Frost heavingFrost heaving (or a frost heave) is an upwards swelling of soil during freezing conditions caused by an increasing presence of ice as it grows towards the surface, upwards from the depth in the soil where freezing temperatures have penetrated into the soil (the freezing front or freezing boundary). Ice growth requires a water supply that delivers water to the freezing front via capillary action in certain soils. The weight of overlying soil restrains vertical growth of the ice and can promote the formation of lens-shaped areas of ice within the soil.
PermafrostPermafrost () is soil or underwater sediment which continuously remains below for two or more years. Land-based permafrost can include the surface layer of the soil, but if the surface is too warm, it may still occur within a few centimeters of the surface down to hundreds of meters. It usually consists of ice holding in place a combination of various types of soil, sand, and rock, though in ice-free ground, perennially frozen non-porous bedrock can serve the same role.
Ice lensIce lenses are bodies of ice formed when moisture, diffused within soil or rock, accumulates in a localized zone. The ice initially accumulates within small collocated pores or pre-existing crack, and, as long as the conditions remain favorable, continues to collect in the ice layer or ice lens, wedging the soil or rock apart. Ice lenses grow parallel to the surface and several centimeters to several decimeters (inches to feet) deep in the soil or rock. Studies from 1990 have demonstrated that rock fracture by ice segregation (i.
Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
Ice segregationIce segregation is the geological phenomenon produced by the formation of ice lenses, which induce erosion when moisture, diffused within soil or rock, accumulates in a localized zone. The ice initially accumulates within small collocated pores or pre-existing cracks, and, as long as the conditions remain favorable, continues to collect in the ice layer or ice lens, wedging the soil or rock apart. Ice lenses grow parallel to the surface and several centimeters to several decimeters (inches to feet) deep in the soil or rock.
Numerical integrationIn analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.
Numerical weather predictionNumerical weather prediction (NWP) uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in the 1950s that numerical weather predictions produced realistic results. A number of global and regional forecast models are run in different countries worldwide, using current weather observations relayed from radiosondes, weather satellites and other observing systems as inputs.
Numerical controlNumerical control (also computer numerical control, abbreviated CNC) is the automated control of machining tools (such as drills, lathes, mills, grinders, routers and 3D printers) by means of a computer. A CNC machine processes a piece of material (metal, plastic, wood, ceramic, stone, or composite) to meet specifications by following coded programmed instructions and without a manual operator directly controlling the machining operation.
Finite difference methodIn numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are discretized, or broken into a finite number of steps, and the value of the solution at these discrete points is approximated by solving algebraic equations containing finite differences and values from nearby points.
Probabilistic numericsProbabilistic numerics is an active field of study at the intersection of applied mathematics, statistics, and machine learning centering on the concept of uncertainty in computation. In probabilistic numerics, tasks in numerical analysis such as finding numerical solutions for integration, linear algebra, optimization and simulation and differential equations are seen as problems of statistical, probabilistic, or Bayesian inference.
