COMPUTATIONAL ENGINEERING

Sir Isaac Newton once said in a letter to Robert Hooke, “If I have seen further it is by standing on the shoulders of giants.”  His letter to Hooke was written in 1676 but still carries significant truth, certainly today.  Let’s face facts; technology is evolutionary and not revolutionary.  The Wright brothers flew a bi-wing airplane made from wood and fabric and not an SR-71.  The first “horseless carriage” was not a Lomborghani.   The use of leeches (for medicinal purposes only) definitely preceded penicillin.  The abacus was a very functional “counting device” centuries before the computer.  You get the picture.  Computational engineering is a fascinating technology, evolutionary in nature.  This discipline did not burst upon the scene overnight but evolved over the years to become one of the most truly viable research tools in today’s arsenal of investigative methodology.  The “proper” definition of computational engineering is as follows:

                “Computational engineering encompasses the design, development, and application of computational systems for the solution of physical problems in engineering and science.  These computational systems include not only the algorithms and software required for the solution of mathematical equations describing physical processes, but also the means and methods of visualizing, analyzing and interpreting computed results and other physical data. “ 

This definition is taken from the High Performance Computing Collaboratory facility at Mississippi State University.  Mississippi State has one of the most respected departments of computational engineering in the United States. 

Another excellent definition comes from The University of Auckland and is as follows:

                “Computational Science (called also Scientific Computing or Numerical Analysis) is the design, development, application, and analysis of computer algorithms and software to solve scientific and engineering problems. It includes not only numerical methods, probabilistic modeling, computer-based statistical inference, and computer simulation required for solving underlying systems of math equations, but also computer visualization, statistical analysis, and interpretation of computed solutions.”

All of this is well and good but why oh why do we need discovery techniques of this nature and why so detailed.  I cannot say it any better than the following statement from Dr. J. Tinsley Oden:

                “Near the end of the twentieth century, much of the industrialized world was becoming aware that the foundations of science and engineering were under rapid, dramatic, and irreversible change brought on by the advent of the computer. The steady increase in computer capabilities and the enormous expansion in the scope and sophistication of computational modeling and simulation place computational sciences as the third pillar of scientific discovery and revolutionize the way engineering is done. Computational engineering and science can impact virtually every aspect of human existence, along with the health, security, productivity, and competitiveness of the nation.”
        J. Tinsley Oden, Associate Vice President for Research, The University of Texas at Austin

  Let us now take a look at the results of computational engineering and the output derived from the process.

Formula 1 Racer

 

As you can see from the JPEG above, knowing the airflow around a Formula 1 race car can provide evidence of laminar flow that could provide a win when the checkered flag is dropped.  Disruption of airflow around an object could create resistance to lessen performance.

This is one of my favorite and shows the air flow around a shuttle craft re-entry vehicle.  Critically important information when considering the fact that re-entry is difficult enough and would be more so if surface-generated turbulence was an added problem.

 

Shuttlecraft

The JPEG below shows results of a study demonstrating the effect of “blunt force trauma” to the human skull.  Studies such as this are very important in understanding what happens when an NFL running back meets Ray Lewis.  We all know there is a class-action lawsuit against the NFL to compensate players who have experienced concussions during their playing years.  Computational engineering can aid efforts to fully understand what happens.

Human Skull

 

There are several schools that offer degrees in computational engineering (CmE), usually at the MS and PhD levels.  A BS degree in computer science, mathematics or engineering is almost always a minimum requirement with BS degrees in CmE not being offered.  Excellent schools offering course work and degrees in this field are as follows:

• University of Tennessee at Chattanooga—SIM Center
• Mississippi State University
• MIT
• University of Texas at Austin
• Georgia Institute of Technology
• Purdue
• Notre Dame
• University of Utah
• Arizona State University

 I am sure there are other, maybe many others, but these are noted for their contributions to the technology.   I certainly hope you will take a look at the possibilities and continue to study what is available relative to seminars and short courses.

