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Journal articles on the topic 'Periodic Unfolding Method'

Author: Grafiati

Published: 8 February 2024

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1

Cioranescu, D., A. Damlamian, and G. Griso. "The Periodic Unfolding Method in Homogenization." SIAM Journal on Mathematical Analysis 40, no. 4 (2008): 1585–620. http://dx.doi.org/10.1137/080713148.

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2

Cioranescu, D., A. Damlamian, P. Donato, G. Griso, and R. Zaki. "The Periodic Unfolding Method in Domains with Holes." SIAM Journal on Mathematical Analysis 44, no. 2 (2012): 718–60. http://dx.doi.org/10.1137/100817942.

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3

DIMINNIE, DAVID C., and RICHARD HABERMAN. "ACTION AND PERIOD OF HOMOCLINIC AND PERIODIC ORBITS FOR THE UNFOLDING OF A SADDLE-CENTER BIFURCATION." International Journal of Bifurcation and Chaos 13, no. 11 (2003): 3519–30. http://dx.doi.org/10.1142/s0218127403008569.

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At a saddle-center bifurcation for Hamiltonian systems, the homoclinic orbit is cusp shaped at the nonlinear nonhyperbolic saddle point. Near but before the bifurcation, orbits are periodic corresponding to the unfolding of the homoclinic orbit, while after the bifurcation a double homoclinic orbit is formed with a local and global branch. The saddle-center bifurcation is dynamically unfolded due to a slowly varying potential. Near the unfolding of the homoclinic orbit, the period and action are analyzed. Asymptotic expansions for the action, period and dissipation are obtained in an overlap r

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4

Cioranescu, Doina, Alain Damlamian, and Riccardo De Arcangelis. "Homogenization of Quasiconvex Integrals via the Periodic Unfolding Method." SIAM Journal on Mathematical Analysis 37, no. 5 (2006): 1435–53. http://dx.doi.org/10.1137/040620898.

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5

Cioranescu, Doina, Alain Damlamian, and Riccardo De Arcangelis. "Homogenization of nonlinear integrals via the periodic unfolding method." Comptes Rendus Mathematique 339, no. 1 (2004): 77–82. http://dx.doi.org/10.1016/j.crma.2004.03.028.

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6

Avila, Jake, and Bituin Cabarrubias. "Periodic unfolding method for domains with very small inclusions." Electronic Journal of Differential Equations 2023, no. 01-?? (2023): 85. http://dx.doi.org/10.58997/ejde.2023.85.

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This work creates a version of the periodic unfolding method suitable for domains with very small inclusions in \(\mathbb{R}^N\) for \(N\geq 3\). In the first part, we explore the properties of the associated operators. The second part involves the application of the method in obtaining the asymptotic behavior of a stationary heat dissipation problem depending on the parameter \( \gamma < 0\). In particular, we consider the cases when \(\gamma \in (-1,0)\), \( \gamma < -1\) and \(\gamma = -1\). We also include here the corresponding corrector results for the solution of the problem, to c

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7

Sánchez-Ochoa, F., Francisco Hidalgo, Miguel Pruneda, and Cecilia Noguez. "Unfolding method for periodic twisted systems with commensurate Moiré patterns." Journal of Physics: Condensed Matter 32, no. 2 (2019): 025501. http://dx.doi.org/10.1088/1361-648x/ab44f0.

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8

Ptashnyk, Mariya. "Locally Periodic Unfolding Method and Two-Scale Convergence on Surfaces of Locally Periodic Microstructures." Multiscale Modeling & Simulation 13, no. 3 (2015): 1061–105. http://dx.doi.org/10.1137/140978405.

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9

Cioranescu, D., A. Damlamian, G. Griso, and D. Onofrei. "The periodic unfolding method for perforated domains and Neumann sieve models." Journal de Mathématiques Pures et Appliquées 89, no. 3 (2008): 248–77. http://dx.doi.org/10.1016/j.matpur.2007.12.008.

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10

Donato, P., K. H. Le Nguyen, and R. Tardieu. "The periodic unfolding method for a class of imperfect transmission problems." Journal of Mathematical Sciences 176, no. 6 (2011): 891–927. http://dx.doi.org/10.1007/s10958-011-0443-2.

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11

Donato, Patrizia, and ZhanYing Yang. "The periodic unfolding method for the heat equation in perforated domains." Science China Mathematics 59, no. 5 (2015): 891–906. http://dx.doi.org/10.1007/s11425-015-5103-4.

