On finitely stable domains, II

2020 ◽  
Vol 12 (2) ◽  
pp. 179-198
Author(s):  
Stefania Gabelli ◽  
Moshe Roitman
Keyword(s):  
Stable Domains

Polydomain Structure of Epitaxial PbTiO3 films on MgO

1997 ◽  
Vol 493 ◽  
Author(s):  
S. P. Alpay ◽  
A. S. Prakash ◽  
S. Aggarwal ◽  
R. Ramesh ◽  
A. L. Roytburd ◽  
...  
Keyword(s):  
Domain Structure ◽  
Pulsed Laser ◽  
Laser Deposition ◽  
X Ray Diffraction ◽  
X Ray ◽  
Theoretical Predictions ◽  
The Stability ◽  
Increasing Temperature ◽  
Stable Domains ◽  
Domain Stability

ABSTRACTA PbTiO3(001) film grown on MgO(001) by pulsed laser deposition is examined as an example to demonstrate the applications of the domain stability map for epitaxial perovskite films which shows regions of stable domains and fractions of domains in a polydomain structure. X-ray diffraction studies indicate that the film has a …c/a/c/a… domain structure in a temperature range of °C to 400°C with the fraction of c-domains decreasing with increasing temperature. These experimental results are in excellent agreement with theoretical predictions based on the stability map.

On uniformly perfect boundary of stable domains in iteration of meromorphic functions II

2002 ◽  
Vol 132 (3) ◽  
pp. 531-544 ◽  
Author(s):  
ZHENG JIAN-HUA
Keyword(s):  
Entire Function ◽  
Meromorphic Function ◽  
Meromorphic Functions ◽  
Julia Set ◽  
Fatou Set ◽  
Deficient Value ◽  
Uniformly Perfect ◽  
Simply Connected ◽  
Stable Domains ◽  
Uniform Perfectness

We investigate uniform perfectness of the Julia set of a transcendental meromorphic function with finitely many poles and prove that the Julia set of such a meromorphic function is not uniformly perfect if it has only bounded components. The Julia set of an entire function is uniformly perfect if and only if the Julia set including infinity is connected and every component of the Fatou set is simply connected. Furthermore if an entire function has a finite deficient value in the sense of Nevanlinna, then it has no multiply connected stable domains. Finally, we give some examples of meromorphic functions with uniformly perfect Julia sets.

On sullivan's classification of periodic stable domains

1990 ◽  
Vol 14 (1-4) ◽  
pp. 211-214 ◽  
Author(s):  
Norbert Steinmetz
Keyword(s):  
Stable Domains

BURSTING TYPES AND STABLE DOMAINS OF RULKOV NEURON NETWORK WITH MEAN FIELD COUPLING

2013 ◽  
Vol 23 (12) ◽  
pp. 1330041 ◽  
Author(s):  
HONGJUN CAO ◽  
YANGUO WU
Keyword(s):  
Parameter Space ◽  
Single Neuron ◽  
Complex Dynamics ◽  
Mean Field ◽  
Flip Bifurcation ◽  
Neuron Network ◽  
Square Wave ◽  
Field Coupling ◽  
The Mean ◽  
Stable Domains

Based on the detailed bifurcation analysis and the master stability function, bursting types and stable domains of the parameter space of the Rulkov map-based neuron network coupled by the mean field are taken into account. One of our main findings is that besides the square-wave bursting, there at least exist two kinds of triangle burstings after the mean field coupling, which can be determined by the crisis bifurcation, the flip bifurcation, and the saddle-node bifurcation. Under certain coupling conditions, there exists two kinds of striking transitions from the square-wave bursting (the spiking) to the triangle bursting (the square-wave bursting). Stable domains of fixed points, periodic solutions, quasiperiodic solutions and their corresponding firing regimes in the parameter space are presented in a rigorous mathematical way. In particular, as a function of the intrinsic control parameters of each single neuron and the external coupling strength, a stable coefficient of the Neimark–Sacker bifurcation is derived in a parameter plane. These results show that there exist complex dynamics and rich firing regimes in such a simple but thought-provoking neuron network.

scholarly journals The largest cartesian closed category of stable domains

1996 ◽  
Vol 166 (1-2) ◽  
pp. 203-219 ◽  
Author(s):  
Guo-Qiang Zhang
Keyword(s):  
Cartesian Closed Category ◽  
Closed Category ◽  
Cartesian Closed ◽  
Stable Domains

scholarly journals Special type of morphological reorganization induced by phorbol ester: reversible partition of cell into motile and stable domains.

1987 ◽  
Vol 84 (12) ◽  
pp. 4122-4125 ◽  
Author(s):  
V. B. Dugina ◽  
T. M. Svitkina ◽  
J. M. Vasiliev ◽  
I. M. Gelfand
Keyword(s):  
Phorbol Ester ◽  
Stable Domains

scholarly journals An algebraic approach to stable domains

1990 ◽  
Vol 64 (2) ◽  
pp. 171-203 ◽  
Author(s):  
Paul Taylor
Keyword(s):  
Algebraic Approach ◽  
Stable Domains

scholarly journals A logical approach to stable domains

2006 ◽  
Vol 368 (1-2) ◽  
pp. 124-148 ◽  
Author(s):  
Yi-Xiang Chen ◽  
Achim Jung
Keyword(s):  
Logical Approach ◽  
Stable Domains

Capillary instability of a streaming fluid-core liquid jet underself-gravitating forces

2007 ◽  
Vol 85 (8) ◽  
pp. 849-861
Author(s):  
A E Radwan ◽  
E E Elmahdy
Keyword(s):  
Capillary Force ◽  
Gravitational Instability ◽  
Axial Flow ◽  
The Self ◽  
Liquid Jet ◽  
Fluid Density ◽  
Fluid Core ◽  
The Stability ◽  
Stable Domains ◽  
Axisymmetric Disturbances

The stability criterion of a fluid cylinder (density ρ(1)) embedded in a different fluid (density ρ(2)) is derived and discussed. The model is capillary unstable in the domain 0 < x < 1 as m = 0 where x and m are the axial and transverse wave numbers, while it is stable in all other domains. The densities ratio ρ(2) / ρ(1) decreases the unstable domains but never suppress them. The streaming increases the unstable domains. Gravitationally, in m = 0 mode the model is unstable in the domain 0 < x < 1.0668 as ρ(2) < ρ(1), while as ρ(2) = ρ(1) it is marginally stable but when ρ(2) > ρ(1) the model is purely unstable for all short and long wavelengths. In m ≠ 0 modes, the self-gravitating model is neutrally stable as ρ(1) = ρ(2), ordinarily stable as ρ(2) < ρ(1), but is purely unstable as ρ(2) > ρ(1). The streaming destabilizing effect makes the self-gravitating instability worse and shrinks the stable domains. The stability analysis of the model under the combined effect of the capillary and self-gravitating forces is performed analytically and verified numerically. When ρ(2) < ρ(1) the capillary force and the axial flow have destabilizing influences but the ratio of the densities ρ(2) / ρ(1) has a stabilizing effect on the gravitating instability. If ρ(1) = ρ(2), the streaming is destabilizing but the capillary force is strongly stabilizing and could suppress the gravitational instability. When ρ(2) > ρ(1) the capillary force improves the gravitational instability and creates domains of much stability and moreover the instability of the self-gravitating force disappears in several cases of axisymmetric disturbances. PACS No.: 47.17+e

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