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Статті в журналах з теми "Physical boundary conditions"

Автор: Grafiati

Опубліковано: 24 липня 2022

Оновлено: 8 серпня 2022

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1

Kausel, E. "Physical interpretation and stability of paraxial boundary conditions." Bulletin of the Seismological Society of America 82, no. 2 (April 1, 1992): 898–913. http://dx.doi.org/10.1785/bssa0820020898.

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Abstract We derive in this paper the dynamic impedance matrices associated with some paraxial boundary conditions for wave motions in unbounded homogenous elastic media and use them to establish the existence of directions of propagation of waves for which the boundaries supply rather than dissipate energy. Also, we explore the existence of solutions of exponential growth and discuss conditions under which they can arise. These considerations may be used to provide a physical interpretation to the paraxial boundaries and to understand possible sources of instability that can develop in time-domain implementations of these schemes with finite differences.

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2

Juffer, A. H., and H. J. C. Berendsen. "Dynamic surface boundary conditions." Molecular Physics 79, no. 3 (June 20, 1993): 623–44. http://dx.doi.org/10.1080/00268979300101501.

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3

Becker, Theodor S., Nele Börsing, Dirk-Jan van Manen, Thomas Haag, Christoph Bärlocher, and Johan O. Robertsson. "Physical implementation of immersive boundary conditions in acoustic waveguides." Journal of the Acoustical Society of America 144, no. 3 (September 2018): 1759. http://dx.doi.org/10.1121/1.5067788.

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4

Marquis‐Favre, Cathy, and Julien Faure. "Physical and perceptual assessment of glass plate boundary conditions." Journal of the Acoustical Society of America 112, no. 5 (November 2002): 2412. http://dx.doi.org/10.1121/1.4779857.

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5

Becker, Theodor S., Dirk-Jan van Manen, Carly Donahue, and Johan O. Robertsson. "Physical implementation of immersive boundary conditions in one dimension." Journal of the Acoustical Society of America 141, no. 5 (May 2017): 3833. http://dx.doi.org/10.1121/1.4988519.

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6

Michelén Ströfer, Carlos A., Xin-Lei Zhang, Heng Xiao, and Olivier Coutier-Delgosha. "Enforcing boundary conditions on physical fields in Bayesian inversion." Computer Methods in Applied Mechanics and Engineering 367 (August 2020): 113097. http://dx.doi.org/10.1016/j.cma.2020.113097.

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7

Roberts, A. J. "Boundary conditions for approximate differential equations." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 34, no. 1 (July 1992): 54–80. http://dx.doi.org/10.1017/s0334270000007384.

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AbstractA large number of mathematical models are expressed as differential equations. Such models are often derived through a slowly-varying approximation under the assumption that the domain of interest is arbitrarily large; however, typical solutions and the physical problem of interest possess finite domains. The issue is: what are the correct boundary conditions to be used at the edge of the domain for such model equations? Centre manifold theory [24] and its generalisations may be used to derive these sorts of approximations, and higher-order refinements, in an appealing and systematic fashion. Furthermore, the centre manifold approach permits the derivation of appropriate initial conditions and forcing for the models [25, 7]. Here I show how to derive asymptotically-correct boundary conditions for models which are based on the slowly-varying approximation. The dominant terms in the boundary conditions typically agree with those obtained through physical arguments. However, refined models of higher order require subtle corrections to the previously-deduced boundary conditions, and also require the provision of additional boundary conditions to form a complete model.

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8

Tian, Qianzhu. "Existence of nonlinear boundary layer solution to the Boltzmann equation with physical boundary conditions." Journal of Mathematical Analysis and Applications 356, no. 1 (August 2009): 42–59. http://dx.doi.org/10.1016/j.jmaa.2009.02.028.

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9

Kim, Jae Wook, and Duck Joo Lee. "Implementation of Boundary Conditions for Optimized High-Order Compact Schemes." Journal of Computational Acoustics 05, no. 02 (June 1997): 177–91. http://dx.doi.org/10.1142/s0218396x97000113.

