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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：μ-basis for a tensor product rational surface with respect to one variable
张量积 有理曲面 变量 μ基
2023/4/28
The method of moving planes and moving quadrics expresses the implicit equation of a rational parametric surface as a compact determinant. Efficient computation of the moving planes and moving quadric...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On Deligne-Beilinson cohomology of the universal K3 surface
泛K3曲面 Deligne-Beilinson 同调
2023/5/15
O'Grady's generalized Franchetta conjecture is concerned with algebraic cycles of codimension 2 on the universal polarized K3 surface of genus g. This conjecture has been confirmed only for certain sm...
COHOMOLOGY OF SL(2, C) CHARACTER VARIETIES OF SURFACE GROUPS AND THE ACTION OF THE TORELLI GROUP
SL(2, C) CHARACTER VARIETIES SURFACE GROUPS TORELLI GROUP
2015/12/17
We determine the action of the Torelli group on the equivariant cohomology of the space of flat SL(2, C) connections on a closed Riemann surface. We show that the trivial part of the action contains t...
COHOMOLOGY OF U(2,1) REPRESENTATION VARIETIES OF SURFACE GROUPS
U(2,1) REPRESENTATION VARIETIES SURFACE GROUPS
2015/12/17
In this paper we use the Morse theory of the Yang-Mills-Higgs functional on the singular space of Higgs bundles on Riemann surfaces to compute the equivariant cohomology of the space of semistable U(2...
SURFACE GROUP REPRESENTATIONS TO SL(2, C) AND HIGGS BUNDLES WITH SMOOTH SPECTRAL DATA
SURFACE GROUP SL(2, C) HIGGS BUNDLES SPECTRAL DATA
2015/12/17
We show that for every nonelementary representation of a surface group into SL(2, C) there is a Riemann surface structure such that the Higgs bundle associated to the representation lies outside the d...
FIRST VARIATION OF THE GENERAL CURVATURE-DEPENDENT SURFACE ENERGY
Surface energy gradient fl ow mean curvature
2015/12/11
We consider general surface energies, which are weighted integrals
over a closed surface with a weight function depending on the position, the
unit normal and the total curvature of the surface. Ene...
Towards self-organization of decaying surface corrugations: A numerical study
A numerical study self-organization
2015/12/11
We study numerically the interplay of surface topography and kinetics in the relaxation of crystal
surface corrugations below roughening in two independent space dimensions. The kinetic processes
ar...
Self-organization of decaying surface corrugations:A numerical study
Self-organization decaying surface corrugations numerical study
2015/10/16
We study numerically the interplay of surface topography and kinetics in the relaxation of crystal surface corrugations below roughening in two independent space dimensions. The kinetic processes are ...
Formulas for the force dipole interaction of surface line defects in homoepitaxy
Formulas for the force surface line defects homoepitaxy
2015/10/16
Using asymptotics, we derive explicit, simplified formulas for integrals representing the force dipole interaction energy per unit length between line defects (steps) of the same sign that form pertur...
DISCRETE AND CONTINUUM RELAXATION DYNAMICS OF FACETED CRYSTAL SURFACE IN EVAPORATION MODELS
crystal surface evaporation facet Burton–Cabrera–Frank model subgradient formalism free-boundary problem shock
2015/10/16
We study linkages of two scales in the relaxation of an axisymmetric crystal with a facet in evaporation-condensation kinetics. The macroscale evolution is driven by the motion of concentric circular,...
Phase-field model for reconstructed stepped surface
Phase-field model reconstructed stepped surface
2015/10/16
We formulate a phase-field, or diffuse-interface, model for the evolution of stepped surfaces under surface diffusion in the presence of distinct material parameters across nanoscale terraces. In the ...
We investigate some properties of equilibrium liquid drops lying on a horizontal plane, when small periodic perturbations arise in the properties of that plane (due for example to chemical contaminati...
We study liquid drops lying on a rough planar surface. The drops are minimizers of an energyfunctional that includes a random adhesion energy. We prove the existence of minimizers and the regularity o...
Almost dense orbit on energy surface.
THE BASIC TOPOLOGY MODEL OF SPHERICAL SURFACE DIGITAL SPACE
SGDM manifold spherical surface digital space
2015/7/6
SGDM (Sphere Grid Data Model) is an efficient method to deal with the global data because of the advantages of multi-resolution and
hierarchy. However, SGDM has no distinct descriptions and lack of r...