Uniformization of geometric structures with aplications to conformal geometry

Combining different semiconductor materials with diverse geometric structures and energy level configurations is an effective strategy for constructing high-activity heterostructure photocatalyst. Using the solvothermal method, 1D TiO2 nanobelts were uniformly...

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The geometric structures and instability of entropic dynamical models

Advances in Mathematics ◽

10.1016/j.aim.2011.02.002 ◽

2011 ◽

Vol 227 (1) ◽

pp. 459-471 ◽

Cited By ~ 16

Author(s):

Linyu Peng ◽

Huafei Sun ◽

Dandi Sun ◽

Jin Yi

Keyword(s):

Dynamical Models ◽

Geometric Structures

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Gauge invariant canonical symplectic algorithms for real-time lattice strong-field quantum electrodynamics

Journal of High Energy Physics ◽

10.1007/jhep02(2021)127 ◽

2021 ◽

Vol 2021 (2) ◽

Author(s):

Qiang Chen ◽

Jianyuan Xiao ◽

Peifeng Fan

Keyword(s):

Field Theory ◽

Real Time ◽

Quantum Electrodynamics ◽

Symplectic Form ◽

Strong Field ◽

Relativistic Quantum ◽

High Order ◽

High Quality ◽

Geometric Structures ◽

Gauge Invariant

Abstract A class of high-order canonical symplectic structure-preserving geometric algorithms are developed for high-quality simulations of the quantized Dirac-Maxwell theory based strong-field quantum electrodynamics (SFQED) and relativistic quantum plasmas (RQP) phenomena. With minimal coupling, the Lagrangian density of an interacting bispinor-gauge fields theory is constructed in a conjugate real fields form. The canonical symplectic form and canonical equations of this field theory are obtained by the general Hamilton’s principle on cotangent bundle. Based on discrete exterior calculus, the gauge field components are discreted to form a cochain complex, and the bispinor components are naturally discreted on a staggered dual lattice as combinations of differential forms. With pull-back and push-forward gauge covariant derivatives, the discrete action is gauge invariant. A well-defined discrete canonical Poisson bracket generates a semi-discrete lattice canonical field theory (LCFT), which admits the canonical symplectic form, unitary property, gauge symmetry and discrete Poincaré subgroup, which are good approximations of the original continuous geometric structures. The Hamiltonian splitting method, Cayley transformation and symmetric composition technique are introduced to construct a class of high-order numerical schemes for the semi-discrete LCFT. These schemes involve two degenerate fermion flavors and are locally unconditional stable, which also preserve the geometric structures. Admitting Nielsen-Ninomiya theorem, the continuous chiral symmetry is partially broken on the lattice. As an extension, a pair of discrete chiral operators are introduced to reconstruct the lattice chirality. Equipped with statistically quantization-equivalent ensemble models of the Dirac vacuum and non-trivial plasma backgrounds, the schemes are expected to have excellent performance in secular simulations of relativistic quantum effects, where the numerical errors of conserved quantities are well bounded by very small values without coherent accumulation. The algorithms are verified in detail by numerical energy spectra. Real-time LCFT simulations are successfully implemented for the nonlinear Schwinger mechanism induced e-e+ pairs creation and vacuum Kerr effect, where the nonlinear and non-perturbative features captured by the solutions provide a complete strong-field physical picture in a very wide range, which open a new door toward high-quality simulations in SFQED and RQP fields.

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A New Adaptive Method for the Extraction of Steel Design Structures from an Integrated Point Cloud

Sensors ◽

10.3390/s21103416 ◽

2021 ◽

Vol 21 (10) ◽

pp. 3416

Author(s):

Pawel Burdziakowski ◽

Angelika Zakrzewska

Keyword(s):

Data Integration ◽

Point Cloud ◽

Laser Scanning ◽

Detection Threshold ◽

Measurement Data ◽

Steel Structures ◽

Adaptive Method ◽

Edge Extraction ◽

Geometric Structures ◽

Redundant Data

The continuous and intensive development of measurement technologies for reality modelling with appropriate data processing algorithms is currently being observed. The most popular methods include remote sensing techniques based on reflected-light digital cameras, and on active methods in which the device emits a beam. This research paper presents the process of data integration from terrestrial laser scanning (TLS) and image data from an unmanned aerial vehicle (UAV) that was aimed at the spatial mapping of a complicated steel structure, and a new automatic structure extraction method. We proposed an innovative method to minimize the data size and automatically extract a set of points (in the form of structural elements) that is vital from the perspective of engineering and comparative analyses. The outcome of the research was a complete technology for the acquisition of precise information with regard to complex and high steel structures. The developed technology includes such elements as a data integration method, a redundant data elimination method, integrated photogrammetric data filtration and a new adaptive method of structure edge extraction. In order to extract significant geometric structures, a new automatic and adaptive algorithm for edge extraction from a random point cloud was developed and presented herein. The proposed algorithm was tested using real measurement data. The developed algorithm is able to realistically reduce the amount of redundant data and correctly extract stable edges representing the geometric structures of a studied object without losing important data and information. The new algorithm automatically self-adapts to the received data. It does not require any pre-setting or initial parameters. The detection threshold is also adaptively selected based on the acquired data.

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