scholarly journals Emittance growth scaling laws for crossing systematic space-charge driven sixth-order resonances and random octupole driven fourth-order resonances in FFAGs

2007 ◽  
Author(s):  
X. Pang ◽  
F. Wang ◽  
X. Wang ◽  
S.Y. Lee ◽  
K.Y. Ng
Keyword(s):  
Space Charge ◽  
Fourth Order ◽  
Scaling Laws ◽  
Sixth Order ◽  
Emittance Growth ◽  
Growth Scaling

scholarly journals Space Charge Effects in Noble-Liquid Calorimeters and Time Projection Chambers

Instruments ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 9
Author(s):  
Sandro Palestini
Keyword(s):  
Space Charge ◽  
Scaling Laws ◽  
Relative Size ◽  
Design Solution ◽  
Space Charge Effects ◽  
Charge Effects ◽  
Time Projection Chambers ◽  
Drift Length ◽  
Calibration Methods ◽  
Time Projection

The subject of space charge in ionization detectors is reviewed, showing how the observations and the formalism used to describe the effects have evolved, starting with applications to calorimeters and reaching recent, large time-projection chambers. General scaling laws, and different ways to present and model the effects are presented. The relations between space-charge effects and the boundary conditions imposed on the side faces of the detector are discussed, together with a design solution that mitigates some of the effects. The implications of the relative size of drift length and transverse detector size are illustrated. Calibration methods are briefly discussed.

Relating renormalizability of D-dimensional higher-order electromagnetic and gravitational models to the classical potential at the origin

2017 ◽  
Vol 32 (08) ◽  
pp. 1750048 ◽  
Author(s):  
Antonio Accioly ◽  
Gilson Correia ◽  
Gustavo P. de Brito ◽  
José de Almeida ◽  
Wallace Herdy
Keyword(s):  
Fourth Order ◽  
Massive Gravity ◽  
Higher Order ◽  
Sixth Order ◽  
Gravity Models ◽  
Local Models ◽  
Order Model ◽  
Functional Generator ◽  
Classical Potential ◽  
Real Poles

Simple prescriptions for computing the D-dimensional classical potential related to electromagnetic and gravitational models, based on the functional generator, are built out. These recipes are employed afterward as a support for probing the premise that renormalizable higher-order systems have a finite classical potential at the origin. It is also shown that the opposite of the conjecture above is not true. In other words, if a higher-order model is renormalizable, it is necessarily endowed with a finite classical potential at the origin, but the reverse of this statement is untrue. The systems used to check the conjecture were D-dimensional fourth-order Lee–Wick electrodynamics, and the D-dimensional fourth- and sixth-order gravity models. A special attention is devoted to New Massive Gravity (NMG) since it was the analysis of this model that inspired our surmise. In particular, we made use of our premise to resolve trivially the issue of the renormalizability of NMG, which was initially considered to be renormalizable, but it was shown some years later to be non-renormalizable. We remark that our analysis is restricted to local models in which the propagator has simple and real poles.

scholarly journals Diagonally Implicit Runge–Kutta Type Method for Directly Solving Special Fourth-Order Ordinary Differential Equations with Ill-Posed Problem of a Beam on Elastic Foundation

Algorithms ◽  
2018 ◽  
Vol 12 (1) ◽  
pp. 10 ◽  
Author(s):  
Nizam Ghawadri ◽  
Norazak Senu ◽  
Firas Adel Fawzi ◽  
Fudziah Ismail ◽  
Zarina Ibrahim
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Elastic Foundation ◽  
Fourth Order ◽  
Sixth Order ◽  
Test Problems ◽  
Type Method ◽  
Ill Posed ◽  
Runge Kutta ◽  
Fifth Order

In this study, fifth-order and sixth-order diagonally implicit Runge–Kutta type (DIRKT) techniques for solving fourth-order ordinary differential equations (ODEs) are derived which are denoted as DIRKT5 and DIRKT6, respectively. The first method has three and the another one has four identical nonzero diagonal elements. A set of test problems are applied to validate the methods and numerical results showed that the proposed methods are more efficient in terms of accuracy and number of function evaluations compared to the existing implicit Runge–Kutta (RK) methods.

Application of a Sixth Order Generalized Stress Function for Determining Limit Loads for Plates with Triangular Penetration Patterns

2002 ◽  
Author(s):  
J. L. Gordon ◽  
D. P. Jones
Keyword(s):  
Finite Element ◽  
Fourth Order ◽  
Limit Load ◽  
Sixth Order ◽  
Numerical Representation ◽  
Order Function ◽  
Practical Applications ◽  
Perfectly Plastic ◽  
Unit Cells ◽  
Elastic Perfectly Plastic

The capability to obtain limit load solutions of plates with triangular penetration patterns using fourth order functions to represent the collapse surface has been presented in previous papers. These papers describe how equivalent solid plate elastic-perfectly plastic finite element capabilities are generated and demonstrate how such capabilities can be used to great advantage in the analysis of tubesheets in large heat exchanger applications. However, these papers have pointed out that although the fourth order functions can produce sufficient accuracy for many practical applications, there are situations where improvements in the accuracy of in-plane and transverse shear are desirable. This paper investigates the use of a sixth order function to represent the collapse surface for improved accuracy of the in-plane response. Explicit elastic-perfectly plastic finite element solutions are obtained for unit cells representing an infinite array of circular penetrations arranged in an equilateral triangular array. These cells are used to create a numerical representation of the complete collapse surfaces for a number of ligament efficiencies (h/P where h is the minimum ligament width and P is the distance between hole centers). Each collapse surface is then fit to a sixth order function that satisfies the periodicity of the hole pattern. Sixth-order collapse functions were developed for h/P values between .05 and .50. Accuracy of the sixth order and the fourth order functions are compared. It was found that the sixth order function is indeed more accurate, reducing the error from 12.2% for the fourth order function to less than 3% for the sixth order function.

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