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Dominion Day
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Dominion Day was a day commemorating the granting of dominion status in certain countries. It was an official public holiday in Canada from 1879 to 1982, where it was celebrated on 1 July. That date is now known as Canada Day. There was also a Dominion Day public holiday in the Dominion of Newfoundland from 1907 to 1949, celebrated on 26 September.
Contents
1 Canada
2 Newfoundland
3 New Zealand
4 References
5 Notes
Canada[edit]
See also: Canada Day
Crowds on Parliament Hill, Ottawa celebrate Dominion Day, 1927, the 60th jubilee of Canadian confederation
Dominion Day was the name of the holiday commemorating the formation of Canada as a Dominion on 1 July 1867. It became an official public holiday in 1879.[1] The holiday was renamed to Canada Day by Act of Parliament on 27 October 1982.
Newfoundland[edit]
See also: Canada Day
Dominion Day was the name of the holiday commemorating the formation of Newfoundland as a Dominion on 26 September 1907 (same day as New Zealand) and was celebrated until it entered into confederation with Canada in 1949.[citation needed]
New Zealand[edit]
See also: Independence of New Zealand and Dominion of New Zealand
Dominion Day was occasionally celebrated in New Zealand to commemorate the anniversary of the granting of dominion status (26 September 1907). It was never a public holiday, although the first Dominion Day was a day off for public servants.[2] Dominion Day soon "faded away as a public event" – there were occasional celebrations in the first few years after 1907, but they were mainly formal events that did not capture the attention of the public.[3] There has been support in some quarters[4] for the day to be revived as an alternative New Zealand Day, instead of renaming Waitangi Day, New Zealand's current national day.
References[edit]
Jump up ^ Why We Should Bring Back Dominion Day , HuffPost Canada, 1 July 2014.
Jump up ^ Dominion status: Page 3 – The first Dominion Day, NZ History.
Jump up ^ Dominion status: Page 4 – Demise of Dominion Day, NZ History.
Jump up ^ "Editorial: Dominion Day debate needless - National - NZ Herald News". The New Zealand Herald. Retrieved 15 January 2016.
Notes[edit]
Retrieved from "https://en.wikipedia.org/w/index.php?title=Dominion_Day&oldid=824088938"
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Finite potential well
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The finite potential well (also known as the finite square well) is a concept from quantum mechanics. It is an extension of the infinite potential well, in which a particle is confined to a box, but one which has finite potential walls. Unlike the infinite potential well, there is a probability associated with the particle being found outside the box. The quantum mechanical interpretation is unlike the classical interpretation, where if the total energy of the particle is less than the potential energy barrier of the walls it cannot be found outside the box. In the quantum interpretation, there is a non-zero probability of the particle being outside the box even when the energy of the particle is less than the potential energy barrier of the walls (cf quantum tunnelling).
Contents
[hide]
1 Particle in a 1-dimensional box
1.1 Inside the box
1.2 Outside the box
1.3 Finding wavefunctions for the bound state
1.4 Unbound states
2 Spherical cavity
3 See also
4 References
Particle in a 1-dimensional box[edit]
For the 1-dimensional case on the x-axis, the time-independent Schrödinger equation can be written as:
− ℏ 2 2 m d 2 ψ d x 2 + V ( x ) ψ = E ψ ( 1 ) {\displaystyle -{\frac {\hbar ^{2}}{2m}}{\frac {d^{2}\psi }{dx^{2}}}+V(x)\psi =E\psi \quad (1)}
where
ℏ = h 2 π {\displaystyle \hbar ={\frac {h}{2\pi }}} ,
h {\displaystyle h\,} is Planck's constant,
m {\displaystyle m\,} is the mass of the particle,
ψ {\displaystyle \psi \,} is the (complex valued) wavefunction that we want to find,
V ( x ) {\displaystyle V\left(x\right)\,} is a function describing the potential energy at each point x, and
E {\displaystyle E\,} is the energy, a real number, sometimes called eigenenergy.

For the case of the particle in a 1-dimensional box of length L, the potential is V 0 {\displaystyle V_{0}} outside the box, and zero for x between − L / 2 {\displaystyle -L/2} and L / 2 {\displaystyle L/2} . The wavefunction is considered to be made up of different wavefunctions at different ranges of x, depending on whether x is inside or outside of the box. Therefore, the wavefunction is defined such that:
ψ = { ψ 1 , if x < − L / 2 (the region outside the box) ψ 2 , if − L / 2 < x < L / 2 (the region inside the box) ψ 3 if x > L / 2 (the region outside the box) {\displaystyle \psi ={\begin{cases}\psi _{1},&{\mbox{if }}x<-L/2{\mbox{ (the region outside the box)}}\\\psi _{2},&{\mbox{if }}-L/2<x<L/2{\mbox{ (the region inside the box)}}\\\psi _{3}&{\mbox{if }}x>L/2{\mbox{ (the region outside the box)}}\end{cases}}}
Inside the box[edit]
For the region Inside the box V(x) = 0 and Equation 1 reduces to
− ℏ 2 2 m d 2 ψ 2 d x 2 = E ψ 2 . {\displaystyle -{\frac {\hbar ^{2}}{2m}}{\frac {d^{2}\psi _{2}}{dx^{2}}}=E\psi _{2}.}
Letting
k = 2 m E ℏ , {\displaystyle k={\frac {\sqrt {2mE}}{\hbar }},}
the equation becomes
d 2 ψ 2 d x 2 = − k 2 ψ 2 . {\displaystyle {\frac {d^{2}\psi _{2}}{dx^{2}}}=-k^{2}\psi _{2}.}
This is a well-studied differential equation and eigenvalue problem with a general solution of
ψ 2 = A sin  ( k x ) + B cos  ( k x ) . {\displaystyle \psi _{2}=A\sin(kx)+B\cos(kx)\quad .}
Hence,
E = k 2 ℏ 2 2 m . {\displaystyle E={\frac {k^{2}\hbar ^{2}}{2m}}.}
Here, A and B can be any complex numbers, and k can be any real number.
Outside the box[edit]
For the region Outside of the box, since the potential is constant, V(x) = V 0 {\displaystyle V_{0}} and Equation 1 becomes:
− ℏ 2 2 m d 2 ψ 1 d x 2 = ( E − V 0 ) ψ 1 {\displaystyle -{\frac {\hbar ^{2}}{2m}}{\frac {d^{2}\psi _{1}}{dx^{2}}}=(E-V_{0})\psi _{1}}
There are two possible families of solutions, depending on whether E is less than V 0 {\displaystyle V_{0}} (the particle is bound in the potential) or E is greater than V 0 {\displaystyle V_{0}} (the particle is free).
