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Relevant bibliographies by topics / Homogeneous Neumann boundary conditions

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Academic literature on the topic 'Homogeneous Neumann boundary conditions'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 March 2023

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Journal articles on the topic "Homogeneous Neumann boundary conditions"

1

Jiang, Jun, Jinfeng Wang, and Yingwei Song. "The Influence of Dirichlet Boundary Conditions on the Dynamics for a Diffusive Predator–Prey System." International Journal of Bifurcation and Chaos 29, no. 09 (2019): 1950113. http://dx.doi.org/10.1142/s021812741950113x.

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A reaction–diffusion predator–prey system with homogeneous Dirichlet boundary conditions describes the lethal risk of predator and prey species on the boundary. The spatial pattern formations with the homogeneous Dirichlet boundary conditions are characterized by the Turing type linear instability of homogeneous state and bifurcation theory. Compared with homogeneous Neumann boundary conditions, we see that the homogeneous Dirichlet boundary conditions may depress the spatial patterns produced through the diffusion-induced instability. In addition, the existence of semi-trivial steady states and the global stability of the trivial steady state are characterized by the comparison technique.

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Baddour, R. E., and W. Parsons. "A Comparison of Dirichlet and Neumann Wavemakers for the Numerical Generation and Propagation of Nonlinear Long-Crested Surface Waves." Journal of Offshore Mechanics and Arctic Engineering 126, no. 4 (2004): 287–96. http://dx.doi.org/10.1115/1.1835987.

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We are studying numerically the problem of generation and propagation of long-crested gravity waves in a tank containing an incompressible inviscid homogeneous fluid initially at rest with a horizontal free surface of finite extent and of infinite depth. A nonorthogonal curvilinear coordinate system, which follows the free surface, is constructed and the full nonlinear kinematic and dynamic free surface boundary conditions are utilized in the algorithm. “Wavemakers” are modeled using both the Dirichlet and Neumann lateral boundary conditions and a full comparison is given. Overall, the Dirichlet model was more stable than the Neumann model, with an upper limit steepness S=2A/λ of 0.08 using good resolution compared with the Neumann’s maximum of 0.05.

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Fiebig-Wittmaack, Mclitta. "Multiplicity of solutions of a nonlinear boundary problem with homogeneous neumann boundary conditions." Applicable Analysis 29, no. 3-4 (1988): 253–68. http://dx.doi.org/10.1080/00036818808839784.

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ENACHE, CRISTIAN. "LOWER BOUNDS FOR BLOW-UP TIME IN SOME NON-LINEAR PARABOLIC PROBLEMS UNDER NEUMANN BOUNDARY CONDITIONS." Glasgow Mathematical Journal 53, no. 3 (2011): 569–75. http://dx.doi.org/10.1017/s0017089511000139.

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AbstractThis paper deals with some non-linear initial-boundary value problems under homogeneous Neumann boundary conditions, in which the solutions may blow up in finite time. Using a first-order differential inequality technique, lower bounds for blow-up time are determined.

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Otero, Jose, Ernesto Hernandez, Ruben Santiago, Raul Martinez, Francisco Castillo, and Joaquin Oseguera. "Non-parabolic interface motion for the one-dimensional Stefan problem: Neumann boundary conditions." Thermal Science 21, no. 6 Part B (2017): 2699–708. http://dx.doi.org/10.2298/tsci151218311o.

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In this work, we study the liquid-solid interface dynamics for large time intervals on a 1-D sample, with homogeneous Neumann boundary conditions. In this kind of boundary value problem, we are able to make new predictions about the interface position by using conservation of energy. These predictions are confirmed through the heat balance integral method of Goodman and a generalized non-classical finite difference scheme. Since Neumann boundary conditions imply that the specimen is thermally isolated, through well stablished thermodynamics, we show that the interface behavior is not parabolic, and some examples are built with a novel interface dynamics that is not found in the literature. Also, it is shown that, on a Neumann boundary value problem, the position of the interface at thermodynamic equilibrium depends entirely on the initial temperature profile. The prediction of the interface position for large time values makes possible to fine tune the numerical methods, and given that energy conservation demands highly precise solutions, we found that it was necessary to develop a general non-classical finite difference scheme where a non-homogeneous moving mesh is considered. Numerical examples are shown to test these predictions and finally, we study the phase transition on a thermally isolated sample with a liquid and a solid phase in aluminum.

