Patterns in naturePatterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time.
Stress–strain curveIn engineering and materials science, a stress–strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring the deformation, from which the stress and strain can be determined (see tensile testing). These curves reveal many of the properties of a material, such as the Young's modulus, the yield strength and the ultimate tensile strength. Generally speaking, curves representing the relationship between stress and strain in any form of deformation can be regarded as stress–strain curves.
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.
Wetted perimeterThe wetted perimeter is the perimeter of the cross sectional area that is "wet". The length of line of the intersection of channel wetted surface with a cross sectional plane normal to the flow direction. The term wetted perimeter is common in civil engineering, environmental engineering, hydrology, geomorphology, and heat transfer applications; it is associated with the hydraulic diameter or hydraulic radius. Engineers commonly cite the cross sectional area of a river.
River channel migrationRiver channel migration is the geomorphological process that involves the lateral migration of an alluvial river channel across its floodplain. This process is mainly driven by the combination of bank erosion of and point bar deposition over time. When referring to river channel migration, it is typically in reference to meandering streams. In braided streams, channel change is driven by sediment transport. It has been proposed that lateral migration is a particularly dominant erosive process in savanna landscapes.
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).
SaôneThe Saône (soʊn , son; Sona; Arar) is a river in eastern France. It is a right tributary of the Rhône, rising at Vioménil in the Vosges department and joining the Rhône in Lyon, at the southern end of the Presqu'île. The name Saône derives from that of the Gallic river goddess Souconna, which has also been connected with a local Celtic tribe, the Sequanes. Monastic copyists progressively transformed Souconna to Saoconna, which ultimately gave rise to Saône. The other recorded ancient names for the river were Brigoulus and Arar.
