The simple analytical formula for estimating a coupling of modes at the joint of optical fibers

2018 ◽  
Author(s):  
Vladimir A. Burdin
Keyword(s):  
Optical Fibers ◽  
Analytical Formula ◽  
Simple Analytical Formula

Pre-Impact Configuration Designing of a Robot Manipulator for Impact Minimization

2017 ◽  
Vol 9 (3) ◽  
Author(s):  
Jingchen Hu ◽  
Tianshu Wang
Keyword(s):  
Impact Force ◽  
Robot Manipulator ◽  
Analytical Formula ◽  
Joint Space ◽  
Collision Problem ◽  
Spatial Operator ◽  
Inertia Ellipsoid ◽  
The Impact ◽  
Maximum Minimum ◽  
Simple Analytical Formula

This paper studies the collision problem of a robot manipulator and presents a method to minimize the impact force by pre-impact configuration designing. First, a general dynamic model of a robot manipulator capturing a target is established by spatial operator algebra (SOA) and a simple analytical formula of the impact force is obtained. Compared with former models proposed in literatures, this model has simpler form, wider range of applications, O(n) computation complexity, and the system Jacobian matrix can be provided as a production of the configuration matrix and the joint matrix. Second, this work utilizes the impulse ellipsoid to analyze the influence of the pre-impact configuration and the impact direction on the impact force. To illustrate the inertia message of each body in the joint space, a new concept of inertia quasi-ellipsoid (IQE) is introduced. We find that the impulse ellipsoid is constituted of the inertia ellipsoids of the robot manipulator and the target, while each inertia ellipsoid is composed of a series of inertia quasi-ellipsoids. When all inertia quasi-ellipsoids exhibit maximum (minimum) coupling, the impulse ellipsoid should be the flattest (roundest). Finally, this paper provides the analytical expression of the impulse ellipsoid, and the eigenvalues and eigenvectors are used as measurements to illustrate the size and direction of the impulse ellipsoid. With this measurement, the desired pre-impact configuration and the impact direction with minimum impact force can be easily solved. The validity and efficiency of this method are verified by a PUMA robot and a spatial robot.

Group Theoretic Approach to the Exponential Cosine Screened Coulomb Potential

1985 ◽  
Vol 40 (5) ◽  
pp. 453-455 ◽  
Author(s):  
Barnana Roy
Keyword(s):  
Perturbation Method ◽  
Coulomb Potential ◽  
Analytical Formula ◽  
Theoretic Approach ◽  
Energy Eigenvalues ◽  
Screened Coulomb Potential ◽  
Simple Analytical Formula

Perturbation method, using the properties of SO (2,1) algebra is applied to get a simple analytical formula for energy eigenvalues of the exponential cosine screened Coulomb potential.

Comparison between different proximity potentials and the double-folding model for spherical–deformed interacting nuclei

2016 ◽  
Vol 94 (1) ◽  
pp. 102-111 ◽  
Author(s):  
M. Ismail ◽  
I.A.M. Abdul-Magead
Keyword(s):  
Coulomb Barrier ◽  
Analytical Formula ◽  
Orientation Angle ◽  
Heavy Ion ◽  
Folding Model ◽  
Deformation Parameters ◽  
Double Folding Model ◽  
Double Folding ◽  
Coulomb Part ◽  
Simple Analytical Formula

The Coulomb barrier parameters have been calculated for a spherical–deformed interacting pair of nuclei using 14 different versions of the proximity approaches and a simple analytical formula for the Coulomb part of the heavy ion potential. The results of these proximity versions have been compared with more accurate results obtained from the double-folding model (DFM). We have considered the interacting pair 48Ca + 238Pu as an example and assumed the presence of the quadrupole, octupole, and hexadecapole deformation parameters for 238Pu. The orientation angle dependence of the Coulomb barrier parameters has been computed for different sets of deformation parameters. We found that the proximity types named Prox77, BW Prox91, AW Prox95, Bass Prox77, and Bass Prox80 are the best ones of the available 14 versions of the proximity approaches for calculating the nuclear part of the interaction potential for a spherical–deformed pair of nuclei.

Four-probe Magnetoresistance of Current-perpendicular-to-plane Structures

2005 ◽  
Vol 906 ◽  
Author(s):  
Hua Zhou ◽  
Mark W. Covington ◽  
Michael A. Seigler
Keyword(s):  
Finite Element ◽  
Current Flow ◽  
Three Dimensional ◽  
Analytical Formula ◽  
Unified Approach ◽  
Uniform Current ◽  
Current Perpendicular To Plane ◽  
Numerical Finite Element ◽  
Simple Analytical Formula ◽  
Probe Geometry

AbstractThe resistance and magnetoresistance (MR) of three-dimensional current-perpendicular-to-plane (CPP) structures have been calculated via numerical finite element solutions of the Laplace equation. This model accounts for the non-uniform current paths in a four-probe geometry that can yield MR that differs from the intrinsic MR of the isolated CPP pillar with spatially uniform current flow. We calculated the four-probe MR for various geometries and resistivities of both the normal metal leads and the magnetoresistive pillar. From a single, unified approach, we are able to consistently account for the disparate behavior that has been previously published. In particular, we identify conditions that produce four-probe MR that differs from the intrinsic MR of the CPP pillar and highlight those situations where the four-probe resistance is negative. Finally, we present a simple analytical formula for the MR ratio that is applicable to narrow CPP pillars with wide, thin leads.