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12

Ganghoffer, Jean-François, Gérard Maurice, and Yosra Rahali. "Determination of closed form expressions of the second-gradient elastic moduli of multi-layer composites using the periodic unfolding method." Mathematics and Mechanics of Solids 24, no. 5 (2018): 1475–502. http://dx.doi.org/10.1177/1081286518798873.

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The present paper aims at introducing a homogenization scheme for the identification of strain–gradient elastic moduli of composite materials, based on the unfolding mathematical method. We expose in the first part of this paper the necessary mathematical apparatus in view of the derivation of the effective first- and second-gradient mechanical properties of two-phase composite materials, focusing on a one-dimensional situation. Each of the two phases is supposed to obey a second-gradient linear elastic constitutive law. Application of the unfolding method to the homogenization of multi-layer

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13

Ene, Horia, and Claudia Timofte. "Microstructure models for composites with imperfect interface via the periodic unfolding method." Asymptotic Analysis 89, no. 1-2 (2014): 111–22. http://dx.doi.org/10.3233/asy-141239.

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14

Cabarrubias, Bituin. "Homogenization of optimal control problems in perforated domains via periodic unfolding method." Applicable Analysis 95, no. 11 (2015): 2517–34. http://dx.doi.org/10.1080/00036811.2015.1094799.

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15

Cioranescu, Doina, Alain Damlamian, and Riccardo De Arcangelis. "Homogenization of integrals with pointwise gradient constraints via the periodic unfolding method." Ricerche di Matematica 55, no. 1 (2006): 31–54. http://dx.doi.org/10.1007/s11587-006-0003-0.

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16

Mohammed, Mogtaba. "Homogenization of nonlinear hyperbolic problem with a dynamical boundary condition." AIMS Mathematics 8, no. 5 (2023): 12093–108. http://dx.doi.org/10.3934/math.2023609.

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<abstract><p>In this work, we look at homogenization results for nonlinear hyperbolic problem with a non-local boundary condition. We use the periodic unfolding method to obtain a homogenized nonlinear hyperbolic equation in a fixed domain. Due to the investigation's peculiarity, the unfolding technique must be developed with special attention, creating an unusual two-scale model. We note that the non-local boundary condition caused a damping on the homogenized model.</p></abstract>

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17

Coatléven, Julien. "Mathematical justification of macroscopic models for diffusion MRI through the periodic unfolding method." Asymptotic Analysis 93, no. 3 (2015): 219–58. http://dx.doi.org/10.3233/asy-151294.

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18

Arrieta, José M., and Manuel Villanueva-Pesqueira. "Unfolding Operator Method for Thin Domains with a Locally Periodic Highly Oscillatory Boundary." SIAM Journal on Mathematical Analysis 48, no. 3 (2016): 1634–71. http://dx.doi.org/10.1137/15m101600x.

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19

Yang, Zhanying. "The periodic unfolding method for a class of parabolic problems with imperfect interfaces." ESAIM: Mathematical Modelling and Numerical Analysis 48, no. 5 (2014): 1279–302. http://dx.doi.org/10.1051/m2an/2013139.

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20

Mohammed, Mogtaba. "Homogenization and correctors for linear stochastic equations via the periodic unfolding methods." Stochastics and Dynamics 19, no. 05 (2019): 1950040. http://dx.doi.org/10.1142/s0219493719500400.

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In this paper, we use the periodic unfolding method and Prokhorov’s and Skorokhod’s probabilistic compactness results to obtain homogenization and corrector results for stochastic partial differential equations (PDEs) with periodically oscillating coefficients. We show the convergence of the solutions of the original problems to the solutions of the homogenized problems. In contrast to the two-scale convergence method, the corrector results obtained in this paper are without any additional regularity assumptions on the solutions of the original problems

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21

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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22

Li, Qunhong, Pu Chen, and Jieqiong Xu. "Codimension-Two Grazing Bifurcations in Three-Degree-of-Freedom Impact Oscillator with Symmetrical Constraints." Discrete Dynamics in Nature and Society 2015 (2015): 1–15. http://dx.doi.org/10.1155/2015/353581.

