THE GENERALIZED BREIT OPERATOR OF A LONG-RANGE TYPE IN THE FRAMEWORK OF THE SECOND-ORDER EFFECTS OF QUANTUM ELECTRODYNAMICS

2010 ◽  
Vol 25 (25) ◽  
pp. 4775-4800
Author(s):  
V. YU. LAZUR ◽  
S. I. MYHALYNA ◽  
O. K. REITY
Keyword(s):  
Quantum Electrodynamics ◽  
Dipole Interaction ◽  
Order Effect ◽  
Second Order ◽  
Order Effects ◽  
Additional Contribution ◽  
Range Type ◽  
Modern Methods ◽  
Relativistic Interaction ◽  
Breit Operator

The problem of interaction of two quasimolecular electrons located at an arbitrary distance from each other and near different atoms (nuclei) is solved. The interaction is considered as a second-order effect of quantum electrodynamics in the coordinate representation. It is shown that a consistent account for the natural condition of the interaction symmetry with respect to both electrons leads to an additional contribution to the relativistic interaction of the two quasimolecular electrons compared with both the standard Breit operator and the generalized Breit operator known previously. The generalized Breit–Pauli operator and the operator of electric dipole–dipole interaction of two quasimolecular electrons located at an arbitrary distance from each other are obtained. Modern methods of accounting for the relativistic and correlative effects in the problem of ion–atom interactions are discussed.

Retardation in non-dispersive interactions between molecules

1966 ◽  
Vol 295 (1443) ◽  
pp. 476-489 ◽  
Keyword(s):  
Quantum Electrodynamics ◽  
Exchange Interactions ◽  
Dipole Interaction ◽  
Second Order ◽  
The Other ◽  
Spin Orbit ◽  
Wave Zone ◽  
Expectation Value ◽  
Near Zone ◽  
The Matrix

The second order T matrix corresponding to the interaction between two molecules is calculated by quantum electrodynamics. In the near zone the matrix reduces to the expectation value of the Breit Hamiltonian for the two-centre problem. In the wave zone a retarded Briet operator is found for exchange interactions. A reduction to the Pauli limit is made. The interactions are discussed severally for the spin-spin, (spin-dipole)-(spin-dipole), spin-orbit and dipole-(spin-dipole) cases. At large separations the T matrix is complex and the imaginary parts, previously given for the dipole-dipole interaction, are found for the other cases.

Simplified Analysis of Second-Order Effect on Staggered Truss Structure

2012 ◽  
Vol 446-449 ◽  
pp. 857-862
Author(s):  
Qi Shi Zhou ◽  
Xu Hong Zhou ◽  
Li Ming Yang
Keyword(s):  
Structural Characteristics ◽  
Order Effect ◽  
Second Order ◽  
Truss Structure ◽  
Order Effects ◽  
Good Precision ◽  
Finite Element Software ◽  
Load Carrying ◽  
Second Order Effects ◽  
Lateral Displacements

Based on the structural characteristics that the distribution of mass and stiffness is symmetrical in staggered truss structure, the load-carrying performance of staggered truss structure is equivalent to a pressure-bend combinational strut in this paper. By analyzing the relationship among curvatures , bending moments and shear forces of the pressure-bend combinational strut, the balance differential equations of the pressure-bend combinational strut is erected. Based on Runge-Kutta method, the lateral iteration equation derived by considering the influence of the second-order effects is derived. This paper analyzes the lateral displacements of floors of the staggered truss structure examples considering second-order effects or not, and gives a comparative analysis with the existing finite element software Ansys. The results show that the calculation method of second-order effects proposed in this paper has a good precision.

