Ganesh Ujwal
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Posts posted by Ganesh Ujwal
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Do magnets (permanent) become weaker as they are exposed to para-magnetic objects? I was thinking about this after seeing this.
I am buying a magnet and wish to know if a magnet (permanent) loses its magnetic domain structure or alignment when exposed to para magnetic materials.
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My questions mostly concern the history of physics. Who found the formula for kinetic energy[latex]E_k =\frac{1}{2}mv^{2}[/latex]and how was this formula actually discovered? I've recently watched Leonard Susskind's lecture where he proves that if you define kinetic and potential energy in this way, then you can show that the total energy is conserved. But that makes me wonder how anyone came to define kinetic energy in that way.My guess is that someone thought along the following lines:Energy is conserved, in the sense that when you lift something up you've done work,but when you let it go back down you're basically back where you started.So it seems that my work and the work of gravity just traded off.But how do I make the concept mathematically rigorous? I suppose I need functions [latex]U[/latex] and [latex]V[/latex], so that the total energy is their sum [latex]E=U+V[/latex], and the time derivative is always zero, [latex]\frac{dE}{dt}=0[/latex].But where do I go from here? How do I leap to eithera) [latex]U=\frac{1}{2}mv^{2}[/latex]b) [latex]F=-\frac{dV}{dt}?[/latex]It seems to me that if you could get to either (a) or (b), then the rest is just algebra, but I do not see how to get to either of these without being told by a physics professor.
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I'm going through Kerr metric, and following the 'Relativist's toolkit' derivation of the surface gravity, I've come to a part that I don't understand.Firstly, the metric is given by[latex]\mathrm{d}s^2=\left(\frac{\Sigma}{\rho^2}\sin^2\theta\omega^2-\frac{\rho^2\Delta}{\Sigma}\right)\mathrm{d}t^2-2\frac{\Sigma}{\rho^2}\sin^2\theta\omega \mathrm{d}\phi \mathrm{d}t+\frac{\Sigma}{\rho^2}\sin^2\theta \mathrm{d}\phi^2+\frac{\rho^2}{\Delta}\mathrm{d}r^2+\rho^2 \mathrm{d}\theta^2[/latex]With[latex]\rho^2=r^2+a^2\cos^2\theta,\quad \Delta=r^2-2Mr+a^2[/latex],[latex]\Sigma=(r^2+a^2)^2-a^2\Delta\sin^2\theta,\quad \omega=\frac{2Mar}{\Sigma}[/latex]The Killing vector that is null at the event horizon is[latex]\chi^\mu=\partial_t+\Omega_H\partial_\phi[/latex]where[latex] \Omega_H[/latex] is angular velocity at the horizon.Now I got the same norm of the Killing vector[latex]\chi^\mu\chi_\mu=g_{\mu\nu}\chi^\mu\chi^\nu=\frac{\Sigma}{\rho^2}\sin^2\theta(\Omega_H-\omega)^2-\frac{\rho^2\Delta}{\Sigma}
[/latex]And now I should use this equation[latex]\nabla_\nu(-\chi^\mu\chi_\mu)=2\kappa\chi_\nu[/latex]And I need to look at the horizon. Now, on the horizon [latex]\omega=\Omega_H[/latex] so my first term in the norm is zero, but, on the horizon [latex]\Delta=0[/latex] too, so how are they deriving that side, and how did they get[latex]\nabla_\nu(-\chi^\mu\chi_\mu)=\frac{\rho^2}{\Sigma}\nabla_\nu\Delta[/latex]if the [latex]\Delta=0[/latex] on the horizon? Since [latex]\rho[/latex]and [latex]\Sigma[/latex] both depend on [latex]r[/latex], and even if I evaluate them at [latex]r_+=M+\sqrt{M^2-a^2}[/latex] they don't cancel each other.How do they get to the end result of [latex]\kappa[/latex]?
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How show the map [latex]f:\mathbb R^2\rightarrow\mathbb R[/latex], defined as [latex]f(x,y)=x+y[/latex] is continuous for all [latex](x,y)\in\mathbb R^2[/latex]?Question: I want to show the map [latex]f:\mathbb R^2\rightarrow\mathbb R[/latex], defined as [latex]f(x,y)=x+y[/latex] is continuous for all [latex](x,y)\in\mathbb R^2[/latex].Issue: I know how to prove this via the epsilon-delta way. I want to prove this using the projection functions [latex]p_1,p_2: \mathbb R^2\rightarrow\mathbb R[/latex] where [latex]p_1[/latex] maps [latex](x,y)\rightarrow x[/latex], similarly for [latex]p_2[/latex]. Now my books says via a result based on continuous functions from [latex]\mathbb R\rightarrow\mathbb R[/latex] that the sum of [latex]p_1+p_2[/latex] is continuous but I don't see how that would be possible as the domain of the functions are [latex]\mathbb R[/latex] and not [latex]\mathbb R^2[/latex].
