Constitutive equations for a one-dimensional, active, polar, viscoelastic liquid are derived by treating the strain field as a slow hydrodynamic variable. Taking into account the couplings between strain and polarity allowed by symmetry, the hydrodynamics of an active, polar, viscoelastic body include an evolution equation for the polarity field that generalizes the damped Kuramoto-Sivashinsky ...

Model order reduction through the POD-Galerkin method can lead to dramatic gains in terms of computational efficiency solving physical problems. However, applicability non linear high-dimensional dynamical systems such as Navier–Stokes equations has been shown be limited, producing inaccurate and sometimes unstable models. This paper proposes a deep learning based closure modeling approach for ...

In this article, a nonic B-spline collocation approach is applied to solve the approximate solution of Kuramoto-Sivashinsky equation (KSE). Here nonlinear term KSE linearizing using Taylo...

We study the spatial power spectra of Nikolaevskii turbulence in one-dimensional space. First, we show that the energy distribution in wave-number space is extensive in nature. Then, we demonstrate that, when varying a particular parameter, the spectrum becomes qualitatively indistinguishable from that of Kuramoto-Sivashinsky turbulence. Next, we derive the critical exponents of turbulent fluct...

Systems such as fluid flows in channels and pipes or the complex Ginzburg-Landau system, defined over periodic domains, exhibit both continuous symmetries, translational and rotational, as well as discrete symmetries under spatial reflections or complex conjugation. The simplest, and very common symmetry of this type is the equivariance of the defining equations under the orthogonal group O(2)....

We present an approach to the design of feedback control laws that stabilize relative equilibria of general nonlinear systems with continuous symmetry. Using a template-based method, we factor out the dynamics associated with the symmetry variables and obtain evolution equations in a reduced frame that evolves in the symmetry direction. The relative equilibria of the original systems are fixed ...

Phase turbulence is suppressed by applying common noise additively to the Kuramoto-Sivashinsky type equation, and the noise-induced phase synchronization is realized. The noise strength necessary for the suppression of phase turbulence is evaluated theoretically. PACS: 05.45.+b, 05.40.+j, 02.50-r Recently, various noise effects to nonlinear systems have been studied. The response of a bistable ...

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 asymptoti...

‎we study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎these equations will be converted to a system of‎ ‎singular integral equations with cauchy type kernels‎. ‎using‎ ‎chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of cauchy type singular integral equation which will ...