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The optimized high-order compact (OHOC) finite difference schemes, proposed as central schemes are used for aeroacoustic computations on interior nodes. On near-boundary nodes, accurate non-central or one-sided compact schemes are formulated and developed in this paper for general computations in domains with non-periodic boundaries. The near-boundary non-central compact schemes are optimized in the wavenumber domain by using Fourier error analysis. Analytic optimization methods are devised to minimize the dispersion and dissipation errors, and to obtain maximum resolution characteristics of the near-boundary compact schemes. With the accurate near-boundary schemes, the feasibility of implementing physical boundary conditions for the OHOC schemes are investigated to provide high-quality wave solutions. Characteristics-based boundary conditions and the free-field impedance conditions are used as the physical boundary conditions for direct computations of linear and nonlinear wave propagation and radiation. It is shown that the OHOC schemes present accurate wave solutions by using the optimized near-boundary compact schemes and the physical boundary conditions.

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10

Evans, Lawrence Christopher, and Robert Gastler. "Some results for the primitive equations with physical boundary conditions." Zeitschrift für angewandte Mathematik und Physik 64, no. 6 (March 20, 2013): 1729–44. http://dx.doi.org/10.1007/s00033-013-0320-6.

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11

Hong, Guangyi, and Zhi-an Wang. "Asymptotic stability of exogenous chemotaxis systems with physical boundary conditions." Quarterly of Applied Mathematics 79, no. 4 (June 29, 2021): 717–43. http://dx.doi.org/10.1090/qam/1599.

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12

Levkin, D. "Correctness conditions for boundary value problems." Energy and automation, no. 3(49) (June 11, 2020): 128–37. http://dx.doi.org/10.31548/energiya2020.03.128.

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The article deals with the issues of mathematical modeling of technological systems that contain physical fields’ sources. It is believed that in the case of a simple spatial form of the object under study, the boundary value problems will be correct. The interest lies in mathematical models for nonlinear, multilayer objects under the influence of load sources, for which, using the traditional theory of existence and unity, it is impossible to guarantee the correctness of boundary value problems. The author considers boundary value problems for systems of differential and pseudo differential equations in a multilayer medium which describe the state of the studied systems under the action of discrete load sources. The correctness of such problems is proven using the theory of distributions over the space of generalized functions. The object of research is boundary value problems for systems of differential and pseudo differential equations in a multilayer medium. The aim of the research is to build correct boundary value problems, which underlie the calculated mathematical models of the process of action of physical fields on multilayer objects. The necessary and sufficient conditions for the correctness of the parabolic boundary value problem in the space of generalized functions are obtained in the article. It is shown that its solution is infinitely differentiated by a spatial variable. The results of the research can be used to obtain the conditions for the correctness of the boundary value problem for differential equations with variable coefficients. Note that, in some cases, the correctness of the calculated mathematical models determines the correctness of applied optimization mathematical models. The application of the author's research is possible when proving the correctness of boundary value problems for a number of technological processes. The universality of the research allows to widely usage of the results obtained in this work to improve the quality of technological processes.

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13

Planelles, Josep. "Ladder operators and boundary conditions." International Journal of Quantum Chemistry 81, no. 2 (2000): 141–47. http://dx.doi.org/10.1002/1097-461x(2001)81:2<141::aid-qua5>3.0.co;2-o.

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14

Petraglio, Gabriele, Matteo Ceccarelli, and Michele Parrinello. "Nonperiodic boundary conditions for solvated systems." Journal of Chemical Physics 123, no. 4 (July 22, 2005): 044103. http://dx.doi.org/10.1063/1.1955449.

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15

Levrel, L., and A. C. Maggs. "Boundary conditions in local electrostatics algorithms." Journal of Chemical Physics 128, no. 21 (June 7, 2008): 214103. http://dx.doi.org/10.1063/1.2918365.

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16

Li, Y. S., J. M. Zhan, and Ming-Guang Sun. "MATCHING BOUNDARY-FITTED GRID GENERATION TO PHYSICAL BOUNDARY CONDITIONS WITH APPLICATIONS TO NATURAL CONVECTION PROBLEMS." Numerical Heat Transfer, Part A: Applications 33, no. 6 (May 1998): 621–34. http://dx.doi.org/10.1080/10407789808913958.

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17

CHOBAN, MITROFAN M., and COSTICĂ N. MOROȘANU. "Well-posedness of a nonlinear second-order anisotropic reaction-diffusion problem with nonlinear and inhomogeneous dynamic boundary conditions." Carpathian Journal of Mathematics 38, no. 1 (November 15, 2021): 95–116. http://dx.doi.org/10.37193/cjm.2022.01.08.

