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Journal articles on the topic 'Hohenberg'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 March 2023

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1

BELKASRI, A., and J. L. RICHARD. "REMARK ON THE EXISTENCE OF LONG-RANGE ORDER IN QUASI-TWO-DIMENSIONAL HUBBARD MODEL." Modern Physics Letters B 10, no. 08 (April 10, 1996): 341–46. http://dx.doi.org/10.1142/s0217984996000389.

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Recently in many works on the mechanism of high temperature superconductivity (see for example Refs. 1–6), quasi-averages like <ck↑c−k↓> were considered even in the case of a dimension less or equal two. But it is well known from the old work of Hohenberg7 that these quasi-averages are zero at T≠0 in case of 1 and 2 dimensions. In this communication we generalize the Hohenberg’s result to any kind of Hubbard type model on lattice and prove that in the case of quasi-two-dimension, the theorem of Hohenberg is not in contradiction with having <ck↑c−k↓>≠0 (at T≠0). In practice this makes sense to compare the data for a thin film (which can be considered as quasi-2D system) to the theoretical analysis based on quasi-two-dimensional models, but not for strictly two-dimensional case.

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2

Autorenlos. "Hohenberg." Zeitschrift des Historischen Vereins für das Württembergische Franken 6, no. 1 (October 19, 2022): 173. http://dx.doi.org/10.53458/zhvwf.v6i1.4202.

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3

Guo, Yanfeng, Chunxiao Guo, and Donglong Li. "Existence and Approximation of Manifolds for the Swift-Hohenberg Equation with a Parameter." Discrete Dynamics in Nature and Society 2018 (July 12, 2018): 1–6. http://dx.doi.org/10.1155/2018/1423170.

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The existence and approximation of manifolds for the Swift-Hohenberg equation with a proper parameter have mainly been studied. Using the backward-forward systems from Swift-Hohenberg equation, the existence and specific representation forms of manifolds for Swift-Hohenberg equation with a parameter have been obtained. Meanwhile, we make use of technique of deposition of lower and higher frequency spaces of solutions and assume the reduced system to obtain the main numeration approximation system of approximation solution for the original system Swift-Hohenberg equation with a proper parameter.

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4

Swift, Jack, and Pierre Hohenberg. "Swift-Hohenberg equation." Scholarpedia 3, no. 9 (2008): 6395. http://dx.doi.org/10.4249/scholarpedia.6395.

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5

GAO, HONGJUN, and QINGKUN XIAO. "BIFURCATION ANALYSIS OF THE 1D AND 2D GENERALIZED SWIFT–HOHENBERG EQUATION." International Journal of Bifurcation and Chaos 20, no. 03 (March 2010): 619–43. http://dx.doi.org/10.1142/s0218127410025922.

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In this paper, bifurcation of the generalized Swift–Hohenberg equation is considered. We first study the bifurcation of the generalized Swift–Hohenberg equation in one spatial dimension with three kinds of boundary conditions. With the help of Liapunov–Schmidt reduction, the original equation is transformed to the reduced system, and then the bifurcation analysis is carried out. Secondly, bifurcation of the generalized Swift–Hohenberg equation in two spatial dimensions with periodic boundary conditions is also considered, using the perturbation method, asymptotic expressions of the nontrivial solutions bifurcated from the trivial solution are obtained. Moreover, the stability of the bifurcated solutions is discussed.

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6

Latas, S. C., M. F. S. Ferreira, and M. Facão. "Swift–Hohenberg soliton explosions." Journal of the Optical Society of America B 35, no. 9 (August 27, 2018): 2266. http://dx.doi.org/10.1364/josab.35.002266.

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7

Guo, Yanfeng, Chunxiao Guo, and Yongping Xi. "Fractal Dimension for the Nonautonomous Stochastic Fifth-Order Swift–Hohenberg Equation." Complexity 2020 (September 16, 2020): 1–11. http://dx.doi.org/10.1155/2020/8864585.

