Physics Discussion Thread

[SaiK]

when you say time is quantized, do you mean it can be broken up into multiple levels like in D/A signals? like audio signals at 64kbps with 256 level of quantization.

why not time being quantized on time scale itself? is that quantization on say x-axis, say at nano second level, one could analyze an event.. or even futher sliced up? what is the lowest one can achieve that makes significance for the events?

can we get to some examples to make it little bit more specific? i hope you guys don't mind asking questions from moorkh level.

[Amber G.]

matrimc,

First, as you know, you can learn/know of EGC much better from other sources than I can give here. EGC was already a very respected professor when I first met him (in late 60's). (At that time, there were very few - as in one can count on one or two hand(s) - indian faculty members in Physics in whole of USA -- there weren't than many Indians in general either). He was then in Syracuse or Rochester NY.

Okay, let me ask you, what you think about the questions I posted before. Also how credible , for example, you will find the report of steel plate leaving with 6 times the escape velocity.

P.S. If you (or anyone else) really interested in EGC's work, the 2006 symposium on "Seven Science Quests" are quite readable...
(These are lectures about:
1) V-A: Universal Theory of Weak Interaction, 2)Symmetry, 3)Spin Statistics,
4)Quantum Optical Coherence: (Sudarshan Representation), 5)Quantum Zeno Effect
6)Theory of Tachyons, 7) Quantum Mechanics of Open Systems

(V-A Theory, Quantum Optical Coherence - Noble prize went to others..), Tachyons are particles faster than light..)
http://quest.ph.utexas.edu/sudarshan_open.html

[member_27873]

This has happened to me in desh streets when I was a kid.. lot of street dogs used to chase me.. some are mad! So, normally I have a certain amount of energy to expend - but when these dogs chase me, I get the extra energy coming from no where! where is that conserved? Is it that we can produce more than we can consume?

WOMAN VS. POLAR BEAR
Adrenaline doesn't just help people lift cars. In Ivujivik, Quebec, in 2006, Lydia Angyiou wrestled a large polar bear that she saw advancing toward her son and another boy while they played hockey. Angyiou tackled the polar bear and fought it while the boys ran for help. While Angyiou suffered some wounds, the polar bear ultimately lost the fight. Angyiou sparred with it long enough that a neighbor was able to shoot the bear four times until it died.


In 2006 in Tucson, Ariz., Tim Boyle watched as a Chevrolet Camaro hit 18-year-old Kyle Holtrust. The car pinned Holtrust, still alive, underneath. Boyle ran to the scene of the accident and lifted the Camaro off the teenager, while the driver of the car pulled him to safety.



Adrenaline and Strength
When we feel fear or are faced with a sudden dangerous situation, the human body undergoes an amazing change. The stressor -- for example, the sight of your son pinned beneath a car -- stimulates the hypothalamus. This region of the brain is responsible for maintaining the balance between stress and relaxation in your body. When it's alerted to danger, it sends out a chemical signal to your adrenal glands, activating the sympathetic system, which sends the body into an excited state. These glands release adrenaline (epinephrine) and noradrenaline (norepinephrine), hormones that create the state of readiness that helps a human confront danger. Together, these hormones raise heart rate, increase respiration, dilate the pupils, slow down digestion and -- perhaps most importantly -- allow muscles to contract.
All of these changes in our normal physical state prepare us to face danger head-on. Combined, they make us more agile, allow us to take in more information and help us use more energy. But adrenaline's effect on muscles accounts for amazing strength. Adrenaline acts on muscles, allowing them to contract more than they can when the body is in a calm or neutral state.
When adrenaline is released by the adrenal medulla -- an interior region of the adrenal glands, which are located just above your kidneys -- it allows blood to flow more easily to your muscles. This means that more oxygen is carried to your muscles by the extra blood, which allows your muscles to function at elevated levels. Skeletal muscles -- those attached to bones by tendons -- are activated by electrical impulses from the nervous system. When they're stimulated, muscles contract, meaning they shorten and tighten. This is what happens when you lift an object, run or throw a punch. Adrenaline also facilitates the conversion of the body's fuel source (glycogen) into its fuel (glucose). This carbohydrate gives energy to muscles, and a sudden burst of glucose also allows muscles to strengthen further.
So does this mean that we have superhuman strength that is unlocked when we're confronted with danger? That's one way to put it.

