*Posted 9 years ago*

Walldog

(6 items)

My wife and I restored this Coca-Cola wall sign this summer for the City of Pittsburg, Texas. It is a city block long. From the art I would say it was originally painted in the late 1940's or early '50s

CokeKid-04,9 years agoGreat job.

I was fortunate enough to see the first ever wall painted Coca Cola sign at Young Brothers Pharmacy in Cartersville (just north of Atlanta).

A good restoration job brings the painted wall sign(s) to life. So vibrant.

Daddy_Nobucks,9 years agoNice job of historical preservation, looks great.

blunderbuss2,9 years agoScrew the technical crap! This is great! Remember the same in Anniston, AL in mid-century.

Roycroftbooksfromme1,9 years agolooks greattttttttttt..

blunderbuss2,9 years agoRoy, it appears I've set a new record! Two posts deleted in less than a week!

pickrknows,9 years agoHey cokekid, have you seen the painted sign on the Denningers building on King St.? Its a local classic very early sign, likely one of the earliest in the Hammer!

blunderbuss2,9 years agoPickr, what's the key to your code? Denningers building? King St.? Hammer?

pickrknows,9 years agoSorry B.B., for Hamiltonians only!! :)

blunderbuss2,9 years agoSnobs! Hey, I've got class! Maybe, lower, but still class!

Roycroftbooksfromme1,9 years agohuh ...lol

HAMILTONIANS

TERENCE TAO

At First glance, the many theories and equations of modern physics exhibit a bewildering diversity: compare for instance classical mechanics to quantum mechanics, non-relativistic physics to relativistic physics, or particle physics to statistical mechanics. However, there are strong unifying themes connecting all of these theories.

One of these is the remarkable fact that in all of these theories, the evolution of a physical system over time (as well as the steady states of that system) is largely

controlled by a single object, the Hamiltonian of that system, which can often be interpreted as describing the total energy of any given state in that system. Roughly speaking, each physical phenomenon (e.g. electromagnetism, atomic bonding, particles in a potential well, etc.) may correspond to a single Hamiltonian H, while each type of mechanics (classical, quantum, statistical, etc.) corresponds to a different way of using that Hamiltonian to describe a physical system. For instance, in classical physics, the Hamiltonian is a function (q; p)!7H(q; p) of the position sq and moment a pof the system, which then evolve according to Hamilton's equations

dq @H dp @H

= ; = ;

dt @p dt @q

while in (non-relativistic) quantum mechanics, the Hamiltonian H becomes a linear operator (which is often a formal combination of the position operator sq and

moment a operator sp), and the wave function of the system then evolves by the Schrodinger equation

d

i~ =H :

dt

In statistical mechanics, the Hamiltonian His a function of the microscopic state (or microstate) of a system, and the probability that a system at a given temperature Twill lie in a given microstate is proportional toe H=kT And so on and so forth.

Many elds of mathematics are closely intertwined with their counterparts in physics, and so it is not surprising that the concept of a Hamiltonian also appears in pure mathematics. For instance, motivated by classical physics, Hamiltonians (as well as generalisations of Hamiltonians, such as moment maps) play a major role in dynamical systems, dierential equations, Lie group theory, and symplectic geometry. Motivated by quantum mechanics, Hamiltonians (as well as generalisations, such as observables or pseudo-dierential operators) are similarly prominent in operator algebras, spectral theory, representation theory, dierential equations, and in microlocal analysis. Because of their ubiquitious presence in many areas of physics and mathematics, Hamiltonians are useful for building bridges between seemingly unrelated elds,for instance in connecting classical mechanics to quantum mechanics, or between 1

2 TERENCE TAO

symplectic mechanics and operator algebras. The properties of a given Hamiltonian often reveal much about the physical or mathematical objects associated to that Hamiltonian; for instance, the symmetries of a Hamiltonian often induce corresponding symmetries on objects described using that Hamiltonian. While not every interesting feature of a mathematical or physical object can be read o directly from its Hamiltonian, this concept is still fundamental to understanding the properties and behavior of such objects.

Department of Mathematics, UCLA, Los Angeles CA 90095-1555

blunderbuss2,9 years agoHey, think I will just stick to keeping flying machines in the air! Lot less complicated!

Dan121156,9 years agoNice job on the sign..

pickrknows,9 years agoHere's an explanation much simpler B.B., I'm from Hamilton, Ont, as is CokeKid, and there is a similar but much older painted sign on a building there.

Told you I was simple!!

blunderbuss2,9 years agoHey, I used to know Hamilton! May have a kid there.

CokeKid-04,9 years agoLOL, funny stuff. I have seen that sign pickr. If I find the photo I took of it I will post, but all my blackberry pics I didn't dl got trashed when I moved to the iphone. Yeah, I guess living in the area for more than 10 years makes me a Hamiltonian. (Go LEAFS!)