Bubbles interactions in fluidized granular medium for the van der Waals hydrodynamic regime

Morad, Adel M.; Selima, Ehab S.; Abu‐Nab, Ahmed K.

doi:10.1140/epjp/s13360-021-01277-3

Cited by 25 publications

(11 citation statements)

References 29 publications

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“…In general, normal forms and perturbation theory, provide a convenient mathematical framework to get insight in otherwise mathematically untractable problems, as the study of multiple-soliton solutions in spatially extended systems [19], the derivation of exact analytical results for incompressible magnetohydrodynamic plasma turbulence [20] or the study of bubble interactions in fluidized granular media [21]. Since the pioneering works by Newell and Whitehead [22] and Kuramoto [23], the cubic-quintic Ginzburg-Landau equation is known to arise as a center manifold reduction of the Navier-Stokes equations that describe turbulent fluids at the Rayleigh-Bernard instability.…”

Section: Introductionmentioning

confidence: 99%

Universality of oscillatory instabilities in fluid mechanical systems

García-Morales,

Tandon,

Kurths

et al. 2024

New J. Phys.

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Oscillatory instability emerges amidst turbulent states in experiments in various turbulent fluid and thermo-fluid systems such as aero-acoustic, thermoacoustic and aeroelastic systems. For the time series of the relevant dynamic variable at the onset of the oscillatory instability, universal scaling behaviors have been discovered in experiments via the Hurst exponent and certain spectral measures. By means of a center manifold reduction, the spatiotemporal dynamics of these real systems can be mapped to a complex Ginzburg-Landau equation with a linear global coupling. In this work, we show that this model is able to capture the universal behaviors of the route to oscillatory instability, elucidating it as a transition from defect to phase turbulence mediated by the global coupling.

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Section: Introductionmentioning

confidence: 99%

Universality of oscillatory instabilities in fluid mechanical systems

García-Morales,

Tandon,

Kurths

et al. 2024

New J. Phys.

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“…In recent years, the various applications of integrability and localized wave solutions of numerous NLPDEs can be noticed such as, the rogue wave and multiple lump solutions in the form of Grammian formula for the (2 + 1)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili (BKP) equation have been obtained by using polynomial function approach in [6]; multiple lump molecules and interaction solutions for the Kadomtsev-Petviashvili I equation are employed by utilizing non-homogeneous polynomial technique in [7]; lump chain solutions for the (2 + 1)dimensional BKP equation have been determined by using the τ-function in the form of Grammian formula in [8]; the soliton-cnoidal wave and lump-type solutions for (2 + 1)-dimensional KdV-mKdV equation are derived by utilizing Lie symmetry analysis and Bäcklund transformation approaches in [9]. The theoretical studies in nonlinear evolution equations have various applications in the diverse area of science and technology, such as: the electrohydrodynamics of a thin suspended liquid film model, which describes an incompressible fluid is examined by the perturbation technique in [10]; the granular model arising in the fluid dynamics has been solved by Painlevé analysis, Bäcklund transformation, Jacobi elliptic function, and tanh function methods in [11]; the magma equation arising in porous media is examined by the Cole-Hopf transformation method in [12]; the turbulent magnetohydrodynamic model in plasma turbulence has been solved using complex ansatz method in [13]; the compressible magnetohydrodynamic equations in cold plasma is examined by using the reductive perturbation method in [14].…”

Section: Introductionmentioning

confidence: 99%

New analytical solutions and integrability for the (2 + 1)-dimensional variable coefficients generalized Nizhnik-Novikov-Veselov system arising in the study of fluid dynamics via auto-Backlund transformation approach

Singh¹,

Ray²

2023

Phys. Scr.

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Recognising the non-uniformity of boundaries and the inhomogeneities of media, nonlinear evolution equations with variable coefficients may display more realistic scenarios dealing with time-varying environments and inhomogeneous media. In this work, the (2 + 1)-dimensional variable coefficients generalized Nizhnik-Novikov-Veselov system that occurs in the domain of fluid dynamics is investigated. Painlevé analysis technique is used to demonstrate the integrability of the above mentioned system. The governing equations are revealed to be integrable in the Painlevé sense under no specific criterion on the variable-coefficients. To derive numerous analytical solutions, the auto-Bäcklund transformation (ABT) method is taken into account. Consequently, three different analytical solutions are found using the ABT technique, which include linear, exponential, rational, and complex solutions. All the solutions are displayed as 3D plots in which variable coefficients and parameters are varied to produce the desired results. These graphs depict the many aspects of the proposed coupled system in the various forms of periodic waves and complex periodic wave surfaces.

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“…Many phenomena are described by mathematical and physical models, including traffic flow, stripe of dune, bubble in the granular medium, and plasma flow [1][2][3][4][5]. Among these phenomena, spatio-temporal patterning is one of the attractive topics in the field of nonlinear physics.…”

Section: Introductionmentioning

confidence: 99%

Convolution Representation of Traveling Pulses in Reaction-Diffusion Systems

Kawaguchi

2023

Advances in Mathematical Physics

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Convolution representation manifests itself as an important tool in the reduction of partial differential equations. In this study, we consider the convolution representation of traveling pulses in reaction-diffusion systems. Under the adiabatic approximation of inhibitor, a two-component reaction-diffusion system is reduced to a one-component reaction-diffusion equation with a convolution term. To find the traveling speed in a reaction-diffusion system with a global coupling term, the stability of the standing pulse and the relation between traveling speed and bifurcation parameter are examined. Additionally, we consider the traveling pulses in the kernel-based Turing model. The stability of the spatially homogeneous state and most unstable wave number are examined. The practical utilities of the convolution representation of reaction-diffusion systems are discussed.

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Bubbles interactions in fluidized granular medium for the van der Waals hydrodynamic regime

Cited by 25 publications

References 29 publications

Universality of oscillatory instabilities in fluid mechanical systems

Universality of oscillatory instabilities in fluid mechanical systems

New analytical solutions and integrability for the (2 + 1)-dimensional variable coefficients generalized Nizhnik-Novikov-Veselov system arising in the study of fluid dynamics via auto-Backlund transformation approach

Convolution Representation of Traveling Pulses in Reaction-Diffusion Systems

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