text:
$$\require{cancel}$$

# 23.5: Electric Generators

Electric generators induce an emf by rotating a coil in a magnetic field, as briefly discussed in "Induced Emf and Magnetic Flux." We will now explore generators in more detail. Consider the following example.

Example $$\PageIndex{1}$$: Calculating the Emf Induced in a Generator Coil

The generator coil shown in Figure $$\PageIndex{1}$$ is rotated through one-fourth of a revolution (from $$\theta = 0^{\circ}$$ to $$\theta = 90^{\circ}$$ ) in 15.0 ms. The 200-turn circular coil has a 5.00 cm radius and is in a uniform 1.25 T magnetic field. What is the average emf induced?

Figure $$\PageIndex{1}$$: When this generator coil is rotated through one-fourth of a revolution, the magnetic flux $$\Phi$$ changes from its maximum to zero, inducing an emf.

Strategy:

We use Faraday’s law of induction to find the average emf induced over a time $$\Delta t$$: $emf = -N\frac{\Delta \Phi}{\Delta t}.\label{23.6.1}$ We know that $$N = 200$$ and $$\Delta t = 15.0 ms$$, and so we must determine the change in flux $$\Delta \Phi$$ to find emf.

Solution:

Since the area of the loop and the magnetic field strength are constant, we see that $\Delta \Phi = \Delta \left(BA\cos{\theta}\right) = AB\Delta\left(\cos{\theta}\right).\label{23.6.2}$ Now, $$\Delta \left(\cos{\theta}\right) = -1.0$$, since it was given that $$\theta$$ goes from $$0^{\circ}$$ to $$90^{\circ}$$. Thus $$\Delta \Phi = -AB$$, and $emf = N\frac{AB}{\Delta t}.\label{23.6.3}$ The area of the loop is $$A = \pi r^{2} = \left(3.14...\right)\left(0.0500 m\right)^{2} = 7.85 \times 10^{-3} m^{2}$$. Entering this value gives $emf = 200\frac{\left(7.85 \times 10^{-3} m^{2} \right) \left(1.25 T\right)}{1.50 \times 10^{-3}s} = 131V.$

Discussion:

This is a practical average value, similar to the 120 V used in household power.

The emf calculated in the example is the average over one-fourth of a revolution. What is the emf at any given instant? It varies with the angle between the magnetic field and a perpendicular to the coil. We can get an expression for emf as a function of time by considering the motional emf on a rotating rectangular coil of width $$\w$$ and height $$l$$ in a uniform magnetic field, as illustrated in Figure $$\PageIndex{2}$$.

Figure $$\PageIndex{2}$$: A generator with a single rectangular coil rotated at constant angular velocity in a uniform magnetic field produces an emf that varies sinusoidally in time. Note the generator is similar to a motor, except the shaft is rotated to produce a current rather than the other way around.

Charges in the wires of the loop experience the magnetic force, because they are moving in a magnetic field. Charges in the vertical wires experience forces parallel to the wire, causing currents. But those in the top and bottom segments feel a force perpendicular to the wire, which does not cause a current. We can thus find the induced emf by considering only the side wires. Motional emf is given to be $$emf = Blv$$, where the velocity $$v$$ is perpendicular to the magnetic field $$B$$. Here the velocity is at an angle $$\theta$$ with $$B$$, so that its component perpendicular to $$B$$ is $$v\sin{\theta}$$ (Figure $$\PageIndex{2}$$). Thus in this case the emf induced on each side is $$emf = Blv\sin{\theta}$$, and they are in the same direction. The total emf around the loop is then

$emf = 2Blv\sin{\theta}.\label{23.6.4}$

This expression is valid, but it does not give emf as a function of time. To find the time dependence of emf, we assume the coil rotates at a constant angular velocity $$\omega$$. The angle $$\theta$$ is related to angular velocity by $$\theta = \omega t$$, so that

$emf = 2Blv\sin{\omega t}.\label{23.6.5}$

Now, linear velovity $$v$$ is related to angular velocity $$\omega$$ by $$v=r\omega$$. Here $$r = \omega /2$$, so that $$v = \left(w/2\right)\omega$$, and

$emf = 2Bl\frac{w}{2} \omega \sin{\omega t} = \left(w\right)B \omega \sin{\omega t}.\label{23.6.6}$

Noting that the area of the loop is $$A = w$$, and allowing for $$N$$ loops, we find that

$emf = NAB \omega \sin{\omega t}\label{23.6.7}$

is the emf induced in a generator coil of $$N$$ turns and area $$A$$ rotating at a constant angular velocity $$\omega$$ in a uniform magnetic field $$B$$. This can also be expressed as

$emf = emf_{0}\sin{\omega t},\label{23.6.8}$

where $emf_{0} = NAB \omega \label{23.6.9}$ is the maximum (peak) emf. Note that the frequency of the oscillation is $$f = \omega / 2\pi$$, and the period is $$T = 1/f = 2\pi / \omega$$. Figure $$\PageIndex{3}$$ shows a graph of emf as a function of time, and it now seems reasonable that AC voltage is sinusoidal.

Figure $$\PageIndex{3}$$:The emf of a generator is sent to a light bulb with the system of rings and brushes shown. The graph gives the emf of the generator as a function of time. $$emf_0$$ is the peak emf. The period is $$T=1/f=2π/ω$$, where $$f$$ is the frequency. Note that the script E stands for emf.

The fact that the peak emf, $$emf_0=NABω$$, makes good sense. The greater the number of coils, the larger their area, and the stronger the field, the greater the output voltage. It is interesting that the faster the generator is spun (greater ω), the greater the emf. This is noticeable on bicycle generators—at least the cheaper varieties. One of the authors as a juvenile found it amusing to ride his bicycle fast enough to burn out his lights, until he had to ride home lightless one dark night.

Figure shows a scheme by which a generator can be made to produce pulsed DC. More elaborate arrangements of multiple coils and split rings can produce smoother DC, although electronic rather than mechanical means are usually used to make ripple-free DC.

Figure $$\PageIndex{4}$$: Split rings, called commutators, produce a pulsed DC emf output in this configuration.

Example $$\PageIndex{2}$$: Calculating the Maximum Emf of a Generator

Calculate the maximum emf, emf0, of the generator that was the subject of Example.

Strategy

Once $$ω$$, the angular velocity, is determined, $$emf_0=NABω$$ can be used to find $$emf_0$$. All other quantities are known.

Solution

Angular velocity is defined to be the change in angle per unit time:

$$ω=\frac{Δθ}{Δt}$$.

One-fourth of a revolution is $$π/2$$ radians, and the time is 0.0150 s; thus,

$$ω=\frac{π/2rad}{0.0150 s}=104.7 rad/s.$$

104.7 rad/s is exactly 1000 rpm. We substitute this value for ω and the information from the previous example into $$emf_0=NABω$$, yielding

$$emf_0=NABω=200(7.85×10^{−3}m^2)(1.25T)(104.7rad/s)=206V$$.

Discussion

The maximum emf is greater than the average emf of 131 V found in the previous example, as it should be.

In real life, electric generators look a lot different than the figures in this section, but the principles are the same. The source of mechanical energy that turns the coil can be falling water (hydropower), steam produced by the burning of fossil fuels, or the kinetic energy of wind. $$\PageIndex{5}$$ shows a cutaway view of a steam turbine; steam moves over the blades connected to the shaft, which rotates the coil within the generator.

Figure $$\PageIndex{5}$$: Steam turbine/generator. The steam produced by burning coal impacts the turbine blades, turning the shaft which is connected to the generator. (credit: Nabonaco, Wikimedia Commons)

Generators illustrated in this section look very much like the motors illustrated previously. This is not coincidental. In fact, a motor becomes a generator when its shaft rotates. Certain early automobiles used their starter motor as a generator. In Back Emf, we shall further explore the action of a motor as a generator.

## Summary

• An electric generator rotates a coil in a magnetic field, inducing an emfgiven as a function of time by

$$emf=NABωsinωt,$$

where $$A$$ is the area of an $$N$$-turn coil rotated at a constant angular velocity ω in a uniform magnetic field $$B$$.

• The peak emf $$emf_0) of a generator is \(emf_0=NABω$$.

Glossary

electric generator
a device for converting mechanical work into electric energy; it induces an emf by rotating a coil in a magnetic field
emf induced in a generator coil
$$emf=NABωsinωt$$, where $$A$$ is the area of an $$N$$-turn coil rotated at a constant angular velocity $$ω$$ in a uniform magnetic field $$B$$, over a period of time $$t$$
peak emf
(emf_0=NABω\)

# Contributors

• Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).


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# How to check the data present in a Series object is monotonically decreasing or not?

PandasServer Side ProgrammingProgramming

To check if the data present in the series is monotonically decreasing or not, we can use the is_monotonic_decreasing property of the pandas Series constructor.

The monotonically decreasing data is nothing but continuously decreasing values. And the attribute “is_monotonic_decreasing” is used to verify that the data in a given series object is always decreasing or not. And this attribute returns a boolean value as an output.

