Although the pulse volume evolution does not necessarily correlate linearly with the expansion of the gas volume, we hypothesized that the projected area A in a vertical plane at right angles to the viewing angle of a three-dimensional expanding ash column can be used to follow the initial expansion dynamics of the pulse.
If quantum transactions are multi-dimensional, expanding beyond linear time, they also expand the usual notions of cause and effect, not to mention space and everything that interacts in space.
This paper describes a new design and fabrication concept that each gore forms three-dimensional expanded shape with a small circumferential radius without elongation of the film by pressure.
To obtain two dimensional images, expanding spiral scanning patterns are imposed on the fiber cantilever by using sinusoidal driving voltages with linearly varying amplitudes, which are generated by an arbitrary function generator (AFG3022B, Tektronics) and amplified by piezo driver modules (E-835, Physik Instrumente).
In the well-designed three dimensional structure, expanded graphite works as a conductive matrix to support Al particles coated by carbon.
Our procedure for representing input variables on the two-dimensional subspace expanded by the two main eigenvectors of C ˜, displays the variables as vectors whose direction is the direction of maximum growth of the variable at a given point; in particular, at the sample points.
These equations are first derived for three-dimensional case and then reduced to the two-dimensional case by expanding mechanical displacement and electric potential as power series.
The three-dimensional equations of motion are reduced to two-dimensional ones by expanding the displacement field in Fourier series in the circumferential direction involving circumferential harmonics.
Our model can be extended from one-dimensional neurites to two-dimensional cellular morphology, thereby expanding our knowledge beyond the easily addressable structure of neurons modeled as a round soma with one-dimensional neurites.
Expanding two-dimensional nests may fragment more easily than the three-dimensional nests characteristic of other species.
