Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userVariations on chaos in physics: from unpredictability to universal laws
62
0
0.0
(
0
)
Authors
Amaury Mouchet
Ask ChatGPT about the research
No Arabic abstract
The tremendous popular success of Chaos Theory shares some common points with the not less fortunate Relativity: they both rely on a misunderstanding. Indeed, ironically , the scientific meaning of these terms for mathematicians and physicists is quite opposite to the one most people have in mind and are attracted by. One may suspect that part of the psychological roots of this seductive appeal relies in the fact that with these ambiguous names, together with some superficial clich{e}s or slogans immediately related to them (the butterfly effect or everything is relative), some have the more or less secret hope to find matter that would undermine two pillars of science, namely its ability to predict and to bring out a universal objectivity. Here I propose to focus on Chaos Theory and illustrate on several examples how, very much like Relativity, it strengthens the position it seems to contend with at first sight: the failure of predictability can be overcome and leads to precise, stable and even more universal predictions.
rate research
Read More
The possibility of complicated dynamic behaviour driven by non-linear feedbacks in dynamical systems has revolutionized science in the latter part of the last century. Yet despite examples of complicated frequency dynamics, the possibility of long-term evolutionary chaos is rarely considered. The concept of survival of the fittest is central to much evolutionary thinking and embodies a perspective of evolution as a directional optimization process exhibiting simple, predictable dynamics. This perspective is adequate for simple scenarios, when frequency-independent selection acts on scalar phenotypes. However, in most organisms many phenotypic properties combine in complicated ways to determine ecological interactions, and hence frequency-dependent selection. Therefore, it is natural to consider models for the evolutionary dynamics generated by frequency-dependent selection acting simultaneously on many different phenotypes. Here we show that complicated, chaotic dynamics of long-term evolutionary trajectories in phenotype space is very common in a large class of such models when the dimension of phenotype space is large, and when there are epistatic interactions between the phenotypic components. Our results suggest that the perspective of evolution as a process with simple, predictable dynamics covers only a small fragment of long-term evolution. Our analysis may also be the first systematic study of the occurrence of chaos in multidimensional and generally dissipative systems as a function of the dimensionality of phase space.
Many research works deal with chaotic neural networks for various fields of application. Unfortunately, up to now these networks are usually claimed to be chaotic without any mathematical proof. The purpose of this paper is to establish, based on a rigorous theoretical framework, an equivalence between chaotic iterations according to Devaney and a particular class of neural networks. On the one hand we show how to build such a network, on the other hand we provide a method to check if a neural network is a chaotic one. Finally, the ability of classical feedforward multilayer perceptrons to learn sets of data obtained from a dynamical system is regarded. Various Boolean functions are iterated on finite states. Iterations of some of them are proven to be chaotic as it is defined by Devaney. In that context, important differences occur in the training process, establishing with various neural networks that chaotic behaviors are far more difficult to learn.
We describe the theoretical ideas, developed between the 1950s-1970s, which led to the prediction of the Higgs boson, the particle that was discovered in 2012. The forces of nature are based on symmetry principles. We explain the nature of these symmetries through an economic analogy. We also discuss the Higgs mechanism, which is necessary to avoid some of the naive consequences of these symmetries, and to explain various features of elementary particles.
As the end products of the hierarchical process of cosmic structure formation, galaxy clusters present some predictable properties, like those mostly driven by gravity, and some others, more affected by astrophysical dissipative processes, that can be recovered from observations and that show remarkable universal behaviour once rescaled by halo mass and redshift. However, a consistent picture that links these universal radial profiles and the integrated values of the thermodynamical quantities of the intracluster medium, also quantifying the deviations from the standard self-similar gravity-driven scenario, has to be demonstrated. In this work, we use a semi-analytic model based on a universal pressure profile in hydrostatic equilibrium within a cold dark matter halo with a defined relation between mass and concentration to reconstruct the scaling laws between the X-ray properties of galaxy clusters. We also quantify any deviation from the self-similar predictions in terms of temperature dependence of a few physical quantities such as the gas mass fraction, the relation between spectroscopic temperature and its global value, and, if present, the hydrostatic mass bias. This model allows to reconstruct both the observed profiles and the scaling laws between integrated quantities. We use the Planck-selected ESZ sample to calibrate the predicted scaling laws between gas mass, temperature, luminosity and total mass. Our universal model reproduces well the observed thermodynamic properties and provides a way to interpret the observed deviations from the standard self-similar behaviour. By combining these results with the constraints on the observed $Y_{SZ}-T$ relation, we show how we can quantify the level of gas clumping affecting the studied sample, estimate the clumping-free gas mass fraction, and suggest the average level of hydrostatic bias present.
Archery lends itself to scientific analysis. In this paper we discuss physics laws that relate to the mechanics of bow and arrow, to the shooting process and to the flight of the arrow. In parallel, we describe experiments that address these laws. The detailed results of these measurements, performed with a specific bow and arrow, provide insight into many aspects of archery and illustrate the importance of quantitative information in the scientific process. Most of the proposed experiments use only modest tools and can be carried out by archers with their own equipment.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
