A language for computation of differential mobility analyzer (DMA) response functions is introduced. The language consists of short programming language expressions that evaluate to the size distribution of particles exiting a DMA. The language permits application of the same framework to single and tandem DMA setups. Expressions are derived for calculation of the convolution matrix used in inversion of size distribution data, calculation of the convolution matrix for transit through tandem DMA systems, and calculation of the size and mobility distribution through DMA systems that involve one or multiple DMAs. The contribution of multiply charged particles to the total response distributions can be explicitly resolved. The derived convolution matrix is suitable for inverting scanning mobility particle sizer response functions using standard regularization techniques. Users can modify and substitute any of the convolution terms-comprising the DMA transfer function, detector efficiency, loss rate, and charging efficiencies-to express response functions of nonstandard DMA configurations. Example applications are presented, including classification of particle size, measurement of size-resolved cloud condensation nuclei activity, characterization of hygroscopicity and volatility tandem DMA response functions, and characterization of the dual tandem DMA system for dimer preparation. The source code and examples are shared as free software and are hosted on an online collaborative software development platform that allows for version tracking and crediting contributors. Adoption of the language may facilitate the design and optimization of custom-built systems that involve unique arrangements of DMAs and detectors.
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