CROSSING RESONANCES IN A NON-SCALING FFAG

2011 ◽  
Vol 26 (10n11) ◽  
pp. 1852-1864 ◽  
Author(s):  
D. TRBOJEVIC ◽  
M. BLASKIEWICZ ◽  
E. FOREST
Keyword(s):  
Cancer Therapy ◽  
Blow Up ◽  
Proton Accelerator ◽  
Fast Proton ◽  
Phase Jump ◽  
Proton Acceleration ◽  
Fixed Field ◽  
The Third ◽  
Theoretical Predictions

There are many possible applications for the non-scaling Fixed Field Alternating Gradient (NS-FFAG): accelerating non-relativistic ions, ion cancer therapy, proton drivers, accelerator driven subcritical reactors, heavy radioactive ions, recirculating linacs, and etc. They are confronted with two significant challenges: first is crossing integer resonances as the tunes vary with energy, and that the required fast acceleration has not yet been achieved in practice. An example of a small 30–250 MeV NS-FFAG proton accelerator is used to study both problems. After an introduction, the second chapter shows theoretical predictions for the emittance blow up from crossing the integer resonances. In the third part, the lattice of the ring is briefly described. The fourth chapter describes the "phase jump" a method for fast proton acceleration, while in the chapter five a six dimensional simulations of acceleration is described, ending with conclusions.

Instability and Collapse in Discrete Wave Equations

2005 ◽  
Vol 5 (3) ◽  
pp. 223-241
Author(s):  
A. Carpio ◽  
G. Duro
Keyword(s):  
Continuum Limit ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Blow Up ◽  
Theoretical Predictions ◽  
Initial States ◽  
The Impact ◽  
The Continuum

AbstractUnstable growth phenomena in spatially discrete wave equations are studied. We characterize sets of initial states leading to instability and collapse and obtain analytical predictions for the blow-up time. The theoretical predictions are con- trasted with the numerical solutions computed by a variety of schemes. The behavior of the systems in the continuum limit and the impact of discreteness and friction are discussed.

scholarly journals Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov-Kuznetsov Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Yun Wu ◽  
Zhengrong Liu
Keyword(s):  
Solitary Waves ◽  
Nonlinear Waves ◽  
Blow Up ◽  
Periodic Waves ◽  
The Third ◽  
Bifurcation Phenomena ◽  
Kink Waves ◽  
Fourth Kind

We study the bifurcation phenomena of nonlinear waves described by a generalized Zakharov-Kuznetsov equationut+au2+bu4ux+γuxxx+δuxyy=0. We reveal four kinds of interesting bifurcation phenomena. The first kind is that the low-kink waves can be bifurcated from the symmetric solitary waves, the 1-blow-up waves, the tall-kink waves, and the antisymmetric solitary waves. The second kind is that the 1-blow-up waves can be bifurcated from the periodic-blow-up waves, the symmetric solitary waves, and the 2-blow-up waves. The third kind is that the periodic-blow-up waves can be bifurcated from the symmetric periodic waves. The fourth kind is that the tall-kink waves can be bifurcated from the symmetric periodic waves.

scholarly journals I. A. Klimov. About the pathways of the cerebellum. Diss. Kazan, 1897

2020 ◽  
Vol V (4) ◽  
pp. 207
Keyword(s):  
Anatomical Structure ◽  
Modern State ◽  
The Third

The work of the author was carried out in the laboratory of the clinic of nervous diseases under the guidance of prof. L.O.Darkshevich. An extensive work, embracing 18 printed sheets, is divided into 4 chapters. In the first chapter, a detailed sketch of the literature is presented, introducing the modern state of science about the connections and pathways of the cerebellum. The second chapter contains a description of the anatomical structure of the cerebellum based on the author's own research. In the third chapter, the setting of experiments is described, methods of investigation are described, and their own data obtained experimentally are given. The fourth chapter is devoted to the analysis of all the factual material and the general conclusions following from it.

Third Consultation

2016 ◽  
pp. 217-226
Author(s):  
Donald W. Winnicott
Keyword(s):  
The Third

The fourth chapter of The Piggle consists of Winnicott’s verbatim report and commentary on the third consultation with Gabrielle, 10 April, 1964, and four letters from her mother.

Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues

2015 ◽  
Vol 25 (09) ◽  
pp. 1663-1763 ◽  
Author(s):  
N. Bellomo ◽  
A. Bellouquid ◽  
Y. Tao ◽  
M. Winkler
Keyword(s):  
Blow Up ◽  
Existence Of Solutions ◽  
Biological Tissues ◽  
Original Model ◽  
Future Research ◽  
Macroscopic Models ◽  
The Third ◽  
Research Activities ◽  
Classical Models ◽  
Chemotaxis Models

This paper proposes a survey and critical analysis focused on a variety of chemotaxis models in biology, namely the classical Keller–Segel model and its subsequent modifications, which, in several cases, have been developed to obtain models that prevent the non-physical blow up of solutions. The presentation is organized in three parts. The first part focuses on a survey of some sample models, namely the original model and some of its developments, such as flux limited models, or models derived according to similar concepts. The second part is devoted to the qualitative analysis of analytic problems, such as the existence of solutions, blow-up and asymptotic behavior. The third part deals with the derivation of macroscopic models from the underlying description, delivered by means of kinetic theory methods. This approach leads to the derivation of classical models as well as that of new models, which might deserve attention as far as the related analytic problems are concerned. Finally, an overview of the entire contents leads to suggestions for future research activities.

Introduction

2016 ◽  
Author(s):  
Ulrika Mörth
Keyword(s):  
Member State ◽  
Policy Making ◽  
Administrative State ◽  
Political Arena ◽  
The Third ◽  
Role Conceptions ◽  
Governance Processes ◽  
Small Member ◽  
The Eu

These chapters revolve around questions concerning what kind of polity Sweden became part of in 1995, in what ways Sweden has been transformed due to membership in the EU, and what role a relatively small member state can play in the European political arena. The first chapter analyzes different interpretations of the governance turn in the EU and how these turns relate to Swedish policy-making. The second chapter examines how the EU has transformed the Swedish administrative state by different governance processes. The third chapter studies the Europeanization of Swedish foreign policy and changed role conceptions. The fourth chapter shows that Sweden influenced EU politics during its presidencies but that the scope and conditions of the influence lie outside the control of the presidency.

FFAGs as Accelerators and Beam Delivery Devices for Ion Cancer Therapy

2009 ◽  
Vol 02 (01) ◽  
pp. 229-251 ◽  
Author(s):  
Dejan Trbojevic
Keyword(s):  
Cancer Therapy ◽  
Delivery System ◽  
Fixed Field ◽  
Basic Concepts ◽  
Beam Delivery ◽  
Beam Delivery System ◽  
Future Plans

First, a review is given of fixed field alternating gradient (FFAG) accelerators, presenting a bit of their history and basic concepts. Special attention is paid to the concept of scaling (S-FFAG) and nonscaling (NS-FFAG) FFAGs. This notation is used only in the NS-FFAG part of the article. A discussion is then provided on operating FFAGs. A presentation is made of the designs being considered for S-FFAGs. A bit more is said about the concept of the NS-FFAG and a resonance crossing problem resulting from designs of the NS-FFAGs. A beam delivery system (gantry) employing the NS-FFAG concept is presented after that and, finally, future plans and R&D requirements are put forward.

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