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The paper is concerned with a qualitative analysis for a nonlinear second-order boundary value problem, endowed with nonlinear and inhomogeneous dynamic boundary conditions, extending the types of bounday conditions already studied. Under certain assumptions on the input data: $f_{_1}(t,x)$, $w(t,x)$ and $u_0(x)$, we prove the well-posedness (the existence, a priori estimates, regularity and uniqueness) of a classical solution in the Sobolev space $W^{1,2}_p(Q)$. This extends previous works concerned with nonlinear dynamic boundary conditions, allowing to the present mathematical model to better approximate the real physical phenomena (the anisotropy effects, phase change in $\Omega$ and at the boundary $\partial\Omega$, etc.).

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18

Lange, Horst, Bruce Toomire, and P. F. Zweifel. "Inflow Boundary Conditions in Quantum Transport Theory." VLSI Design 9, no. 4 (January 1, 1999): 385–96. http://dx.doi.org/10.1155/1999/84905.

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A linear (given potential) steady-state Wigner equation is considered in conjunction with inflow boundary conditions and relaxation-time terms. A brief review of the use of inflow conditions in the classical case is also discussed. An analytic expansion of solutions is shown and a recursion relation derived for the given problem under certain regularity assumptions on the given inflow data. The uniqueness of the physical current of the solutions is shown and a brief discussion of the lack of charge conservation associated with the relaxation-time is given.

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19

Eymard, Robert, Thierry Gallouët, and Jullien Vovelle. "Limit boundary conditions for finite volume approximations of some physical problems." Journal of Computational and Applied Mathematics 161, no. 2 (December 2003): 349–69. http://dx.doi.org/10.1016/j.cam.2003.05.003.

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20

Steiner, Roee. "General rule for boundary conditions from the action principle." International Journal of Modern Physics A 31, no. 08 (March 14, 2016): 1650032. http://dx.doi.org/10.1142/s0217751x16500329.

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We construct models where initial and boundary conditions can be found from the fundamental rules of physics, without the need to assume them, they will be derived from the action principle. Those constraints are established from physical viewpoint, and it is not in the form of Lagrange multipliers. We show some examples from the past and some new examples that can be useful, where constraint can be obtained from the action principle. Those actions represent physical models. We show that it is possible to use our rule to get those constraints directly.

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21

FÜLÖP, TAMÁS, HITOSHI MIYAZAKI, and IZUMI TSUTSUI. "QUANTUM FORCE DUE TO DISTINCT BOUNDARY CONDITIONS." Modern Physics Letters A 18, no. 40 (December 28, 2003): 2863–71. http://dx.doi.org/10.1142/s0217732303012799.

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We calculate the quantum statistical force acting on a partition wall that divides a one-dimensional box into two halves. The two half boxes containing the same (fixed) number of noninteracting bosons are kept at the same temperature, and admit the same boundary conditions at the outer walls; the only difference is the distinct boundary conditions imposed at the two sides of the partition wall. The net force acting on the partition wall is nonzero at zero temperature and remains almost constant for low temperatures. As the temperature increases, the force starts to decrease considerably, but after reaching a minimum it starts to increase, and tends to infinity with a square-root-of-temperature asympotics. This example demonstrates clearly that distinct boundary conditions cause remarkable physical effects for quantum systems.

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22

González-Melchor, Minerva, Pedro Orea, Jorge López-Lemus, Fernando Bresme, and José Alejandre. "Stress anisotropy induced by periodic boundary conditions." Journal of Chemical Physics 122, no. 9 (March 2005): 094503. http://dx.doi.org/10.1063/1.1854625.

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23

Chen, Hui, Xin Yue Bi, Li Jia Zhang, and Yan Shen. "Temperature-Graded Ferroelectric Thin Films under Two Boundary Conditions." Advanced Materials Research 750-752 (August 2013): 1910–13. http://dx.doi.org/10.4028/www.scientific.net/amr.750-752.1910.

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In the framework of the mean field approximation, a transverse Ising model (TIM) was adopted to analyze the polarization properties of temperature-graded ferroelectric films under two boundary conditions, free boundary condition (FBC) and clamped boundary condition (CBC). Due to the ferroelectric distortion aroused by temperature gradient across the film, the elastic thermal stress increased. A distribution function was introduced to characterize the different boundary conditions. The results show that boundary conditions have very important influence on film properties. Polarizations under FBC are larger than that under CBC, polarization variations aroused by changed film thickness and temperature gradient under FBC are not as obvious as that under CBC, and films under different boundary conditions present obviously different physical behavior.

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24

Rempfer, Dietmar. "On Boundary Conditions for Incompressible Navier-Stokes Problems." Applied Mechanics Reviews 59, no. 3 (May 1, 2006): 107–25. http://dx.doi.org/10.1115/1.2177683.

