Stability considerations play a central role in structural dynamics to determine states that are robust against perturbations during the operation. Linear stability concepts, such as the complex eigenvalue analysis, constitute the core of analysis approaches in engineering reality. However, most stability concepts are limited to local perturbations, i.e. they can only measure a state’s stability against small perturbations. Recently, the concept of basin stability has been proposed as a global stability concept for multi-stable systems. As multi-stability is a well-known property of a range of nonlinear dynamical systems, this work studies the basin stability of bi-stable mechanical oscillators that are affected and self-excited by dry friction. The results indicate how the basin stability complements the classical binary stability concepts for quantifying how stable a state is given a set of permissible perturbations.

Recently, light traps using light-emitting diode (LED) lights have been applied to monitor or control insect pests. The oriental armyworm, Mythimna separata Walker, is an important insect pest that has caused damage to several cereal crops, including corn, wheat and rice. The present study aims to seek out a sensitive wavelength causing high phototactic response in M. separata. The study evaluated the phototactic responses of M. separata moths to several LED lights of different wavelengths and luminance intensities under laboratory condition. Results showed that green (520 nm) LED light resulted in significant phototactic response of M. separata moths compared to LED lights of other wavelengths. Additionally, the highest attraction rate of the moths to green LED light appeared in luminance intensity group of 200 lux compared to the other intensities groups. Experiments under optimum conditions based on the above experiments revealed that the green LED light exhibited the strongest attraction rate (64.44%) among all experimental groups. An experiment performed in a net cage also showed that green LED light resulted in the highest phototactic response of M. separata moths, 1.7 times more than a commercial black light used as control. These findings clearly demonstrate that M. separata moths have a high sensitivity to the green LED light. Therefore, a light trap equipped with green LED light could be useful for monitoring and controlling M. separata moths.

In our study, we assessed the effects of verbenone, the most widely studied bark beetle aggregation inhibitor, on saproxylic beetles of a Mediterranean pine forest in Tuscany. Verbenone pouches were devised in the laboratory and then applied to Ips sexdentatus pheromone traps so that catches could be compared to those of traps with just the bait. The trial was carried out in spring-summer 2023, collecting insect catches every two weeks. A total of 9440 beetles were collected, belonging to 32 different families and 57 species. About 80% of captures were bark beetles, mainly Orthotomicus erosus. Beetle predators accounted for about 17% of the captures, with a total of 12 species. Some of these predator species had never been studied yet in relation to verbenone effects, like other saproxylic beetles recorded in this study. A significant reduction of captures was recorded for some beetles (e.g. I. sexdentatus and O. erosus), for other species no differences emerged, and in some cases captures increased significantly when verbenone was present in the traps (i.e.. Hylurgus ligniperda, Corticeus pini, Aulonium ruficorne). The diversity of caught saproxylic beetles increased significantly in verbenone traps, highlighting possible implications of the use of verbenone when managing bark beetle outbreaks.

Human keratinocytes and melanoma can stick together to form clusters after eight days in co-culture. As in dynamic system concepts, one can consider cluster formation as the system attractor, cell seeding as the initial condition, and density change over time as a path within the basin of attraction. Herein, Cellular Automata, which is a class of Agent-Based Models, and Boolean Networks are discrete modeling methods used in population dynamics such that running the dynamics of cellular automata backward reveals an underlying network in terms of basin of attraction, also known as global dynamics. Thus, we hypothesize that one can estimate the local dynamic of an agent-based model from the basin of attraction of a boolean network. Here, we propose an approach to estimating these agent-based model rules, which consists of comparing the density states within each state transition and reaching a consensus among state transitions belonging to a basin of attraction of a boolean network. The objectives of this study are: (1) to infer a boolean network from the co-culture growth curve; (2) to estimate the rules of agent-based models; and (3) to implement spatial dynamics simulations. The binarization of the growth curve shows high population density after four days; the estimated agent-based model rules were compatible with cell proliferation and migration in agreement with literature, so we had to propose individual rules for survival and death. Spatial dynamics shows that (1) keratinocytes exhibit a higher density in neighborhoods where melanoma is present; (2) the chance of keratinocyte migration increases until the fourth day, then decreases, and the probability of survival increases substantially after four days; and (3) cells with low proliferation capacity die and free space for those with high ones. Our approach suggests that the attractor state of cell co-culture is induced mainly by an increase in keratinocyte migration and survival. Our approach has the potential to offer valuable clues about microenvironmental interactions or configurations that drive population dynamics.