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YIN, Zhaoyang. "Global existence for quasilinear parabolic systems with homogeneous Neumann boundary conditions." Nonlinear Differential Equations and Applications NoDEA 13, no. 2 (2006): 235–48. http://dx.doi.org/10.1007/s00030-005-0038-z.

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Solà-Morales, J., and M. València. "Trend to spatial homogeneity for solutions to semilinear damped wave equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 105, no. 1 (1987): 117–26. http://dx.doi.org/10.1017/s0308210500021958.

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SynopsisThe semilinear damped wave equationssubject to homogeneous Neumann boundary conditions, admit spatially homogeneous solutions (i.e. u(x, t) = u(t)). In order that every solution tends to a spatially homogeneous one, we look for conditions on the coefficients a and d, and on the Lipschitz constant of f with respect to u.

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Amo-Navarro, Jesús, Ricardo Vinuesa, J. Alberto Conejero, and Sergio Hoyas. "Two-Dimensional Compact-Finite-Difference Schemes for Solving the bi-Laplacian Operator with Homogeneous Wall-Normal Derivatives." Mathematics 9, no. 19 (2021): 2508. http://dx.doi.org/10.3390/math9192508.

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In fluid mechanics, the bi-Laplacian operator with Neumann homogeneous boundary conditions emerges when transforming the Navier–Stokes equations to the vorticity–velocity formulation. In the case of problems with a periodic direction, the problem can be transformed into multiple, independent, two-dimensional fourth-order elliptic problems. An efficient method to solve these two-dimensional bi-Laplacian operators with Neumann homogeneus boundary conditions was designed and validated using 2D compact finite difference schemes. The solution is formulated as a linear combination of auxiliary solutions, as many as the number of points on the boundary, a method that was prohibitive some years ago due to the large memory requirements to store all these auxiliary functions. The validation has been made for different field configurations, grid sizes, and stencils of the numerical scheme, showing its potential to tackle high gradient fields as those that can be found in turbulent flows.

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Kirk, Colleen M., and W. Edward Olmstead. "Thermal blow-up in a finite strip with superdiffusive properties." Fractional Calculus and Applied Analysis 21, no. 4 (2018): 949–59. http://dx.doi.org/10.1515/fca-2018-0052.

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Abstract We investigate the problem of a high-energy source localized within a one-dimensional superdiffusive medium of finite length. The problem is modeled by a fractional diffusion equation with a nonlinear source term. For the boundary conditions, we consider both the case of homogeneous Dirichlet conditions and the case of homogeneous Neumann conditions. We investigate this model to determine whether or not blow-up occurs. It is demonstrated that a blow-up may or may not occur for the Dirichlet case. On the other hand, a blow-up is unavoidable for the Neumann case.

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Subani, Norazlina, Muhammad Aniq Qayyum Mohamad Sukry, Muhammad Arif Hannan, Faizzuddin Jamaluddin, and Ahmad Danial Hidayatullah Badrolhisam. "Analysis of Different Boundary Conditions on Homogeneous One-Dimensional Heat Equation." Malaysian Journal of Science Health & Technology 7, no. 1 (2021): 15–21. http://dx.doi.org/10.33102/mjosht.v7i1.153.