 

 

UNIVERSAL LANGUAGE

UNIVERSAL LANGUAGE

Merriam-Webster defines language as “A systematic means of communicating ideas or feelings by the use of conventionalized signs, sounds, gestures or marks having understood meanings.”  The operative words in this definition are ‘means of communicating’ and ‘understood meanings’.  There are 116 different “official” languages spoken on our planet today but 6900 languages AND dialects. The difference between a language and a dialect can be somewhat arbitrary so care must be taken when doing a “count”.  English, French, German, Greek, Japanese, Spanish etc, all have specific and peculiar dialects; not to mention slang words and expressions so the discernment between a language and a dialect may be somewhat confusing to say the least.. 

The book of Genesis (Genesis 11: vs. 1-9) recounts a period of time, during the reign of King Nebuchadnezzar, when an attempt was made, by mankind, to become equal with God and that one language was spoken by all the people.  We are told that the attempt was not met with too much favor and God was pretty turned off by the whole thing.  Go figure!    With this being the case, He, decided to confound their language so that no one understood the other.  This, as you might expect, lead to significant confusion and a great deal of “babbling” resulted.  (Imagine a session of our United States Congress.)  Another significant result was the dispersion of mankind over the earth—another direct result from their unwise attempt.  This dispersion of the populace “placed” a specific language in a specific location and that “stuck”. 

Regardless of the language spoken, the very basic components of any language are similar; i.e. nouns, verbs, adjectives, adverbs, pronouns, etc.  You get the picture. The use and structure of these language elements within a sentence do vary.  This fact is the essence of a particular language itself. 

Would mankind not benefit from a common language?  Would commerce not be greatly simplified if we could all understand each other? Think of all the money saved if everything written and everything spoken—every road sign and every label on a can of soup—could be read by 6.8 billion people.  Why oh why have we not worked towards that over the centuries as a collective species.  Surely someone has had that thought before.  OK, national pride, but let’s swallow our collective egos and admit that we would be well-served by the movement, ever so gradual, towards one universal language.  Let me backup one minute.  We do have one example of a world-wide common language—

MATHEMATICS

Like all other languages, it has its own grammar, syntax, vocabulary, and word order, synonyms, negations, conventions, abbreviations, sentence and paragraph structure.  Those elements do exist AND they are universal.  No matter what language I speak, the formula for the area of a circle is A=π/4 (D)². 

• π  =  3.14159 26535 89793
• log(10)e  =  0.43429 44819 03252
• (x+y)(x-y)  =  x²-y²
• R(1),R(2)  =  [-b ± ( b²-4ac)]^0.5/2a
• The prime numbers are 2,3,5,7,11,13,17,19,23,29,31,37—You get the picture.
• sinѲcscѲ = 1

 Mathematics has developed over the past 2500 years and is really one of the very oldest of the “sciences”. One remarkably significant development was the use of zero (0)—which has only been “in fashion” over the past millennium.  Centuries ago, men such as Euclid and Archimedes made the following discoveries and the following pronouncements:

If a straight line be cut at random, the square on the whole is equal to the squares on the segments and twice the rectangle contained by the segments. (Euclid, Elements, II.4, 300 B.C.) This lead to the formula:  (a + b)² = a² + b² + 2ab

The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference, of the circle. (Archimedes, Measurement of a Circle, (225 B.C.)  Again, this gives us the following formula: 

A = 2pr·r/2 = pr ² 

These discoveries and these accompanying formulas work for ANY language we might speak. Mathematics then becomes the UNIVERSAL LANGUAGE.

