Stokes Shift

Viscous forces, like friction, are intermolecular forces that resist the relative motion of molecules over each other. When a solid body moves through a liquid, viscous forces drag it in the opposite direction. The force's magnitude depends on the solid's shape and size, as well as its speed and the liquid's coefficient of viscosity, density and temperature. The expression for the force on a solid spherical object in a fluid is called Stokes' law. Stokes' law is valid only for low Reynolds...

Source: McCullagh, E. A., et al. Coherent Anti-Stokes Raman Spectroscopy (CARS) Application for Imaging Myelination in Brain Slices. J. Vis. Exp. (2022)The video demonstrates fluorescence and Coherent Anti-Stokes Raman Spectroscopy (CARS) imaging to visualize neuronal architecture in rodent brain tissue. Nissl staining labels cell bodies by binding to ribosomal RNA, while CARS imaging targets lipid-rich myelin through laser-induced signals. Overlaying the fluorescence and CARS images provides a...

The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write numerous physical laws...

For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...

Stokes’ Theorem provides a fundamental connection between the circulation of a vector field along a closed boundary and the cumulative rotational behavior across the surface it encloses. For a smooth three-dimensional surface with an oriented boundary curve, this theorem offers a unified way to relate motion along the edge to local rotational effects distributed over the surface.Mathematical FormulationThe theorem states that the circulation of a vector field along a closed curve is equal to...