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Physical Sciences and Mathematics Commons™
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- Keyword
-
- Critical buckling load, Hollomon’s law, Axial plastic columns, High strength metals, Work-hardening (1)
- Dewetting (1)
- Falkner-Skan equation; Heat transfer; approximation method;GAM (1)
- Finite element solution, Ritz-Galerkin method, Nonlinear Euler-Bernoulli beam, Power-law, Work hardening material, Hollomon's equation, Convergence, Error estimate, Hermite elements (1)
- Gaussian (GA) (1)
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- Generalized fifth-order Korteweg-de Vries (gfKdV) (1)
- Generalized sine, Hamilton system, nonlinear spring, vibration, analytic solution (1)
- Global solvability, fourth-order, nonlinear boundary value problems, monotone operator, Leray-Schauder fixed point theorem, coercivity (1)
- Interfacial stabil- ity (1)
- Inverse multiquadric (IMQ) (1)
- Liquid bilayer films (1)
- Meshless (1)
- Method of lines (MOL) (1)
- Multiquadric (MQ) (1)
- Nanopatterning (1)
- Nonstrict hyperbolicity, singularity formation, damping (1)
- Proudman-Johnson equation, blow-up (1)
- Pulsed laser irradiation (1)
- Radial basis function (RBF) (1)
- Self-organization (1)
- Thermocapillary convection (1)
Articles 1 - 12 of 12
Full-Text Articles in Physical Sciences and Mathematics
Analytic And Finite Element Solutions Of The Power-Law Euler-Bernoulli Beams, Dongming Wei, Yu Liu
Analytic And Finite Element Solutions Of The Power-Law Euler-Bernoulli Beams, Dongming Wei, Yu Liu
Mathematics Faculty Publications
In this paper, we use Hermite cubic finite elements to approximate the solutions
of a nonlinear Euler-Bernoulli beam equation. The equation is derived
from Hollomon’s generalized Hooke’s law for work hardening materials with
the assumptions of the Euler-Bernoulli beam theory. The Ritz-Galerkin finite
element procedure is used to form a finite dimensional nonlinear program
problem, and a nonlinear conjugate gradient scheme is implemented to find
the minimizer of the Lagrangian. Convergence of the finite element approximations
is analyzed and some error estimates are presented. A Matlab finite
element code is developed to provide numerical solutions to the beam equation.
Some …
Controlling Nanoparticles Formation In Molten Metallic Bilayers By Pulsed-Laser Interference Heating, Mikhail Khenner, Sagar Yadavali, Ramki Kalyanaraman
Controlling Nanoparticles Formation In Molten Metallic Bilayers By Pulsed-Laser Interference Heating, Mikhail Khenner, Sagar Yadavali, Ramki Kalyanaraman
Mathematics Faculty Publications
The impacts of the two-beam interference heating on the number of core-shell and embedded nanoparticles and on nanostructure coarsening are studied numerically based on the non-linear dynamical model for dewetting of the pulsed-laser irradiated, thin (< 20 nm) metallic bilayers. The model incorporates thermocapillary forces and disjoining pressures, and assumes dewetting from the optically transparent substrate atop of the reflective support layer, which results in the complicated dependence of light reflectivity and absorption on the thicknesses of the layers. Stabilizing thermocapillary effect is due to the local thickness-dependent, steady- state temperature profile in the liquid, which is derived based on the mean substrate temperature estimated from the elaborate thermal model of transient heating and melting/freezing. Linear stability analysis of the model equations set for Ag/Co bilayer predicts the dewetting length scales in the qualitative agreement with experiment.
Influence Of Damping On Hyperbolic Equations With Parabolic Degeneracy, Katarzyna Saxton, Ralph Saxton
Influence Of Damping On Hyperbolic Equations With Parabolic Degeneracy, Katarzyna Saxton, Ralph Saxton
Mathematics Faculty Publications
This paper examines the effect of damping on a nonstrictly hyperbolic 2 x 2 system. It is shown that the growth of singularities is not restricted as in the strictly hyperbolic case where dissipation can be strong enough to preserve the smoothness of solutions globally in time. Here, irrespective of the stabilizing properties of damping, solutions are found to break down in finite time on a line where two eigenvalues coincide in state space.
Critical Buckling Loads Of The Perfect Hollomon’S Power-Law Columns, Dongming Wei, Alejandro Sarria, Mohamed Elgindi
Critical Buckling Loads Of The Perfect Hollomon’S Power-Law Columns, Dongming Wei, Alejandro Sarria, Mohamed Elgindi
Mathematics Faculty Publications
In this work, we present analytic formulas for calculating the critical buckling states of some plastic axial columns of constant cross-sections. The associated critical buckling loads are calculated by Euler-type analytic formulas and the associated deformed shapes are presented in terms of generalized trigonometric functions. The plasticity of the material is defined by the Holloman’s power-law equation. This is an extension of the Euler critical buckling loads of perfect elastic columns to perfect plastic columns. In particular, critical loads for perfect straight plastic columns with circular and rectangular cross-sections are calculated for a list of commonly used metals. Connections and …
On The Global Solvability Of A Class Of Fourth-Order Nonlinear Boundary Value Problems, M.B.M. Elgindi, Dongming Wei
On The Global Solvability Of A Class Of Fourth-Order Nonlinear Boundary Value Problems, M.B.M. Elgindi, Dongming Wei
Mathematics Faculty Publications
In this paper we prove the global solvability of a class of fourth-order nonlinear boundary value problems that govern the deformation of a Hollomon’s power-law plastic beam subject to an axial compression and nonlinear lateral constrains. For certain ranges of the acting axial compression force, the solvability of the equations follows from the monotonicity of the fourth order nonlinear differential operator. Beyond these ranges the monotonicity of the operator is lost. It is shown that, in this case, the global solvability may be generated by the lower order nonlinear terms of the equations for a certain type of constrains.