For a free particle, E > V o {\displaystyle V_{o}} , and letting
k ′ = 2 m ( E − V 0 ) ℏ {\displaystyle k'={\frac {\sqrt {2m(E-V_{0})}}{\hbar }}}
produces
d 2 ψ 1 d x 2 = − k ′ 2 ψ 1 {\displaystyle {\frac {d^{2}\psi _{1}}{dx^{2}}}=-k'^{2}\psi _{1}}
with the same solution form as the inside-well case:
ψ 1 = C sin  ( k ′ x ) + D cos  ( k ′ x ) {\displaystyle \psi _{1}=C\sin(k'x)+D\cos(k'x)\quad }
This analysis will focus on the bound state, where V 0 {\displaystyle V_{0}} > E. Letting
α = 2 m ( V 0 − E ) ℏ {\displaystyle \alpha ={\frac {\sqrt {2m(V_{0}-E)}}{\hbar }}}
produces
d 2 ψ 1 d x 2 = α 2 ψ 1 {\displaystyle {\frac {d^{2}\psi _{1}}{dx^{2}}}=\alpha ^{2}\psi _{1}}
where the general solution is exponential:
ψ 1 = F e − α x + G e α x {\displaystyle \psi _{1}=Fe^{-\alpha x}+Ge^{\alpha x}\,\!}
Similarly, for the other region outside the box:
ψ 3 = H e − α x + I e α x {\displaystyle \psi _{3}=He^{-\alpha x}+Ie^{\alpha x}\,\!}
Now in order to find the specific solution for the problem at hand, we must specify the appropriate boundary conditions and find the values for A, B, F, G, H and I that satisfy those conditions.
Finding wavefunctions for the bound state[edit]
Solutions to the Schrödinger equation must be continuous, and continuously differentiable.[1] These requirements are boundary conditions on the differential equations previously derived, that is, the matching conditions between the solutions inside and outside the well.
In this case, the finite potential well is symmetrical, so symmetry can be exploited to reduce the necessary calculations.
Summarizing the previous section:
ψ = { ψ 1 , if x < − L / 2 (the region outside the box) ψ 2 , if − L / 2 < x < L / 2 (the region inside the box) ψ 3 if x > L / 2 (the region outside the box) {\displaystyle \psi ={\begin{cases}\psi _{1},&{\mbox{if }}x<-L/2{\mbox{ (the region outside the box)}}\\\psi _{2},&{\mbox{if }}-L/2<x<L/2{\mbox{ (the region inside the box)}}\\\psi _{3}&{\mbox{if }}x>L/2{\mbox{ (the region outside the box)}}\end{cases}}}
where we found ψ 1 , ψ 2 {\displaystyle \psi _{1},\psi _{2}\,\!} and ψ 3 {\displaystyle \psi _{3}\,\!} to be:
ψ 1 = F e − α x + G e α x {\displaystyle \psi _{1}=Fe^{-\alpha x}+Ge^{\alpha x}\,\!}
ψ 2 = A sin  ( k x ) + B cos  ( k x ) {\displaystyle \psi _{2}=A\sin(kx)+B\cos(kx)\quad }
ψ 3 = H e − α x + I e α x {\displaystyle \psi _{3}=He^{-\alpha x}+Ie^{\alpha x}\,\!}
We see that as x {\displaystyle x} goes to − ∞ {\displaystyle -\infty } , the F {\displaystyle F} term goes to infinity. Likewise, as x {\displaystyle x} goes to + ∞ {\displaystyle +\infty } , the I {\displaystyle I} term goes to infinity. In order for the wave function to be square integrable, we must set F = I = 0 {\displaystyle F=I=0} , and we have:
ψ 1 = G e α x {\displaystyle \psi _{1}=Ge^{\alpha x}\,\!} and ψ 3 = H e − α x {\displaystyle \psi _{3}=He^{-\alpha x}\,\!}
Next, we know that the overall ψ {\displaystyle \psi \,\!} function must be continuous and differentiable. In other words, the values of the functions and their derivatives must match up at the dividing points:
ψ 1 ( − L / 2 ) = ψ 2 ( − L / 2 ) {\displaystyle \psi _{1}(-L/2)=\psi _{2}(-L/2)\,\!} ψ 2 ( L / 2 ) = ψ 3 ( L / 2 ) {\displaystyle \psi _{2}(L/2)=\psi _{3}(L/2)\,\!}
d ψ 1 d x ( − L / 2 ) = d ψ 2 d x ( − L / 2 ) {\displaystyle {\frac {d\psi _{1}}{dx}}(-L/2)={\frac {d\psi _{2}}{dx}}(-L/2)\,\!} d ψ 2 d x ( L / 2 ) = d ψ 3 d x ( L / 2 ) {\displaystyle {\frac {d\psi _{2}}{dx}}(L/2)={\frac {d\psi _{3}}{dx}}(L/2)\,\!}
These equations have two sorts of solutions, symmetric, for which A = 0 {\displaystyle A=0} and G = H {\displaystyle G=H} , and antisymmetric, for which B = 0 {\displaystyle B=0} and G = − H {\displaystyle G=-H} . For the symmetric case we get
H e − α L / 2 = B cos  ( k L / 2 ) {\displaystyle He^{-\alpha L/2}=B\cos(kL/2)}
− α H e − α L / 2 = − k B sin  ( k L / 2 ) {\displaystyle -\alpha He^{-\alpha L/2}=-kB\sin(kL/2)}
so taking the ratio gives
α = k tan  ( k L / 2 ) {\displaystyle \alpha =k\tan(kL/2)} .
Similarly for the antisymmetric case we get
α = − k cot  ( k L / 2 ) {\displaystyle \alpha =-k\cot(kL/2)} .
