## 3 Examples of Equation-Based Modeling in COMSOL Multiphysics®

##### Caty Fairclough December 20, 2017

Creating new physics interfaces that you can save and share, modifying the underlying equations of a model, and simulating a wider variety of devices and processes: These are just a few ways you can benefit from the equation-based modeling capabilities of the COMSOL Multiphysics® software.

Read More##### Bjorn Sjodin June 20, 2017

You can generate and visualize randomized material data with specified statistical properties determined by a spectral density distribution by using the tools available under the Results node in the COMSOL Multiphysics® software. In this blog post, we show examples that are quite general and have potential uses in many application areas, including heat transfer, structural mechanics, subsurface flow, and more.

Read More##### Bjorn Sjodin June 2, 2017

To easily generate random-looking geometric surfaces, the COMSOL Multiphysics® software provides a powerful set of built-in functions and operators, such as functions for uniform and Gaussian random distributions and a very useful sum operator. In this blog post, we show you how to generate a randomized surface with what amounts to a “one liner” expression with detailed control of the constituent spatial frequency components that determine the nature of the surface’s roughness.

Read More##### Temesgen Kindo May 9, 2017

When your simulations consume significant memory, do you buy a bigger computer? When they take too long to solve, do you just run them overnight? Often, you don’t have another option. But sometimes, if you have the right tools, you can find a better approach by exploiting the mathematical structure. Today, we will show you how to use the so-called maximum principles to save computational resources and time in the COMSOL Multiphysics® software.

Read More##### Walter Frei March 2, 2017

Have you ever modeled deforming objects in the COMSOL Multiphysics® software and wanted to know the distance between them? In today’s blog post, we will look at how to compute distances between objects using methods for determining the closest distance field. We’ll also find out how to use the distance field as a part of a multiphysics model.

Read More##### Caty Fairclough February 21, 2017

The COMSOL Multiphysics® software includes many built-in physics equations and interfaces, but there may be times when you need to implement physics that aren’t part of the software to solve your modeling problem. You can use the flexibility of the COMSOL® software to add user-defined equations via equation-based modeling. Today, we discuss using equation-based modeling to solve a shallow water equation, which can be used to analyze coastal erosion.

Read More##### Amlan Barua November 10, 2016

In a previous blog post, we discussed the physiological basis of generating action potential in the excitable cells of living organisms. We spoke about the simple Fitzhugh-Nagumo model, which emulates the process of depolarization and repolarization in a cell’s membrane potential. Today, we analyze a more advanced model for simulating action potential, the Hodgkin-Huxley model. We also go over how to use a computational app to streamline this type of analysis.

Read More##### Amlan Barua October 7, 2016

In 1961, R. Fitzhugh (Ref. 1) and J. Nagumo proposed a model for emulating the current signal observed in a living organism’s excitable cells. This became known as the FitzHugh-Nagumo (FN) model of mathematical neuroscience and is a simpler version of the Hodgkin-Huxley (HH) model (Ref. 2), which demonstrates the spiking currents in neurons. In today’s blog post, we’ll examine the dynamics of the FN model by building an interactive app in the COMSOL Multiphysics® software.

Read More##### Temesgen Kindo October 6, 2016

In a previous blog post, we discussed integration methods in time and space, touching on how to compute antiderivatives using integration coupling operators. Today, we’ll expand on that idea and show you how to analyze spatial integrals over variable limits, whether they are prescribed explicitly or defined implicitly. The technique that we will describe can be helpful for analyzing results as well as for solving integral and integro-differential equations in the COMSOL Multiphysics® software.

Read More##### Temesgen Kindo October 5, 2016

Cylindrical coordinates are useful for efficiently solving and postprocessing rotationally symmetric problems. The COMSOL Multiphysics® software has built-in support for cylindrical coordinates in the axisymmetry physics interfaces. When defining custom partial differential equations (PDEs) using the mathematical interfaces, paying close attention to their meaning is important. The PDE interfaces assume partial differentiation in a Cartesian system, requiring manual coordinate transformations to change to a cylindrical system. See how to account for such coordinate transformations when using your own PDEs.

Read More##### Caty Fairclough May 9, 2016

Have you ever wondered how tigers develop their stripes? Alan Turing’s theory of morphogenesis offers one possible explanation for this occurrence, suggesting that patterns, such as stripes, develop naturally from initially homogeneous states. Today, we’ll take a closer look at Turing’s theory and explore some modern research on this topic, including the modeling of branching morphogenesis in COMSOL Multiphysics.

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