OpenLLM-France/wikimedia huggingface dataset:
# Statistical Mechanics/Quantum Gases

As per the spin-statistics theorem, there are really only two types of particles: fermions and bosons. Thus if we can study each one separately fairly well, then we know quite a bit!
We will be using the grand partition function 'Infrastructure' developed earlier for these models (in order to make it even more general). Specifically, we can use the grand partition function to create distribution functions, and use those to study specific properties of fermi/bose gases.

## The Distribution Functions
### Fermi Gas

Using our earlier definition:
f(ε) := <N(ε)>
Now, for a given orbital (i.e., for a given ε), there can only be two options with a fermion, either there's one particle or none. Therefore, we can use our previous defined method to calculate an average quantity in order to calculate <N(ε)> (we will do the sum by brute force, it's not too hard, only two terms at most):
f(ε)=1/(exp((ε-μ)/kT) + 1)

### Bose Gas

The process is the same, only instead of none or one, we have 0 to infinite. If we use some sum relations we come up with:
f(ε)=1/(exp((ε-μ)/kT) - 1)
Which is surprisingly similar to the fermi gas case, but the minus sign causes EXTREME differences in behavior compared to the fermi gas.

## The Classical Limit

Despite overall behavior of the fermi and bose gases, in a certain limit, we see that the two distributions are nearly similar. We call this limit 'The Classical Limit'. In particular, this limit is:
exp((ε-μ)/kT) >> 1
The only importance of this limit is to determine when we don't have to worry about the two gases distinct behaviors.

## Fermi Energy

Because of the 0 or 1 limit, at very cold temperatures (note that cold is a fairly comparative term, for the free electrons on a sheet of metals, this can be up to hundred of degrees farenheight! Which shows that this odd quantum stuff does affect your daily life) fermi gases can only get 'locked down' to so many orbitals. They can't all fall into the ground state. The energy at which the gas is 'locked in' is known as the fermi energy.
In terms of the distribution function, this means at this 'cold' temperature, the function drops off sharply at one point.

## Bose-Einstein Condensation

Unlike the fermi energy occurrence with a fermi gas, bosons can condense all they want, this is where the minus sign comes into play. As the energy level is lower and lower, eventually they might pass the chemical potential, which causes the exponential in the bose distribution function to be less than one, and thus the function to be negative, i.e., an impossible value. In fact, as ε approaches μ, the function approaches a singularity. Physically, this means that all the bosons can 'condense' into the same low energy spot at low temperatures: a phenomena known as boson condensation.
# Statistical Mechanics/The Foundations/Ensembles

Due to the large number of particles in a macroscopic system, it is in general not possible to find an exact solution of the microscopic equations of motion for a large number of particles, given a certain initial condition. Luckily, this is a problem that we are usually not very much interested in. On the one hand we cannot practically measure the exact position and momentum of every particle in a macroscopic sample of matter, while on the other hand this information is much too detailed for what we usually need in applications. We can for example easily measure the temperature, pressure and volume of a volume of gas and these are also the variables that seem to be the most relevant. The vector containing the exact position and momentum of every particle is usually referred to as the micro-state, while the vector containing only the values of a few macroscopic observables, such as temperature, pressure and volume, is called the macro-state.
Although we only observe the macro-state of a system at a certain point in time, the particles that make up the system are still in a certain micro-state. The particles are in a configuration that is compatible with the given macro-state. This is in general a many-to-one relation: many of the possible microscopic configuration result in the same macro-state. A second reason why many microscopic configurations can be connected to one macroscopic measurement is the temporal resolution of the measurement. A measurement is always performed over a certain amount of time. During the time of the measurement, the microscopic state of the object of interest changes. Hence to one value of the measurement corresponds an entire trajectory of micro-states.
Since we have no way of choosing between all the possible microscopic configurations corresponding to the values we have measured, there is an uncertainty on the microscopic level. Mathematically, the fact that we do not select one specific micro-state is represented by means of probability distributions on the set of all possible micro-states. These distributions tell us what the probability is to find the constituent particles in a certain configuration.
We will first introduce some general elements of probability theory, the theory describing probability distributions. Then these distributions are applied to physical systems, where they are called ensembles. Finally, we will see how an ensemble evolves in time, given the equations of motion for the microscopic variables.
# Introduction

Although the two-state model has directly useful applications (as we will see in binary mixtures), it is really useful as an introductory model to Statistical Mechanics. For example, calculating entropy and other thermodynamic properties, and their meaning in certain contexts.
The two-state problem itself deals with a number of sites that can have either of two configurations: material A or material B, up or down, 0 or 1.
To keep with a good example that has thermodynamic properties, we will choose up or down spin statistics.

