Rapidly varying flow (RVF) in open channels is characterized by abrupt changes in flow depth over a short distance, with the rate of depth change relative to distance often approaching unity. These flows are inherently complex due to their transient and multi-dimensional nature, making exact analysis difficult. However, approximate solutions using simplified models provide valuable insights into their behavior.Key Features of Rapidly Varying FlowRVF is commonly observed in scenarios involving...

Cells migrating in response to external stimuli form lamellipodia, which are thin membrane protrusions supported by a mesh of linked, branched, or unbranched actin filaments. These actin filaments interact with myosin motor proteins, creating the dynamic actomyosin complex within the cytoskeleton. Contractility, or the ability to generate contractile stress, is inherent to the actomyosin complex. It helps cells detect the stiffness of the surrounding ECM and exert contractile force for...

When a fluid is in constant acceleration, the pressure and buoyant force equations are modified. Suppose a beaker is placed in an elevator accelerating upward with a constant acceleration, a. In the beaker, assume there is a thin cylinder of height h with an infinitesimal cross-sectional area, ΔS.
The motion of the liquid within this infinitesimal cylinder is considered to obtain the pressure difference. Three vertical forces act on this liquid:

Filopodia are thin, actin-rich cellular protrusions that play an important role in many fundamental cellular functions. They vary in their occurrence, length, and positioning in different cell types, suggesting their diverse roles.
Their main function is to guide migrating cells during normal tissue morphogenesis or cancer metastasis by recognizing and making initial contacts with the extracellular matrix. However, they can also act as stationary cell anchors or help to establish communication...

Mitogen-activated protein kinase, or MAPK pathway, activates three sequential kinases to regulate cellular responses such as proliferation, differentiation, survival, and apoptosis. The canonical MAPK pathway starts with a mitogen or growth factor binding to an RTK. The activated RTKs stimulate Ras, which recruits Raf or MAP3 Kinase (MAPKKK), the first kinase of the MAPK signaling cascade. Raf further phosphorylates and activates MEK or MAP2 Kinases (MAPKK), which in turn phosphorylates MAP...

When a ligand binds to a cell-surface receptor, the receptor's intracellular domain changes shape, which may either activate its enzyme function or allow its binding to other molecules. The initial signal is amplified by most signal transduction pathways. This means that a single ligand molecule can activate multiple molecules of a downstream target. Proteins that relay a signal are most commonly phosphorylated at one or more sites, activating or inactivating the protein. Kinases catalyze...