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Applied and Computational Mathematics Division

Nurturing trust in NIST metrology and scientific computing.

The Applied and Computational Mathematics Division is one of seven technical divisions in the Information Technology Laboratory.

Mathematical models are how we express our understanding of the world. They are essential for interpreting the results of scientific experiments, as well as in the design of products, from airplanes to cell phones. New and challenging mathematical problems arise every day at the NIST Information Technology Laboratory’s Applied and Computational Mathematics Division. We provide leadership and expertise in the use of applied mathematics and scientific computing to solve numerous problems. As a part of this work, we develop mathematical and computational techniques and tools that have wide application in science and technology. The use of such state-of-the-art techniques and carefully validated tools helps build trust in measurement science and scientific computing, which are both essential for industrial innovation. 

Examples of Our Work


From 1998, of ACMD staff members Don Porter (left) and Mike Donahue (center) discussing micromagnetic modeling with NIST physicist Bob McMichael.

Micromagnetic Modeling

Magnetic materials have many uses, from computer data storage to sensors used in brakes and medical appliances. Modern innovations in such materials require the understanding of magnetic properties at very fine scales, measured in tens of nanometers. Computer modeling is an essential tool for exploring such properties, and how they can be exploited for use in new products. ACMD works with the research community to help ensure that the mathematical methods used in such studies are accurate and reliable. 

DLMF’s interactive 3D graphics allow the user to change viewpoints, rotate and zoom, rescale, change colormaps and to explore the intersection of the surface with cutting planes.

Digital Library of Mathematical Functions

A function is a mathematical tool that expresses how a quantity of interest (the output) depends on its input. Mathematical functions are essential components of mathematical models in all areas of science and engineering. They are used to help describe everything from how sunlight creates rainbows to how atoms interact. The NIST Digital Library of Mathematical Functions is a free online reference that describes the properties of commonly occurring mathematical functions. 

Snapshot from a simulation of the mortar SRM in a double-helix rheometer. The white plane shows the initial location of the top of the suspension before starting the rheometer.
Credit: NIST

Development of a Standard Reference Mortar

Mortar, a mixture of cement, sand, and water, is a very common building material, used, for example, to bind stones or bricks together. One indication of how well a given batch of mortar will perform is to measure its flow rate, or viscosity. But, measuring flow rates of such soft solids is very challenging. ACMD uses computer simulations and immersive visualization to study the flow properties of such materials. With the NIST Engineering Laboratory, ACMD recently developed a standard reference mortar which can be used to calibrate rheometers, i.e., instruments which measure flow rates. This is the first NIST standard reference material to be developed with the use of a supercomputer. 

NIST IR 8306 cover image

Details of technical activities of the Division are provided in our Yearly Report for 2019. Recent past reports can be found here: 2018201720162015.  For prior years contact Ronald Boisvert.

For more information, visit the Applied and Computational Mathematics Division Projects/Programs.


Industry Impacts