An analytical formula for estimating the bending angle by laser forming

2006 ◽  
Vol 220 (2) ◽  
pp. 243-247 ◽  
Author(s):  
H Shen ◽  
Z Yao ◽  
Y Shi ◽  
J Hu
Keyword(s):  
Experimental Data ◽  
Solid Mechanics ◽  
Present Model ◽  
Analytical Formula ◽  
Laser Forming ◽  
Compatibility Conditions ◽  
Bending Angle ◽  
Metal Plates ◽  
External Forces ◽  
Simple Analytical Formula

Laser forming of metal plates offers the advantages of requiring no external forces and thus reduced cost and increased flexibility. It also enables forming of some materials and shapes that are impossible by using the traditional methods. Based on the conventional equilibrium and compatibility conditions used in solid mechanics, a simple analytical formula for predicting the bending angle is derived. The present model is compared with other models and available experimental data, from which the superiority of the present model is demonstrated.

scholarly journals Off-axis Fresnel numbers in laser systems

2014 ◽  
Vol 2 ◽  
Author(s):  
Yudong Yao ◽  
Junyong Zhang ◽  
Yanli Zhang ◽  
Qunyu Bi ◽  
Jianqiang Zhu
Keyword(s):  
Correction Factor ◽  
Intensity Distribution ◽  
Physical Meaning ◽  
Analytical Formula ◽  
Numerical Calculations ◽  
Optical Systems ◽  
Circular Aperture ◽  
Fresnel Number ◽  
Laser Systems ◽  
Simple Analytical Formula

Abstract The physical meaning and essence of Fresnel numbers are discussed, and two definitions of these numbers for off-axis optical systems are proposed. The universal Fresnel number is found to be $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}N=(a^{2}/\lambda z ) \ast C_{1} +C_{2} $ . The Rayleigh–Sommerfeld nonparaxial diffraction formula states that a simple analytical formula for the nonparaxial intensity distribution after a circular aperture can be obtained. Theoretical derivations and numerical calculations reveal that the first correction factor $C_{1} $ is equal to $\cos \theta $ and the second factor $C_{2} $ is a function of the incident wavefront and the shape of the diffractive aperture. Finally, some diffraction phenomena in off-axis optical systems are explained by the off-axis Fresnel number.

Fusion barrier parameters for a spherically deformed pair of nuclei

2014 ◽  
Vol 92 (11) ◽  
pp. 1411-1418 ◽  
Author(s):  
M. Ismail ◽  
A.Y. Ellithi ◽  
M.M. Botros ◽  
A.F. Abdel Reheem
Keyword(s):  
Density Functional ◽  
Density Functional Method ◽  
Analytical Formula ◽  
Functional Method ◽  
Effective Density ◽  
Folding Model ◽  
Energy Density Functional ◽  
Deformation Parameters ◽  
Double Folding ◽  
Simple Analytical Formula

The interactions of 48Ca spherical nucleus are considered with the deformed targets 224Ra and 244Pu to form the super heavy elements 272Hs and 292114 (292Fl), respectively. The double folding model with effective density dependent M3Y-NN force, and the energy density functional method based on Skyrme force are used to derive the nucleus–nucleus interaction. The effect of deformation and orientation on the Coulomb barrier parameters is studied, and the results are compared with the corresponding quantities derived from a simple model based on the proximity approach for the nuclear part and simple analytical formula for the Coulomb interaction. Consistent behavior of the results is obtained at certain ranges for deformation parameters and orientations.

NEW MEASURES FOR COMPARING THE SPECIES DIVERSITY FOUND IN TWO OR MORE HABITATS

2010 ◽  
Vol 18 (06) ◽  
pp. 691-720 ◽  
Author(s):  
RADU CORNEL GUIASU ◽  
SILVIU GUIASU
Keyword(s):  
Shannon Entropy ◽  
Economic Value ◽  
Analytical Formula ◽  
Phylogenetic Distance ◽  
Simpson Index ◽  
Quadratic Index ◽  
The Rich ◽  
Ecological Importance ◽  
Weighted Entropy ◽  
Simple Analytical Formula

Both the weighted entropy, which generalizes the Shannon entropy, and the weighted quadratic index, which generalizes the Gini-Simpson index, are used for getting a unified treatment of some diversity measures proposed recently in ecology. The weights may reflect the ecological importance, rarity, or economic value of the species from a given habitat. The weighted measures, being concave functions, may be used in the additive partition of diversity. The weighted quadratic index has a special advantage over the weighted entropy because its maximum value has a simple analytical formula which allows us to introduce a normed measure of dissimilarity between habitats. A special case of weighted quadratic index is the Rich-Gini-Simpson index which, unlike the Shannon entropy and the classic Gini-Simpson index, behaves well when the number of species is very large. The weighted entropy and the weighted quadratic index may also be used to measure the global diversity among the subsets of species. In this context, Rao's quadratic index of diversity between the pairs of species, based on the phylogenetic distance between species, is obtained as a particular case and is generalized to measure the diversity among the triads of species as well.

scholarly journals Quantifying the contribution of asymptomatic infection to the cumulative incidence

2017 ◽  
Vol 145 (6) ◽  
pp. 1256-1258 ◽  
Author(s):  
D. CHAMPREDON ◽  
S. M. MOGHADAS
Keyword(s):  
Mathematical Model ◽  
Infectious Diseases ◽  
Cumulative Incidence ◽  
Analytical Formula ◽  
Asymptomatic Infection ◽  
Simple Analytical Formula

SUMMARYMany infectious diseases in humans may manifest with no or mild symptoms. While numerous studies have estimated the proportion of infectious individuals in whom symptoms are absent during the entire course of infection, the contribution of asymptomatic cases to the overall cumulative incidence is difficult to untangle. Here, with a mathematical model, we provide a simple analytical formula to quantify this contribution and highlight the potential for large errors that can arise when naively estimating it.

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