Growth bound theorem for semigroups

2020 ◽  
pp. 185-192
Keyword(s):  
Bound Theorem ◽  
Growth Bound

scholarly journals Maximum Ionization in Restricted and Unrestricted Hartree-Fock Theory

Atoms ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 13
Author(s):  
Hazel Cox ◽  
Michael Melgaard ◽  
Ville J. J. Syrjanen
Keyword(s):  
Upper Bound ◽  
Detailed Account ◽  
Hartree Fock ◽  
Bound Theorem ◽  
Maximum Ionization

In this paper, we investigate the maximum number of electrons that can be bound to a system of nuclei modelled by Hartree-Fock theory. We consider both the Restricted and Unrestricted Hartree-Fock models. We are taking a non-existence approach (necessary but not sufficient), in other words we are finding an upper bound on the maximum number of electrons. In giving a detailed account of the proof of Lieb’s bound [Theorem 1, Phys. Rev. A 29 (1984), 3018] for the Hartree-Fock models we establish several new auxiliary results, furthermore we propose a condition that, if satisfied, will give an improved upper bound on the maximum number of electrons within the Restricted Hartree-Fock model. For two-electron atoms we show that the latter condition holds.

Microcosmic bound theorem of Daycy’s law and its application

2004 ◽  
Vol 25 (3) ◽  
pp. 279-287 ◽  
Author(s):  
Xu You-sheng ◽  
Liu Ci-qun ◽  
Lin Ji
Keyword(s):  
Bound Theorem

Elastic Shakedown in Pressure Vessel Components Under Non-Proportional Loading

2002 ◽  
Author(s):  
Martin Muscat ◽  
Robert Hamilton
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Pressure Vessel ◽  
Proportional Loading ◽  
Linear Superposition ◽  
Element Analysis ◽  
Mechanical Loads ◽  
Bound Theorem ◽  
Square Plate ◽  
Elastic Shakedown

Bounding techniques for calculating shakedown loads are of great importance in design since this eliminates the need for performing full elasto-plastic cyclic loading analyses. The classical Melan’s lower bound theorem is widely used for calculating shakedown loads of pressure vessel components under proportional loading. Polizzotto extended the Melan’s theorem to the case of non-proportional loading acting on a structure. This paper presents a finite element method, based on Polizzotto’s theorem, to estimate the elastic shakedown load for a structure subjected to a combination of steady and cyclic mechanical loads. This method, called non-linear superposition, is then applied to investigate the shakedown behaviour of a pressure vessel component — a nozzle/cylinder intersection and that of a biaxially loaded square plate with a central hole. Results obtained for both problems are compared with those available in the literature and are verified by means of cyclic elasto-plastic finite element analysis.

Selection of the Optimal Distribution for the Upper Bound Theorem in Indentation Processes

2014 ◽  
Vol 797 ◽  
pp. 117-122 ◽  
Author(s):  
Carolina Bermudo ◽  
F. Martín ◽  
Lorenzo Sevilla
Keyword(s):  
Upper Bound ◽  
Geometric Distribution ◽  
Optimal Choice ◽  
Optimal Distribution ◽  
Upper Bound Theorem ◽  
Modular Model ◽  
Bound Theorem ◽  
Rigid Zones ◽  
Dimensionless Relation ◽  
Selection Of

It has been established, in previous studies, the best adaptation and solution for the implementation of the modular model, being the current choice based on the minimization of the p/2k dimensionless relation obtained for each one of the model, analyzed under the same boundary conditions and efforts. Among the different cases covered, this paper shows the study for the optimal choice of the geometric distribution of zones. The Upper Bound Theorem (UBT) by its Triangular Rigid Zones (TRZ) consideration, under modular distribution, is applied to indentation processes. To extend the application of the model, cases of different thicknesses are considered

Upper Bound Solutions to Plane-Strain Extrusion Problems

1970 ◽  
Vol 92 (1) ◽  
pp. 158-164 ◽  
Author(s):  
P. C. T. Chen
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Material Properties ◽  
Incompressible Material ◽  
Velocity Fields ◽  
Deformation Pattern ◽  
Upper Bound Theorem ◽  
Admissible Velocity ◽  
Die Geometry ◽  
Bound Theorem

A method for selecting admissible velocity fields is presented for incompressible material. As illustrations, extrusion processes through three basic types of curved dies have been treated: cosine, elliptic, and hyperbolic. Upper-bound theorem is used in obtaining mean extrusion pressures and also in choosing the most suitable deformation pattern for extrusion through square dies. Effects of die geometry, friction, and material properties are discussed.

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