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Journal articles on the topic 'Oscillating boundary domains'

Author: Grafiati

Published: 6 September 2023

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1

Amirat, Youcef, Olivier Bodart, Gregory A. Chechkin, and Andrey L. Piatnitski. "Boundary homogenization in domains with randomly oscillating boundary." Stochastic Processes and their Applications 121, no. 1 (2011): 1–23. http://dx.doi.org/10.1016/j.spa.2010.08.011.

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2

Amirat, Youcef, Gregory A. Chechkin, and Rustem R. Gadyl’shin. "Spectral boundary homogenization in domains with oscillating boundaries." Nonlinear Analysis: Real World Applications 11, no. 6 (2010): 4492–99. http://dx.doi.org/10.1016/j.nonrwa.2008.11.023.

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3

Chechkin, Gregory A., Avner Friedman, and Andrey L. Piatnitski. "The Boundary-value Problem in Domains with Very Rapidly Oscillating Boundary." Journal of Mathematical Analysis and Applications 231, no. 1 (1999): 213–34. http://dx.doi.org/10.1006/jmaa.1998.6226.

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4

Aiyappan, S., A. K. Nandakumaran, and Ravi Prakash. "Semi-linear optimal control problem on a smooth oscillating domain." Communications in Contemporary Mathematics 22, no. 04 (2019): 1950029. http://dx.doi.org/10.1142/s0219199719500299.

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We demonstrate the asymptotic analysis of a semi-linear optimal control problem posed on a smooth oscillating boundary domain in the present paper. We have considered a more general oscillating domain than the usual “pillar-type” domains. Consideration of such general domains will be useful in more realistic applications like circular domain with rugose boundary. We study the asymptotic behavior of the problem under consideration using a new generalized periodic unfolding operator. Further, we are studying the homogenization of a non-linear optimal control problem and such non-linear problems

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5

Eger, V., O. A. Oleinik, and T. A. Shaposhnikova. "Homogenization of boundary value problems in domains with rapidly oscillating nonperiodic boundary." Differential Equations 36, no. 6 (2000): 833–46. http://dx.doi.org/10.1007/bf02754407.

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6

Feldman, William M. "Homogenization of the oscillating Dirichlet boundary condition in general domains." Journal de Mathématiques Pures et Appliquées 101, no. 5 (2014): 599–622. http://dx.doi.org/10.1016/j.matpur.2013.07.003.

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7

OULD-HAMMOUDA, AMAR, and RACHAD ZAKI. "Homogenization of a class of elliptic problems with nonlinear boundary conditions in domains with small holes." Carpathian Journal of Mathematics 31, no. 1 (2015): 77–88. http://dx.doi.org/10.37193/cjm.2015.01.09.

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We consider a class of second order elliptic problems in a domain of RN , N > 2, ε-periodically perforated by holes of size r(ε) , with r(ε)/ε → 0 as ε → 0. A nonlinear Robin-type condition is prescribed on the boundary of some holes while on the boundary of the others as well as on the external boundary of the domain, a Dirichlet condition is imposed. We are interested in the asymptotic behavior of the solutions as ε → 0. We use the periodic unfolding method introduced in [Cioranescu, D., Damlamian, A. and Griso, G., Periodic unfolding and homogenization, C. R. Acad. Sci. Paris, Ser. I, 33

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8

Pettersson, Irina. "Two-scale convergence in thin domains with locally periodic rapidly oscillating boundary." Differential Equations & Applications, no. 3 (2017): 393–412. http://dx.doi.org/10.7153/dea-2017-09-28.

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9

Zhuge, Jinping. "First-order expansions for eigenvalues and eigenfunctions in periodic homogenization." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 5 (2019): 2189–215. http://dx.doi.org/10.1017/prm.2019.8.

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AbstractFor a family of elliptic operators with periodically oscillating coefficients, $-{\rm div}(A(\cdot /\varepsilon )\nabla )$ with tiny ε > 0, we comprehensively study the first-order expansions of eigenvalues and eigenfunctions (eigenspaces) for both the Dirichlet and Neumann problems in bounded, smooth and strictly convex domains (or more general domains of finite type). A new first-order correction term is introduced to derive the expansion of eigenfunctions in L2 or $H^1_{\rm loc}$. Our results rely on the recent progress on the homogenization of boundary layer problems.