Second order effects in dissipative media

1966 ◽  
Vol 292 (1428) ◽  
pp. 14-50 ◽  
Keyword(s):  
Strain Hardening ◽  
Tensile Load ◽  
Order Effect ◽  
Elastic Cylinder ◽  
Second Order ◽  
Tensile Creep ◽  
Order Effects ◽  
Elastic Solids ◽  
Viscoelastic Media ◽  
Second Order Effects

Second order or ‘cross’ effects arise as a result of quadratic terms in the constitutive equations of isotropic elastic, viscous and viscoelastic media, which are required by the condition of tensor invariance of those relations. The most pronounced second order effects arise when these are clearly separable from the first order deformation, as in the case of second order elongation and volume change of an elastic cylinder subject to a twisting moment, or of second order normal stress in the case of shear flow of polymeric liquids. The recent I. U. T. A. M. Conference on Second Order Effects (Pergamon Press, London, 1964) was mainly concerned with these two phenomena. The paper discusses second order effects in dissipative (viscoelastic, plastic and strain ­ hardening) solids and reports the results of experiments in which these effects were observed. While the experiments on elastomers confirm the Rivlin-Ericksen theory of those effects in viscoelastic media, the existence of a new accumulating second order effect has been discovered by experiments on aluminium specimens in reversed torsion (Ronay 1965). This effect, which has not been observed before, is probably responsible for the rapid acceleration of tensile creep in metals by small amplitudes of reversed torsion. While the second order effects in elastic solids vanish at zero strain since they are reversible, and vanish at zero velocity in polymeric fluids, they accumulate with the number of repeated torsion cycles in strain-hardening media. Hence their observation is very simple and does not require the elaborate procedures necessary for the observation of second order effects in elastic solids and viscous fluids. The theory of accumulating second order effects in strain-hardening media is developed; the linearity of the interaction between tensile load and torsion amplitude is demonstrated by the experiments.

Second-Order Effect of Staggered Truss and Simplified Formula

2010 ◽  
Vol 163-167 ◽  
pp. 808-811
Author(s):  
Lin Feng Lu ◽  
Li Lin
Keyword(s):  
Critical Factor ◽  
Order Effect ◽  
Internal Force ◽  
Second Order ◽  
Order Effects ◽  
Magnification Factor ◽  
Design Code ◽  
The World ◽  
Second Order Effects ◽  
Simplified Formula

This paper summarizes the regulations about steel frame second-order effect of some design code in the world, and find out a critical factor of controlling second-order effect. The second-order effects of staggered truss were studied systematically by using ETABS program, and put forward design proposals the second-order effects of internal force and displacement, the simplified formula on second-order effect magnification factor of displacement was given.

Beyond tit-for-tat in cyberspace: Political warfare and lateral sources of escalation online

2020 ◽  
Vol 5 (2) ◽  
pp. 195-214
Author(s):  
Christopher Whyte
Keyword(s):  
Order Effect ◽  
The United States ◽  
Second Order ◽  
The Political ◽  
Order Effects ◽  
Relative Power ◽  
Political Warfare ◽  
Limited Opportunity ◽  
Tit For Tat ◽  
Direct Outcome

AbstractAt present, most scholarship on the potential for escalation in cyberspace couches analysis in terms of the technological dynamics of the domain for relative power maneuvering. The result has been a conceptualisation of the logic of operation in cyberspace as one of ‘tit-for-tat’ exchanges motivated by attribution problems and limited opportunity for strategic gain. This article argues that this dominant perspective overlooks alternative notions of how cyber tools are used to influence. This, in turn, has largely led scholars to ignore second-order effects – meaning follow-on effects triggered by a more direct outcome of an initial cyber action – on domestic conditions, institutions, and individual stakeholders. This article uses the case of cyber-enabled political warfare targeting the United States in 2016 to show how escalation can occur as a second-order effect of cyber operations. Specifically, the episode led to a re-evaluation of foreign cyber strategy on the part of American defence thinkers that motivated an offensive shift in doctrine by 2018. The episode also directly affected both the political positions taken by important domestic actors and the attitude of parts of the electorate towards interference, both of which have reinforced the commitment of military planners towards assertive cyber actions.