Recall that both α {\displaystyle \alpha } and k {\displaystyle k} depend on the energy. What we have found is that the continuity conditions cannot be satisfied for an arbitrary value of the energy. Only certain energy values, which are solutions to one or either of these two equations, are allowed. Hence we find that the energy levels of the system below V 0 {\displaystyle V_{0}} are discrete; the corresponding eigenfunctions are bound states. (By contrast, for the energy levels above V 0 {\displaystyle V_{0}} are continuous.[2])
The energy equations cannot be solved analytically. Nevertheless, we will see that in the symmetric case, there always exists at least one bound state, even if the well is very shallow.[3] Graphical or numerical solutions to the energy equations are aided by rewriting them a little. If we introduce the dimensionless variables u = α L / 2 {\displaystyle u=\alpha L/2} and v = k L / 2 {\displaystyle v=kL/2} , and note from the definitions of α {\displaystyle \alpha } and k {\displaystyle k} that u 2 = u 0 2 − v 2 {\displaystyle u^{2}=u_{0}^{2}-v^{2}} , where u 0 2 = m L 2 V 0 / 2 ℏ 2 {\displaystyle u_{0}^{2}=mL^{2}V_{0}/2\hbar ^{2}} , the master equations read
u 0 2 − v 2 = { v tan  v , (symmetric case) − v cot  v , (antisymmetric case) {\displaystyle {\sqrt {u_{0}^{2}-v^{2}}}={\begin{cases}v\tan v,&{\mbox{(symmetric case) }}\\-v\cot v,&{\mbox{(antisymmetric case) }}\end{cases}}}
In the plot to the right, for u 0 2 = 20 {\displaystyle u_{0}^{2}=20} , solutions exist where the blue semicircle intersects the purple or grey curves ( v tan  v {\displaystyle v\tan v} and − v cot  v {\displaystyle -v\cot v} ). Each purple or grey curve represents a possible solution, v i {\displaystyle v_{i}} within the range π 2 ( i − 1 ) ≤ v i < π 2 i {\displaystyle {\frac {\pi }{2}}(i-1)\leq v_{i}<{\frac {\pi }{2}}i} . The total number of solutions, N {\displaystyle N} , (i.e., the number of purple/grey curves that are intersected by the blue circle) is therefore determined by dividing the radius of the blue circle, u 0 {\displaystyle u_{0}} , by the range of each solution π / 2 {\displaystyle \pi /2} .
N = ⌊ 2 u 0 π ⌋ + 1 = ⌈ 2 u 0 π ⌉ {\displaystyle N=\left\lfloor {\frac {2u_{0}}{\pi }}\right\rfloor +1=\left\lceil {\frac {2u_{0}}{\pi }}\right\rceil }
In this case there are exactly three solutions, since N = ⌊ 2 20 / π ⌋ + 1 = ⌊ 2.85 ⌋ + 1 = 2 + 1 = 3 {\displaystyle N=\lfloor 2{\sqrt {20}}/\pi \rfloor +1=\lfloor 2.85\rfloor +1=2+1=3} .
v 1 = 1.28 , v 2 = 2.54 {\displaystyle v_{1}=1.28,v_{2}=2.54} and v 3 = 3.73 {\displaystyle v_{3}=3.73} , with the corresponding energies
E n = 2 ℏ 2 v n 2 m L 2 {\displaystyle E_{n}={2\hbar ^{2}v_{n}^{2} \over mL^{2}}} .
If we want, we can go back and find the values of the constants A , B , G , H {\displaystyle A,B,G,H} in the equations now (we also need to impose the normalisation condition). On the right we show the energy levels and wave functions in this case (where x 0 ≡ ℏ / 2 m V 0 {\displaystyle x_{0}\equiv \hbar /{\sqrt {2mV_{0}}}} ):
We note that however small u 0 {\displaystyle u_{0}} is (however shallow or narrow the well), there is always at least one bound state.
Two special cases are worth noting. As the height of the potential becomes large, V 0 → ∞ {\displaystyle V_{0}\to \infty } , the radius of the semicircle gets larger and the roots get closer and closer to the values v n = n π / 2 {\displaystyle v_{n}=n\pi /2} , and we recover the case of the infinite square well.
The other case is that of a very narrow, deep well - specifically the case V 0 → ∞ {\displaystyle V_{0}\to \infty } and L → 0 {\displaystyle L\to 0} with V 0 L {\displaystyle V_{0}L} fixed. As u 0 ∝ V 0 L 2 {\displaystyle u_{0}\propto V_{0}L^{2}} it will tend to zero, and so there will only be one bound state. The approximate solution is then v 2 = u 0 2 − u 0 4 {\displaystyle v^{2}=u_{0}^{2}-u_{0}^{4}} , and the energy tends to E = − m L 2 V 0 2 / 2 ℏ 2 {\displaystyle E=-mL^{2}V_{0}^{2}/2\hbar ^{2}} . But this is just the energy of the bound state of a Delta function potential of strength V 0 L {\displaystyle V_{0}L} , as it should be.
A simpler graphical solution for the energy levels can be obtained by normalizing the potential and the energy through multiplication by 8 m L 2 / h 2 {\displaystyle {8m}{L^{2}}/h^{2}} . The normalized quantities are
V ~ 0 = V 0 8 m h 2 L 2 E ~ = E 8 m h 2 L 2 {\displaystyle {\tilde {V}}_{0}=V_{0}{\frac {8m}{h^{2}}}L^{2}\qquad {\tilde {E}}=E{\frac {8m}{h^{2}}}L^{2}}
giving directly the relation between the allowed couples ( V 0 , E ) {\displaystyle (V_{0},E)} as[4]
V ~ 0 = E ~ | sec  ( E ~ π / 2 ) | , V ~ 0 = E ~ | csc  ( E ~ π / 2 ) | {\displaystyle {\sqrt {{\tilde {V}}_{0}}}={\sqrt {\tilde {E}}}\,\left|{\sec({\sqrt {\tilde {E}}}\,{\pi }/{2})}\right|,\qquad {\sqrt {{\tilde {V}}_{0}}}={\sqrt {\tilde {E}}}\,\left|{\csc({\sqrt {\tilde {E}}}\,{\pi }/{2})}\right|}
for the even and odd parity wave functions, respectively. In the previous equations only the positive derivative parts of the functions have to be considered. The chart giving directly the allowed couples ( V 0 , E ) {\displaystyle (V_{0},E)} is reported in the figure.
Note: The above derivation does not consider the possibility that the effective mass of the particle could be different inside the potential well and the region outside the well.
Unbound states[edit]
If we solve the time-independent Schrödinger equation for an energy E > V 0 {\displaystyle E>V_{0}} , the solutions will be oscillatory both inside and outside the well. Thus, the solution is never square integrable; that is, it is always a non-normalizable state. This does not mean, however, that it is impossible for a quantum particle to have energy greater than V 0 {\displaystyle V_{0}} , it merely means that the system has continuous spectrum above V 0 {\displaystyle V_{0}} . The non-normalizable eigenstates are close enough to being square integrable that they still contribute to the spectrum of the Hamiltonian as an unbounded operator.[5]
Spherical cavity[edit]
The results above can be used to show that, contrary to the one-dimensional case, there is not always a bound state in a spherical cavity.