[Vayutuvan]

AmberG, looks like EGC was at Syracuse around the same time John Alan Robinson (Automatic Theorem Proving through Proof by Contradiction using what is known as resolution principle). That is interesting would they have had contact?

[SaiK]

yadagiri, my apologies earlier to my post. i wish i had not posted that.

i am considering myself ill-knowledged on fizzics matter or energy or something that has both.

[Prem Kumar]

Regarding quantization: Brian Greene's string theory book (though its been around for a while) is very interesting. It talks about how the strings impose minimum length restriction, doing away with the infinities associated with merging general relativity & quantum physics. This minimal length provides a "bounce" effect if you try to probe smaller lengths.

Since Einstein talked about space & time as not necessarily separate entities, I dont know if this implies some sort of "minimum duration of time" restriction.

Mathematically speaking, will quantization of space affect, say calculus which assumes continuum? If we are talking Planck lengths, I'd assume that the basic rules of calculus would still apply except under extreme conditions.

However these days, string theory has become somewhat of a Nostradamus prediction list. The theory predicts nothing & almost everything observed can be somehow retrofitted into it under the garb of "richness" of the theory

On an aside, AmberG: is ECG justifiably upset at being passed over for the Nobel?

[Vayutuvan]

Prem Kumar,

Since Einstein talked about space & time as not necessarily separate entities,

That is an interesting point. If one is proved to be quantized does that imply the other to be quantized?

[SriKumar]

Also looks like there is an agreement while discussing dew under a tree. But I did not see any post here about experimental results. What do people really see? Is there less dew or not ? Have you noticed any difference?

It does seem like there is lesser dew beneath a tree. Some googling suggests that air prevented from rising by the 'brolly/bough' of a tree might be a cause. But at first glance, it seems less likely- one could argue that warm air can seep through the leaves or go around the brolly/bough and still escape the tree zone.

[negi]

Well without rigorous math at times some topics veer off dangerously close to philosophy , not that I know about these even without math (math se to fatathii thi apni , number aa jate the wo alag baat hai). So if jirga indulges me since we are talking about time , my question is did Time exist before the Big Bang ? Or the best answer is still the thousand or so year old verse from Nasadiya Sukta from Rig veda which can be summed as being agnostic ?

[Vayutuvan]

negi moshay, nAsadIya sUkta is the precursor to the theory that time had no meaning before big bang.

[Prem Kumar]

Prem Kumar,

Since Einstein talked about space & time as not necessarily separate entities,

That is an interesting point. If one is proved to be quantized does that imply the other to be quantized?

Dont know. If min length is say L, then there must be a minimum time T which is the time taken by light to cover distance L in vacuum. Any unit of time smaller than T cannot be probed, I guess.

But one thing for sure: if quantization is proved, even special relativity has to be reformulated. The Lorentz contraction formula describes a continuous length contraction all the way to zero as an object approaches the speed of light. If there is a minimum length restriction, the equation needs to reflect that.

If quantization is true, we should also have a rethink of what distance & speed mean .......

[SaiK]

negi moshay, nAsadIya sUkta is the precursor to the theory that time had no meaning before big bang.

wouldn't that be relative? if we consider t=0, at big bang, and before that if one could not argue on the state of matter, it should mean only that at t=-1 is only not relative to t>=0?

in the sense, is it okay to say, at t<=0, time has no meaning?

--

q: if any unit of time(δt) or length (δl) so small can't be probed, would it be because of we have reached the ultimate δ that can be probed but time has not moved, in the sense δt is so tiny, that it is irrelevant or in a state of constant?, or our probes are limited to some δx + T technological limit?

i was talking from time in yocto seconds or even smaller? I think somewhere we have to stop, and say, we can divide time only to a level that makes sense for us or relevant. i am trying to understand what you all are talking.

did i fumble?

--

btw, bad news for fizzics grads... per npr today afternoon, they were talking about statistics (part of the STEM (bill gates)) that at least 50-80% are jobless or not doing the job that is fizzics based.

[Vayutuvan]

Prem kumar just a heads-up that I wrote a continuation to my previous post on "deciphering Indus script" thread.

