Partial differential equations (PDEs) play a central role in describing the dynamics of
physical systems in research and in practical applications. However, equations appearing in …

Thermocapillary instability and formation of waves for a thin viscous falling film with broken
time-reversal-symmetry have been discussed in this present study. The film is flowing over a …

Hydrodynamics and instabilities of a thin viscous liquid film flowing down an undulated
inclined plate with linear temperature variation have been investigated. Using the long-wave …

Recent releases of open-source research codes and solvers for numerically solving partial
differential equations in Python present a great opportunity for educators to integrate these …

Microbial communities are shaped by complex metabolic interactions such as cooperation
and competition for resources. Methods to control such interactions could lead to major …

Hydrodynamic instability and formation of waves for thin viscous film flowing down a slippery
inclined substrate with broken time-reversal-symmetry have been discussed in this present …

We investigate the phase change effect at the thin film interface with broken time-reversal-
symmetry falling down an inclined flat wall. We consider the impact of evaporation and as …

Evolution of waves and hydrodynamic instabilities of a thin viscoelastic fluid film flowing
down an inclined wavy bottom of moderate steepness have been analyzed analytically and …

The stability and dynamics of a falling liquid film over an anisotropic porous medium are
studied using a one-domain approach. Our stability analysis shows a significant departure …

Stable water isotopes in ice cores serve as a valuable proxy for the climate of the past
hundreds of thousands of years. Over time, water isotope diffusion causes significant …