The ground state of a spherically symmetric potential will always have zero orbital angular momentum, and the reduced wave function U ( r ) ≡ r ψ ( r ) {\displaystyle U(r)\equiv r\psi (r)} satisfies the equation
− ℏ 2 2 m d 2 U d r 2 + V ( r ) U ( r ) = E U ( r ) {\displaystyle -{\frac {\hbar ^{2}}{2m}}{d^{2}U \over dr^{2}}+V(r)U(r)=EU(r)}
This is identical to the one-dimensional equation, except for the boundary conditions. As before, U ( r ) {\displaystyle U(r)} and its first derivative must be continuous at the edge of the well r = R {\displaystyle r=R} . However, there is another condition, that ψ ( 0 ) {\displaystyle \psi (0)} must be finite, and that requires U ( 0 ) = 0 {\displaystyle U(0)=0} .
By comparison with the solutions above, we can see that only the antisymmetric ones have nodes at the origin. Thus only the solutions to α = − k cot  ( k R ) {\displaystyle \alpha =-k\cot(kR)} are allowed. These correspond to the intersection of the semicircle with the grey curves, and so if the cavity is too shallow or small, there will be no bound state.
See also[edit]
Potential well
Delta function potential
Infinite potential well
Semicircle potential well
Quantum tunnelling
References[edit]
Jump up ^ Hall 2013 Proposition 5.1
Jump up ^ Hall 2013 Section 5.5
Jump up ^ Hall 2013 Proposition 5.3
Jump up ^ Chiani, M. (2016). "A chart for the energy levels of the square quantum well". arXiv:1610.04468  [physics.gen-ph].
Jump up ^ Hall 2013 Section 5.5 and Exercise 4 in Chapter 3
Griffiths, David J. (2005). Introduction to Quantum Mechanics (2nd ed.). Prentice-Hall. ISBN 0-13-111892-7.
Hall, Brian C. (2013), Quantum Theory for Mathematicians, Graduate Texts in Mathematics, 267, Springer .
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Chicken Little
From Wikipedia, the free encyclopedia
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This article is about the folk tale. For other uses, see Chicken Little (disambiguation).
Chicken Little, also known as Henny Penny and sometimes as Chicken Licken, is a European folk tale with a moral in the form of a cumulative tale about a chicken who believes the world is coming to an end. The phrase "The sky is falling!" featured prominently in the story, and has passed into the English language as a common idiom indicating a hysterical or mistaken belief that disaster is imminent. Versions of the story go back more than 25 centuries;[1] it continues to be referred to in a variety of media.
Contents
1 The story and its name
2 History
3 Idiomatic usage
4 Adaptations
5 Popular references
6 Related stories
7 Notes
8 References
9 External links
The story and its name[edit]
Illustration for the story "Chicken Little", 1916
The story is listed as Aarne-Thompson-Uther type 20C, which includes international examples of folktales that make light of paranoia and mass hysteria.[2] There are several Western versions of the story, of which the best-known concerns a chick that believes the sky is falling when an acorn falls on its head. The chick decides to tell the King and on its journey meets other animals (mostly other fowl) which join it in the quest. After this point, there are many endings. In the most familiar, a fox invites them to its lair and then eats them all. Alternatively, the last one, usually Cocky Lockey, survives long enough to warn the chick, who escapes. In others all are rescued and finally speak to the King.
In most retellings, the animals have rhyming names, commonly Chicken Licken or Chicken Little, Henny Penny or Hen-Len, Cocky Locky, Ducky Lucky or Ducky Daddles, Drakey Lakey, Goosey Loosey or Goosey Poosey, Gander Lander, Turkey Lurkey and Foxy Loxy or Foxy Woxy.
The moral to be drawn changes, depending on the version. Where there is a "happy ending", the moral is not to be a "Chicken" but to have courage. In other versions where the birds are eaten by the fox, the fable is interpreted as a warning not to believe everything one is told.
In the United States, the most common name for the story is "Chicken Little", as attested by illustrated books for children dating from the early 19th century. In Britain and its other former colonies, it is best known as "Henny Penny" and "Chicken Licken", titles by which it also went in the United States.[note 1]
History[edit]
"There was once a little chick named Kluk": beginning of the 1823 Danish version of the story.
The story was part of the oral folk tradition and only began to appear in print after the Brothers Grimm had set a European example with their collection of German tales in the early years of the 19th century. One of the earliest to collect tales from Scandinavian sources was Just Mathias Thiele, who in 1823 published an early version of the Henny Penny story in the Danish language.[4] The names of the characters there are Kylling Kluk,[5] Høne Pøne,[6] Hane Pane,[7] And Svand,[8] Gaase Paase,[9] and Ræv Skræv.[10] In Thiele's untitled account, a nut falls on Kylling Kluk's back and knocks him over. He then goes to each of the other characters, proclaiming that "I think all the world is falling" and setting them all running. The fox Ræv Skræv joins in the flight and, when they reach the wood, counts them over from behind and eats them one by one. Eventually the tale was translated into English by Benjamin Thorpe after several other versions had appeared.
Once the story began to appear in the English language, the titles by which they went varied considerably and have continued to do so. John Greene Chandler (1815-1879), an illustrator and wood engraver from Petersham, Massachusetts, published an illustrated children's book titled The Remarkable Story of Chicken Little in 1840.[11][12][13] In this American version of the story, the characters' names are Chicken Little, Hen-Pen, Duck-Luck, Goose-Loose, and Fox-Lox; Chicken Little is frightened by a leaf falling on her tail.[14]
First two pages of the 1840 children's illustrated book: The Remarkable Story of Chicken Little
A Scots version of the tale is found in Robert Chambers's Popular Rhymes, Fireside Stories, and Amusements of Scotland of 1842.[15] It appeared among the "Fireside Nursery Stories" and was titled "The hen and her fellow travellers". The characters included Henny Penny, Cocky Locky, Ducky Daddles, Goosie Poosie, and an unnamed "tod" (fox). Henny Penny became convinced that "the lifts were faun" (the heavens were falling) when a pea fell on her head.
In 1849, a "very different" English version was published under the title "The Story of Chicken-Licken" by Joseph Orchard Halliwell.[16] In this Chicken-licken was startled when "an acorn fell on her bald pate" and encounters the characters Hen-len, Cock-lock, Duck-luck, Drake-lake, Goose-loose, Gander-lander, Turkey-lurkey and Fox-lox.
