2007 Nobel Prize in Physics

Goes to Albert Fert and Peter Grünberg, for the discovery of Giant Magnetoresistance.

http://nobelprize.org/nobel_prizes/physics/laureates/2007/

This discovery made the iPod possible.

http://www.nytimes.com/2007/10/09/health/09iht-nobel.4.7820918.html?_r=1&emc=eta1

Schrodinger's Cat

Queen's Brian May

Just earned his PhD in astrophysics from Imperial College by completing his dissertation on interstellar dust, 35 years after he dropped out to concentrate on his music.

Diffusion with a source on a semi-infinite line

(Budak/Samarskii/Tikhonov, problem 3.7)

u_t = a²u_xx + f(x,t)
u(x,0) = φ(x)
u(0,t) = μ(t)
0 ≤ x < ∞ and 0 ≤ t < ∞

The solution of the problem can be represented as a sum
u(x,t) = u₁(x,t) + u₂(x,t) + u₃(x,t)
where u₁(x,t) represents the effect of the initial condition u(x,o) = φ(x), u₂(x,t) represents the effect of the boundary condition u(0,t) = μ(t), and u₃(x,t) represents the effect of the nonhomogeneous term f(x,t).

Solution for u₁

u_t = a²u_xx
u₁(x,0) = φ(x)
u₁(0,t) = 0

u₁(x,t) = ½ (1/√π) ∫₀^∞ 1/√(a²t) [ e ^{-(x-x')2/4a2t} - e ^{-(x+x')2/4a2t} ] φ(x') dx'

Solution for u₂

u_t = a²u_xx
u₂(x,0) = 0
u₂(0,t) = μ(t)

u₂(x,t) = ½ (a²/√π) ∫₀^t x/[a²(t-t')]^3/2 e^{-x2/4a2(t-t')} μ(t') dt'

Solution for u₃

u₃(x,t) = ½ (1/√π) ∫₀^∞ dx' ∫₀^t dt' { 1/√[a²(t-t')] [ e ^{-(x-x')2/4a2(t-t')} - e ^{-(x+y)2/4a2(t-t')} ] f(x',t') }

Financial Mathematics

Since finishing my ASA late last year, I've started rediscovering my interest in financial mathematics. I will be posting assorted theorems, problems, observations, etc, from my readings in my finance and investments blog from time to time.

The E8 Lie Group Successfully Mapped

Computer scientists and mathematicians from the United States and Europe said they had mapped the Lie group E8, a problem that was discovered in 1887.

[Thanks to LL for sending me the link.]

How Ticked Off Physicists Write Checks

[Thanks to NE for sending me this.]