The computer modeling process

 

Modeling, in the technical use of the term, refers to the translation of objects or phenomena from the real world into mathematical equations. Computer modeling is the representation of three-dimensional objects on a computer, using some form of software designed for the purpose. Among the uses of computer modeling are war games and disaster simulations, situations in which computers offer a safe, relatively inexpensive means of creating or re-creating events without the attendant loss of life or property.

Mathematical modeling dates to advances in geometry and other disciplines during the late eighteenth century. Among these was the descriptive geometry of French mathematician Gaspard Monge, whose technique was so valuable to Napoleon's artillery that it remained a classified defense secret for many years. Nearly one and a half centuries later, at the end of World War II, mathematicians and scientists working for the United States war effort developed a machine for readily translating mathematical models into forms easily grasped by non-mathematicians.

That machine was the computer, and during the last two decades of the twentieth century, varieties of three-dimensional modeling software proliferate d. These included any number of computer animation and gaming packages, as well as varieties of CAD/CAM systems. CAD allowed engineers and architects, for instance, to create elaborate models that allowed them to "see into" unbuilt structures, and to test the vulnerabilities of those structures without risking lives or dollars.

One notable variety of three-dimensional software is virtual reality modeling language, abbreviated VRML and pronounced "ver-mal." Necessary for representing three-dimensional objects on the World Wide Web (that portion of the Internet to which general users are most accustomed), VRML creates a virtual world, or hyperspace, that can be viewed through the two-dimensional computer screen. By pressing designated keys, the user is able to move not only up, down, right, and left, but forward and backward, within this virtual world.

Scientists seek to understand nature by using a mix of theory, experimentation, and computer modeling. Theorists explain things using mathematical models such as partial differential equations. Experimentalists measure natural phenomena and collect and analyze the resulting experimental data. Computer modelers develop computer programs that produce synthetic data, which can then be collected and analyzed.

Starting with some real life phenomenon, called the physical system, computer modeling consists of a series of transformations from one intermediate model to another (see on the left). The physical system is first abstracted into a physical model that identifies the scale and scope of the phenomenon of interest. The physical model is then transformed into some mathematical model, typically continuous partial differential equations, that often do not have closed form solutions. In these cases, the mathematical model must be transformed into some discrete numerical model (such as a mesh) that can be solved on a computer. The numerical model is then transformed into a computer model, which is a program (often called a solver or a simulation) that produces synthetic data that approximates the behavior of the physical system. Finally, the raw synthetic data from the solver is validated against experimental data, reduced, and transformed into a more compact representation (such as a graph or an image) that hopefully provides the modeler with some insight into the original physical system.

Scientific computing is the research area that tackles problems associated with the activities along the bottom row of figure above: (a) building numerical models, (b) building computer models, and (c) querying and analyzing experimental and synthetic data. By nature, scientific computing is broad and multi-disciplinary, drawing on aspects of physics, applied mathematics, algorithms, computational geometry, parallel and distributed computing, database systems, graphics, signal processing, graphics, and visualization.

Modeling is a process that always occurs in science, in a sense that the phenomenon of interest must be simplified, in order to be studied. That is the first step of abstraction. A model has to take into account the relevant features of a phenomenon. It obviously means that we are supposed to know which features are relevant. That is possible because there is always some theoretical ground that we start from when doing science.

A simplified model of a phenomenon means that we have a sort of description in some symbolic language, which enables us to predict observable/measurable consequences of given changes in a system. Theory, experiment and simulation are all about (more or less detailed) models of phenomena. Sometimes there are some special constraints put on models such as e.g. required conservatism (a consequence of general Precautionary principle). Conservative models are made in safety related systems. It means that it must be assumed that uncontrolled parameters (those not explicitly modelled, or those outside the modeling system) have their worst (most unfavorable) credible value.

It is always necessary to “benchmark” new models against old models in known specific cases and analyze their relative strengths/weaknesses. It is the part of Comparison: Does it work?

In recent years computation which comprises computer-based modeling and simulation has become the third research methodology within Computational Science (CS), complementing theory and experiment.

CS has emerged, at the intersection of Computer Science, applied mathematics, and science disciplines in both theoretical investigation and experimentation.

Mastery of CS tools, such as modeling with 3D visualization and computer simulation, efficient handling of large data sets, ability to access a variety of distributed resources and collaborate with other experts over the Internet, etc. are now expected of university graduates, not necessarily CS majors. Those skills are becoming a part of scientific culture.

Today, computing environments and methods for using them have become powerful enough to tackle problems of great complexity. With the dramatic changes in computing, the need for dynamic and flexible Computational Science becomes ever more obvious.