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This paper investigates the codimension-two grazing bifurcations of a three-degree-of-freedom vibroimpact system with symmetrical rigid stops since little research can be found on this important issue. The criterion for existence of double grazing periodic motion is presented. Using the classical discontinuity mapping method, the Poincaré mapping of double grazing periodic motion is obtained. Based on it, the sufficient condition of codimension-two bifurcation of double grazing periodic motion is formulated, which is simplified further using the Jacobian matrix of smooth Poincaré mapping. At t

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23

Aiyappan, Srinivasan, Giuseppe Cardone, Carmen Perugia, and Ravi Prakash. "Homogenization of a nonlinear monotone problem in a locally periodic domain via unfolding method." Nonlinear Analysis: Real World Applications 66 (August 2022): 103537. http://dx.doi.org/10.1016/j.nonrwa.2022.103537.

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24

Zaki, Rachad. "Homogenization of a Stokes problem in a porous medium by the periodic unfolding method." Asymptotic Analysis 79, no. 3-4 (2012): 229–50. http://dx.doi.org/10.3233/asy-2012-1094.

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25

Graf, Isabell, and Malte A. Peter. "A convergence result for the periodic unfolding method related to fast diffusion on manifolds." Comptes Rendus Mathematique 352, no. 6 (2014): 485–90. http://dx.doi.org/10.1016/j.crma.2014.03.002.

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26

Yang, Zhanying. "Homogenization and correctors for the hyperbolic problems with imperfect interfaces via the periodic unfolding method." Communications on Pure & Applied Analysis 13, no. 1 (2014): 249–72. http://dx.doi.org/10.3934/cpaa.2014.13.249.

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27

CAPATINA, ANCA, and HORIA ENE. "Homogenisation of the Stokes problem with a pure non-homogeneous slip boundary condition by the periodic unfolding method." European Journal of Applied Mathematics 22, no. 4 (2011): 333–45. http://dx.doi.org/10.1017/s0956792511000088.

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We study the homogenisation of the Stokes system with a non-homogeneous Fourier boundary condition on the boundary of the holes, depending on a parameter γ. Such systems arise in the modelling of the flow of an incompressible viscous fluid through a porous medium under the influence of body forces. At the limit, by using the periodic unfolding method in perforated domains, we obtain, following the values of γ, different Darcy's laws of typeMu= −N∇p+Fwith suitable matricesMandNwithFdepending on the right-hand side in the bulk term and in the boundary condition.

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28

TORRESI, A. M., G. L. CALANDRINI, P. A. BONFILI, and J. L. MOIOLA. "GENERALIZED HOPF BIFURCATION IN A FREQUENCY DOMAIN FORMULATION." International Journal of Bifurcation and Chaos 22, no. 08 (2012): 1250197. http://dx.doi.org/10.1142/s0218127412501970.

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The multiplicity problem of limit cycles arising from a weak focus is addressed. The proposed methodology is a combination of the frequency domain method to handle some degenerate Hopf bifurcations with the powerful tools of the singularity theory. The frequency domain approach uses the harmonic balance method to study the existence of periodic solutions. On the other hand, the singularity theory provides the conditions and formulas for the classification problem of the unfolding of the singularity in terms of the distinguished and auxiliary parameters. A classical example introduced by Bautin

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29

Zappale, Elvira. "A note on dimension reduction for unbounded integrals with periodic microstructure via the unfolding method for slender domains." Evolution Equations & Control Theory 6, no. 2 (2017): 299–318. http://dx.doi.org/10.3934/eect.2017016.

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30

Mohammed, Mogtaba, and Noor Ahmed. "Homogenization and correctors of Robin problem for linear stochastic equations in periodically perforated domains." Asymptotic Analysis 120, no. 1-2 (2020): 123–49. http://dx.doi.org/10.3233/asy-191582.

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In this paper, we present homogenization and corrector results for stochastic linear parabolic equations in periodically perforated domains with non-homogeneous Robin conditions on the holes. We use the periodic unfolding method and probabilistic compactness results. Homogenization results presented in this paper are stochastic counterparts of some fundamental work given in [Cioranescu, Donato and Zaki in Port. Math. (N.S.) 63 (2006), 467–496]. We show that the sequence of solutions of the original problem converges in suitable topologies to the solution of a homogenized problem, which is a pa

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31

Gentile, Franco S., and Jorge L. Moiola. "Hopf Bifurcation Analysis of Distributed Delay Equations with Applications to Neural Networks." International Journal of Bifurcation and Chaos 25, no. 11 (2015): 1550156. http://dx.doi.org/10.1142/s0218127415501564.