# Contents

* Multiplicity
* Properties of the Two-State System
# Statistical Mechanics/Thermal Radiation
## Planck Distribution Function

For thermal radiation we know the following equation:
ε$_n$=sℏω$_n$
which we can apply our previously made Partition-function 'Infrastructure' to:
Z = Σ$_{s=0}$ exp(-sℏω$_n$/T)
By algebra:
= 1/(1 - exp(-ℏω$_n$/T))
Therefore, we can also find the probability:
P(s) = exp(-sℏω$_n$/T)/Z
Now, we can start calculating some interesting thermodynamic quantities. Let's start with the thermal average of s, the average mode of thermal radiation given a certain temperature:

 = Σ$_{s=0}$ sP(s) = Z$^{-1}$ Σsexp(-sℏω$_n$/T)
Which if we carry out the mathematics of the sum:

=1/(exp(ℏω$_n$/T) - 1)

## Stefan-Boltzmann Law

Remember that for a mode:
ε$_n$=sℏω$_n$
Average it:
<ε$_n$> = <sℏω$_n$>
= 
ℏω$_s$
From the previous section:
= ℏω$_n$/(exp(ℏω$_n$/T) - 1)
Thus, if we sum up over all the modes:
U = Σ$_n$ ℏω$_n$/(exp(ℏω$_n$/T) - 1)
Note that ω$_n$ = nπc/L, now because ℏ is so small, we can approximate this sum to an integral. In the process we will change the coordinates of the integral over n in spherical coordinates, and we will let x = πℏcn/LT (an extra 1/8 comes in because we are integrating over only positive values of n, and an extra 2 due to two independent set of cavity modes of frequencies):
Note: actually, this is a density of states problem with D(n) = 4n$^2$ because of the spherical shell * 1/8 * 2 = n$^2$, ε=ℏω$_n$, and f(ε)=(exp(ℏω$_n$/T) - 1)$^{-1}$
U = (L$^3$T$^4$/π$^2$ℏ$^3$c$^3$) ∫$_0$$^∞$ x$^3$/(exp(x) - 1) dx
The integral has a definite value found in an integral table, L$^3$=V, and thus we come upon the Stefan-Boltzmann law of radiation:
U/V = π$^2$/15π$^2$ℏ$^3$c$^3$ T$^4$

## Planck Radiation Law

Now, in our previous derivation, instead of integrating in terms of dn, say we left it as dω, there would be something of the form:
U/V = ∫dω u$_ω$
Carrying along the comparison with statistical properties, this is like a density, to be specific, a spectral density, if we carry the math out:
u$_ω$ = ℏ/π$^2$c$^3$ ω$^3$/(exp(ℏω/T) - 1)
And this is known as Planck's radiation Law.

## Kirchhoff's Law

Say we are concerned with the radiant flux density, by the definition of flux density:
J$_U$ = cU(T)/4V (the extra 4 is a geometrical factor)
If we take and apply the Stefan-Boltzmann law to this:
J$_U$ = π$^2$T$^4$/60ℏ$^3$c$^2$
The only difference between this and Kirchhoff's law is an extra constant thrown in known as the absorption/emissivity constant, dependent on the material.
# Introduction

