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Within this semi-classical method, the group velocity and the mass tensor are calculated using the DFT band dispersion.
The underlying physics behind this investigation is the fact that Schrödinger equation with position dependent mass tensor and potentials has a covariant form which follows the coordinate transformation.
Therefore, we deal with the shape optimization problem to maximize low-frequency band gaps; their bounds are determined by analysing the effective mass tensor of the homogenized medium.
Using this technique we obtain the exact spatial form of the mass tensor and potentials for a variety of cloaks with different shapes.
We study how the anisotropy of the effective mass tensor acts on the uniform approximation of the first K eigenvalues and eigenvectors and their sequential arrangement.
The calculations made allowed application of the semi-analytical model developed previously for nonlinear structural vibration involving three tensors, namely the mass tensor mij, the linear rigidity tensor kij and the nonlinearity tensor bijkl.
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First, the Hamilton's principle is employed to obtain the stiffness, mass tensors and modal values of the vibrating structure subjected to hygrothermal stresses.
In multiple space dimensions the approach naturally reveals the form of the added mass tensors in the equations governing the motion of the rigid body.
On the other hand, the mobility coefficient (which is related to the distribution of the second derivative of the energy, i.e. to the effective-mass tensor) is here temperature-dependent while in the parabolic case is constant.
Explicit formulae for the mass density tensor and bulk modulus are derived in terms of the transformation function.
This paper proposes an effective method for identifying the complete inertia parameters (including the mass, inertia tensor and center of mass position) of a space robotic system.
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