Travelling Wave Solutions Of Burgers' Equation For Gee-Lyon Fluid Flows, Dongming Wei, Ken Holladay
Travelling Wave Solutions Of Burgers' Equation For Gee-Lyon Fluid Flows, Dongming Wei, Ken Holladay
Mathematics Faculty Publications
In this work we present some analytic and semi-analytic traveling wave solutions of generalized Burger' equation for isothermal unidirectional flow of viscous non-Newtonian fluids obeying Gee-Lyon nonlinear rheological equation. The solution of Burgers' equation for Newtonian flow as a special case. We also derive estimates of shock thickness for non-Newtonian flows.
An H1 Model For Inextensible Strings, Stephen C. Preston, Ralph Saxton
An H1 Model For Inextensible Strings, Stephen C. Preston, Ralph Saxton
Mathematics Faculty Publications
We study geodesics of the H1 Riemannian metric (see article for equation) on the space of inextensible curves (see article for equation). This metric is a regularization of the usual L2 metric on curves, for which the submanifold geometry and geodesic equations have been analyzed already. The H1 geodesic equation represents a limiting case of the Pochhammer-Chree equation from elasticity theory. We show the geodesic equation is C∞ in the Banach topology C1 ([0,1], R2), and thus there is a smooth Riemannian exponential map. Furthermore, if we hold one of the curves fixed, …
Blow-Up Of Solutions To The Generalized Inviscid Proudman-Johnson Equation, Alejandro Sarria, Ralph Saxton
Blow-Up Of Solutions To The Generalized Inviscid Proudman-Johnson Equation, Alejandro Sarria, Ralph Saxton
Mathematics Faculty Publications
For arbitrary values of a parameter --- finite-time blowup of solutions to the generalized, inviscid Proudman Johnson equation is studied via a direct approach which involves the derivation of representation formulae for solutions to the problem.
Some Generalized Trigonometric Sine Functions And Their Applications, Dongming Wei, Yu Liu, Mohamed B. Elgindi
Some Generalized Trigonometric Sine Functions And Their Applications, Dongming Wei, Yu Liu, Mohamed B. Elgindi
Mathematics Faculty Publications
In this paper, it is shown that D. Shelupsky's generalized sine function, and various general sine functions developed by P. Drabek, R. Manasevich and M. Otani, P. Lindqvist, including the generalized Jacobi elliptic sine function of S. Takeuchi can be defined by systems of first order nonlinear ordinary differential equations with initial conditions. The structure of the system of differential equations is shown to be related to the Hamilton System in Lagrangian Mechanics. Numerical solutions of the ODE systems are solved to demonstrate the sine functions graphically. It is also demonstrated that the some of the generalized sine functions can …
A Study Of The Gam Approach To Solve Laminar Boundary Layer Equations In The Presence Of A Wedge, Rahmat Ali Khan, Muhammad Usman
A Study Of The Gam Approach To Solve Laminar Boundary Layer Equations In The Presence Of A Wedge, Rahmat Ali Khan, Muhammad Usman
Mathematics Faculty Publications
We apply an easy and simple technique, the generalized ap- proximation method (GAM) to investigate the temperature field associated with the Falkner-Skan boundary-layer problem. The nonlinear partial differ- ential equations are transformed to nonlinear ordinary differential equations using the similarity transformations. An iterative scheme for the non-linear ordinary differential equations associated with the velocity and temperature profiles are developed via GAM. Numerical results for the dimensionless ve- locity and temperature profiles of the wedge flow are presented graphically for different values of the wedge angle and Prandtl number.
A Meshless Numerical Solution Of The Family Of Generalized Fifth-Order Korteweg-De Vries Equations, Syed Tauseef Mohyud-Din, Elham Negahdary, Muhammad Usman
A Meshless Numerical Solution Of The Family Of Generalized Fifth-Order Korteweg-De Vries Equations, Syed Tauseef Mohyud-Din, Elham Negahdary, Muhammad Usman
Mathematics Faculty Publications
In this paper we present a numerical solution of a family of generalized fifth-order Korteweg-de Vries equations using a meshless method of lines. This method uses radial basis functions for spatial derivatives and Runge-Kutta method as a time integrator. This method exhibits high accuracy as seen from the comparison with the exact solutions.
Bounded Solutions Of Almost Linear Volterra Equations, Muhammad Islam, Youssef Raffoul
Bounded Solutions Of Almost Linear Volterra Equations, Muhammad Islam, Youssef Raffoul
Mathematics Faculty Publications
Fixed point theorem of Krasnosel’skii is used as the primary mathematical tool to study the boundedness of solutions of certain Volterra type equations. These equations are studied under a set of assumptions on the functions involved in the equations. The equations will be called almost linear when these assumptions hold.