## Example 1

import pandas as pd

# create a series
s = pd.Series([100,57,23,10,5])

print(s)

print("Is monotonically decreasing: ", s.is_monotonic_decreasing)

## Explanation

Here, we initialized a Series with a python list of integer values of length 5. Then we applied the is_monotonic_decreasing property on our series object “s”.

## Output

0 100
1  57
2  23
3  10
4   5
dtype: int64

Is monotonically decreasing: True

In the above output, we can see the initial series object, and also the output of the is_monotonic_decreasing attribute.

For the following example, The is_monotonic_decreasing attribute returns True. which means the data in the given series is continuously decreasing.

## Example 2

import pandas as pd

# create a series
s = pd.Series(list("abcdef"))

print(s)

print("Is monotonically decreasing: ", s.is_monotonic_decreasing)

## Explanation

Let’s take another example for checking if the values in a series object is monotonically decreasing or not. Here, we have initialized a series object with a python list of strings. After that, we applied the is_monotonic_decreasing property over the data of the series object “s”.

## Output

0 a
1 b
2 c
3 d
4 e
5 f
dtype: object

Is monotonically decreasing: False

We got the boolean value “False” as a result of the following example. which means that the values present in the given series object is not decreasing continuously.

Updated on 09-Mar-2022 06:27:22

format: plain


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# 1981 IMO Problems/Problem 4

## Problem

(a) For which values of $n>2$ is there a set of $n$ consecutive positive integers such that the largest number in the set is a divisor of the least common multiple of the remaining $n-1$ numbers?

(b) For which values of $n>2$ is there exactly one set having the stated property?

## Solution

Let $k = \prod p_i^{e_i}$ be the greatest element of the set, written in its prime factorization. Then $k$ divides the least common multiple of the other elements of the set if and only if the set has cardinality at least $\max \{ p_i^{e_i} \}$, since for any of the $p_i^{e_i}$, we must go down at least to $k-p_i^{e_i}$ to obtain another multiple of $p_i^{e_i}$. In particular, there is no set of cardinality 3 satisfying our conditions, because each number greater than or equal to 3 must be divisible by a number that is greater than two and is a power of a prime.

For $n > 3$, we may let $k = \mbox{lcm} (n-1, n-2) = (n-1)(n-2)$, since all the $p_i^{e_i}$ must clearly be less than $n$ and this product must also be greater than $n$ if $n$ is at least 4. For $n > 4$, we may also let $k = \mbox{lcm} (n-2, n-3) = (n-2)(n-3)$, for the same reasons. However, for $n = 4$, this does not work, and indeed no set works other than $\{ 3,4,5,6 \}$. To prove this, we simply note that for any integer not equal to 6 and greater than 4 must have some power-of-a-prime factor greater than 3.

Q.E.D.

## Alternate Solution

Let, for some $n$ and $m$ with $m>n$, $m\ |\ \mbox{lcm}(m-1,m-2,\cdots,m-n+1)\ |\ (m-1)(m-2)\cdots(m-n+1)$.

We can trivially check that, there is no such $m$ for $n=3$, only $m=3$ works for $n=4$ and $m=3,8$ works for $n=5$.

Now, consider, $n>5$. By Bertrand's postulate there is a prime $p$ such that $2 \le \left\lfloor\frac{n}{2}\right\rfloor < p < 2\left\lfloor\frac{n}{2}\right\rfloor$.

Which implies, $p< n \le 2p$.

As, $n-1 \ge p,3,2$, there must be a multiple of $p$, a multiple of $3$ and a multiple of $2$ in the set, $\{m-1,m-2,\cdots,m-n+1\}$.

So, $2p\ |\ \mbox{lcm}(m-1,m-2,\cdots,m-n+1)$ and $3p\ |\ \mbox{lcm}(m-1,m-2,\cdots,m-n+1)$.

So, $m=2p$ and $m=3p$ both work for $n>5$.

So,

There exists solution for all $n>3$,

Only one Solution for $n=4$.

Q.E.D.

 1981 IMO (Problems) • Resources) Preceded byProblem 3 1 • 2 • 3 • 4 • 5 • 6 Followed byProblem 5 All IMO Problems and Solutions


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# What can't TeX do?

What are TeX's limitations in typography, book design and publishing? (and here TeX also includes all its derivatives, like pdfTeX, LuaTeX, and macro packages built upon it, LaTeX, ConTeXt etc.).

Some things (like math and references) are extremely easy in TeX. There are some things that are harder to do in TeX-based systems, but they are possible, even if cumbersome (like precise control of images' placement or manual control over layout and design). Solutions to some problems have been found (like microtype). Some things are rarely talked about (like color profiles).

Please mention what is either extremely hard to achieve with TeX or is not possible at all (due to inherent limitations of TeX, or due to bugs/limitations in the available tool chain). Please mention also which technological steps do not fit well with TeX workflow.

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I think this is an acceptable question for this site, as a community wiki, where people should answer one tex limitation per answer. – Lev Bishop Sep 4 '11 at 14:56
Color profiles are not well supported in latex, although you can always use raw pdftex primitives if you know what you want. I believe Context has good support for them though. – Lev Bishop Sep 4 '11 at 14:58
I think the question should be closed or reworded. There are things that TeX can't do at the moment, but things change and the answers will possibly invalid in the future and therefore misleading. - If we answer the question, we should define first what TeX is. – topskip Sep 4 '11 at 17:35
Well TeX can't prevent the coming Apocalypse, for example... – Yuji Sep 4 '11 at 17:51
I was tempted to post something along the lines of @Yuji ... TeX can't bake cakes :) As for the rewording: I guess it makes sense to specify the current state of TeX in some way, and also to ask about limitations or borders, to indicate the relatedness of the impossible tasks, which is implicit so far. – doncherry Sep 4 '11 at 22:06

TeX has no real way to do river, lake and hole elimination. This would require a much more expensive paragraph layout algorithm than the Knuth and Plass dynamic programming.

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I think it is possible but impossible within manageable time. It is possible to implement such an algorithm in Lua or even TeX. But I only heard of such an algorithm at the order O(n^3), cannot remember where I read about it – Yan Zhou Sep 4 '11 at 15:06
For more discussion on this see question 4507: avoiding-rivers-in-successive-lines-of-type – mas Sep 4 '11 at 16:08
Are there other programs that are known to avoid them automatically? – ℝaphink Sep 5 '11 at 16:28
@Raphink ant.berlios.de (Ant) states that it does so, but even with the help from the author I was unable to see any river elimination. (I did a bit of research on that area). And there are rumors that InDesign does that, but there is no official note from Adobe about that, so river elimination is probably due to the total fit algorithm in ID. – topskip Sep 7 '11 at 6:00
@ℝaphink Yes: Patoline – yo' Mar 8 '13 at 21:49

The definitive answer to this is perhaps Donald Knuth's own answers, given in an earthshaking announcement in 2010 and recorded in this video and transcribed in the TUG journal, TUGboat, Volume 31 (2010), No. 2, pp121ff.

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Some things that are perhaps possible in TeX (with some programming) but not built in LaTeX or plain TeX itself:

• Automatic paragraph flow around arbitrary shapes (like images)
• Autokerning based on the shape of the glyphs
• good multi column support (balancing, images/formulae crossing multiple columns)
• text areas with overflow capabilities ("read more on page 3")
• Output to an "open" format such as InDesign (for editing afterwards) or XML
• Some way of splitting a vbox at a point (should break an image in two parts for example)
• XML input
• This list could be continued, but you get the point: magazine layout is not easy in TeX
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you should divide this list into separate answers, since as you say, some of these have solutions, whereas others have only partial solutions/workarounds or could only be solved in principle with tricky tex programming that nobody has done yet. If you put it into separate answers, people can more easily edit in additional information. – Lev Bishop Sep 8 '11 at 15:21
Very good answer. Thank you. – sastanin Sep 11 '11 at 8:31

One of the things that are impossible in TeX90 is typesetting the first line of a paragraph in a different font than the rest of the para - with the possibility of hyphenation between the first and second line.

EDIT: It seems the magaz package implements this.

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Are you sure? \documentclass[11pt]{article} \usepackage{lipsum,magaz} \begin{document}\FirstLine{\lipsum*[6]}\end{document} – Will Robertson Sep 5 '11 at 16:01
@WillRobertson: No, I'm not sure anymore. Thanks. :-) – Martin Schröder Sep 5 '11 at 16:20
There are some limitations to this approach, though, such as that it will break if there's much more than plain paragraph text. But overall a nice solution as far as it goes. – Will Robertson Sep 5 '11 at 23:00

TeX does not perform a global optimization of its cost functions but does so on a page by page basis. While I think it might be possible to solve this without touching the kernel, this must be pretty hard to do efficiently and transparently and I am not aware of any package that has tried to do this.

For an example of the practical effects of this deficiency, see How to spread floats automatically over a whole chapter?

