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Distant side-walls cause slow amplitude modulation of cellular convection

https://doi.org/10.1017/s0022112069000127
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1002/sapm1967461133openalex-snapshot
The Propagation of Nonlinear Wave Envelopes
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On the Stability of Two‐Dimensional Convection in a Layer Heated from Below
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Studies in Non-Linear Stability Theory
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Note on flow instability in heated ducts
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HILL'S EQUATION
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On the tendency towards hexagonal cells in steady convection
inferredcites →https://doi.org/10.1017/s002211206500023xopenalex-snapshot
The non-linear interaction of a finite number of disturbances to a layer of fluid heated from below
inferredcites →https://doi.org/10.1017/s0022112065001271openalex-snapshot
On the stability of steady finite amplitude convection
inferredcites →https://doi.org/10.1017/s0022112067001259openalex-snapshot
On convection under an air surface
inferredcites →https://doi.org/10.1017/s002211206700134xopenalex-snapshot
Finite amplitude cellular convection induced by surface tension
inferredcites →https://doi.org/10.1017/s0022112067001545openalex-snapshot
Convection in a box: linear theory
inferredcites →https://doi.org/10.1017/s0022112067001661openalex-snapshot
The stability of finite amplitude cellular convection and its relation to an extremum principle
inferredcites →https://doi.org/10.1017/s0022112067001697openalex-snapshot
The interfacial stability of a ferromagnetic fluid
inferredcites →https://doi.org/10.1017/s0022112068000017openalex-snapshot
Evolution of two-dimensional periodic Rayleigh convection cells of arbitrary wave-numbers
inferredcites →https://doi.org/10.1017/s0022112068000923openalex-snapshot
Convection in a box: on the dependence of preferred wave-number upon the Rayleigh number at finite amplitude
inferredcites →https://doi.org/10.1017/s0022112068001436openalex-snapshot
Finite amplitude convection with changing mean temperature. Part 1. Theory
inferredcites →https://doi.org/10.1017/s0022112069000176openalex-snapshot
Finite bandwidth, finite amplitude convection
inferredcites →https://doi.org/10.1017/s002211206900111xopenalex-snapshot
Wave-number selection at finite amplitude in rotating Couette flow
inferredcites →https://doi.org/10.1063/1.1691940openalex-snapshot
Effects of Surface Curvature and Property Variation on Cellular Convection
inferredcites →https://doi.org/10.1063/1.1762472openalex-snapshot
Recent Mathematical Treatments of Laminar Flow and Transition Problems
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Thermal Convection in Horizontal Fluid Layers
inferredcites →https://doi.org/10.1093/imamat/4.1.113openalex-snapshot
Two-Variable Expansions for Singular Perturbations

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Shear flow instabilities and transition
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Wavelength selection and pattern localization in buckling problems
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Effect of boundaries on periodic patterns
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Wavelength selection through boundaries in 1-D cellular structures
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Convection patterns in large aspect ratio systems
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Modelisation and simulation of convection in extended geometry
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Amplitude equations for non linear convection in high vertical channels
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Non adiabatic phenomena in cellular structures
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Patterns and Interfaces in Dissipative Dynamics
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Pattern Formation in Dissipative Systems: A Particle Approach
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The Language of Pattern and Form
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Electrohydrodynamic Convection in Nematics
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Patterns and Interfaces in Dissipative Dynamics
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Synergetics: Basic Concepts
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Mantle Convection
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Patterns and Interfaces in Dissipative Dynamics
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Localized Instabilities in the Convection of Nematic Liquid Crystals
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Chaos and Coherent Structres in Fluid Flows
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Spatial Hidden Symmetries in Pattern Formation
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Appendices
