The Partition of India was the division of British India into two independent Dominions: India and Pakistan. The two states have since gone through further reorganization: the Dominion of India is today the Republic of India (since 1950); while the Dominion of Pakistan was composed of what is known today as the Islamic Republic of Pakistan (since 1956) and the People's Republic of Bangladesh (since 1971). The partition involved the division of two provinces, Bengal and Punjab, based on district-wide non-Muslim or Muslim majorities. The partition also saw the division of the British Indian Army, the Royal Indian Navy, the Indian Civil Service, the railways, and the central treasury. The partition was outlined in the Indian Independence Act 1947 and resulted in the dissolution of the British Raj, i.e. Crown rule in India. The two self-governing independent Dominions of India and Pakistan legally came into existence at midnight on 15 August 1947.
The partition displaced between 10 and 20 million people along religious lines, creating overwhelming refugee crises in the newly constituted dominions. There was large-scale violence, with estimates of the loss of life accompanying or preceding the partition disputed and varying between several hundred thousand and two million. The violent nature of the partition created an atmosphere of hostility and suspicion between India and Pakistan that affects their relationship to this day.
The term partition of India does not cover the secession of Bangladesh from Pakistan in 1971, nor the earlier separations of Burma (now Myanmar) and Ceylon (now Sri Lanka) from the administration of British India. The term also does not cover the political integration of princely states into the two new dominions, nor the disputes of annexation or division arising in the princely states of Hyderabad, Junagadh, and Jammu and Kashmir, though violence along religious lines did break out in some princely states at the time of the partition. It does not cover the incorporation of the enclaves of French India into India during the period 1947–1954, nor the annexation of Goa and other districts of Portuguese India by India in 1961. Other contemporaneous political entities in the region in 1947—the Kingdom of Sikkim, Kingdom of Bhutan, Kingdom of Nepal, and the Maldives—were unaffected by the partition.Among princely states, the violence was often highly organised with the involvement or complicity of the rulers. It is believed that in the Sikh states (except for Jind and Kapurthala), the Maharajas were complicit in the ethnic cleansing of Muslims, while other Maharajas such as those of Patiala, Faridkot, and Bharatpur were heavily involved in ordering them. The ruler of Bharatpur, in particular, is said to have witnessed the ethnic cleansing of his population, especially at places such as Deeg.
1) At first my answer was ##n!
\begin{pmatrix}
n+r-1 \\
r - 1
\end{pmatrix}
##
But I think that's not correct because let say first group consists of person A and B, by multiplying with n!, I also consider first group to be B and A which is just the same as A and B so there is double counting...
My main question here is about how we actually justify, hopefully fairly rigorously, the steps leading towards converting the sum to an integral.
My work is below:
If we consider the canonical ensemble then, after tracing over the corresponding exponential we get:
$$Z = \sum_{n=0}^\infty...
##Z = \sum_{-i}^{i} = e^{-E_n \beta}##
##Z = \sum_{0}^j e^{nh\beta} + \sum_{0}^j e^{-nh\beta}##
Those sums are 2 finites geometric series
##Z = \frac{1- e^{h\beta(i+1)}}{1-e^{h\beta}} + \frac{1-e^{-h\beta(i+1)}}{1-e^{-h\beta}}##
I don't think this is ring since from that I can't get 2 sinh...
I have a cubic lattice, and I am trying to find the partition function and the expected value of the dipole moment. I represent the dipole moment as a unit vector pointing to one the 8 corners of the system. I know nothing about the average dipole moment , but I do know that the mean-field...
$$H = - J ( \sum_{i = odd}) \sigma_i \sigma_{i+1} - \mu H ( \sum_{i} \sigma_i ) $$
So basically, my idea was to separate the particles in this way::
##N_{\uparrow}## is the number of up spin particles
##N_{\downarrow}## "" down spin particles
##N_1## is the number of pairs of particles close...
Let's say that we have a one-particle Hamiltonian that admits only a continuous spectrum of eigenvalues ##E(k)=\alpha k^2## parameterized by asymptotic momentum ##\mathbf{k}## (assuming the eigenfunctions become planewaves far from the origin), would the partition function then be $$Z=\int...
In hamiltonian formalism we have the generalized coordinates ##q_i## and the conjugates moments ##p_i##.
For a dipole in a give magnetic field ##B## the Hamiltonian is ##H=-\mu B cos \theta## where ##\theta## is the angle between ##\vec \mu## and ##\vec B##.
Can i consider ##\theta## or ##cos...
Hey, I have a question about proving Saha's equation for ionizing hydrogen atoms.
The formula is
\frac{P_{p}}{P_{H}} = \frac{k_{B} T}{P_{e}} \left(\frac{2\pi m_{e} k_{B}T}{h^2} \right)^{\frac{3}{2}}e^{\frac{-I}{k_{B} T}}
with
P_{p} pressure proton's,
P_{H} pressure hydrogen atoms,
m_{e}...
I determined the partition function of the particle A, B and C.
C should be the same as B.
