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Journal articles on the topic 'FREE-FREE BOUNDARY'

Author: Grafiati

Published: 11 September 2023

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1

Chistyakov, A. E., E. A. Protsenko, and E. F. Timofeeva. "Mathematical modeling of oscillatory processes with a free boundary." COMPUTATIONAL MATHEMATICS AND INFORMATION TECHNOLOGIES 1, no. 1 (2017): 102–12. http://dx.doi.org/10.23947/2587-8999-2017-1-1-102-112.

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2

Gurevich, Alex. "Boundary regularity for free boundary problems." Communications on Pure and Applied Mathematics 52, no. 3 (March 1999): 363–403. http://dx.doi.org/10.1002/(sici)1097-0312(199903)52:3<363::aid-cpa3>3.0.co;2-u.

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3

Jiang, Yingchun, and Qingqing Sun. "Three-Dimensional Biorthogonal Divergence-Free and Curl-Free Wavelets with Free-Slip Boundary." Journal of Applied Mathematics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/954717.

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This paper deals with the construction of divergence-free and curl-free wavelets on the unit cube, which satisfies the free-slip boundary conditions. First, interval wavelets adapted to our construction are introduced. Then, we provide the biorthogonal divergence-free and curl-free wavelets with free-slip boundary and simple structure, based on the characterization of corresponding spaces. Moreover, the bases are also stable.

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4

SUSSMAN, MARK, and PETER SMEREKA. "Axisymmetric free boundary problems." Journal of Fluid Mechanics 341 (June 25, 1997): 269–94. http://dx.doi.org/10.1017/s0022112097005570.

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We present a number of three-dimensional axisymmetric free boundary problems for two immiscible fluids, such as air and water. A level set method is used where the interface is the zero level set of a continuous function while the two fluids are solutions of the incompressible Navier–Stokes equation. We examine the rise and distortion of an initially spherical bubble into cap bubbles and toroidal bubbles. Steady solutions for gas bubbles rising in a liquid are computed, with favourable comparisons to experimental data. We also study the inviscid limit and compare our results with a boundary integral method. The problems of an air bubble bursting at a free surface and a liquid drop hitting a free surface are also computed.

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5

Dovì, V. G., H. Preisig, and O. Paladino. "Inverse free boundary problems." Applied Mathematics Letters 2, no. 1 (1989): 91–96. http://dx.doi.org/10.1016/0893-9659(89)90125-0.

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6

Lortz, D. "Plane free-boundary equilibria." Plasma Physics and Controlled Fusion 33, no. 1 (January 1, 1991): 77–89. http://dx.doi.org/10.1088/0741-3335/33/1/005.

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7

Shargorodsky, E., and J. F. Toland. "Bernoulli free-boundary problems." Memoirs of the American Mathematical Society 196, no. 914 (2008): 0. http://dx.doi.org/10.1090/memo/0914.

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8

Park, Sung-Ho, and Juncheol Pyo. "Free boundary minimal hypersurfaces with spherical boundary." Mathematische Nachrichten 290, no. 5-6 (May 31, 2016): 885–89. http://dx.doi.org/10.1002/mana.201500399.

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9

Edelen, Nick. "The free-boundary Brakke flow." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 758 (January 1, 2020): 95–137. http://dx.doi.org/10.1515/crelle-2017-0053.

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AbstractWe develop the notion of Brakke flow with free-boundary in a barrier surface. Unlike the classical free-boundary mean curvature flow, the free-boundary Brakke flow must “pop” upon tangential contact with the barrier. We prove a compactness theorem for free-boundary Brakke flows, define a Gaussian monotonicity formula valid at all points, and use this to adapt the local regularity theorem of White [23] to the free-boundary setting. Using Ilmanen’s elliptic regularization procedure [10], we prove existence of free-boundary Brakke flows.

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10

MATSUSHITA, Osami. "Modelling; Free from boundary condition." Journal of the Japan Society for Precision Engineering 54, no. 5 (1988): 848–52. http://dx.doi.org/10.2493/jjspe.54.848.

