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Mangioni SE, Deza RR. Stochastic dissipative solitons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:032116. [PMID: 26465435 DOI: 10.1103/physreve.92.032116] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2013] [Indexed: 06/05/2023]
Abstract
By the effect of aggregating currents, some systems display an effective diffusion coefficient that becomes negative in a range of the order parameter, giving rise to bistability among homogeneous states (HSs). By applying a proper multiplicative noise, localized (pinning) states are shown to become stable at the expense of one of the HSs. They are, however, not static, but their location fluctuates with a variance that increases with the noise intensity. The numerical results are supported by an analytical estimate in the spirit of the so-called solvability condition.
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Affiliation(s)
- Sergio E Mangioni
- Instituto de Física de Mar del Plata, Universidad Nacional de Mar del Plata, and CONICET, Deán Funes 3350, B7602AYL Mar del Plata, Buenos Aires, Argentina
| | - Roberto R Deza
- Instituto de Física de Mar del Plata, Universidad Nacional de Mar del Plata, and CONICET, Deán Funes 3350, B7602AYL Mar del Plata, Buenos Aires, Argentina
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2
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Welch KJ, Hastings-Hauss I, Parthasarathy R, Corwin EI. Ballistic and diffusive dynamics in a two-dimensional ideal gas of macroscopic chaotic Faraday waves. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:042143. [PMID: 24827228 DOI: 10.1103/physreve.89.042143] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2013] [Indexed: 06/03/2023]
Abstract
We have constructed a macroscopic driven system of chaotic Faraday waves whose statistical mechanics, we find, are surprisingly simple, mimicking those of a thermal gas. We use real-time tracking of a single floating probe, energy equipartition, and the Stokes-Einstein relation to define and measure a pseudotemperature and diffusion constant and then self-consistently determine a coefficient of viscous friction for a test particle in this pseudothermal gas. Because of its simplicity, this system can serve as a model for direct experimental investigation of nonequilibrium statistical mechanics, much as the ideal gas epitomizes equilibrium statistical mechanics.
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Affiliation(s)
- Kyle J Welch
- Materials Science Institute and Department of Physics, University of Oregon, Eugene, Oregon 97403, USA
| | - Isaac Hastings-Hauss
- Materials Science Institute and Department of Physics, University of Oregon, Eugene, Oregon 97403, USA
| | - Raghuveer Parthasarathy
- Materials Science Institute and Department of Physics, University of Oregon, Eugene, Oregon 97403, USA
| | - Eric I Corwin
- Materials Science Institute and Department of Physics, University of Oregon, Eugene, Oregon 97403, USA
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Clerc MG, Garcia-Ñustes MA, Zárate Y, Coulibaly S. Phase shielding soliton in parametrically driven systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:052915. [PMID: 23767606 DOI: 10.1103/physreve.87.052915] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2012] [Revised: 02/07/2013] [Indexed: 06/02/2023]
Abstract
Parametrically driven extended systems exhibit dissipative localized states. Analytical solutions of these states are characterized by a uniform phase and a bell-shaped modulus. Recently, a type of dissipative localized state with a nonuniform phase structure has been reported: the phase shielding solitons. Using the parametrically driven and damped nonlinear Schrödinger equation, we investigate the main properties of this kind of solution in one and two dimensions and develop an analytical description for its structure and dynamics. Numerical simulations are consistent with our analytical results, showing good agreement. A numerical exploration conducted in an anisotropic ferromagnetic system in one and two dimensions indicates the presence of phase shielding solitons. The structure of these dissipative solitons is well described also by our analytical results. The presence of corrective higher-order terms is relevant in the description of the observed phase dynamical behavior.
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Affiliation(s)
- Marcel G Clerc
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile.
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Clerc MG, Coulibaly S, Garcia-Ñustes MA, Zárate Y. Dissipative localized States with shieldlike phase structure. PHYSICAL REVIEW LETTERS 2011; 107:254102. [PMID: 22243078 DOI: 10.1103/physrevlett.107.254102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2011] [Indexed: 05/31/2023]
Abstract
A novel type of parametrically excited dissipative solitons is unveiled. It differs from the well-known solitons with constant phase by an intrinsically dynamical evolving shell-type phase front. Analytical and numerical characterizations are proposed, displaying quite a good agreement. In one spatial dimension, the system shows three types of stationary solitons with shell-like structure whereas in two spatial dimensions it displays only one, characterized by a π-phase jump far from the soliton position.