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10

Piatnitski, A., and V. Rybalko. "Homogenization of boundary value problems for monotone operators in perforated domains with rapidly oscillating boundary conditions of fourier type." Journal of Mathematical Sciences 177, no. 1 (2011): 109–40. http://dx.doi.org/10.1007/s10958-011-0450-3.

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11

Durante, Tiziana, Luisa Faella, and Carmen Perugia. "Homogenization and behaviour of optimal controls for the wave equation in domains with oscillating boundary." Nonlinear Differential Equations and Applications NoDEA 14, no. 5-6 (2007): 455–89. http://dx.doi.org/10.1007/s00030-007-3043-6.

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12

Guckenberger, Achim, and Stephan Gekle. "A boundary integral method with volume-changing objects for ultrasound-triggered margination of microbubbles." Journal of Fluid Mechanics 836 (December 19, 2017): 952–97. http://dx.doi.org/10.1017/jfm.2017.836.

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A variety of numerical methods exist for the study of deformable particles in dense suspensions. None of the standard tools, however, currently include volume-changing objects such as oscillating microbubbles in three-dimensional periodic domains. In the first part of this work, we develop a novel method to include such entities based on the boundary integral method. We show that the well-known boundary integral equation must be amended with two additional terms containing the volume flux through the bubble surface. We rigorously prove the existence and uniqueness of the solution. Our proof co

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13

Trefry, M. G., D. McLaughlin, G. Metcalfe, et al. "On oscillating flows in randomly heterogeneous porous media." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1910 (2010): 197–216. http://dx.doi.org/10.1098/rsta.2009.0186.

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The emergence of structure in reactive geofluid systems is of current interest. In geofluid systems, the fluids are supported by a porous medium whose physical and chemical properties may vary in space and time, sometimes sharply, and which may also evolve in reaction with the local fluids. Geofluids may also experience pressure and temperature conditions within the porous medium that drive their momentum relations beyond the normal Darcy regime. Furthermore, natural geofluid systems may experience forcings that are periodic in nature, or at least episodic. The combination of transient forcing

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14

Durante, Danilo, and Riccardo Broglia. "A Residual Theorem Approach Applied to Stokes’ Problems with Generally Periodic Boundary Conditions including a Pressure Gradient Term." Mathematical Problems in Engineering 2018 (August 28, 2018): 1–16. http://dx.doi.org/10.1155/2018/1267689.

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The differential problem given by a parabolic equation describing the purely viscous flow generated by a constant or an oscillating motion of a boundary is the well-known Stokes’ problem. The one-dimensional equation is generally solved for unbounded or bounded domains; for the latter, either free slip (i.e., zero normal gradient) or no-slip (i.e., zero velocity) conditions are enforced on one boundary. Generally, the analytical strategy to solve these problems is based on finding the solutions of the Laplace-transformed (in time) equation and on inverting these solutions. In the present paper

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15

ter Heege, J. H., J. H. P. de Bresser, and C. J. Spiers. "Dynamic Recrystallization of Dense Polycrystalline NaCl: Dependence of Grain Size Distribution on Stress and Temperature." Materials Science Forum 467-470 (October 2004): 1187–92. http://dx.doi.org/10.4028/www.scientific.net/msf.467-470.1187.

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Only few models explain the development of a steady state grain size during dynamic recrystallization, and their microphysical basis is poorly understood. In this study, we investigate mechanical and microstructural data on dry and wet NaCl, deformed at a range of stresses and temperatures at elevated pressure, with the aim to evaluate the different models. The results show that dry NaCl continuously work hardens and shows evidence for recrystallization dominated by progressive subgrain rotation, while the wet material shows, at similar conditions, oscillating stressstrain behaviour and recrys

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16

Pinto Jr, E. A., M. Das N. Gomes, L. A. O. Rocha, E. D. dos Santos, and L. A. Isoldi. "EVALUATION OF STATIC PRESSURE BEHAVIOR IN AN OSCILLATING WATER COLUMN WAVE ENERGY CONVERTER." Revista de Engenharia Térmica 18, no. 1 (2019): 36. http://dx.doi.org/10.5380/reterm.v18i1.67045.