The goal of statistical mechanics is to bridge the gap that exists between the microscopic and the macroscopic world. Take for example the equation governing the behaviour of microscopic particles: the quantum mechanical Schrödinger equation. Based on this equation, a quantum physicist will tell you everything you want to know about a particle by itself. If you ask, he will even be able to give you a solution for the wave function of a system of two particles. However, once you add a third or more, things start to get more complicated. There is no longer an analytic solution, and one must turn to computers to solve the problem numerically - and the results the computer will spit out are quite accurate for systems of 3, 4 or more particles. Even when considering classical Hamiltonian mechanics, there is no analytical solution for many-body problems such as the motion of the planets, although we can simulate them accurately numerically.
But what happens when the number of particles you have is much larger - not just ten or twenty, or even a thousand - what happens when you have a cup of water for example, with ~10$^{25}$ particles? Each of the 10$^{25}$ particles interacts with every single one of the 10$^{25}$ other particles - that's a total number of interactions of the order of 10$^{50}$ that would have to be computed at every instant! Even a computer that could perform a trillion calculations per second would take 10$^{20}$ times longer than the age of the universe to compute the exact state of your cup of water for a single instant in time. Clearly such a computation is not possible. It is therefore not possible, in practice, to solve the equations governing macroscopic systems.
Statistical mechanics provides the tools required to take the information given by quantum physics and use it to describe macroscopic systems and predict how they will evolve in time. By far the most important of these tools is probability theory. Instead of saying that a physical system is in exactly one or the other configuration, we will talk about the probability of it being in a certain configuration. For example, in a room filled with gas, it is far more probable that the gas is spread evenly rather than being bunched up in one corner. This may seem to be nothing more than common sense, but it has profound implications, especially when the probabilities involved are studied quantitatively. Through the use of this and other tools, statistical mechanics enables physicists to gain fundamental insight into the workings of the macroscopic world.

## Contents

* Macroscopic Properties of Matter
* Extensive and Intensive Parameters
* Definitions
* Fundamental Equations
* The Postulates
# Statistical Mechanics/The Foundations/Definitions

So, how do we define temperature? Pressure?
Extensive parameters are given with the problem, but these Intensive parameters have a much deeper meaning that gives truth to the reasoning of why we separate between extensive and intensive parameters. So, without further ado:
T = (∂U/∂S)$_{V,N}$
P = -(∂U/∂V)$_{S,N}$
μ = (∂U/∂N)$_{S,V}$
# Statistical Mechanics/The Foundations/The Postulates

The Three famous Postulates of Thermodynamics.
* There exists a function called the entropy of extensive parameters of any system, defined for all stabilized states having the property that the entropy maximizes.
* The entropy of a composite system is additive over constituent subsystems. As a function, it's also continuous, differentiable, and monotically increasing with respect to energy.
* If (∂u/∂S)$_{V,N}$=0, then S=0
The only other thing of note is notice in Postulate Two:
(The Entropy is a) monotonically increasing with respect to energy.
in other words:
∂S/∂U > 0
1/T > 0
Temperature can never be negative.
# Water Resources Directory/USA/Culture

Waters - People - Organizations - Education - Research - Best Practices - Laws - Ethics - Economics - Projects - Assistance - Data & Maps - News - Culture - Library

### History

* Development of Federal Water Supply Policy, in: Water Supply Handbook, U.S. Army Corps of Engineers, December 1998, page 1-1.
* Water Resources Update, journal of the Universities Council on Water Resources, special millenium issue, 2000.
* Historian's Office, Institute for Water Resources, U.S. Army Corps of Engineers.

### Photography

* U.S. Army Corps of Engineers - online photo library
# Water Resources Directory/USA/Assistance

Waters - People - Organizations - Education - Research - Best Practices - Laws - Ethics - Economics - Projects - Assistance - Data & Maps - News - Culture - Library
Local Government Environmental Assistance Network

### Technical and Funding Assistance, listed by organization

   * Federal agencies
   * State agencies
   * Foundations
   * Industry
   * NonGovernment Organizations

### Technical Assistance, listed by topic

   * Water quality
   * Wastewater
   * Water supply
   * Fish and wildlife
   * Public health
# Water Resources Directory/USA/Ethics

Waters - People - Organizations - Education - Research - Best Practices - Laws - Ethics - Economics - Projects - Assistance - Data & Maps - News - Culture - Library
Things To Do:
* check to see which of the organizations below have guidelines regarding ethical procurement procedures. Write a brief summary for each guideline.
* need a similar list and summary for the major professional organizations such as AWRA, WEF, ASCE.

