Narrow Results

This study introduces a mathematical model aimed at evaluating the potential influence of aerosol introduction into the atmosphere for inducing rainfall and managing atmospheric pollution. By expanding on the proposed model, we incorporate stochastic elements to encompass environmental white noises that impact the system’s dynamics. Both mathematical and numerical methods are employed to analyze the system’s behavior. In the context of the deterministic model, we examine the solutions’ positivity and boundedness, identify feasible equilibria, and scrutinize the stability characteristics both locally and globally. The analysis of the stochastic system encompasses discussions regarding the existence of a unique solution, its ultimate boundedness, and the conditions that prompt the establishment of a unique stationary distribution characterized by ergodic properties. Our simulations illustrate that augmenting cloud formation rates and externally introduced aerosols can amplify rainfall while mitigating atmospheric pollution levels. Minor intensities of white noise do not alter the system’s behavior, whereas significant intensities result in high-amplitude oscillations of the system’s variables. We explore the effects of white noise intensities using histograms and stationary distributions, highlighting long-term rainfall trends in a noisy environment.

Adoption processes are often heavily influenced by interpersonal communication. Marketing managers are increasingly trying to use these relationships to foster the market penetration of their products. In an empirical study of the US market for an innovative medical device, we survey the social network of (mostly chief) anesthetists from 151 hospitals. We confirm the influences from personal communication on individual adoption decisions through hazard regressions. We then use a multi-agent modeling framework trying to identify what seeding strategies would have been optimal to achieve a fast market penetration, i.e. which and how many anesthetists should be selected to initiate personal communication processes.

As the source of replenishment, rainfall has an extensive impact because its variability shapes biologically efficient pulses of soil moisture recharge across layers from rainfall events. In this paper, a mathematical model is proposed to explore the importance of transpiration from agricultural crops and aerosols on the pattern of rainfall. For the system without seeding, the simulation results show destabilizing roles of parameters related to formation of cloud drops due to transpiration of agricultural crops, formation of raindrops due to cloud drops and growth of agricultural crops due to rain. The model without seeding is extended to its stochastic counterpart to encapsulate the uncertainty observed in some important parameters. We observe the variability in the system’s variables and found their distributions at certain fixed times, which explore the importance of stochasticity in the system. Our findings show that transpiration through agricultural crops plays an important role in cloud formation, and thus, affects the effectiveness of different rainfall events. Moreover, the combined actions of transpiration and seeding are much more beneficial in producing rain. Finally, we see the behavior of system by considering seasonal variations of some rate parameters.

Adoption processes are often heavily influenced by interpersonal communication. Marketing managers are increasingly trying to use these relationships to foster the market penetration of their products. In an empirical study of the US market for an innovative medical device, we survey the social network of (mostly chief) anesthetists from 151 hospitals. We confirm the influences from personal communication on individual adoption decisions through hazard regressions. We then use a multi-agent modeling framework trying to identify what seeding strategies would have been optimal to achieve a fast market penetration, i.e., which and how many anesthetists should be selected to initiate personal communication processes.