alternative way to adjust the band-gaps of phononic crystals.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2021)
Article
Mathematics, Applied
R. U. M. I. N. G. Zhang
Summary: In this paper, a new spectral decomposition method is proposed for simulating wave propagation in complex waveguides. The efficient approximation of the Dirichlet-to-Neumann (DtN) map is crucial for solving waveguide scattering problems numerically. By decomposing the physical solution into a family of generalized eigenfunctions, the DtN map can be explicitly written using these functions. The DtN map is approximated using a finite truncation based on the exponential decay of the generalized eigenfunctions, and the approximation is proven to converge exponentially. The truncated DtN map is utilized to truncate the unbounded domain into a bounded one, and a variational formulation is set up for solving the problem in this bounded domain. The truncated problem is then solved using a finite element method. Error estimation is provided for the numerical algorithm, and numerical examples are provided to demonstrate the efficiency of the algorithm.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2023)
Article
Mathematics, Applied
Pei Su
Summary: This paper investigates the asymptotic behavior of small-amplitude gravity water waves in a rectangular domain with shallow water depth. By applying horizontal acceleration at one lateral boundary, the solution of the water waves system is shown to converge to the solution of the one-dimensional wave equation with Neumann boundary control in the shallow water limit.
ASYMPTOTIC ANALYSIS
(2023)
Article
Mathematics, Applied
Yanjun Ma, Genqian Liu
Summary: In this paper, logarithmic stability estimates for the magnetic and electric potentials associated to the first order perturbation of the biharmonic operator are proven, when the Dirichlet-to-Neumann maps are made on the whole boundary. (c) 2023 Elsevier Inc. All rights reserved.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Engineering, Geological
Mario Duran, Eduardo Godoy, Esteban Roman Catafau, Patricio A. Toledo
Summary: With the decreasing ore-grade in mineral deposits, open-pit mining requires greater depths and steeper slope angles, which can lead to geomechanical instabilities. Mathematical modelling and numerical simulation are used to determine excavation stability by calculating the rock-mass stress-state, but the lack of clear borders around the excavation presents a challenge. The DtN-FEM procedure is applied in this study to efficiently calculate displacements and stresses in open-pit slopes, allowing for quick simulation of multiple slope configurations and potential for flexible designing tools.
INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES
(2022)
Article
Mathematics, Applied
Deepak Garg, Paolo Papale, Antonella Longo
Summary: This work presents a partitioned fluid-structure interaction solver that combines various methods such as time discontinuous deforming domain stabilized space-time finite element method. It successfully detects the accurate interaction between fluid and structure by using pressure primitive variables for flow computation and non-linear material models for structural deformation. The numerical code is verified and validated on multiple compressible and incompressible flow benchmarks, demonstrating its efficacy.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Yongjie Shi, Chengjie Yu
Summary: This paper introduces Dirichlet-to-Neumann maps for differential forms on graphs, which can be seen as a discrete analogue of the corresponding Dirichlet-to-Neumann maps on compact Riemannian manifolds with boundary and a higher degree generalization of the Dirichlet-to-Neumann map on graphs introduced by Hua-Huang-Wang [14] and Hassannezhad-Miclo [11]. Then, some Raulot-Savo-type estimates on the eigenvalues of the introduced DtN maps are derived.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
A. S. Fokas, M. C. van der Weele
Summary: This paper presents a new approach for solving the generalized Dirichlet-to-Neumann map for linear evolution PDEs on the half-line with time-periodic boundary conditions. It demonstrates that the solution becomes time-periodic for large t using the unified transform, and that the coefficients of the unknown boundary values can be explicitly determined in a simple, algebraic way. The approach is illustrated on second-order linear evolution equations and those containing spatial derivatives of arbitrary order.
STUDIES IN APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Murdhy Aldawsari, Tatiana Savina
Summary: This paper focuses on the reflection of harmonic functions defined near a real-analytic curve in the plane subject to the Robin condition, deriving a reflection formula and showing the equivalence of two different formulae in certain cases. Examples of reflection formulae for non-homogeneous Neumann and Robin conditions on common curves in mathematical physics are also provided.
APPLICABLE ANALYSIS
(2022)
Article
Mathematics, Applied
Guang-Hui Zheng, Zhi-Qiang Miao
Summary: This paper investigates the uniqueness and nonuniqueness for internal potential reconstruction in a core-shell structure from one boundary measurement, connected to the steady state Schrodinger equation. A uniqueness theorem for the inverse problem is established, along with a nonuniqueness theorem when considering different potentials and shapes. Moreover, the Tikhonov regularization method is utilized to solve the reconstruction problem, with numerical examples confirming the theoretical results and efficacy of the proposed method.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)