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References in periodicals archive ?
With the characterization of the weight function by using the proportion of the current introduced in this paper, the mathematical constraint of the natural boundary condition is weakened, and the convenience for the calculation is provided.
Similarly using the natural boundary condition for [theta], (3.16), (3.17), we obtain [Q.sup.1.sub.2] + [Q.sup.2.sub.1] + [Q.sup.3.sub.1] = ([Q.sup.1.sub.22] + [Q.sup.2.sub.31]) + ([Q.sup.2.sub.12] + [Q.sup.3.sub.11]) = -(1/2) [Q.sup.1.sub.22] and [Q.sup.2.sub.31] are equal and opposite and hence this sum is zero.
where n is the outward normal vector at the boundary, [[GAMMA].sub.T] is the part of the boundary where the traction vector is given as a natural boundary condition, [[GAMMA].sub.u] is the part of the boundary where the velocity is given as an essential boundary condition, t is the prescribed value of traction vector on [[GAMMA].sub.T] and u is the prescribed value of velocity on [[GAMMA].sub.u].
Thus by substituting [r.sub.i] = 0 in equation (4) a natural boundary condition is obtained: (6) [Mathematical Expression Omitted]
At the line FY where the metal head is in contact with the air, we will assume a similar natural boundary condition as for the polymer-air interface.
(2017) An Efficient Solution of Heat and Mass Transfer Equations Using Programmable General Purpose Processing Unit under Natural Boundary Conditions in Capillary Porous Solid and Hollow Cylinder.
In contrast to the above-mentioned references, where the authors analysed the integer order differential equations with classical boundary/initial conditions or fractional differential equations with the Dirichlet or natural boundary conditions, in this paper we consider the second-order differential equation with the fractional/generalised boundary conditions.
The stress and mass flow rate of the wetting and non-wetting phase at the boundary are provided by the natural boundary conditions
When employing the Ritz method, fortunately it is not necessary to subject the coordinate functions to the natural boundary conditions [18, 19].
where, the natural boundary conditions appear after integrating by parts which is given by
With the given natural boundary conditions, interests of different groups of inhabitants and other users are in conflict.
The natural boundary conditions, namely the symmetry conditions at the mid-plane, the full-slip (zero friction) condition at the contact point, and the zero force at the free surface are implemented by substituting the boundary terms in the residual equations.