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Partial differential equations involve results of unknown functions when there are multiple independent variables. There is a need for analytical solutions to ensure partial differential equations could be solved accurately. Thus, these partial differential equations could be solved using the right initial and boundaries conditions. In this light, boundary conditions depend on the general solution; the partial differential equations should present particular solutions when paired with varied boundary conditions. This study analysed the use of variable separation to provide an analytical solution of the homogeneous, one-dimensional heat equation. This study is applied to varied boundary conditions to examine the flow attributes of the heat equation. The solution is verified through different boundary conditions: Dirichlet, Neumann, and mixed-insulated boundary conditions. the initial value was kept constant despite the varied boundary conditions. There are two significant findings in this study. First, the temperature profile changes are influenced by the boundary conditions, and that the boundary conditions are dependent on the heat equation’s flow attributes.

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Dissertations / Theses on the topic "Homogeneous Neumann boundary conditions"

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Benincasa, Tommaso <1981&gt. "Analysis and optimal control for the phase-field transition system with non-homogeneous Cauchy-Neumann boundary conditions." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2010. http://amsdottorato.unibo.it/3066/1/benincasa_tommaso_tesi.pdf.

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Benincasa, Tommaso <1981&gt. "Analysis and optimal control for the phase-field transition system with non-homogeneous Cauchy-Neumann boundary conditions." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2010. http://amsdottorato.unibo.it/3066/.

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CISTERNINO, MARCO. "A parallel second order Cartesian method for elliptic interface problems and its application to tumor growth model." Doctoral thesis, Politecnico di Torino, 2012. http://hdl.handle.net/11583/2497156.

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This theses deals with a parallel Cartesian method to solve elliptic problems with complex interfaces and its application to elliptic irregular domain problems in the framework of a tumor growth model. This method is based on a finite differences scheme and is second order accurate in the whole domain. The originality of the method lies in the use of additional unknowns located on the interface, allowing to express the interface transmission conditions. The method is described and the details of its parallelization, performed with the PETSc library, are provided. Numerical validations of the method follow with comparisons to other related methods in literature. A numerical study of the parallelized method is also given. Then, the method is applied to solve elliptic irregular domain problems appearing in a three-dimensional continuous tumor growth model, the two-species Darcy model. The approach used in this application is based on the penalization of the interface transmission conditions, in order to impose homogeneous Neumann boundary conditions on the border of an irregular domain. The simulations of model are provided and they show the ability of the method to impose a good approximation of the considered boundary conditions.

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Cisternino, Marco. "A parallel second order Cartesian method for elliptic interface problems and its application to tumor growth model." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2012. http://tel.archives-ouvertes.fr/tel-00690743.

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Cette thèse porte sur une méthode cartésienne parallèle pour résoudre des problèmes elliptiques avec interfaces complexes et sur son application aux problèmes elliptiques en domaine irrégulier dans le cadre d'un modèle de croissance tumorale. La méthode est basée sur un schéma aux différences fi nies et sa précision est d'ordre deux sur tout le domaine. L'originalité de la méthode consiste en l'utilisation d'inconnues additionnelles situées sur l'interface et qui permettent d'exprimer les conditions de transmission à l'interface. La méthode est décrite et les détails sur la parallélisation, réalisée avec la bibliothèque PETSc, sont donnés. La méthode est validée et les résultats sont comparés avec ceux d'autres méthodes du même type disponibles dans la littérature. Une étude numérique de la méthode parallélisée est fournie. La méthode est appliquée aux problèmes elliptiques dans un domaine irrégulier apparaissant dans un modèle continue et tridimensionnel de croissance tumorale, le modèle à deux espèces du type Darcy . L'approche utilisée dans cette application est basée sur la pénalisation des conditions de transmission a l'interface, afin de imposer des conditions de Neumann homogènes sur le bord d'un domaine irrégulier. Les simulations du modèle sont fournies et montrent la capacité de la méthode à imposer une bonne approximation de conditions au bord considérées.

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Miller, Charles E. "Minimal Nodal Domains for Strictly Elliptic Partial Differential Equations with Homogeneous Boundary Conditions." DigitalCommons@USU, 2006. https://digitalcommons.usu.edu/etd/7142.

