The stability function of a theory

1978 ◽  
Vol 43 (3) ◽  
pp. 481-486 ◽  
Author(s):  
H. Jerome Keisler
Keyword(s):  
Complete Theory ◽  
Stability Function ◽  
Stability Functions ◽  
The Stability

AbstractLet T be a complete theory with infinite models in a countable language. The stability function gT(κ) is defined as the supremum of the number of types over models of T of power κ. It is proved that there are only six possible stability functions, namely κ, κ + 2ω, κω, ded κ, (ded κ)ω, 2κ.

MASTER STABILITY FUNCTIONS FOR SYNCHRONIZED COUPLED SYSTEMS

1999 ◽  
Vol 09 (12) ◽  
pp. 2315-2320 ◽  
Author(s):  
LOUIS M. PECORA ◽  
THOMAS L. CARROLL
Keyword(s):  
Simple Form ◽  
Coupled Systems ◽  
Stability Function ◽  
Coupled Oscillator ◽  
Synchronous State ◽  
Master Stability Function ◽  
Stability Functions ◽  
The Stability

We show that many coupled oscillator array configurations considered in the literature can be put into a simple form so that determining the stability of the synchronous state can be done by a master stability function which solves, once and for all, the problem of synchronous stability for many couplings of that oscillator.

Is There a Relation Between Synchronization Stability and Bifurcation Type?

2020 ◽  
Vol 30 (08) ◽  
pp. 2050123
Author(s):  
Zahra Faghani ◽  
Zhen Wang ◽  
Fatemeh Parastesh ◽  
Sajad Jafari ◽  
Matjaž Perc
Keyword(s):  
Complex Networks ◽  
Nonlinear Dynamical Systems ◽  
General Relation ◽  
Dynamical Behavior ◽  
Stability Function ◽  
Nonlinear Dynamical ◽  
Practical Applications ◽  
Stability Functions ◽  
Stability And Bifurcation ◽  
The Stability

Synchronization in complex networks is an evergreen subject with many practical applications across the natural and social sciences. The stability of synchronization is thereby crucial for determining whether the dynamical behavior is stable or not. The master stability function is commonly used to that effect. In this paper, we study whether there is a relation between the stability of synchronization and the proximity to certain bifurcation types. We consider four different nonlinear dynamical systems, and we determine their master stability functions in dependence on key bifurcation parameters. We also calculate the corresponding bifurcation diagrams. By means of systematic comparisons, we show that, although there are some variations in the master stability functions in dependence on bifurcation proximity and type, there is in fact no general relation between synchronization stability and bifurcation type. This has important implication for the restrained generalizability of findings concerning synchronization in complex networks for one type of node dynamics to others.

Design of Optimized Multiobjective Function for Bipedal Locomotion Based on Energy and Stability

2019 ◽  
Vol 28 (1) ◽  
pp. 133-152 ◽  
Author(s):  
Manish Raj ◽  
Gora C. Nandi
Keyword(s):  
Energy Function ◽  
Orbital Energy ◽  
Stability Function ◽  
Energy Functions ◽  
Stability Functions ◽  
Nao Robot ◽  
Real Coded Genetic Algorithm ◽  
Unique Approach ◽  
Zero Moment ◽  
The Stability

Abstract This paper presents a novel analytical method to develop the multiobjective function including energy and stability functions. The energy function has been developed by unique approach of orbital energy concept and the stability function obtained by modifying the pre-existing zero moment point (ZMP) trajectory. These functions are optimized using real coded genetic algorithm to produce an optimum set of walk parameters. The analytical results show that, when the energy function is optimized, the stability of the robot decreases. Similarly, if the stability function is optimized, the energy consumed by the robot increases. Thus, there is a clear trade-off between the stability and energy functions. Thus, we propose the multiobjective evolutionary algorithm to yield the optimum value of the walk parameters. The results are verified by Nao robot. This approach increases the energy efficiency of Nao robot by 67.05%, and stability increases by 75%. Furthermore, this method can be utilized on all ZMP classed bipeds.

scholarly journals Sensitivity of an Idealized Tropical Cyclone to the Configuration of the Global Forecast System–Eddy Diffusivity Mass Flux Planetary Boundary Layer Scheme

Atmosphere ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 284
Author(s):  
Evan A. Kalina ◽  
Mrinal K. Biswas ◽  
Jun A. Zhang ◽  
Kathryn M. Newman
Keyword(s):  
Boundary Layer ◽  
Planetary Boundary Layer ◽  
Weather Prediction ◽  
Intensity Change ◽  
Rapid Intensification ◽  
Forecast System ◽  
Stability Functions ◽  
Non Local ◽  
The Stability ◽  
Heat And Moisture

