Abstract: The stability analysis of Marangoni convection in porous media with a deformable upper free surface is investigated. The linear stability theory and the normal mode analysis are applied and the resulting eigenvalue problem is solved exactly. The Darcy law and the Brinkman model are used to describe the flow in the porous medium heated from below. The effect of the Crispation number, Bond number and the Biot number are analyzed for the stability of the system. It is found that a decrease in the Crispation number and an increase in the Bond number delay the onset of convection in porous media. In addition, the system becomes more stable when the Biot number is increases and the Daeff number is decreases.
Abstract: In this paper, an analytical approach for free vibration
analysis of four edges simply supported rectangular Kirchhoff plates
is presented. The method is based on wave approach. From wave
standpoint vibration propagate, reflect and transmit in a structure.
Firstly, the propagation and reflection matrices for plate with simply
supported boundary condition are derived. Then, these matrices are
combined to provide a concise and systematic approach to free
vibration analysis of a simply supported rectangular Kirchhoff plate.
Subsequently, the eigenvalue problem for free vibration of plates is
formulated and the equation of plate natural frequencies is
constructed. Finally, the effectiveness of the approach is shown by
comparison of the results with existing classical solution.
Abstract: The Linear discriminant analysis (LDA) can be
generalized into a nonlinear form - kernel LDA (KLDA) expediently
by using the kernel functions. But KLDA is often referred to a general
eigenvalue problem in singular case. To avoid this complication, this
paper proposes an iterative algorithm for the two-class KLDA. The
proposed KLDA is used as a nonlinear discriminant classifier, and the
experiments show that it has a comparable performance with SVM.
Abstract: This research work is concerned with the eigenvalue problem for the integral operators which are obtained by linearization of a nonlocal evolution equation. The purpose of section II.A is to describe the nature of the problem and the objective of the project. The problem is related to the “stable solution" of the evolution equation which is the so-called “instanton" that describe the interface between two stable phases. The analysis of the instanton and its asymptotic behavior are described in section II.C by imposing the Green function and making use of a probability kernel. As a result , a classical Theorem which is important for an instanton is proved. Section III devoted to a study of the integral operators related to interface dynamics which concern the analysis of the Cauchy problem for the evolution equation with initial data close to different phases and different regions of space.
Abstract: This paper presents an exact analytical model for
optimizing stability of thin-walled, composite, functionally graded
pipes conveying fluid. The critical flow velocity at which divergence
occurs is maximized for a specified total structural mass in order to
ensure the economic feasibility of the attained optimum designs. The
composition of the material of construction is optimized by defining
the spatial distribution of volume fractions of the material
constituents using piecewise variations along the pipe length. The
major aim is to tailor the material distribution in the axial direction so
as to avoid the occurrence of divergence instability without the
penalty of increasing structural mass. Three types of boundary
conditions have been examined; namely, Hinged-Hinged, Clamped-
Hinged and Clamped-Clamped pipelines. The resulting optimization
problem has been formulated as a nonlinear mathematical
programming problem solved by invoking the MatLab optimization
toolbox routines, which implement constrained function
minimization routine named “fmincon" interacting with the
associated eigenvalue problem routines. In fact, the proposed
mathematical models have succeeded in maximizing the critical flow
velocity without mass penalty and producing efficient and economic
designs having enhanced stability characteristics as compared with
the baseline designs.
Abstract: A complete spectral representation for the
electromagnetic field of planar multilayered waveguides
inhomogeneously filled with omega media is presented. The problem
of guided electromagnetic propagation is reduced to an eigenvalue
equation related to a 2 ´ 2 matrix differential operator. Using the
concept of adjoint waveguide, general bi-orthogonality relations for
the hybrid modes (either from the discrete or from the continuous
spectrum) are derived. For the special case of homogeneous layers
the linear operator formalism is reduced to a simple 2 ´ 2 coupling
matrix eigenvalue problem. Finally, as an example of application, the
surface and the radiation modes of a grounded omega slab waveguide
are analyzed.