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Irregular C2 surface construction using bi-polynomial rectangular patches
The construction of C2 surfaces using bi-polynomial
parametric rectangular patches is studied. In particular, the analy-
sis of the C2 continuity conditions for the case of n patches meeting at
an n-vertex is developed
The Construction of Curves and Surfaces Using Numerical Optimization Techniques
Numerical optimization techniques are playing an increasing role in curve and surface construction. Often difficult problems in curve and surface construction, especially when some aspect of shape control is involved, can be phrased as a constrained optimization problem. Four such classes of problems are explored: parametric curve fitting with non-linear shape constraints; explicit surface fitting with linear shape constraints; surface fitting to scattered data giving rise to ill-posed problems; finally, variable knot problems. In each of these problems there is a nonlinear aspect: either the shape of the curve or surface is important for manufacturing or engineering reasons or the shape affects the convergence of numerical algorithms which use the curve or surface or the placement of knots affects the accuracy of the fits. In all cases the class of functions used is that of parametric spline curves and tensor or direct product spline surfaces. The reason for choosing this class is that splines provide flexible models that are easily evaluated and stored. Furthermore, the B-spline representation of splines leads to convenient expressions for shape control over regions
Assessment of the Lunar Surface Layer and in Situ Materials to Sustain Construction-related Applications
Present and future technologies to facilitate lunar composition and resource assessment with applications to lunar surface construction are presented. We are particularly interested in the construction activity associated with lunar-based astronomy. We address, as an example, the use of ground-probing radar to help assess subsurface conditions at sites for observatories and other facilities
Global Permutationally Invariant Potential Energy Surface for Ozone Forming Reaction
We constructed new global potential energy surface for O + O2 → O3 reaction. It is based on high level electronic structure theory calculations and employs fitting by permutationally invariant polynomial functions. This method of surface construction takes full advantage of permutation symmetry of three O nuclei and allows reducing dramatically the number of ab initio data points needed for accurate surface representation. New potential energy surface offers dramatic improvement over older surface of ozone in terms of dissociation energy and behavior along the minimum energy path. It can be used to refine the existing theories of ozone formation
Solution of a quadratic quaternion equation with mixed coefficients
A comprehensive analysis of the morphology of the solution space for a
special type of quadratic quaternion equation is presented. This equation,
which arises in a surface construction problem, incorporates linear terms in a
quaternion variable and its conjugate with right and left quaternion
coefficients, while the quadratic term has a quaternion coefficient placed
between the variable and its conjugate. It is proved that, for generic
coefficients, the equation has two, one, or no solutions, but in certain
special instances the solution set may comprise a circle or a 3-sphere in the
quaternion space . The analysis yields solutions for each case, and
intuitive interpretations of them in terms of the four-dimensional geometry of
the quaternion space .Comment: 19 pages, to appear in the Journal of Symbolic Computatio
Topological classification of intrinsic 3D superconductors using anomalous surface construction
Intrinsic topological superconductors have protected gapless Majorana modes,
bound and/or propagating, at the natural boundaries of the sample, without
requiring field, defect, or heterostructure. We establish the complete
classification/construction of intrinsic topological superconductors jointly
protected by point-group and time-reversal symmetries in three dimensions. This
is obtained from enumerating distinct ways for stacking th-order irreducible
building blocks, minimal anomalous surface states of th-order topological
superconductors. Particularly, our method provides a unified description of
possible surface anomalies away from high-symmetry points/lines in terms of the
homotopy group of the surface mass field.Comment: 43 pages, 9 figures, 4 table
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