I then considered the situation, where all particles are in the system at the same time, and drew a diagram of all possible arrangements:
The grey boxes are the different partitions, given that we...
I have a question about statistical physics. Suppose we have a closed container with two compartments, each with volume V , in thermal contact with a heat bath at temperature T, and we discuss the problem from the perspective of a canonic ensemble. At a certain moment the separating wall is...
Summary:: Proving that entropy change in mixing of gas is positive definite
>
>An ideal gas is separated by a piston in such a way that the entropy of one prat is## S_1## and that of the other part is ##S_2##. Given that ##S_1>S_2##, if the piston is removed then the total entropy of the...
equation i need to proof. the N in here, is the avarege number of particles, N0 is the total number of particles,V is total volume, v0 I am not quite sure what it is because it isn't mentioned in the homework, but I am assuming it is the volume of which space.
My attempt : $$P(n) = \frac{1}{\mathcal{Z}} Exp[(n\mu -E)/\tau]$$, use $$\lambda = e^{\mu/\tau}$$, then the distribution can be written as $$P(n) = \frac{1}{\mathcal{Z}} \lambda^nExp[-E/\tau]$$
Note that the average number of particle can be written as $$<N>= \lambda \partial \lambda ( log...
I'm reading "Calculus on manifolds" by Spivak and i can't understand the role that the partition of unity play and why this properties are important , Spivak say:
What is the purpose of the partition of unity? if someone can give me examples, bibliography or clear my doubt i'll appreciate it.
Here is the solution I have been given:
But I really don't understand this solution. Why can I just add these two exponential factors (adding two individual partition...
Hello fellow physicists,
I need to calculate the rotational partition function for a CO2 molecule. I'm running into problems because I've found examples were they say this rotational partition function is:
##\zeta^r= \frac T {\sigma \theta_r} = \frac {2IkT} {\sigma \hbar^3}##
Where...
If my partition function is for a continuous distribution of energy, can I simply say that the probability of my ensemble being in a state with energy ##cU## is ##e^{-\beta cU} /Z##? I believe that isn't right as my energy distribution is continuous, and I need to be integrating over small...
I am not sure, but since the partition function Z is just the sum of all Boltzmann Factor
We can just add:
(some terms don't appear in the image, by the way, the estimative is nice, the result is above ANS)
But i didn't understand what the author did:
While i didn't even care about the...
$$Q_{(\alpha, \beta)} = \sum_{N=0}^{\infty} e^{\alpha N} Z_{N}(\alpha, \beta) \hspace{1cm} (3.127)$$
Where ##Q## is the grand partition function, ##Z_N## is the canonical partition function and:
$$\beta = \frac{1}{kT} \hspace{1cm} \alpha = \frac{\mu}{kT} \hspace{1cm} (3.128)$$
In the case of an...
Greetings,
similar to my previous thread
(https://www.physicsforums.com/threads/lennard-jones-potential-and-the-average-distance-between-two-particles.990055/#post-6355442),
I am trying to calculate the average inter-particle distance of particles that interact via Lennard Jones potentials...
In quantum mechanics, we have the partition function Z[j] = e-W[j] = ∫ eiS+ jiOi. The propagator between two points 1 and 2 can be calculated as
## \frac{\delta}{\delta j_1}\frac{\delta}{\delta j_2} Z = \langle O_1 O_2 \rangle##
The S in the path integral has been replaced by S → S + jiOi...
I'm given the following density of states
$$ \Omega(E) = \delta(E) + N\delta(E-\Delta) + \theta(E-\Delta)\left(\frac{1}{\Delta}\right)\left(\frac{E}{N\Delta}\right)^N $$
where $ \Delta $ is a positive constant. From here I have to "calculate the canonical partition function as a function of $$...
$$H=-J\sum_{i=1}^{N-1}\sigma_i\sigma_{i+1}$$ There is no external magnetic field, so the Hamiltonian is different than normal, and the spins $\sigma_i$ can be -1, 0, or 1. The boundary conditions are non-periodic (the chain just ends with the Nth spin)
$$Z=e^{-\beta H}$$...
For 2 bosons each of which can occupy any of the energy levels 0 and E the microstates will be 3
0 E
a a
aa -
- aa
the partition function is therefore $$z=1+e^{-\beta E}+e^{-2\beta E}...(1)$$
Another approach to do..
The single particle partition function is
$$z=1+e^{-\beta E} $$...
Hey! :o
let $A\neq \emptyset\neq B$ be sets, $C\subseteq A$, $D\subseteq B$ subsets and $f:A\rightarrow B$ a map.
I want to show that the set $\{f^{-1}(\{x\})\mid x\in \text{im} f\}$ is a partition of $A$. To show that the set $\{f^{-1}(\{x\})\mid x\in \text{im} f\}$ is a partition of $A$, we...
The actual data for the problem and my (and my friend's) attempt at a solution are in the attached file.
In a nutshell, this is what happened.
I obtained a solution based on the fact that the system is isolated. Thus the initially hot gas moves the partition doing work onto the initially cold...