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We revisit the issue of finding proper boundary conditions for the field equations describing incompressible flow problems, for quantities like pressure or vorticity, which often do not have immediately obvious “physical” boundary conditions. Most of the issues are discussed for the example of a primitive-variables formulation of the incompressible Navier-Stokes equations in the form of momentum equations plus the pressure Poisson equation. However, analogous problems also exist in other formulations, some of which are briefly reviewed as well. This review article cites 95 references.

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25

Wang, Chun Lei, Wen Bin Su, Hua Peng, Yuan Hu Zhu, Jian Liu, and Ji Chao Li. "Boundary Condition Effect on Thermoelectric Coefficients." Materials Science Forum 743-744 (January 2013): 116–19. http://dx.doi.org/10.4028/www.scientific.net/msf.743-744.116.

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nfluence of physical boundary conditions on the thermoelectric transportation coefficients has been analyzed starting form Onsager equations. Four boundary conditions have been considered: electric short, i.e, the chemical potential difference is zero; electric open, or electric current free; isothermal, i.e., no temperature difference; adiabatic, or heat flux free. Four kinds of thermoelectric equations have been derived with different boundary conditions. It was found that the influence of boundary cannot be ignored when figure-of-merit is near and larger than 1.0. This results could be useful in designing thermoelectric device with high performance thermoelectric materials.

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26

PAPADAKIS, JOHN S. "EXACT, NONREFLECTING BOUNDARY CONDITIONS FOR PARABOLIC-TYPE APPROXIMATIONS IN UNDERWATER ACOUSTICS." Journal of Computational Acoustics 02, no. 02 (June 1994): 83–98. http://dx.doi.org/10.1142/s0218396x94000075.

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In the different parabolic approximations to the reduced wave equation which model acoustic propagation in the ocean, the bottom is usually modeled as an interface and the domain of propagation includes an absorbing layer below the bottom interface. Thus the boundary value problem to be solved has zero boundary conditions at the surface as well as at the bottom boundary. In this paper exact boundary conditions are developed and numerically implemented along the physical bottom boundary if it is horizontal, otherwise, along an artificially placed horizontal computational boundary inside the bottom. These boundary conditions are nonlocal but integrable and can be incorporated in finite difference schemes for the parabolic equations.

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27

Amara, M., D. Capatina-Papaghiuc, and D. Trujillo. "Stabilized finite element method for Navier--Stokes equations with physical boundary conditions." Mathematics of Computation 76, no. 259 (March 15, 2007): 1195–218. http://dx.doi.org/10.1090/s0025-5718-07-01929-1.

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28

Ben Amara, J., and A. A. Shkalikov. "A sturm-liouville problem with physical and spectral parameters in boundary conditions." Mathematical Notes 66, no. 2 (August 1999): 127–34. http://dx.doi.org/10.1007/bf02674866.

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29

Kolafa, Jiří. "Nebula boundary conditions in Monte Carlo simulations." Molecular Physics 74, no. 1 (September 1991): 143–51. http://dx.doi.org/10.1080/00268979100102121.

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30

Blijenberg, Harry M. "Application of physical modelling of debris flow triggering to field conditions: Limitations posed by boundary conditions." Engineering Geology 91, no. 1 (April 2007): 25–33. http://dx.doi.org/10.1016/j.enggeo.2006.12.010.

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31

Martinelli, Sheri L. "Numerical Boundary Conditions for Specular Reflection in a Level-Sets-Based Wavefront Propagation Method." Communications in Computational Physics 14, no. 2 (August 2013): 509–36. http://dx.doi.org/10.4208/cicp.130312.301012a.

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AbstractWe study the simulation of specular reflection in a level set method implementation for wavefront propagation in high frequency acoustics using WENO spatial operators. To implement WENO efficiently and maintain convergence rate, a rectangular grid is used over the physical space. When the physical domain does not conform to the rectangular grid, appropriate boundary conditions to represent reflection must be derived to apply at grid locations that are not coincident with the reflecting boundary. A related problem is the extraction of the normal vectors to the boundary, which are required to formulate the reflection condition. A separate level set method is applied to pre-compute the boundary normals which are then stored for use in the wavefront method. Two approaches to handling the reflection boundary condition are proposed and studied: one uses an approximation to the boundary location, and the other uses a local reflection principle. The second method is shown to produce superior results.

