Two-dimensional surface integral representations for a rotationally invariant anisotropic medium: applications to scattering

1991 ◽  
Vol 39 (1) ◽  
pp. 108-111 ◽  
Author(s):  
J.C. Monzon
Keyword(s):  
Anisotropic Medium ◽  
Integral Representations ◽  
Two Dimensional ◽  
Surface Integral ◽  
Rotationally Invariant ◽  
Dimensional Surface

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

Asymptotic analysis of some two-dimensional diffusion problems

1995 ◽  
Vol 448 (1933) ◽  
pp. 213-236 ◽  
Keyword(s):  
Linear Problem ◽  
Vacancy Concentration ◽  
Surface Concentration ◽  
Two Dimensional ◽  
Surface Source ◽  
Dimensional Diffusion ◽  
Equilibrium Vacancy ◽  
Equilibrium Vacancy Concentration ◽  
Dimensional Surface ◽  
Diffusion Problems

In this paper we discuss two-dimensional surface source and implant problems for a substitutional-interstitial diffusion model. We present asymptotic solutions in the limit of the surface concentration of impurity (or peak concentration of the implant) being far greater than the equilibrium vacancy concentration. Using leading order composite solutions we plot contours of constant impurity concentration. Some of these contours differ markedly from those of the corresponding linear problem, having the ‘bird’s beak’ shape which is frequently observed in experiments. We also discuss a two-dimensional surface source problem for a va­cancy model.

Anisotropic Coarsening of Two-Dimensional Surface Domains in Copolymer Thin Films

1999 ◽  
Vol 32 (26) ◽  
pp. 9007-9012 ◽  
Author(s):  
Jakob Heier ◽  
Easan Sivaniah ◽  
Edward J. Kramer
Keyword(s):  
Thin Films ◽  
Two Dimensional ◽  
Surface Domains ◽  
Dimensional Surface

A Two-Dimensional Surface Profile Imaging Technique Based on Heterodyne Interferometer

2005 ◽  
Vol 295-296 ◽  
pp. 477-482
Author(s):  
K.W. Wang ◽  
Z.J. Cai ◽  
Li Jiang Zeng
Keyword(s):  
High Speed ◽  
Imaging Technique ◽  
Surface Profile ◽  
Ccd Camera ◽  
Measurement Range ◽  
Interference Signal ◽  
Two Dimensional ◽  
Step Method ◽  
Heterodyne Interferometer ◽  
Dimensional Surface

A two-dimensional surface profile imaging technique based on heterodyne interferometer is proposed. A piezo translator vibrated grating is used to generate a heterodyne signal. A high speed CCD camera is used to extract the interference signal using a five step method. The uncertainty in the displacement measurement is approximately 0.035 µm within a measurement range of 1.7 µm, confirming the two dimensional heterodyne interferometer is valid for measuring the surface profile. The method is also available for low coherence heterodyne interferometer due to the optical frequency shifts caused by the vibration of grating independent on the wavelength.

Two-dimensional surface alloys: Copper on W(100)

1987 ◽  
Vol 188 (3) ◽  
pp. 589-598 ◽  
Author(s):  
Gary A. Attard ◽  
David A. King
Keyword(s):  
Two Dimensional ◽  
Surface Alloys ◽  
Dimensional Surface
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