It was followed in 1850 by "The wonderful story of Henny Penny" in Joseph Cundall's compilation, The Treasury of pleasure books for young children.[17] Each story there is presented as if it were a separate book, and in this case had two illustrations by Harrison Weir. In reality the story is a repetition of the Chambers narration in standard English, except that the dialect phrase "so she gaed, and she gaed, and she gaed" is retained and the cause of panic is mistranslated as "the clouds are falling".
Benjamin Thorpe's translation of Thiele's Danish story was published in 1853 and given the title "The Little Chicken Kluk and his companions"[18] Thorpe describes the tale there as "a pendant to the Scottish story…printed in Chambers" (see above) and gives the characters approximately the same names as in Chambers.
Comparing the different versions, we find that in the Scots and English stories the animals want "to tell the king" that the skies are falling; while in the American story, as in the Danish, they are not given any specific motivation. In all versions they are eaten by the fox, although in different circumstances.
Comparison of early publications
Source
Title
Main character
Other characters
Initial event
Fear
Motivation
Fate
Thiele, 1823 [untitled] Kylling Kluk[5] Høne Pøne[6]
Hane Pane [7]
And Svand [8]
Gaase Paase [9]
Ræv Skræv[10] A nut falls on Kylling Kluk's back All the world is falling (al Verden falder) So let us run (Saa lad os løbe) Raev Skraev runs with them into the wood and eats them one by one
Chandler, 1840 The Remarkable Story of Chicken Little Chicken Little Hen Pen
Duck Luck
Goose Loose
Turkey Lurkey
Fox Lox The leaf of a rose-bush falls on Chicken Little's tail The sky is falling None given, except that Chicken Little is frightened Fox Lox invites the animals into his den, kills the others, and eats Chicken Little
Chambers, 1842 The Hen and Her Fellow-Travellers henny-penny cocky-locky
ducky-daddles
goose-poosie
unnamed "tod" (fox) A pea falls on henny-penny's head "The lifts were faun" (the heavens were falling) To tell the king about it A "tod" (fox) takes them to his hole, forces them inside, then he and his young ones eat them
Halliwell, 1849 The Story of Chicken-licken Chicken-licken Hen-len
Cock-lock
Duck-luck
Drake-lake
Goose-loose
Gander-lander
Turkey-lurkey
Fox-lox An acorn falls upon Chicken-licken's bald pate The sky had fallen To tell the king Fox-lox takes them to his hole, then he and his young ones eat them
Thorpe, 1853 (translation of Thiele 1823) The Little Chicken Kluk and His Companions Chicken Kluk Henny Penny
Cocky Locky
Ducky Lucky
Goosy Poosy
Foxy Coxy A nut falls on Chicken Kluk's back All the world is falling Then let us run Foxy Coxy runs with them into the wood and eats them one by one
Idiomatic usage[edit]
Title page of The Remarkable Story of Chicken Little
The name "Chicken Little" — and the fable's central phrase, The sky is falling! — have been applied to people accused of being unreasonably afraid, or those trying to incite an unreasonable fear in those around them.
The first use of the name "Chicken Little" to "one who warns of or predicts calamity, especially without justification" recorded by the Merriam-Webster Dictionary is in 1895,[19] but idiomatic use of the name significantly predates that attestation. In fact, this usage is recorded in the United States very soon after the publication of Chandler's illustrated children's book in 1840. Already, in 1842, a journal article about the Government of Haiti referred to "Chicken Little" in an offhand manner.[20] An "oration" delivered to the city of Boston on July 4, 1844, contains the passage:
To hear their harangues on the eve of the election, one would suppose that the fable of Chicken Little was about to become a truth, and that the sky was actually falling.[21]
Fear mongering — whether justified or not — can sometimes elicit a societal response called Chicken Little syndrome, described as "inferring catastrophic conclusions possibly resulting in paralysis".[22] It has also been defined as "a sense of despair or passivity which blocks the audience from actions".[23] The term began appearing in the 1950s[24] and the phenomenon has been noted in many different societal contexts.
Adaptations[edit]
Walt Disney Pictures has made two animated versions of the story. The first was Chicken Little,[25] a 1943 animated short released during World War II as one of a series produced at the request of the U.S. government for the purpose of discrediting Nazism. It tells a variant of the parable in which Foxy Loxy takes the advice of a book on psychology (on the original 1943 cut, it is Mein Kampf) by striking the least intelligent first. Dim-witted Chicken Little is convinced by him that the sky is falling and whips the farmyard into mass hysteria, which the unscrupulous fox manipulates for his own benefit. The dark comedy is used as an allegory for the idea that fear-mongering weakens the war effort and costs lives. It is also one of the versions of the story in which Chicken Little appears as a character distinct from Henny Penny.
The second Disney film was the very loosely adapted Chicken Little, released in 2005 as a 3D computer-animated feature. It is an updated science fiction sequel to the original fable in which Chicken Little is partly justified in his fears. In this version, Foxy Loxy is changed from a male to a female, and from the main antagonist to a local bully. Another film adaptation was the animated TV episode "Henny Penny" (1999), which was part of the series Happily Ever After: Fairy Tales for Every Child. In this modern update, the story is given a satirical and political interpretation.
There have also been a number of musical settings. American composer Vincent Persichetti used the fable as the plot of his only opera The Sibyl: A Parable of Chicken Little (Parable XX), op. 135 (1976), which premiered in 1985. On the sitcom The Golden Girls, there was a 1991 episode in which the characters perform a short musical based on the fable (here titled "Henny Penny") at a school recital.[26] In 1998, there was Joy Chaitin and Sarah Stevens-Estabrook's equally light-hearted musical version of the fable, "Henny Penny".[27] Designed for between six and a hundred junior actors, it has additional characters as optional extras: Funky Monkey, Sheepy Weepy, Mama Llama, Pandy Handy and Giraffy Laughy (plus an aggressive oak-tree).