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In this paper, we study how to capture smooth oscillations arising from delay-differential equations with distributed delays. For this purpose, we introduce a modified version of the frequency-domain method based on the Graphical Hopf Bifurcation Theorem. Our approach takes advantage of a simple interpretation of the distributed delay effect by means of some Laplace-transformed properties. Our theoretical results are illustrated through an example of two coupled neurons with distributed delay in their communication channel. For this system, we compute several bifurcation diagrams and approxima

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32

Belyamoun, M. H., and S. Zouhdi. "On the modeling of effective constitutive parameters of bianisotropic media by a periodic unfolding method in time and frequency domains." Applied Physics A 103, no. 3 (2011): 881–87. http://dx.doi.org/10.1007/s00339-011-6250-2.

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33

Griso, Georges, Larysa Khilkova, Julia Orlik, and Olena Sivak. "Homogenization of Perforated Elastic Structures." Journal of Elasticity 141, no. 2 (2020): 181–225. http://dx.doi.org/10.1007/s10659-020-09781-w.

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Abstract The paper is dedicated to the asymptotic behavior of $\varepsilon$ ε -periodically perforated elastic (3-dimensional, plate-like or beam-like) structures as $\varepsilon \to 0$ ε → 0 . In case of plate-like or beam-like structures the asymptotic reduction of dimension from $3D$ 3 D to $2D$ 2 D or $1D$ 1 D respectively takes place. An example of the structure under consideration can be obtained by a periodic repetition of an elementary “flattened” ball or cylinder for plate-like or beam-like structures in such a way that the contact surface between two neighboring balls/cylinders has a

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34

Nassar, H., A. Lebée, and L. Monasse. "Curvature, metric and parametrization of origami tessellations: theory and application to the eggbox pattern." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2197 (2017): 20160705. http://dx.doi.org/10.1098/rspa.2016.0705.

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Origami tessellations are particular textured morphing shell structures. Their unique folding and unfolding mechanisms on a local scale aggregate and bring on large changes in shape, curvature and elongation on a global scale. The existence of these global deformation modes allows for origami tessellations to fit non-trivial surfaces thus inspiring applications across a wide range of domains including structural engineering, architectural design and aerospace engineering. The present paper suggests a homogenization-type two-scale asymptotic method which, combined with standard tools from diffe

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35

Wang, Meiqi, Wenli Ma, Enli Chen, and Yujian Chang. "Study on a Class of Piecewise Nonlinear Systems with Fractional Delay." Shock and Vibration 2021 (October 7, 2021): 1–13. http://dx.doi.org/10.1155/2021/3411390.

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In this paper, a dynamic model of piecewise nonlinear system with fractional-order time delay is simplified. The amplitude frequency response equation of the dynamic model of piecewise nonlinear system with fractional-order time delay under periodic excitation is obtained by using the average method. It is found that the amplitude of the system changes when the external excitation frequency changes. At the same time, the amplitude frequency response characteristics of the system under different time delay parameters, different fractional-order parameters, and coefficient are studied. By analyz

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36

Li, Songtao, Qunhong Li, and Zhongchuan Meng. "Dynamic Behaviors of a Two-Degree-of-Freedom Impact Oscillator with Two-Sided Constraints." Shock and Vibration 2021 (April 1, 2021): 1–14. http://dx.doi.org/10.1155/2021/8854115.

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The dynamic model of a vibroimpact system subjected to harmonic excitation with symmetric elastic constraints is investigated with analytical and numerical methods. The codimension-one bifurcation diagrams with respect to frequency of the excitation are obtained by means of the continuation technique, and the different types of bifurcations are detected, such as grazing bifurcation, saddle-node bifurcation, and period-doubling bifurcation, which predicts the complexity of the system considered. Based on the grazing phenomenon obtained, the zero-time-discontinuity mapping is extended from the s

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37

Martin, Sébastien. "Influence of Multiscale Roughness Patterns in Cavitated Flows: Applications to Journal Bearings." Mathematical Problems in Engineering 2008 (2008): 1–26. http://dx.doi.org/10.1155/2008/439319.

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This paper deals with the coupling of two major problems in lubrication theory: cavitation phenomena and roughness of the surfaces in relative motion. Cavitation is defined as the rupture of the continuous film due to the formation of air bubbles, leading to the presence of a liquid-gas mixture. For this, the Elrod-Adams model (which is a pressure-saturation model) is classically used to describe the behavior of a cavitated thin film flow. In addition, in practical situations, the surfaces of the devices are rough, due to manufacturing processes which induce defaults. Thus, we study the behavi

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38

CIORANESCU, D. "Homogenization of nonlinear integrals via the periodic unfolding method." Comptes Rendus Mathematique, May 2004. http://dx.doi.org/10.1016/s1631-073x(04)00165-7.