I stole this picture from there:

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TeX was not really designed for fully automatic typesetting, as you may want when the source document is computer-generated (for things like database reports or equipment manuals), or needs to be typeset in many different page geometries. These things are possible, but they need some care. The main problem is that TeX wants to set beautiful paragraphs and if it can't do that, then it throws an overfull hbox and expects the author to deal with it (eg, by rewording the offending text, or marking additional hyphenation locations). Some discussion of lowering TeX's standards is in this FAQ answer, which will eliminate overfull boxes, but it's still true that TeX is at it's best at when beautiful paragraphs are possible.

Here's an example:

\documentclass{article}
\usepackage[text={3.01cm,8in}]{geometry}
\begin{document}
{%Help TeX not to give up too easily....
\tolerance=9999
\setlength{\emergencystretch}{1em}
TeX was not really designed for fully automatic typesetting, as you may want
when the source document is computer-generated (for things like database reports
or equipment manuals), or needs to be typeset in many different page geometries.\par}

%I'd rather see something like this
TeX was not\break really designed for\break fully automatic typesetting,
as you may want when the\break source document is computer-generated (for
things like\break database reports or equipment manuals), or needs to be
typeset in many different page geometries.
\end{document}

Result:

Automatic breaking of displayed equations is another difficult aspect of automatic typesetting, although the breqn package makes an attempt at this.

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sorry, but this is simply false. You can tweak linke breaking, so that no overfull boxes will be generated. You can do even multi pass line breaking with different parameters, so that you really get the best paragraph shape. In our database publishing software (speedata.github.com/publisher) that we use for creating high quality product catalogs (100% automatic) we get awesome typography due to the full control we have over TeX. – topskip Sep 7 '11 at 6:04
@Patrick: That sounds really interesting! I haven't been able to find any examples of the documents produced with Speedata Publisher on your website. Is there a showcase somewhere? – Jake Sep 7 '11 at 6:17
@Jake Not yet. We are still in the process of opening our software. There is even no english translation of the manual yet. We will have a more or less finished package by spring 2012. – topskip Sep 7 '11 at 6:24
@patrick: if the situation is easy: short words, wide textblock, long paragraphs, then beautiful (or at least decent) paragraphs are possible, and TeX will certainly find them. If the situation is difficult: long non-hyphenatable words, narrow columns, short paragraphs, then many paragraphs will need to be ugly. Yes you can tweak the parameters so that TeX doesn't produce overfull boxes in such cases (as I wrote), but still TeX's formula for "badness" (sum of cubes of the stretches/shrinks) isn't optimal for choosing which ugly paragraph is least bad. I edited my answer to clarify. – Lev Bishop Sep 7 '11 at 6:25
@Lev but then the typesetting task is simply impossible or extremely hard and this is not TeX's fault. Show me a formatter that is better then TeX (with a specific paragraph). IMO TeX is by far the best software out there for unattended typesetting and for database publishing (in terms of speed, quality, robustness, features and so on), and this is why we chose TeX (specifically LuaTeX) for that task. – topskip Sep 7 '11 at 6:32

To shamelessly copy and paste from the answer so that SX won't auto-comment my answer anymore:

Tex/Latex have what is called monolithic state: you can't cleanly isolate the configuration done by one package from another, which is one of the reasons why incompatibilities are possible. This means there is no way to identify how to undo what changes the \usepackage command has caused.

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TeX, and Lua in LuaTeX are both Turing complete languages. So they should be able to do pretty much anything.

However, some things are more difficult due to the limited sets of features of the language. Some other things requires new algorithm, which may not perform reasonable well (Say it requires O(n^2) or even more computing times.

One particular example I can think of is Grid typesetting. This is one thing I always one to do but haven't found any elegant solutions in the TeX world yet.

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No, TeX being Turing complete does not mean that in principle it can do "pretty much anything". One major point is that TeX doesn't know how the glyphs it uses look like - it only knows the bounding boxes. (This question of mine gives an idea what I mean.) – Hendrik Vogt Sep 4 '11 at 16:29
Grid computing is no problem with ConTeXt and there is also a solution with KOMA-Script, but I didn't find it – Herbert Sep 4 '11 at 16:29
@Herbert: That's the gridset alpha package -- but it provides only a partial solution (a \vskipnextgrid macro). – lockstep Sep 4 '11 at 20:38
In my experiments, I've found out that grid isn't a problem until you have inline maths. – morbusg Sep 7 '11 at 6:25
I wonder why you do your typesetting in TeX then at all. Just use a Turing machine – it can do everything TeX can. – Christian Jun 22 '13 at 14:57

Automatic splitting of floats for a better overall look (http://tex.stackexchange.com/a/4682/13450).

This is of course related to the general problem of a lack of global optimization but more specific. It would be nice to have floating text environments (tables, listings, text boxes, subfigure collections ...) that were split into two smaller parts if this were to improve the overall layout of the document (footnotes already do something like this).

-

TeX and LaTeX is not really good at constructing dictionary-style texts.

It's really designed to expect tables and text as separate entities, and is not really good at flowing text from one minipage to another (like in magazines - continued on page ...).

One document i am writing at the moment, has a formatted set of formulae definitions, followed by a few paragraphs of text, and then a few more formulae, and then more text. I am currently doing this with the {tabbing} environment, with the \kill line set in the preface sections. It works, i suppose.

I'm still trying to get hanging numbers to work. Some places, such as running text, it is appropriate to use hanging numbers, rather than block numbers, but i can't see how to do this. I downloaded a package printnum where the documentation is in hanging numbers in the required style, but it's set to decimal, rather than twelfty.

-

TeX is Turing complete, therefore it can do anything any other language can do. Therefore it can't do anything any other language can't do.

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Please see the existing answer by Yan Zhou and the discussion under that post, especially the comment by Hendrik Vogt. Repeating this fundamental misunderstanding of what computability means doesn't make it any more true. This post also can be read as alluding to mysticism in that there are real physical entities that can do something computers principally can't (mostly humans are these entities). While you might hold this belief, it is note what the Church-Turing thesis states. – Christian Mar 26 '13 at 14:46


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# Oil reserves

Last updated

Oil reserves denote the amount of crude oil that can be technically recovered at a cost that is financially feasible at the present price of oil. [1] Hence reserves will change with the price, unlike oil resources, which include all oil that can be technically recovered at any price. Reserves may be for a well, a reservoir, a field, a nation, or the world. Different classifications of reserves are related to their degree of certainty.

Petroleum is a naturally occurring, yellowish-black liquid found in geological formations beneath the Earth's surface. It is commonly refined into various types of fuels. Components of petroleum are separated using a technique called fractional distillation, i.e. separation of a liquid mixture into fractions differing in boiling point by means of distillation, typically using a fractionating column.

## Contents

The total estimated amount of oil in an oil reservoir, including both producible and non-producible oil, is called oil in place . However, because of reservoir characteristics and limitations in petroleum extraction technologies, only a fraction of this oil can be brought to the surface, and it is only this producible fraction that is considered to be reserves. The ratio of reserves to the total amount of oil in a particular reservoir is called the recovery factor. Determining a recovery factor for a given field depends on several features of the operation, including method of oil recovery used and technological developments. [2]

Oil in place (OIP) is a specialist term in petroleum geology that refers to the total oil content of an oil reservoir. As this quantity cannot be measured directly, it has to be estimated from other parameters measured prior to drilling or after production has begun.

Reservoir engineering is a branch of petroleum engineering that applies scientific principles to the fluid flow through porous medium during the development and production of oil and gas reservoirs so as to obtain a high economic recovery. The working tools of the reservoir engineer are subsurface geology, applied mathematics, and the basic laws of physics and chemistry governing the behavior of liquid and vapor phases of crude oil, natural gas, and water in reservoir rock. Of particular interest to reservoir engineers is generating accurate reserves estimates for use in financial reporting to the SEC and other regulatory bodies. Other job responsibilities include numerical reservoir modeling, production forecasting, well testing, well drilling and workover planning, economic modeling, and PVT analysis of reservoir fluids. Reservoir engineers also play a central role in field development planning, recommending appropriate and cost effective reservoir depletion schemes such as waterflooding or gas injection to maximize hydrocarbon recovery. Due to legislative changes in many hydrocarbon producing countries, they are also involved in the design and implementation of carbon sequestration projects in order to minimise the emission of greenhouse gases.

The extraction of petroleum is the process by which usable petroleum is drawn out from beneath the earth's surface location

Based on data from OPEC at the beginning of 2013 the highest proved oil reserves including non-conventional oil deposits are in Venezuela (20% of global reserves), Saudi Arabia (18% of global reserves), Canada (13% of global reserves), and Iran (9%). [3]

The Organization of the Petroleum Exporting Countries is an intergovernmental organization of 14 nations, founded in 1960 in Baghdad by the first five members, and headquartered since 1965 in Vienna, Austria. As of September 2018, the then 14 member countries accounted for an estimated 44 percent of global oil production and 81.5 percent of the world's "proven" oil reserves, giving OPEC a major influence on global oil prices that were previously determined by the so called "Seven Sisters” grouping of multinational oil companies.

