with the P4 out of the picture, you have to decide what else other than CPU power you would like in your lappy. If you want a very powerful CPU combined with long battery life I recommend the Dothan 2.0 (and I do so as a hardcore AMD fan). This processor follows te AMD 64 in terms of pure power but I really doubt that you will find it not powerful enough for the type of work you will be doing.
Understand that most people here are gamers and benchmarkers who love to see their machine going faster even if it is a matter of a couple seconds less. One example, a 7200 60GB HD will give roughly 9-10 sec bettr boot-up times (on the same machine) than a 4200rpm 80GB HardDrive. Yet, just look around, and you will see that most of us "brag" with how fast the bootup is after having paid 200 for a new drive. Off course getting a 7200 drive will give you better performance than a 4200 HD but, I mean, ask yourself are 10sec or so gonna change your life? Truth is that gamers and benchmarkers are crazy about performance and truth is that most people, when in the market for a PC, try to buy a machine that is much, much faster than their actual needs. I am sure this is the case with you too just like it is/was with me. When we try to buy a PC/laptop we always try to go for the fastest but we hardly ask ourselves whether we realy need it. Furthermore, it is a rule of thumb that a 10% increase in performance, whether due to faster CPU, HD, more RAM, etc., remain undescernable for most people's senses.
I understand that you will be doing a lot of number crunching but unless you will be doing some supercomputing a 2.0 Dothan will be more than enough for you. I personally bought a 1.7 Dothan (before the Dothan came out Intel didn't exist for me at all) and find it more than capable for simulations in physics/astrophysics. Chances are the 2.0 Dothan would be more than you will actually need in terms of pure power in CPU, especially when coupled with 1-1.5 GB RAM.
This being said, if you are really convinces that your simulationjs will ask for the very last CPU cycle you could get, my advise is to go with an AMD64 Mobile 3400+ (3200+ will aslo be enough). This cpu takes the best of both worlds, so to speak, it is more powerfull than any P4 (ExtremeEdition or not) and has a much better battery life than a P4, but traces the Dothan, of course. I doubt that you will be overclocking your cpu but AMD 64 chips are among the most overclockable cpus you can find. If overclocked, no P4EE can even touch the AMD in bencmarks, a said note to all Intel fans.
Above, in my last post, I said that a 3200+ powered eMachines M6809 lasts for about 2.5-3hrs. With the Mobile 3400+ eMachines M6811 the battery life should be (have not encountered reviews yet) about 2.5hrs and slightly less. A similar P4 would give about an hour or so (plus their form factors, as mentioned by me and others, are the heaviest of all. Again, the 2.0 Dothan, depending on the screen size (smaller screen - more battery life) will give anywhere between 4hrs and even more if the it is a 15inch screen.
You have to decide for yourself what are yu gonna need the laptop for.
If you decide to go for RAW but relatively efficient power, again the AMD64 MOBILE is the way to go for a very powerful and hghly efficient, in battery terms, cpu there is no alternative to the Dothan.
I mentioned the Sager NP4750 as an AMD alternative to eMachines M6811 but the Sager comes with a 17inch screen and this will bring battery life down to 2 hrs which is under heavy, heavy gaming - this may not sound a lot but is in fact a very respectable result impossible for a P4 cpu. The big screen also contributes to less battery life. I am not sure, however, that Sager uses the Mobile AMD64. To tell you the truth I CANNOT think of any 15inch laptop that has an AMD64 higher than 2800+ (not that this is not a powerful cpu). Only the Acer Ferrari 3200 has the AMD64 2800+ and comes with 15inch screen but I doubt that you will like the red painting on the cover. Apart from that it is a great machine.
There are many A64 laptops out there but most of them come with 15.4 inch screens - Uniwill, eMachines, HP, Compaq and others however I am not convinced that you will find one of these to have everything you may need for good 3D graphics in their stock configurations. Yor best bet, IMO, would be to configure the system by yourself.
Right now, I cannot refer you to any RESPECTABLE vendors who have AMD 64 laptops and will not rip you off (read Allienware, Hypersonic, etc). The only guys I can think of are ibuypower.com and cyberpower.com but their good prices are coupled with some horrible reviews on service, quality, and tech support. My best bet for an AMD laptop is emachines M6811 which had some issues with cracking hinge covers (just the covers) but they seem to be fixing it right now. Apart from that the laptop comes for about 1500-1600 but again since it is a stock configuration yoy may have to upgrade to a faster HD and more ram in order to get the best out of the AMD 64 3400+ cpu the M6811 comes with. The graphics card is an ATI 9600 64MB which will be enough for rendering 3D graphics and some nice gaming but is hardly the choice of the HEAVY gamers.
For Dothan 2.0 I can advise you to look at Acer TM8006 (a bit expensive at ~2500), Compal CL56, and ASUS M6(B)Ne. The Acer and the Compal come with 15.inch displays while the stock Asus M6ne has a 15.1 inch but is also available with 15.4inch and its name gets changed to M6BNe with the B for BROAD, I guess.
I do not believe that the Acer is offered as configurable by any on-line vendor. However, the Compal CL56 and ASUS M6(B)Ne are offered at sites like:www.powernotebooks.comwww.discountlaptops.comwww.proportable.comwww.rjtech.comwww.geared2play.com
The best (read best prices coupled with great tech support, customer service, warrenties, reviews, etc.) are the first two:www.powernotebooks.comwww.discountlaptops.com
For reviews go to www.resellerratings.com
My personal choice, and I guess of all those who have the money and know what ASUS stands for in quality, is the ASUS M6(B)Ne. The compal cl56 is a great notebook which will cost you slightly less but, IMO, the price difference is cancelled by the ASUS's screen (Samsung it is - second only to Sony's xBrite) and its superior overall quality.
At powernotebooks.com you will be able to get low latency Corsair RAM and some other luxeries not offered by discountlaptops.com for a very affordable price difference.
Please note that discountlaptops.com offer the 15.4 ASUS only with ATI 9600 while powernotebooks.com give you the choice for ATI 9700 for abot 100 bucks more in the total cost of the laptop.
Hope this helps.