scholarly journals Boundary Behavior and Confinement of Screw Dislocations

MRS Advances ◽  
2017 ◽  
Vol 2 (48) ◽  
pp. 2633-2638
Author(s):  
Marco Morandotti
Keyword(s):  
Boundary Conditions ◽  
Boundary Behavior ◽  
Screw Dislocations ◽  
Numerical Evidence ◽  
Analytical Results

ABSTRACTIn this note we discuss two aspects of screw dislocations dynamics: their behavior near the boundary and a way to confine them inside the material. In the former case, we obtain analytical results on the estimates of collision times (one dislocation with the boundary and two dislocations with opposite Burgers vectors with each other); numerical evidence is also provided. In the latter, we obtain analytical results stating that, under imposing a certain type of boundary conditions, it is energetically favorable for dislocations to remain confined inside the domain.

Flexural Vibration Response of Beams With General Boundary Conditions: A Transfer Matrix Approach

1991 ◽  
Author(s):  
T. Önsay
Keyword(s):  
Boundary Conditions ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Vibration Response ◽  
General Boundary ◽  
Phase Variable ◽  
General Boundary Conditions ◽  
Transfer Matrices ◽  
Analytical Results

Abstract The wave-mode representation is utilized to obtain a more efficient form to the conventional transfer matrix method for bending vibrations of beams. The proposed improvement is based on a phase-variable canonical state representation of the equation governing the time-harmonic flexural vibrations of a beam. Transfer matrices are obtained for external forces, step-change of beam properties, intermediate supports and for boundaries. The transfer matrices are utilized to obtain the vibration response of a point-excited single-span beam with general boundary conditions. The general characteristic equation and the transfer mobility of a single-span beam are determined. The application of the analytical results are demonstrated on physical structures with different boundary conditions. A hybrid model is developed to incorporate measured impedance of nonideal boundaries into the transfer matrix method. The analytical results are found to be in excellent agreement with experimental measurements.

Solution of axisymmetric torsion problems by point matching

1971 ◽  
Vol 6 (2) ◽  
pp. 124-133 ◽  
Author(s):  
G J Matthews ◽  
C J Hooke
Keyword(s):  
Boundary Conditions ◽  
Numerical Technique ◽  
Point Matching ◽  
Analytical Results ◽  
Elasticity Equations ◽  
Matching Technique ◽  
Basic Solutions ◽  
Axisymmetric Bodies

A general numerical technique is presented for the solution of the problem of torsion of axisymmetric bodies. The method superimposes a number of basic solutions of the elasticity equations using the point-matching technique so as to satisfy approximately the prescribed boundary conditions of a body. Results obtained by this technique are compared with those obtained by alternative experimental and theoretical techniques for various body geometries to assess the accuracy of the method. The technique is then applied to the problem of the torsion of shouldered shafts since large discrepancies exist between the experimental and analytical results available for this type of structure.

An Inverse Method for Simultaneous Estimation of the Center and Surface Thermal Behavior of a Heated Cylinder Normal to a Turbulent Air Stream

2002 ◽  
Vol 124 (4) ◽  
pp. 601-608 ◽  
Author(s):  
Jiin-Hong Lin ◽  
Cha’o-Kuang Chen ◽  
Yue-Tzu Yang
Keyword(s):  
Boundary Conditions ◽  
Thermal Behavior ◽  
Measurement Errors ◽  
Boundary Behavior ◽  
Traditional Approach ◽  
Simultaneous Estimation ◽  
Unknown Boundary ◽  
Heated Cylinder ◽  
Air Stream ◽  
Unknown Boundary Conditions

