The divergence of a vector field at a point is the net outward flow of the flux out of a small volume through a closed surface enclosing the volume, as the volume tends to zero. More practically, divergence measures how much a vector field spreads out or diverges from a given point. For an outgoing flux, conventionally, the divergence is positive. The diverging point is often called the "source" of the field. Meanwhile, the negative divergence of a vector field at a point means that the vector...

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...

The seminal work of Ohno in 1970 popularized the idea of gene duplication and divergence. DNA sequence comparison studies reveal that a large portion of the genes in bacteria, archaebacteria, and eukaryotes was  generated by gene duplication and divergence, indicating its critical role in evolution.
The duplicated copies of the gene are called Paralogs. Paralogs with similar sequences and functions form a gene family. Across several species, a large number of gene families are...

Skeletal muscles, the key players in our body's movement, can be classified into two groups based on their location and function: axial muscles and appendicular muscles. These classifications reflect the primary roles the muscles play in the body's structure and movement.
Axial Muscles
Axial muscles, situated along the body's midline, are intricately connected to the axial skeleton, which includes the skull, spine, ribs, and sternum. These muscles facilitate facial expressions and...

The skeleton is subdivided into two major divisions—the axial skeleton and the appendicular skeleton. The axial skeleton forms the vertical, central axis of the body. It includes all of the bones of the head, neck, chest, and back. It protects the brain, spinal cord, heart, and lungs. It also serves as the attachment site for muscles that move the head, neck, and back and for muscles that act across the shoulder and hip joints to move their corresponding limbs.
The axial skeleton of the...

Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from symmetrical bending, which are essential for designing structures to withstand different loading conditions.
Consider a member subjected to equal and opposite forces that are applied along a line that does not coincide with the member's neutral axis. In unsymmetrical...