INSIGHTS ON COMPETITION FROM A SCIENCE-BASED ANALYSIS

The work presented here uses a science-based approach to obtain new understandings on the mechanisms and the ramifications of competition in everyday life. Assuming competition of a Darwinian nature we can deduce an S-shaped pattern for growth in most competitive environments. Examples range from a rabbit population growing in a fenced-off grass field to scientists competing for Nobel-Prize awards. There are secrets embedded in the mathematical law that describes growth in competition. The rate of growth being proportional to the amount of growth already achieved makes beginnings difficult and sheds light on such proverbial wisdom as “you need goal to make gold”. It also argues for the necessity to engage teachers in the learning process. Other revelations are linked to the symmetry of a life-cycle pattern, which possesses predictive power and demystifies the easy-come-easy-go phenomenon. Predictive power characterizes the rapid-growth phase of the S-shaped pattern (rheostasis) as well as the end of the pattern when growth reaches a ceiling (homeostasis) where supply and demand are in equilibrium. The latter phenomenon is best exemplified by society’s tolerance of deadly car accidents because deaths from car accidents have remained at an invariant level for many decades reflecting equilibrium. The mathematical equation for growth in competition when cast in discrete form reveals fluctuations of chaotic nature before and after the rapid-growth phase. This can illuminate the turbulent times before and after the formation of the USSR as well as the tumultuous times of the 1930s in America. Extending the quantitative approach to two species competing in the same niche involves introducing coupling constants that account for how one species impacts the growth rate of the other. A celebrated example is the predator-prey relationship, which is only one of six possible interactions all of which can be encountered in the marketplace where products and companies compete like species. There are six possible dimensions for action in a two-species competitive struggle that can be exploited toward managing competition and setting one’s role/image in the marketplace. An example dealt in detail is the evolution of the number of American Noble-Prize winners whose numbers are not about to begin diminishing. Americans are involved in a win-win competitive struggle with non-American scholars, but Americans are drawing more of a benefit.

Improving 3D Path Tracking of Unmanned Aerial Vehicles through Optimization of Compensated PD and PID Controllers

The development of quadrotor unmanned aerial vehicles (QUAVs) is a growing field due to their wide range of applications. QUAVs are complex nonlinear systems with a chaotic nature that require a controller with extended dynamics. PD and PID controllers can be successfully applied when the parameters are accurate. However, this parameterization process is complicated and time-consuming; most of the time, parameters are chosen by trial and error without guaranteeing good performance. The originality of this work is to present a novel nonlinear mathematical model with aerodynamic moments and forces in the Newton–Euler formulation, and identify metaheuristic algorithms applied to parameter optimization of compensated PD and PID controls for tracking the trajectories of a QUAV. Eight metaheuristic algorithms (PSO, GWO, HGS, LSHADE, LSPACMA, MPA, SMA and WOA) are reported, and RMSE is used to measure each dynamic performance of the simulations. For the PD control, the best performance is obtained with the HGS algorithm with an RMSE = 0.037247252379126. For the PID control, the best performance is obtained with the HGS algorithm with an RMSE = 0.032594309723623. Trajectory tracking was successful for the QUAV by minimizing the error between the desired and actual dynamics.

“Thief in the Name of Kidd”: Unscrupulous Opportunism and Cheap Print in Late Regency London

William Kidd saw himself as a struggling small publisher of illustrated books operating during the 1830s in a marketplace that favoured large scale firms. His response to his perceived disadvantages was twofold. In seeking to reach a rapidly expanding cohort of leisure-based readers, Kidd deployed aggressive marketing policies that frequently sailed close to the law and generated considerable controversy. He was also less than honest about just who had written or illustrated his books. At the same time, he initiated new genres of relatively cheap illustrated publications based on the recreational interest and habits of an emerging lower middle class and artisan reading public. In particular, he took advantage of the wood engraving as a cheap reprographic medium, and employed highly capable draughtsmen such as Robert Cruikshank, Robert Seymour and George Bonner to illustrate his books and pamphlets. His pocket guides to British seaside resorts, his development of the illustrated reprints known as jeu d’esprit or Facetiae and his packaging up of sayings, mottos and nuggets of information into small format gatherings all show a lively minded and innovative response to the rapidly changing literary marketplace. Kidd’s career suggests both the legally chaotic nature of the literary marketplace and the entrepreneurial opportunities offered to a shrewd if unscrupulous publisher in late Regency London.

Rare Event Sampling Improves Mercury Instability Statistics

Due to the chaotic nature of planetary dynamics, there is a non-zero probability that Mercury’s orbit will become unstable in the future. Previous efforts have estimated the probability of this happening between 3 and 5 billion years in the future using a large number of direct numerical simulations with an N-body code, but were not able to obtain accurate estimates before 3 billion years in the future because Mercury instability events are too rare. In this paper we use a new rare-event sampling technique, Quantile Diffusion Monte Carlo (QDMC), to estimate that the probability of a Mercury instability event in the next 2 billion years is approximately 10−4 in the REBOUND N-body code. We show that QDMC provides unbiased probability estimates at a computational cost of up to 100 times less than direct numerical simulation. QDMC is easy to implement and could be applied to many problems in planetary dynamics in which it is necessary to estimate the probability of a rare event.

