Ondine's curse: the origin of the myth

Archimedes' principle states that an upward buoyant force exerted on a body that is immersed partially or entirely in a fluid is equal to the weight of the fluid displaced by it. To understand how much buoyant force is needed to make an object float, let us think about what happens when a submerged object is removed from a fluid. If the object were not in the fluid, the space occupied by the object would be filled by the fluid having a weight wfl. This weight is supported by the...

In human women, oogenesis produces one mature egg cell or ovum for every precursor cell that enters meiosis. This process differs in two unique ways from the equivalent procedure of spermatogenesis in males. First, meiotic divisions during oogenesis are asymmetric, meaning that a large oocyte (containing most of the cytoplasm) and minor polar body are produced as a result of meiosis I, and again following meiosis II. Since only oocytes will go on to form embryos if fertilized, this unequal...

Oogenesis,  the process of developing egg cells (female gametes), occurs within the ovaries and is fundamental to female fertility. This sequence begins during fetal development when diploid oogonia in the developing ovaries undergo mitotic divisions to produce primary oocytes. By birth, these primary oocytes enter prophase I of meiosis but become arrested in this stage, remaining suspended until puberty.
Each primary oocyte is surrounded by a layer of pre-granulosa cells, forming what is...

In the years before Newton, a general belief prevailed that different laws governed objects in the sky than objects on Earth. When Kepler wrote down the three laws of planetary motion, explaining in detail the geometrical properties of the planetary orbits around the Sun, there was no immediate idea to discern their connection with more fundamental laws. It was Isaac Newton who, in 1665–66, figured out the connection between planetary motion, the motion of the moon around the Earth, and...

Castigliano's theorem analyzes displacements and rotations in elastic structures. It relates the derivative of elastic strain energy to the applied forces or moments, allowing for the calculation of deformations. The theorem states that the partial derivative of the total strain energy of a system with respect to a specific load results in the displacement at the point where the load is applied. This principle applies to both forces and moments.

Motion draws our attention. Motion itself can be beautiful, causing us to marvel at the forces needed to create spectacular sights, such as that of a dolphin jumping out of the water, the flight of a bird, or the orbit of a satellite. The study of motion is kinematics, but kinematics only describes the way objects move—their velocity and acceleration. Dynamics considers the forces that affect the motion of moving objects and systems. Newton's laws of motion are the foundation of...