Concrete cracks have a detrimental effect on the strength properties and durability of the structures. So, repairing of concrete cracks to recover their strength parameters is more important task in civil engineering. To repair concrete cracks, MICP has been widely analysed in recent times; but, zero research is conducted to deeply investigate the repair effects of MICP on concrete cracks with rough surface by using the theoretic model. In current research, MICP with a novel mathematical model was attained by taking the precipitation of calcium carbonate (CaCO3), ureolysis, suspended biomass, geochemistry, transport of solute and biofilm growth. Furthermore, crack repair experiments were performed to check the workability of the new mathematical method. The outcomes revealed that the designed suspended biomass concentrations in cracks diminished step by step. The comparison in between the experimental results and calculated results verified the precision of migration behaviour of the suspended biomass. At the inlet, the solute concentrations and biofilm volume fractions was higher, causing in rise of yield amounts for calcium carbonate. The consumed solutes concentrations were higher for cracks of less rough surface, ultimately causing in smaller sonic time; and the values of sonic time for upper portions of cracks was smaller, showing good repair impacts. The recommended mathematical model provides a better tool that controls repair time and microbial metabolism process to report a new adjustive, bioremediation and biomineralization to concrete, which could provide a firm base for remediation of material in civil engineering field.

Amidst China's new economic normal, the real economy faces various domestic and global challenges. Technological innovation, with its capital intensity and uncertain returns, is crucial to rejuvenate emerging industries and revamp the industrial structure. Meanwhile, financial agglomeration plays a dual role: directly fostering real economic development and indirectly affecting it through technological innovation. This study analyzes data from 30 mainland Chinese provinces and cities between 2011 and 2018, utilizing fuzzy matter-element analysis and location entropy method. Relying on a spatial econometric model, we explore the impact of technological innovation and financial clustering on real economic growth, including spatial ripple effects. The conclusions are derived from Chinese evidence and offer valuable insights into the evolving innovation and financial dynamics within the participating nations.