scholarly journals Spectrum of the Laplacian on regular polyhedra

2021 ◽  
Vol 20 (1) ◽  
pp. 193-214
Author(s):  
Evan Greif ◽  
◽  
Daniel Kaplan ◽  
Robert S. Strichartz ◽  
Samuel C. Wiese ◽  
...  
Keyword(s):  
Regular Polyhedra ◽  
Spectrum Of The Laplacian

scholarly journals Exact spectrum of the Laplacian on a domain in the Sierpinski gasket

2019 ◽  
Vol 277 (3) ◽  
pp. 806-888 ◽  
Author(s):  
Hua Qiu
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket ◽  
Spectrum Of The Laplacian

On the spectrum of the Laplacian with frequently alternating boundary conditions

1999 ◽  
Vol 118 (3) ◽  
pp. 272-277 ◽  
Author(s):  
D. I. Borisov ◽  
R. R. Gadyl’shin
Keyword(s):  
Boundary Conditions ◽  
Spectrum Of The Laplacian

On regular polyhedra with hidden symmetries

1987 ◽  
Vol 12 (3-4) ◽  
pp. 450-458
Author(s):  
Jörg M. Wills
Keyword(s):  
Hidden Symmetries ◽  
Regular Polyhedra

The Spectrum of the Laplacian on the Pentagasket

2003 ◽  
pp. 1-24 ◽  
Author(s):  
Bryant Adams ◽  
S. Alex Smith ◽  
Robert S. Strichartz ◽  
Alexander Teplyaev
Keyword(s):  
Spectrum Of The Laplacian

Regular polyhedra—old and new

1977 ◽  
Vol 16 (1-2) ◽  
pp. 1-20 ◽  
Author(s):  
Branko Grünbaum
Keyword(s):  
Regular Polyhedra

Regular Polyhedra

2000 ◽  
pp. 193-210
Author(s):  
Vladimir Rovenski
Keyword(s):  
Regular Polyhedra

scholarly journals Spectrum of the Laplacian on a manifold of negative curvature. II

1979 ◽  
Vol 14 (4) ◽  
pp. 609-620 ◽  
Author(s):  
Mark A. Pinsky
Keyword(s):  
Negative Curvature ◽  
Spectrum Of The Laplacian

scholarly journals PRODUCING DESIGN OBJECTS FROM REGULAR POLYHEDRA: A PRACTICAL APPROACH

2018 ◽  
pp. 49-55
Author(s):  
Beniamino Polimeni
Keyword(s):  
3D Printing ◽  
Creative Process ◽  
Practical Approach ◽  
Complex Geometries ◽  
Regular Polyhedra ◽  
Modelling Techniques ◽  
Digital Modelling ◽  
Practical Guidance ◽  
Design Objects ◽  
Architecture And Design

In the last few years, digital modelling techniques have played a major role in architecture and design, influencing, at the same time, the creative process and the fabrication of objects. This revolution has produced a new productive generation of architects and designers focused on the expanding possibilities of material and formal production, reinforcing the idea of architecture as an interaction between art and artisanship. This original perspective inspires this paper, which illustrates the contemporary scenario and provides some practical guidance about tools and technologies the designers most often use for creating geometric sculptures with 3D printing. Creative possibilities of topological mesh modelling are used to generate complex geometries from regular polyhedra. This process explores how combining different geometric operations can activate architectural inquiry and generate fascinating shapes with creative flexibility.

scholarly journals DISTRIBUTION OF MAXIMA OF THE ANTISYMMETRIZED WAVE FUNCTION FOR THE NUCLEONS OF A CLOSED-SHELL AND FOR THE NUCLEONS OF ALL CLOSED-SHELLS IN A NUCLEUS.

2020 ◽  
Vol 15 ◽  
pp. 57
Author(s):  
G. S. Anagnostatos
Keyword(s):  
Wave Function ◽  
Mathematical Problem ◽  
Closed Shell ◽  
Wave Functions ◽  
Pictorial Representation ◽  
One Dimensional ◽  
Regular Polyhedra ◽  
Closed Shell Nuclei ◽  
Simple Systems ◽  
Closed Shells

The significant features of exchange symmetry are displayed by simple systems such as two identical, spinless fermions in a one-dimensional well with infinite walls. The conclusion is that the maxima of probability of the antisymmetrized wave function of these two fermions lie at the same positions as if a repulsive force (of unknown nature) was applied between these two fermions. This conclusion is combined with the solution of a mathematical problem dealing with the equilibrium of identical repulsive particles (of one or two kinds) on one or more spheres like neutrons and protons on nuclear shells. Such particles are at equilibrium only for specific numbers of particles and, in addition, if these particles lie on the vertices of regular polyhedra or their derivative polyhedra. Finally, this result leads to a pictorial representation of the structure of all closed shell nuclei. This representation could be used as a laboratory for determining nuclear properties and corresponding wave functions.

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