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This work presents a proof of the dependence of the first eigenvalue for uniformly elliptic partial differential equations on the domain in a less abstract setting than that of Ivo Babushka and Rudolf Vyborny in 1965. The proof contained here, under rather mild conditions on the boundary of the domain, �Ω, demonstrates that the first eigenvalue of elliptic partial differential equation [ �� + �� = 0 �� Ω [ � = 0 �� Ω depends continuously on the domain in the following sense. If a sequence of domains is such that, then the corresponding first eigenvalues satisfy is the first eigenvalue for [ �� + �� = 0 �� Ω [ � = 0 �� Ω The work also reviews and utilizes the Sturmian comparison results of John G. Heywood, E. S. Noussair, and Charles A. Swanson. For a continuously parameterized family of domains, say with μ ∈ = [a, b], the continuous dependence of the eigenvalue on the domain combined with the Sturmian comparison results provide a theorem that insures, under certain conditions, that the elliptic partial differential equation [ �� = 0 �� Ω [ � = 0 �� Ω has a solution which is positive on a nodal domain That is there is a least value of μ [a, b] so that a positive solution u exists for [ �� = 0 �� Ωμ [ � = 0 �� Ωμ Beyond these results the work contains a theorem that shows for certain types of domains, rectangles in , among them, that there is a critical dimension smaller than which, no solution to the problem [ �� + �� = 0 �� Ω [ � = 0 �� Ω exists when the eigenvalue is fixed. During the investigations taken up in this work, certain observations were made regarding linear approximations to eigenvalue problems in R2 using a standard numerical approximation scheme. One such observation is that if a linear approximation to an eigenvalue problem contains an incorrect estimate for an eigenvalue, the resulting graphical approximation seems to betray whether or not the estimate was low or high. The observations made do not appear to exist in the literature.

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Mäder-Baumdicker, Elena [Verfasser], and Ernst [Akademischer Betreuer] Kuwert. "The area preserving curve shortening flow with Neumann free boundary conditions = Der flächenerhaltende Curve Shortening Fluss mit einer freien Neumann-Randbedingung." Freiburg : Universität, 2014. http://d-nb.info/1123480648/34.

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PERROTTA, Antea. "Differential Formulation coupled to the Dirichlet-to-Neumann operator for scattering problems." Doctoral thesis, Università degli studi di Cassino, 2020. http://hdl.handle.net/11580/75845.

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This Thesis proposes the use of the Dirichlet-to-Neumann (DtN) operator to improve the accuracy and the efficiency of the numerical solution of an electromagnetic scattering problem, described in terms of a differential formulation. From a general perspective, the DtN operator provides the “connection” (the mapping) between the Dirichlet and the Neumann data onto a proper closed surface. This allows truncation of the computational domain when treating a scattering problem in an unbounded media. Moreover, the DtN operator provides an exact boundary condition, in contrast to other methods such as Perfectly Matching Layer (PML) or Absorbing Boundary Conditions (ABC). In addition, when the surface where the DtN is introduced has a canonical shape, as in the present contribution, the DtN operator can be computed analytically. This thesis is focused on a 2D geometry under TM illumination. The numerical model combines a differential formulation with the DtN operator defined onto a canonical surface where it can be computed analytically. Test cases demonstrate the accuracy and the computational advantage of the proposed technique.

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Straub, Steffen [Verfasser], and B. [Akademischer Betreuer] Frohnapfel. "Non-homogeneous thermal boundary conditions in low to medium Prandtl number turbulent pipe flows / Steffen Straub ; Betreuer: B. Frohnapfel." Karlsruhe : KIT-Bibliothek, 2020. http://d-nb.info/1213351804/34.

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Sriskandasingam, Mayuran. "Non-homogeneous Boundary Value Problems of a Class of Fifth Order Korteweg-de Vries Equation posed on a Finite Interval." University of Cincinnati / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1626357151760691.