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11

Mendes, Abraão. "Rigidity of free boundary MOTS." Nonlinear Analysis 220 (July 2022): 112841. http://dx.doi.org/10.1016/j.na.2022.112841.

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12

Agelmenev, M. E. "The Modeling with Free Boundary." Molecular Crystals and Liquid Crystals 545, no. 1 (June 30, 2011): 190/[1414]—203/[1427]. http://dx.doi.org/10.1080/15421406.2011.572010.

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13

Hilhorst, Danielle, and Josephus Hulshof. "A free boundary focusing problem." Proceedings of the American Mathematical Society 121, no. 4 (April 1, 1994): 1193. http://dx.doi.org/10.1090/s0002-9939-1994-1233975-9.

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14

Dipierro, Serena, Ovidiu Savin, and Enrico Valdinoci. "A Nonlocal Free Boundary Problem." SIAM Journal on Mathematical Analysis 47, no. 6 (January 2015): 4559–605. http://dx.doi.org/10.1137/140999712.

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15

Friedman, Avner. "Free boundary problems in biology." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, no. 2050 (September 13, 2015): 20140368. http://dx.doi.org/10.1098/rsta.2014.0368.

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In this paper, I review several free boundary problems that arise in the mathematical modelling of biological processes. The biological topics are quite diverse: cancer, wound healing, biofilms, granulomas and atherosclerosis. For each of these topics, I describe the biological background and the mathematical model, and then proceed to state mathematical results, including existence and uniqueness theorems, stability and asymptotic limits, and the behaviour of the free boundary. I also suggest, for each of the topics, open mathematical problems.

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16

Zheng, L. J. "Free boundary ballooning mode representation." Physics of Plasmas 19, no. 10 (October 2012): 102506. http://dx.doi.org/10.1063/1.4759012.

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17

Nührenberg, C. "Free-boundary perturbed MHD equilibria." Journal of Physics: Conference Series 401 (December 3, 2012): 012018. http://dx.doi.org/10.1088/1742-6596/401/1/012018.

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18

Soltanov, K. N., and E. B. Novruzov. "On a free boundary problem." Izvestiya: Mathematics 66, no. 4 (August 31, 2002): 807–27. http://dx.doi.org/10.1070/im2002v066n04abeh000398.

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19

Bensid, Sabri, and S. M. Bouguima. "On a free boundary problem." Nonlinear Analysis: Theory, Methods & Applications 68, no. 8 (April 2008): 2328–48. http://dx.doi.org/10.1016/j.na.2007.01.047.

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20

Frolova, E. V. "Free Boundary Problem of Magnetohydrodynamics." Journal of Mathematical Sciences 210, no. 6 (October 1, 2015): 857–77. http://dx.doi.org/10.1007/s10958-015-2596-x.

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21

Chen, Eugene Y., H. L. Berk, B. Breizman, and L. J. Zheng. "Free-boundary toroidal Alfvén eigenmodes." Physics of Plasmas 18, no. 5 (May 2011): 052503. http://dx.doi.org/10.1063/1.3575157.

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22

Cryer, Colin C., and John Crank. "Free and Moving Boundary Problems." Mathematics of Computation 46, no. 174 (April 1986): 765. http://dx.doi.org/10.2307/2008018.

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23

CRASTER, R. V. "Two related free boundary problems." IMA Journal of Applied Mathematics 52, no. 3 (1994): 253–70. http://dx.doi.org/10.1093/imamat/52.3.253.

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24

Remizova, E. V. "A problem with free boundary." Journal of Soviet Mathematics 45, no. 3 (May 1989): 1163–72. http://dx.doi.org/10.1007/bf01096148.

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25

Boucherif, Abdelkader, and Sidi Mohammed Bouguima. "On a Free Boundary Problem." Mathematical Methods in the Applied Sciences 19, no. 15 (October 1996): 1257–64. http://dx.doi.org/10.1002/(sici)1099-1476(199610)19:15<1257::aid-mma834>3.0.co;2-t.