In Singapore, a more involved musical was performed in 2005. This was Brian Seward's The Acorn - the true story of Chicken Licken.[28] It is a tale of mixed motivations as certain creatures (including some among the 'good guys') take advantage of the panic caused by Chicken Licken.[29] In 2007 American singer and composer Gary Bachlund set the text of Margaret Free's reading version of "Chicken Little" (The Primer, 1910) for high voice and piano. In his note to the score Bachlund makes it clear that he intends a reference to alarmism and its tragic consequences.[30]
Popular references[edit]
There are many novels, films, CDs and songs titled "The Sky is Falling", but the majority refer to the idiomatic use of the phrase rather than to the fable from which it derives. The following are some lyrics which genuinely refer or allude to the story:
British band Happy Mondays have the lines "Henny Penny, Cocky Locky, Goosey Loosey, Turkey Lurkey, Ducky Lucky, Chicken Little, It seems they are all on the move when the sun is falling in" in the song "Moving in with" on their second album, Bummed (1986).[31]
The Aerosmith song "Livin' on the Edge" (1993) has the lines "If Chicken Little tells you that the sky is falling, Even if it wasn't would you still come crawling back again?"[32]
"Chicken Little" is a song from the 1997 album Fancy, by the California avantrock band Idiot Flesh; it contains the line, "The sky is falling, gotta tell the king".[33]
"The Sky Is Falling" is a song by Owsley from the 1999 debut album Owsley; it includes the line "Chicken Little had a big day today".[34]
Related stories[edit]
A very early example containing the basic motif and many of the elements of the tale is some 25 centuries old and appears in the Buddhist scriptures as the Daddabha Jataka (J 322).[1] In it, the Buddha, on hearing about some particular religious practices, comments that there is no special merit in them, but rather that they are "like the noise the hare heard." He then tells the story of a hare disturbed by a falling fruit who believes that the earth is coming to an end. The hare starts a stampede among the other animals until a lion halts them, investigates the cause of the panic and restores calm. The fable teaches the necessity for deductive reasoning and subsequent investigation.
The Tibetan version of the Jataka tale has been told in rhyme by Australian author Ursula Dubosarsky in her book The Terrible Plop (2009), which has since been dramatised, using the original title Plop!.[35] In this, the animal stampede is halted by a bear, rather than a lion. The ending has been changed from the Tibetan original as well.[36]
There also exists a Br'er Rabbit story that is closer to the Eastern versions. In this story, Br'er Rabbit initiates the panic but does not take part in the mass flight, although Br'er Fox does. In this case it is Br'er Terrapin that leads the animals back to question Br'er Rabbit.[37]
Notes[edit]
Jump up ^ Before Lightnin' Hopkins' "Henny Penny Blues" from the 1940s, there was a 1906 comic strip version.[3] A more recent instance is the Golden Girls' TV skit titled "Henny Penny" (1991). The Yale Book of Quotations cites the nursery tale "Chicken Licken" as the source for 'the sky is falling' and the character is mentioned in John Cheever's short story "The 5.48".
References[edit]
^ Jump up to: a b "Jataka Tales of the Buddha, Part III, retold by Ken & Visakha Kawasaki". Retrieved 19 September 2014.
Jump up ^ The End of the World The Sky Is Falling, folktales of Aarne-Thompson-Uther type 20C (including former type 2033), in which storytellers from around the world make light of paranoia and mass hysteria, selected and edited by D. L. Ashliman, 1999
Jump up ^ C365 in the Opie Collection. "List of Fairy Tale Books in the Opie Collection", Opie Collection of Children's Literature, Bodleian Library (bodleian.ox.ac.uk), revised 1994. Retrieved 1 May 2015.
Jump up ^ Thiele, J. M. (1823). Danske folkesagn. 4. Copenhagen: A. Seidelin. pp. 165–167. OCLC 458278434.
^ Jump up to: a b Kylling means "chick" (baby chicken); Kluk is an onomatopoeic representation of a chicken's vocalization, similar to English "cluck"
^ Jump up to: a b Høne means "hen"; Pøne means "penny"
^ Jump up to: a b Hane means "cock"/"rooster"
^ Jump up to: a b And means "duck"
^ Jump up to: a b Gaase (modern Danish Gåse) means "goose"
^ Jump up to: a b Ræv means "fox"
Jump up ^ Chandler, John Greene (1840). The Remarkable Story of Chicken Little. Roxbury, MA: J.G. Chandler. OCLC 191238925.
Jump up ^ "Archived copy". Archived from the original on 2015-09-18. Retrieved 2014-10-21. CS1 maint: Archived copy as title (link)
Jump up ^ Chandler, John Greene. "Self-Portrait" – via arcade.nyarc.org Library Catalog.
Jump up ^ The text of the story is reprinted in Fowle, William Bentley (1856). The Mind and Heart, Or, School and Fireside Reading for Children. Boston, MA: Morris Cotton. pp. 121–122. OCLC 27730411.
Jump up ^ Chambers, Robert (1842). Popular Rhymes, Fireside Stories, and Amusements of Scotland. Edinburgh: William and Robert Chambers. pp. 51–52. OCLC 316602150.
Jump up ^ Halliwell, James Orchard (1849). Popular rhymes and nursery tales: a sequel to the Nursery rhymes of England. London: John Russell Smith. pp. 29–30. OCLC 3155930.
Jump up ^ "The Treasury of pleasure books for young children". W.G. Baker. 1 January 1850 – via Google Books.
Jump up ^ Thorpe (ed.), Benjamin (1853). Yule-Tide Stories: a collection of Scandinavian and North German popular tales and traditions. London: Henry G. Bohn. pp. 421–422. OCLC 877309110. CS1 maint: Extra text: authors list (link)
Jump up ^ Merriam-Webster Dictionary. Retrieved 19 September 2014.
Jump up ^ "Life in Hayti", in The Knickerbocker, or New York monthly magazine, volume xix. New York: John Bisco. 1842. p. 454. : "In the words of an infantile philosopher, yclept 'Chicken Little', how can he help knowing it?"
Jump up ^ Chandler, Peleg W. The Morals of Freedom: An Oration delivered Before the Authorities of the City of Boston July 4, 1844. Boston, MA: John H. Eastburn. p. 29. OCLC 982157.
Jump up ^ Landry, John R. (1998). Can Mission Statements Plant the "Seeds" of Dysfunctional Behaviors in an Organization's Memory? in Proceedings of the Thirty-First Hawaii International Conference on System Sciences. p. 169. CiteSeerX 10.1.1.108.2917.
Jump up ^ Li, Xinghua, "Communicating the "incommunicable green": a comparative study of the structures of desire in environmental advertising in the United States and China", PhD diss., p.81, University of Iowa, 2010.
Jump up ^ See, e.g., Audio Visual Communication Review, v.3-4, pp. 226-227, National Education Association of the United States Dept. of Audiovisual Instruction, 1955
Jump up ^ Walt Disney (1943), available at Youtube
Jump up ^ "Henny Penny". YouTube. Retrieved 19 September 2014.
Jump up ^ Henny Penny: A Play with Optional Music. Retrieved 19 September 2014.
Jump up ^ "Brian Seward - Playwright". Retrieved 19 September 2014.
