scholarly journals On the Thermal Dynamics of Metallic and Superconducting Wires. Bifurcations, Quench, the Destruction of Bistability and Temperature Blowup

J ◽  
2021 ◽  
Vol 4 (4) ◽  
pp. 803-823
Author(s):  
Rizos N. Krikkis
Keyword(s):  
Bifurcation Analysis ◽  
Superconducting Magnets ◽  
Thermal Runaway ◽  
Unified Framework ◽  
Thermal Dynamics ◽  
Superconducting Wires ◽  
Quenching Process ◽  
Current Value ◽  
Numerical Bifurcation ◽  
Static Criterion

In the present study, a numerical bifurcation analysis is carried out in order to investigate the multiplicity and the thermal runaway features of metallic and superconducting wires in a unified framework. The analysis reveals that the electrical resistance, combined with the boiling curve, are the dominant factors shaping the conditions of bistability—which result in a quenching process—and the conditions of multistability—which may lead to a temperature blowup in the wire. An interesting finding of the theoretical analysis is that, for the case of multistability, there are two ways that a thermal runaway may be triggered. One is associated with a high current value (“normal” runaway) whereas the other one is associated with a lower current value (“premature” runaway), as has been experimentally observed with certain types of superconducting magnets. Moreover, the results of the bifurcation analysis suggest that a static criterion of a warm or a cold thermal wave propagation may be established based on the limit points obtained.

NUMERICAL BIFURCATION ANALYSIS OF DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

2001 ◽  
Vol 11 (03) ◽  
pp. 737-753 ◽  
Author(s):  
TATYANA LUZYANINA ◽  
KOEN ENGELBORGHS ◽  
DIRK ROOSE
Keyword(s):  
Differential Equations ◽  
Bifurcation Analysis ◽  
Delay Differential Equations ◽  
Constant Delay ◽  
State Dependent ◽  
State Dependent Delay ◽  
Numerical Bifurcation ◽  
Delay Differential ◽  
Steady State Solutions ◽  
Numerical Bifurcation Analysis

In this paper we apply existing numerical methods for bifurcation analysis of delay differential equations with constant delay to equations with state-dependent delay. In particular, we study the computation, continuation and stability analysis of steady state solutions and periodic solutions. We collect the relevant theory and describe open theoretical problems in the context of bifurcation analysis. We present computational results for two examples and compare with analytical results whenever possible.

Numerical Bifurcation Analysis of Delayed Recycle Stream in a Continuously Stirred Tank Reactor

2010 ◽  
Author(s):  
Nalwala Rohitbabu Gangadhar ◽  
Periyasamy Balasubramanian ◽  
Swapan Paruya ◽  
Samarjit Kar ◽  
Suchismita Roy
Keyword(s):  
Bifurcation Analysis ◽  
Stirred Tank ◽  
Stirred Tank Reactor ◽  
Tank Reactor ◽  
Continuously Stirred Tank Reactor ◽  
Numerical Bifurcation ◽  
Numerical Bifurcation Analysis

scholarly journals Numerical Bifurcation Analysis of a Film Flowing over a Patterned Surface through Enhanced Lubrication Theory

Fluids ◽  
2021 ◽  
Vol 6 (11) ◽  
pp. 405
Author(s):  
Nicola Suzzi ◽  
Giulio Croce
Keyword(s):  
Contact Angle ◽  
Bifurcation Analysis ◽  
Dynamic Contact Angle ◽  
Flow Characteristics ◽  
Dynamic Contact ◽  
Contact Angles ◽  
Inclined Plate ◽  
Lubrication Equation ◽  
Static Contact ◽  
Numerical Bifurcation

The bifurcation analysis of a film falling down an hybrid surface is conducted via the numerical solution of the governing lubrication equation. Instability phenomena, that lead to film breakage and growth of fingers, are induced by multiple contamination spots. Contact angles up to 75∘ are investigated due to the full implementation of the free surface curvature, which replaces the small slope approximation, accurate for film slope lower than 30∘. The dynamic contact angle is first verified with the Hoffman–Voinov–Tanner law in case of a stable film down an inclined plate with uniform surface wettability. Then, contamination spots, characterized by an increased value of the static contact angle, are considered in order to induce film instability and several parametric computations are run, with different film patterns observed. The effects of the flow characteristics and of the hybrid pattern geometry are investigated and the corresponding bifurcation diagram with the number of observed rivulets is built. The long term evolution of induced film instabilities shows a complex behavior: different flow regimes can be observed at the same flow characteristics under slightly different hybrid configurations. This suggest the possibility of controlling the rivulet/film transition via a proper design of the surfaces, thus opening the way for relevant practical application.

scholarly journals Numerical bifurcation analysis of a ?car-following? model

PAMM ◽  
2004 ◽  
Vol 4 (1) ◽  
pp. 552-553
Author(s):  
Gabriele Sirito ◽  
Ingeniun Gasser ◽  
Tilman Seidel
Keyword(s):  
Bifurcation Analysis ◽  
Car Following ◽  
Car Following Model ◽  
Numerical Bifurcation ◽  
Numerical Bifurcation Analysis

Numerical Bifurcation Analysis of Multimode Impact Oscillations Between a Pantograph and a Rigid Conductor Line

2012 ◽  
Author(s):  
Kiyotaka Yamashita ◽  
Tomoaki Nakayama ◽  
Toshihiko Sugiura ◽  
Hiroshi Yabuno
Keyword(s):  
Bifurcation Analysis ◽  
Numerical Technique ◽  
Single Mode ◽  
Current Collection ◽  
Conductor Line ◽  
Mode Solution ◽  
Numerical Bifurcation ◽  
The Impact ◽  
Impact Oscillations ◽  
Numerical Bifurcation Analysis

This paper deals with the numerical bifurcation analysis of the contact loss between a pantograph and an overhead rigid conductor line in a railway current collection system. In the previous study, we modeled this problem as impact oscillations of an intermediate spring-supported beam excited by an oscillating plate. We have already derived the modal interaction relationship equations that describe the velocities immediately after an impact as functions of the velocities before impact for each vibration mode. A numerical calculation using these relationship equations was performed to clarify the impact oscillations with multiple vibration modes. In this paper, we propose a numerical technique based on maps that transform the state of the system at the impact to the subsequent state at the next impact. This numerical method produces stability analyses of the fixed points of the map that describes an impact oscillation with multiple modes. These results can differ surprisingly from the expectations based on a single-mode solution. These results are compared with experiments undertaken in our laboratory, utilizing a thin stainless steel beam. The typical features of impact oscillations, which were theoretically predicted, were confirmed qualitatively.

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