Application of the Ramsey graph theory to the analysis of physical systems is reported. Physical interactions may be very generally classified as attractive and repulsive. This classification creates the premises for the application of the Ramsey theory to the analysis of physical systems built of electrical charges, electric and magnetic dipoles. The notions of mathematical logic, such as transitivity and intransitivity relations, become crucial for understanding of the behavior of physical systems. The Ramsey theory explains why nature prefers cubic lattices over hexagonal ones for systems built of electric or magnetic dipoles. The Ramsey approach may be applied to the analysis of mechanical systems when actual and virtual paths between the states in the configurational space are considered. Irreversible mechanical and thermodynamic processes are seen within the reported approach as directed graphs. Chains of irreversible processes appear as transitive tournaments. These tournaments are acyclic; the transitive tournaments necessarily contain the Hamiltonian path. The set of states in the phase space of the physical system, between which irreversible processes are possible, is considered. The Hamiltonian path of the tournament emerging from the graph uniting these states is a relativistic invariant. Applications of the Ramsey theory to the general relativity become possible when the discrete changes in the metric tensor are assumed. Reconsideration of the concept of “simultaneity” within the Ramsey approach is reported.

The research presented in this paper concerns the determination of the attraction basins of the Newton’s iterative method which was used to solve the non-linear systems of observational equations associated with the geodetic measurements. The authors considered simple observation systems corresponding to the intersections, or linear and angular resections, used in practice. The main goal was to investigate the properties of the sets of convergent in the initial points of the applied iterative method. An important issue regarding the possibility of automatic and quick selection of such points was also considered. Therefore, the answers to the questions regarding the geometric structure of the basins, their limitations, connectedness or self-similarity were sought. The research also concerned the iterative structures of the basins, i.e. maps of the number of iterations which are necessary to achieve the convergence of the Newton’s method. The determined basins were compared with the areas of convergence that result from theorems on the convergence of the Newton’s method, i.e. the conditions imposed on the eigenvalues and norms of the matrices of the studied iterative systems. One of the essential results of the research is the indication that the obtained basins of attraction contain areas resulting from the theoretical premises and their diameters can be comparable with the sizes of the analyzed geodetic structures. Consequently, in the analyzed cases it is possible to construct methods that enable quick selection of the initial starting points or automation of such selection. The paper also characterizes the global convergence mechanism of the Newton’s method for disconnected basins and, as a consequence, the non-local initial points, i.e. located far from the solution points.

Laboratory experiments and investigations into natural phenomena in this research series have unveiled the presence of a gravitational repulsion force that permeates our environment on both microscopic and macroscopic scales, contingent upon the thermal energy present. This paper presents a study exploring novel properties of gravitational forces among gas molecules, employing principles of thermodynamics. A model has been devised based on the interactions between pairs of gas molecules. While traditional models treat gravitational interaction as a singular force, our experimental approach validates it as the composite of two distinct forces: gravitational repulsion and attraction. By utilizing established experimental data on gas thermodynamics, our model demonstrates robust performance both analytically and experimentally. It verifies the coexistence of gravitational repulsion and attraction forces among gas molecules, showcases their Inverse-Cube relationship with distance, and elucidates the direct proportionality of the repulsion force to absolute temperature. This bridges a crucial gap between energy and fundamental forces. The order of magnitudes of gravitational repulsion and attraction forces are found to be considerably large, contrasting with the low values predicted by classical theory, which results from their amalgamation. Recognizing these forces as substantial in magnitude promises unprecedented outcomes and advancements.

Voronoi mosaics inspired by the seed points placed on the Archimedes Spirals are reported. Voronoi entropy was calculated for these patterns. Equidistant and non-equidistant patterns are treated. Voronoi mosaics built from a sells of equal size which are of a primary importance for decorative arts are reported. The pronounced prevalence of hexagons is inherent for the patterns with an equidistant and non-equidistant distribution of points, when the distance between the seed points is of the same order of magnitude as the distance between the turns of the spiral. Penta- and heptagonal “defected” cells appeared in the Voronoi diagrams due to the finite nature of the pattern. The ordered Voronoi tessellations demonstrating the Voronoi entropy larger than 1.71, reported for the random 2D distribution of points, were revealed. The dependence of the Voronoi entropy on the total number of the seed points located on the Archimedes Spirals is reported. Voronoi tessellations generated by the phyllotaxis-inspired patterns are addressed. The aesthetic attraction of the Voronoi mosaics arising from seed points placed on the Archimedes Spirals is discussed.

We construct a family of two-step optimal fourth order iterative methods for finding single root of non-linear equations. We generalize these methods to simultaneous iterative methods for determining all the distinct as well as multiple roots of single variable non-linear equations. Convergence analysis is present for both cases to show that the order of convergence is four in case of single root finding method and is twelve for simultaneous determination of all roots of non-linear equation. The computational cost, Basin of attraction, efficiency, log of residual and numerical test examples shows, the newly constructed methods are more efficient as compared to the existing methods in literature.