We derive for crystal optics in coordinate-invariant way the cone approximation of refraction vectors in the neighborhood of optic axes and determine its invariants and eigenvectors. It proved to describe an elliptic ...We derive for crystal optics in coordinate-invariant way the cone approximation of refraction vectors in the neighborhood of optic axes and determine its invariants and eigenvectors. It proved to describe an elliptic cone. The second invariant of the operator of the wave equation with respect to similarity transformations determines the special cases of degeneration including the optic axes where the polarization of the waves due to self-intersection of the dispersion surface is not uniquely determined. This second invariant is included in all investigations and it is taken into account in the illustrations. It is biquadratic in the refraction vectors and the corresponding forth-order surface in three-dimensional space splits in two separate shells and a non-rational product decomposition describing this is found. We give also a more general classification of all possible solutions of an equation with an arbitrary three-dimensional operator.展开更多
In this paper,it is shown that for stable,steady state operation of devices typical of microwave and millimeter wave electronics,no negative differential capacitance is possible with conventional thinking.However,it m...In this paper,it is shown that for stable,steady state operation of devices typical of microwave and millimeter wave electronics,no negative differential capacitance is possible with conventional thinking.However,it may be possible,with strain engineering of materials,to obtain some if not all elements of the differential capacitance tensor which are negative.Rigorous derivations are provided based upon analyzing the physics using thermodynamic phenomenological free energy.It should be emphasized that,even with strain engineering,and possible discovery of some negative capacitive elements,stable operation will not be obtained because the thermodynamics precludes it.展开更多
文摘We derive for crystal optics in coordinate-invariant way the cone approximation of refraction vectors in the neighborhood of optic axes and determine its invariants and eigenvectors. It proved to describe an elliptic cone. The second invariant of the operator of the wave equation with respect to similarity transformations determines the special cases of degeneration including the optic axes where the polarization of the waves due to self-intersection of the dispersion surface is not uniquely determined. This second invariant is included in all investigations and it is taken into account in the illustrations. It is biquadratic in the refraction vectors and the corresponding forth-order surface in three-dimensional space splits in two separate shells and a non-rational product decomposition describing this is found. We give also a more general classification of all possible solutions of an equation with an arbitrary three-dimensional operator.
文摘In this paper,it is shown that for stable,steady state operation of devices typical of microwave and millimeter wave electronics,no negative differential capacitance is possible with conventional thinking.However,it may be possible,with strain engineering of materials,to obtain some if not all elements of the differential capacitance tensor which are negative.Rigorous derivations are provided based upon analyzing the physics using thermodynamic phenomenological free energy.It should be emphasized that,even with strain engineering,and possible discovery of some negative capacitive elements,stable operation will not be obtained because the thermodynamics precludes it.