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cicada 3301 became internet Phenomenon, but still puzzle is unsolved.
but i have a doubt who's behind cicada 3301? will it reveal the time machine?
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This morning, my father scolded me for getting low marks. I knew that if I started crying, he would stop scolding me. But what to cry about? Then I had it! Yesterday, I saw a video at shock site that I couldn't buy and that made me cry all afternoon! So I thought about the video again. But it wasn't working! Why is it, when we need to cry, it just doesn't work?
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I'm trying to derive (14.25) in B&J QFT. This is
[latex]U(\epsilon)A^\mu(x)U^{-1}(\epsilon) = A^\mu(x') - \epsilon^{\mu\nu}A_\nu(x') + \frac{\partial \lambda(x',\epsilon)}{\partial x'_\mu}[/latex], where [latex]\lambda(x',\epsilon)[/latex] is an operator gauge function.
This is all being done in the radiation gauge, i.e. [latex]A_0 = 0[/latex] and [latex]\partial_i A^i=0[/latex], with [latex]i \in {1,2,3}[/latex].[latex]\epsilon[/latex] is an infinitesimal parameter of a Lorentz transformation [latex]\Lambda[/latex].Under this transformation, [latex]A^\mu(x) \rightarrow A'^\mu(x')=U(\epsilon)A^\mu(x)U^{-1}(\epsilon)[/latex].The unitary operator [latex]U[/latex] which generates the infinitesimal Lorentz transformation[latex]x^{\mu} \rightarrow x'^{\mu} = x^{\mu} + \epsilon^{\mu}_{\nu}x^{\nu}[/latex] is[latex]U(\epsilon)=1 - \frac{i}{2}\epsilon_{\mu\nu}M^{\mu\nu}[/latex]where [/latex]M[/latex] are the generators of Lorentz transformations. (I guess really I should have [latex]M^{\mu\nu}=(M^{\rho\sigma})^{\mu\nu}[/latex]. M is a hermitian operator, so[latex]U^{-1}(\epsilon)=1 + \frac{i}{2}\epsilon_{\mu\nu}M^{\mu\nu}[/latex]Now I tried writing out [latex]U(\epsilon)A^\mu(x)U^{-1}(\epsilon)[/latex] explicitly but it didn't really get me anywhere. The answer is supposed to have [latex]x'[/latex] as the argument of [latex]A^\mu[/latex] on the RHS but I only get [latex]x[/latex]. I'm not sure how to Lorentz transform the function and the argument at the same time.Underneath the formula in B&J it says the gauge term is necessary because [latex]UA_0U^{-1}=0[/latex] since [latex]A_0=0[/latex]. I don't see why this warrants the need of a gauge term I'm guessing it's needed because otherwise there will be no conjugate momenta for the [latex]A_0[/latex].I also want to find what [latex]\lambda[/latex] explicitly is.0 -
I come cross one proof the Landau-Yang Theorem, which states that a [latex]J^P=1^+[/latex] particle cannot decay into two photons, in this paper (page 4).The basic idea is, the photon's wavefunction should be symmetric under exchange, however the spin part is anti-symmetric and the space part is symmetric and therefore forbidden.I have trouble understanding the argument about the space part:Since the photons conserve linear momentum in the particle rest frame and space is isotropic, they must be emitted in spherical waves.Why the space is isotropic? Is isotropy an intrinsic property of original particle or just because the final particles are identical?I guess the right answer is the latter one, because [latex]\rho^+ \to \pi^+ \pi^0[/latex] the final pions lie in [latex]P[/latex] wave and it doesn't bothered by the Bose-Einstein statistics. (Compare this with [latex]\rho^0\to \pi^0 \pi^0[/latex], which is forbidden.)However, I still believe the isotropy is an intrinsic property of the original particle. I'm looking for an explanation more mathematically, or a definition of isotropy in the language of group theory.Any suggestions?
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how to receive notifications to my email, if somebody replied to my post?