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Generic Aspects of Pattern-Forming Instabilities
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Bifurcation Analysis of the Eckhaus Instability
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General Mathematical Description of Pattern-Forming Instabilities
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A Guide to Literature Related to the Taylor-Couette Problem
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Macroscopic Theory of Fluctuations and Instabilities in Optics and Hydrodynamics
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Non-Linear Thermal Convection
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Phase-Mean Drift Equation for Convection Patterns in Large Aspect Ratio Containers
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Caustics of Nonlinear Waves and Related Questions
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Defects and Order to Disorder Transition in Non-Equilibrium Structures
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Patterns and Defects in Liquid Crystals
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Defect-Mediated Turbulence in Spatio-Temporal Patterns
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Mathematical Justification of Steady Ginzburg-Landau Equation Starting from Navier-Stokes
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Amplitude Equations for Hexagonal Patterns of Convection in Non-Boussinesq Fluids
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Weak Turbulence and the Dynamics of Topological Defects
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Introduction
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Longwave Modulations of Shortwave Patterns
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Transport Phenomena in Viscoplastic Materials
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Reaction-Diffusion Systems and Propagation of Limit Cycles with Chaotic Dynamics
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The Turing Model and Discrete Limit Cycles with Eddy and Convection
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Compatibility
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Compatibility
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2-D Generalized Turing Maps and Discrete Limit Cycles with Phase Shift
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Regular and Chaotic Patterns of Rayleigh-Benard Convection
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Time-Delayed Feedback Control of Spatio-Temporal Self-Organized Patterns in Dissipative Systems
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Intermittency and Transport Barriers in Fluids and Plasmas
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Fractional Dynamics of Media with Long-Range Interaction
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Patterns and Interfaces in Dissipative Dynamics
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Three Caveats for Linear Stability Theory: Rayleigh-Bénard Convection
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On the Effect of Sidewalls in Cellular Convection
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Review of the Finite Bandwidth Concept
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Stability Regions of Cellular Fluid Flow
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Bifurcation and Nonlinear Focusing
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Pattern Selection in Cellular Structures
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Pattern Selection in Anisotropic Systems
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Structure Formation by Propagating Fronts
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The Dynamics of Patterns: A Survey
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Defects in Waves
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Phase Dynamics — A Review and a Perspective
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Convection in Viscoelastic Fluids
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On the Absolute/Convective Nature of Primary and Secondary Instabilities
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Stability of Cellular Wave Structures in Oscillatory Pattern-Forming Systems near Onset
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Interaction of Defects in Nonlinear Dissipative Fields
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Stability of Nonuniform States in Systems Exhibiting Continuous Bifurcation
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Nonlinear Phenomena in Dissipative Systems
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Shear Flow Instabilities and Transition
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Defects and Disorder of Non-Linear Waves in Convection
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Ginzburg-Landau models of non-equilibrium
