6,632 research outputs found
Integrable lattices and their sublattices II. From the B-quadrilateral lattice to the self-adjoint schemes on the triangular and the honeycomb lattices
An integrable self-adjoint 7-point scheme on the triangular lattice and an
integrable self-adjoint scheme on the honeycomb lattice are studied using the
sublattice approach. The star-triangle relation between these systems is
introduced, and the Darboux transformations for both linear problems from the
Moutard transformation of the B-(Moutard) quadrilateral lattice are obtained. A
geometric interpretation of the Laplace transformations of the self-adjoint
7-point scheme is given and the corresponding novel integrable discrete 3D
system is constructed.Comment: 15 pages, 6 figures; references added, some typos correcte
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Generation of Porous Structures Using Fused Deposition
The Fused Deposition Modeling process uses hardware and software machine-level
language that are very similar to that of a pen-plotter. Consequently, the·use of patterns with
poly-lines as basic geometric features, instead of the current method based on filled polygons
(monolithic models), can increase its efficiency.
In the current study, various toolpath planning methods have been developed to fabricate
porous structures. Computational domain decomposition methods can be applied to the physical
or to slice-level domains to generate structured and unstructured grids. Also, textures can be
created using periodic tiling of the layer with unit cells (squares, honeycombs, etc). Methods
'based on curves include fractal space filling curves and.change of effective road width Within a
layer or within a continuous curve. Individual phases can also be placed in binary compositions.
In present investigation, a custom software has been developed and implemented to
generate build files (SML) and slice files (SSL) for the above-mentioned structures, demonstrating the efficient control ofthe size, shape, and distribution ofporosity.Mechanical Engineerin
Menelaus' theorem, Clifford configurations and inversive geometry of the Schwarzian KP hierarchy
It is shown that the integrable discrete Schwarzian KP (dSKP) equation which
constitutes an algebraic superposition formula associated with, for instance,
the Schwarzian KP hierarchy, the classical Darboux transformation and
quasi-conformal mappings encapsulates nothing but a fundamental theorem of
ancient Greek geometry. Thus, it is demonstrated that the connection with
Menelaus' theorem and, more generally, Clifford configurations renders the dSKP
equation a natural object of inversive geometry on the plane. The geometric and
algebraic integrability of dSKP lattices and their reductions to lattices of
Menelaus-Darboux, Schwarzian KdV, Schwarzian Boussinesq and Schramm type is
discussed. The dSKP and discrete Schwarzian Boussinesq equations are shown to
represent discretizations of families of quasi-conformal mappings.Comment: 26 pages, 9 figure
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Dynamic deformability of individual PbSe nanocrystals during superlattice phase transitions
The behavior of individual nanocrystals during superlattice phase transitions can profoundly affect the structural perfection and electronic properties of the resulting superlattices. However, details of nanocrystal morphological changes during superlattice phase transitions are largely unknown due to the lack of direct observation. Here, we report the dynamic deformability of PbSe semiconductor nanocrystals during superlattice phase transitions that are driven by ligand displacement. Real-time high-resolution imaging with liquid-phase transmission electron microscopy reveals that following ligand removal, the individual PbSe nanocrystals experience drastic directional shape deformation when the spacing between nanocrystals reaches 2 to 4 nm. The deformation can be completely recovered when two nanocrystals move apart or it can be retained when they attach. The large deformation, which is responsible for the structural defects in the epitaxially fused nanocrystal superlattice, may arise from internanocrystal dipole-dipole interactions
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