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Affiliation(s)
- Marcel G Clerc
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
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Clerc MG, Coulibaly S, Gordillo L, Mujica N, Navarro R. Coalescence cascade of dissipative solitons in parametrically driven systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:036205. [PMID: 22060473 DOI: 10.1103/physreve.84.036205] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2011] [Indexed: 05/31/2023]
Abstract
Parametrically driven spatially extended systems exhibit uniform oscillations which are modulationally unstable. The resulting periodic state evolves to the creation of a gas of dissipative solitons. Driven by the interaction of dissipative solitons, the multisoliton state undergoes a cascade of coalescence processes, where the average soliton separation distance obeys a temporal self-similar law. Starting from the soliton pair interaction law, we have derived analytically and characterized the law of this multisoliton coarsening process. A comparison of numerical results obtained with different models such as the parametrically driven damped nonlinear Schrödinger equation, a vertically driven chain of pendula, and a parametrically forced magnetic wire, shows remarkable agreement. Both phenomena, the pair interaction law and the coarsening process, are also observed experimentally in a quasi-one-dimensional layer of Newtonian fluid which is oscillated vertically.
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Affiliation(s)
- M G Clerc
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
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Barashenkov IV, Zemlyanaya EV, van Heerden TC. Time-periodic solitons in a damped-driven nonlinear Schrödinger equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:056609. [PMID: 21728684 DOI: 10.1103/physreve.83.056609] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2010] [Indexed: 05/31/2023]
Abstract
Time-periodic solitons of the parametrically driven damped nonlinear Schrödinger equation are obtained as solutions of the boundary-value problem on a two-dimensional spatiotemporal domain. We follow the transformation of the periodic solitons as the strength of the driver is varied. The resulting bifurcation diagrams provide a natural explanation for the overall form and details of the attractor chart compiled previously via direct numerical simulations. In particular, the diagrams confirm the occurrence of the period-doubling transition to temporal chaos for small values of dissipation and the absence of such transitions for larger dampings. This difference in the soliton's response to the increasing driving strength can be traced to the difference in the radiation frequencies in the two cases. Finally, we relate the soliton's temporal chaos to the homoclinic bifurcation.
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Affiliation(s)
- I V Barashenkov
- Department of Mathematics, University of Cape Town, Rondebosch 7701, South Africa.
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Gomez H, París J. Numerical simulation of asymptotic states of the damped Kuramoto-Sivashinsky equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:046702. [PMID: 21599329 DOI: 10.1103/physreve.83.046702] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2010] [Revised: 02/21/2011] [Indexed: 05/30/2023]
Abstract
The damped Kuramoto-Sivashinsky equation has emerged as a fundamental tool for the understanding of the onset and evolution of secondary instabilities in a wide range of physical phenomena. Most existing studies about this equation deal with its asymptotic states on one-dimensional settings or on periodic square domains. We utilize a large-scale numerical simulation to investigate the asymptotic states of the damped Kuramoto-Sivashinsky equation on annular two-dimensional geometries and three-dimensional domains. To this end, we propose an accurate, efficient, and robust algorithm based on a recently introduced numerical methodology, namely, isogeometric analysis. We compared our two-dimensional results with several experiments of directed percolation on square and annular geometries, and found qualitative agreement.
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Affiliation(s)
- Hector Gomez
- University of A Coruña, Campus de Elviña s/n, 15071, A Coruña, Spain.
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Kenig E, Malomed BA, Cross MC, Lifshitz R. Intrinsic localized modes in parametrically driven arrays of nonlinear resonators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:046202. [PMID: 19905410 DOI: 10.1103/physreve.80.046202] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2009] [Revised: 08/13/2009] [Indexed: 05/28/2023]
Abstract
We study intrinsic localized modes (ILMs), or solitons, in arrays of parametrically driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). The analysis is performed using an amplitude equation in the form of a nonlinear Schrödinger equation with a term corresponding to nonlinear damping (also known as a forced complex Ginzburg-Landau equation), which is derived directly from the underlying equations of motion of the coupled resonators, using the method of multiple scales. We investigate the creation, stability, and interaction of ILMs, show that they can form bound states, and that under certain conditions one ILM can split into two. Our findings are confirmed by simulations of the underlying equations of motion of the resonators, suggesting possible experimental tests of the theory.