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Defects and Defect-Mediated Turbulence
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Phase Dynamics — The Concept and Some Recent Developments
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Transition to Turbulence in Open Flows
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Introduction to Convection
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Onset of Convection
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Phase description of almost periodic patterns
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Weak Noise Limit and Nonequilibrium Potentials of Dissipative Dynamical Systems
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Large Scale Instabilities of Cellular Flows
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Spatio-Temporal Instabilities in Closed and Open Flows
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Models of Pattern Formation from a Singularity Theory Point of View
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Cosmic Arrhythmias
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Defects in Macroscopic Structures: Ginzburg-Landau Approach
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Transition Between Different Symmetries in Convection
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The effect of imperfectly insulated sidewalls on natural convection in porous media
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Nonlinear analysis of spatial structures in two-dimensional anisotropic pattern forming systems
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Symmetry-breaking effects of distant sidewalls in Rayleigh-Bénard convection
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Well-Posedness for Fractional Cauchy Problems Involving Discrete Convolution Operators
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Conditional stability of front solutions
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Mode Interactions in Large Aspect Ratio Convection
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Monotonicity and one-dimensional symmetry of solutions for fractional reaction-diffusion equations and various applications of sliding methods
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inferred← citeshttps://doi.org/10.1007/s40065-020-00280-3openalex-snapshot
Exponential finite difference methods for solving Newell–Whitehead–Segel equation
inferred← citeshttps://doi.org/10.1007/s40314-019-0845-1openalex-snapshot
Shifted fractional Jacobi spectral algorithm for solving distributed order time-fractional reaction–diffusion equations
inferred← citeshttps://doi.org/10.1007/s42452-021-04229-9openalex-snapshot
Nonlinear emergent macroscale PDEs, with error bound, for nonlinear microscale systems
inferred← citeshttps://doi.org/10.1016/0012-8252(90)90048-zopenalex-snapshot
An interfacial model equation for the bifurcation of solidification patterns during LPEE processes
inferred← citeshttps://doi.org/10.1016/0017-9310(70)90051-7openalex-snapshot
Heat transfer—A review of 1969 literature
inferred← citeshttps://doi.org/10.1016/0017-9310(70)90142-0openalex-snapshot
Stability of buoyancy-driven convection in a tilted slot
inferred← citeshttps://doi.org/10.1016/0017-9310(70)90181-xopenalex-snapshot
Thermoconvective instability in a bounded cylindrical fluid layer
inferred← citeshttps://doi.org/10.1016/0017-9310(71)90037-8openalex-snapshot
On thermoconvective instability in a bounded cylindrical fluid layer
inferred← citeshttps://doi.org/10.1016/0017-9310(74)90079-9openalex-snapshot
Natural convection flow in a finite, rectangular slot arbitrarily oriented with respect to the gravity vector
inferred← citeshttps://doi.org/10.1016/0017-9310(76)90012-0openalex-snapshot
Onset of instability in a fluid layer heated sinusoidally from below
inferred← citeshttps://doi.org/10.1016/0017-9310(78)90008-xopenalex-snapshot
Surface tension driven instability of a liquid film flow down a heated incline
inferred← citeshttps://doi.org/10.1016/0017-9310(94)00310-ropenalex-snapshot
Nonlinear instability of travelling waves with a continuous spectrum
inferred← citeshttps://doi.org/10.1016/0020-7225(86)90149-7openalex-snapshot
The effect of microstructure on the thermal convection in a rectangular box of fluid heated from below
inferred← citeshttps://doi.org/10.1016/0020-7225(95)00034-uopenalex-snapshot
The Bénard problem for deep convection: Derivation of the Landau-Ginzburg equation
inferred← citeshttps://doi.org/10.1016/0020-7683(86)90042-9openalex-snapshot
Wavelength selection in the postbuckling of a long rectangular plate
inferred← citeshttps://doi.org/10.1016/0020-7683(92)90092-8openalex-snapshot
Influence of distributed and localized imperfections on the buckling of cyindrical shells under external pressure
inferred← citeshttps://doi.org/10.1016/0022-0248(84)90106-4openalex-snapshot
On the stability of hexagonal interfacial patterns in directional solidification of binary mixtures