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26

Clarelli, Fabrizio, Antonio Fasano, and Roberto Natalini. "Free-boundary models of sulphation." PAMM 7, no. 1 (December 2007): 1110201–2. http://dx.doi.org/10.1002/pamm.200700288.

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27

Kuznetsov, V. V., and O. A. Frolovskaya. "Boundary layers in free convection." Journal of Applied Mechanics and Technical Physics 41, no. 3 (May 2000): 461–69. http://dx.doi.org/10.1007/bf02465297.

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28

Mikayelyan, Hayk, and Henrik Shahgholian. "Convexity of the free boundary for an exterior free boundary problem involving the perimeter." Communications on Pure & Applied Analysis 12, no. 3 (2013): 1431–43. http://dx.doi.org/10.3934/cpaa.2013.12.1431.

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29

Centen, P., M. P. H. Weenink, and W. Schuurman. "Minimum-energy principle for a free-boundary, force-free plasma." Plasma Physics and Controlled Fusion 28, no. 1B (January 1, 1986): 347–55. http://dx.doi.org/10.1088/0741-3335/28/1b/009.

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30

Gupta, A. K., and D. Surya. "Benard-Marangoni Convection with Free Slip Bottom and Mixed Thermal Boundary Conditions." Mathematical Journal of Interdisciplinary Sciences 2, no. 2 (March 3, 2014): 141–54. http://dx.doi.org/10.15415/mjis.2014.22011.

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31

Okuma, Masaaki, and Qinzhong Shi. "Identification of Principal Rigid Body Modes Under Free-Free Boundary Condition." Journal of Vibration and Acoustics 119, no. 3 (July 1, 1997): 341–45. http://dx.doi.org/10.1115/1.2889729.

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This paper focuses on the problem of identifying all individual principal rigid body modes and the associated mass or principal inertia of moment, which can be called modal mass, of flexible structures under the free-free boundary condition with fewer multi-location excitations than the number of those modes. The rigid body mass matrix of the structure can be identified by using both the parameters of inertia, which are determined previously by a modal parameter estimation, and the coordinates of measurement points. As all rigid body properties can be obtained from the mass matrix, it becomes possible to simulate the FRFs between any two measurement points with inclusion of the contribution of rigid body motions even by only experimental modal analysis technique. First, the theory is explained. Then, a numerical simulation and two actual identifications for a plate structure and an automotive body component are carried out to demonstrate the validity and the usefulness of the theory.

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32

Yi,, Tong Y., and Parviz E. Nikravesh. "Extraction of Free-Free Modes from Constrained Vibration Data for Flexible Multibody Models." Journal of Vibration and Acoustics 123, no. 3 (February 1, 2001): 383–89. http://dx.doi.org/10.1115/1.1375814.

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This paper presents a method for identifying the free-free modes of a structure by utilizing the vibration data of the same structure with boundary conditions. In modal formulations for flexible body dynamics, modal data are primary known quantities that are obtained either experimentally or analytically. The vibration measurements may be obtained for a flexible body that is constrained differently than its boundary conditions in a multibody system. For a flexible body model in a multibody system, depending upon the formulation used, we may need a set of free-free modal data or a set of constrained modal data. If a finite element model of the flexible body is available, its vibration data can be obtained analytically under any desired boundary conditions. However, if a finite element model is not available, the vibration data may be determined experimentally. Since experimentally measured vibration data are obtained for a flexible body supported by some form of boundary conditions, we may need to determine its free-free vibration data. The aim of this study is to extract, based on experimentally obtained vibration data, the necessary free-free frequencies and the associated modes for flexible bodies to be used in multibody formulations. The available vibration data may be obtained for a structure supported either by springs or by fixed boundary conditions. Furthermore, the available modes may be either a complete set, having as many modes as the number of degrees of freedom of the associated FE model, or an incomplete set.

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33

Samira, Khatmi, and Barkatou Mohammed. "On some overdetermined free boundary problems." ANZIAM Journal 49 (November 22, 2007): 11. http://dx.doi.org/10.21914/anziamj.v49i0.168.

