A MarketPlace of Ideas                        

Small nuclear reactors in the 70 MW thermal or 25 MW electrical power range. 

Unlike conventional designs, the proposed reactor is self-regulating through the inherent properties of uranium hydride, which serves as a combination fuel and moderator. The temperature-driven mobility of the hydrogen contained in the hydride controls the nuclear activity. If the core temperature increases over the set point, the hydrogen is driven out of the core, the moderation drops, and the power production decreases. If the temperature drops, the hydrogen returns and the process is reversed. Thus the design is inherently fail-safe and will require minimal human oversight. The compact nature and inherent safety open the possibility for low-cost mass production and operation of the reactors.

The Hyperion design takes advantage of the economy of mass-production instead of the economy of scale (as is done presently with traditional reactors). HPG estimates that approximately 4,000 of the first module design will be needed to meet initial demand.  This feature will likely yield a much more widespread adoption of this nuclear technology.

Their website is: www.hyperionpowergeneration.com

You can watch the focus fusion Google TechTalk here

• We need cheaper energy not more expensive alternatives.
• In order to merely provide the rest of the world with european level power will require 4X current energy investment.  We won’t get there from here.  That includes fossil, nuclear, solar and wind power.  All together insufficient.

 Currently popular alternatives are not energy dense enough to get the price of energy down.  Material costs are too much.  Added benefit?  If we can make it work it will lead to propulsion that will allow sending probes to the nearest stars.

Gun control - Socialized Medicine - NO THANKS !  — Keep the change.

This is my mental image of all male unDemocrat voters.  Testosterone reorganizes the brain in males as we go through puberty.  In males with sufficient intellectual capacity it turns on mathematical and logical thought like a light switch.   However if you lack the testosterone this will not occur and you will sadly end up an Obama fan boi.

The beautiful equation tying pi, 1, 0, e and i all together.  You have to love that.

I am using wpmathpub.

The wpmathpub math publisher plugin for WordPress.org blogs is now available directly from WordPress.org’s plugin site. The WordPress.org hosted version manages several promotional and support features:

• Overview of the plugin here>
• Overview of the PHP Math Publisher library here>
• Installation instructions here>
• Example of how wpmathpub works, and how to install it here>
• Frequently Asked Questions and their answers too here>
• Metrics here>
• Download from WordPress.org here>

And most importantly for me now that I have it all installed

• a reference page on usage syntax.
• Complete syntax listing

Another

In a previous article entropy was defined as the expected number of bits in a binary number required to enumerate all the outcomes.  This was expressed as follows:

entropy= H(x)=  

In physics ( nature ) it is found that the probability distribution that represents a physical process is the one that has the maximum entropy given the constraints on the physical system.   What are constraints?  An example of a probabalistic system is a die with 6 sides.  For now pretend you do not know that it is equally likely to show any 1 of the 6 faces when you roll it.  Assume only that it is balanced.

In the case of a die the above summation is equivalent to the following sort of computation:

• Initial assumption set of 6 probabilities that  sum up = 1  … this is a given as it has to be at least one of the 6 faces unless it stands on edge Twilight Zone style.  Lets assume P(x_i) = 0.05, 0.05, 0.05, 0.05,0.05, 0.75  …. you know instinctively this is not correct but demonstrates the maximum entropy principle

The total entropy given these probabilities = (.05) * (4.322) * 5 + 0.75 * (.415)= 1.0805 + .311= 1.39 bits

Let us use our common sense now.  We know there are 6 equally probable states that can roll up.  So its easy to calculate the number of bits required.  

• Bits required = log₂6 = 2.585 bits 

Thus we can see our initial assumption of probabilities yields an entropy number less than we would expect from common sense.   How do we find the maximum entropy possible? 

• Use the Langrangian maximization method. 
• Maximize the entropy phrase with the constraint that  

                 …. sum over all probabities must = 1

The langrangian is formed as follows:

Now differentiating the langrangian and setting the derivative = 0 we can find the maximal entropic probability

         solving for the P_i  yields

        All the P_i= the same constant with the probabilities summing to 1….Thus P_i=1/6 since N=6

While this is alot of work to derive the obvious it there is a purpose. In the case of more complicated situations where the probability distribution is not obvious this method works.  For example in the case of the Black Body emission curve of Planck.  Given just the quantization of energy levels you can derive the black body curve!!  This principle is woven all through nature.  Learn it because it will serve you well. 

Some interesting Notes to myself — myself? I meant me.

• Maximum Entropy Modeling - including some open source software