Hello,
From wikipedia, this is the partition function for a "classical continuous system":
This is the pillar of classical statistical physics, but it can be seen as a mere kind of "mathematical transform" .
It can be used even without thinking to statistics or temperature.
If we focus only...
Summary: I want to basically multipartition my pc and use MY android OS copied from my phone as the dual boot OS.
Hi all, it's been awhile since I've posted. Sorry for AWOL.
What I want to do:
Partition my hard drive and run my exact copy of android on the other partition.
Why:
I want to...
Hi everyone,
I understand that the grand-canonical partition function is given by
$$Z = \sum_i e^{-\beta(E_i - \mu N_i)}$$
Is there any interpretation to the quantity ##E_i - \mu N_i## here? In the canonical ensemble this would simply be energy of the ##i##th state, so I suppose this would be...
Homework Statement
A thermally insulated, rigid vessel is divided into two equal compartments. One contains steam at 100 bar and 400 degrees Celcius, and the other is evacuated. The partition is removed. Calculate the resulting pressure and temperature.
(Please let me know if this is the wrong...
Hi all, I am slightly confused with regard to some ideas related to the GCE and CE. Assistance is greatly appreciated.
Since the GCE's partition function is different from that of the CE's, are all state variables that are derived from the their respective partition functions still equal in...
Homework Statement
A vessel having a volume ##V## initially contains ##N## atoms of dilute (ideal) helium gas in thermal equilibrium with the surroundings at a temperature ##T##, with initial pressure ##P_{i} (T ,V ) = \frac{NRT}{V}## . After some time, a number of helium atoms adhere to the...
I've seen the partition function calculated for the SHO before in a thermodynamics course in order to calculate entropy. Is it possible to calculate it for a driven harmonic oscillator?
Homework Statement
Basically the units of the Canonical Partition Function within the logarithms should be zero
Homework Equations
The Attempt at a Solution
N here is a number so we ignore the left logarithms, applying a "Unit function " for the terms within the logarithm...
Hi,
Where would I find data for rotational/vibrational temperatures for a particular molecule (ethane)? I tried googling but had no luck. Also can you compute the moments of inerta for a particular (simple) molecule?
Starting from the definition of energy levels ##e_n## and occupations ##a_n## and
the conditions ##\sum_n a_n = N## (2.2) and ##\sum_n a_n e_n = E## (2.3) where ##N## and ##E## are fixed I'm trying to find the distribution which extremizes the Shannon entropy.
Using the frequency ##f_n=a_n/N##...
The partition function should essentially be the sum of probabilities of being in various states, I believe. Why is it then the sum of Boltzmann factors even for fermions and bosons? I've never seen a good motivation for this in literature.
Homework Statement
I'm attempting to calculate the translational entropy for N2 and I get a value of 207.8 J/Kmol. The tabulated value is given as 150.4 and I am stumped as to why the decrepancy.
T = 298.15 K and P = 0.99 atm and V = 24.8 L
R = 8.314 J/Kmol[/B]
Homework Equations
Strans =...
Homework Statement
I'm asked to compute the molar entropy of oxygen gas @ 298.15 K & 1 bar given:
molecular mass of 5.312×10−26 kg, Θvib = 2256 K, Θrot = 2.07 K, σ = 2, and ge1 = 3. I'm currently stuck on the vibrational entropy calculation.
Homework Equations
[/B]S = NkT ∂/∂T {ln q} + Nk...
<Re-opening approved by mentor.>
Hi, I've always wondered why when calculating the partition function for a quantum system, we only sum over the eigenstates and not superimposed states. Thus I decided to actually try summing over all normalized states and see what would happen. Feedback is...
Hi, would very much appreciate it if I could get some help for something I was trying to calculate. I'm not very good at latex so I've just attached images of my attempt. I would very much appreciate it if you could look over the images I've taken and provide some feedback, thank you.
I've been...
Homework Statement
For 300 level Statistical Mechanics, we are asked to find the partition function for a Quantum Harmonic Oscillator with energy levels E(n) = hw(n+1/2). No big deal.
We are then asked to find the partition function N such oscillators. Here I am confused.
Homework Equations...
Self-repost from physics.SE; I underestimated how dead it was.
So this follows Schroeder's Intro to Thermal Physics equations 6.1-6.7, but the question isn't book specific. Please let me be clear: I know for a fact I'm wrong. However, it feels like performing seemingly allowed manipulations, I...
Homework Statement
Consider a gas sufficiently diluted containing N identical molecules of mass m in a box of dimensions Lx, Ly, Lz.
Calculate the probability of finding the molecules in any of their quantum states.
Calculate the energy of each quantum state εr, as a function of the quantum...
Homework Statement
Can you partition the positive integers in such a way that if x, y are member of A, then x+y is not a member of A. x and y have to be distinct. That is, {1, 2, 3} cannot be in the same set, since 1+2 = 3, but 1 and 2 can be, since 1+1=2, but 1 and 1 are not distinct...