Chaos Driven Evolutionary Algorithm: a Novel Approach for Optimization

This research deals with the initial investigations on the concept of a chaos-driven evolutionary algorithm Differential evolution. This paper is aimed at the embedding of simple two-dimensional chaotic system, which is Lozi map, in the form of chaos pseudo random number generator for Differential Evolution. The chaotic system of interest is the discrete dissipative system. Repeated simulations were performed on standard benchmark Schwefel’s test function in higher dimensions. Finally, the obtained results are compared with canonical Differential Evolution.

A mechanism of abiogenesis based on complex reaction networks organized by seed-dependent autocatalytic systems

The core of the origin-of-life problem is to explain how a complex dissipative system could emerge spontaneously from a simple environment, perpetuate itself, and complexify over time. This would only be possible, we argue, if prebiotic chemical reaction networks had autocatalytic features organized in a way that permitted the accretion of complexity even in the absence of genetic control. To evaluate this claim, we developed tools to analyze the autocatalytic organization of food-driven reaction networks and applied these tools to both abiotic and biotic networks. Both networks contained seed-dependent autocatalytic systems (SDASs), which are subnetworks that can use a flux of food chemicals to self-propagate if, and only if, they are first seeded by some non-food chemicals. Moreover, SDASs were organized such that the activation of a lower-tier SDAS could render new higher-tier SDASs accessible. The organization of SDASs is, thus, similar to trophic levels (producer, primary consumer, etc.) in a biological ecosystem. Furthermore, similar to ecological succession, we found that higher-tier SDASs may produce chemicals that enhance the ability of the entire chemical ecosystem to utilize food more efficiently. The SDAS concept explains how driven abiotic environments, namely ones receiving an ongoing flux of food chemicals, can incrementally complexify even without genetic polymers. This framework predicts that it ought to be possible to detect the spontaneous emergence of life-like features, such as self-propagation and adaptability, in driven chemical systems in the laboratory. Additionally, SDAS theory may be useful for exploring general properties of other complex systems.

The Landslide Velocity

Proper knowledge of velocity is required in accurately determining the enormous destructive energy carried by a landslide. We present the first, simple and physics-based general analytical landslide velocity model that simultaneously incorporates the internal deformation (non-linear advection) and externally applied forces, consisting of the net driving force and the viscous resistant. From the physical point of view, the model stands as a novel class of non-linear advective – dissipative system where classical Voellmy and inviscid Burgers' equation are specifications of this general model. We show that the non-linear advection and external forcing fundamentally regulate the state of motion and deformation, which substantially enhances our understanding of the velocity of a coherently deforming landslide. Since analytical solutions provide the fastest, the most cost-effective and the best rigorous answer to the problem, we construct several new and general exact analytical solutions. These solutions cover the wider spectrum of landslide velocity and directly reduce to the mass point motion. New solutions bridge the existing gap between the negligibly deforming and geometrically massively deforming landslides through their internal deformations. This provides a novel, rapid and consistent method for efficient coupling of different types of mass transports. The mechanism of landslide advection, stretching and approaching to the steady-state has been explained. We reveal the fact that shifting, up-lifting and stretching of the velocity field stem from the forcing and non-linear advection. The intrinsic mechanism of our solution describes the fascinating breaking wave and emergence of landslide folding. This happens collectively as the solution system simultaneously introduces downslope propagation of the domain, velocity up-lift and non-linear advection. We disclose the fact that the domain translation and stretching solely depends on the net driving force, and along with advection, the viscous drag fully controls the shock wave generation, wave breaking, folding, and also the velocity magnitude. This demonstrates that landslide dynamics are architectured by advection and reigned by the system forcing. The analytically obtained velocities are close to observed values in natural events. These solutions constitute a new foundation of landslide velocity in solving technical problems. This provides the practitioners with the key information in instantly and accurately estimating the impact force that is very important in delineating hazard zones and for the mitigation of landslide hazards.

Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching

The advancement of Chinese education informatisation construction has injected new vitality into the development of Chinese educational technology in the new era and brought new challenges to the development of Chinese educational technology. Nonlinear dissipative structure theory has been a necessary enlightenment for the development of education informatisation. Based on the theory of nonlinear dissipative structure, the paper explores the relationship between the theory and education and teaching. It constructs a diversified regression calculation model of the information-based teaching ecology. Finally, it points out the strategies and ways to apply the dissipative structure theory to improve information-based teaching.

Quasinormal modes of a semi-holographic black brane and thermalization

We study the quasinormal modes and non-linear dynamics of a simplified model of semi-holography, which consistently integrates mutually interacting perturbative and strongly coupled holographic degrees of freedom such that the full system has a total conserved energy. We show that the thermalization of the full system can be parametrically slow when the mutual coupling is weak. For typical homogeneous initial states, we find that initially energy is transferred from the black brane to the perturbative sector, later giving way to complete transfer of energy to the black brane at a slow and constant rate, while the entropy grows monotonically for all time. Larger mutual coupling between the two sectors leads to larger extraction of energy from the black brane by the boundary perturbative system, but also quicker irreversible transfer of energy back to the black brane. The quasinormal modes replicate features of a dissipative system with a softly broken symmetry including the so-called k-gap. Furthermore, when the mutual coupling is below a critical value, there exists a hybrid zero mode with finite momentum which becomes unstable at higher values of momentum, indicating a Gregory-Laflamme type instability. This could imply turbulent equipartitioning of energy between the boundary and the holographic degrees of freedom in the presence of inhomogeneities.

Dynamic transitions and bifurcations of 1D reaction-diffusion equations: The Self-adjoint case

This paper deals with the classification of transition phenomena in the most basic dissipative system possible, namely the 1D reaction diffusion equation. The emphasis is on the relation between the linear and nonlinear terms and the effect of the boundaries which influence the first transitions. We consider the cases where the linear part is self-adjoint with 2nd order and 4th order derivatives which is the case which most often arises in applications. We assume that the nonlinear term depends on the function and its first derivative which is basically the semilinear case for the second order reaction-diffusion system. As for the boundary conditions, we consider the typical Dirichlet, Neumann and periodic boundary settings. In all the cases, the equations admit a trivial steady state which loses stability at a critical parameter. We aim to classify all possible transitions and bifurcations that take place. Our analysis shows that these systems display all three types of transitions: continuous, jump and mixed and display transcritical, supercritical bifurcations with bifurcated states such as finite equilibria, circle of equilibria, and slowly rotating limit cycle. Many applications found in the literature are basically corollaries of our main results. We apply our results to classify the first transitions of the Chaffee-Infante equation, the Fisher-KPP equation, the Kuramoto Sivashinsky equation and the Swift-Hohenberg equation.

4D Investigation of Vortex Fluid Motion Inside the Eyeball

The eye is a complex system of boundaries and fluids with different viscosities within the boundaries. At present, there are no experimental possibilities to thoroughly observe the dynamic 4D processes after one or another method of eye treatment is applied. The complexity of cumulative, i.e., focusing, and dissipative, i.e., scattering, convective and diffusion 4D fluxes of fluids in the eye requires 4D analytical and numerical models of fluid transfer in the human eyeball to be developed. The purpose of the study was to develop and then verify a numerical model of 4D cumulative-dissipative processes of fluid transfer in the eyeball. The study was the first to numerically evaluate the values of the characteristic time of the drug substance in the vitreous cavity until it is completely washed out, depending on the injection site; to visualize the paths of the vortex motion of the drug in the vitreous cavity; to determine the main parameters of the 4D fluid flows of the medicinal substance in the vitreous cavity, depending on the presence or absence of vitreous detachment from the wall of the posterior chamber of the eye. The results obtained are verified by the experimental data available to doctors. In the eye, as a partially open cumulative-dissipative system, Euler regions with high rates of cumulative flows and regions with low speeds or stagnant Lagrange flow zones are defined