FluidIn physics, a fluid is a liquid, gas, or other material that continuously deforms (flows) under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear force applied to them. Although the term fluid generally includes both the liquid and gas phases, its definition varies among branches of science. Definitions of solid vary as well, and depending on field, some substances can be both fluid and solid.
Compressive strengthIn mechanics, compressive strength (or compression strength) is the capacity of a material or structure to withstand loads tending to reduce size (as opposed to tensile strength which withstands loads tending to elongate). In other words, compressive strength resists compression (being pushed together), whereas tensile strength resists tension (being pulled apart). In the study of strength of materials, tensile strength, compressive strength, and shear strength can be analyzed independently.
Curve-shortening flowIn mathematics, the curve-shortening flow is a process that modifies a smooth curve in the Euclidean plane by moving its points perpendicularly to the curve at a speed proportional to the curvature. The curve-shortening flow is an example of a geometric flow, and is the one-dimensional case of the mean curvature flow. Other names for the same process include the Euclidean shortening flow, geometric heat flow, and arc length evolution. As the points of any smooth simple closed curve move in this way, the curve remains simple and smooth.
Dental erosionAcid erosion is a type of tooth wear. It is defined as the irreversible loss of tooth structure due to chemical dissolution by acids not of bacterial origin. Dental erosion is the most common chronic condition of children ages 5–17, although it is only relatively recently that it has been recognised as a dental health problem. There is generally widespread ignorance of the damaging effects of acid erosion; this is particularly the case with erosion due to consumption of fruit juices because they tend to be considered as healthy.
Tooth decayTooth decay, also known as cavities or caries, is the breakdown of teeth due to acids produced by bacteria. The cavities may be a number of different colors from yellow to black. Symptoms may include pain and difficulty with eating. Complications may include inflammation of the tissue around the tooth, tooth loss and infection or abscess formation. The cause of cavities is acid from bacteria dissolving the hard tissues of the teeth (enamel, dentin and cementum).
Mean curvature flowIn the field of differential geometry in mathematics, mean curvature flow is an example of a geometric flow of hypersurfaces in a Riemannian manifold (for example, smooth surfaces in 3-dimensional Euclidean space). Intuitively, a family of surfaces evolves under mean curvature flow if the normal component of the velocity of which a point on the surface moves is given by the mean curvature of the surface. For example, a round sphere evolves under mean curvature flow by shrinking inward uniformly (since the mean curvature vector of a sphere points inward).
Volume of an n-ballIn geometry, a ball is a region in a space comprising all points within a fixed distance, called the radius, from a given point; that is, it is the region enclosed by a sphere or hypersphere. An n-ball is a ball in an n-dimensional Euclidean space. The volume of a n-ball is the Lebesgue measure of this ball, which generalizes to any dimension the usual volume of a ball in 3-dimensional space. The volume of a n-ball of radius R is where is the volume of the unit n-ball, the n-ball of radius 1.
Periapical cystCommonly known as a dental cyst, the periapical cyst is the most common odontogenic cyst. It may develop rapidly from a periapical granuloma, as a consequence of untreated chronic periapical periodontitis. Periapical is defined as "the tissues surrounding the apex of the root of a tooth" and a cyst is "a pathological cavity lined by epithelium, having fluid or gaseous content that is not created by the accumulation of pus." Most frequently located in the maxillary anterior region, the cyst is caused by pulpal necrosis secondary to dental caries or trauma.
