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We introduce one- and two-dimensional (1D and 2D) models of parity-time ($% \mathcal{PT}$) -symmetric couplers with the mutually balanced linear gain and loss applied to the two cores, and cubic-quintic (CQ) nonlinearity acting in each one.…

Numerous accidents caused by parametric rolling have been reported on container ships and pure car carriers (PCCs). A number of theoretical studies have been performed to estimate the occurrence condition of parametric rolling in both…

It is shown that a sub-luminal electromagnetic plasma wave, propagating in phase with a background sub-luminal gravitational wave in a dispersive medium, can undergo parametric amplification. For this phenomena to occur, the dispersive…

Interferometric gravitational wave detectors operate with high optical power in their arms in order to achieve high shot-noise limited strain sensitivity. A significant limitation to increasing the optical power is the phenomenon of…

The effects of an intracavity photonic crystal in a multimode optical parametric oscillator are studied, with a special focus on quantum fluctuations. The capability to either stimulate or inhibit the spatial instability, lowering or…

We continue our study of the problem of mixing for a class of PDEs with very degenerate noise. As we established earlier, the uniqueness of stationary measure and its exponential stability in the dual-Lipschitz metric holds under the…

Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…

The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…

We study the stability of a compressible magnetic plane Couette flow and show that compressibility profoundly alters the stability properties if the magnetic field has a component perpendicular to the direction of flow. The necessary…

Periodically-driven quantum systems are currently explored in view of realizing novel many-body phases of matter. This approach is particularly promising in gases of ultracold atoms, where sophisticated shaking protocols can be realized and…

Ion-ion instability is excited due to the counter streaming of ion beams in any plasma system. An experiment has been carried out to observe the ion-ion instability in dusty plasma and in presence of different gas compositions viz., H2, Ar,…

Learning from two-level voltage source converters, the existing impedance-based stability analyses of modular multilevel converters (MMCs) primarily focus on system modes with finite closed-loop transfer functions, which consider…

Experimental manipulations perturb the neuronal activity. This phenomenon is manifested in the fMRI response. Dynamic causal model and its variants can model these neuronal responses along with the BOLD responses [1, 2, 3, 4, 5] .…

Understanding the phase behavior of mixtures with many components is important in many contexts, including as a key step toward a physics-based description of intracellular compartmentalization. Here, we study the instabilities of a mixture…

In a recent one-dimensional numerical fluid simulation study [Saxena et al., Phys. Plasmas 13,032309 (2006)], it was found that an instability is associated with a special class of one-dimensional nonlinear solutions for modulated light…

We study thermal instability in a magnetized and partially ionized plasma with charged dust particles. Our linear analysis shows that the growth rate of the unstable modes in the presence of dust particles strongly depends on the ratio of…

We examine the steady state and dynamic behaviour of an optical resonator comprised of two interlinked fibre loops sharing a common pump. A coupled Ikeda map models with great accuracy the field evolution within and exchange between both…

Three-mode parametric interactions can occur in triply-resonant opto-mechanical systems in which two orthogonal optical modes are coupled with an appropriate mechanical mode. Using an optical cavity with a membrane inside, we report the…

The filamentation instability occurring when a non relativistic electron beam passes through a quantum magnetized plasma is investigated by means of a cold quantum magnetohydrodynamic model. It is proved that the instability can be…

We revisit the mean field model of globally and harmonically coupled parametric oscillators subject to periodic block pulses with initially random phases. The phase diagram of regions of collective parametric instability is presented, as is…