The phrase 'process of emergence' is correct and usable in written English, and it can be used anytime you want to refer to a gradual development or rise of something.
For example, "The process of emergence of a new social network has been quite rapid."
Despite this, a growing trend in emerging disease research attempts to empirically analyze the process of emergence and move towards predictive capacity for new zoonoses.
Health geography emerged from medical geography over the past 30 years and the process of emergence is continuing.
Thanks to the process of emergence, we have become something more than other animals.
T B healing was a highly dynamic process of emergence and maintenance of peri-graft bone.
As we emerge from that war, those of us who are writers might point a spotlight on that process of emergence — and hopefully help it along".
Physicist and systems theorist, Fritjof Capra, noted that: "Throughout the living world, the creativity of life expresses itself through the process of emergence".
As new infectious diseases emerge, identifying the processes of emergence and the areas and persons at greatest risk is critical.
His current research interest focuses on 1) Modelling processes of emergence by using Meta-Structures; 2) the emerging of a post-Bertalanffy Systemics; 3) the Dynamic Usage of Models (DYSAM), Logical Openness; 4) Architecture and Design as the design of social meta-structures to influence processes of emergence in social systems.
Through these interactions, patterns emerge and the system is continually self-organizing through processes of emergence and feedback.
The paper discusses current trends to conceptualize SB in traditional engineering terms and contrast this from design speculations in terms of bottom-up processes of emergence and self-organization.
4. Minati, G., Abram, M. and Pessa, E., (eds)., (2009), Processes of emergence of systems and systemic properties.