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32

Kobryn, Alexander E., and Andriy Kovalenko. "Molecular theory of hydrodynamic boundary conditions in nanofluidics." Journal of Chemical Physics 129, no. 13 (October 7, 2008): 134701. http://dx.doi.org/10.1063/1.2972978.

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33

Cole, R. G., V. Protopopescu, and T. Keyes. "Stationary transport with partially reflecting boundary conditions. II." Journal of Chemical Physics 83, no. 5 (September 1985): 2384–89. http://dx.doi.org/10.1063/1.449282.

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34

Asorey, M., D. García-Alvarez, and J. M. Muñoz-Castañeda. "Boundary effects in bosonic and fermionic field theories." International Journal of Geometric Methods in Modern Physics 12, no. 06 (June 25, 2015): 1560004. http://dx.doi.org/10.1142/s021988781560004x.

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The dynamics of quantum field theories on bounded domains requires the introduction of boundary conditions on the quantum fields. We address the problem from a very general perspective by using charge conservation as a fundamental principle for scalar and fermionic quantum field theories. Unitarity arises as a consequence of the choice of charge preserving boundary conditions. This provides a powerful framework for the analysis of global geometrical and topological properties of the space of physical boundary conditions. Boundary conditions which allow the existence of edge states can only arise in theories with a mass gap which is also a physical requirement for topological insulators.

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35

KITRON-BELINKOV, MYRA, AMY NOVICK-COHEN, and NADAV LIRON. "A SLIP CONDITION BASED ON MINIMAL ENERGY DISSIPATION." Mathematical Models and Methods in Applied Sciences 06, no. 04 (June 1996): 467–80. http://dx.doi.org/10.1142/s0218202596000171.

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An intrinsic difficulty arises when solving Stokes equations in Ω ⊂ ℝ2 when the boundary conditions on the velocity are discontinuous: the solution is physically unacceptable since the force exerted by the fluid on the boundary is logarithmically singular. To illustrate this phenomena, we present an explicit solution in which the logarithmic singularity appears in a particularly simple form. A common method of avoiding the appearance of these singular forces is via an alteration of the boundary velocity profile in the vicinity of the discontinuity. However, there is no obvious physical criterion according to which the velocity profile along the boundary should be chosen. We consider a possible physically motivated criterion based on minimal energy dissipation. We prove the existence of a unique minimizing profile and demonstrate that the resultant velocity field does indeed exert a finite force along the boundary. Lastly, the minimizing profile is calculated numerically and the effect of free parameters is considered.

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36

Da, Hoang Van. "Solution of the partial derivative equation with nonlinear boundary conditions." Vietnam Journal of Mechanics 9, no. 1 (March 31, 1987): 16–21. http://dx.doi.org/10.15625/0866-7136/10338.

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In this paper, the asymptotic method has been used to construct the solution of the partial derivative equation with nonlinear conditions, describing vibration of the rectangular thin plate. It is shown that the physical nonlinearity of the boundary has influence on oscillational characteristics of systems.

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37

Fernandes, Paolo, and Gianni Gilardi. "Magnetostatic and Electrostatic Problems in Inhomogeneous Anisotropic Media with Irregular Boundary and Mixed Boundary Conditions." Mathematical Models and Methods in Applied Sciences 07, no. 07 (November 1997): 957–91. http://dx.doi.org/10.1142/s0218202597000487.

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Magnetostatic and electrostatic problems with mixed boundary conditions are studied. The medium can have a nonsmooth boundary and very irregular physical properties due to inhomogeneity and anisotropy. The topological assumptions are general enough to meet the requirements of the engineering applications. Necessary and sufficient conditions for solvability are found and the set of the solutions is characterized. Moreover, uniqueness is recovered by means of a finite number of supplementary conditions which are equivalent to prescribing a finite number of suitably chosen fluxes or potentials. A functional framework in which other important problems of electromagnetics naturally fit is developed.

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38

Liang, Xin-Zhong, Hyun I. Choi, Kenneth E. Kunkel, Yongjiu Dai, Everette Joseph, Julian X. L. Wang, and Praveen Kumar. "Surface Boundary Conditions for Mesoscale Regional Climate Models." Earth Interactions 9, no. 18 (October 1, 2005): 1–28. http://dx.doi.org/10.1175/ei151.1.

