Probability Distributions for Complex Systems:  Adaptive Umbrella Sampling of the Potential Energy

1998 ◽  
Vol 102 (5) ◽  
pp. 865-880 ◽  
Author(s):  
Christian Bartels ◽  
Martin Karplus
Keyword(s):  
Potential Energy ◽  
Complex Systems ◽  
Probability Distributions ◽  
Umbrella Sampling

Valence–Bond Order (VBO): A New Approach to Modeling Reactive Potential Energy Surfaces for Complex Systems, Materials, and Nanoparticles

2009 ◽  
Vol 5 (3) ◽  
pp. 594-604 ◽  
Author(s):  
Meiyu Zhao ◽  
Mark A. Iron ◽  
Przemysław Staszewski ◽  
Nathan E. Schultz ◽  
Rosendo Valero ◽  
...  
Keyword(s):  
Potential Energy ◽  
Complex Systems ◽  
Potential Energy Surfaces ◽  
Bond Order ◽  
Valence Bond ◽  
New Approach ◽  
Reactive Potential ◽  
Energy Surfaces

scholarly journals Probing Potential Energy Surface Exploration Strategies for Complex Systems

2015 ◽  
Vol 11 (4) ◽  
pp. 1970-1977 ◽  
Author(s):  
Gawonou Kokou N’Tsouaglo ◽  
Laurent Karim Béland ◽  
Jean-François Joly ◽  
Peter Brommer ◽  
Normand Mousseau ◽  
...  
Keyword(s):  
Potential Energy ◽  
Complex Systems ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Surface Exploration

Star-shaped order for distributions characterized by several parameters and some applications

2021 ◽  
pp. 1-11
Author(s):  
Idir Arab ◽  
Milto Hadjikyriakou ◽  
Paulo Eduardo Oliveira ◽  
Beatriz Santos
Keyword(s):  
Complex Systems ◽  
Probability Distributions ◽  
Real Parameter ◽  
Applied Probability ◽  
Aging Properties ◽  
Multidimensional Parameter ◽  
Complex Models

Abstract The star-shaped ordering between probability distributions is a common way to express aging properties. A well-known criterion was proposed by Saunders and Moran [(1978). On the quantiles of the gamma and F distributions. Journal of Applied Probability 15(2): 426–432], to order families of distributions depending on one real parameter. However, the lifetime of complex systems usually depends on several parameters, especially when considering heterogeneous components. We extend the Saunders and Moran criterion characterizing the star-shaped order when the multidimensional parameter moves along a given direction. A few applications to the lifetime of complex models, namely parallel and series models assuming different individual components behavior, are discussed.

More complex systems

2003 ◽  
Keyword(s):  
Energy Transfer ◽  
Potential Energy ◽  
Complex Systems ◽  
Chemical Reactions ◽  
Potential Energy Surfaces ◽  
Electronic States ◽  
Polyatomic Molecules ◽  
Polyatomic Systems ◽  
Energy Surfaces ◽  
Semi Empirical

By more complex systems we mean systems containing on the order of hundreds or thousands of atoms, or molecules with less atoms but with “complicated” motions, the latter being the case when considering collisions between polyatomic molecules. In the present chapter we deal with quantum-classical methods for treating energy transfer in collisions involving polyatomic molecules, molecule surface scattering, reactions in polyatomic systems and solution. We will assume that it is possible to construct realistical potential energy surfaces for the systems. Obviously, these surfaces will be of empirical or semi-empirical nature. In some of the methods, as for instance the reaction path method, one tries to minimize the information needed on potential energy surfaces. Chemical reactions and energy transfer processes in the gas phase are often studied using just a single adiabatic Born-Oppenheimer potential energy surface. However non-adiabatic effects, that is, coupling between different electronic states, is an important aspect in chemistry. If the coupling between the various electronic states can be neglected, the “electronic” effect reduces to that of a statistical degeneracy factor ge [180].

Reliability analysis for complex systems subject to competing failure processes in an uncertain environment

2020 ◽  
Vol 39 (3) ◽  
pp. 4331-4339
Author(s):  
Baoliang Liu ◽  
Zhiqiang Zhang ◽  
Yanqing Wen ◽  
Shugui Kang ◽  
Yanxin Guo ◽  
...  
Keyword(s):  
Complex Systems ◽  
Reliability Analysis ◽  
Uncertainty Theory ◽  
Probability Distributions ◽  
External Shocks ◽  
Process Reliability ◽  
Degradation Models ◽  
Renewal Reward Process ◽  
Internal Degradation

Reliability analysis of complex systems subject to competing failure processes based on probability theory has received increasing attention. However, in many situations, the observed data is too limited to estimate the parameters and probability distributions of the system by statistic methods. To address this problem, an uncertain degradation models is proposed in this paper under the framework of uncertainty theory. Based on this model, a complex system which is subject to both continuous internal degradation and external shocks is introduced. The continuous internal degradation of the system is controlled by some uncertain factors, and the external shocks are deemed to an uncertain renewal reward process. Reliability for the complex systems is obtained by employing the uncertainty theory. Finally, a case study is presented to demonstrate the effectiveness of the results obtained in the paper.

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