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39

Mohammed, Mogtaba, and Waseem Asghar Khan. "Homogenization and Correctors for Stochastic Hyperbolic Equations in Domains with Periodically Distributed Holes." Journal of Multiscale Modelling 12, no. 03 (2021). http://dx.doi.org/10.1142/s1756973721500086.

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The goal of this paper is to present new results on homogenization and correctors for stochastic linear hyperbolic equations in periodically perforated domains with homogeneous Neumann conditions on the holes. The main tools are the periodic unfolding method, energy estimates, probabilistic and deterministic compactness results. The findings of this paper are stochastic counterparts of the celebrated work [D. Cioranescu, P. Donato and R. Zaki, The periodic unfolding method in perforated domains, Port. Math. (N.S.) 63 (2006) 467–496]. The convergence of the solution of the original problem to a

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40

Li, Yanqiu, and Lei Zhang. "Bifurcations in a General Delay Sel’kov–Schnakenberg Reaction–Diffusion System." International Journal of Bifurcation and Chaos 33, no. 16 (2023). http://dx.doi.org/10.1142/s021812742350195x.

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The dynamics of a delay Sel’kov–Schnakenberg reaction–diffusion system are explored. The existence and the occurrence conditions of the Turing and the Hopf bifurcations of the system are found by taking the diffusion coefficient and the time delay as the bifurcation parameters. Based on that, the existence of codimension-2 bifurcations including Turing–Turing, Hopf–Hopf and Turing–Hopf bifurcations are given. Using the center manifold theory and the normal form method, the universal unfolding of the Turing–Hopf bifurcation at the positive constant steady-state is demonstrated. According to the

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41

Bader, Fakhrielddine, Mostafa Bendahmane, Mazen Saad, and Raafat Talhouk. "Microscopic tridomain model of electrical activity in the heart with dynamical gap junctions. Part 2 – Derivation of the macroscopic tridomain model by unfolding homogenization method." Asymptotic Analysis, September 8, 2022, 1–32. http://dx.doi.org/10.3233/asy-221804.

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We study the homogenization of a novel microscopic tridomain system, allowing for a more detailed analysis of the properties of cardiac conduction than the classical bidomain and monodomain models. In (Acta Appl.Math. 179 (2022) 1–35), we detail this model in which gap junctions are considered as the connections between adjacent cells in cardiac muscle and could serve as alternative or supporting pathways for cell-to-cell electrical signal propagation. Departing from this microscopic cellular model, we apply the periodic unfolding method to derive the macroscopic tridomain model. Several diffi

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42

Raimondi, Federica. "Homogenization of a class of singular elliptic problems in two-component domains." Asymptotic Analysis, June 6, 2022, 1–27. http://dx.doi.org/10.3233/asy-221783.

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This paper deals with the homogenization of a quasilinear elliptic problem having a singular lower order term and posed in a two-component domain with an ε-periodic imperfect interface. We prescribe a Dirichlet condition on the exterior boundary, while we assume that the continuous heat flux is proportional to the jump of the solution on the interface via a function of order ε γ . We prove an homogenization result for − 1 < γ < 1 by means of the periodic unfolding method (see SIAM J. Math. Anal. 40 (2008) 1585–1620 and The Periodic Unfolding Method (2018) Springer), adapted to two-compon

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43

Neukamm, Stefan, Mario Varga, and Marcus Waurick. "Two-scale homogenization of abstract linear time-dependent PDEs." Asymptotic Analysis, November 10, 2020, 1–41. http://dx.doi.org/10.3233/asy-201654.

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Many time-dependent linear partial differential equations of mathematical physics and continuum mechanics can be phrased in the form of an abstract evolutionary system defined on a Hilbert space. In this paper we discuss a general framework for homogenization (periodic and stochastic) of such systems. The method combines a unified Hilbert space approach to evolutionary systems with an operator theoretic reformulation of the well-established periodic unfolding method in homogenization. Regarding the latter, we introduce a well-structured family of unitary operators on a Hilbert space that allow

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44

Donato, Patrizia, and Iulian Ţenţea. "Homogenization of an elastic double-porosity medium with imperfect interface via the periodic unfolding method." Boundary Value Problems 2013, no. 1 (2013). http://dx.doi.org/10.1186/1687-2770-2013-265.

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45

Pei, Lijun, and Chenyu Wang. "Periodic, Quasi-Periodic and Phase-Locked Oscillations and Stability in the Fiscal Dynamical Model with Tax Collection and Decision-Making Delays." International Journal of Bifurcation and Chaos 31, no. 16 (2021). http://dx.doi.org/10.1142/s0218127421502473.

