Lumped

Lumped refers to a modeling approach used in science and engineering in which the spatial variation of properties within a system is neglected. The system is represented by a small set of discrete, spatially uniform elements, each with averaged properties. This approach converts distributed physical phenomena into a network of lumped components, such as resistors, capacitors, inductors, masses, springs, and dampers, and reduces governing equations from partial differential equations to ordinary differential equations.

In electrical engineering, lumped-parameter models assume that the electrical state variables are uniform within each element, and that interaction between elements occurs instantaneously. This is valid when the physical size of components is small compared with the wavelength of signals of interest, and when signal propagation delays and internal gradients are negligible.

The lumped approach is common in thermal and mechanical analyses as well. For heat transfer, the lumped capacitance model treats an object as having a uniform temperature, with its heat storage described by a single thermal capacitance. In mechanics, a mass-spring-damper system is treated as lumped, with motion described by ordinary differential equations.

Limitations arise when internal gradients are significant or when wave propagation, diffusion, or distributed effects cannot be ignored. In such cases, distributed parameter models or continuum descriptions, described by partial differential equations, are required. Practitioners assess lumped-model validity by comparing characteristic lengths or times to relevant wavelengths, diffusion scales, or time constants.