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Some dynamics behaviors for the nonautonomous stochastic fifth-order Swift–Hohenberg equation with additive white noise are considered. The existence of pullback random attractors for the nonautonomous stochastic fifth-order Swift–Hohenberg equation with some properties is mainly investigated on the bounded domain and unbounded domain, through the Ornstein–Uhlenbeck transformation and tail-term estimates. Furthermore, on the basis of some conditions, the finiteness of fractal dimension of random attractor is proved.

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8

Wang, Jingying, and Shuying Zhai. "A Fast and Efficient Numerical Algorithm for the Nonlocal Conservative Swift–Hohenberg Equation." Mathematical Problems in Engineering 2020 (January 6, 2020): 1–9. http://dx.doi.org/10.1155/2020/7012483.

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In this paper, we consider a new Swift–Hohenberg equation, where the total mass of this model is conserved through a nonlocal Lagrange multiplier. Based on the operator splitting method and spectral method, a fast and efficient numerical algorithm is proposed. Three numerical examples in both two and three dimensions are provided to illustrate that the proposed algorithm is a practical, accurate, and efficient simulation tool for the nonlocal Swift–Hohenberg equation.

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9

Gao, Peng. "The stochastic Swift–Hohenberg equation." Nonlinearity 30, no. 9 (August 14, 2017): 3516–59. http://dx.doi.org/10.1088/1361-6544/aa7e99.

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10

Lega, J., J. V. Moloney, and A. C. Newell. "Swift-Hohenberg Equation for Lasers." Physical Review Letters 73, no. 22 (November 28, 1994): 2978–81. http://dx.doi.org/10.1103/physrevlett.73.2978.

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11

Wei�, Gunter, and Claudia Kunnert. "Herstellung Linearer Risse nach Hohenberg." Journal of Geometry 47, no. 1-2 (July 1993): 186–98. http://dx.doi.org/10.1007/bf01223817.

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12

Dehghan, Mehdi, Mostafa Abbaszadeh, Amirreza Khodadadian, and Clemens Heitzinger. "Galerkin proper orthogonal decomposition-reduced order method (POD-ROM) for solving generalized Swift-Hohenberg equation." International Journal of Numerical Methods for Heat & Fluid Flow 29, no. 8 (August 5, 2019): 2642–65. http://dx.doi.org/10.1108/hff-11-2018-0647.

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Purpose The current paper aims to develop a reduced order discontinuous Galerkin method for solving the generalized Swift–Hohenberg equation with application in biological science and mechanical engineering. The generalized Swift–Hohenberg equation is a fourth-order PDE; thus, this paper uses the local discontinuous Galerkin (LDG) method for it. Design/methodology/approach At first, the spatial direction has been discretized by the LDG technique, as this process results in a nonlinear system of equations based on the time variable. Thus, to achieve more accurate outcomes, this paper uses an exponential time differencing scheme for solving the obtained system of ordinary differential equations. Finally, to decrease the used CPU time, this study combines the proper orthogonal decomposition approach with the LDG method and obtains a reduced order LDG method. The circular and rectangular computational domains have been selected to solve the generalized Swift–Hohenberg equation. Furthermore, the energy stability for the semi-discrete LDG scheme has been discussed. Findings The results show that the new numerical procedure has not only suitable and acceptable accuracy but also less computational cost compared to the local DG without the proper orthogonal decomposition (POD) approach. Originality/value The local DG technique is an efficient numerical procedure for solving models in the fluid flow. The current paper combines the POD approach and the local LDG technique to solve the generalized Swift–Hohenberg equation with application in the fluid mechanics. In the new technique, the computational cost and the used CPU time of the local DG have been reduced.

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13

Scheiblechner, Wolfgang. "Nachschmiedung der Spatha von Hohenberg, Steiermark." Archaeologia Austriaca 89, no. 1 (2008): 255–68. http://dx.doi.org/10.1553/archaeologia89s255.