### Procurement Organizations

National Association of State Chief Information Officers State Procurement/Purchasing Departments.
National Association of Counties County governments in the United States.
National Institute of Government Purchasing Professional organization for government procurement professionals.
National Association of State Procurement Officials Professional organization for state procurement officials.
National Contract Managers Association Professional organization for contract management professionals. http://www.ncmahq.org/
# Water Resources Directory/USA

Waters - People - Organizations - Education - Research - Best Practices - Laws - Ethics - Economics - Projects - Assistance - Data & Maps - News - Culture - Library

## Water Resources Directory for each state

| Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware Florida Georgia | Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland | Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire New Jersey | New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina | South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming |
# Water Resources Directory/USA/Assistance/Federal agencies

Waters - People - Organizations - Education - Research - Best Practices - Laws - Ethics - Economics - Projects - Assistance - Data & Maps - News - Culture - Library
Listed below are selected federal organizations having any water related responsibilities or activities.
          A complete list of federal organizations is online.

## Executive Departments

   * Department of Agriculture (USDA)
      * Forest Service
      * Natural Resources Conservation Service (NRCS)
   * Department of Commerce (DOC)
      * National Oceanic and Atmospheric Administration (NOAA)
   * Department of Defense (DOD)
      * U.S. Army Corps of Engineers (USACE)
         * Institute for Water Resources (Alexandria, VA)
         * Hydrologic Engineering Center (Davis, CA)
         * Waterways Experiment Station (Vicksburg, MS)
         * Construction Engineering Research Center (Champaign, IL)
         * Army Environmental Policy Institute
   * Department of Education (ED)
   * Department of Energy (DOE)
   * Department of Health and Human Services (HHS)
   * Department of Housing and Urban Development (HUD)
   * Department of Justice (DOJ)
   * Department of Labor (DOL)
   * Department of Interior (DOI)
       U.S. Geological Survey (USGS) ]
       National Park Service
   * Department of Transportation (DOT)

## Independent Agencies

   * Environmental Protection Agency (EPA)
   * Tennessee Valley Authority
   * Federal Maritime Commission
   * National Science Foundation
   * Office of Government Ethics
   * U.S. Office of Special Council (FOIA)
   * Small Business Administration
   * Securities and Exchange Commission
   * U.S. National Archives and Records Administration
   * Institute of Museum and Library Services
   * Corporation for National and Community Service (Vista Volunteers)

## Boards, Commissions and Committees

   * Appalachian Regional Commission
   * Delaware River Basin Commission
   * Interstate Commission on the Potomac River Basin
   * Mississippi River Commission
   * Susquehanna River Basin Commission
   * Committee on Foreign Investments in the US
   * Endangered Species Committee
   * Federal Advisory Committees
   * Federal Executive Boards
   * Federal Laboratory Consortium for Technology Transfer
   * Federal Library and Information Center Committee
   * Illinois and Michigan Canal National Heritage Corridor Commission
   * Interagency Alternative Dispute Resolution Working Group
   * Marine Mammal Commission
   * Migratory Bird Conservation Commission
   * Millennium Challenge Corporation. (Natural Resources Management Indicator Search)
   * Morris K. Udall Foundation: Scholarship and Excellence in National Environmental Policy
   * National Park Foundation
   * Northwest Power Planning Council
   * Nuclear Regulatory Commission
   * President's Council on Integrity and Efficiency (Inspector General)
   * Regulatory Information Service Center (B/C of rulemaking)
# Water Resources Directory/USA/Economics
### Wastewater Infrastructure

* "Clean Water State Revolving Fund Programs: 2005 Annual Report."
       Press release from USEPA (24 March 2006) states "the federal government and the states have invested almost $53 billion in the Clean Water State Revolving Fund (CWSRF) program to rebuild and refurbish the nation's wastewater infrastructure over the last 18 years. ...The CWSRF has made almost 17,000 loans since the program's inception in 1988. ... The CWSRF includes annual EPA contributions matched with at least an additional 20 percent from the states. The states, in turn, make low-interest loans to local utilities." See also: General information about CWSRF.

### National Water Projects

* Civil Works budget for U.S. Army Corps of Engineers, FY 08 Final Draft Budget EC 11-2-187.

