scholarly journals WEAK FIELD EXPANSION OF GRAVITY: GRAPHS, MATRICES AND TOPOLOGY

1999 ◽  
Vol 14 (17) ◽  
pp. 2705-2743
Author(s):  
SHOICHI ICHINOSE ◽  
NORIAKI IKEDA
Keyword(s):  
Graphical Representation ◽  
Young Tableau ◽  
Flat Space ◽  
Weak Field ◽  
Main Theme ◽  
Leading Order ◽  
Group Approach ◽  
And Topology ◽  
Diagram Approach ◽  
Scalar Gravity

We present some approaches to the perturbative analysis of the classical and quantum gravity. First we introduce a graphical representation for a global SO (n) tensor (∂)dhαβ, which generally appears in the weak field expansion around the flat space: gμν=δμν+hμν. Making use of this representation, we explain (1) Generating function of graphs (Feynman diagram approach), (2) Adjacency matrix (Matrix approach), (3) Graphical classification in terms of "topology indices" (Topology approach), (4) The Young tableau (Symmetric group approach). We systematically construct the global SO (n) invariants. How to show the independence and completeness of those invariants is the main theme. We explain it taking simple examples of ∂∂h-, and (∂∂h)2-invariants in the text. The results are applied to the analysis of the independence of general invariants and (the leading order of) the Weyl anomalies of scalar-gravity theories in "diverse" dimensions (2,4,6,8,10 dimensions).

scholarly journals Weak Deflection Angle of some Classes of non-linear Electrodynamics Black Holes via Gauss-Bonnet Theorem

2020 ◽  
Author(s):  
Hasan El Moumni ◽  
Karima Masmar ◽  
Ali Övgün
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Weak Field ◽  
Leading Order ◽  
Plasma Medium ◽  
Non Linear ◽  
The Deflection Angle ◽  
Bonnet Theorem

In this paper, we study the gravitational lensing by some black hole classes within the non-linear electrodynamics in weak field limits. First, we calculate an optical geometry of the non-linear electrodynamics black hole then we use the Gauss-Bonnet theorem for finding deflection angle in weak field limits. The effect of non-linear electrodynamics on the deflection angle in leading order terms is studied. Furthermore, we discuss the effects of the plasma medium on the weak deflection angle.

Solution of Topology Embryonic Graph and Topology Graph for Unified Planar-Spatial Mechanisms

2003 ◽  
Author(s):  
Lu Yi ◽  
Tatu Leinonen
Keyword(s):  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Matrix Approach ◽  
Group Approach ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
And Topology ◽  
Topology Graph ◽  
Relative Theory

An analysis matrix approach for solving an isomeric topology embryonic graph and a digital group approach for solving an isomeric topology graph of a unified planar-spatial mechanism are presented and the relative theory is discussed. Firstly, all binary links are removed from each acceptable linkage system with different degrees of freedom, many analysis matrixes are constructed, and many topology embryonic graphs of the mechanism are derived. Secondly, from an acceptable multi-element link combination of planar or spatial mechanisms, a rule for determining the isomeric topology embryonic graphs and an unreasonable topology embryonic graph is obtained. Thirdly, by considering the degree of freedom of the mechanism and the configuration of a planar or spatial mechanism, the number of binary links is determined. Finally, all removed binary links are rearranged systematically back into an isomeric topology embryonic graph, and the acceptable topology graphs of the mechanism are derived by using a digital group approach. Some illustrations show that the two approaches are simple and effective tools and can be employed to synthesize both planar and spatial mechanisms.

scholarly journals On the discrete Christoffel symbols

2019 ◽  
Vol 34 (30) ◽  
pp. 1950186 ◽  
Author(s):  
V. M. Khatsymovsky
Keyword(s):  
Affine Connection ◽  
Flat Space ◽  
Discrete Analogue ◽  
Connection Form ◽  
Leading Order ◽  
Piecewise Affine ◽  
Order Form ◽  
Christoffel Symbols ◽  
Difference Form ◽  
Torsion Free

The piecewise flat space–time is equipped with a set of edge lengths and vertex coordinates. This defines a piecewise affine coordinate system and a piecewise affine metric in it, the discrete analogue of the unique torsion-free metric-compatible affine connection or of the Levi-Civita connection (or of the standard expression of the Christoffel symbols in terms of metric) mentioned in the literature, and, substituting this into the affine connection form of the Regge action of our previous work, we get a second-order form of the action. This can be expanded over metric variations from simplex to simplex. For a particular periodic simplicial structure and coordinates of the vertices, the leading order over metric variations is found to coincide with a certain finite difference form of the Hilbert–Einstein action.

