scholarly journals Caustics of Non-Paraxial Perfect Optical Vortices Generated by Toroidal Vortex Lenses

Photonics ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 259
Author(s):  
Svetlana N. Khonina ◽  
Sergey I. Kharitonov ◽  
Sergey G. Volotovskiy ◽  
Viktor A. Soifer
Keyword(s):  
Numerical Analysis ◽  
Theoretical Analysis ◽  
Linear Dependence ◽  
Optical Vortices ◽  
Toroidal Vortex ◽  
Optical Elements ◽  
Phase Singularity ◽  
Vortex Phase ◽  
Ring Radius ◽  
Diffraction Effects

In this paper, we consider the comparative formation of perfect optical vortices in the non-paraxial mode using various optical elements: non-paraxial and parabolic toroidal vortex lenses, as well as a vortex axicon in combination with a parabolic lens. The theoretical analysis of the action of these optical elements, as well as the calculation of caustic surfaces, is carried out using a hybrid geometrical-optical and wave approach. Numerical analysis performed on the basis of the expansion in conical waves qualitatively confirms the results obtained and makes it possible to reveal more details associated with diffraction effects. Equations of 3D-caustic surfaces are obtained and the conditions of the ring radius dependence on the order of the vortex phase singularity are analyzed. In the non-paraxial mode, when small light rings (several tens of wavelengths) are formed, a linear dependence of the ring radius on the vortex order is shown. The revealed features should be taken into account when using the considered optical elements forming the POV in various applications.

scholarly journals A neutral core of degressively proportional allocations under lexicographic preferences of agents

2021 ◽  
Author(s):  
Katarzyna Cegiełka ◽  
Piotr Dniestrzański ◽  
Janusz Łyko ◽  
Arkadiusz Maciuk ◽  
Maciej Szczeciński
Keyword(s):  
European Union ◽  
Numerical Analysis ◽  
Theoretical Analysis ◽  
Boundary Conditions ◽  
Case Studies ◽  
The European Union ◽  
Practical Applications ◽  
Lexicographic Preferences ◽  
Degree Of Acceptance ◽  
Feasible Solutions

AbstractOne of the main problems of practical applications of degressively proportional allocations of goods and burdens is lack of uniqueness of this principle. Even under given boundary conditions of allocation, i.e. determined minimal and maximal amounts of a good that can be assigned in a given allocation, there are usually many feasible solutions. The lack of formal rules of allocation is the reason why the allocation is typically a result of negotiations among its agents. A number of allocations favor some of agents or their groups, therefore other agents cannot accept them. The aim of this paper is to indicate a way of reducing the set of all feasible solutions exclusively to those that are neutral to all agents. As a result of the term of lexicographic preference of allocation agents defined on the basis of the relation theory followed by a numerical analysis of sets of all feasible solutions, it is possible to determine a core of this set in the form of a subset of all feasible solutions that are acceptable by all agents. In addition, this subset can be further divided into smaller subsets with regard to the degree of acceptance of their elements. Theoretical analysis is complemented by case studies, one of which is application of this idea to the allocation of seats in the European Parliament among the member states of the European Union.

Experimental and Theoretical Analysis of Phase Singularity Dynamics in Cardiac Tissue

2001 ◽  
Vol 12 (6) ◽  
pp. 716-722 ◽  
Author(s):  
MARK-ANTHONY BRAY ◽  
SHIEN-FONG LIN ◽  
RUBIN R. ALIEV ◽  
BRADLEY J. ROTH ◽  
JOHN P. WIKSWO
Keyword(s):  
Theoretical Analysis ◽  
Cardiac Tissue ◽  
Phase Singularity

scholarly journals Numerical analysis of optical vortices generation with nanostructured phase masks

2020 ◽  
Vol 28 (14) ◽  
pp. 21143
Author(s):  
Hue Thi Nguyen ◽  
Alicja Anuszkiewicz ◽  
Jolanta Lisowska ◽  
Adam Filipkowski ◽  
Rafal Kasztelanic ◽  
...  
Keyword(s):  
Numerical Analysis ◽  
Optical Vortices

Theoretical and numerical analysis of stress and stress intensity factor in bi-material

2019 ◽  
Vol 10 (1) ◽  
pp. 76-84
Author(s):  
Hamid Hamli Benzahar
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Numerical Analysis ◽  
Intensity Factor ◽  
Theoretical Analysis ◽  
Main Crack ◽  
Content Type ◽  
Analytical Functions ◽  
Theoretical And Numerical Analysis ◽  
Two Parameters

