Dave, even though frequently questioning my degrees/titles/etc, I'm trying not to go into details of my background as this forum is not a place to submit resumes to find a job. I am trying to talk only on technical things using a simplified language that everybody can understand. This way, talking only on technical matters, I guess, is more fun than talking about our titles, degrees, etc. If someones hadn't frequently asked what my background, what my degree titles, etc etc were, I wouldn't have said on this forum I had spent years on the researches. Ask NewAgtalk forum where I have frequented there and talked there for 4 years - folks there don't know what research background I have if I didn't mention once in last months. Having said these, maybe, I should tell a little now so that "some" can learn "new" old mathematics.
Age 11-14 to 40: On and off 15-20 years farming (sometimes like-full time working at the nights, sometimes part-time, etc). I didn't say exactly 2 decades. I said "about" 2 decades farming. By mentioning this, I meant I am not a new to farming at all.
Age 15-18: High school (industrial, engine/motor dept.) During this period, I also worked at small industry (repair of cars, tractors, etc) as a worker.
Age 18-23: Undergraduate education in mechanical engineering (took 5.5 years because 1 year was for learning languages and I didn't go to university for 1 year due to my economical reasons.) During this period, I also worked at the small industry as a technican and part time (summer, etc) farming.
Age 23-25: After the graduation, full time engineer at a petrolium valve industry and at the same time I started my master degree MSc in engineering.
Age 25-27: Moving from the industry to my university job at 25 (as teaching&research assistant) and completed my MSc there at university and also travelled to international research centers also during this period to learn and gain experiences on modern experimental studies in fluid dynamics.
Age 27 - 35: Started my PhD at mech. engineering at 27. At the 4th year of PhD study in fluid dynamics, I was actually independent of mechanical engineering staffs as I had gone into more theoretical (mathematical) approaches and mech. engineering staffs were not helpful on my engineering PhD anymore. At 4th year of my engineering PhD, I was actually playing with formulae like a mathematican. This is the year I moved my PhD and research & teaching job at the university to mathematical physics department of science faculty. I was like 30-31 yrs old. My new PhD thesis there was a group theory (a mathematical branch - infinitesimal point symmetry groups) and its applications to classical physics. Since I was familiar with fluid flows in my previous studies in engineering I had applied this kind of semi-pure mathematics to fluid flows in general and chaotic/turbulent flows in particular. I was using symbolic algebra/mathematics (Matematica Software based on C++ was newly popular at that time) to analyse the nonlinear partial differental equations and to lower their dimensions using newly found symmetries. Then, Since I was pursing PhD I had MSc students preparing simple computational fluid dynamic programmes written in Fortran for my specific test flow cases. I handled not only one specific flow type, but many different flow types as I was searching symmetries in a generalized version of turbulence (i.e. full space-time Navier-Stokes equation). Sometime an inviscid flow, sometimes dissipation dominated flow, sometimes simple one dimensional nonlinear wave flow. I also played with equations of other fields such as biomechanics, economics, electromagnetics, etc. Since mathematicans weren't understanding from engineering (emphirical) equations of fluid dynamics I was educating the pure mathematic professors there about them and since engineering professors weren't understanding from pure-mathematics I was educating them about their engineering formulaes in engineering field. This is why I am saying I had students who were old age professors. One of my studies was to combine pure math. and engineering application; a study of infinitesimal symmetries of a full engineering emphirical equation formed by engineers after lab. tests.. This study was very important because computational engineers were solving their emphirical formulaes using computational fluid dynamic programmes. My so-called PhD supervisor had forced me to publish this study or to give a seminar at a national classical mechanic meeting. I did join, but while I was presenting my specific study, I had to fight some scholars whose sole intention was to attack personals as they usually do before approving your PhD title. You know you need to kiss a** all over the world when you want to get your degree especially if it is a PhD that will title you and put you in the system of zen-ish scholars powering the system with irrelevant, semi-politics business scholing games. That's why I always hated to publish the studies. But, hey, many professors have published parts of my studies without using my name and without giving any reference. Thieves aren't only in businesses, but also in the science much, much.. By the way, since internet (Gopher,ect) was introduced more after 1990s, I was like an independent researcher exchanging studies with young PhD scholars around the world around different universities and research centers like Nasa because my studies (at science faculty) were symbolic mathematics and internet was sufficient enough to exchange the simple symple symbolic algebra programmes via email, internet.
Okay - it became a long story. As seen here, 8 years PhD research studies during 27-35 (if we also add 1 year of MSc, it's 9 years.) and 9-10 years of teaching & research job at the universities between the ages 25/26 and 35. Left the university at 35 mainly due to economic reasons. Engineering, consultant, etc again a year or two after 35 and foreign trade, etc in last years as well as hobby farming, etc.
Well, this became like a resume - and I am not good at writing resumes. Should I also say my hobbies? lol - okay, here is; I am like a professional player of these games; billard, bridge (card game), table tennis, etc (but not made any money from these games - so, I am not a professional, but very good at these games.) - well, I can also make knots at a weaving loom to make rugs that I call "natural fine arts" - Whatelse should be told in a resume? lol
Okay, I don't want to go into irrelevant talks more. Last one question to Dave; I read the abstract of your study on that page you gave. One thing I didn't understand there is that you add a new term? Is this "new term" an artifical numerical term which doesn't exist in the partial (semi-emphirical?) differential equations there? and was that new term behaving exactly like a dissipation term in the flow equations? I mean this new term added to numerical/discreatized equations wasn't disturbing actual physical original form of flow. I have a feeling that you did somethings like a conversion of physical Eularian flow to a kind of flow with some little dissipation, a flow with a dummy small visous term. Was this no problem because your equations had some semi-emphirical parameters? Unless you disturbed the flow numerically, it's a good study. Otherwise, it can trick nonlinear potentials there. Anyway, I can't say I am good at the computational fluid dynamic or at tricks of discrete formulizations.
Ps: As seen here, I can talk about anything. lol - So, whats your problem CCI? We can also talk about them here in this thread. What? Painting of Pieter's tillers aren't so good? Pieter is also a painter artist- he can paint an even a pictoral scenes on his tillers lol.
Ps2: edited to say: I'm 40 and I agree with Dave in that having a research title doesn't mean you are an authorized one although most of professor scholars consider themselves so. To me, whoever making money is authorized - but also RESPONSIBLE!