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The international scenario of non-renewable resources scarcity coupled with increasing energy demand are incentives for the diversification of the world's energy matrix with a focus on renewable energy sources. Among these sources, energy from sea waves is especially attractive because its global resource is estimated around 2 TW, comparable to the average electrical power consumed worldwide each year. There are currently several technologies proposed for the sea wave energy conversion into electricity. Among them it stands out the Oscillating Water Column (OWC) converter, which basically cons

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17

CHAPMAN, C. J. "Energy paths in edge waves." Journal of Fluid Mechanics 426 (January 10, 2001): 135–54. http://dx.doi.org/10.1017/s0022112000002184.

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In this paper the energy streamlines, energy paths, and energy streak lines in a steady or unsteady inhomogeneous acoustic field next to an unstable oscillating boundary, such as a vortex sheet or shear layer, are determined. The theory in the paper applies also to an evanescent wave produced by total internal reflection, and to any other type of edge wave, e.g. a coastally or topographically trapped wave in geophysical fluid dynamics. The idea of the paper is that energy velocity, i.e. energy flux divided by energy density, is defined at every point in space and time, not merely when averaged

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18

Li, Zele, Decheng Feng, Mohammad Noori, Dipanjan Basu, and Wael A. Altabey. "Dynamic response analysis of Euler–Bernoulli beam on spatially random transversely isotropic viscoelastic soil." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 236, no. 5 (2022): 1037–52. http://dx.doi.org/10.1177/14644207211067442.

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A novel dynamic soil-structure interaction model is developed for analysis for Euler–Bernoulli beam rests on a spatially random transversely isotropic viscoelastic foundation subjected to moving and oscillating loads. The dynamic equilibrium equation of beam-soil system is established using the extended Hamilton's principle, and the corresponding partial differential equations describing the displacement of beam and soil and boundary conditions are further obtained by the variational principles. These partial differential equations are discretized in spatial and time domains and solved by the

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19

Cessi, Paola, and Pantxika Otheguy. "Oceanic Teleconnections: Remote Response to Decadal Wind Forcing." Journal of Physical Oceanography 33, no. 8 (2003): 1604–17. http://dx.doi.org/10.1175/2400.1.

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Abstract The transhemispheric and interbasin response to time-dependent wind forcing localized in the Northern Hemisphere of a single basin is examined using the reduced-gravity shallow-water equations in domains of simple geometry. On decadal timescales, the pressure on the eastern boundary fluctuates synchronously in both hemispheres and thus communicates a signal to latitudes distant from the forcing. The signal then penetrates into the interior through westward radiation of Rossby waves. Associated with the eastern boundary pressure fluctuation is a time-dependent mass flux across the equa

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20

Zhao, Jie, and Juan Wang. "Homogenization Problem in a Domain with Double Oscillating Boundary." Mathematical Problems in Engineering 2018 (October 21, 2018): 1–14. http://dx.doi.org/10.1155/2018/3746562.

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In this paper, we study the convergence of solutions for homogenization problems about the Poisson equation in a domain with double oscillating locally periodic boundary. Such a problem arises in the processing of devices with very small features. We utilize second-order Taylor expansion of boundary data in combination with boundary correctors to obtain the convergence rate in H1-norm. This work explores the domain with double oscillating boundary and also shows the influence of the amplitudes and periods of the oscillations to convergence rates of solutions.

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21

Natroshvili, David, Guram Sadunishvili, and Irine Sigua. "Some Remarks Concerning Jones Eigenfrequencies and Jones Modes." gmj 12, no. 2 (2005): 337–48. http://dx.doi.org/10.1515/gmj.2005.337.

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Abstract Three-dimensional fluid-solid interaction problems with regard for thermal stresses are considered. An elastic structure is assumed to be a bounded homogeneous isotropic body occupying a domain , where the thermoelastic four dimensional field is defined, while in the unbounded exterior domain there is defined the scalar (acoustic pressure) field. These two fields satisfy the differential equations of steady state oscillations in the corresponding domains along with the transmission conditions of special type on the interface ∂Ω±. We show that uniqueness of solutions strongly depends o

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22

Kupershtokh, A. L., E. V. Ermanyuk, and N. V. Gavrilov. "The Rupture of Thin Liquid Films Placed on Solid and Liquid Substrates in Gravity Body Forces." Communications in Computational Physics 17, no. 5 (2015): 1301–19. http://dx.doi.org/10.4208/cicp.2014.m340.