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In this paper, we consider the complex dynamics of a fiscal dynamical model, which was improved from Wolfstetter classical growth cycle model by Sportelli et al. The main work of the present paper is to study the impact of fiscal policy delays on the national income adjustment processes using a dynamical method, such as double Hopf bifurcation analysis. We first use DDE-BIFTOOL to find the double Hopf bifurcation points of the system, and draw the bifurcation diagrams with two bifurcation parameters, i.e. the tax collection delay [Formula: see text] and the public expenditure decision-making d

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46

Ma, Hongru, and Yanbin Tang. "Homogenization of a semilinear elliptic problem in a thin composite domain with an imperfect interface." Mathematical Methods in the Applied Sciences, August 19, 2023. http://dx.doi.org/10.1002/mma.9628.

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In this paper, we consider the asymptotic behavior of a semilinear elliptic problem in a thin two‐composite domain with an imperfect interface, where the flux is discontinuous. For this thin domain, both the height and the period are of order . We first use Minty–Browder theorem to prove the well‐posedness of the problem and then apply the periodic unfolding method to obtain the limit problems and some corrector results for three cases of a real parameter , and , respectively. To deal with the semilinear terms, the extension operator and the averaged function are used.

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47

Amar, M., D. Andreucci, and C. Timofte. "Interface potential in composites with general imperfect transmission conditions." Zeitschrift für angewandte Mathematik und Physik 74, no. 5 (2023). http://dx.doi.org/10.1007/s00033-023-02094-7.

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AbstractThe model analyzed in this paper has its origins in the description of composites made by a hosting medium containing a periodic array of inclusions coated by a thin layer consisting of sublayers of two different materials. This two-phase coating material is such that the external part has a low diffusivity in the orthogonal direction, while the internal one has high diffusivity along the tangential direction. In a previous paper (Amar in IFB 21:41–59, 2019), by means of a concentration procedure, the internal layer was replaced by an imperfect interface. The present paper is concerned

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48

Grant Kirkland, W., and S. C. Sinha. "Symbolic Computation of Quantities Associated With Time-Periodic Dynamical Systems1." Journal of Computational and Nonlinear Dynamics 11, no. 4 (2016). http://dx.doi.org/10.1115/1.4033382.

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Many dynamical systems can be modeled by a set of linear/nonlinear ordinary differential equations with periodic time-varying coefficients. The state transition matrix (STM) Φ(t,α), associated with the linear part of the equation, can be expressed in terms of the periodic Lyapunov–Floquét (L-F) transformation matrix Q(t,α) and a time-invariant matrix R(α) containing a set of symbolic system parameters α. Computation of Q(t,α) and R(α) in symbolic form as a function of α is of paramount importance in stability, bifurcation analysis, and control system design. In earlier studies, since Q(t,α) an

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49

Nandakumaran, Akambadath, and Abu Sufian. "Oscillating PDE in a rough domain with a curved interface: homogenization of an optimal control problem." ESAIM: Control, Optimisation and Calculus of Variations, July 21, 2020. http://dx.doi.org/10.1051/cocv/2020045.

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Homogenization of an elliptic PDE with periodic oscillating coefficients and an associated optimal control problems with energy type cost functional is considered. The domain is a 3-dimensional region (method applies to any $n$ dimensional region) with oscillating boundary, where the base of the oscillation is curved and it is given by a Lipschitz function. Further, we consider a general elliptic PDE with oscillating coefficients. We also include very general type cost functional of Dirichlet type given with oscillating coefficients which can be different from the coefficient matrix of the equ

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Yu, Guodong, Zewen Wu, Zhen Zhan, Mikhail I. Katsnelson, and Shengjun Yuan. "Dodecagonal bilayer graphene quasicrystal and its approximants." npj Computational Materials 5, no. 1 (2019). http://dx.doi.org/10.1038/s41524-019-0258-0.

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AbstractDodecagonal bilayer graphene quasicrystal has 12-fold rotational order but lacks translational symmetry which prevents the application of band theory. In this paper, we study the electronic and optical properties of graphene quasicrystal with large-scale tight-binding calculations involving more than ten million atoms. We propose a series of periodic approximants which reproduce accurately the properties of quasicrystal within a finite unit cell. By utilizing the band-unfolding method on the smallest approximant with only 2702 atoms, the effective band structure of graphene quasicrysta

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