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34

Hussein, M. S., D. Lesnic, and M. Ivanchov. "Free Boundary Determination in Nonlinear Diffusion." East Asian Journal on Applied Mathematics 3, no. 4 (November 2013): 295–310. http://dx.doi.org/10.4208/eajam.100913.061113a.

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AbstractFree boundary problems with nonlinear diffusion occur in various applications, such as solidification over a mould with dissimilar nonlinear thermal properties and saturated or unsaturated absorption in the soil beneath a pond. In this article, we consider a novel inverse problem where a free boundary is determined from the mass/energy specification in a well-posed one-dimensional nonlinear diffusion problem, and a stability estimate is established. The problem is recast as a nonlinear least-squares minimisation problem, which is solved numerically using the lsqnonlin routine from the MATLAB toolbox. Accurate and stable numerical solutions are achieved. For noisy data, instability is manifest in the derivative of the moving free surface, but not in the free surface itself nor in the concentration or temperature.

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35

Friedman, Avner. "Free boundary problems arising in biology." Discrete & Continuous Dynamical Systems - B 23, no. 1 (2018): 193–202. http://dx.doi.org/10.3934/dcdsb.2018013.

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36

S., L. R., and P. Neittaanmaki. "Numerical Methods for Free Boundary Problems." Mathematics of Computation 63, no. 207 (July 1994): 426. http://dx.doi.org/10.2307/2153589.

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37

KIM, INWON C. "A Free Boundary Problem with Curvature." Communications in Partial Differential Equations 30, no. 1-2 (April 2005): 121–38. http://dx.doi.org/10.1081/pde-200044474.

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38

Huysmans, G. T. A., J. P. Goedbloed, and W. Kerner. "Free boundary resistive modes in tokamaks." Physics of Fluids B: Plasma Physics 5, no. 5 (May 1993): 1545–58. http://dx.doi.org/10.1063/1.860894.

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39

Lewis, John L., and Andrew L. Vogel. "Uniqueness in a Free Boundary Problem." Communications in Partial Differential Equations 31, no. 11 (November 2006): 1591–614. http://dx.doi.org/10.1080/03605300500455909.

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40

Lamboley, Jimmy, Yannick Sire, and Eduardo V. Teixeira. "Free boundary problems involving singular weights." Communications in Partial Differential Equations 45, no. 7 (January 25, 2020): 758–75. http://dx.doi.org/10.1080/03605302.2020.1716003.

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41

Reusch, Michael F. "Free boundary skin current magnetohydrodynamic equilibria." Physics of Fluids 31, no. 10 (1988): 2962. http://dx.doi.org/10.1063/1.866953.

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42

De Silva, Daniela, and David Jerison. "A singular energy minimizing free boundary." Journal für die reine und angewandte Mathematik (Crelles Journal) 2009, no. 635 (January 2009): 1–21. http://dx.doi.org/10.1515/crelle.2009.074.

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43

Hongler, Clément, and Kalle Kytölä. "Ising interfaces and free boundary conditions." Journal of the American Mathematical Society 26, no. 4 (June 25, 2013): 1107–89. http://dx.doi.org/10.1090/s0894-0347-2013-00774-2.

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44

Emamizadeh, B., and M. Marras. "Rearrangement Optimization Problems with Free Boundary." Numerical Functional Analysis and Optimization 35, no. 4 (March 7, 2014): 404–22. http://dx.doi.org/10.1080/01630563.2014.884587.

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45

CHIPPADA, S., T. C. JUE, S. W. JOO, M. F. WHEELER, and B. RAMASWAMY. "Numerical Simulation of Free-Boundary Problems." International Journal of Computational Fluid Dynamics 7, no. 1-2 (July 1996): 91–118. http://dx.doi.org/10.1080/10618569608940754.

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46

Clain, S. "Chemical Attack in Free Boundary Domains." Journal of Applied Analysis 5, no. 1 (January 1999): 35–58. http://dx.doi.org/10.1515/jaa.1999.35.