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Affiliation(s)
- Eyal Kenig
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel
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Clerc MG, Coulibaly S, Mujica N, Navarro R, Sauma T. Soliton pair interaction law in parametrically driven Newtonian fluid. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2009; 367:3213-3226. [PMID: 19620119 DOI: 10.1098/rsta.2009.0072] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
An experimental and theoretical study of the motion and interaction of the localized excitations in a vertically driven small rectangular water container is reported. Close to the Faraday instability, the parametrically driven damped nonlinear Schrödinger equation models this system. This model allows one to characterize the pair interaction law between localized excitations. Experimentally we have a good agreement with the pair interaction law.
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Affiliation(s)
- M G Clerc
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile.
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Dror N, Malomed BA. Spontaneous symmetry breaking in coupled parametrically driven waveguides. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:016605. [PMID: 19257158 DOI: 10.1103/physreve.79.016605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2008] [Indexed: 05/27/2023]
Abstract
We introduce a system of linearly coupled parametrically driven damped nonlinear Schrödinger equations, which models a laser based on a nonlinear dual-core waveguide with parametric amplification symmetrically applied to both cores. The model may also be realized in terms of parallel ferromagnetic films, in which the parametric gain is provided by an external field. We analyze spontaneous symmetry breaking (SSB) of fundamental and multiple solitons in this system, which was not studied systematically before in linearly coupled dissipative systems with intrinsic nonlinearity. For fundamental solitons, the analysis reveals three distinct SSB scenarios. Unlike the standard dual-core-fiber model, the present system gives rise to a vast bistability region, which may be relevant to applications. Other noteworthy findings are restabilization of the symmetric soliton after it was destabilized by the SSB bifurcation, and the existence of a generic situation with all solitons unstable in the single-component (decoupled) model, while both symmetric and asymmetric solitons may be stable in the coupled system. The stability of the asymmetric solitons is identified via direct simulations, while for symmetric and antisymmetric ones the stability is verified too through the computation of stability eigenvalues, families of antisymmetric solitons being entirely unstable. In this way, full stability maps for the symmetric solitons are produced. We also investigate the SSB bifurcation of two-soliton bound states (it breaks the symmetry between the two components, while the two peaks in the shape of the soliton remain mutually symmetric). The family of the asymmetric double-peak states may decouple from its symmetric counterpart, being no longer connected to it by the bifurcation, with a large portion of the asymmetric family remaining stable.
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Affiliation(s)
- Nir Dror
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
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Gaididei YB, Christiansen PL. Ising and Bloch domain walls in a two-dimensional parametrically driven Ginzburg-Landau equation model with nonlinearity management. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:026610. [PMID: 18850965 DOI: 10.1103/physreve.78.026610] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2008] [Indexed: 05/26/2023]
Abstract
We study a parametrically driven Ginzburg-Landau equation model with nonlinear management. The system is made of laterally coupled long active waveguides placed along a circumference. Stationary solutions of three kinds are found: periodic Ising states and two types of Bloch states, staggered and unstaggered. The stability of these states is investigated analytically and numerically. The nonlinear dynamics of the Bloch states are described by a complex Ginzburg-Landau equation with linear and nonlinear parametric driving. The switching between the staggered and unstaggered Bloch states under the action of direct ac forces is shown.
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Affiliation(s)
- Yu B Gaididei
- Bogolyubov Institute for Theoretical Physics, Metrologichna Street 14 B, 03680, Kiev, Ukraine
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Clerc MG, Coulibaly S, Laroze D. Localized states beyond the asymptotic parametrically driven amplitude equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:056209. [PMID: 18643144 DOI: 10.1103/physreve.77.056209] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2007] [Revised: 01/08/2008] [Indexed: 05/26/2023]
Abstract
We study theoretically a family of localized states which asymptotically connect a uniform oscillatory state in the magnetization of an easy-plane ferromagnetic spin chain when an oscillatory magnetic field is applied and in a parametrically driven damped pendula chain. The conventional approach to these systems, the parametrically driven damped nonlinear Schrödinger equation, does not account for these states. Adding higher order terms to this model we were able to obtain these localized structures.