Venezuela, officially the Bolivarian Republic of Venezuela, is a country on the northern coast of South America, consisting of a continental landmass and a large number of small islands and islets in the Caribbean Sea. The capital and largest urban agglomeration is the city of Caracas. It has a territorial extension of 916,445 km2. The continental territory is bordered on the north by the Caribbean Sea and the Atlantic Ocean, on the west by Colombia, Brazil on the south, Trinidad and Tobago to the north-east and on the east by Guyana. With this last country, the Venezuelan government maintains a claim for Guayana Esequiba over an area of 159,542 km2. For its maritime areas, it exercises sovereignty over 71,295 km2 of territorial waters, 22,224 km2 in its contiguous zone, 471,507 km2 of the Caribbean Sea and the Atlantic Ocean under the concept of exclusive economic zone, and 99,889 km2 of continental shelf. This marine area borders those of 13 states. The country has extremely high biodiversity and is ranked seventh in the world's list of nations with the most number of species. There are habitats ranging from the Andes Mountains in the west to the Amazon basin rain-forest in the south via extensive llanos plains, the Caribbean coast and the Orinoco River Delta in the east.

Energy in Saudi Arabia involves petroleum and natural gas production, consumption, and exports, and electricity production. Saudi Arabia is the world's leading oil producer and exporter. Saudi Arabia's economy is petroleum-based; oil accounts for 90% of the country's exports and nearly 75% of government revenue. The oil industry produces about 45% of Saudi Arabia's gross domestic product, against 40% from the private sector. Saudi Arabia has per capita GDP of \$20,700. The economy is still very dependent on oil despite diversification, in particular in the petrochemical sector.

Because the geology of the subsurface cannot be examined directly, indirect techniques must be used to estimate the size and recoverability of the resource. While new technologies have increased the accuracy of these techniques, significant uncertainties still remain. In general, most early estimates of the reserves of an oil field are conservative and tend to grow with time. This phenomenon is called reserves growth . [4]

Geology is an earth science concerned with the solid Earth, the rocks of which it is composed, and the processes by which they change over time. Geology can also include the study of the solid features of any terrestrial planet or natural satellite such as Mars or the Moon. Modern geology significantly overlaps all other earth sciences, including hydrology and the atmospheric sciences, and so is treated as one major aspect of integrated earth system science and planetary science.

Exploration geophysics is an applied branch of geophysics and economic geology, which uses physical methods, such as seismic, gravitational, magnetic, electrical and electromagnetic at the surface of the Earth to measure the physical properties of the subsurface, along with the anomalies in those properties. It is most often used to detect or infer the presence and position of economically useful geological deposits, such as ore minerals; fossil fuels and other hydrocarbons; geothermal reservoirs; and groundwater reservoirs.

Reflection seismology is a method of exploration geophysics that uses the principles of seismology to estimate the properties of the Earth's subsurface from reflected seismic waves. The method requires a controlled seismic source of energy, such as dynamite or Tovex blast, a specialized air gun or a seismic vibrator, commonly known by the trademark name Vibroseis. Reflection seismology is similar to sonar and echolocation. This article is about surface seismic surveys; for vertical seismic profiles, see VSP.

Many oil-producing nations do not reveal their reservoir engineering field data and instead provide unaudited claims for their oil reserves. The numbers disclosed by some national governments are suspected of being manipulated for political reasons. [5] [6]

## Classifications

All reserve estimates involve uncertainty, depending on the amount of reliable geologic and engineering data available and the interpretation of that data. The relative degree of uncertainty can be expressed by dividing reserves into two principal classifications—"proven" (or "proved") and "unproven" (or "unproved"). [7] Unproven reserves can further be divided into two subcategories—"probable" and "possible"—to indicate the relative degree of uncertainty about their existence. [7] The most commonly accepted definitions of these are based on those approved by the Society of Petroleum Engineers (SPE) and the World Petroleum Council (WPC) in 1997. [8]

The Society of Petroleum Engineers (SPE) is a 501(c)(3) not-for-profit professional organization whose mission is to collect, disseminate, and exchange technical knowledge concerning the exploration, development and production of oil and gas resources and related technologies for the public benefit and to provide opportunities for professionals to enhance their technical and professional competence.

The World Petroleum Council (WPC) is an oil and gas industry forum and international organization representing the petroleum sector worldwide

### Proven reserves

Proven reserves are those reserves claimed to have a reasonable certainty (normally at least 90% confidence) of being recoverable under existing economic and political conditions, with existing technology. Industry specialists refer to this as "P90" (that is, having a 90% certainty of being produced). Proven reserves are also known in the industry as "1P". [9] [10]

Proven reserves are further subdivided into "proven developed" (PD) and "proven undeveloped" (PUD). [10] [11] PD reserves are reserves that can be produced with existing wells and perforations, or from additional reservoirs where minimal additional investment (operating expense) is required. [11] PUD reserves require additional capital investment (e.g., drilling new wells) to bring the oil to the surface. [9] [11]

Until December 2009 "1P" proven reserves were the only type the U.S. Securities and Exchange Commission allowed oil companies to report to investors. Companies listed on U.S. stock exchanges must substantiate their claims, but many governments and national oil companies do not disclose verifying data to support their claims. Since January 2010 the SEC now allows companies to also provide additional optional information declaring 2P (both proven and probable) and 3P (proven plus probable plus possible) provided the evaluation is verified by qualified third party consultants, though many companies choose to use 2P and 3P estimates only for internal purposes.

### Unproven reserves

Unproven reserves are based on geological and/or engineering data similar to that used in estimates of proven reserves, but technical, contractual, or regulatory uncertainties preclude such reserves being classified as proven. [12] Unproven reserves may be used internally by oil companies and government agencies for future planning purposes but are not routinely compiled. They are sub-classified as probable and possible. [12]

Probable reserves are attributed to known accumulations and claim a 50% confidence level of recovery. Industry specialists refer to them as "P50" (i.e., having a 50% certainty of being produced). The sum of proven plus probable reserves is also referred to in the industry as "2P" (proven plus probable). [9]

Possible reserves are attributed to known accumulations that have a less likely chance of being recovered than probable reserves. This term is often used for reserves which are claimed to have at least a 10% certainty of being produced ("P10"). Reasons for classifying reserves as possible include varying interpretations of geology, reserves not producible at commercial rates, uncertainty due to reserve infill (seepage from adjacent areas) and projected reserves based on future recovery methods. The cumulative amount of proven, probable and possible resources are referred to in the industry as "3P" (proven plus probable plus possible). [9]

### Russian reserve categories

In Russia, reserves categories A, B, and C1 correspond roughly to proved developed producing, proved developed nonproducing, and proved undeveloped, respectively; the designation ABC1 corresponds to proved reserves. The Russian category C2 includes probable and possible reserves. [13]

### Strategic petroleum reserves

Many countries maintain government-controlled oil reserves for both economic and national security reasons. According to the United States Energy Information Administration, approximately 4.1 billion barrels (650,000,000 m3) of oil are held in strategic reserves, of which 1.4 billion is government-controlled. These reserves are generally not counted when computing a nation's oil reserves.

### Resources

A more sophisticated system of evaluating petroleum accumulations was adopted in 2007 by the Society of Petroleum Engineers (SPE), World Petroleum Council (WPC), American Association of Petroleum Geologists (AAPG), and Society of Petroleum Evaluation Engineers (SPEE). It incorporates the 1997 definitions for reserves, but adds categories for contingent resources and prospective resources. [7]

Contingent resources are those quantities of petroleum estimated, as of a given date, to be potentially recoverable from known accumulations, but the applied project(s) are not yet considered mature enough for commercial development due to one or more contingencies. Contingent resources may include, for example, projects for which there are no viable markets, or where commercial recovery is dependent on technology under development, or where evaluation of the accumulation is insufficient to clearly assess commerciality.

Prospective resources are those quantities of petroleum estimated, as of a given date, to be potentially recoverable from undiscovered accumulations by application of future development projects. Prospective resources have both an associated chance of discovery and a chance of development.

The United States Geological Survey uses the terms technically and economically recoverable resources when making its petroleum resource assessments. Technically recoverable resources represent that proportion of assessed in-place petroleum that may be recoverable using current recovery technology, without regard to cost. Economically recoverable resources are technically recoverable petroleum for which the costs of discovery, development, production, and transport, including a return to capital, can be recovered at a given market price.

"Unconventional resources" exist in petroleum accumulations that are pervasive throughout a large area. Examples include extra heavy oil, oil sand, and oil shale deposits. Unlike "conventional resources", in which the petroleum is recovered through wellbores and typically requires minimal processing prior to sale, unconventional resources require specialized extraction technology to produce. For example, steam and/or solvents are used to mobilize bitumen for in-situ recovery. Moreover, the extracted petroleum may require significant processing prior to sale (e.g., bitumen upgraders). [7] The total amount of unconventional oil resources in the world considerably exceeds the amount of conventional oil reserves, but are much more difficult and expensive to develop.

