Sentence examples for time dependent coordinate from inspiring English sources

This scheme is based on a space and time dependent coordinate transformation which redistributes resolution in particle property space according to the shapes of recent solutions for the particle property distribution.

The key prerequisite of the adaptive grid is a time-dependent coordinate transformation, implemented rigorously throughout the governing equations of the model.

A time-dependent coordinate transformation of a constant coefficient hyperbolic system of equations which results in a variable coefficient system of equations is considered.

A coarse grid is generated by a moving mesh finite difference method that is based on equidistribution, and this grid is used to construct a time-dependent coordinate transformation.

Following the idea of the Reynolds transport theorem we consider the temporal derivative of the volume, i.e., the determinant of the time-dependent metric tensor | g ( x, t ) | in order to study the conservation of a density function in variable volumes and obtain the strong conservation form for time-dependent coordinate systems: | g | K = ∂ t ( | g | d ) + ∂ i ( | g | U i d ), (26).

The problem is solved: (a) for small-amplitude motions, by means of the so-called mean position (MP) analysis and (b) for large amplitude oscillations of the outer cylinder for which a time-dependent coordinate transformation (TDCT) is used to fix the computational domain.

The strong conservation form of the continuity equation ∂ t ρ + div ( ρ u ) = 0. is given for time-dependent coordinates by ∂ t ( | g | ρ ) + ∂ i ( | g | e i ⋅ ( u − x ˙ ) ρ ) = 0.

We next state the strong conservation form for time-dependent general coordinate systems.

The present paper derives the complete contravariant form of the Navier Stokes equations in a time-dependent curvilinear coordinate system from the intrinsic derivative of contravariant vectors in a moving frame.

The stability of the systems was studied by molecular dynamics simulation with the further analysis of the time dependent root-mean-square coordinate deviation (RMSD) from the initial structure, and temperature factors.

end{aligned} (7) Here z is the coordinate along the TL, V and I the time and coordinate dependent voltages and currents on each of the conductors, and L, C, are the (n times n) per-unit-length inductance and capacitance matrices.