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Affiliation(s)
- M G Clerc
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
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Barashenkov IV, Woodford SR. Complexes of stationary domain walls in the resonantly forced Ginsburg-Landau equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:026613. [PMID: 15783447 DOI: 10.1103/physreve.71.026613] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2004] [Revised: 11/15/2004] [Indexed: 05/24/2023]
Abstract
The parametrically driven Ginsburg-Landau equation has well-known stationary solutions-the so-called Bloch and Ne el, or Ising, walls. In this paper, we construct an explicit stationary solution describing a bound state of two walls. We also demonstrate that stationary complexes of more than two walls do not exist.
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Affiliation(s)
- I V Barashenkov
- Department of Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa
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Vega JM, Rüdiger S, Viñals J. Phenomenological model of weakly damped Faraday waves and the associated mean flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:046306. [PMID: 15600518 DOI: 10.1103/physreve.70.046306] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2004] [Indexed: 05/24/2023]
Abstract
A phenomenological model of parametric surface waves (Faraday waves) is introduced in the limit of small viscous dissipation that accounts for the coupling between surface motion and slowly varying streaming and large-scale flows (mean flow). The primary bifurcation of the model is to a set of standing waves (stripes, given the functional form of the model nonlinearities chosen here). Our results for the secondary instabilities of the primary wave show that the mean flow leads to a weak destabilization of the base state against Eckhaus and transverse amplitude modulation instabilities, and introduces a longitudinal oscillatory instability which is absent without the coupling. We compare our results with recent one-dimensional amplitude equations for this system systematically derived from the governing hydrodynamic equations.
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Affiliation(s)
- José M Vega
- E.T.S.I. Aeronáuticos, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid, Spain
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Barashenkov IV, Cross S, Malomed BA. Multistable pulselike solutions in a parametrically driven Ginzburg-Landau equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:056605. [PMID: 14682904 DOI: 10.1103/physreve.68.056605] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2003] [Indexed: 05/24/2023]
Abstract
It is well known that pulselike solutions of the cubic complex Ginzburg-Landau equation are unstable but can be stabilized by the addition of quintic terms. In this paper we explore an alternative mechanism where the role of the stabilizing agent is played by the parametric driver. Our analysis is based on the numerical continuation of solutions in one of the parameters of the Ginzburg-Landau equation (the diffusion coefficient c), starting from the nonlinear Schrödinger limit (for which c=0). The continuation generates, recursively, a sequence of coexisting stable solutions with increasing number of humps. The sequence "converges" to a long pulse which can be interpreted as a bound state of two fronts with opposite polarities.
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Affiliation(s)
- I V Barashenkov
- Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa.
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Barashenkov IV, Woodford SR, Zemlyanaya EV. Parametrically driven dark solitons. PHYSICAL REVIEW LETTERS 2003; 90:054103. [PMID: 12633360 DOI: 10.1103/physrevlett.90.054103] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2002] [Indexed: 05/24/2023]
Abstract
We show that unlike the bright solitons, the parametrically driven kinks are immune from instabilities for all dampings and forcing amplitudes; they can also form stable bound states. In the undamped case, the two types of stable kinks and their complexes can travel with nonzero velocities.
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Affiliation(s)
- I V Barashenkov
- Department of Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa
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de Valcárcel GJ, Pérez-Arjona I, Roldán E. Domain walls and ising-BLOCH transitions in parametrically driven systems. PHYSICAL REVIEW LETTERS 2002; 89:164101. [PMID: 12398725 DOI: 10.1103/physrevlett.89.164101] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2000] [Revised: 06/27/2002] [Indexed: 05/24/2023]
Abstract
Parametrically driven systems sustaining sech solitons are shown to support a new kind of localized state. These structures are walls connecting two regions oscillating in antiphase that form in the parameter domain where the sech soliton is unstable. Depending on the parameter set the oppositely phased domains can be either spatially uniform or patterned. Both chiral (Bloch) and nonchiral (Ising) walls are found, which bifurcate one into the other via an Ising-Bloch transition. While Ising walls are at rest Bloch walls move and may display secondary bifurcations leading to chaotic wall motion.
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Affiliation(s)
- Germán J de Valcárcel
- Departament d'Optica, Universitat de València, Dr. Moliner 50, 46100-Burjassot, Spain.