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It's my understanding that when something is going near the speed of light in reference to an observer, time dilation occurs and time goes slower for that fast-moving object. However, when that object goes back to "rest", it has genuinely aged compared to the observer. It's not like time goes slow for a while, and then speeds back to "normal," so that the age of the observer once again matches the object. The time dilation is permanent. Why wouldn't the same thing happen with length contraction? Since the two are so related, you'd think if one is permanent, the other would be also. And from everything I've read so far, length contraction is not permanent. An object will be at rest touching an observer, go far away near light speed, return to touching the observer, and be the same length it was at the beginning. It shortens, and then grows long again, as if its shrinkage was an illusion the whole time. Did I just not read the right things or what? Were my facts gathered incorrectly?
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We all (sooner or later) have noticed that foods relatively high in protein (especially those low in fat) are very prone to sticking to a pan, or in general to any non-specially-coated metal surface. For example really lean white fish, which is almost all protein, is one of those devils which will always want to stick. Likewise, egg whites can stick. To some extent, almost any food that doesn't have a generous amount of easy-rendering fat seems to stick, but higher protein is more sticky.
To counteract this tendency, one learns to compensate by putting some kind of fat (usually oil or butter) into the pan in advance of the food. Most people seem to get the best result by preheating the dry pan some, then adding the oil, letting it get up to temperature, then adding the food.
I was just trying to ask myself what would be a simple and general sketch of what is going on on the surface of a pan when sticking takes place, and in particular:
1) what features of a material (density, chemical composition, elasticity, specific heat,etc.)
2) and of the state of the surface (temperature, roughness, etc.) have a dominant role in the physics of such a system.
3) Which phenomena (lubrication, intermolecular forces, order-disorder phase-transitions, etc.) are more likely to be responsible for what we experience in our every-day life.
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I figure that at large enough distances, the potential field of an ion is just the Coulomb potential for its net charge. But what happens at scales comparable to the ion's Bohr radius? Could there be, for example, some sort of screening effect from the electron shell that changes the potential? (depending on what the test charge is, like if you dropped a single electron near an ion)
I'm a bit rusty on quantum mechanics, but I do remember that the math for atoms that aren't hydrogen gets complicated. Is there a known good way to approximate this potential? Or is my best bet to go download some quantum chemistry software?
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If the electric field and boundary conditions are known exactly for a region of space, is it true that there exists only one charge distribution in that region of space that could have produced it?
My understanding of the uniqueness theorem in electrostatics is that for a given charge distribution and boundary conditions for a volume, there exists only one (unique) solution to Poisson's equation, and thus the electric field in that volume is uniquely determined. Does the arrow point the other way, too? If we know the field and boundary conditions, is the charge distribution uniquely determined in the volume? Is there a simple example that illustrates why or why not?
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I'm working through Sakurai's Modern Quantum Mechanics and in the section on Permutation Symmetry and Young Tableaux, he mentions that a tableau constructed of [latex]\square = \boxed{1},\boxed{2},\boxed{3}[/latex] corresponds to a irrep of [latex]SU(3)[/latex], but if each box is instead a [latex]j=1[/latex] object, a tableau is not a irrep of the rotation group.He then goes on to discuss this in detail, although I cannot follow his argument other than taking a guess that the decomposition of the mixed symmetry tableau leads to some incompatibilities in representing the rotation group.Can anyone clear up why a tableau composed of a [latex]\square = \boxed{1},\boxed{2},\boxed{3}[/latex] can correspond to a definite representation of [latex]SU(3)[/latex] but not to a [latex]3[/latex]-dimensional representation of [latex]SU(2)[/latex], or the rotation group?
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Weinberg-Witten theorem states that massless particles (either composite or elementary) with spin [latex]j > 1/2[/latex] cannot carry a Lorentz-covariant current, while massless particles with spin [latex]j > 1[/latex] cannot carry a Lorentz-covariant stress-energy. The theorem is usually interpreted to mean that the graviton ([latex]j = 2[/latex]) cannot be a composite particle in a relativistic quantum field theory.While the argument is so strong and weird, how is it possible? Why can we not construct a theory which is massless charged vector field and therefore carry a Lorentz-covariant current ? And although we assume the second argument is right, which says massless particles with spin [latex]j > 1[/latex] cannot carry a Lorentz-covariant stress-energy, how does it imply that the graviton ([latex]j = 2[/latex]) cannot be a composite particle ?
