Sentence examples for material derivatives from inspiring English sources

An alternative approach, which is called the continuous approach, describes the domain variation with a mapping function and applies the concept of material derivatives to derive the sensitivity, which is known as a shape gradient function.

(1.7) where dot{u}=u_{t}+uu_{x} quadtextit{and}quad ddot {u}= dot{u}_{t}+udot{u}_{x} (1.8) denote the material derivatives of u and (dot{u}), respectively.

We find that the driving forces of mass diffusion can be written in terms of covariant material derivatives reflecting, in a purely geometrical manner, the presence of a (first-order) torsion and a (second-order) curvature.

Classical irreversible thermodynamics is upscaled from the microscale to the macroscale and used to provide a connection among material derivatives that arise from the conservation and balance equations under near-equilibrium conditions.

It is shown that the non-linear wave equations (partly new), can be written in a form similar to the linear acoustics ones (mostly known), by taking into account the self-convection of sound by sound; this implies replacing the linear local and material derivatives, byself-convected and non-linear extensions of these (Table 2), which also affect the sound speed.

We derive the material derivative of the proposed objective, termed as the configurational derivative, that describes sensitivity of arbitrary functionals to arbitrary motions of the inclusion/hole as well as the domain boundaries.

Both problems are formulated as distributed-parameter shape optimization problems, and the shape gradient functions are derived using the material derivative method and the adjoint variable method.

A general formula is derived using the material derivative concept for the shape design sensitivity of the stress defined at a local segment.

The shape gradient function and the optimality conditions for this problem are derived theoretically using the material derivative method and the adjoint variable method.

The shape gradient function, the size gradient function, and the optimality conditions for this problem are theoretically derived with the Lagrange multiplier method, the material derivative method, and the adjoint variable method.

We derive the shape gradient function by using the material derivative method and apply it to the free-form optimization method for determining the optimal shape.