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Coco, Armando. "Finite-Difference Ghost-Cell Multigrid Methods for Elliptic problems with Mixed Boundary Conditions and Discontinuous Coefficients." Doctoral thesis, Università di Catania, 2012. http://hdl.handle.net/10761/1107.

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The work of this thesis is devoted to the development of an original and general numerical method for solving the elliptic equation in an arbitrary domain (described by a level-set function) with general boundary conditions (Dirichlet, Neumann, Robin, ...) using Cartesian grids. It can be then considered an immersed boundary method, and the scheme we use is based on a finite-difference ghost-cell technique. The entire problem is solved by an effective multigrid solver, whose components have been suitably constructed in order to be applied to the scheme. The method is extended to the more challenging case of discontinuous coefficients, and the multigrid is suitable modified in order to attain the optimal convergence factor of the whole iteration procedure. The development of the multigrid is an important feature of this thesis, since multigrid solvers for discontinuous coefficients maintaining the optimal convergence factor without depending on the jump in the coefficient and on the problem size is recently studied in literature. The method is second order accurate in the solution and its gradient. A convergence proof for the first order scheme is provided, while second order is confirmed by several numerical tests.

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Books on the topic "Homogeneous Neumann boundary conditions"

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Chiavassa, G. On the effective construction of compactly supported wavelets satisfying homogeneous boundary conditions on the interval. ICASE, 1996.

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Sun, Xian-He. A high-order direct solver for helmholtz equations with neumann boundary conditions. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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Sun, Xian-He. A high-order direct solver for helmholtz equations with neumann boundary conditions. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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Sun, Xian-He. A high-order direct solver for helmholtz equations with neumann boundary conditions. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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Sun, Xian-He. A high-order direct solver for Helmholtz equations with Neumann boundary conditions. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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National Aeronautics and Space Administration (NASA) Staff. High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions. Independently Published, 2018.

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Mann, Peter. The Stationary Action Principle. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0007.

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This crucial chapter focuses on the stationary action principle. It introduces Lagrangian mechanics, using first-order variational calculus to derive the Euler–Lagrange equation, and the inverse problem is described. The chapter then considers the Ostrogradsky equation and discusses the properties of the extrema using the second-order variation to the action. It then discusses the difference between action functions (of Dirichlet boundary conditions) and action functionals of the extremal path. The different types of boundary conditions (Dirichlet vs Neumann) are elucidated. Topics discussed include Hessian conditions, Douglas’s theorem, the Jacobi last multiplier, Helmholtz conditions, Noether-type variation and Frenet–Serret frames, as well as concepts such as on shell and off shell. Actions of non-continuous extremals are examined using Weierstrass–Erdmann corner conditions, and the action principle is written in the most general form as the Hamilton–Suslov principle. Important applications of the Euler–Lagrange formulation are highlighted, including protein folding.

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Edmunds, D. E., and W. D. Evans. Second-Order Differential Operators on Arbitrary Open Sets. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0007.

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In this chapter, three different methods are described for obtaining nice operators generated in some L2 space by second-order differential expressions and either Dirichlet or Neumann boundary conditions. The first is based on sesquilinear forms and the determination of m-sectorial operators by Kato’s First Representation Theorem; the second produces an m-accretive realization by a technique due to Kato using his distributional inequality; the third has its roots in the work of Levinson and Titchmarsh and gives operators T that are such that iT is m-accretive. The class of such operators includes the self-adjoint operators, even ones that are not bounded below. The essential self-adjointness of Schrödinger operators whose potentials have strong local singularities are considered, and the quantum-mechanical interpretation of essential self-adjointness is discussed.

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Geier, János, and Mariann Hudák. Changing the Chevreul Illusion by a Background Luminance Ramp. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780199794607.003.0044.