Investigation of Huge Wave in Gas-Liquid Two-Phase Churn Flow

Churn flow frequently occurs in power plants, chemical engineering, petroleum, and other industrial applications. Due to its chaotic nature, churn flow has a significant influence on safety and management control. As one of the essential characteristics of churn flow, depth knowledge of the huge wave is crucial for a better understanding churn flow. However, relevant studies on these issues are still in shortage because it is difficult to capture its behaviours experimentally. In this study, we employed the high-speed camera to capture the evolution and properties of huge waves under churn flow conditions in a vertical pipe. The inner diameter of the pipe is 19 mm. Based on the observation, the flooding of the falling film in churn flow is demonstrated to be the slug/churn transition mechanism. Additionally, the liquid distribution in the cross-section of the tube is provided and discussed in detail. Compared with the existing experiment data, we carefully analyze the properties of huge waves, such as frequency and amplitude.

Devising a self-adjusting zero-order Brown’s model for predicting irreversible processes and phenomena

A self-adjusting zero-order Brown’s model has been devised. This model makes it possible to predict with high accuracy not only fires in the premises but also irreversible processes and phenomena of a random and chaotic nature under actual conditions. The essence of the self-adjusting model is that, based on Kalman’s approach, it is proposed to set the smoothing parameter for each time moment. Such a parameter is determined depending on the resulting current forecast error, taking into consideration the real and unknown dynamics of the studied series and noise. That does not require the selection of the smoothing parameter characteristic of known models. In addition, the proposed Brown’s model, unlike the known modifications, does not require setting a dynamics model of the level of the examined time series. The self-adjusting model provides negligible errors and efficiency of the forecast. The operability of the devised model was checked using an example of the experimental time series for the current measure of the recurrence of the increments of the state of the air medium in the laboratory chamber during alcohol combustion. As quantitative indicators of the quality of the forecast error, the current values for the square and absolute values were considered. It has been established that the current square of the forecast error is more than six orders of magnitude smaller compared to the case of a fixed smoothing parameter from a beyond-the-limit set. However, the current square of the forecast error for abrupt changes in the dynamics of the series level is half that of the fixed parameter of the beyond-the-limit set. It is noted that the results confirm the feasibility of the proposed self-adjusting Brown’s model

The potential benefit of the use of seasonal forecast during the agricultural economic year 2019-2020 in Bulgaria

Seasonal forecasting gained ground in the last decades by building up knowledge on the processes staying behind the climate variability at the seasonal time scale, constructing ever more sophisticated general circulation models and ensemble prediction systems and thus enhancing forecast skill. The seasonal forecast is a climate forecast and is therefore probabilistic in nature. The predictability of the atmospheric circulation at the seasonal scale is limited in the middle latitudes, where Europe and Bulgaria are situated, by its chaotic nature. The current standard is to give forecast of the potential anomalies of the mean seasonal temperature and the seasonal amount of precipitation. The National Institute of Meteorology and Hydrology of Bulgaria has been issuing operationally seasonal forecast for the country since 2005. The goal of this work is to discuss the seasonal forecast for the last agricultural year 2019-2020. The year was characterized by its drought conditions especially in Eastern Bulgaria. This work would show the extent to which it was successfully predicted and how the seasonal forecast could have been used for decision making. The use of agrometeorological indices for the analysis of the skill of the seasonal forecast has been shown.

Influence of the ultrasonic vibration on system dynamic responses in the multi-ball surface burnishing process

With the urgent demand of high-end equipment for high quality surfaces, the technique of ultrasonic vibration-assisted burnishing is introduced to strengthen the surface properties. To explore the influence of the ultrasonic vibration on the dynamic response of a burnishing system, the burnishing friction force generated from a multi-ball surface burnishing system was characterized by chaos theory. The system had four assisted forms: no ultrasonic vibration, one-dimensional (1D) ultrasonic in x-axis, 1D ultrasonic in z-axis, and 2D ultrasonic in xz-axis. The results showed that any burnishing system had chaotic nature. Under the 2D ultrasonic vibration-assisted burnishing, the burnishing friction force was reconstructed to be a chaotic attractor with high convergence degree. Moreover, the burnishing system has notable complexity and stability. The burnished Al7075 alloy sample has an excellent surface with a higher smoothness and hardness. The burnishing with 2D ultrasonic vibration in xz-axis is a technique to enhance surface properties.

Correlation between Spatial Fractal and Temporal Chaos During the Sliding Wear Process of AISI 5120 Steel

The purpose of this paper is to establish the relationship between surface morphology and friction coefficient in the wear process. Different wear stage tests of AISI 52100 ring sliding against AISI 5120 disc were designed and conducted on a rotating setup. The fractal and chaos theories were employed to study the nonlinear features of surface structure and friction signal from spatial and temporal scales. The results showed that 3D surface morphology has fractal nature. The fractal dimension Ds first increased and then stabilized at a maximum and finally decreases dramatically. The multifractal spectrum width Δα presented an contrary evolution trend. The friction coefficient signal has chaotic nature. The standard deviation of distance matrix STD obeyed the evolution rule of a bathtub curve. The correlation value between Ds and STD was − 0.7727, and the correlation value between Δα and STD was 0.7130. The strong correlation between spatial and temporal scales is beneficial to on-line recognition and prediction of wear states in real time.