PurposeThe purpose of this paper is to evaluate theoretically and numerically the stress and stress intensity factor (SIF) at the time of propagation of the crack in bi-material. The problem is formulated using two thin materials which are bound by a cracked adhesive at the tip and having a micro-crack in one of these two materials.Design/methodology/approachThe plane stresses and the SIF will be determined as a function of two parameters (Poisson’s ratio and Shear modulus). The numerical analysis is carried out on a flat element, having a main crack in one of these ends, and a micro-crack varies in the vicinity of this main crack. The problem is analyzed by the finite element method and processed by computational software (ABAQUS).FindingsThe numerical and theoretical analysis allowed the author to determine and compare the values of plane stresses and SIF in each area of the material.Originality/valueThe theoretical analysis of SIF is based mainly on a mathematical calculation of equations of plane stresses; these equations are determined by development of complex analytical functions of bi-materials given by other researchers. Using the numerical method, several models are modeled by changing the micro-crack position relative to the main crack to determine the plane stresses and SIF for each position.

Experimental and Numerical Analysis of Timber-Lightweight Concrete Composite with Adhesive Connection

2014 ◽  
Vol 969 ◽  
pp. 155-160 ◽  
Author(s):  
Ján Kanócz ◽  
Viktória Bajzecerová ◽  
Marek Mojdis
Keyword(s):  
Numerical Analysis ◽  
Theoretical Analysis ◽  
Experimental Test ◽  
Lightweight Concrete ◽  
Composite Beams ◽  
Short Term ◽  
Shear Connection ◽  
Theoretical Results

In this paper experimental and numerical analysis of timber-lightweight concrete composite floor elements with glued shear connection under short term loading is presented. The composite connection of two materials by special adhesive for bounding wet concrete to timber was performed. For experimental test and theoretical analysis two type of composite beams was used. Comparison of test with theoretical results is finally presented.

Photoionisation of ethylene and benzene: a theoretical analysis of multicentre diffraction effects

1986 ◽  
Vol 107 (2-3) ◽  
pp. 255-282 ◽  
Author(s):  
David A.L. Kilcoyne ◽  
Sture Nordholm ◽  
Noel S. Hush
Keyword(s):  
Theoretical Analysis ◽  
Diffraction Effects

Study on the Analysis Model of the Self-Centering Wall

2013 ◽  
Vol 353-356 ◽  
pp. 1850-1857 ◽  
Author(s):  
Xiao Bin Hu ◽  
Wen Xia Li ◽  
Hao Xiang ◽  
Hui Gao He
Keyword(s):  
Finite Element ◽  
Numerical Analysis ◽  
Theoretical Analysis ◽  
Mechanical Behavior ◽  
Numerical Simulations ◽  
The Self ◽  
Hysteresis Curve ◽  
Analysis Model ◽  
Horizontal Connection ◽  
Analysis Models

The self-centering wall including both prestressed tendons and dampers is proposed in this paper, and the corresponding general finite element numerical analysis model, simplified numerical analysis model and theoretical analysis model were established respectively, focusing on how to simulate the prestressed tendons, dampers and the horizontal connection between the wall and the foundation. The numerical simulations of the self-centering wall subjected to reversal loading were performed using the above two numerical analysis models, and the results were compared to those obtained from theoretical analysis. It is indicated that the hysteresis curve of the self-centering wall under reversal loading exhibits flag shape and no residual displacement exists after the wall is unloaded completely. The numerical analysis results match well with those from theoretical analysis, which shows the two numerical analysis models proposed in this paper can be well used to capture the mechanical behavior of the self-centering wall.

Treatment of Well Point during Numerical Analysis about Water Pumping

2012 ◽  
Vol 594-597 ◽  
pp. 2574-2577
Author(s):  
Hua Yuan ◽  
Chao Yan
Keyword(s):  
Numerical Simulation ◽  
Numerical Analysis ◽  
Theoretical Analysis ◽  
Pumping Test ◽  
Future Research ◽  
Substructure Method ◽  
The Past ◽  
Water Pumping ◽  
Long Time ◽  
Effective Role

During a long time in the past, the treatment of well point has been a difficulty in academia. However well pumping is still inevitable in civil engineering circles due to its effective role on groundwater control. Firstly, the currently available treatment methods of well point are summarized. Through comparison between these existing methods and theoretical analysis, a drainage substructure is advanced, of which the inner layer is a square having equal perimeter with the actual well pipe. Results of numerical simulation upon a field pumping test prove the effectiveness and feasibility of proposed drainage substructure method, which may contribute to the well point simplification in future research.

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