inferred← citeshttps://doi.org/10.1016/0022-0248(92)90079-xopenalex-snapshot
Directional solidification: interface dynamics and weak remote flow
inferred← citeshttps://doi.org/10.1016/0022-0396(88)90063-0openalex-snapshot
Global characterization of the normal form for a vector field near a closed orbit
inferred← citeshttps://doi.org/10.1016/0022-5096(91)90010-lopenalex-snapshot
Localized buckling in long axially-loaded cylindrical shells
inferred← citeshttps://doi.org/10.1016/0030-4018(89)90180-6openalex-snapshot
Optical vortices
inferred← citeshttps://doi.org/10.1016/0031-9201(72)90092-1openalex-snapshot
Moving heaters as a model of continental drift
inferred← citeshttps://doi.org/10.1016/0045-7825(91)90051-7openalex-snapshot
Defect-mediated turbulence
inferred← citeshttps://doi.org/10.1016/0167-2789(83)90321-4openalex-snapshot
On cellular instability in the solidification of a dilute binary alloy
inferred← citeshttps://doi.org/10.1016/0167-2789(84)90136-2openalex-snapshot
Effects of boundary conditions on spatially periodic states
inferred← citeshttps://doi.org/10.1016/0167-2789(84)90181-7openalex-snapshot
Convection patterns in large aspect ratio systems
inferred← citeshttps://doi.org/10.1016/0167-2789(85)90059-4openalex-snapshot
On the Eckhaus instability for spatially periodic patterns
inferred← citeshttps://doi.org/10.1016/0167-2789(86)90104-1openalex-snapshot
Front motion, metastability and subcritical bifurcations in hydrodynamics
inferred← citeshttps://doi.org/10.1016/0167-2789(86)90129-6openalex-snapshot
Wavenumber selection and Eckhaus instability in Couette-Taylor flow
inferred← citeshttps://doi.org/10.1016/0167-2789(86)90140-5openalex-snapshot
Benjamin-Feir turbulence in convective binary fluid mixtures
inferred← citeshttps://doi.org/10.1016/0167-2789(86)90165-xopenalex-snapshot
Chaos and coherent structures in partial differential equations
inferred← citeshttps://doi.org/10.1016/0167-2789(87)90016-9openalex-snapshot
Influence of lateral boundaries on the Eckhaus instability in anisotropic pattern-forming systems
inferred← citeshttps://doi.org/10.1016/0167-2789(87)90056-xopenalex-snapshot
Nonlinear oscillatory convection: A quantitative phase dynamics approach
inferred← citeshttps://doi.org/10.1016/0167-2789(88)90024-3openalex-snapshot
Nonlinear and nonlocal dynamics of spatially extended systems: Stationary states, bifurcations and stability
inferred← citeshttps://doi.org/10.1016/0167-2789(88)90090-5openalex-snapshot
Structure and dynamics of dislocations in an anisotropic pattern-forming systems
inferred← citeshttps://doi.org/10.1016/0167-2789(89)90025-0openalex-snapshot
Stability of cellular wave structures in oscillatory pattern-forming systems near onset
inferred← citeshttps://doi.org/10.1016/0167-2789(89)90043-2openalex-snapshot
Strong selection or rejection of spatially periodic patterns in degenerate bifurcations
inferred← citeshttps://doi.org/10.1016/0167-2789(89)90119-xopenalex-snapshot
A form of turbulence associated with defects
inferred← citeshttps://doi.org/10.1016/0167-2789(89)90138-3openalex-snapshot
Nonlinear waves of the oscillatory instability on finite convective rolls
inferred← citeshttps://doi.org/10.1016/0167-2789(89)90245-5openalex-snapshot
Phase dynamics in aligned coordinate frame
inferred← citeshttps://doi.org/10.1016/0167-2789(90)90014-gopenalex-snapshot
Role of conservation laws in small Reynolds number closures: Application to large-scale dynamics of compressible flows
inferred← citeshttps://doi.org/10.1016/0167-2789(90)90113-4openalex-snapshot
Bifurcation analysis of the Eckhaus instability
inferred← citeshttps://doi.org/10.1016/0167-2789(91)90249-9openalex-snapshot
Experiments with pattern-forming systems
inferred← citeshttps://doi.org/10.1016/0167-2789(91)90261-7openalex-snapshot
Extended systems: the impact of nonlinear science
inferred← citeshttps://doi.org/10.1016/0167-2789(92)90035-lopenalex-snapshot
Coupled nonlocal complex Ginzburg-Landau equations in gasless combustion
inferred← citeshttps://doi.org/10.1016/0167-2789(92)90061-qopenalex-snapshot
Spatio-temporal intermittency in a 1D convective pattern: Theoretical model and experiments
inferred← citeshttps://doi.org/10.1016/0167-2789(92)90073-vopenalex-snapshot
Mean flow effects in the electro-hydrodynamic convection in nematic liquid crystals
inferred← citeshttps://doi.org/10.1016/0167-2789(92)90166-kopenalex-snapshot
Long time behavior of solutions of nonlinear classical field equations: the example of NLS defocusing
inferred← citeshttps://doi.org/10.1016/0167-2789(92)90192-popenalex-snapshot
Convection-front propagation and wavenumber selection
inferred← citeshttps://doi.org/10.1016/0167-2789(93)90206-gopenalex-snapshot
Long wavelength instabilities of square patterns
inferred← citeshttps://doi.org/10.1016/0167-2789(93)90252-vopenalex-snapshot
Localized states in fluid convection and multi-photon lasers
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