Elastic knots

Anchoring junctions are multiprotein complexes that help cells connect to other cells and the extracellular matrix. Anchoring junctions are present on the lateral and basal surfaces of cells, providing strong and flexible connections. Focal adhesions are often formed due to cell interactions with the ECM substrata, which initiate signal transduction via kinase cascades and other mechanisms. Together, they provide stability and tissue integrity. There are three types of anchoring junctions:...

Fibrous joints are a type of joint where the bones are connected by fibrous connective tissue. These joints provide stability and minimal to no movement between the articulating bones. There are three types of fibrous joints.
Suture
All the bones of the skull, except for the mandible, are joined to each other by a fibrous joint called a suture. The fibrous connective tissue found at a suture strongly unites the adjacent skull bones and thus helps to protect the brain and form the face. In...

In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...

Consider a cylindrical shaft with a length denoted by L and a consistent cross-sectional radius referred to as r. This shaft undergoes a torque at the free end. The highest shearing strain within the shaft is directly proportional to the twist angle and the radial distance from the shaft axis. When the shaft behaves elastically, this shearing strain can be articulated using variables such as the applied torque, radial distance, the polar moment of inertia, and the modulus of rigidity. By...

Dense connective tissue contains more collagen fibers than loose connective tissue. As a consequence, it displays greater resistance to stretching. There are two major categories of dense connective tissue— regular and irregular.
Dense Regular Connective Tissue
In dense regular connective tissue, fibers are arranged parallel to each other, enhancing its tensile strength and resistance to stretching in the direction of the fiber orientations. Ligaments and tendons are made of dense regular...

The method of joints is a commonly used technique to analyze the forces in structural trusses. The method is based on the principle of equilibrium, which assumes that the truss members are connected by frictionless pins. The forces at each joint can be determined by considering the equilibrium of the forces acting on that joint.
Since plane truss members are in the same plane, each joint is subjected to a coplanar and concurrent force system. To apply the method of joints, the first step is to...