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Abstract This paper utilizes the best available quality data from multiple sources to develop consistent surface boundary conditions (SBCs) for mesoscale regional climate model (RCM) applications. The primary SBCs include 1) fields of soil characteristic (bedrock depth, and sand and clay fraction profiles), which for the first time have been consistently introduced to define 3D soil properties; 2) fields of vegetation characteristic fields (land-cover category, and static fractional vegetation cover and varying leaf-plus-stem-area indices) to represent spatial and temporal variations of vegetation with improved data coherence and physical realism; and 3) daily sea surface temperature variations based on the most appropriate data currently available or other value-added alternatives. For each field, multiple data sources are compared to quantify uncertainties for selecting the best one or merged to create a consistent and complete spatial and temporal coverage. The SBCs so developed can be readily incorporated into any RCM suitable for U.S. climate and hydrology modeling studies, while the data processing and validation procedures can be more generally applied to construct SBCs for any specific domain over the globe.

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39

Saxton, Curtis J. "Effects of Lower Boundary Conditions on the Stability of Radiative Shocks." Publications of the Astronomical Society of Australia 19, no. 2 (2002): 282–92. http://dx.doi.org/10.1071/as02004.

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AbstractThermal instabilities can cause a radiative shock to oscillate, thereby modulating the emission from the post-shock region. The mode frequencies are approximately quantised in analogy to those of a vibrating pipe. The stability properties depend on the cooling processes, the electron–ion energy exchange, and the boundary conditions. This paper considers the effects of the lower boundary condition on the post-shock flow, both ideally and for some specific physical models. Specific cases include constant perturbed velocity, pressure, density, flow rate, or temperature at the lower boundary, and the situation with nonzero stationary flow velocity at the lower boundary. It is found that for cases with zero terminal stationary velocity, the stability properties are insensitive to the perturbed hydrodynamic variables at the lower boundary. The luminosity responses are generally dependent on the lower boundary condition.

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40

Costantini, C. "Diffusion Approximation for a Class of Transport Processes with Physical Reflection Boundary Conditions." Annals of Probability 19, no. 3 (July 1991): 1071–101. http://dx.doi.org/10.1214/aop/1176990335.

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41

Kopp, Reiner, and Franz-Dieter Philipp. "Physical parameters and boundary conditions for the numerical simulation of hot forming processes." Steel Research 63, no. 9 (September 1992): 392–98. http://dx.doi.org/10.1002/srin.199201729.

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42

Nadarajah, Arunan, Franz Rosenberger, and J. Iwan D. Alexander. "Effects of buoyancy-driven flow and thermal boundary conditions on physical vapor transport." Journal of Crystal Growth 118, no. 1-2 (March 1992): 49–59. http://dx.doi.org/10.1016/0022-0248(92)90048-n.

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43

Kravtsov, A., D. Levkin, and O. Makarov. "Mathematical model implementation in conditions of uncertainty and possible risks." Energy and automation, no. 4(56) (August 30, 2021): 137–45. http://dx.doi.org/10.31548/energiya2021.04.137.

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The article presents the theoretical and methodological principles for forecasting and mathematical modeling of possible risks in technological and biotechnological systems. The authors investigated in details the possible approach to the calculation of the goal function and its parameters. Considerable attention is paid to substantiating the correctness of boundary value problems and Cauchy problems. In mechanics, engineering, and biology, Cauchy problems and boundary value problems of differential equations are used to model physical processes. It is important that differential equations have a single physically sound solution. The authors of this article investigate the specific features of boundary value problems and Cauchy problems with boundary conditions in a two-point medium, and determine the conditions for the correctness of such problems in the spaces of power growth functions. The theory of pseudo-differential operators in the space of generalized functions was used to prove the correctness of boundary value problems. The application of the obtained results will make it possible to guarantee the correctness of mathematical models built in conditions of uncertainty and possible risks. As an example of a computational mathematical model that describes the state of the studied object of non-standard shape, the authors considered the boundary value problem of the system of differential equations of thermal conductivity for the embryo under the action of a laser beam. For such a boundary value problem, it is impossible to guarantee the existence and uniqueness of the solution of the system of differential equations. To be sure of the existence of a single solution, it is necessary either not to take into account the three-layer structure of the microbiological object, or to determine the conditions for the correctness of the boundary value problem. Applying the results obtained by the authors, the correctness of the boundary value problem of systems of differential equations of thermal conductivity for the embryo is proved taking into account the three-layer structure of the microbiological object. This makes it possible to increase the accuracy and speed of its implementation on the computer. Key words: forecasting, risk, correctness, boundary value problems, conditions of uncertainty

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44

Basu, Rahul. "Effect of Boundary Conditions on Phase Change in Rectilinear and Spherical Porous Media." Applied Mechanics and Materials 852 (September 2016): 625–31. http://dx.doi.org/10.4028/www.scientific.net/amm.852.625.

