scholarly journals Oriented area as a Morse function on polygon spaces

2020 ◽  
Vol 19 (1) ◽  
pp. 155-171
Author(s):  
Daniil Mamaev
Keyword(s):  
Morse Function ◽  
Oriented Area

scholarly journals Oriented area is a perfect Morse function

2018 ◽  
Vol 29 (3) ◽  
pp. 469-474
Author(s):  
G. Panina
Keyword(s):  
Morse Function ◽  
Oriented Area

Relations between Varshni and Morse potential energy parameters

Open Physics ◽  
2009 ◽  
Vol 7 (1) ◽  
Author(s):  
Teik-Cheng Lim ◽  
Rajendra Udyavara
Keyword(s):  
Potential Energy ◽  
Force Constant ◽  
Morse Potential ◽  
Morse Function ◽  
Energy Integral ◽  
Equal Energy ◽  
Molecular Force ◽  
Parameter Conversion ◽  
Bond Stretching ◽  
Small Change

AbstractA set of relationships between the Morse and Varshni potential functions for describing covalent bondstretching energy has been developed by imposing equal force constant and equal energy integral. In view of the extensive adoption of Morse function in molecular force fields, this paper suggests two sets of parameter conversions from Varshni to Morse. The parameter conversion based on equal force constant is applicable for small change in bond length, while the parameter conversion based on equal energy integral is more applicable for significant bond-stretching. Plotted results reveal that the Varshni potential function is more suitable for describing hard bonds rather than soft bonds.

scholarly journals WITTEN DEFORMATION FOR NONCOMPACT MANIFOLDS WITH BOUNDED GEOMETRY

2021 ◽  
pp. 1-38
Author(s):  
Xianzhe Dai ◽  
Junrong Yan
Keyword(s):  
Essential Role ◽  
Morse Function ◽  
Noncompact Manifold ◽  
Morse Inequalities ◽  
Bounded Geometry ◽  
Noncompact Manifolds ◽  
Witten Laplacian ◽  
Relative Cohomology ◽  
Witten Deformation ◽  
Small Eigenvalues

Abstract Motivated by the Landau–Ginzburg model, we study the Witten deformation on a noncompact manifold with bounded geometry, together with some tameness condition on the growth of the Morse function f near infinity. We prove that the cohomology of the Witten deformation $d_{Tf}$ acting on the complex of smooth $L^2$ forms is isomorphic to the cohomology of the Thom–Smale complex of f as well as the relative cohomology of a certain pair $(M, U)$ for sufficiently large T. We establish an Agmon estimate for eigenforms of the Witten Laplacian which plays an essential role in identifying these cohomologies via Witten’s instanton complex, defined in terms of eigenspaces of the Witten Laplacian for small eigenvalues. As an application, we obtain the strong Morse inequalities in this setting.

Surface fractures and deformation of the magnitude 5.6 earthquake near Reykjavík on 20 October 2020

2021 ◽  
Author(s):  
Sigurjón Jónsson ◽  
Yunmeng Cao ◽  
Hannes Vasyura-Bathke ◽  
Xing Li
Keyword(s):  
Covariance Structure ◽  
Surface Displacement ◽  
Earthquake Rupture ◽  
Fault Rupture ◽  
Source Modeling ◽  
Oriented Area ◽  
Vertical Displacements ◽  
The City ◽  
Limited Surface ◽  
East West

<p>On 20 October 2020, Reykjavík was rocked by the largest earthquake in southwest Iceland in over a decade when a magnitude 5.6 event occurred only 25 km from the city. The earthquake caused movement on multiple surface fractures, distributed over an 8-km-long north-south oriented area, indicating the location of the underlaying right-lateral strike-slip fault rupture. We mapped the coseismic surface fractures and deformation using Sentinel-1 and TerraSAR-X InSAR data, selecting with a new method the best pre- and post-earthquake SAR scenes from analyzing the tropospheric signals on each SAR image. This method does not require masking out deformed areas when determining the InSAR covariance structure and thus yields better earthquake source estimations. As the InSAR data are primarily sensitive to east-west and vertical displacements, we additionally used split-beam interferometry to obtain more information about north-south displacements. For this, we used burst-overlap interferometry (BOI), in the case of Sentinel-1 data, and multiple-aperture interferometry (MAI) on the TerraSAR-X data. Together with the standard InSAR data, we estimated the full 3D coseismic surface displacement field of the earthquake. The results show that most of the fractures had limited surface offsets, apart from a 2-3 km long north-south trending segment just north of the epicenter that was right-laterally offset by about 15 cm. Source modeling of the earthquake shows that the deformation is consistent with a near vertical north-south striking fault with up to ~30 cm of slip located at roughly 3 km depth below the surface. The estimated geodetic moment of the model amounts to a magnitude 5.6 earthquake, consistent with seismological estimates. Most of the modeled fault slip and mapped surface fractures are located north of the earthquake epicenter, indicating that the earthquake ruptured unilaterally from south to north, which agrees with the more severe surface effects and shaking reported from near the northern end of the earthquake rupture.</p>

scholarly journals Architectural and ecological integration of postindustrial landscapes revitalization into socially oriented space of the embankment

2018 ◽  
Vol 193 ◽  
pp. 01032
Author(s):  
Nina Ivanova ◽  
Olga Ganzha ◽  
Vyacheslav Prokopenko ◽  
Alexandra Artyukhina
Keyword(s):  
System Analysis ◽  
Ecological Model ◽  
Coastal Landscape ◽  
Scientific Databases ◽  
Environment Quality ◽  
Oriented Area ◽  
Ecological Principles ◽  
Experimental Project ◽  
Definition Of ◽  
The City

The architectural and ecological model of civil engineering of socially oriented spaces of coastal landscape aimed at providing comfortable vital environment, development of the greatest possible variety of city activities, solution of environmental and social problems of the city, and development of the embankment as a self-valuable fragment of well-arranged natural landscape is substantiated. The research objective is the development of methodical bases for the process of architectural revitalization of postindustrial coastal landscape. The researchers utilize the methods of system analysis, reviewing of design practice, analysis of available scientific databases as well as referential and normative resources. The methods of modeling and experimental projecting were also used in the study. Architectural proposals on integration of the revitalized postindustrial coastal areas into socially oriented area of the Volgograd embankment are presented. The analysis of the experience in building and recovery of postindustrial landscapes of river basins is preformed to substantiate the proposed architectural and ecological principles of revitalization, "tree of properties" with the definition of environment quality indicator, the sequence of stages in planning of socially oriented area of the city embankment, and experimental project on integration of the studied coastal area into the vital space of the city of Volgograd.

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