[Vayutuvan]

SaiK, it would be great if AmberG could talk about the arrow of time and time cones. Think about t=0 - one can always do an affine transformation so that there is no t < 0. There is no constraint along time axis.

[SaiK]

may be i was thinking before t=0, and t spanning into states where t=0 was just an initial state for big bang, and a final state for whatever that was earlier? for the vedics : shanti mantra point(poornamadah). perhaps a stringed states, and a quantum jump from one string to another by a big bang.

[Amber G.]

Also looks like there is an agreement while discussing dew under a tree. But I did not see any post here about experimental results. What do people really see? Is there less dew or not ? Have you noticed any difference?

It does seem like there is lesser dew beneath a tree. Some googling suggests that air prevented from rising by the 'brolly/bough' of a tree might be a cause. But at first glance, it seems less likely- one could argue that warm air can seep through the leaves or go around the brolly/bough and still escape the tree zone.

Yes, I have noticed it and It is quite noticeable (If one likes to see starts, it is comfortable to watch it while lying down on sleeping bag - without tent - and it is quite noticeable)..

One can see photos like:


Where snow has melted... (Check out any similar photos or in real life)

Or, If you have infrared camera ..


Or practical use like:
Checking a tree's health by taking its temperature
(Infrared sensors offer possibility of automating irrigation scheduling and evaporative cooling to maximize yields and reduce water use)

[Vayutuvan]

AmberG those photos (esp. the ir one) nicely illustrate where the temp is high. So it is along the trunk but for the where the trunk meets the ground. Will pose this question to my daughter and her classmates.

[Amber G.]

R
On an aside, AmberG: is ECG justifiably upset at being passed over for the Nobel?

Prem,

There was quite a bit of discussion in BRF (and also among physicists and Indian media) when Glauber got the Nobel.

Everyone understands that Nobel (or any other prize for that matter) is also subjective and many deserving people have not gotten it. I don't think he was "upset" for being passed over, from what I have seen "upset" is too strong a word... Many were disappointed though.

What did upset us all (including ECG and many of serious physicists) was Nobel committee sighted Sudarshan diagonal representation (Calling it "Glauber-Sudarshan representation" which is inaccurate although some others have called it by that name, the work is all Sudarshan's and in fact Glauber mocked/criticized it when Sudarshan first published it....IOW it was awarded on ECG's work but NOT to ECG.. (Perhaps Mandel and perhaps Walls, (or Mehta ) could have shared with ECG, but not Glauber, if that work was cited for the Nobel).
ECG had a famous quote around that time something to the effect "Noble committee can award the prize whoever they want but they should not award it to some one else about my work"

(FWIW as one can tell, I do not particularly like Glauber - so did some others I knew, because he was a little arrogant and really not nice IMO - his statements after the Nobel wrt to ECG were not nice either IMO)

I do think 2005 prize, specially when it was awarded for his work should have been given to him.

IMO, 1979 too when the prize was awarded to Glashow, Abdus Salam and Weinberg their work was based on his work - V-A theory (which ECG regards as his finest work, and Oppenheimer, for example assessed as "beautiful") never got Nobel. It was essentially the same theory as that proposed by Feynman and Gell-Mann the structure of the weak interaction. (Actually Gell-Mann had been let in on Sudarshan's work by Sudarshan). Feynman later credited ECG - though he did not know of his work at that time )

[ramana]

AmberG, The Jules Verne book was titled "From the Earth to the Moon".

[SriKumar]

The above picture brings up another point. I am guessing the tree is radiating heat because of the heat generated internally as a by-product of respiration (and not emitting absorbed solar radiation as originally suggested by moi). The trunks appear too thin to conserve heat absorbed from an external source i.e enough heat to melt snow (no calcs to support this supposition).


Musing aloud here.....IF Red=warmest; and blue=coolest. Why is the base of the trunk cool? And the ground hot? Perhaps the picture was taken during daytime (which would explain the red ground), and the tree's roots go deeper than 2 meters- into soil that is cold (i.e. at winter temperature) thus cooling the tree near the trunk.

[Amber G.]

AmberG, The Jules Verne book was titled "From the Earth to the Moon".