Leading order of quantum corrections to black hole entropy sum relations

2019 ◽  
Vol 34 (32) ◽  
pp. 1950216
Author(s):  
Tairan Liang ◽  
Wei Xu
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Quantum Physics ◽  
Black Hole Entropy ◽  
Flat Space ◽  
Quantum Corrections ◽  
Leading Order ◽  
Physics Of Black Holes ◽  
Mass Dependent ◽  
Modified Entropy

It has been found recently that the entropy relations of horizons have the universality of black hole mass-independence for many black holes. These universal entropy relations have some geometric and CFT understanding, which may provide further insight into the quantum physics of black holes. In this paper, we present the leading order of black hole entropy sum relations under the quantum corrections. It is found that the modified entropy sum becomes mass-dependent for some black holes in asymptotical (A)dS and flat space–times. We also give an example that the modified entropy sum of regular Bardeen AdS black holes is mass-independent, which may be quantized in the form of the electric charge and the cosmological constant.

scholarly journals A maquete como um croqui

2013 ◽  
Author(s):  
Juliano Carlos Cecílio Batista Oliveira
Keyword(s):  
Graphical Representation ◽  
Teaching Experience ◽  
Scale Model ◽  
Main Element ◽  
Main Theme ◽  
Design Practice ◽  
Product Analysis ◽  
Scale Models ◽  
Beginning Students

Presents the teaching experience of using scale models as a means for the presentation and manipulation of the first ideas by students in a Project of the Built Environment 1 course in a School of Architecture and Urban Design. Discusses, as its main theme, the possibilities of creation and representation of the first ideas by beginning students. We perceive that the difficulties that arise at the beginning of design activities become intertwined, in beginning students, with difficulties related to architectural representation. What is the role of different types of representation in architecture for beginner student? It was possible to obtain better results while "teaching experience" subverting the classic role of graphical representation exercises in a studio? The work raises questions about the teaching of architecture design and possible methodological repercussions that help the beginner of design practice in the development of their ideas. The paper begins by discussing issues related to the representation in architecture, both graphically and through scale models. Then presents a methodological proposal for the exercises in the studio, discussing the results reported. The synthesis of the project, through the model, allows a clearer analysis even for the inexperienced student in dealing with projectual constraints and the project itself, thus obtaining interesting results as well as process and as product. Analysis of the results shows that the application of the scale model as the main element of discussion and presentation of the first ideas for the realization of the project was quite fertile, given the conditions that the exercise was developed and which must be observed: the student is beginner in design practice - are their first experiences in Workshops Project; the creation of a culture on the theme worked is essential - the study of similar projects, visit to the site, the clarity of the instruments of labor; the constant presentation and critique of the object designed by both the student and his colleagues as the teacher - activity performed in all classes, in the various stages of development.

Position, momentum, and wave spreading in curved space

2021 ◽  
Vol 36 (08n09) ◽  
pp. 2150065
Author(s):  
Mohammad Khorrami
Keyword(s):  
Quantum Mechanics ◽  
Wave Packet ◽  
Free Particle ◽  
Flat Space ◽  
Quantum Evolution ◽  
Leading Order ◽  
Position Space ◽  
Curved Space ◽  
Minimum Uncertainty ◽  
Geometry Deviation

The effect of the geometry (deviation from the flat space) on the quantum evolution of the momentum and position of a free particle is discussed. It is shown that beginning with a wave-packet of minimum uncertainty (a Gaussian wave), there is a usual increase in the product of the volume uncertainties in the momentum and position space, as seen in the quantum mechanics on a flat spaces. But there is also a contribution from geometry. The leading order of this contribution is calculated.

scholarly journals New Algorithm for Tensor Calculation in Field Theories

1998 ◽  
Vol 09 (02) ◽  
pp. 243-264 ◽  
Author(s):  
Shoichi Ichinose
Keyword(s):  
Quantum Gravity ◽  
Special Interest ◽  
Weak Field ◽  
Field Theories ◽  
Leading Order ◽  
Perturbative Approach ◽  
Order Calculation ◽  
C Program

Tensor calculation of suffix-contraction is carried out by a C-program. Tensors are represented graphically, and the algorithm makes use of the topology of the graphs. Classical and quantum gravity, in the weak-field perturbative approach, is a special interest. Examples of the leading order calculation of some general invariants such as RμνλσRμνλσ are given. Application to Weyl anomaly calculation is also discussed.

A Lie Group Approach to the Modular Modeling of Kinematically Non-Redundant Parallel Mechanisms

2019 ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Lie Group ◽  
Robotic Systems ◽  
Parallel Mechanisms ◽  
Parallel Kinematics ◽  
Task Space ◽  
Group Approach ◽  
Modular Modeling ◽  
Modeling Approach ◽  
And Topology ◽  
Space Formulation

Abstract Parallel kinematics manupulators (PKM) are established robotic systems. Yet there is no established modeling approach that takes into account the special kinematics of the (usually structurally identical) limbs. In this paper a modeling approach is proposed that accounts for the special kinematics and topology of PKM. It makes use of modern Lie group formulations for rigid body systems that admits efficient description independent of modeling conventions. A task space formulation is presented that can be directly used for model-based control purposes.

scholarly journals Controlled Reeb dynamics — Three lectures not in Cala Gonone

2019 ◽  
Vol 6 (1) ◽  
pp. 118-137
Author(s):  
Hansjörg Geiges
Keyword(s):  
Periodic Orbits ◽  
Group Actions ◽  
Main Theme ◽  
Contact Topology ◽  
Hamiltonian Flows ◽  
Weinstein Conjecture ◽  
Reeb Flows ◽  
And Topology

AbstractThese are notes based on a mini-course at the conference RIEMain in Contact, held in Cagliari, Sardinia, in June 2018. The main theme is the connection between Reeb dynamics and topology. Topics discussed include traps for Reeb flows, plugs for Hamiltonian flows, the Weinstein conjecture, Reeb flows with finite numbers of periodic orbits, and global surfaces of section for Reeb flows. The emphasis is on methods of construction, e.g. contact cuts and lifting group actions in Boothby–Wang bundles, that might be useful for other applications in contact topology.

Sign in / Sign up

Export Citation Format

Share Document