With that being the case, why do we not introduce the “Language of Mathematics” to our middle-school and high school pupils?  Is any school district doing that?  I know several countries in Western Europe started this practice some years ago with marvelous results.  This “language” is taught prior to the introduction of Algebra and certainly prior to Differential Equations.  It has been proven extremely effective and beneficial for those students who are intimidated by the subject.  The “dread” melts away as the syntax and structure becomes evident.  Coupled with this introduction is a semester on the great men and women of mathematics—their lives, their families, were they lived, what they ate, what they smoked, how they survived on a math teacher’s salary.  These people had lives and by some accounts were absolutely fascinating individuals in their own right.  Sir Isaac Newton invented calculus, was a real grouch, a real pain in the drain AND, had been jilted in his earlier years.  Never married, never (again) even had a girlfriend, etc etc.  You get the picture.  The greatest mathematicians of all time are said to be the following:

Isaac Newton Carl F. Gauss Archimedes Leonhard Euler Euclid		Bernhard Riemann Henri Poincaré David Hilbert Joseph-Louis Lagrange Gottfried W. Leibniz		Alexander Grothendieck Pierre de Fermat Niels Abel Évariste Galois John von Neumann
Srinivasa Ramanujan Karl W. T. Weierstrass Brahmagupta René Déscartes Augustin Cauchy		Carl G. J. Jacobi Hermann K. H. Weyl Peter G. L. Dirichlet Leonardo `Fibonacci’ Georg Cantor		Arthur Cayley Emma Noether Eudoxus of Cnidus Muhammed al-Khowârizmi Pythagoras of Samos

What do we really know about these guys?  Do we ever study them when we use their wonderful work?  I think not.  I honestly believe the study would be much more enjoyable IF we knew something about the men and women making the contributions they did.   Think about it.  PLEASE!!!!!!!!!!!!

MATH MALL

A very interesting article recently appeared in our local newspaper (Chattanooga Times Free Press).  “UTC revamping math classes with a MATH MALL”.  Catchy title now let us look at some history.

The University of Tennessee at Chattanooga is a campus in the University of Tennessee Educational System of schools.  It has an annual enrollment of approximately 9,000 students, both undergraduate and graduate.   Chattanooga University was founded in 18886 and for 83 years was local and private.  In 1969, the university merged with the University of Tennessee.  UTC is a very important “player” in the life of the greater Chattanooga area and provides the tri-state region with a significant number of graduates populating the employment pool.  UTC had a very direct influence on VW during their process of selecting a “state-side” site for their North American assembly plant.  The factory is now under construction and will be operational in 2011.  There have been sixty-five thousand applicants for twelve hundred jobs.

Now, back to math.  The Times states that “math classes have become a major headache and turnoff for students at UTC”.  This information comes to us from a survey taken by the school with information volunteered by the students.   Students described “bad math teachers” and having to take remedial math courses over and over and over again.  “One student stated that she liked math, but would not major in anything related to math so that she would avoid UTC’s math department and professors”.

As a mechanical engineer, I had to have a minor in mathematics—we all did.  Thirty hours minimum and we struggled through the courses but felt we had earned our “red badge of courage” when we could see the light at the end of the tunnel.   I do remember that, with only one exception, all of my teachers were “old, white guys”, excellent math technicians, all PHDs, fairly humorless and for the most part, graded their own papers.  During those days I never saw a TA (teaching assistant not tits and ass).  There was this one fascinating lecture in which our professor proclaimed that the very best mathematicians had the following enviable characteristics:

• Fearless
• Immune to criticism
• Had the largest waste basket with a verity of wadded papers representing a multitude of false-starts
• No pencil with erasers

In other words, math is a contact sport.  You definitely learn by doing, not thinking about doing.  Trial and error but mostly error.  This is apparently what UTC recognized and in hopes of addressing their problem, they have authorized $360,000 dollars to develop an interactive “math mall” in which the students work at their own pace.  Just the student and the PC.  As a matter of fact, the PC would eventually replace the in-class teacher AND the math lecture.  The only personal interaction would be a tutor; available during all math sessions.  The school cites successes at the University of Alabama, The University of Mississippi, Virginia Tech, Cleveland State and several other notable universities.   Apparently, this is desperately needed because 50% of the entering freshmen are required to take remedial math courses.  Personally, I think this is absolutely appalling but I suppose it is a sign of the times.  In a country in which there are only 70,000 engineering graduates per year, as compared to China with 600,000 engineering graduates per year, there certainly must be something terribly wrong with our ability to keep the interest of students who might have even a partial interest of making a technical profession their individual aim.

Personally, I like the “old white guys”.