## Estimation techniques

The amount of oil in a subsurface reservoir is called oil in place (OIP). [11] Only a fraction of this oil can be recovered from a reservoir. This fraction is called the recovery factor . [11] The portion that can be recovered is considered to be a reserve. The portion that is not recoverable is not included unless and until methods are implemented to produce it. [12]

### Volumetric method

Volumetric methods attempt to determine the amount of oil in place by using the size of the reservoir as well as the physical properties of its rocks and fluids. Then a recovery factor is assumed, using assumptions from fields with similar characteristics. OIP is multiplied by the recovery factor to arrive at a reserve number. Current recovery factors for oil fields around the world typically range between 10 and 60 percent; some are over 80 percent. The wide variance is due largely to the diversity of fluid and reservoir characteristics for different deposits. [15] [16] [17] The method is most useful early in the life of the reservoir, before significant production has occurred.

### Materials balance method

The materials balance method for an oil field uses an equation that relates the volume of oil, water and gas that has been produced from a reservoir and the change in reservoir pressure to calculate the remaining oil. It assumes that, as fluids from the reservoir are produced, there will be a change in the reservoir pressure that depends on the remaining volume of oil and gas. The method requires extensive pressure-volume-temperature analysis and an accurate pressure history of the field. It requires some production to occur (typically 5% to 10% of ultimate recovery), unless reliable pressure history can be used from a field with similar rock and fluid characteristics. [12]

### Production decline curve method

The decline curve method uses production data to fit a decline curve and estimate future oil production. The three most common forms of decline curves are exponential, hyperbolic, and harmonic. It is assumed that the production will decline on a reasonably smooth curve, and so allowances must be made for wells shut in and production restrictions. The curve can be expressed mathematically or plotted on a graph to estimate future production. It has the advantage of (implicitly) including all reservoir characteristics. It requires a sufficient history to establish a statistically significant trend, ideally when production is not curtailed by regulatory or other artificial conditions. [12]

## Reserves growth

Experience shows that initial estimates of the size of newly discovered oil fields are usually too low. As years pass, successive estimates of the ultimate recovery of fields tend to increase. The term reserve growth refers to the typical increases in estimated ultimate recovery that occur as oil fields are developed and produced. [4]

## Estimated reserves by country

The unit bbl = barrel of oil. A sample calculation for the reserve/production ratio is ${\displaystyle (296.5\times 1000)/(2.1\times 365)=386.8}$for Venezuela.

Summary of Proven Reserve Data as of 2012 [3]
CountryReserves [19]
109 bbl
Reserves
109 m3
Production [20]
106 bbl/d
Production
103 m3/d
Reserve/ Production Ratio1
years
1 Venezuela 296.5047.1402.1330387
2 Saudi Arabia 265.4042.1958.91,41082
4 Iran 151.2024.0394.1650101
5 Iraq 143.1022.7513.4540115
6 Kuwait 101.5016.1372.337027
7 United Arab Emirates 97.8015.5492.438018
8 Russia 80.0012.71910.01,59015
9 Libya 47.007.4721.727076
10 Nigeria 37.005.8832.540041
11 Kazakhstan 30.004.7701.524055
12 Qatar 25.414.0401.11705
13 China 25.404.0384.165017
14 United States 25.003.9757.01,11010
15 Angola 13.502.1461.930019
16 Algeria 13.422.1341.727015
17 Brazil 13.202.0992.133017
Total of top seventeen reserves1,540.43244.90959.59,46071
Notes:
1 Reserve to Production ratio (in years), calculated as reserves / annual production. (from above)

It is estimated that between 100 and 135 billion tonnes (which equals between 133 and 180 billions m3 of oil) of the world's oil reserves have been used between 1850 and the present. [21]

## OPEC countries

Since OPEC started to set production quotas on the basis of reserves levels in the 1980s, many of its members have reported significant increases in their official reserves. [22] [23] There are doubts about the reliability of these estimates, which are not provided with any form of verification that meet external reporting standards. [22]

The sudden revisions in OPEC reserves, totaling nearly 300 bn barrels, have been much debated. [24] Some of it is defended partly by the shift in ownership of reserves away from international oil companies, some of whom were obliged to report reserves under conservative US Securities and Exchange Commission rules. [22] [25] The most prominent explanation of the revisions is prompted by a change in OPEC rules which set production quotas (partly) on reserves. In any event, the revisions in official data had little to do with the actual discovery of new reserves. [22]

Total reserves in many OPEC countries hardly changed in the 1990s. [22] Official reserves in Kuwait, for example, were unchanged at 96.5 Gbbl (15.34×109 m3) (including its share of the Neutral Zone) from 1991 to 2002, even though the country produced more than 8 Gbbl (1.3×109 m3) and did not make any important new discoveries during that period. [22] The case of Saudi Arabia is also striking, with proven reserves estimated at between 260 and 264 billion barrels (4.20×1010 m3) in the past 18 years, a variation of less than 2%, [22] while extracting approximately 60 billion barrels (9.5×109 m3) during this period.

Sadad al-Huseini, former head of exploration and production at Saudi Aramco, estimates 300 Gbbl (48×109 m3) of the world's 1,200 Gbbl (190×109 m3) of proven reserves should be recategorized as speculative resources, though he did not specify which countries had inflated their reserves. [26] Dr. Ali Samsam Bakhtiari, a former senior expert of the National Iranian Oil Company, has estimated that Iran, Iraq, Kuwait, Saudi Arabia and the United Arab Emirates have overstated reserves by a combined 320–390bn barrels and has said, "As for Iran, the usually accepted official 132 billion barrels (2.10×1010 m3) is almost one hundred billion over any realistic assay." [27] Petroleum Intelligence Weekly reported that official confidential Kuwaiti documents estimate reserves of Kuwait were only 48 billion barrels (7.6×109 m3), of which half were proven and half were possible. The combined value of proven and possible is half of the official public estimate of proven reserves. [23]

In July 2011, OPEC's Annual Statistical Review showed Venezuela's reserves to be larger than Saudi Arabia's. [28] [29]

## Prospective resources

### Arctic prospective resources

A 2008 United States Geological Survey estimates that areas north of the Arctic Circle have 90 billion barrels (1.4×1010 m3) of undiscovered, technically recoverable oil and 44 billion barrels (7.0×109 m3) of natural gas liquids in 25 geologically defined areas thought to have potential for petroleum. This represented 13% of the expected undiscovered oil in the world. Of the estimated totals, more than half of the undiscovered oil resources were estimated to occur in just three geologic provinces—Arctic Alaska, the Amerasia Basin, and the East Greenland Rift Basins. More than 70% of the mean undiscovered oil resources was estimated to occur in five provinces: Arctic Alaska, Amerasia Basin, East Greenland Rift Basins, East Barents Basins, and West Greenland–East Canada. It was further estimated that approximately 84% of the oil and gas would occur offshore. The USGS did not consider economic factors such as the effects of permanent sea ice or oceanic water depth in its assessment of undiscovered oil and gas resources. This assessment was lower than a 2000 survey, which had included lands south of the Arctic Circle. [30] [31] [32]

## Unconventional prospective resources

In October 2009, the USGS updated the quantity of the Orinoco tar sands, in Venezuela, to 513 billion barrels (8.16×1010 m3). [33]

In June 2013 the U.S. Energy Information Administration published a global inventory of estimated recoverable tight oil and tight gas resources in shale formations, "Technically Recoverable Shale Oil and Shale Gas Resources: An Assessment of 137 Shale Formations in 41 Countries Outside the United States." The inventory is incomplete due to exclusion of tight oil and gas from sources other than shale such as sandstone or carbonates, formations underlying the large oil fields located in the Middle East and the Caspian region, off shore formations, or about which there is little information. Estimated technically recoverable shale oil resources total 335 to 345 billion barrels. [34]

Energy and resources:

## Related Research Articles

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Peak oil is the theorized point in time when the maximum rate of extraction of petroleum is reached, after which it is expected to enter terminal decline. Peak oil theory is based on the observed rise, peak, fall, and depletion of aggregate production rate in oil fields over time. It is often confused with oil depletion; however, whereas depletion refers to a period of falling reserves and supply, peak oil refers to the point of maximum production. The concept of peak oil is often credited to geologist M. King Hubbert whose 1956 paper first presented a formal theory.

The question of whether to drill for oil in the Arctic National Wildlife Refuge (ANWR) has been an ongoing political controversy in the United States since 1977. As of 2017, Republicans have attempted to allow drilling in ANWR almost fifty times, finally being successful with the passage of the Tax Cuts and Jobs Act of 2017.