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This paper examines a model for coupled heat and mass transfer for freezing in a porous matrix with Dirichlet and convective boundary conditions. Variables include porosity, heat transfer coefficients, thermal and mass diffusivity, density, latent heat and boundary temperatures. It is shown that heat and mass transfer balance at the interface can affect stability. The effect of boundary conditions on the velocity of freezing is computed for some cases, and applications to physical problems highlighted

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45

Falletta, Silvia, and Giovanni Monegato. "Exact nonreflecting boundary conditions for exterior wave equation problems." Publications de l'Institut Math?matique (Belgrade) 96, no. 110 (2014): 103–23. http://dx.doi.org/10.2298/pim1410103f.

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We consider the classical wave equation problem defined on the exterior of a bounded 2D space domain, possibly having far field sources. We consider this problem in the time domain, but also in the frequency domain. For its solution we propose to associate with it a boundary integral equation (BIE) defined on an artificial boundary surrounding the region of interest. This boundary condition is nonreflecting (or transparent) for both outgoing and incoming waves and it does not have to include necessarily the problem datum supports. The problem physical domain can even be a multi-domain, defined by the union of several disjoint domains. These domains can be convex or nonconvex. This transparent boundary condition is imposed pointwise on the chosen artificial boundary; therefore, its (space collocation) discretization can be coupled with a (space) finite difference or finite element method for the associated PDE problem. In the time-domain case, a classical (explicit or implicit) time integrator is also used. We present a consistency result for the BIE discretization and a sample of the intensive numerical testing we have performed.

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46

Grobbelaar-Van Dalsen, Maríe, and Niko Sauer. "Dynamic boundary conditions for the Navier–Stokes equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 113, no. 1-2 (1989): 1–11. http://dx.doi.org/10.1017/s030821050002391x.

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SynopsisWhen a symmetric rigid body performs a rotation in a fluid, the system of governing equations consists of conservation of linear momentum of the fluid and conservation of angular momentum of the rigid body. Since the torque at the interface involves the drag due to the fluid flow, the conservation of angular momentum may be viewed as a boundary condition for the field equations of fluid motion. These equations at the boundary contain a time derivative and thus are of a dynamic nature. The familiar no-slip condition becomes an additional equation in the system which not only governs the fluid motion, but also the motion of the rigid body. The unknown functions in the system of equations are the velocity and pressure fields of the fluid motion and the angular velocity of the rigid body.In this paper we formulate the physical problem for the case of rotation about an axis of symmetry as an abstract ordinary differential equation in two Banach spaces in which the velocity field is the only unknown. To achieve this, a method for the elimination of the pressure field, which also occurs in the boundary condition, is developed. Existence and uniqueness results for the abstract equation are derived with the aid of the theory of B-evolutions and the associated theory of fractional powers of a closed pair of operators.

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47

Fricke, Mathis, and Dieter Bothe. "Boundary conditions for dynamic wetting - A mathematical analysis." European Physical Journal Special Topics 229, no. 10 (September 2020): 1849–65. http://dx.doi.org/10.1140/epjst/e2020-900249-7.

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Abstract The moving contact line paradox discussed in the famous paper by Huh and Scriven has lead to an extensive scientific discussion about singularities in continuum mechanical models of dynamic wetting in the framework of the two-phase Navier–Stokes equations. Since the no-slip condition introduces a non-integrable and therefore unphysical singularity into the model, various models to relax the singularity have been proposed. Many of the relaxation mechanisms still retain a weak (integrable) singularity, while other approaches look for completely regular solutions with finite curvature and pressure at the moving contact line. In particular, the model introduced recently in [A.V. Lukyanov, T. Pryer, Langmuir 33, 8582 (2017)] aims for regular solutions through modified boundary conditions. The present work applies the mathematical tool of compatibility analysis to continuum models of dynamic wetting. The basic idea is that the boundary conditions have to be compatible at the contact line in order to allow for regular solutions. Remarkably, the method allows to compute explicit expressions for the pressure and the curvature locally at the moving contact line for regular solutions to the model of Lukyanov and Pryer. It is found that solutions may still be singular for the latter model.

