Spectral Curves of the Hyperelliptic Hitchin Systems

2019 ◽  
Vol 53 (4) ◽  
pp. 291-303
Author(s):  
O. K. Sheinman
Keyword(s):  
Spectral Curves ◽  
Hitchin Systems

scholarly journals Spectral curves are transcendental

2021 ◽  
Vol 111 (1) ◽  
Author(s):  
H. W. Braden
Keyword(s):  
Spectral Curve ◽  
Spectral Curves ◽  
Arithmetic Properties ◽  
A Charge

AbstractSome arithmetic properties of spectral curves are discussed: the spectral curve, for example, of a charge $$n\ge 2$$ n ≥ 2 Euclidean BPS monopole is not defined over $$\overline{\mathbb {Q}}$$ Q ¯ if smooth.

scholarly journals Folding of Hitchin Systems and Crepant Resolutions

2021 ◽  
Author(s):  
Florian Beck ◽  
Ron Donagi ◽  
Katrin Wendland
Keyword(s):  
Fixed Point ◽  
Lie Algebras ◽  
Integrable Systems ◽  
Trace Back ◽  
Dynkin Diagrams ◽  
Or Groups ◽  
Hitchin Systems ◽  
Singular Fibers ◽  
Crepant Resolutions ◽  
Intermediate Jacobian

Abstract Folding of ADE-Dynkin diagrams according to graph automorphisms yields irreducible Dynkin diagrams of $\textrm{ABCDEFG}$-types. This folding procedure allows to trace back the properties of the corresponding simple Lie algebras or groups to those of $\textrm{ADE}$-type. In this article, we implement the techniques of folding by graph automorphisms for Hitchin integrable systems. We show that the fixed point loci of these automorphisms are isomorphic as algebraic integrable systems to the Hitchin systems of the folded groups away from singular fibers. The latter Hitchin systems are isomorphic to the intermediate Jacobian fibrations of Calabi–Yau orbifold stacks constructed by the 1st author. We construct simultaneous crepant resolutions of the associated singular quasi-projective Calabi–Yau three-folds and compare the resulting intermediate Jacobian fibrations to the corresponding Hitchin systems.

scholarly journals Seiberg-Witten equations and non-commutative spectral curves in Liouville theory

2013 ◽  
Vol 54 (2) ◽  
pp. 022306 ◽  
Author(s):  
Leonid Chekhov ◽  
Bertrand Eynard ◽  
Sylvain Ribault
Keyword(s):  
Liouville Theory ◽  
Spectral Curves

scholarly journals MICROSPECTROPHOTOMETRY OF NEWLY SYNTHESIZED STARCH IN SITU

1970 ◽  
Vol 18 (6) ◽  
pp. 439-449
Author(s):  
GEORGE E. WHEELER
Keyword(s):  
Absorption Maximum ◽  
In Vitro Studies ◽  
Phosphate Solution ◽  
Starch Digestion ◽  
Spectral Curves ◽  
Similarities And Differences

Many of the cells in stem sections of several Commelinaceae species synthesized much new starch when incubated in buffered 1% glucose 1-phosphate solution. The starch appeared in the cytoplasm rather than in the plastids. Although the starch I2-KI color was uniform within any one cell, there was considerable variation from cell to cell, even in the same section. The colors with I2-KI ranged from blue, through purples to magenta and mahogany. Tests with α-amylase and with β-amylase showed the starch to be amylose. Microspectrophotometrically determined extinction curves, based on the new starch in situ, varied with the visualized color. As expected, starch which stained blue with I2-KI had an absorption maximum in the orange-red wavelengths above 600 mµ; increasingly red I2-KI colors were characterized by shifts of the absorption maximum further into the shorter wavelengths. The course of new starch digestion by α-amylase and by β-amylase was followed visually and with the microspectrophotometer. Similarities and differences between these spectral curves and those published for in vitro studies are pointed out. The difficulties met with in using the microspectrophotometric method are discussed.

PECULIAR PROPERTIES OF ELECTROMAGNETIC RADIATION PROPAGATION IN PHOTONIC CRYSTALLINE METAL-DIELECTRIC SYSTEMS BASED ON OPALS

2021 ◽  
pp. 89-99
Author(s):  
S. D. Khanin ◽  
A. I. Vanin ◽  
Yu. A. Kumzerov ◽  
V. G. Solovyev ◽  
A. V. Cvetkov ◽  
...  
Keyword(s):  
Electromagnetic Waves ◽  
Bragg Diffraction ◽  
Opal Matrix ◽  
Spectral Curves ◽  
Absorption Of Light ◽  
Anomalous Transmission ◽  
Asymmetric Form ◽  
Transmission And Absorption ◽  
Crystalline Metal ◽  
Plasmon Polaritons

The article studies the propagation of electromagnetic waves in metal-dielectric systems based on opals. We revealed anomalous transmission and absorption of light by hybrid plasmon- photonic layered heterostructures associated with the excitation of surface plasmon polaritons propagating along the metal-dielectric interface. The position of maxima in the reflection spectra of nanocomposites, obtained by filling the opal matrix with metal by the electrothermodiffusion method, is explained by the Bragg diffraction, and the asymmetric form of the spectral curves is attributed to the Fano resonance.

scholarly journals Geotechnical Site Investigation Using S-waves with Implications for Ground Motion Analysis

2017 ◽  
Vol 64 (4) ◽  
pp. 205-219
Author(s):  
Bilal Hassan ◽  
Stephen D. Butt ◽  
Charles A. Hurich
Keyword(s):  
Ground Motion ◽  
Structural Integrity ◽  
Wave Attenuation ◽  
Crack Surface ◽  
Spectral Ratio ◽  
Site Investigation ◽  
Stress Regime ◽  
Fractured Bedrock ◽  
Spectral Curves ◽  
Fracture Orientation

AbstractEvaluation results of shear wave attenuation-based ground motion restricted by fracture orientation and rheology, from among those of an extended experimental study, are presented herein. The issues of competence of fractured bedrock dynamically disturbed multilaterally are assessed. Disturbance is primarily modelled by Sh and Sv stimulation, given fracture orientation, while subjected to direct fracture stress regime conditions varying in time. Hence, directionalities of polarisation and stress are taken into consideration simultaneously following simple site-specific non-erodetic approach. Comparison of spectral curves and spectral ratio curves of attenuation with respect to variations of direction and stress emphasise the amplification of the ‘seismic response’ in one direction compared to the other, i.e. vertical vs. horizontal, in terms of weighing possibilities of or predicting structural integrity against failure. The composite analyses of multiple spectral curves not only enable determination of the orientation of the fracture set/s in space but also allow inferring the nature of more amplified response perpendicular to the crack surface compared to that of a response parallel to the crack surface.

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