Computer simulation makes it possible to investigate regimes that are beyond current experimental capabilities and to study phenomena that cannot be replicated in laboratories, such as the evolution of the universe. In the realm of science, computer simulations are guided by theory as well as experimental results, while the computational results often suggest new experiments and theoretical models. In engineering, many more design options can be explored through computer models than by building physical ones, usually at a small fraction of the cost and elapsed time. Simulations such as the galaxy formation studies on the left can only be conducted on very powerful computers. Science often proceeds with bursts of intense research activity. Even though the term ''simulation'' is old, it reflects the way in which a good deal of science will be done in the next century. Scientists will perform computer experiments in addition to testing scientific hypotheses by performing experiments on actual physical objects of investigation. One can also say that simulation represents a fundamental discipline in its own right regardless of the specific application.

Computational science involves the use of computers (''supercomputers'') for visualization and simulation of complex and large-scale phenomena. Studies involving N body simulations, molecular dynamics, weather prediction and finite element analysis are within the thrust of computational science. If Computer Science has its basis in computability theory, then computational science has its basis in computer simulation. In the Key Concepts section you can read about some of the key focus areas of the past we have taken to shed light on the potential or existing role that simulation plays in each of them: Chaos and Complex Systems; Virtual Reality; Artificial Life; Physically Based Modeling and Computer Animation.

The computing power of present day machines enables us to simulate an increasing number of phenomena and processes; especially the non-linear ones. Modern graphic capabilities makes this method a very attractive and user friendly. For example, researchers from A*STAR's Institute of Materials Research and Engineering (IMRE) have developed an innovative method for creating sharp, full-spectrum colour images at 100,000 dots per inch (dpi), using metal-laced nanometer-sized structures, without the need for inks or dyes. The inspiration for the research was derived from stained glass, which is traditionally made by mixing tiny fragments of metal into the glass. It was found that nanoparticles from these metal fragments scattered light passing through the glass to give stained glass its colours. Using a similar concept with the help of modern nanotechnology tools, the researchers precisely patterned metal nanostructures, and designed the surface to reflect the light to achieve the colour images. "Instead of using different dyes for different colours, we encoded colour information into the size and position of tiny metal disks. These disks then interacted with light through the phenomenon of plasmon resonances," said Dr Joel Yang, the project leader of the research. "The team built a database of colour that corresponded to a specific nanostructure pattern, size and spacing. These nanostructures were then positioned accordingly. Similar to a child's 'colouring-by-numbers' image, the sizes and positions of these nanostructures defined the 'numbers'. But instead of sequentially colouring each area with a different ink, an ultrathin and uniform metal film was deposited across the entire image causing the 'encoded' colours to appear all at once, almost like magic!" added Dr Joel Yang. In comparison, current industrial printers such as inkjet and laserjet printers can only achieve up to 10,000 dpi while research grade methods are able to dispense dyes for only single colour images. The researchers from IMRE had also collaborated with A*STAR's Institute of High Performance Computing (IHPC) to design the pattern using computer simulation and modeling. Dr Ravi Hegde of IHPC said, "The computer simulations were vital in understanding how the structures gave rise to such rich colours. This knowledge is currently being used to predict the behaviour of more complicated nanostructure arrays." The researchers are currently working with Exploit Technologies Pte Ltd (ETPL), A*STAR's technology transfer arm, to engage potential collaborators and to explore licensing the technology. The research was published online on August 12, 2012 in Nature Nanotechnology.

 

 

4. Find and learn Russian equivalents for the following words and expressions:

1)  elapsed time	a)
2) non-linear process	b)
3)  nanometer-sized structures	c)
4)  plasmon resonances	d)
5) uniform metal film	e)
6) descriptive geometry	f)
7) computer-aided manufacturing	g)
8) designated keys	h)

5. Find and learn English equivalents for the following words and expressions:

1)  металло-решетчатые структуры	a)
2) витражное стекло	b)
3) монохромное изображение	c)
4) наноструктурная решетка	d)
5) трёхмерные объекты	e)
6) автоматизированное проектирование	f)
7) язык моделирования виртуальной реальности	g)
8) вычислительные науки	9)

Artificial Life

AL is an outcome of computational science that challenges our definition of the term experiment. An experiment in artificial life is one where a computer program is written to simulate artificial life forms, often carrying along metaphors such as genetic reproduction and mutation.

Chaos and Complex Systems

The idea that one can observe complexity within a structurally simple deterministic model is of fundamental interest. Qualitative topological phase space features of linear systems may be determined statically, but for non-linear systems simulation must be used.

Computer modeling

The use of a computer to develop a mathematical model of a complex system or process and to provide conditions for testing it.

Computer simulation

The technique of representing the real world by a computer program; "a simulation should imitate the internal processes and not merely the results of the thing being simulated".

solver

A generic term indicating a piece of

mathematical software, possibly in the form of a stand-alone computer program or as a software library, that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculate their solution. In a solver, the emphasis is on creating a program or library that can easily be applied to other problems of similar type.