The development and stability analysis of a nonlinear growth model for microorganisms

A nonlinear dynamic model of microbial growth is established based on the theories of the diffusion response of thermodynamics and the chemotactic response of biology. Except for the two traditional variables, i.e. the density of bacteria and the concentration of attractant, the pH value, a crucial influencing factor to the microbial growth, is also considered in this model. The pH effect on the microbial growth is taken as a Gaussian function G0e-(f- fc)2/G1, where G0, G1 and fc are constants, f represents the pH value and fc represents the critical pH value that best fits for microbial growth. To study the effects of the reproduction rate of the bacteria and the pH value on the stability of the system, three parameters a, G0 and G1 are studied in detail, where a denotes the reproduction rate of the bacteria, G0 denotes the impacting intensity of the pH value to microbial growth and G1 denotes the bacterial adaptability to the pH value. When the effect of the pH value of the solution which microorganisms live in is ignored in the governing equations of the model, the microbial system is more stable with larger a. When the effect of the bacterial chemotaxis is ignored, the microbial system is more stable with the larger G1 and more unstable with the larger G0 for f0 > fc. However, the stability of the microbial system is almost unaffected by the variation G0 and G1 and it is always stable for f0 < fc under the assumed conditions in this paper. In the whole system model, it is more unstable with larger G1 and more stable with larger G0 for f0 < fc. The system is more stable with larger G1 and more unstable with larger G0 for f0 > fc. However, the system is more unstable with larger a for f0 < fc and the stability of the system is almost unaffected by a for f0 > fc. The results obtained in this study provide a biophysical insight into the understanding of the growth and stability behavior of microorganisms.

Empowering, degrading or a 'mutually exploitative' exchange For women?: Characterising the power relations of the strip club

This paper seeks to characterise the gendered and sexualised power relations of both female and male strip clubs, and to signal what this means for establishing positive definitions of female desire. It is argued that while it is not useful to present female strippers, or female patrons of male strip clubs as purely passive victims of male heterosexism within these venues, it is equally damaging to assume that these venues represent a whole-scale challenge to conventional oppressive gender and sexual relations for women. Some research has even suggested that both strippers and their patrons are engaged in a 'mutually exploitative' power relationship. Moreover, further empirical research documents key points where female dancers have perhaps wielded 'more' power over patrons at certain moments, and female dancers have highlighted feelings of empowerment and highlighted potential for gender and sexual relations which position women as passive to be subverted within stripping. However, such feelings are often temporally specific and are not applicable to all women in the strip industry. It may be particularly hard for these to manifest in women concentrated in the least economically-rewarding areas of the industry who have less 'power' to resist compromising their bodily boundaries. Furthermore, it is argued that women watching male strippers does little to reverse the 'male gaze', and nor does this male occupation carry as much negative social stigma with it as female stripping suffers. It is thus argued that the overwhelming picture, stemming largely from accounts of former dancers and from empirical studies of individual clubs, suggests these venues in fact do very little to challenge normative hetero-oppressive sexual scripts.