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AbstractThis paper presents a numerical and experimental study on hydrodynamic behavior of thin liquid films in rectangular domains. Three-dimensional computer simulations were performed using the lattice Boltzmann equation method (LBM). The liquid films laying on solid and liquid substrates are considered. The rupture of liquid films in computations is initiated via the thermocapillary (Marangoni) effect by applying an initial spatially localized temperature perturbation. The rupture scenario is found to depend on the shape of the temperature distribution and on the wettability of the solid s

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23

Ruan, Xiaozhou, and Andrew F. Thompson. "Bottom Boundary Potential Vorticity Injection from an Oscillating Flow: A PV Pump." Journal of Physical Oceanography 46, no. 11 (2016): 3509–26. http://dx.doi.org/10.1175/jpo-d-15-0222.1.

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AbstractOceanic boundary currents over the continental slope exhibit variability with a range of time scales. Numerical studies of steady, along-slope currents over a sloping bathymetry have shown that cross-slope Ekman transport can advect buoyancy surfaces in a bottom boundary layer (BBL) so as to produce vertically sheared geostrophic flows that bring the total flow to rest: a process known as buoyancy shutdown of Ekman transport or Ekman arrest. This study considers the generation and evolution of near-bottom flows due to a barotropic, oscillating, and laterally sheared flow over a slope.

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24

Fyrillas, Marios M., and Andrew J. Szeri. "Dissolution or growth of soluble spherical oscillating bubbles." Journal of Fluid Mechanics 277 (October 25, 1994): 381–407. http://dx.doi.org/10.1017/s0022112094002806.

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A new theoretical formulation is presented for mass transport across the dynamic interface associated with a spherical bubble undergoing volume oscillations. As a consequence of the changing internal pressure of the bubble that accompanies volume oscillations, the concentration of the dissolved gas in the liquid at the interface undergoes large-amplitude oscillations. The convection-diffusion equations governing transport of dissolved gas in the liquid are written in Lagrangian coordinates to account for the moving domain. The Henry's law boundary condition is split into a constant and an osci

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25

Ly, E., and J. Nakamichi. "Time-linearised transonic computations including entropy, vorticity and shock wave motion effects." Aeronautical Journal 107, no. 1077 (2003): 687–95. http://dx.doi.org/10.1017/s0001924000013555.

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Abstract The effect of small perturbations on steady nonlinear transonic small disturbance flowfields, in the context of two-dimensional flows governed by the general-frequency transonic small disturbance equation with nonreflecting far-field boundary conditions, is investigated. This paper presents a time-linearised time-domain solution method that includes effects due to the shock-generated entropy and vorticity and shock wave motions. The solution procedure correctly accounts for the small-amplitude shock wave motion due to small unsteady changes in the aerofoil boundary conditions, and cor

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26

Mozolyako, P. "Boundary oscillations of harmonic functions in Lipschitz domains." Collectanea Mathematica 68, no. 3 (2016): 359–76. http://dx.doi.org/10.1007/s13348-016-0177-z.

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27

D’ Alessio, Gorizia, Arianna Pucci, Giulia Guida, and Francesca Casini. "Numerical study on the effects of groundwater table oscillation beneath the “Palazzaccio” courthouse in Rome." E3S Web of Conferences 382 (2023): 17006. http://dx.doi.org/10.1051/e3sconf/202338217006.

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This work aims to evaluate the settlement induced by the river Tiber groundwater table oscillations. A representative section of the subsoil beneath the courthouse “Palazzaccio”, close to the river in the city centre of Rome, is analysed via the finite element method with a fully coupled hydro-mechanicalmodel. The effects of wetting-drying cycles induced by the water table oscillation are accounted for by adopting the Barcelona Basic Model for the unsaturated layers, whose model parameters are calibrated using experimental results on saturated and unsaturated samples and literature data. The v

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28

BLANCHARD, DOMINIQUE, ANTONIO GAUDIELLO, and JACQUELINE MOSSINO. "HIGHLY OSCILLATING BOUNDARIES AND REDUCTION OF DIMENSION: THE CRITICAL CASE." Analysis and Applications 05, no. 02 (2007): 137–63. http://dx.doi.org/10.1142/s0219530507000924.

