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Mathematics and models

The stage is set for accelerating the pace of discovery in engineering and science. The vast and rapidly growing amount of data and information, with increasingly complex interrelationships, is becoming so much more accessible to researchers and analysts. Massive databases, the internet, and powerful search engines enable these data to be accessed and shared easily and quickly. The information is rich and varied, due to inexpensive and sensitive measurement systems, improvements in sensors, and technologies in new areas such as proteomics and genomics. Additionally, an increasing emphasis on how this research can more rapidly drive toward commercialisation calls for more unified approaches to scientific exploration and product development.

In Release 13, Simulink and SimMechanics support multi-domain modeling of mechanical systems. Here they are used to model and simulate the dynamics of an automotive engine, which is visualised with the Virtual Reality Toolbox viewer

So what does this portend for research in the next 10 years? Engineering and science are combining in ways that create breakthroughs for both product development and advancing basic understanding. Examples include how a detailed analysis of a car engine's combustion dynamics leads to improved control of that engine's fuel consumption, power generation, and emissions, or how deciphering genetic behaviour can lead to treatments for disease.

This is critical because many research areas will depend on the synthesis of engineering and science. One example is nanoscale technology, to build systems in a context where the laws of physics sometimes fail to apply. Another is the fusion of the biological sciences and bioengineering, both for computational biology and for designing engineering systems based on biological organisms. It is likely that biology will join electronics, mechanisms, and hydraulics as a fundamental engineering discipline.

Meanwhile, 'Model-Based Design' provides a fast-track to convert those research ideas into innovations. Model-based design uses simulatable models as the backbone of all stages of development: specification, rapid prototyping and trade-off analysis, detailed design, implementation, and test and verification. Today, engineers and scientists in many fields use model-based design in place of document-based processes to accelerate and improve system development. In the future, model-based design will become a standard way to develop and test many types of complex systems, especially embedded systems. The models will form a growing inventory of intellectual property that can be reused, refined, and extended for subsequent designs with increasing sophistication, complexity, and quality.

Research breakthroughs can be rapidly incorporated into those new designs and providing differentiating value for new products. The implementation of those products will continue to be streamlined through automatic generation of software and hardware designs. Today, a small percentage of components and embedded applications are generated automatically. In the next ten years, that percentage will increase dramatically, as more systems are generated automatically from the models.

That is important because those exciting research areas, such as nanoscale engineering and the convergence of biology and engineering, are dealing with complex systems that blend and leverage topics that have, until now, been treated separately. The people doing advanced research and product development require tools that enable them to build new disciplines by bringing together established disciplines that have traditionally been treated as separate silos of knowledge. The people implementing those systems require tools that enable them to build systems in one or several 'form factors': hardware and software; single-chip and networked systems; and where 'hardware' may comprise electrical, mechanical, hydraulic, and maybe someday biological, components.

Clearly, the underlying representation that enables such a unified view is mathematics. But the real value will come from having tools that can provide that mathematical view while focusing at a tangible level, where applied research, engineering, product development, and unified testing can take place. The MATLAB and Simulink platforms have successfully done this for a wide range of applications to date. These types of environments will evolve to encompass that wide range of topics, provide tools for combining and synthesising them into new disciplines, and provide a clear path for turning the resulting new ideas into real things.

Jack Little is president, CEO, and a co-founder of The MathWorks

Media Partners