The Western Canadian Sedimentary Basin (WCSB) is a vast sedimentary basin underlying 1,400,000 square kilometres (540,000 sq mi) of Western Canada including southwestern Manitoba, southern Saskatchewan, Alberta, northeastern British Columbia and the southwest corner of the Northwest Territories. It consists of a massive wedge of sedimentary rock extending from the Rocky Mountains in the west to the Canadian Shield in the east. This wedge is about 6 kilometres (3.7 mi) thick under the Rocky Mountains, but thins to zero at its eastern margins. The WCSB contains one of the world's largest reserves of petroleum and natural gas and supplies much of the North American market, producing more than 16,000,000,000 cubic feet (450,000,000 m3) per day of gas in 2000. It also has huge reserves of coal. Of the provinces and territories within the WCSB, Alberta has most of the oil and gas reserves and almost all of the oil sands.

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The petroleum industry in Russia is one of the largest in the world. Russia has the largest reserves and is the largest exporter of natural gas. It has the second largest coal reserves, the eighth largest oil reserves, and is one of the largest producers of oil. It is the third largest energy user.

Proven reserves, also called measured reserves, 1P, and reserves, are industry specific terms regarding fossil fuel energy sources. They are defined as a "Quantity of energy sources estimated with reasonable certainty, from the analysis of geologic and engineering data, to be recoverable from well established or known reservoirs with the existing equipment and under the existing operating conditions." A reserve is considered a proven reserve if it is probable that 90% or more of the resource is recoverable while being economically profitable. These terms relate to common fossil fuel reserves such as oil reserves, natural gas reserves, or coal reserves.

The Bakken Formation is a rock unit from the Late Devonian to Early Mississippian age occupying about 200,000 square miles (520,000 km2) of the subsurface of the Williston Basin, underlying parts of Montana, North Dakota, Saskatchewan and Manitoba. The formation was initially described by geologist J.W. Nordquist in 1953. The formation is entirely in the subsurface, and has no surface outcrop. It is named after Henry Bakken, a farmer in Tioga, North Dakota, who owned the land where the formation was initially discovered, during drilling for oil.

The Lost Hills Oil Field is a large oil field in the Lost Hills Range, north of the town of Lost Hills in western Kern County, California, in the United States.

Proved oil reserves in Iran, according to its government, rank fourth largest in the world at approximately as of 2013, although it ranks third if Canadian reserves of unconventional oil are excluded. This is roughly 10% of the world's total proven petroleum reserves. At 2006 rates of production, Iran's oil reserves would last 98 years if no new oil was found.

The Monterey Formation is an extensive Miocene oil-rich geological sedimentary formation in California, with outcrops of the formation in parts of the California Coast Ranges, Peninsular Ranges, and on some of California's off-shore islands. The type locality is near the city of Monterey, California. The Monterey Formation is the major source-rock for 37 to 38 billion barrels of oil in conventional traps such as sandstones. This is most of California's known oil resources. The Monterey has been extensively investigated and mapped for petroleum potential, and is of major importance for understanding the complex geological history of California. Its rocks are mostly highly siliceous strata that vary greatly in composition, stratigraphy, and tectono-stratigraphic history.

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There have been widely varying estimates of proven oil reserves in Russia. Most estimates included only Western Siberian reserves, which have been exploited since the 1970s and supply two-thirds of Russian oil. However, there are potentially huge reserves elsewhere. In 2005, the Russian Ministry of Natural Resources estimated that another 4.7 billion barrels of oil exist in Eastern Siberia. In July 2013, the Russian Natural Resources Ministry made official estimates of reserves available for the first time. According to Russian Natural Resources Minister Sergey Donskoy, as of 1 January 2012, recoverable reserves of oil in Russia under category ABC1 were 17.8 billion tons and category C2 reserves were 10.9 billion tons.

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an organic rich shale, with Total Organic Content (TOC) of 1-8%, with silt and sand beds mixed in. It lies in a broad shelf, with minimal relief and has nice light oil of 38-42 gravity with excellent porosity of 6-12% in thickness varying 200 to 550 feet thick.

## References

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2. "Oil reserve definitions". bp.com. BP. Retrieved 4 December 2013.
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14. Alboudwarej; et al. (Summer 2006). "Highlighting Heavy Oil" (PDF). Oilfield Review. Archived from the original (PDF) on 2008-05-27. Retrieved 2008-05-24.
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16. E. Tzimas, (2005). "Enhanced Oil Recovery using Carbon Dioxide in the European Energy System" (PDF). European Commission Joint Research Center. Retrieved 2008-08-23.
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19. PennWell Corporation, Oil & Gas Journal, Vol. 105.48 (December 24, 2007), except United States. Oil includes crude oil and condensate. Data for the United States are from the Energy Information Administration, U.S. Crude Oil, Natural Gas, and Natural Gas Liquids Reserves, 2006 Annual Report, DOE/EIA-0216(2007) (November 2007). Oil & Gas Journal's oil reserve estimate for Canada includes 5.392 billion barrels (857,300,000 m3) of conventional crude oil and condensate reserves and 173.2 billion barrels (2.754×1010 m3) of oil sands reserves. Information collated by EIA
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34. "Technically Recoverable Shale Oil and Shale Gas Resources: An Assessment of 137 Shale Formations in 41 Countries Outside the United States" (PDF). U.S. Energy Information Administration (EIA). June 2013. Retrieved June 11, 2013.


text:
# Potential to be real?

If we have a potential with two fields psi and phi with a phase Exp(itheta) , how can we get rid of the field in order for the potential to be real?

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berkeman
Mentor
Your question is not really clear. The notation $$e^{i \theta}$$ represents a field that is oscillating at some frequency and has a phase offset from some reference phase. What do you mean to make the potential "real"? You want to make it DC instead of AC?

Your question is not really clear. The notation $$e^{i \theta}$$ represents a field that is oscillating at some frequency and has a phase offset from some reference phase. What do you mean to make the potential "real"? You want to make it DC instead of AC?
Sorry , may be I was not clear enough, but I mean by the potential, the one which appear in quantum field theory

berkeman
Mentor
Sorry , may be I was not clear enough, but I mean by the potential, the one which appear in quantum field theory
Oopsies, sorry for my misinterpretation. I'm of no help on QFT.

berkeman
Mentor
Sorry , may be I was not clear enough, but I mean by the potential, the one which appear in quantum field theory
I had someone who does understand QFT look at your question, and he doesn't understand what you are asking. Could you please provide more of a context for the question, and more details about the question?

I had someone who does understand QFT look at your question, and he doesn't understand what you are asking. Could you please provide more of a context for the question, and more details about the question?
Thank you for your effort bereman
The potential is as follow:V=Psi Phi Exp(itheta) in order for the potential to be real, we should get rid of the imaginery part , how can we do that?
Thanks again

berkeman
Mentor
Thank you for your effort bereman
The potential is as follow:V=Psi Phi Exp(itheta) in order for the potential to be real, we should get rid of the imaginery part , how can we do that?
Thanks again
I'm glad to try to help out. But what you've posted there is pretty much just a repeat of your original post. Could you please provide more context? What is the course, what is the textbook, what similar questions are from the same section of this course? Can you provide a physical example where this question would apply?

Thank you berkeman for all what have you done.
The problem by the grace of God had been solved


text:
# Do l don't come to the gym with you

###### Question:

Do l don't come to the gym with you

### In the 2006 season, Tom Brady threw for 3,529yards. In the 2007 season, he threw for 2,806yards. What is the percentage decrease

In the 2006 season, Tom Brady threw for 3,529 yards. In the 2007 season, he threw for 2,806 yards. What is the percentage decrease...

### Which number line shows the solution to inequality 3x – 3 < 12?

Which number line shows the solution to inequality 3x – 3 < 12? $Which number line shows the solution to inequality 3x – 3 < 12?$...

### What basic economic goals can be achieved easily in a traditional economy? Which cannot? Explain.

What basic economic goals can be achieved easily in a traditional economy? Which cannot? Explain....