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14

Schindlmayr, Arno. "Universality of the Hohenberg–Kohn functional." American Journal of Physics 67, no. 10 (October 1999): 933–34. http://dx.doi.org/10.1119/1.19156.

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15

McCalla, S. G., and B. Sandstede. "Spots in the Swift--Hohenberg Equation." SIAM Journal on Applied Dynamical Systems 12, no. 2 (January 2013): 831–77. http://dx.doi.org/10.1137/120882111.

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16

Bylander, D. M., and Leonard Kleinman. "Hohenberg-Kohn kernel K(r-r’)." Physical Review B 36, no. 3 (July 15, 1987): 1775–78. http://dx.doi.org/10.1103/physrevb.36.1775.

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17

Pan, Xiao-Yin, and Viraht Sahni. "Corollary to the Hohenberg-Kohn theorem." International Journal of Quantum Chemistry 95, no. 4-5 (2003): 387–93. http://dx.doi.org/10.1002/qua.10595.

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18

Jani, Haresh P., and Twinkle R. Singh. "Some examples of Swift–Hohenberg equation." Examples and Counterexamples 2 (November 2022): 100090. http://dx.doi.org/10.1016/j.exco.2022.100090.

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19

Prakasha, D. G., P. Veeresha, and Haci Mehmet Baskonus. "Residual Power Series Method for Fractional Swift–Hohenberg Equation." Fractal and Fractional 3, no. 1 (March 7, 2019): 9. http://dx.doi.org/10.3390/fractalfract3010009.

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In this paper, the approximated analytical solution for the fractional Swift–Hohenberg (S–H) equation has been investigated with the help of the residual power series method (RPSM). To ensure the applicability and efficiency of the proposed technique, we consider a non-linear fractional order Swift–Hohenberg equation in the presence and absence of dispersive terms. The effect of bifurcation and dispersive parameters with physical importance on the probability density function for distinct fractional Brownian and standard motions are studied and presented through plots. The results obtained show that the proposed technique is simple to implement and very effective for analyzing the complex problems that arise in connected areas of science and technology.

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20

Lee, Hyun Geun. "An Efficient and Accurate Method for the Conservative Swift–Hohenberg Equation and Its Numerical Implementation." Mathematics 8, no. 9 (September 4, 2020): 1502. http://dx.doi.org/10.3390/math8091502.

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The conservative Swift–Hohenberg equation was introduced to reformulate the phase-field crystal model. A challenge in solving the conservative Swift–Hohenberg equation numerically is how to treat the nonlinear term to preserve mass conservation without compromising efficiency and accuracy. To resolve this problem, we present a linear, high-order, and mass conservative method by placing the linear and nonlinear terms in the implicit and explicit parts, respectively, and employing the implicit-explicit Runge–Kutta method. We show analytically that the method inherits the mass conservation. Numerical experiments are presented demonstrating the efficiency and accuracy of the proposed method. In particular, long time simulation for pattern formation in 2D is carried out, where the phase diagram can be observed clearly. The MATLAB code for numerical implementation of the proposed method is provided in Appendix.

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21

Gao, Peng. "Averaging principles for the Swift-Hohenberg equation." Communications on Pure & Applied Analysis 19, no. 1 (2020): 293–310. http://dx.doi.org/10.3934/cpaa.2020016.

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22

Lammert, Paul E. "In search of the Hohenberg-Kohn theorem." Journal of Mathematical Physics 59, no. 4 (April 2018): 042110. http://dx.doi.org/10.1063/1.5034215.

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23

Mohammed, Wael W., Dirk Blömker, and Konrad Klepel. "Modulation Equation for Stochastic Swift--Hohenberg Equation." SIAM Journal on Mathematical Analysis 45, no. 1 (January 2013): 14–30. http://dx.doi.org/10.1137/110846336.

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24

Li, Tie-cheng, and Pei-qing Tong. "Hohenberg-Kohn theorem for time-dependent ensembles." Physical Review A 31, no. 3 (March 1, 1985): 1950–51. http://dx.doi.org/10.1103/physreva.31.1950.

