Dynamic Response Analysis of a Forced Fractional Viscoelastic Beam ∗

In this paper, dynamic response analysis of a forced fractional viscoelastic beam under moving external load is studied. The beauty of this study is that the effect of values of fractional order, the effect of internal damping, and the effect of intensity value of the moving force load on the dynamic response of the beam are analyzed. Constitutive equations for fractional order viscoelastic beam are constructed in the manner of Euler–Bernoulli beam theory. Solution of the fractional beam system is obtained by using Bernoulli collocation method. Obtained results are presented in the tables and graphical forms for two different beam systems, which are polybutadiene beam and butyl B252 beam.

The Kerr-Schild double copy in Lifshitz spacetime

The Kerr-Schild double copy is a map between exact solutions of general relativity and Maxwell’s theory, where the nonlinear nature of general relativity is circumvented by considering solutions in the Kerr-Schild form. In this paper, we give a general formulation, where no simplifying assumption about the background metric is made, and show that the gauge theory source is affected by a curvature term that characterizes the deviation of the background spacetime from a constant curvature spacetime. We demonstrate this effect explicitly by studying gravitational solutions with non-zero cosmological constant. We show that, when the background is flat, the constant charge density filling all space in the gauge theory that has been observed in previous works is a consequence of this curvature term. As an example of a solution with a curved background, we study the Lifshitz black hole with two different matter couplings. The curvature of the background, i.e., the Lifshitz spacetime, again yields a constant charge density; however, unlike the previous examples, it is canceled by the contribution from the matter fields. For one of the matter couplings, there remains no additional non-localized source term, providing an example for a non-vacuum gravity solution corresponding to a vacuum gauge theory solution in arbitrary dimensions.

Game Theory: Business and Growth Strategies

In the present note, we have discussed the growth strategies to enhance the overall business of a company using game theory. An optimal game theory solution happens when one of the companies participating in the game reaches the maximal outcome. Business and growth strategy is an emulsion of not only the innovation of the company but also the ability to access the moves of the competitors.

Study of Pipeline Penetration Based on CEL in Clay

In deep water, pipelines are usually laid directly on the seabed. During the laying process, the pipe typically penetrates into the seabed by a fraction of a diameter. The vertical embedment of pipeline and formation of berm during penetration have a significant effect on the pipeline stability. This study aims to investigate the vertical pipeline penetration at uniform and normal consolidated clay, by carrying out a series of numerical analyses, in which the coupled Eulerian-Lagrangian method (CEL) is incorporated to enable large deformation simulation. These analyses have been compared with collapse loads calculated using the theory solution. The results show that the CEL method is very suitable for simulating large-deformation pipesoil interaction.

How to Assign Points for Chores

Many parents reward their children for doing different chores. The problem is that: while in the beginning, kids are very enthusiastic about performing chores and collecting points, by the time when they have accumulated a sufficient number of points, they become less and less interested. In this paper, we provide a decision theory solution on how many points to assign for consecutive chores.

The formal Kuranishi parameterization via the universal homological perturbation theory solution of the deformation equation

Using homological perturbation theory, we develop a formal version of the miniversal deformation associated with a deformation problem controlled by a differential graded Lie algebra over a field of characteristic zero. Our approach includes a formal version of the Kuranishi method in the theory of deformations of complex manifolds.