Yes. This is a famous book, actually around Apollo 11's launch many many were commenting about it.
(Capsule was "Columbia", launched from Florida (Almost the same site as in the book), landed back in pacific ocean - uncanny - almost same size capsule, took almost exactly the same time to travel to the moon etc.. etc.)

Anyway, the reason the travel time, escape velocity etc ..were not a coincidence because Verne's friend (who was good in physics) did all the calculations.. basic facts/physics about orbits etc were known then (thanks to people like Newton). (One fact did bother Verne that he did know that a gun will not be able to shoot the capsule in space (I gave the reason in other posts) but though he had a very good imagination, he did not imagine rockets).

BTW, BRF is amazing because there was this discussion about 5 years ago!!! (see below)

(And again merits of gun type (or fast burn rockets) missiles and why they are not likely to be successful for sending things in orbit or beyond were discussed... and I did mention the same principle then too. Please check out these posts..... [edited by mod to delete reference to N^3 profession]

(On a side note, I certainly miss many of the sharp people who do not post in brf anymore)

Any way check out these posts from 2008 (and a few posts above and below)
http://forums.bharat-rakshak.com/viewto ... 81#p501781

shiv wrote:
Isn't any gun that is fired into the air "fast burn" missile launcher? Jules Verne etc. [end quote]

I don't know exactly what you mean, but a "gun', no matter how much initial velocity it gives, will have a very finite range. (Due to air resistance - it will reach terminal velocity and/or burn very soon) (actually on first order - the length of the "bullet" alone (of a know material) will determine how far it will go... (A good/popular physics problem often given)

Actually Jules Verne "knew" that a gun could not fire the missile he described to the moon staying under the atmosphere as it would never reach the escape velocity.

I liked N^3's quotes on madarasa type math and wild claims.. he ends up:

..But the Bofors reaches maybe Mach 3 tops (?) whereas you need about Mach 8 or 10 for a long range missile. Orbit shot requires about Mach 30, and moon shot requires about Mach 45. Gun will be either very strong or very long, and the astronauts will be very short and squat like Shrilleen. Or thin as a dosa.

http://forums.bharat-rakshak.com/viewto ... 86#p501786

BTW, there is quite a big difference between Harp type missiles (which is quite consistent with common sense) and 900 Kg mass flying with 6 types escape velocity. (The KE energy ratio is MORE THAN 1000!) (3.6Km (Mach 10-11)- harp is still about 1/3 of the escape velocity ... and even a few hundred Km range - which one can obviously see from Newton type calculations -- is nowhere close to shooting it into space (or even in earth's orbit) as N^3 says above..

[Amber G.]

The above picture brings up another point. I am guessing the tree is radiating heat because of the heat generated internally as a by-product of respiration (and not emitting absorbed solar radiation as originally suggested by moi). The trunks appear too thin to conserve heat absorbed from an external source i.e enough heat to melt snow (no calcs to support this supposition).

No, I am not saying anything about respiration - A tree (as long as it is above absolute zero temperature) will emit radiation. (In day the tree, receives radiation mainly emitted from Sun, and emits back - A steady-state temperature is reached, in night it is emitting and temperature of the tree goes a little down but it is still radiating.

(Energy or heat radiated by the tree per unit area is = e*k*T^4 , k is Stefan–Boltzmann constant, (e for tree is almost 1 and T is absolute temperature of the tree)

[Amber G.]

There were many good and interesting posts about whether a reactor can explode (or not) like an atomic bomb. Here are some of my comments.

I am putting these comments here because I think it is important for brf to know these facts, and be able to explain the logic to aam janata, since these facts, in spite of all the hulla gulla, are not widely known (or even sometimes misunderstood).

An atomic bomb requires fast (not moderated) neutrons in order to have the entire 80 or so generations of atom splitting over with before the bomb blows itself apart. After 80 generations the temperature reaches very high (millions of degrees). The only reason the bomb does not blow apart at this point is that there simply isn't enough time as everything happens quite fast. With moderated neutrons (neutrons are very slow) chain reaction is much slower.