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25

Siegel, Matt. "Dynes, Hohenberg and Larkin Receive London Prize." Physics Today 43, no. 9 (September 1990): 119. http://dx.doi.org/10.1063/1.2810698.

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26

HARAGUS, MARIANA, and ARND SCHEEL. "Grain boundaries in the Swift–Hohenberg equation." European Journal of Applied Mathematics 23, no. 6 (August 10, 2012): 737–59. http://dx.doi.org/10.1017/s0956792512000241.

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We study the existence of grain boundaries in the Swift–Hohenberg equation. The analysis relies on a spatial dynamics formulation of the existence problem and a centre-manifold reduction. In this setting, the grain boundaries are found as heteroclinic orbits of a reduced system of ordinary differential equations in normal form. We show persistence of the leading-order approximation using transversality induced by wavenumber selection.

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27

Haragus, Mariana, and Arnd Scheel. "Dislocations in an Anisotropic Swift-Hohenberg Equation." Communications in Mathematical Physics 315, no. 2 (September 15, 2012): 311–35. http://dx.doi.org/10.1007/s00220-012-1569-x.

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28

Hoang, Tung, and Hyung Ju Hwang. "Dynamic pattern formation in Swift-Hohenberg equations." Quarterly of Applied Mathematics 69, no. 3 (April 26, 2011): 603–12. http://dx.doi.org/10.1090/s0033-569x-2011-01260-1.

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29

Longhi, S., and A. Geraci. "Swift-Hohenberg equation for optical parametric oscillators." Physical Review A 54, no. 5 (November 1, 1996): 4581–84. http://dx.doi.org/10.1103/physreva.54.4581.

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30

Roidos, Nikolaos. "The Swift-Hohenberg equation on conic manifolds." Journal of Mathematical Analysis and Applications 481, no. 2 (January 2020): 123491. http://dx.doi.org/10.1016/j.jmaa.2019.123491.

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31

Datta, S. N. "Relativistic extension of the Hohenberg-Kohn theorem." Pramana 28, no. 6 (June 1987): 633–39. http://dx.doi.org/10.1007/bf02892864.

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32

Jones, J. C. "On the application of the Hohenberg correlation." Fuel 88, no. 11 (November 2009): 2325. http://dx.doi.org/10.1016/j.fuel.2009.02.027.

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33

Zhou, Aihui. "A mathematical aspect of Hohenberg-Kohn theorem." Science China Mathematics 62, no. 1 (September 17, 2018): 63–68. http://dx.doi.org/10.1007/s11425-018-9337-2.

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34

Carey, James W. "John Hohenberg, John Hohenberg: The Pursuit of Excellence. Gainesville: University Press of Florid, 1995. 295 pp. Cloth, $39.95." American Journalism 12, no. 4 (October 1995): 505–8. http://dx.doi.org/10.1080/08821127.1995.10731778.

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35

Ban, Tao, and Run-Qing Cui. "He’s homotopy perturbation method for solving time fractional Swift-Hohenberg equations." Thermal Science 22, no. 4 (2018): 1601–5. http://dx.doi.org/10.2298/tsci1804601b.

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This paper find the most effective method to solve the time-fractional Swift-Hohenberg equation with cubicquintic non-linearity by combining the homotopy perturbation method and the fractional complex transform. The solution reveals some intermittent properties of thermal physics.

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36

Khanolkar, Ankita, Yimin Zang, and Andy Chong. "Complex Swift Hohenberg equation dissipative soliton fiber laser." Photonics Research 9, no. 6 (May 24, 2021): 1033. http://dx.doi.org/10.1364/prj.419686.

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37

Han, Jongmin, and Masoud Yari. "Dynamic bifurcation of the complex Swift-Hohenberg equation." Discrete & Continuous Dynamical Systems - B 11, no. 4 (2009): 875–91. http://dx.doi.org/10.3934/dcdsb.2009.11.875.

