Singular points of the continuous spectrum of a two-dimensional periodic waveguide

1989 ◽  
Vol 45 (3) ◽  
pp. 1199-1205
Author(s):  
V. I. Derguzov
Keyword(s):  
Continuous Spectrum ◽  
Singular Points ◽  
Periodic Waveguide ◽  
Two Dimensional

Two-dimensional hydrogen atom. Reciprocal expansions of the polar and parabolic bases of the continuous spectrum

1986 ◽  
Vol 66 (2) ◽  
pp. 146-153 ◽  
Author(s):  
L. S. Davtyan ◽  
G. S. Pogosyan ◽  
A. N. Sisakyan ◽  
V. M. Ter-Antonyan
Keyword(s):  
Hydrogen Atom ◽  
Continuous Spectrum ◽  
Two Dimensional

A note on tuning in Roseau's alternative edge waves

1999 ◽  
Vol 382 ◽  
pp. 245-262 ◽  
Author(s):  
ULF TORSTEN EHRENMARK
Keyword(s):  
Continuous Spectrum ◽  
Two Dimensional ◽  
Edge Waves ◽  
Modal Number ◽  
Stagnation Points ◽  
Bounded State ◽  
Wave Guides ◽  
Recent Method ◽  
Wave Profiles ◽  
Standing Edge Waves

Ursell's edge waves are derived systematically using a new method. Computed profiles are then compared with the lesser known shoreline singular waves first constructed by Roseau (1958). A recent method of writing the continuous spectrum solutions on a plane beach is thereby extended to the discrete spectrum to enable the reconstruction of both types of edge waves so that, in particular, the unbounded wave profiles are more easily computed. The existence of stagnation points on the bed for standing edge waves is considered and demonstrated for the first few modes. A ramification of this is the existence of (two-dimensional-cross-shore) dividing ‘streamlines’ from the bed to the surface also, the number of which appears to equate to the modal number of the edge wave. These dividing streamlines, along with other streamlines, are computed for the first few modes of both the Ursell and the (alternative) singular waves constructed by Roseau.It follows that these waves can also exist in the presence of solid cylinders bounded by fixed streamlines and, in particular therefore, that the hitherto unbounded Roseau waves can exist in a bounded state since a region including the origin can be removed from the flow by exploiting a dividing streamline. It is confirmed that the wavenumbers of the Roseau waves interlace those of the Ursell waves. An examination of available evidence leaves open to further research the question of whether the alternative Roseau waves have been ‘inadvertently’ observed either in the laboratory or, by means of contamination of data, in the field. Further laboratory simulations using longshore solid cylinders as ‘wave guides’ are proposed.

On: “A Method to minimize edge effects in two‐dimensional discrete Fourier transforms” by Yanick Ricard and Richard J. Blakely (GEOPHYSICS, 53, 1113–1117, August 1988).

Geophysics ◽  
1990 ◽  
Vol 55 (11) ◽  
pp. 1514-1514 ◽  
Author(s):  
Kenneth F. Sprenke
Keyword(s):  
Continuous Spectrum ◽  
Edge Effects ◽  
Fourier Transforms ◽  
Interpolation Process ◽  
Two Dimensional ◽  
Discrete Fourier Transforms ◽  
Sampling Grid ◽  
Valuable Method ◽  
Sampling Window ◽  
Rotational Transform

The authors of this paper have created a very valuable method for approximating the two‐dimensional continuous spectrum by repeatedly rotating a rectangular sampling grid and averaging the resulting spectra. The authors state that their rotational transform “eliminates artifacts associated with the orientation of the rectangular sampling window.” However, I believe that one aspect of their method, the interpolation process, actually creates artifacts:

Translation and Development in Two Dimensional Fields with Special Reference to Pressure Variations

1948 ◽  
Vol 1 (4) ◽  
pp. 412
Author(s):  
RW James
Keyword(s):  
Special Reference ◽  
Least Squares ◽  
Singular Points ◽  
Rate Of Change ◽  
Special Importance ◽  
Two Dimensional ◽  
Practical Result ◽  
Weighting Factors ◽  
Least Squares Fit

In previous studies of translation of field entities attention has been focused on singular points and lines of the field, with the result that the complementary concept of development in the field has been left either not at all, or quite arbitrarily, defined. By determining the least-squares fit to the rate of change of the entity throughout the field, rigid and unique definitions are derived of both the translation and rotation of the system of isolines of the entity, and also of the local and total development in the field. The practical result is to derive a system of weighting factors for the translation of elements of the field, and to stress the special importance of those regions where the gradient of the entity is greatest. In meteorology this means that the movement of pressure-systems is dominated by that of the regions of strongest wind. Comparison is made with earlier results, and the question of the consistent motion of coexistent fields (e.g. pressure and temperature) is discussed.

Transformations between parabolic bases of the two-dimensional hydrogen atom in the continuous spectrum

1988 ◽  
Vol 74 (2) ◽  
pp. 157-161 ◽  
Author(s):  
L. S. Davtyan ◽  
G. S. Pogosyan ◽  
A. N. Sisakyan ◽  
V. M. Ter-Antonyan
Keyword(s):  
Hydrogen Atom ◽  
Continuous Spectrum ◽  
Two Dimensional

scholarly journals Analysis for Lorentzian conformal field theories through sine-square deformation

2020 ◽  
Vol 2020 (6) ◽  
Author(s):  
Xun Liu ◽  
Tsukasa Tada
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Continuous Spectrum ◽  
Central Charge ◽  
Virasoro Algebra ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
The Third

Abstract We reexamine two-dimensional Lorentzian conformal field theory using the formalism previously developed in a study of sine-square deformation of Euclidean conformal field theory. We construct three types of Virasoro algebra. One of them reproduces the result by Lüscher and Mack, while another type exhibits divergence in the central charge term. The third leads to a continuous spectrum and contains no closed time-like curve in the system.

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