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The Chevreul illusion comprises adjacent homogeneous grey bands of different luminance, which are perceived as inhomogeneous. It is generally explained by lateral inhibition. When the Chevreul staircase is placed in a luminance ramp background, the illusion noticeably changes. Since all conditions of the lateral inhibition account are untouched within the staircase, lateral inhibition (which is a local model) fails to model these perceptual changes. Another ramp was placed around the staircase, whose direction was opposite to that of the original, larger ramp. The result here is that though the inner ramp is rather narrow, it still dominates perception. The chapter concludes that long-range interactions between boundary edges and areas enclosed by them provide a much more plausible account for these brightness phenomena, and local models are insufficient.

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Tiwari, Sandip. Electromechanics and its devices. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198759874.003.0005.

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Electromechanics—coupling of mechanical forces with others—exhibits a continuum-to-discrete spectrum of properties. In this chapter, classical and newer analysis techniques are developed for devices ranging from inertial sensors to scanning probes to quantify limits and sensitivities. Mechanical response, energy storage, transduction and dynamic characteristics of various devices are analyzed. The Lagrangian approach is developed for multidomain analysis and to bring out nonlinearity. The approach is extended to nanoscale fluidic systems where nonlinearities, fluctuation effects and the classical-quantum boundary is quite central. This leads to the study of measurement limits using power spectrum and, correlations with slow and fast forces. After a diversion to acoustic waves and piezoelectric phenomena, nonlinearities are explored in depth: homogeneous and forced conditions of excitation, chaos, bifurcations and other consequences, Melnikov analysis and the classic phase portaiture. The chapter ends with comments on multiphysics such as of nanotube-based systems and electromechanobiological biomotor systems.

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Book chapters on the topic "Homogeneous Neumann boundary conditions"

1

Sayas, Francisco-Javier, Thomas S. Brown, and Matthew E. Hassell. "Neumann boundary conditions." In Variational Techniques for Elliptic Partial Differential Equations. CRC Press, 2019. http://dx.doi.org/10.1201/9780429507069-6.

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Arendt, Wolfgang, and Karsten Urban. "Neumann and Robin boundary conditions." In Partial Differential Equations. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-13379-4_7.

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Droniou, Jérôme, Robert Eymard, Thierry Gallouët, Cindy Guichard, and Raphaèle Herbin. "Neumann, Fourier and Mixed Boundary Conditions." In Mathématiques et Applications. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-79042-8_3.

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Adomian, George. "Decomposition Solutions for Neumann Boundary Conditions." In Solving Frontier Problems of Physics: The Decomposition Method. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-015-8289-6_7.

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Motreanu, Dumitru, Viorica Venera Motreanu, and Nikolaos Papageorgiou. "Nonlinear Elliptic Equations with Neumann Boundary Conditions." In Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-9323-5_12.

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Leung, Anthony W. "Large Systems under Neumann Boundary Conditions, Bifurcations." In Systems of Nonlinear Partial Differential Equations. Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-015-3937-1_7.

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Feltrin, Guglielmo. "Neumann and Periodic Boundary Conditions: Existence Results." In Positive Solutions to Indefinite Problems. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94238-4_3.

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Feltrin, Guglielmo. "Neumann and Periodic Boundary Conditions: Multiplicity Results." In Positive Solutions to Indefinite Problems. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94238-4_4.

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Gomes, Gabriela, and Ian Stewart. "Hopf Bifurcations on Generalized Rectangles with Neumann Boundary Conditions." In Dynamics, Bifurcation and Symmetry. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0956-7_13.

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Arendt, Wolfgang, and Mahamadi Warma. "Dirichlet and Neumann boundary conditions: What is in between?" In Nonlinear Evolution Equations and Related Topics. Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-7924-8_6.

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Conference papers on the topic "Homogeneous Neumann boundary conditions"

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Klimek, Malgorzata. "Simple Case of Fractional Sturm-Liouville Problem with Homogeneous von Neumann Boundary Conditions." In 2018 23rd International Conference on Methods & Models in Automation & Robotics (MMAR). IEEE, 2018. http://dx.doi.org/10.1109/mmar.2018.8486100.