### Selected accounts with some amounts omitted are as follows Work in Process Oct. 1 Balance 20,000 Oct.

Selected accounts with some amounts omitted are as follows Work in Process Oct. 1 Balance 20,000 Oct. 31 Finished Goods X 31 Direct materials 96,700 31 Direct labor 201,000 31 Factory overhead X Finished Goods Oct. 1 Balance 52,000 31 Goods finished 360,000 If the balance of Work in Process on Octob...
Someone answer pleaseee $Someone answer pleaseee$...


text:
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Register now and save up to 200 Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code ## ISB, Washington Olin, Tippie with big scholarships This topic has 3 member replies dip.dada Newbie | Next Rank: 10 Posts Joined 17 Feb 2011 Posted: 2 messages Upvotes: 2 #### ISB, Washington Olin, Tippie with big scholarships Fri Nov 22, 2013 7:52 am I have been a silent member of BTG for almost a year. From the initial days of my GMAT preparation to securing final admits, I have greatly benefited from this website. It is time that I give back something to the BTG community so that all B-school aspirants can benefit from my experience and words of wisdom. I will keep posting my GMAT preparation notes, application tips, interview experiences and strategies in the days to come. Do PM me if you need additional help Summary It was around 2 years ago when I first decided to pursue my MBA dream. Initially, the task seemed herculean. There were so many things to decide - which B-school to target? Which exam to take - CAT or GMAT? Where to go - US or India? Moreover, the fact that I was posted in a remote place in the interiors of West Bengal did not help me either. There was no one I could look forward to for words of advice or encouragement. There were people all around me ridiculing me for even daring to think about IIMs, ISB or any global B-school. With average communication skills and extremely humble financial background, all odds seemed to be stacked against me. Yet I dared to dream - a dream of evolving myself into a world-class professional and proving my abilities to everyone around me. Thankfully, a solid action plan (That I had created for myself for the next 2 years addressing all aspects of a career goal - what to achieve, how to achieve and when to achieve) and some good intuitive decisions paved the way for a successful journey that eventually culminated in admits from 3 business schools, with 100% success rate and hefty scholarships!! GMAT or CAT? From the very beginning, I had decided that I wouldn’t appear for CAT (the most sought after B-school entrance exam in India). The standardized nature of the GMAT exam appealed to me a lot more than that of CAT. Also, I realised that the content of the GMAT exam was more aligned to my academic strengths than that of CAT. Once the exam was finalized, I knew that I had to start my preparation in an effective manner. My posting in a remote place and the lack of awareness about MBA among my colleagues in the workplace meant that I had to rely solely on my own dedication and hard work complemented by the right guidance. I wanted to get a top into a top B-school in my first attempt itself. Hence, ensuring the correct mentor for my GMAT Preparation as well as the admissions process was the core of my entire MBA dream. Preparing for GMAT I realised that I did not need a commercialized coaching; rather, I needed the help of a ‘Mentor’ who would not only provide me with genuine help in all aspects of preparation but would also understand me as a person, my aspirations, my apprehensions, and my weaknesses thereby providing me with authentic guidance all along. I needed a true mentor who would provide personalized guidance rather than a high-profile commercial consultant for whom student benefit and satisfaction comes next to money. After weeks of frantic internet searches and after talking to many people involved in GMAT coaching, I eventually zeroed in on Experts Global after realising that it was the only institute which seemed to match my criteria exactly. To speak truly, the simplicity and yet, the power-packed content of the website, the feedback from students in the testimonials, and a brief conversation with their founder really bowled me over. It was the most important and intuitive decision that I had taken (considering that I didn’t take the opinion of anyone or didn’t go by any referral) and needless to say, I wouldn’t be in a position of writing this story of mine without Experts Global. However, soon after I enrolled with Experts, I realised that the guidance provided to me would be useless if I didn’t put in sufficient effort and hard work from my side. This is true not only for Experts but for any consultant that you might end up choosing. In the next 4-5 months, I used to study for at least 2-3 hours daily going through almost all materials provided to me. I also used to visit several forums like Beat the GMAT, Pagalguy, GMAT Club, etc. getting valuable preparation strategies and tips from successful GMAT takers. I also took almost all available practice tests like Manhattan Test Series, Veritas Prep, Kaplan, GMAT Powerprep, etc. under perfectly timed and simulated conditions. Carrying on the preparation alongside my job was really very tough and it was solely my dedication, hard work and motivation that propelled me forward. Mr Mayank Srivastava, my mentor at Experts was really very helpful and was only a call or e-mail way during the entire stage of GMAT preparation. His prompt help and reply to all my questions, doubts or inhibitions ensured that my morale was high throughout and that I didn’t lose faith in myself. I ended up getting a decent GMAT score of 730. Although the score was a bit low considering the fact that I had reached a score of 760 in one of the practice tests, my mentor at Experts advised me not to re-take the GMAT and instead focus on the applications. This is the most common mistake made my many applicants. They tend to focus so much on the GMAT exam that they end up ignoring or giving less effort in the entire applications process. At the end of the day, one should remember that GMAT score is only one parameter and a final B-school admit is dependent on so many other parameters like undergrad performance, work-experience, extra-curricular activities, social work, leadership potential, communication skills, interview performance and so on. My success in securing admits from all the 3 b-schools that I had applied to with scholarships reinforces this fact. The Application Process Though I took my GMAT in 2012, I decided to apply for the 2014 intake as I realized the lack of professional affluence in my profile and felt the need for an extra year of work-ex to have elaborate stories to talk about. Hence, I had the luxury of devoting an entire year for the applications!! I started my application process with Experts Global in end of 2012 and, over the next one year, worked sincerely at workplace while managing the applications work alongside. For the applications preparation, I was assigned another mentor Mr Shailesh Otari, who worked with me in brainstorming all minute aspects of my profile which showcased all the parameters that I have mentioned in the previous paragraph. Through the various discussions with my mentor, I realised that I had already achieved so much in life without actually realising it. This is the single most important aspect of the entire applications process. For most B-schools, the applications are so designed that one gets a chance to reflect on their own lives and accomplishments, which we take for granted in the hustle and bustle of our daily lives. The mentor made me realise that I was already a winner and the essays simply reflected what I had already achieved but in a much more presentable and precise fashion. To all future aspirants, my advice would be not to take the applications guidance as an essay-editing service but rather as a learning avenue where you get an opportunity for self-introspection. Need for Scholarship Since, I am from a very humble background, my budget for applying to B-schools was highly constrained. Also, scholarships, placements and ROI were important aspects in deciding which B-schools I needed to apply to. My mentors at Experts understood my requirement and made me apply to ISB, Olin and Tippie. After an effective guidance in the entire applications, I was also provided with thorough preparation for interviews. It was at this stage that I realised that the brainstorming sessions during the applications guidance were extremely helpful in giving convincing answers to every question imaginable during the interviews. The mock-interviews helped me fine-tune my responses and my endless online research work of the three B-schools ensured that I was fully prepared for the interviews. The Results For someone like me coming from a PSU background, with only average communication skills and experience of only one interview in my lifetime (during campus placements in my college!!), cracking 3 tough interviews in a span of 1 month was really the experience of a lifetime. Moreover, the 100% scholarship from Tippie,40000 scholarship from Olin and finally the Rs. 5 lakh scholarship from my dream school, ISB was really an icing on the cake.

Sincere thanks to my mentors at Experts Global Training Services

A sincere word of thanks to Mayank Sir and Shailesh Sir - You have made my dream come true and I will always remember your support over almost two years. Students will always be in safe hands as long as people like you exist!!

My 2 cents of wisdom to all MBA aspirants

Hard work and sincerity are the two aspects that can get you through to any B-school that you aspire to be in. Never stop believing in yourself and learn to go by your instincts. I am sure that in a year or so from now, you will be writing one of these “success-story” posts for the next generation of MBA aspirants!

All the best !!
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Thanked by: faraz_jeddah, johnystorm
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prakhargupta Newbie | Next Rank: 10 Posts
Joined
03 Jan 2012
Posted:
3 messages
Mon Feb 24, 2014 10:50 pm
Hey.
So did you join Experts Global? If yes, what kind of experience you had with them?

Regards,
Prakhar

samranhabib wrote:

I have gone through your both threads and I would say that it was really inspiring and after seeing your success and especially in scholarships, I have started considering Experts Global. I have contacted them and will see how and where to start.

Anyways great posts and congrats for your success and wish you best of luck for your studies.

By the way could you update which option you have chosen and why?

It will be great to listen from you.

samranhabib Newbie | Next Rank: 10 Posts
Joined
02 Aug 2010
Posted:
3 messages
2
Test Date:
29 Jan 2014
Target GMAT Score:
760
Wed Dec 04, 2013 10:38 pm

I have gone through your both threads and I would say that it was really inspiring and after seeing your success and especially in scholarships, I have started considering Experts Global. I have contacted them and will see how and where to start.

Anyways great posts and congrats for your success and wish you best of luck for your studies.

By the way could you update which option you have chosen and why?

It will be great to listen from you.

prakhargupta Newbie | Next Rank: 10 Posts
Joined
03 Jan 2012
Posted:
3 messages
Mon Feb 24, 2014 10:50 pm
Hey.
So did you join Experts Global? If yes, what kind of experience you had with them?

Regards,
Prakhar

samranhabib wrote:

I have gone through your both threads and I would say that it was really inspiring and after seeing your success and especially in scholarships, I have started considering Experts Global. I have contacted them and will see how and where to start.

Anyways great posts and congrats for your success and wish you best of luck for your studies.

By the way could you update which option you have chosen and why?

It will be great to listen from you.