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In [4], the first two authors studied a nonlinear monotone problem in a multidomain composed of a part [Formula: see text], with a highly oscillating boundary, placed upon an asymptotically flat part of thickness hε. More precisely, [Formula: see text] is a "forest" of cylinders with fixed height and small cross section of size ε, distributed with ε-periodicity upon the flat domain. The analysis was achieved under the assumption εp/hε → 0 (p - 1 is the growth order of the operator at infinity), as ε tends to 0, and for rescaled external forces hε fε converging to 0 in the (rescaled) flat domai

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29

Zhang, Yang, and Chunhua Zhou. "Reduction of Numerical Oscillations in Simulating Moving-Boundary Problems by the Local DFD Method." Advances in Applied Mathematics and Mechanics 8, no. 1 (2015): 145–65. http://dx.doi.org/10.4208/aamm.2014.m590.

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AbstractIn this work, the hybrid solution reconstruction formulation proposed by Luo et al. [H. Luo, H. Dai, P. F. de Sousa and B. Yin, On the numerical oscillation of the direct-forcing immersed-boundary method for moving boundaries, Computers & Fluids, 56 (2012), pp. 61–76] for the finite-difference discretization on Cartesian meshes is implemented in the finite-element framework of the local domain-free discretization (DFD) method to reduce the numerical oscillations in the simulation of moving-boundary flows. The reconstruction formulation is applied at fluid nodes in the immediate vic

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30

Podolskiy, A. V., and T. A. Shaposhnikova. "Homogenization of the boundary value problem for the poisson equation with rapidly oscillating nonlinear boundary conditions: space dimension n ≥ 3, critical case." Доклады Академии наук 485, no. 3 (2019): 263–68. http://dx.doi.org/10.31857/s0869-56524853263-268.

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The homogenization of the Poisson equation in a bounded domain with rapidly oscillating boundary conditions specied on a part of the domain boundary is studied. A Neumann boundary condition alternates with an ε-periodically distributed nonlinear Robin condition involving the coefficient ε-β, where β ∈ R. The diameter of the boundary portions with a nonlinear Robin condition is of order O(εα), α > 1. A critical relation between the parameters α and β is considered

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31

Mossino, Jacqueline, and Ali Sili. "Limit behavior of thin heterogeneous domain with rapidly oscillating boundary." Ricerche di Matematica 56, no. 1 (2007): 119–48. http://dx.doi.org/10.1007/s11587-007-0009-2.

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32

Nakasato, Jean Carlos, and Marcone Corrêa Pereira. "The p-Laplacian in thin channels with locally periodic roughness and different scales*." Nonlinearity 35, no. 5 (2022): 2474–512. http://dx.doi.org/10.1088/1361-6544/ac62e0.

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Abstract In this work we analyse the asymptotic behaviour of the solutions of the p-Laplacian equation with homogeneous Neumann boundary conditions posed in bounded thin domains as R ε = ( x , y ) ∈ R 2 : x ∈ ( 0 , 1 ) and 0 < y < ε G x , x / ε α for some α > 0. We take a smooth function G : ( 0 , 1 ) × R ↦ R , L-periodic in the second variable, which allows us to consider locally periodic oscillations at the upper boundary. The thin domain situation is established passing to the limit in the solutions as the positive parameter ɛ goes to zero and we determine the limit regime for thre

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33

Mishra, Indira. "Homogenization of boundary optimal control problem." Electronic Journal of Differential Equations 2022, no. 01-87 (2022): 12. http://dx.doi.org/10.58997/ejde.2022.12.

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In this article, we study the asymptotic behavior of solutions to some optimal control problems, governed by an elliptic boundary value problem with Robin boundary conditions in a periodically perforated domain. The coefficients of the differential operator in the state equation and in the cost-functional are rapidly oscillating. We also study the boundary homogenization of some optimal control problems.

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34

Blanchard, Dominique, Luciano Carbone, and Antonio Gaudiello. "Homogenization of a monotone problem in a domain with oscillating boundary." ESAIM: Mathematical Modelling and Numerical Analysis 33, no. 5 (1999): 1057–70. http://dx.doi.org/10.1051/m2an:1999134.

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35

Belyaev, A. G., A. L. Pyatnitskii, and G. A. Chechkin. "Averaging in a perforated domain with an oscillating third boundary condition." Sbornik: Mathematics 192, no. 7 (2001): 933–49. http://dx.doi.org/10.1070/sm2001v192n07abeh000576.