A two-dimensional inverse analysis utilizes a different perspective to simultaneously estimate the center and surface thermal behavior of a heated cylinder normal to a turbulent air stream. A finite-difference method is used to discretize the governing equations and then a linear inverse model is constructed to identify the unknown boundary conditions. The present approach is to rearrange the matrix forms of the governing differential equations and estimate the unknown boundary conditions of the heated cylinder. Then, the linear least-squares-error method is adopted to find the solutions. The results show that only a few measuring points inside the cylinder are needed to estimate the unknown quantities of the thermal boundary behavior, even when measurement errors are considered. In contrast to the traditional approach, the advantages of this method are that no prior information is needed on the functional form of the unknown quantities, no initial guesses are required, no iterations in the calculating process are necessary, and the inverse problem can be solved in a linear domain. Furthermore, the existence and uniqueness of the solutions can easily be identified.

scholarly journals ON THE EMERGENCE OF COLLECTIVE ORDER IN SWARMING SYSTEMS: A RECENT DEBATE

2009 ◽  
Vol 23 (18) ◽  
pp. 3661-3685 ◽  
Author(s):  
M. ALDANA ◽  
H. LARRALDE ◽  
B. VÁZQUEZ
Keyword(s):  
Phase Transition ◽  
Boundary Conditions ◽  
Numerical Results ◽  
Dynamical Phase Transition ◽  
Vicsek Model ◽  
Numerical Evidence ◽  
First Order ◽  
Dynamical Phase ◽  
Recent Debate ◽  
Order Continuous

In this work, we consider the phase transition from ordered to disordered states that occur in the Vicsek model of self-propelled particles. This model was proposed to describe the emergence of collective order in swarming systems. When noise is added to the motion of the particles, the onset of collective order occurs through a dynamical phase transition. Based on their numerical results, Vicsek and his colleagues originally concluded that this phase transition was of second order (continuous). However, recent numerical evidence seems to indicate that the phase transition might be of first order (discontinuous), thus challenging Vicsek's original results. In this work, we review the evidence supporting both aspects of this debate. We also show new numerical results indicating that the apparent discontinuity of the phase transition may in fact be a numerical artifact produced by the artificial periodicity of the boundary conditions.

Turing Instability and Hopf Bifurcation for the General Brusselator System

2011 ◽  
Vol 255-260 ◽  
pp. 2126-2130
Author(s):  
Gai Hui Guo ◽  
Bing Fang Li
Keyword(s):  
Hopf Bifurcation ◽  
Boundary Conditions ◽  
Numerical Simulations ◽  
Equilibrium Solution ◽  
Neumann Boundary ◽  
Turing Instability ◽  
Neumann Boundary Conditions ◽  
Homogeneous Equilibrium ◽  
Analytical Results

The Brusselator system subject to homogeneous Neumann boundary conditions is investigated. It is firstly shown that the homogeneous equilibrium solution becomes Turing unstable or diffusively unstable when parameters are chosen properly. Then the existence of Hopf bifurcation to the ODE and PDE models is obtained. Examples of numerical simulations are also shown to support and supplement the analytical results.

scholarly journals Approximate nonradial solutions for the Lane-Emden problem in the ball

2021 ◽  
Vol 11 (1) ◽  
pp. 268-284
Author(s):  
Borbála Fazekas ◽  
Filomena Pacella ◽  
Michael Plum
Keyword(s):  
Dirichlet Problem ◽  
Unit Ball ◽  
Numerical Approximation ◽  
Numerical Results ◽  
Radial Solutions ◽  
Numerical Evidence ◽  
Analytical Results ◽  
First Case

Abstract In this paper we provide a numerical approximation of bifurcation branches from nodal radial solutions of the Lane Emden Dirichlet problem in the unit ball in ℝ2, as the exponent of the nonlinearity varies. We consider solutions with two or three nodal regions. In the first case our numerical results complement the analytical ones recently obtained in [11]. In the case of solutions with three nodal regions, for which no analytical results are available, our analysis gives numerical evidence of the existence of bifurcation branches. We also compute additional approximations indicating presence of an unexpected branch of solutions with six nodal regions. In all cases the numerical results allow to formulate interesting conjectures.

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