Growth Of Chaos Research Articles

Worldview, philosophical, anthropological and ideological principles of national security

The article deals with the worldview, philosophical-anthropological and ideological principles of national safety. It proves that the national safety issues arise from the growth of chaos in the human society. The worldview reason for the chaos is the priority of the material over the spiritual, and the methodological basis is the concept of “every person is an individual”, legitimizing the mediocre person’s right to power and leadership. It grounds that the worldview condition to ride the chaos is the priority of the spiritual over the material, and the methodological basis refers to the metaphysical theory of personality, the centerpiece of which is the worldview law “Personality is the origin of being”. The foundation of national safety under the conditions of paradigmatic changes in the Ukrainian society is the priority of the spiritual, the organization of public life according to the principle: “Personality is the principle of being” and the ideology of personalism.

Black holes, complexity and quantum chaos

We study aspects of black holes and quantum chaos through the behavior of computational costs, which are distance notions in the manifold of unitaries of the theory. To this end, we enlarge Nielsen geometric approach to quantum computation and provide metrics for finite temperature/energy scenarios and CFT’s. From the framework, it is clear that costs can grow in two different ways: operator vs ‘simple’ growths. The first type mixes operators associated to different penalties, while the second does not. Important examples of simple growths are those related to symmetry transformations, and we describe the costs of rotations, translations, and boosts. For black holes, this analysis shows how infalling particle costs are controlled by the maximal Lyapunov exponent, and motivates a further bound on the growth of chaos. The analysis also suggests a correspondence between proper energies in the bulk and average ‘local’ scaling dimensions in the boundary. Finally, we describe these complexity features from a dual perspective. Using recent results on SYK we compute a lower bound to the computational cost growth in SYK at infinite temperature. At intermediate times it is controlled by the Lyapunov exponent, while at long times it saturates to a linear growth, as expected from the gravity description.

КЛІПОВА ХАОТИЧНІСТЬ ЯК ЗАСІБ АБСУРДИЗАЦІЇ ТА МАНІПУЛЯТИВНА ТЕХНОЛОГІЯ

Стаття присвячена теоретичному аналізу наукової літератури щодо застосування кліпової хаотичності з метою актуалізації абсурдності змісту інформації на теренах кіберпростору як новітньої маніпулятивної технології цілеспрямованого впливу на індивідуальну та масову свідомість. Охарактеризовано новітні інформаційно-комунікативні технології, що можуть призвести до непоправних небезпечних наслідків для нашого суспільства.
 Констатується, що кліпова хаотичність кіберпростору як засіб абсурдизації та маніпулятивна технологія соціально-психологічного впливу в інформаційному просторі перш за все спрямована на часткове, або повне «розбалансування» гармонійного співвідношення між концептуальним і кліповим рівнями мислення. 
 Зроблено висновок про те, що еволюційний період зміни свідомості людини в самому розпалі, особистість ще не дійшла до того рівня розвитку, щоб в результаті хаотизації інформаційно-комунікативних потоків (марафонів) на достатньому рівні вміти трансформувати свій когнітивно-стратегічний потенціал і встигати займатися ефективною обробкою інформації за короткий часовий проміжок. А це, водночас, надає можливість застосовувати маніпулятивні технології впливу на індивідуальну та соціальну свідомість.
 Ключові слова: кліпова хаотичність кіберпростору, логіка абсурду, абсурдизація, кліпова культура, кліпове мислення, концептуальне мислення. 

Потеря будущего

The author, an eminent economist and politician, analyzes alarming trends in global development that found their reflection in the voting for Brexit in the United Kingdom, in the outcome of the 2016 presidential elections in the United States, in the migration crisis in Europe and in a number of other landmark events and phenomena of our times. As a follow-up to the concept proposed in his book “Realeconomik”, he notes that what is happening now is far from being accidental. The current tremendous amount of events derive from the factors that have gained strength in the last quarter of the twentieth century. Among them were the following: a) the growth of global inequality in its various manifestations combined with a sense of inability to surmount them; b) the disorganization of the world order that emerged after the World War 2; c) the transformation in the sphere of information and communication technologies that outstrip the development of human consciousness; d) the change in the laws governing the functioning of the world economy. The author critically examines the urge for a political “U-turn”, which has become a spontaneous response to a severe contemporary issues. He believes that the thoughtful attitude of global and national elites toward the factors he suggested for consideration, the awareness of political leaders of the world of their responsibility for its development can prevent an inaccurate reaction that inevitably will result in the growth of chaos. In the second part of the article, the author provides us with a short, but an in-depth analysis of serious changes in the global ratio of centers of political and economic power. He considers the large-scale changes in the world order, called differently (“change of leadership”, the formation of a “multipolar” (polycentric) world, “new normality” in international relations, etc.). In his opinion, all the above terms express the same essence, i.e. the back-pedaling to the past models of global equilibrium. His special concern is the increasingly diminishing role of Europe, which loses not only political and economic power, but also value-oriented and sense-oriented guidance, which is fraught with negative implications for the civilization based – in one way or another – on the ideals of European modernity. The author expresses and substantiates doubts about the existence in the modern world of an integral alternative concept that could replace them, and sees the eventual starting point for overcoming the global crisis in a qualitatively new comprehension of the current situation on the basis of European values.