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Mekhonoshin VV, Lange A. Faraday instability on viscous ferrofluids in a horizontal magnetic field: oblique rolls of arbitrary orientation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:061509. [PMID: 12188734 DOI: 10.1103/physreve.65.061509] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2001] [Indexed: 05/23/2023]
Abstract
A linear stability analysis of the free surface of a horizontally unbounded ferrofluid layer of arbitrary depth subjected to vertical vibrations and a horizontal magnetic field is performed. A nonmonotonic dependence of the stability threshold on the magnetic field is found at high frequencies of the vibrations. The reasons for the decrease of the critical acceleration amplitude caused by a horizontal magnetic field are discussed. It is revealed that the magnetic field can be used to select the first unstable pattern of Faraday waves. In particular, a rhombic pattern as a superposition of two different oblique rolls can occur. A scaling law is presented which maps all data into one graph for the tested range of viscosities, frequencies, magnetic fields, and layer thicknesses.
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Affiliation(s)
- V V Mekhonoshin
- Institut für Theoretische Physik, Universität Magdeburg, Universitätsplatz 2, D-39106, Magdeburg, Germany
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Park HK. Frequency locking in spatially extended systems. PHYSICAL REVIEW LETTERS 2001; 86:1130-1133. [PMID: 11178027 DOI: 10.1103/physrevlett.86.1130] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2000] [Revised: 10/06/2000] [Indexed: 05/23/2023]
Abstract
A variant of the complex Ginzburg-Landau equation is used to investigate the frequency-locking phenomena in spatially extended systems. With appropriate parameter values, a variety of frequency-locked patterns including flats, pi fronts, labyrinths, and 2pi/3 fronts emerge. We show that in spatially extended systems, frequency locking can be enhanced or suppressed by diffusive coupling. Novel patterns such as chaotically bursting domains and target patterns are also observed during the transition to locking.
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Affiliation(s)
- H K Park
- Department of Physics, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea
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Longhi S. Nonadiabatic pattern formation in optical parametric oscillators. PHYSICAL REVIEW LETTERS 2000; 84:5756-5759. [PMID: 10991047 DOI: 10.1103/physrevlett.84.5756] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/1999] [Revised: 02/16/2000] [Indexed: 05/23/2023]
Abstract
A nonadiabatic mechanism for pattern formation in parametrically forced systems subjected to a slow periodic modulation of the excitation frequency is proposed and discussed in detail for the case of an optical parametric oscillator. It is demonstrated that nonautonomous dynamics may induce nonadiabatic off-axis emission of down-converted photons even when the signal field is blueshifted from the nearby cavity resonance.
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Affiliation(s)
- S Longhi
- Istituto Nazionale di Fisica per la Materia, Dipartimento di Fisica and CEQSE-CNR, Politecnico di Milano, Piazza L. da Vinci, 32 I-20133 Milano, Italy
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Blair D, Aranson IS, Crabtree GW, Vinokur V, Tsimring LS, Josserand C. Patterns in thin vibrated granular layers: interfaces, hexagons, and superoscillons. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:5600-5610. [PMID: 11031614 DOI: 10.1103/physreve.61.5600] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/1999] [Indexed: 05/23/2023]
Abstract
A theoretical and experimental study of patterns in vibrated granular layers is presented. An order parameter model based on the parametric Ginzburg-Landau equation is used to describe strongly nonlinear excitations including hexagons, interfaces between flat antiphase domains, and new localized objects, superoscillons. The experiments confirm the existence of superoscillons and bound states of superoscillons and interfaces. On the basis of the order parameter model we predict analytically and confirm experimentally that additional subharmonic driving results in the controlled motion of interfaces.
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Affiliation(s)
- D Blair
- Argonne National Laboratory, Illinois 60439, USA
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Trillo S, Haelterman M, Sheppard A. Stable topological spatial solitons in optical parametric oscillators. OPTICS LETTERS 1997; 22:970-972. [PMID: 18185722 DOI: 10.1364/ol.22.000970] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
We predict that nearly resonant optical parametric oscillators support stable topological spatial solitons as a result of the interplay between diffraction and parametric amplification due to chi((2)) nonlinearities. Robust soliton stripes are observed in two transverse dimensions. Their stability is ensured by the phase-sensitive nature of the underlying parametric process.
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Kudrolli A, Gollub JP. Localized spatiotemporal chaos in surface waves. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:R1052-R1055. [PMID: 9965321 DOI: 10.1103/physreve.54.r1052] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Longhi S. Stable multipulse states in a nonlinear dispersive cavity with parametric gain. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:5520-5522. [PMID: 9964894 DOI: 10.1103/physreve.53.5520] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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