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47

Hou, Thomas Y. "Numerical Solutions to Free Boundary Problems." Acta Numerica 4 (January 1995): 335–415. http://dx.doi.org/10.1017/s0962492900002567.

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Many physically interesting problems involve propagation of free surfaces. Vortex-sheet roll-up in hydrodynamic instability, wave interactions on the ocean's free surface, the solidification problem for crystal growth and Hele-Shaw cells for pattern formation are some of the significant examples. These problems present a great challenge to physicists and applied mathematicians because the underlying problem is very singular. The physical solution is sensitive to small perturbations. Naïve discretisations may lead to numerical instabilities. Other numerical difficulties include singularity formation and possible change of topology in the moving free surfaces, and the severe time-stepping stability constraint due to the stiffness of high-order regularisation effects, such as surface tension.This paper reviews some of the recent advances in developing stable and efficient numerical algorithms for solving free boundary-value problems arising from fluid dynamics and materials science. In particular, we will consider boundary integral methods and the level-set approach for water waves, general multi-fluid interfaces, Hele–Shaw cells, crystal growth and solidification. We will also consider the stabilising effect of surface tension and curvature regularisation. The issue of numerical stability and convergence will be discussed, and the related theoretical results for the continuum equations will be addressed. This paper is not intended to be a detailed survey and the discussion is limited by both the taste and expertise of the author.

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48

Fotouhi, Morteza, and Henrik Shahgholian. "A semilinear PDE with free boundary." Nonlinear Analysis: Theory, Methods & Applications 151 (March 2017): 145–63. http://dx.doi.org/10.1016/j.na.2016.11.019.

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49

BERON-VERA, F. J., and P. RIPA. "Free boundary effects on baroclinic instability." Journal of Fluid Mechanics 352 (December 10, 1997): 245–64. http://dx.doi.org/10.1017/s0022112097007222.

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The effects of a free boundary on the stability of a baroclinic parallel flow are investigated using a reduced-gravity model. The basic state has uniform density stratification and a parallel flow with uniform vertical shear in thermal-wind balance with the horizontal buoyancy gradient. A finite value of the velocity at the free (lower) boundary requires the interface to have a uniform slope in the direction transversal to that of the flow. Normal-mode perturbations with arbitrary vertical structure are studied in the limit of small Rossby number. This solution is restricted to neither a horizontal lower boundary nor a weak stratification in the basic state.In the limit of a very weak stratification and bottom slope there is a large separation between the first two deformation radii and hence short or long perturbations may be identified:(a) The short-perturbation limit corresponds to the well-known Eady problem in which case the layer bottom is effectively rigid and its slope in the basic state is immaterial.(b) In the long-perturbation limit the bottom is free to deform and the unstable wave solutions, which appear for any value of the Richardson number Ri, are sensible to its slope in the basic state. In fact, a sloped bottom is found to stabilize the basic flow.At stronger stratifications there is no distinction between short and long perturbations, and the bottom always behaves as a free boundary. Unstable wave solutions are found for Ri→∞ (unlike the case of long perturbations). The increase in stratification is found to stabilize the basic flow. At the maximum stratification compatible with static stability, the perturbation has a vanishing growth rate at all wavenumbers.Results in the long-perturbation limit corroborate those predicted by an approximate layer model that restricts the buoyancy perturbations to have a linear vertical structure. The approximate model is less successful in the short-perturbation limit since the constraint to a linear density profile does not allow the correct representation of the exponential trapping of the exact eigensolutions. With strong stratification, only the growth rate of long enough perturbations superimposed on basic states with gently sloped lower boundaries behaves similarly to that of the exact model. However, the stabilizing tendency on the basic flow as the stratification reaches its maximum is also found in the approximate model. Its partial success in this case is also attributed to the limited vertical structure allowed by the model.

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50

Lions, P. L., and N. Masmoudi. "On a free boundary barotropic model." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 16, no. 3 (May 1999): 373–410. http://dx.doi.org/10.1016/s0294-1449(99)80018-3.

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