Onset of many-body chaos in the O(N) model

The growth of commutators of initially commuting local operators diagnoses the onset of chaos in quantum many-body systems. We compute such commutators of local field operators with $N$ components in the $(2+1)$-dimensional $O(N)$ nonlinear sigma model to leading order in $1/N$. The system is taken to be in thermal equilibrium at a temperature $T$ above the zero temperature quantum critical point separating the symmetry broken and unbroken phases. The commutator grows exponentially in time with a rate denoted $\lambda_L$. At large $N$ the growth of chaos as measured by $\lambda_L$ is slow because the model is weakly interacting, and we find $\lambda_L \approx 3.2 T/N$. The scaling with temperature is dictated by conformal invariance of the underlying quantum critical point. We also show that operators grow ballistically in space with a "butterfly velocity" given by $v_B/c \approx 1$ where $c$ is the Lorentz-invariant speed of particle excitations in the system. We briefly comment on the behavior of $\lambda_L$ and $v_B$ in the neighboring symmetry broken and unbroken phases.

A comparison of two numerical weather prediction methods for diagnosing fast‐physics errors in climate models

AbstractAn important aspect of the assessment of climate models is the representation of fast physical processes, which have a strong impact on climate projections. Since these fast processes also have a strong impact on weather forecasts, there is potential in using numerical weather prediction (NWP)‐based methodologies in climate model assessments.Two NWP‐based methods have been proposed in the literature. The first is referred to as the ‘initial tendency’ approach and assesses the systematic departure in the first few hours of short climate model resolution forecasts from the weather trajectory. For this method, the forecast model needs data assimilation capabilities to create initial conditions consistent with the model physics. The second approach is referred to as the ‘transpose‐AMIP’ method. This makes use of analyses produced with a different forecast model to initiate weather forecasts with a climate model. It is generally recommended that errors are diagnosed after a few forecast days to minimise the impact of the non‐native initial conditions.Here we compare these two methods in one NWP model over the subtropical South Pacific, which encompasses climatologically important regimes and transitions between them. The impact of the non‐native initial conditions is compared with the impact of an error introduced in the convection scheme.Results show that care is needed in the design and evaluation of transpose‐AMIP‐style experiments if model errors are to be disentangled from, at short lead‐times, the initial shock of using non‐native initial conditions and, at longer lead‐times, the complicating effects of interactions and the growth of chaos. On the other hand, the initial tendency approach is able to identify the introduced model error. This provides some evidence that it might be worthwhile for climate centres to explore the use of data assimilation.

Free motion around black holes with discs or rings: between integrability and chaos - I

Geodesic dynamics is regular in the fields of isolated stationary black holes. However, due to the presence of unstable periodic orbits, it easily becomes chaotic under various perturbations. Here we examine what amount of chaoticity is induced in Schwarzschild space-time by a presence of an additional source. Following astrophysical motivation, we specifically consider thin rings or discs lying symmetrically around the hole, and describe the total field in terms of exact static and axially symmetric solutions of Einstein's equations. The growth of chaos in time-like geodesic motion is illustrated on Poincar\'e sections, on time series of position or velocity and their Fourier spectra, and on time evolution of the orbital `latitudinal action'. The results are discussed in dependence on the mass and position of the ring/disc and on geodesic parameters (energy and angular momentum). In the Introduction, we also add an overview of the literature.

Parametric oscillations of a non-linear string

A study of the nature of periodic oscillations, bifurcation of vibrations and growth of chaos is presented. With the negative stiffness parametric oscillations of a non-linear stretched string used as a model, the influences of the variables on the behavior of the oscillations are analyzed. The variables studied are the damping factor, the frequency ratio, the non-linear term, the parametric driving amplitude qand the linear stiffness p. The oscillations of this system were approximated and calculated by computer. These results were analyzed in several ways: trajectories, Poincaré maps, probability density functions of displacement and velocity, root mean square responses and Lyapunov exponents. These pictorial representations were in good agreement with the independently calculated map of chaotic/periodic regions over ( p, q). It was found that the magnitudes of the linear stiffness and the parametric driving amplitude are the most important determinants of the presence of chaos. Additionally, the damping factor was found to influence the appearance of chaos. Varying the non-linear term was found to have only a minimal effect on the appearance of chaos. Similarly, the frequency ratio was found not to effect the occurrence of chaos.