In this paper, we examine the divide between stable and unstable first-order theories in model theory. We begin by defining a stable theory and proving Shelah’s theorem, which reduces the question of stability to a problem of examining a single formula. Afterwards, we will provide some applications of the stability/instability divide to other model-theoretic questions, such as the question of c...

We implement a volume-of-fluid algorithm with a parabolic re-construction of the interface for the calculation of the surface tension force VOF-PROST). This achieves higher accuracy for drop deformation simulations in comparison with existing VOF methods based on a piecewise inear interface re-construction. The algorithm is formulated for the Giesekus constitutive law. The evolution of a drop s...

In this paper, analysis of linear and nonlinear buckling of relatively thick orthotropic graphene sheets is carried out under mechanical load based on elasticity theories. With the help of  nonlocal elasticity theory, the principle of virtual work, first order shear theory and Von-Karman nonlinear strain, the dominant relationship in terms of obtained displacements has been obtained, and the me...

In the last decade, many efforts have been devoted to the exploration of techniques for learning and refining first order theories, as the necessary step for applying machine learning methodologies to real world applications. In this paper, we present a new approach to the integration of inductive and deductive learning techniques that seems to overcome some of the limitations of existing learn...

Second-order shear deformation theory (SSDT) is employed to analyze vibration of temperature-dependent solar functionally graded plates (SFGP’s). Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Two different types of SFGP’s such as ZrO2/Ti-6Al-4V and Si3N4/SUS304 are considered. Uniform, linear, nonlinear, heat-flux and sinusoida...

This study investigates geometrical non-linear analysis of composite circular cylindrical shells under external pressure over part of their surfaces and also shells subjected to combined axial compression and triangular external pressure. Donnell non-linear shell theory along with first order shear deformation theory (FOSD) are adopted in the analysis. In the case of combined axial compression ...

In this paper a third order shear deformation rectangular nanoplate with simply supported boundary conditions is developed for bending, buckling and vibration analysis. to consider the small-scale effects, modified couple stress theory, one length scale parameter, used. The bending rates dimensionless values under uniform surface traction sinusoidal load, critical force uniaxial in x direction ...

The deformation of red blood cells in microvessels was investigated numerically for various vessel diameters, hematocrits, and shear rates. We simulated blood flow in circular channels with diameters ranging from 9 to 50 μm, hematocrits from 20% to 45%, and shear rates from 20 to 150 s(-1) using a particle-based model with parallel computing. The apparent viscosity predicted by the simulation w...