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text:
# intersect_line (method)¶

intersect_line(self, Z1, Z2)[source]

Return a list (0, 1 or 2 complex) of coordinates of the intersection of the arc with a line defined by two complex

Parameters: self (Arc) – An Arc object Z_list – Complex coordinates of the intersection (if any) list


text:
Home OALib Journal OALib PrePrints Submit Ranking News My Lib FAQ About Us Follow Us+
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Search Results: 1 - 10 of 100 matches for " "
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 Louis Crane Physics , 2006, Abstract: We explore the possibility of replacing point set topology by higher category theory and topos theory as the foundation for quantum general relativity. We discuss the BC model and problems of its interpretation, and connect with the construction of causal sites.
 Physics , 2003, Abstract: It was generally believed that, in general relativity, the fundamental laws of nature should be invariant or covariant under a general coordinate transformation. In general relativity, the equivalence principle tells us the existence of a local inertial coordinate system and the fundamental laws in the local inertial coordinate system which are the same as those in inertial reference system. Then, after a general coordinate transformation, the fundamental laws of nature in arbitrary coordinate system or in arbitrary curved space-time can be obtained. However, through a simple example, we find that, under a general coordinate transformation, basic physical equations in general relativity do not transform covariantly, especially they do not preserve their forms under the transformation from a local inertial coordinate system to a curved space-time. The origination of the violation of the general covariance is then studied, and a general theory on general coordinate transformations is developed. Because of the the existence of the non-homogeneous term, the fundamental laws of nature in arbitrary curved space-time can not be expressed by space-time metric, physical observable and their derivatives. In other words, basic physical equations obtained from the equivalence principle and the principle of general covariance are different from those in general relativity. Both the equivalence principle and the principle of general covariance can not be treated as foundations of general relativity. So, what are the foundations of General Relativity? Such kind of essential problems on General Relativity can be avoided in the physical picture of gravity. Quantum gauge theory of gravity, which is founded in the physics picture of gravity, does not have such kind of fundamental problems.
 Jean-Francois Pommaret Journal of Modern Physics (JMP) , 2014, DOI: 10.4236/jmp.2014.55026 Abstract: We start recalling with critical eyes the mathematical methods used in gauge theory and prove that they are not coherent with continuum mechanics, in particular the analytical mechanics of rigid bodies (despite using the same group theoretical methods) and the well known couplings existing between elasticity and electromagnetism (piezzo electricity, photo elasticity, streaming birefringence). The purpose of this paper is to avoid such contradictions by using new mathematical methods coming from the formal theory of systems of partial differential equations and Lie pseudo groups. These results finally allow unifying the previous independent tentatives done by the brothers E. and F. Cosserat in 1909 for elasticity or H. Weyl in 1918 for electromagnetism by using respectively the group of rigid motions of space or the conformal group of space-time. Meanwhile we explain why the Poincaré duality scheme existing between geometry and physics has to do with homological algebra and algebraic analysis. We insist on the fact that these results could not have been obtained before 1975 as the corresponding tools were not known before.
 Charles Francis Physics , 1999, Abstract: The k-calculus was advocated by Hermann Bondi as a means of explaining special relativity using only GCSE level mathematics and ideas. We review the central derivations, using proofs which are only a little more elegant than those in Bondi's books, and extend his development to include the scalar product and the mass shell condition. As used by Bondi, k is the Doppler red shift, and we extend the k calculus to include the gravitational red shift and give a derivation of Newton's law of gravity using only 'A' level calculus and basic quantum mechanics.
 Sanjay M. Wagh Physics , 2005, Abstract: Earlier, we had presented \cite{heuristic} heuristic arguments to show that a {\em natural unification} of the ideas of the quantum theory and those underlying the general principle of relativity is achievable by way of the measure theory and the theory of dynamical systems. Here, in Part I, we provide the complete physical foundations for this, to be called, the {\em Universal Theory of Relativity}. Newton's theory and the special theory of relativity arise, situationally, in this Universal Relativity. Explanations of quantum indeterminacy are also shown to arise in it. Part II provides its mathematical foundations. One experimental test is also discussed before concluding remarks.
 Mathematics , 2010, Abstract: We provide an introduction to selected recent advances in the mathematical understanding of Einstein's theory of gravitation.
 Miguel A. Oliveira Physics , 2011, Abstract: In this work we generalize an earlier treatment of the measurements of velocities at the event horizon of a black hole. This is intended as a pedagogical exercise as well as one more contribution to the resolution of some unphysical interpretations related to velocity measurements by generalized observers. We now use a more general metric and, non-geodesic observer sets to show that the velocity of a test particle at the event horizon is less than the speed of light.
 Physics , 2001, DOI: 10.1142/S0218271897000029 Abstract: Everyday experience with centrifugal forces has always guided thinking on the close relationship between gravitational forces and accelerated systems of reference. Once spatial gravitational forces and accelerations are introduced into general relativity through a splitting of spacetime into space-plus-time associated with a family of test observers, one may further split the local rest space of those observers with respect to the direction of relative motion of a test particle world line in order to define longitudinal and transverse accelerations as well. The intrinsic covariant derivative (induced connection) along such a world line is the appropriate mathematical tool to analyze this problem, and by modifying this operator to correspond to the observer measurements, one understands more clearly the work of Abramowicz et al who define an optical centrifugal force'' in static axisymmetric spacetimes and attempt to generalize it and other inertial forces to arbitrary spacetimes. In a companion article the application of this framework to some familiar stationary axisymmetric spacetimes helps give a more intuitive picture of their rotational features including spin precession effects, and puts related work of de Felice and others on circular orbits in black hole spacetimes into a more general context.
 Abhay Ashtekar Physics , 1994, Abstract: After a brief chronological sketch of developments in non-perturbative canonical quantum gravity, some of the recent mathematical results are reviewed. These include: i) an explicit construction of the quantum counterpart of Wheeler's superspace; ii) a rigorous procedure leading to the general solution of the diffeomorphism constraint in quantum geometrodynamics as well as connection dynamics; and, iii) a scheme to incorporate the reality conditions in quantum connection dynamics. Furthermore, there is a new language to formulate the central questions and techniques to answer them. These developments put the program on a sounder footing and, in particular, address certain concerns and reservations about consistency of the overall scheme.
 Physics , 2002, DOI: 10.1088/0264-9381/22/4/C02 Abstract: The aim of this paper is twofold. First, we set up the theory of elastic matter sources within the framework of general relativity in a self-contained manner. The discussion is primarily based on the presentation of Carter and Quintana but also includes new methods and results as well as some modifications that in our opinion make the theory more modern and transparent. For instance, the equations of motion for the matter are shown to take a neat form when expressed in terms of the relativistic Hadamard elasticity tensor. Using this formulation we obtain simple formulae for the speeds of elastic wave propagation along eigendirections of the pressure tensor. Secondly, we apply the theory to static spherically symmetric configurations using a specific equation of state and consider models either having an elastic crust or core.
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text:
# Elucidation of Reaction Mechanisms - Kinetic Isotope Effects

## Kinetic Solvent Isotope Effects

In many cases, the reaction rate is influenced by an isotopic exchange even if it is an atom of the solvent, rather than that of a reactant that has been exchanged for one of its isotopes. Such an effect is called kinetic solvent isotope effect. This effect can occur, for instance, when the solvent $H2O$ is exchanged for $D2O$, or when $C2H5OH$ is exchanged for $C2H5OD$.

Principally speaking, kinetic solvent isotope effects depict all known values from primary and secondary kinetic isotope effects (kH/kD about 0.7 to 8). This range of kH/kD values is the result of the fact that kinetic solvent isotope effects, in reality, are "hidden" primary or secondary kinetic isotope effects.

Take a look at the acid-catalysed cleavage of ethyl vinyl ether, for instance.

Fig.1
Acid-catalysed cleavage of ethyl vinyl ether.

Essentially, there are three factors that lead to kinetic solvent isotope effects:

1. Solvent molecules participate as reactants in the reaction. Depending on the other preconditions, actual primary or secondary kinetic isotope effects then appear. In the ethyl vinyl ether cleavage, for example, the solvent molecule $H3O+$ serves as a reactant. In connection with H1, a primary kinetic isotope effect occurs, while a secondary kinetic isotope effect results with H2 and H3.
2. The of the reaction can be stabilized by interactions between the reactants and solvent molecules. The extent of these interactions in isotope-substituted solvents can differ from that in the original solvent. As a result, the transition state's energy and thus, the $Ea$ of the respective reaction step (elementary reaction) are altered. If this particular reaction step is the rate-determining step, the result is a kinetic isotope effect. The positively charged transition state of the ethyl vinyl ether cleavage, for example, interacts with the polar water molecules to a considerable degree.
3. Especially in acidic, deuterated solvents (e.g. $D2O$ or $C2H5OD$), an H/D exchange or a D transfer between the solvent molecules and the reactants can occur. Consequently, an actual primary or secondary kinetic isotope effect is obtained. After it has been transferred to ethyl vinyl ether, D (H2) could cause a secondary kinetic isotope effect if the rate-determining step still follows.

Data about the the rate-determining step and the structure of the transition state, as well as the participation of solvent molecules in the reaction by either solvating the transition state or acting as reactants can be inferred from kinetic solvent isotope effects and not only from pure and obvious primary or secondary kinetic isotope effects. It should be taken into consideration that the formerly mentioned causes of kinetic isotope effects can occur simultaneously and can enhance each other, as is the case in the ethyl vinyl ether cleavage.

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