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36

Fernández Bonder, Julián, Rafael Orive, and Julio D. Rossi. "The best Sobolev trace constant in a domain with oscillating boundary." Nonlinear Analysis: Theory, Methods & Applications 67, no. 4 (2007): 1173–80. http://dx.doi.org/10.1016/j.na.2006.07.005.

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37

Amirat, Y., and O. Bodart. "Boundary Layer Correctors for the Solution of Laplace Equation in a Domain with Oscillating Boundary." Zeitschrift für Analysis und ihre Anwendungen 20, no. 4 (2001): 929–40. http://dx.doi.org/10.4171/zaa/1052.

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38

Iwano, Kaoru. "Bloch Oscillations Due to Quantum Domain Breathing in One-Dimensional Electronic Photoinduced Phase Transitions." Applied Sciences 9, no. 12 (2019): 2461. http://dx.doi.org/10.3390/app9122461.

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We theoretically predict a novel oscillation that will be observed during the dynamical processes of one-dimensional electronic photoinduced phase transitions. This oscillation is considered to be a breathing mode of a quantum domain of a photoinduced phase in the background of the initial phase. When the initial phase is sufficiently stable, being far apart from the phase boundary, the domain feels a constant attractive force depending on its size or the distance between the two domain walls. This fact allows an interpretation that this oscillation is essentially the same as a so-called Bloch

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39

WANG, Q. X., and J. R. BLAKE. "Non-spherical bubble dynamics in a compressible liquid. Part 1. Travelling acoustic wave." Journal of Fluid Mechanics 659 (July 27, 2010): 191–224. http://dx.doi.org/10.1017/s0022112010002430.

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Micro-cavitation bubbles generated by ultrasound have wide and important applications in medical ultrasonics and sonochemistry. An approximate theory is developed for nonlinear and non-spherical bubbles in a compressible liquid by using the method of matched asymptotic expansions. The perturbation is performed to the second order in terms of a small parameter, the bubble-wall Mach number. The inner flow near the bubble can be approximated as incompressible at the first and second orders, leading to the use of Laplace's equation, whereas the outer flow far away from the bubble can be described

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40

Simakov, Sergey T. "Initial and boundary value problems of internal gravity waves." Journal of Fluid Mechanics 248 (March 1993): 55–65. http://dx.doi.org/10.1017/s0022112093000680.

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The paper considers the generation of Boussinesq internal waves in the framework of the Green's function method. For certain domains it is shown how to construct Green's functions using the fundamental solution of the equation. The behaviour of the solution at large times for an impulsively started monochromatic point source is studied, attention being focused on the growth rate of the oscillation amplitude on the characteristic surfaces of the steady-oscillation equation which are emitted from the point source. In addition a simple extended source is considered, for which a focusing singulari

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41

Wong, L. H., and S. M. Calisal. "A Numerical Solution for Potential Flows Including the Effects of Vortex Shedding." Journal of Offshore Mechanics and Arctic Engineering 115, no. 2 (1993): 111–15. http://dx.doi.org/10.1115/1.2920099.

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This paper reports on an attempt to include vortex shedding effects into potential flow calculations using the boundary element method. Significant computational advantages result because of the relatively simple approach to handling separation at the sharp edges while working only with the boundary values. A discrete vortex method was incorporated into a time domain boundary element algorithm for the numerical simulation of oscillating flow past a normal flat plate. Separation from a sharp edge results in the formation of a vortex sheet issuing from the edge. This vortex sheet is modeled by a

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42

Amirat, Youcef, Gregory A. Chechkin, and Rustem R. Gadyl'shin. "Asymptotics for eigenelements of Laplacian in domain with oscillating boundary: multiple eigenvalues." Applicable Analysis 86, no. 7 (2007): 873–97. http://dx.doi.org/10.1080/00036810701461238.

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43

Muthukumar, T., and K. Sankar. "Homogenization of the Stokes System in a Domain with an Oscillating Boundary." Multiscale Modeling & Simulation 20, no. 4 (2022): 1361–93. http://dx.doi.org/10.1137/22m1474345.