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When a ray of light is projected, (say) from the surface of Earth to outside in space. The condition is that, there is no obstruction to it till infinity (it travels only in vaccum). My question is that how far can that ray of light go?
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Also, instead of a ray of light, if I consider a beam of laser with same conditions, then how far can a beam of laser go?
Compare both the situations.
And does the light(ray of light and beam of laser) stops after traveling some distance or it has no end?
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Here are the 2+1D gravitational Chern-Simons action of the connection [latex]\Gamma[/latex] or spin-connection:
[latex]S=\int\Gamma\wedge\mathrm{d}\Gamma + \frac{2}{3}\Gamma\wedge\Gamma\wedge\Gamma \tag{1}[/latex][latex]S=\int\omega\wedge\mathrm{d}\omega + \frac{2}{3}\omega\wedge\omega\wedge\omega \tag{2}[/latex]
Usual Chern-Simons theory is said to be topological, since [latex]S=\int A\wedge\mathrm{d}A + \frac{2}{3}A\wedge A \wedge A[/latex] does not depend on the spacetime metric.
(1) Are they topological or not?
(2) Do they depend on the spacetime metric (the action including the integrand)?
(3) Do we have topological gravitational Chern-Simons theory then? What do (1) and (2) mean in this context?
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Anxiety sometimes cause diarrhea, sometimes constipation, and sometimes both. It's interesting because it seems their underlying neurophysiology is somehow different. What are underlying physiological processes that lead to these two symptoms in anxious people? Particularly in terms of the activity of sympathetic and parasympathetic nervous system?
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I know that first generation H1 antagonists, commonly known as antihistamines have anticholinergic effects. Their sedative side effects go away due to tolerance, but as for their anticholinergic side effects well that's something that is unknown to me at least. You might say use second generation H1 antagonists, but for this application the antiemetic effects that are unique to H1 antagonists that cross the BBB (i.e., first generation H1 antagonists) are desired.
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I know that the [latex]5HT_{1A}[/latex] and α2 adrenoreceptors receptors serve as autoreceptors for serotonin (5-HT) and norepinephrine respectively and are down-regulated by repeat exposure to their respective ligands, it's believed that this is likely the cause for the therapeutic delay in the actions of antidepressants that target the serotonergic and noradrenergic systems. My question is this: "Is this the case for all autoreceptors? Are all autoreceptors down-regulated by the actions of their respective ligands?"
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I understand that too much close reading will strain the ciliary muscles of the eyes. But what about small fonts? The contraction of the ciliary muscles is dependent on the distance not font size.
In other words, it is better to read from a closer monitor with bigger font or from a further monitor with smaller font?0 -
I'm trying to get the data for the Human and Mouse 12 and 23 Recomination Signal Sequences (RSS), to run a classification algorithm on it. I'm not a biologist, so I apologise in advance for my misunderstandings and confusion.
A version of the data is available here, but I thought I would try to get it from www.imgt.org, if possible. There is also another slightly different version available for the mouse here.
I'm trying to follow the instructions at IMGT-FAQ to obtain Recombination Signal Sequences for the mouse.
Here is what I have selected at the search page:
Identification:
Species : Mus Musculus
GeneType: any
Functionality: functional
MolecularComponent: any
Clone name: <blank>
IMGT group: IGHV
IMGT subgroup: any
IMGT gene: <blank>I'm not clear what "Locus", "Main locus", and "IGMT group" mean here exactly. Specifically, what is the difference between "Locus" and "Main locus"?
I think, but am not sure, that IGHV corresponds to V genes in the Immunoglobulin heavy locus (IGH@) on chromosome 14, where locus here denotes collections of genes. Clarifications and corrections appreciated.
I would have expected that the IGH locus would correspond to "IMGT group" entries like "IGHJ, IGHV" etc, and the IGK locus would correspond to IMGT group entries like "IGK, IGKJ, IGKV", but no matter what I select for Locus, it does not change the possible entries for "IMGT group".
Running the search gives
Number of resulting genes : 218 Number of resulting alleles : 350
As instructed, I went to the bottom, selected "Select all genes", clicked on "Choose label(s) for extraction", and selected "V-RS".
