non linear systems
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2022 ◽  
Author(s):  
Xinghua Liu ◽  
Jianwei Guan ◽  
Rui Jiang ◽  
Xiang Gao ◽  
Badong Chen ◽  
...  

2021 ◽  
pp. 317-321
Author(s):  
Helga Nowotny

AbstractThe assumption of digital humanism that a human-centered approach is possible in the design, use, and further development of AI entails an alignment with human values. If the more ambitious goal of building a good digital society along the co-evolutionary path between humans and the digital machines invented by them is to be reached, inherent tensions need to be confronted. Some of them are the result of already existing inequalities and divergent economic, social, and political interests, exacerbated by the impact of digital technologies. Others arise from the question what makes us human and how our interaction with digital machines changes our identity and relations to each other. If digital humanism is to succeed, a widely shared set of practices and attitudes is needed that sensitize us to the diversity of social contexts in which digital technologies are deployed and how to deal with complex, non-linear systems.


2021 ◽  
Author(s):  
Brandon Foley ◽  
Neil Razdan

Dynamic catalysis—the forced oscillation of catalytic reaction coordinate potential energy surfaces (PES)—has recently emerged as a promising method for the acceleration of heterogeneously-catalyzed reactions. Theoretical study of enhancement of rates and supra-equilibrium product yield via dynamic catalysis has, to-date, been severely limited by onerous computational demands of forward integration of stiff, coupled ordinary differential equations (ODEs) that are necessary to quantitatively describe periodic cycling between PESs. We establish a new approach that reduces, by ≳108×, the computational cost of finding the time-averaged rate at dynamic steady state (i.e. the limit cycle for linear and nonlinear systems of kinetic equations). Our developments are motivated by and conceived from physical and mathematical insight drawn from examination of a simple, didactic case study for which closed-form solutions of rate enhancement are derived in explicit terms of periods of oscillation and elementary step rate constants. Generalization of such closed-form solutions to more complex catalytic systems is achieved by introducing a periodic boundary condition requiring the dynamic steady state solution to have the same periodicity as the kinetic oscillations and solving the corresponding differential equations by linear algebra or Newton-Raphson-based approaches. The methodology is well-suited to extension to non-linear systems for which we detail the potential for multiple solutions or solutions with different periodicities. For linear and non-linear systems alike, the acute decrement in computational expense enables rapid optimization of oscillation waveforms and, consequently, accelerates understanding of the key catalyst properties that enable maximization of reaction rates, conversions, and selectivities during dynamic catalysis.


2021 ◽  
Author(s):  
◽  
Richard John Logan

<p>Whilst a lot of our strategic focus in the public sector is on linear policy approaches, many systems/ phenomena of importance are defined as non-linear or far from equilibrium. Traditional approaches to linear forecasting have not proved effective for non-linear systems, since non-linear systems follow a different set of rules. Historically, non-linear systems were too hard to forecast, but over recent decades some rules and approaches are starting to emerge. One important and clearly defined category of non-linear systems are those that follow a ‘power-law’ distribution rather than the ‘normal’ distribution, which is often associated with linear systems or systems in equilibrium. My research collects, analyses, and does a comparative analysis of the different power law populations, as well as the main strategic forecasting techniques that can be applied to those populations/ systems. Overall Conclusions and observations. Just as in science and mathematics, there is now a clearly defined separation and understanding of linear and non-linear systems and the rules that apply to each. My thesis has as its central theme, the idea that strategy as a subject also fits this same philosophical separation of approaches, which I have called the strategic planning versus the strategic thinking divide. Strategic planning is essentially the linear approach – being rational and assuming relatively stable conditions. Strategic thinking assumes the world is effectively non-linear and ‘far from equilibrium’. Non-linear approaches mean acknowledging concepts like; punctuated equilibrium, power law ‘log-log’ graphs, ‘scale-free’ characteristics, ‘self organising criticality’, accepting only pattern prediction (including 1/f formulas) and not precise prediction etc. Understanding non-linearity is essential to understand such things as ‘Black Swans’. Luck, serendipity and ‘bounded rationality’ are always involved in non-linear complex adaptive systems, whereas linear systems tend to comply with the so called ‘rational’ traditions in science and economics. Power law statistical distributions can be seen in a wide variety of non-linear natural and man-made phenomena, from earthquakes and solar flares to populations of cities and sales of books. This sheer diversity of effects that have power law distributions is actually an amazing fact that has only become evident over the last decade or so. Since the world contains aspects that are clearly linear and other aspects that are clearly non-linear, it is essential for someone interested in strategy to be able to understand both systems and be able to apply the correct techniques to each approach. The two parts of ‘punctuated equilibrium’ effectively link the two strategic approaches together as there is only one world and not two separate realities. It therefore follows that a strategist needs a good understanding of both strategic planning and strategic thinking, since both are needed for different phases or periods, and perhaps both are needed for any period when you can't tell what phase you are in, which can also happen. I suggest that under a linear phase, the strategic planning approach should be dominant, but supported by strategic thinking (since you never know when events will turn abruptly); whereas in a turbulent non-linear period the strategic thinking approach should be dominant, but supported by strategic planning (since you know that great turbulence will not last). This is a sort of a swapping dominant/ recessive situation, which has a loose parallel in the theory of the left/ right brain split, where it is not wise to use only one style of thinking, since there are two styles which suit different situations. The key is to pick the right thinking style for the right situation. Just as we have one brain, but two thinking styles, so in the strategy toolbox we also have two valid, useful and complimentary general strategic approaches. However for this thesis, I have focused on the non-linear power law aspects of life which have strong implications for strategic thinking, since that is the new area for me as well as one of the new knowledge frontiers for strategy as a subject (and for leadership, politics and many other areas).</p>


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