Jump up ^ "The True Story of Chicken Licken". YouTube. Retrieved 19 September 2014.
Jump up ^ "Chicken Little (2007), Margaret Free and Harriette Taylor Treadwell, originally for high voice and piano". Retrieved 19 September 2014.
Jump up ^ "Happy Mondays - Moving In With". YouTube. Retrieved 19 September 2014.
Jump up ^ "Aerosmith - Livin' On The Edge (Lyrics)". YouTube. Retrieved 19 September 2014.
Jump up ^ "Idiot Flesh - Chicken Little". YouTube. Retrieved 19 September 2014.
Jump up ^ ""The Sky Is Falling" by The Semantics". YouTube. Retrieved 19 September 2014.
Jump up ^ "Archived copy". Archived from the original on 2012-05-11. Retrieved 2012-07-03. CS1 maint: Archived copy as title (link)
Jump up ^ "Archived copy". Archived from the original on 2010-12-26. Retrieved 2011-02-04. CS1 maint: Archived copy as title (link)
Jump up ^ Joel Chandler Harris, Nights with Uncle Remus: Myths and Legends of the Old Plantation (Boston and New York: Houghton, Mifflin, and Company, 1883), no. 20, pp. 108-13. Online at Brother Rabbit Takes Some Exercise, at The End of the World The Sky Is Falling, folktales of Aarne-Thompson-Uther type 20C (including former type 2033), in which storytellers from around the world make light of paranoia and mass hysteria, selected and edited by D. L. Ashliman, 1999
External links[edit]
Wikimedia Commons has media related to Chicken Little.
The Remarkable Story of Chicken Little printed in Boston between 1865-71.
SurLaLune Fairy Tale Site, Henny-Penny as collected by Joseph Jacobs, 1890
The Cock and Hen That Went to the Dovrefell a Norwegian variant, 1888
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Earth's internal heat budget
From Wikipedia, the free encyclopedia
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Global map of the flux of heat, in mW/m2, from Earth's interior to the surface.[1] The largest values of heat flux coincide with mid ocean ridges, and the smallest values of heat flux occur in stable continental interiors.
The flow of heat from Earth's interior to the surface is estimated at 47 terawatts (TW)[1] and comes from two main sources in roughly equal amounts: the radiogenic heat produced by the radioactive decay of isotopes in the mantle and crust, and the primordial heat left over from the formation of the Earth.[2]
Earth's internal heat powers most geological processes[3] and drives plate tectonics.[2] Despite its geological significance, this heat energy coming from Earth's interior is actually only 0.03% of Earth's total energy budget at the surface, which is dominated by 173,000 TW of incoming solar radiation.[4] The insolation that eventually, after reflection, reaches the surface penetrates only several tens of centimeters on the daily cycle and only several tens of meters on the annual cycle. This renders solar radiation irrelevant for internal processes.[5]
Contents
[hide]
1 Heat and early estimate of Earth's age
2 Global internal heat flow
3 Radiogenic heat
4 Primordial heat
5 Heat flow and plate tectonics
6 See also
7 References
Heat and early estimate of Earth's age[edit]
Based on calculations of Earth's cooling rate, which assumed constant conductivity in the Earth's interior, in 1862 William Thomson (later made Lord Kelvin) estimated the age of the Earth at 98 million years,[6] which contrasts with the age of 4.5 billion years obtained in the 20th century by radiometric dating.[7] As pointed out by John Perry in 1895[8] a variable conductivity in the Earth's interior could expand the computed age of the Earth to billions of years, as later confirmed by radiometric dating. Contrary to the usual representation of Kelvin's argument, the observed thermal gradient of the Earth's crust would not be explained by the addition of radioactivity as a heat source. More significantly, mantle convection alters how heat is transported within the Earth, invalidating Kelvin's assumption of purely conductive cooling.
Global internal heat flow[edit]
Cross section of the Earth showing its main divisions and their approximate contributions to Earth's total internal heat flow to the surface, and the dominant heat transport mechanisms within the Earth.
Estimates of the total heat flow from Earth’s interior to surface span a range of 43 to 49 terawatts (TW) (a terawatt is 1012 watts).[9] One recent estimate is 47 TW,[1] equivalent to an average heat flux of 91.6 mW/m2, and is based on more than 38,000 measurements. The respective mean heat flows of continental and oceanic crust are 70.9 and 105.4 mW/m2.[1]
While the total internal Earth heat flow to the surface is well constrained, the relative contribution of the two main sources of Earth's heat, radiogenic and primordial heat, are highly uncertain because their direct measurement is difficult. Chemical and physical models give estimated ranges of 15–41 TW and 12–30 TW for radiogenic heat and primordial heat, respectively,[9] and recent results indicate their contributions may be roughly equal.[10][when?]
The structure of the Earth is a rigid outer crust that is composed of thicker continental crust and thinner oceanic crust, solid but plastically flowing mantle, a liquid outer core, and a solid inner core. The fluidity of a material is proportional to temperature; thus, the solid mantle can still flow on long time scales, as a function of its temperature[2] and therefore as a function of the flow of Earth's internal heat. The mantle convects in response to heat escaping from Earth's interior, with hotter and more buoyant mantle rising and cooler, and therefore denser, mantle sinking. This convective flow of the mantle drives the movement of Earth's lithospheric plates; thus, an additional reservoir of heat in the lower mantle is critical for the operation of plate tectonics and one possible source is an enrichment of radioactive elements in the lower mantle.[11]
Earth heat transport occurs by conduction, mantle convection, hydrothermal convection, and volcanic advection.[12] Earth's internal heat flow to the surface is thought to be 80% due to mantle convection, with the remaining heat mostly originating in the Earth's crust,[13] with about 1% due to volcanic activity, earthquakes, and mountain building.[2] Thus, about 99% of Earth's internal heat loss at the surface is by conduction through the crust, and mantle convection is the dominant control on heat transport from deep within the Earth. Most of the heat flow from the thicker continental crust is attributed to internal radiogenic sources, in contrast the thinner oceanic crust has only 2% internal radiogenic heat.[2] The remaining heat flow at the surface would be due to basal heating of the crust from mantle convection. Heat fluxes are negatively correlated with rock age,[1] with the highest heat fluxes from the youngest rock at mid-ocean ridge spreading centers (zones of mantle upwelling), as observed in the global map of Earth heat flow.[1]
Radiogenic heat[edit]
The evolution of Earth's radiogenic heat flow over time.