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48

Legusha, F., and Yu Popov. "Acoustic wave absorption in a waveguide with impedance boundary conditions." Transactions of the Krylov State Research Centre 2, no. 396 (May 21, 2021): 113–21. http://dx.doi.org/10.24937/2542-2324-2021-2-396-113-121.

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Object and purpose of research. The study of the acoustic pulse changes regularities during its propagation in con-fined media is one of the fundamental problems of acoustics, which allows to pose and solve the inverse problem of determining the dissipative and resonant properties of these media. The physical processes occurring during the propagation of a pulse in a cylindrical waveguide with rigid walls were investigated. Materials and methods. To analyze the mechanism of dissipation, experimental studies of pulse propagation in a hy-droacoustic tube were carried out, and the theoretical description of the obtained results was carried out using analytical methods. The simulation of the propagating pulse in the finite element waveguide model was used to confirm the theoretical assessments and the experiment. Main results. Experimental studies of physical processes during the propagation of an acoustic pulse in confined medium of cylindrical waveguide bounded by walls with characteristics close to absolutely rigid are carried out. The data showed that it is possible to control changes in the phase velocity, amplitude, and waveform, which made it possible to quantify the impedance of the internal walls of the waveguide and the dissipation of acoustic energy with a sufficient degree of accuracy. The numerical model calculation, taking into account the theoretically obtained quantitative assessments of the dissipation values and the impedance value of the waveguide inner surface, showed a good correspondence between the model and experimental characteristics of the change in the propagating pulse. Conclusion. In the studies devoted to the propagation description of acoustic waves in waveguides, the issues of energy dissipation are usually not considered, especially in cases where it has a weak effect on the measurement result. The theoretical value of the research is to quantify the wave energy dissipation by the parameters that can be determined with sufficient accuracy in the experiment: the phase velocity, the pulse form. Further accuracy improvement of the experimental data, especially in a wide frequency range, will improve the theoretical model of dissipation by taking into account the mechanism of inhomogeneous viscous and thermal waves near the inner surface of the waveguide. The practical significance of the research is to increase the reliability of experimental data and to develop physical and mathematical models of underwater sound absorption due to a forced variable flow with a highly transformed velocity of a viscous liquid in a thin surface layer near the elastic wall.

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Akhtyamov, A. M., and Kh R. Mamedov. "Uniqueness theorem for Inverse Sturm–Liouville Problem with Nonseparated Boundary Conditions." Proceedings of the Mavlyutov Institute of Mechanics 11, no. 2 (2016): 167–70. http://dx.doi.org/10.21662/uim2016.2.024.

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Consider the string, which vibrates in a medium with the variable elasticity coefficient q(x). Interesting to follow the inverse problem: is it possible to determine the variable elasticity coefficient q(x) by the natural frequencies of string vibrations. In 1946, G. Borg has been shown that a spectrum of frequencies is not sufficient to uniquely identify the medium elasticity coefficient q(x). He offered the use of two frequency spectrum to uniquely identify of the medium elasticity coefficient q(x). The second frequency spectrum is obtained by fastening the string to change at one of its ends to the other fastening. It was shown that these two frequency spectra already sufficient to uniquely identify q(x) and the boundary conditions of both problems. The case where the string fastening at one end depends on the other end fastening, is more difficult to solve. The boundary conditions, appropriate for the occasion, called nonseparated. Two spectra (of two boundary value problems) to restore both q(x), and the nonseparated boundary conditions are not enough. In modern studies the spectra of the two eigenvalues boundary problems and an infinite sequence of signs is generally used for an uniqueness recovery. While this approach is useful in theoretical mathematics, it is inconvenient for the mechanics, because not clear the physical meaning of the corresponding sequence of signs. In this article, instead of the two spectra and the sequence of signs as the spectral data are offered to use 7 of the eigenvalues of the initial boundary value problem, the spectrum, and the so-called norming constants of other boundary value problem. The physical sense of these data is quite clear. The first 7 eigenvalues of an initial boundary problem mean the first 7 natural frequencies of string vibrations. Norming constants represent norms from eigenfunctions. The spectrum and norming constants express a so-called spectral function. The spectral function gives a frequency spectrum with columns of vibrations amplitudes characteristics for string vibrations with other types of fastening.

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50

Zhou, Xin, Denis Andrienko, Luigi Delle Site, and Kurt Kremer. "Flow boundary conditions for chain-end adsorbing polymer blends." Journal of Chemical Physics 123, no. 10 (September 8, 2005): 104904. http://dx.doi.org/10.1063/1.2009735.

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