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Valyaev, V. Yu, and A. V. Shanin. "Measurement of the Diffraction Coefficient of a Trihedral Cone with Homogeneous Neumann Boundary Conditions." In 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama). IEEE, 2018. http://dx.doi.org/10.23919/piers.2018.8597926.

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Rionero, S., and A. Tataranni. "Absorbing Sets of the Positive Solutions of the Schnackenberg Reaction-Diffusion System under Neumann Homogeneous Boundary Conditions." In Proceedings of the International Conference in Honour of Brian Straughan. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814293228_0017.

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Baddour, R. E., and W. Parsons. "A Comparison of Dirichlet and Neumann Wavemakers for the Numerical Generation and Propagation of Nonlinear Long-Crested Surface Waves." In ASME 2003 22nd International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2003. http://dx.doi.org/10.1115/omae2003-37281.

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We are studying numerically the problem of generation and propagation of gravity long-crested waves in a tank containing an incompressible inviscid homogeneous fluid initially at rest with a horizontal free surface of finite extent and of infinite depth. A non-orthogonal curvilinear coordinate system, which follows the free surface is constructed and the full nonlinear kinematic and dynamic free surface boundary conditions are utilized in the algorithm. “Wavemakers” are modeled using both the Dirichlet and Neumann lateral boundary conditions and a full comparison is given.

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Parks, Michael. "On Neumann-type Boundary Conditions for Nonlocal Models." In Proposed for presentation at the Mechanistic Machine Learning and Digital Twins for Computational Science, Engineering & Technology held September 27-29, 2021 in San Diego, CA. US DOE, 2021. http://dx.doi.org/10.2172/1889347.

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Gámez, José L. "Local bifurcation for elliptic problems: Neumann versus Dirichlet boundary conditions." In The First 60 Years of Nonlinear Analysis of Jean Mawhin. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702906_0006.

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Kuryliak, D. B., and Z. T. Nazarchuk. "Wave scattering by wedge with Dirichlet and Neumann boundary conditions." In Proceedings of III International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory. DIPED-98. IEEE, 1998. http://dx.doi.org/10.1109/diped.1998.730938.

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Pacheco, J. Rafael, Tamara Rodic, and Arturo Pacheco-Vega. "On the Boundary Conditions for Heat Transfer Using Immersed Boundary Methods." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-16240.

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Abstract:

We describe the implementation of a general interpolation technique which allows the accurate imposition of the Dirichlet, Neumann and mixed boundary conditions on complex geometries when using the immersed boundary technique on Cartesian grids. The scheme is general in that it does not involve any special treatment to handle either one of the three types of boundary conditions. The accuracy of the interpolation algorithm on the boundary is assessed using three heat transfer problems: (1) forced convection over a cylinder placed in an unbounded flow, (2) natural convection on a cylinder placed inside a cavity, and (3) heat diffusion inside an annulus. The results show that the accuracy of the scheme is second order and are in agreement with analytical and/or numerical data.

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Valdés-Parada, Francisco J., Benoi^t Goyeau, J. Alberto Ochoa-Tapia, and Kambiz Vafai. "Derivation of Complete Jump Boundary Conditions Between Homogeneous Media." In POROUS MEDIA AND ITS APPLICATIONS IN SCIENCE, ENGINEERING, AND INDUSTRY: 3rd International Conference. AIP, 2010. http://dx.doi.org/10.1063/1.3453846.

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Ishimaru, A., J. D. Rockway, S. W. Lee, and Y. Kuga. "Green's function for rough surface with Dirichlet, Neumann, and impedance boundary conditions." In Proceedings of ISAPE 2000: Fifth International Symposium on Antennas, Propagation, and EM Theory. IEEE, 2000. http://dx.doi.org/10.1109/isape.2000.894708.

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