scholarly journals Alternative Design Procedure for RC-Braced Long Columns Based on New Moment Magnifiers Matrix

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Mohamed Farouk ◽  
Majed Alzara ◽  
A. Ehab ◽  
A. M. Yosri
Keyword(s):  
Flexural Rigidity ◽  
Design Procedure ◽  
Bending Moment ◽  
Order Effect ◽  
Second Order ◽  
Effective Length ◽  
Column Height ◽  
Order Effects ◽  
Order Analysis ◽  
Proposed Model

Based on modified methods for the results of first-order analysis of RC columns, different codes approximate the second-order effects by using equations focusing on the maximum additional moment through the column height. These equations did not refer to the additional moments between the column and the connected beam, only the effect of the connected beams is taken into consideration by dealing with the effective length of the column, not the total length. Moreover, these equations did not take into account the second-order effect, which is caused by axial force and the inverse moments due to beam restriction for the column ends. This paper presents a new moment magnifiers matrix for the additional moments at the connection between braced columns and the connected beams as a simplified computation that can be used in the design procedure. That is through an equation based on transforming the original long column in second-order analysis to an equivalent isolated column. The equivalent column was represented as an element restricted with rotational spring support at its ends, and it is subjected to lateral distributed loads that have the same influence of the second-order effect on the induced additional moments in the long column. The suggested equivalent column can be used to form the additional bending moment diagram, also to compute the additional deformations as well. Numerous factors were analyzed linearly by using the presented new moment magnifiers matrix and finite element method, and the results proved the efficiency of the proposed model. Although the presented suggested model is based on the isolated analysis of the long column, the effect of the additional moments in the adjacent long column can be considered by presented two suggestions to improve the model. Also, development was proceeded on the model by modifying the flexural rigidity (EI) which is recommended in ACI to appropriate the time of failure. The additional moment values of the developed model were close to the values calculated by the ACI equation.

scholarly journals A Simple Approach for the Design of Ductile Earthquake-Resisting Frame Structures Counting for P-Delta Effect

Buildings ◽  
2019 ◽  
Vol 9 (10) ◽  
pp. 216
Author(s):  
Shehu ◽  
Angjeliu ◽  
Bilgin
Keyword(s):  
Order Effect ◽  
Simple Approach ◽  
Second Order ◽  
Frame Structures ◽  
Order Effects ◽  
Lateral Loads ◽  
Stability Coefficient ◽  
Internal Forces ◽  
Second Order Effects ◽  
The Stability

In the last decades, the possibility to use the inelastic capacities of structures have driven the seismic design philosophy to conceive structures with ductile elements, able to obtain large deformations without compromising structural safety. In particular, the utilization of high-strength elements combined with the purpose of reducing inertial masses of the construction has highlighted the second-order effect as a result of the “lightweight” structure’s flexibility. Computational aspects of inclusion of the second-order effects in the structural analysis remain an open issue and the most common method in the current design practices uses the stability coefficient θ. The stability coefficient estimates the ratio between the second-order effect and lateral loads’ effects. This coefficient is used then to amplify the lateral loads’ effects in order to consider the second-order effects, within a certain range proposed by codes of practices. In the present paper, we propose a simple approach, as an alternative to the stability coefficient method, in order to take into consideration P-Delta effects for earthquake-resisting ductile frame structures in the design process. The expected plastic deformations, which can be assessed by the behavior factor and the elastic deformations of the structure, are expected to magnify the P-Delta effects compared to those estimated from an elastic approach. The real internal forces are approximated by modifying the stiffness matrix of the structure in such a way as to provide a compatible amplification effect. This concept is herein implemented with a three-step procedure and illustrated with well-documented case studies from the current literature. The obtained results show that the method, although simple, provides a good approximation compared to more refined and computationally expensive methods. The proposed method seems promising for facilitating the design computations and increasing the accuracy of the internal forces considering the second-order effects and the amplification from the inelastic deformations.

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