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38

Mehofer, Mathias. "Technologische Analysen an der Spatha von Hohenberg, Steiermark." Archaeologia Austriaca 89, no. 1 (2008): 251–54. http://dx.doi.org/10.1553/archaeologia89s251.

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39

Han, Jong-Min, and Masoud Yari. "DYNAMIC BIFURCATION OF THE PERIODIC SWIFT-HOHENBERG EQUATION." Bulletin of the Korean Mathematical Society 49, no. 5 (September 30, 2012): 923–37. http://dx.doi.org/10.4134/bkms.2012.49.5.923.

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40

Choi, Yuncherl, Jongmin Han, and Jungho Park. "Dynamical Bifurcation of the Generalized Swift–Hohenberg Equation." International Journal of Bifurcation and Chaos 25, no. 08 (July 2015): 1550095. http://dx.doi.org/10.1142/s0218127415500959.

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In this paper, we prove that the generalized Swift–Hohenberg equation bifurcates from the trivial states to an attractor as the control parameter α passes through critical points. The bifurcation is divided into two groups according to the dimension of the center manifolds. We show that the bifurcated attractor is homeomorphic to S1 or S3 and it contains invariant circles of static solutions. We provide a criterion on the quadratic instability parameter μ which determines the bifurcation to be supercritical or subcritical.

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41

Burke, John, and Jonathan H. P. Dawes. "Localized States in an Extended Swift–Hohenberg Equation." SIAM Journal on Applied Dynamical Systems 11, no. 1 (January 2012): 261–84. http://dx.doi.org/10.1137/110843976.

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42

Lloyd, David, and Björn Sandstede. "Localized radial solutions of the Swift–Hohenberg equation." Nonlinearity 22, no. 2 (January 20, 2009): 485–524. http://dx.doi.org/10.1088/0951-7715/22/2/013.

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43

Pass, Brendan. "Remarks on the semi-classical Hohenberg–Kohn functional." Nonlinearity 26, no. 9 (August 22, 2013): 2731–44. http://dx.doi.org/10.1088/0951-7715/26/9/2731.

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44

Haragus, Mariana, and Arnd Scheel. "Interfaces between rolls in the Swift-Hohenberg equation." International Journal of Dynamical Systems and Differential Equations 1, no. 2 (2007): 89. http://dx.doi.org/10.1504/ijdsde.2007.016510.

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45

Kulagin, N. E., L. M. Lerman, and T. G. Shmakova. "On radial solutions of the Swift-Hohenberg equation." Proceedings of the Steklov Institute of Mathematics 261, no. 1 (July 2008): 183–203. http://dx.doi.org/10.1134/s0081543808020144.

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46

Peletier, L. A., and J. F. Williams. "Some Canonical Bifurcations in the Swift–Hohenberg Equation." SIAM Journal on Imaging Sciences 1, no. 1 (2008): 208. http://dx.doi.org/10.1137/test7.

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47

Vilar, J. M. G., and J. M. Rubí. "Spatiotemporal Stochastic Resonance in the Swift-Hohenberg Equation." Physical Review Letters 78, no. 15 (April 14, 1997): 2886–89. http://dx.doi.org/10.1103/physrevlett.78.2886.

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48

Ouchi, Katsuya, and Hirokazu Fujisaka. "Phase ordering kinetics in the Swift-Hohenberg equation." Physical Review E 54, no. 4 (October 1, 1996): 3895–98. http://dx.doi.org/10.1103/physreve.54.3895.

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49

Xiao, Qingkun, and Hongjun Gao. "Bifurcation analysis of a modified Swift–Hohenberg equation." Nonlinear Analysis: Real World Applications 11, no. 5 (October 2010): 4451–64. http://dx.doi.org/10.1016/j.nonrwa.2010.05.028.

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50

Görling, Andreas. "Density-functional theory beyond the Hohenberg-Kohn theorem." Physical Review A 59, no. 5 (May 1, 1999): 3359–74. http://dx.doi.org/10.1103/physreva.59.3359.

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