scholarly journals Global linearization and fiber bundle structure of invariant manifolds

Nonlinearity ◽  
2018 ◽  
Vol 31 (9) ◽  
pp. 4202-4245 ◽  
Author(s):  
Jaap Eldering ◽  
Matthew Kvalheim ◽  
Shai Revzen
Keyword(s):  
Fiber Bundle ◽  
Invariant Manifolds ◽  
Global Linearization ◽  
Bundle Structure

scholarly journals HOPF MAP AND QUANTIZATION ON SPHERE

1999 ◽  
Vol 14 (38) ◽  
pp. 2649-2655 ◽  
Author(s):  
HITOSHI IKEMORI ◽  
SHINSAKU KITAKADO ◽  
HIDEHARU OTSU ◽  
TOSHIRO SATO
Keyword(s):  
Fiber Bundle ◽  
Square Root ◽  
Hopf Map ◽  
Bundle Structure

Quantization of a system constrained to move on a sphere is considered by taking a square root of the "on sphere condition". We arrive at the fiber bundle structure of the Hopf map in S2 and S4. This leads to more geometrical understanding of monopole and instanton gauge structures that emerge in the course of quantization.

FIVE-DIMENSIONAL CHERN–SIMONS GRAVITY WITH NONLINEAR ELECTRODYNAMICS

2001 ◽  
Vol 16 (38) ◽  
pp. 2421-2429 ◽  
Author(s):  
ALFREDO MACÍAS ◽  
ENRIQUE LOZANO
Keyword(s):  
Gauge Theory ◽  
Cosmological Constant ◽  
Dimensional Reduction ◽  
Fiber Bundle ◽  
Reduction Process ◽  
Nonlinear Electrodynamics ◽  
Dimensional Theory ◽  
Chern Simons ◽  
Bonnet Term ◽  
Bundle Structure

We consider five-dimensional theory of gravity proposed recently by Chamseddine. It is based on the Chern–Simons five-form and the SO(1,5) gauge group. The action naturally contains a Gauss–Bonnet term, an Einstein term and a cosmological constant. We shall see that by imposing to this action the five-dimensional principal fiber bundle structure and the toroidal dimensional reduction process, the resulting U(1) gauge theory contains non-minimal couplings to gravity and nonlinear modifications to the standard Einstein–Maxwell–dilaton theory.

A fiber bundle structure with uniform transmission characteristics for high-density astronomical optical cables

2019 ◽  
Vol 19 (8) ◽  
pp. 119
Author(s):  
Qi Yan ◽  
Tao Geng ◽  
Hang Jiang ◽  
Chuang Zhao ◽  
Ying-Hua Zhang ◽  
...  
Keyword(s):  
Fiber Bundle ◽  
High Density ◽  
Transmission Characteristics ◽  
Bundle Structure

scholarly journals Simulation of Leather Visco-Elastic Behavior Based on Collagen Fiber-Bundle Properties and a Meso-Structure Network Model

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 1894
Author(s):  
Sascha Dietrich ◽  
Olga Lykhachova ◽  
Xiaoyin Cheng ◽  
Michael Godehardt ◽  
Markus Kronenberger ◽  
...  
Keyword(s):  
Elastic Properties ◽  
Fiber Bundle ◽  
Structural Model ◽  
Tensile Tests ◽  
Optimal Choice ◽  
Elastic Behavior ◽  
Natural Material ◽  
Structure Model ◽  
Micro Computed Tomography ◽  
Bundle Structure

Simulation-based prediction of mechanical properties is highly desirable for optimal choice and treatment of leather. Nowadays, this is state-of-the-art for many man-made materials. For the natural material leather, this task is however much more demanding due to the leather’s high variability and its extremely intricate structure. Here, essential geometric features of the leather’s meso-scale are derived from 3D images obtained by micro-computed tomography and subsumed in a parameterizable structural model. That is, the fiber-bundle structure is modeled. The structure model is combined with bundle properties derived from tensile tests. Then the effective leather visco-elastic properties are simulated numerically in the finite element representation of the bundle structure model with sliding contacts between bundles. The simulation results are validated experimentally for two animal types, several tanning procedures, and varying sample positions within the hide. Finally, a complete workflow for assessing leather quality by multi-scale simulation of elastic and visco-elastic properties is established and validated.

scholarly journals QUANTUM GRAVITY WITHOUT GHOSTS

1998 ◽  
Vol 13 (30) ◽  
pp. 2475-2479 ◽  
Author(s):  
BRYCE DEWITT ◽  
C. MOLINA-PARÍS
Keyword(s):  
Black Holes ◽  
Effective Action ◽  
Fiber Bundle ◽  
Radiative Decay ◽  
Initial Conditions ◽  
Back Reaction ◽  
Expectation Values ◽  
Dynamical Equations ◽  
Gauge Fixing ◽  
Bundle Structure

We give an outline of a recently discovered technique for building quantum effective action that is completely independent of gauge-fixing choices and ghost determinants. One makes maximum use of the geometry and fiber bundle structure of the space of field histories and introduces a set of nonlocal composite fields: the geodesic normal fields based on Vilkovisky's connection on the space of histories. The closed-time-path formalism of Schwinger, Bakshi, Mahantappa et al. can be adapted for these fields, and a set of gauge-fixing-independent dynamical equations for their expectation values (starting from given initial conditions) can be computed. An obvious application for such equations is to the study of the formation and radiative decay of black holes, and to other back-reaction problems.

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