I got
Number of results=98
The first few results were
X02459|IGHV1-4*02|Mus musculus_BALB/c|F|V-RS|395..432|38 nt|NR| | | |
|38+0=38| | |
cacagtggtgcaaccacatcccgactgtgtcagaaacc
>X02064|IGHV1-54*02|Mus musculus|F|V-RS|295..332|38 nt|NR| | | | |38+0=38|
| |
cacagtgttgcaaccacatcctgagtgtgtcagaaatc
>M34978|IGHV1-58*02|Mus musculus_A/J|P|V-RS|554..560|7 nt|NR| | | |
|7+0=7|partial in 3'| |
cacagtgOk, now I'm confused. The lengths of the RSS should be 28 or 39. but I counted lengths of 4,7, 31, 38, and 39. Are the results here not supposed to contain the 12 and 23 RSS?
So, I must be misunderstanding things here. Possibly many things. Any explanations and clarifications are appreciated.
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If [latex]r:I\rightarrow J[/latex] is a smooth surjective function between perfect subspaces [latex]I[/latex] and [latex]J[/latex] of [latex]\mathbb{R}[/latex], can we always find a right inverse smooth function [latex]s : J \rightarrow I[/latex], i.e. [latex]r\circ s = id_{J}[/latex]?
In the same fashion, does every smooth injective [latex]s:I\rightarrow J[/latex] have an smooth injective left inverse?
A necessary condition is for the derivatives of [latex]r[/latex] and [latex]s[/latex] to be non-singular (in [latex]s(J)[/latex] and [latex]J[/latex] or in [latex]r(I)[/latex] and [latex]I[/latex] respectively at least).
So one should at least assume that.
This also implies that [latex]r[/latex] and [latex]s[/latex] are locally invertible there.
For example:
Loosening the question a bit,
if [latex]s : J \rightarrow I[/latex] is continuous and injective, then by the intermediate value theorem we can conlude that [latex]s[/latex] is monotone on every connected component of [latex]J[/latex].
If [latex]J = [a,b][/latex] is a compact interval, one can define a retraction [latex]r : I \rightarrow J[/latex] by inverting [latex]s[/latex] on [latex]s(J)[/latex] whilst being constantly [latex]a[/latex] or [latex]b[/latex] on the parts above and below [latex]s(J)[/latex] in [latex]I[/latex].
But what is if we really talk about smooth functions?
Where can I find a discussion on this and are there some nice counter-examples?
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Maybe it is fruitful to also generalize and rephrase this question in terms of categories.
I want to investigate the relations between the following kinds of maps in [latex]\mathcal{C}[/latex]:
- surjective maps [latex]o[/latex]
- injective maps [latex]i[/latex]
- right-cancellable maps (epics) [latex]e[/latex]
- left-cancellable maps (monics) [latex]m[/latex]
- right-invertible maps (split epics/retractions) [latex]r[/latex]
- left-invertible maps (split monics/sections) [latex]s[/latex]
where [latex]\mathcal{C}[/latex] is some adequate category of topological/smooth spaces.
In the square brackets stands the name I’d prefer to use for maps with the corresponding property.
Categorically we have the implications “[latex]r \Rightarrow e[/latex]” and “[latex]s \Rightarrow m[/latex]”.
In concrete categories I understand we also have “[latex]o \Rightarrow e[/latex]” and “[latex]i \Rightarrow m[/latex]”.
Now, I’m mainly interested in the implications “[latex]e \Rightarrow r[/latex]” and “[latex]m \Rightarrow s[/latex]“, that is:
> For which categories [latex]\mathcal{C}[/latex] of euclidian (topological/smooth) spaces is:
>
> - every epic a retraction, and
> - every monic a section?
And I’d be more than happy to have an answer only for categories in which the objects are perfect subspaces of [latex]\mathbb{R}[/latex] and morphisms are [latex]C^1[/latex] or [latex]C^\infty[/latex].
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I am just curious for what religious reasons there might have been. In certain sects of Hinduism, women are asked to not enter the kitchen, eat and sleep separately from the rest of the family, not enter temples, etc. when they are menstruating. One obvious reason may have been sanitary reasons, but it is still followed in 2014 when it is no longer a reason. Are there any other, religious reasons for this?
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Cosmic rays and neutrinos
in Astronomy and Cosmology
Posted
I'm reading Gaggero's Cosmic Ray Diffusion in the Galaxy and Diffuse Gamma Emission and he makes the claim,
The existence of neutrinos stems from relativistic protons colliding with ambient protons. Neutral pions are the primary decay mode for [latex]pp[/latex] collisions, but charged pions can also be made alongside the neutrinos.
My question is then would the non-detection of neutrinos be a statistic issue or would it suggest Supernova Remnants do not accelerate protons?