Rayleigh-Taylor (RT) instability has a growing importance in many fields including aircraft industry and astrophysics. The development and the growth of RT instability were investigated using sinusoidal disturbances with different wavelength at the interface of the two fluids. Numerical simulations were performed by solving Navier-Stokes unsteady equations with the VOF formulation. Results of the 2D simulation are compared with experimental results.It is shown that beyond a critical time, not captured experimentally, the mushroom shape of RT instability turns into a helical path or breaks down into a patchy shape depending on the shape of disturbance. Nonlinear instabilities responsible for such behavior are apparent when the wavelength exceeds 10 times the length scale introduced in this study.

This paper investigates the distributed controllability of nonlocal Rayleigh beam. The mathematical problem is formulated as an abstract di, erential equation. It is shown that a sequence of eigenfunction of nonlocal Rayleigh beam forms Riesz basis. Based on Riesz basis properties and theory of abstract di, erential equation, it is proved that a vibrating nonlocal Rayleigh beam is approximately controllable under suitable distributed control force while it is not exponentially stable.

This paper presents exact joint confidence regions for the parameters of the Rayleigh distribution based on record data. By providing some appropriate pivotal quantities, we construct several joint confidence regions for the Rayleigh parameters. These joint confidence regions are useful for constructing confidence regions for functions of the unknown parameters. Applications of the joint confidence regions using two environmental data sets are presented for illustrative purposes. Finally, a simulation study is conducted to study the performance of the proposed joint confidence regions.

As a result of environmental and accidental actions, damage occurs in structures. The early detection of any defect can be achieved by regular inspection and condition assessment. In this way, the safety and reliability of structures can be increased. This paper is devoted to propose a new and effective method for detecting, locating, and quantifying beam-like structures. This method is based on Rayleigh-Ritz approach and requires a few numbers of natural frequencies and mode shapes associated with the undamaged and damaged states of the structure. The great advantage of the proposed approach against the other methods is that it considers all kinds of boundary and damping effects. To detect damage using the penalty method, this article considers lumped rotational and translational springs for determining the boundary conditions. Result will show that the proposed method is an effective and reliable tool for damage detection, localization, and quantification in the beam-like structures with different boundary conditions even when the modal data are contaminated by noise.

In this work, the problem of Rayleigh wave propagation is considered in the context of the theory of thermoelastic diffusion. The formulation is applied to a homogeneous isotropic thermoelastic half space with mass diffusion at the stress free, isothermal, is oconcentrated boundary. Using the potential functions and harmonic wave solution, three coupled dilatational waves and a shear wave is obtained. After developing mathematical formulation, the dispersion equation is obtained, which results to be complex and irrational. This equation is converted into a polynomial form of higher degree. The roots of this polynomial equation are verified for not satisfying the original dispersion equation and therefore are filtered out and the remaining roots are checked with the property of decay with depth. Phase velocity and attenuation coefficient of the Rayleigh wave are computed numerically and depicted graphically. Behavior of particle motion of these waves inside and at the surface of the thermoelastic medium with mass diffusion is studied. Some particular cases are also deduced from the present investigation.

In this paper, a discrete analog of the beta-Rayleigh distribution is studied. This new distribution contains the generalized discrete Rayleigh and discrete Rayleigh distributions as special sub-models. Some distributional and moment properties of the new discrete distribution as well as its order statistics are discussed. We will see that the hazard rate function of the new model can be increasing, bathtub-shaped and upside-down bathtub. Estimation of the parameters is illustrated and, finally, the model with a real data set is examined.