The intensity and structure of simulated tropical cyclones (TCs) are known to be sensitive to the planetary boundary layer (PBL) parameterization in numerical weather prediction models. In this paper, we use an idealized version of the Hurricane Weather Research and Forecast system (HWRF) with constant sea-surface temperature (SST) to examine how the configuration of the PBL scheme used in the operational HWRF affects TC intensity change (including rapid intensification) and structure. The configuration changes explored in this study include disabling non-local vertical mixing, changing the coefficients in the stability functions for momentum and heat, and directly modifying the Prandtl number (Pr), which controls the ratio of momentum to heat and moisture exchange in the PBL. Relative to the control simulation, disabling non-local mixing produced a ~15% larger storm that intensified more gradually, while changing the coefficient values used in the stability functions had little effect. Varying Pr within the PBL had the greatest impact, with the largest Pr (~1.6 versus ~0.8) associated with more rapid intensification (~38 versus 29 m s−1 per day) but a 5–10 m s−1 weaker intensity after the initial period of strengthening. This seemingly paradoxical result is likely due to a decrease in the radius of maximum wind (~15 versus 20 km), but smaller enthalpy fluxes, in simulated storms with larger Pr. These results underscore the importance of measuring the vertical eddy diffusivities of momentum, heat, and moisture under high-wind, open-ocean conditions to reduce uncertainty in Pr in the TC PBL.

Model and Stability of the Traffic Flow Consisting of Heterogeneous Drivers

2015 ◽  
Vol 10 (3) ◽  
Author(s):  
Da Yang ◽  
Liling Zhu ◽  
Yun Pu
Keyword(s):  
Traffic Flow ◽  
Heterogeneous Traffic ◽  
Model Parameters ◽  
Optimal Velocity ◽  
Stability Functions ◽  
Car Following Model ◽  
Traffic Wave ◽  
The Stability ◽  
Different Characteristics ◽  
Stationary Velocity

Although traffic flow has attracted a great amount of attention in past decades, few of the studies focused on heterogeneous traffic flow consisting of different types of drivers or vehicles. This paper attempts to investigate the model and stability analysis of the heterogeneous traffic flow, including drivers with different characteristics. The two critical characteristics of drivers, sensitivity and cautiousness, are taken into account, which produce four types of drivers: the sensitive and cautious driver (S-C), the sensitive and incautious driver (S-IC), the insensitive and cautious driver (IS-C), and the insensitive and incautious driver (IS-IC). The homogeneous optimal velocity car-following model is developed into a heterogeneous form to describe the heterogeneous traffic flow, including the four types of drivers. The stability criterion of the heterogeneous traffic flow is derived, which shows that the proportions of the four types of drivers and their stability functions only relating to model parameters are two critical factors to affect the stability. Numerical simulations are also conducted to verify the derived stability condition and further explore the influences of the driver characteristics on the heterogeneous traffic flow. The simulations reveal that the IS-IC drivers are always the most unstable drivers, the S-C drivers are always the most stable drivers, and the stability effects of the IS-C and the S-IC drivers depend on the stationary velocity. The simulations also indicate that a wider extent of the driver heterogeneity can attenuate the traffic wave.

Calculation of Excess Stability Functions of Four Binary Alloys

2021 ◽  
Vol 14 (3) ◽  
pp. 193-200
Keyword(s):  
Thermodynamic Properties ◽  
Concentration Fluctuation ◽  
Ideal Solution ◽  
Nearest Neighbour ◽  
Stability Function ◽  
Stability Functions ◽  
Atomic Correlation ◽  
Neighbour Shell ◽  
The Ideal ◽  
Excess Stability

Abstract: The thermodynamic model based on cluster of two atoms is considered with the view to obtaining Scc(0) and the excess stability function of Scc(0). Concentration-concentration fluctuation; Scc(0) of four binary molten alloys was calculated. The thermodynamic properties of these alloys are evaluated based on cluster of two atoms (A & B) or (B & A). Each system has the view of obtaining concentration-concentration fluctuation; Scc(0) enumerating the low-order atomic correlation in the nearest neighbour shell of liquid binary alloys.The highlights of excess stability functions(ES) of Scc(0) of these alloys were reported. The values of Scc(0) for all these alloys are higher than the ideal solution values. The values of Scc(0) for Bi-Cd alloy is close to the ideal Scc (0). The indication of the excess stability of Scc(0) for some alloys is in support of homocoordination. The Scc(0) and excess stability function of Scc (0) for the four alloys are presented. Keywords: Concentration-concentration fluctuation, Excess stability function, Ordering energy.

Notes on the stability of separably closed fields

1979 ◽  
Vol 44 (3) ◽  
pp. 412-416 ◽  
Author(s):  
Carol Wood
Keyword(s):  
Differential Algebra ◽  
Complete Theory ◽  
Model Completeness ◽  
Closed Fields ◽  
Superstable Theories ◽  
Basic Facts ◽  
The Stability ◽  
Differential Fields

AbstractThe stability of each of the theories of separably closed fields is proved, in the manner of Shelah's proof of the corresponding result for differentially closed fields. These are at present the only known stable but not superstable theories of fields. We indicate in §3 how each of the theories of separably closed fields can be associated with a model complete theory in the language of differential algebra. We assume familiarity with some basic facts about model completeness [4], stability [7], separably closed fields [2] or [3], and (for §3 only) differential fields [8].

Sign in / Sign up

Export Citation Format

Share Document