The radioactive decay of elements in the Earth's mantle and crust results in production of daughter isotopes and release of particles and heat energy, or radiogenic heat. Four radioactive isotopes are responsible for the majority of radiogenic heat, uranium-238 (238U), uranium-235 (235U), thorium-232 (232Th), and potassium-40 (40K).[14] Due to a lack of rock samples from below 200 km depth, it is not possible to do a simple radiogenic heat estimate of known radioactive isotope concentrations in rock throughout the whole mantle.[14] For the Earth's core, geochemical studies indicate that it is unlikely to be a significant source of radiogenic heat due to an expected low concentration of radioactive elements.[2] Radiogenic heat production in the mantle is linked to the structure of mantle convection, a topic of much debate, and it is thought that the mantle may either have a layered structure with a higher concentration of radioactive heat-producing elements in the lower mantle, or small reservoirs enriched in radioactive elements dispersed throughout the whole mantle.[15]
Geoneutrino detectors can detect the decay of 238U and 232Th and thus allow estimation of their contribution to the present radiogenic heat budget, while 235U is unobserved, and 40K is not detectable but is known to contribute 4 TW of heating.[10] However, the decay of 235U and 40K contributed a large fraction of radiogenic heat flux to the early Earth, which was also much hotter than at present.[11] Initial results from measuring the geoneutrino products of radioactive decay from within the Earth, a proxy for radiogenic heat, yielded a new estimate of half of the total Earth internal heat source being radiogenic,[10] and this is consistent with previous estimates.[15]
Primordial heat[edit]
Primordial heat is the heat lost by the Earth as it continues to cool from its original formation, and this is in contrast to its still actively-produced radiogenic heat. The Earth core's heat flow—heat leaving the core and flowing into the overlying mantle—is thought to be due to primordial heat, and is estimated at 5–15 TW.[16] Estimates of mantle primordial heat loss range between 7 and 15 TW.[9]
The early formation of the Earth's dense core could have caused superheating and rapid heat loss, and the heat loss rate would slow once the mantle solidified.[16] Heat flow from the core is necessary for maintaining the convecting outer core and the geodynamo and Earth's magnetic field, therefore primordial heat from the core enabled Earth's atmosphere and thus helped retain Earth's liquid water.[15]
Heat flow and plate tectonics[edit]
Earth's tectonic evolution over time from a molten state at 4.5 Ga,[7] to a single-plate lithosphere,[17] to modern plate tectonics sometime between 3.2 Ga[18] and 1.0 Ga.[19]
Controversy over the exact nature of mantle convection makes the linked evolution of Earth's heat budget and the dynamics and structure of the mantle difficult to unravel.[15] There is evidence that the processes of plate tectonics were not active in the Earth before 3.2 billion years ago, and that early Earth's internal heat loss could have been dominated by advection via heat-pipe volcanism.[17] Terrestrial bodies with lower heat flows, such as the Moon and Mars, conduct their internal heat through a single lithospheric plate, and higher heat flows, such as on Jupiter's moon Io, result in advective heat transport via enhanced volcanism, while the active plate tectonics of Earth occur with an intermediate heat flow and a convecting mantle.[17]
See also[edit]
Wikimedia Commons has media related to Earth's internal heat budget.
Geothermal energy
Geothermal gradient
References[edit]
^ Jump up to: a b c d e f Davies, J. H., & Davies, D. R. (2010). Earth's surface heat flux. Solid Earth, 1(1), 5–24.
^ Jump up to: a b c d e f Turcotte, D. L., & Schubert, G. (2002). Geodynamics. Cambridge University Press.
Jump up ^ Buffett, B. A. (2007). Taking earth's temperature. Science, 315(5820), 1801–1802.
Jump up ^ Archer, D. (2012). Global Warming: Understanding the Forecast. ISBN 978-0-470-94341-0.
Jump up ^ Lowrie, W. (2007). Fundamentals of geophysics. Cambridge: CUP, 2nd ed.
Jump up ^ Thomson, William. (1864). On the secular cooling of the earth, read 28 April 1862. Transactions of the Royal Society of Edinburgh, 23, 157–170.
^ Jump up to: a b Taylor, S. R. (2007). .1 The Formation of the Earth and Moon. Developments in Precambrian Geology, 15, 21–30.
Jump up ^ England, P., Molnar, P., Richter, F. (2007). John Perry’s neglected critique of Kelvin’s age for the Earth: A missed opportunity in geodynamics. 4 JANUARY 2007, GSA Today : v. 17, no. 1, doi: 10.1130/GSAT01701A.1
^ Jump up to: a b c Dye, S. T. (2012). Geoneutrinos and the radioactive power of the Earth. Reviews of Geophysics, 50(3).
^ Jump up to: a b c Gando, A., Dwyer, D. A., McKeown, R. D., & Zhang, C. (2011). Partial radiogenic heat model for Earth revealed by geoneutrino measurements. Nature Geoscience, 4(9), 647–651.
^ Jump up to: a b Arevalo Jr, R., McDonough, W. F., & Luong, M. (2009). The K/U ratio of the silicate Earth: Insights into mantle composition, structure and thermal evolution. Earth and Planetary Science Letters, 278(3), 361–369.
Jump up ^ Jaupart, C., & Mareschal, J. C. (2007). Heat flow and thermal structure of the lithosphere. Treatise on Geophysics, 6, 217–251.
Jump up ^ Korenaga, J. (2003). Energetics of mantle convection and the fate of fossil heat. Geophysical Research Letters, 30(8), 1437.
^ Jump up to: a b Korenaga, J. (2011). Earth's heat budget: Clairvoyant geoneutrinos. Nature Geoscience, 4(9), 581–582.
^ Jump up to: a b c d Korenaga, J. (2008). Urey ratio and the structure and evolution of Earth's mantle. Reviews of Geophysics, 46(2).
^ Jump up to: a b Lay, T., Hernlund, J., & Buffett, B. A. (2008). Core–mantle boundary heat flow. Nature Geoscience, 1(1), 25-32.
^ Jump up to: a b c Moore, W. B., & Webb, A. A. G. (2013). Heat-pipe Earth. Nature, 501(7468), 501–505.
Jump up ^ Pease, V., Percival, J., Smithies, H., Stevens, G., & Van Kranendonk, M. (2008). When did plate tectonics begin? Evidence from the orogenic record. When did plate tectonics begin on planet Earth, 199–208.
Jump up ^ Stern, R. J. (2008). Modern-style plate tectonics began in Neoproterozoic time: An alternative interpretation of Earth’s tectonic history. When did plate tectonics begin on planet Earth, 265–280.
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