### Organizations

* Center for the Applied Study of Economics and the Environment
# Water Resources Directory/USA/Education

Waters - People - Organizations - Education - Research - Best Practices - Laws - Ethics - Economics - Projects - Assistance - Data & Maps - News - Culture - Library

## Graduate degree programs
### Environmental Engineering (Pollution Control)

* Cornell University -

### Environmental Sciences

* University of North Carolina (UNC) at Chapel Hill

### Hydrology

* Cornell University -

### Water Resources Management

(Top five programs are numbered.)
1. Cornell University - Environmental & Water Resources Systems program in School of Civil and Environmental Engineering
      * Master of Engineering (1 year with 30 semester hours plus a design project)
      * Master of Science (2 years with 24 semester hours plus a research thesis)
      * PhD (about 5 years with research and dissertation)
      * Note: also has graduate programs in Hydrology and in Environmental Engineering
2. Duke University - Master of Environmental Management (48 credit units) with specialized tracks of study:
      * Coastal Environmental Management (CEM)
      * Conservation Science and Policy (CSP)
      * Environmental Economics and Policy (EEP)
      * Ecosystem Science and Management (ESM)
      * Energy and Environment (EE)
      * Environmental Health and Security (EHS)
      * Forest Resource Management (FRM)
      * Global Environmental Change (GEC)
      * Water and Air Resources (WAR)
3. Colorado State University - M.E. Civil Engineering with water resources focus
      * 30 semester hours with some distance learning courses, no thesis.
* Harvard University - Center for the Environment
      * Environmental Science and Public Policy - "founded on the premise that the ability to form rational judgments concerning many of the complex challenges confronting society today involving the environment requires both an understanding of the underlying scientific and technical issues and an appreciation for the relevant economic, political, legal, historical, and ethical dimensions."

### Water Resources Planning
## Short Courses (professional education)
### Water Resources Planning

USACE Short Courses for Planners (Reference):
* Planning Orientation Workshop
* Planning Process Workshop
* Plan Formulation Workshop
* Environmental Considerations in Planning
* Economic Analysis in Planning
* Hydrologic & Hydraulic Considerations in Planning
* Public Involvement and Teaming in Planning
USEPA Short Courses
* Catalog of Watershed Courses

## Homeowners

* Drinking Water Quality
# Water Resources Directory/U.S. Environmental Protection Agency

Waters - People - Organizations - Education - Research - Best Practices - Laws - Ethics - Economics - Projects - Assistance - Data & Maps - News - Culture - Library

### Financial Assistance

* Watershed funding sources main list
* Environmental Financing Information Network
* Water Quality Cooperative Agreements
       Note: need to go through list and add relevant projects by category
# Water Resources Directory/USA/Data

* Non-native Species
* Biological Community Condition
* Landscape Pattern
* Air Quality
* Data Gaps and Monitoring Infrastructure
* Change in Stream Flows
* Ecosystem Services
* Carbon Storage
* Harmful Algae
# Water Resources Directory/USA/Assistance/NGOs

Waters - People - Organizations - Education - Research - Best Practices - Laws - Ethics - Economics - Projects - Assistance - Data & Maps - News - Culture - Library
# Taxation in the United Kingdom/Definitions/Furnished lettings

Paragraph 4(2) of Section 15(1) of ICTA (which sets out what is meant by Schedule A) defines furnished lettings as being where:
* A sum is payable in repset of the use of premises, and
* The tenant or other person entitled to the use of the premises is also entitled in connection with that use, to the use of furniture.
For these purposes, premises is taken to include a caravan or houseboat.
# Levies on specific goods

Alcohol, hydrocarbons, tobacco, etc
# Taxation in the United Kingdom/Legislation/Schedule A2 to the Income and Corporation Taxes Act 1988

This Schedule supplemented Section 13AB of ICTA, which introduces the non-corporate distribution régime. It had effect for distributions made between 1 April 2004 and 31 March 2006.
# Taxation in the United Kingdom/Definitions

The following definitions may be relevant:
* Caravan
* Company
* Furnished lettings
* Houseboat
* Profession
* Profits
* Qualifying distribution
# Taxation in the United Kingdom/Definitions/Company

Company is defined for the purposes of the Income and Corporation Taxes Act 1988 by Section 832 of ICTA as:
However, this definition is subject to Section 468 of ICTA and does not apply to the following provisions of ICTA:
* Chapter 1 of Part XVII (Cancellation of tax advantages from certain transactions in securities)
* Sections 774 to 777
* Section 839 (Connected persons)
* Paragraph 15 of Schedule 3 (which has now been repealed)
Nor does it apply where the context requires otherwise because some other definition of "company" applies.