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44

Muthukumar, T., Jean-Pierre Raymond, and K. Sankar. "Homogenization of parabolic equation in an evolving domain with an oscillating boundary." Journal of Mathematical Analysis and Applications 463, no. 2 (2018): 838–68. http://dx.doi.org/10.1016/j.jmaa.2018.03.063.

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45

Yoshida, Norio. "Forced oscillations of solutions of parabolic equations." Bulletin of the Australian Mathematical Society 36, no. 2 (1987): 289–94. http://dx.doi.org/10.1017/s0004972700026563.

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46

Moroz, I. P. "THE CORRECTING FUNCTIONS METHOD FOR SOLVING A BOUNDARY VALUE PROBLEM FOR THE AMBIPOLAR DIFFUSION EQUATION IN A DOMAIN WITH A CURVILINEAR BOUNDARIES." Journal of Numerical and Applied Mathematics, no. 2 (2022): 91–97. http://dx.doi.org/10.17721/2706-9699.2022.2.11.

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An approach for the ambipolar diffusion equation boundary value problem solving, which is posed in a two-dimensional domain with oscillating boundaries, is proposed. The construction of the solution of the model problem is based on the corresponding problem for a certain internal canonical majorant domain and the methodology for constructing the so-called corrective corrections based on the use of the perturbation theory elements. A feature of this problem is that it is not the problem equation or boundary conditions that are perturbed, but the region. And this leads to the construction of a f

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Wooyi, Young, and Hee-Chang Lim. "Synthetic Inflow GeneratorhavingVarious Oscillations." International Journal of Advance Research and Innovation 7, no. 1 (2019): 82–85. http://dx.doi.org/10.51976/ijari.711912.

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Large Eddy Simulation (LES), which has recently been developed and used for the climate local environment and turbulent boundary layer flow, can be applied for a variety of area. In particular, in order to achieve a faster performance, an artificial generation of inflow turbulent flowwould be necessary to make the faster convergence as well as to maintain the real turbulent flow in the calculation domain.In this study, the synthetic inflow generator has been developed based on spatial and temporal correlation functions, which have a form similar to an exponential function. This inflow data hav

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Abdulle, Assyr, Doghonay Arjmand, and Edoardo Paganoni. "A parabolic local problem with exponential decay of the resonance error for numerical homogenization." Mathematical Models and Methods in Applied Sciences 31, no. 13 (2021): 2733–72. http://dx.doi.org/10.1142/s0218202521500603.

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This paper aims at an accurate and efficient computation of effective quantities, e.g. the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a micro–macro-coupling, where the macromodel describes the coarse scale behavior, and the micromodel is solved only locally to upscale the effective quantities, which are missing in the macromodel. The fact that the microproblems are solved over small domains within the entire macroscopic domain, implies imposing artificial boundary conditions o

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Aina, B., and S. Isa. "Influence of Heat Generation/Absorption on Mixed Convection Flow Behaviour in the Presence of Lorentz Forces in a Vertical Micro Circular Duct Having Time Periodic Boundary Conditions: Steady Periodic Regime." International Journal of Applied Mechanics and Engineering 25, no. 4 (2020): 1–21. http://dx.doi.org/10.2478/ijame-2020-0046.

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AbstractThe problem of mixed convection flow of a heat generating/absorbing fluid in the presence existence of Lorentz forces in a vertical micro circular subjected to a periodic sinusoidal temperature change at the surface has been studied taking the first-order slip and jump effects into consideration. The research analysis is carried out by considering a fully developed parallel flow and steady periodic regime. The governing equations, together with the constraint equations which arise from the definition of mean velocity and temperature, are written in a dimensionless form and mapped into

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Orchini, A., S. J. Illingworth, and M. P. Juniper. "Frequency domain and time domain analysis of thermoacoustic oscillations with wave-based acoustics." Journal of Fluid Mechanics 775 (June 25, 2015): 387–414. http://dx.doi.org/10.1017/jfm.2015.139.

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Many thermoacoustic systems exhibit rich nonlinear behaviour. Recent studies show that this nonlinear dynamics can be well captured by low-order time domain models that couple a level set kinematic model for a laminar flame, the $G$-equation, with a state-space realization of the linearized acoustic equations. However, so far the $G$-equation has been coupled only with straight ducts with uniform mean acoustic properties, which is a simplistic configuration. In this study, we incorporate a wave-based model of the acoustic network, containing area and temperature variations and frequency-depend

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