This is important:

Commercial reactors depend on slow neutrons. The reason this is crucial is, if the reactor begins to "run away" - say operator made a mistake or something really bad occurred - the chain reaction begins to go exponentially (starts doubling); then slowness of the neutrons limits the size of the explosion. (At about a few thousand degrees the atoms of the fuel is moving much faster than the neutrons). Neutrons can't catchup, so to speak, and the chain reaction stops. Yes there can be an explosion, (about the same magnitude as if that much TNT exploded), and this explosion can be large, but it is still about a million times less than a nuclear bomb. (Meltdown is not the same as nuclear explosion)

A chain reaction that depends on slow neutrons can not give rise to a nuclear explosion.

There are dangers of such reactors, but blowing up like a nuclear bomb is not one of them.


Hope this helps.

[Vayutuvan]

AmberG, asking for a small clarification here which is not clear to me from the above explanation.

"Fast" neutrons are neutrons in their natural state but in nuclear reactor they are slowed down due to heavy water etc.? Is it dependent on the density (i.e. >= critical mass is assembled under pressure of an implosion) as well as a large surfaces area is contact (let us say two hemispheres are pushed together then the area of volume/area of contact is proportional to $r^{1.5}$. Does that matter also?

[Amber G.]

Matrimc,

Slow or fast neutrons are basically what one will assume they are. Higher velocity means - faster neutrons (which will have higher energy). Energy is just 1/2 mv^2 ( for really fast, one use relativistic formula mc^2 where m=m_0/sqrt(1-v^2/c^2) etc))

Normal language uses:

Thermal Neutron (internal energy equal to KE of a normal room temp particle) = about 0.025 eV
Slow Neutron -- about 1-10 eV
Fast Neutron -- Typically about 1-20 MeV (1000000 eV to 20,000000 eV)
Relativistic Neutrons - > 20 MeV

1 eV = is of course, about 1.6*10^(-19) Joules)

A typical neutron coming out of U235 fission fast (about 2 MeV) (It is a distribution with different
energies)... (Water (or D2O etc) is used in a typical reactor so that these are slowed down to about 1 eV)



One can calculate velocity (1/2mV^2), 1MeV is for neutron is about (simple calculation) 14000 Km/sec (yes quite fast!)

1GV neutron is about 90% speed of light..
1 eV neutron is about 14 km/sec (Yes, it is more than escape velocity!)
Thermal neutrons are about 2Km/sec.

It is all simple math...!

[SaiK]

The scheme may have an intriguing medical application: the set-up generates beams able to both detect and treat cancerous cells on human skin (which absorb THz wavelengths differently than healthy skin cells).

http://www.frontline.in/science-and-tec ... 038358.ece

interesting, that means such identified cancer cells can be exterminated by certain modulated wave pattern. no?

[Amber G.]

"Fast" neutrons are neutrons in their natural state but in nuclear reactor they are slowed down due to heavy water etc.?

I do not understand exactly what you mean here by "their natural state"?
Do you mean a neutron which was produced from a U235 fission?
(And yes these neutrons indeed are slowed down by water or D2O)

(Neutrons outside a nucleus - coming out from radioactive decay, or fission reaction have very widely varying energies..some are slow, some are fast. A typical U235 atom, when it fissions, gives
out energy in the form or KE of split nuclei- heat etc -(main part of explosion)+ some gamma rays+
fast neutrons... Typically about 2% of the released energy is of the form of KE of neutron(s) - hence
the typical neutron coming out from a U fission has a energy of about 2 MeV.. and is quite fast.

(If there are enough U235 nuclei packed close by (> critical mass) the neutron has a chance to spilt another U nuclei before it just flies away. If neutron is somehow slowed, say by a moderator, it spends more time and has a better chance to spilt another U235 even if you have less than critical mass.. or concentration of U235 in U is only 3-4%)

[Amber G.]

The scheme may have an intriguing medical application: the set-up generates beams able to both detect and treat cancerous cells on human skin (which absorb THz wavelengths differently than healthy skin cells).

http://www.frontline.in/science-and-tec ... 038358.ece

interesting, that means such identified cancer cells can be exterminated by certain modulated wave pattern. no?

Interesting and most likely will yield practical benefits.

[Vayutuvan]

"Fast" neutrons are neutrons in their natural state but in nuclear reactor they are slowed down due to heavy water etc.?

I do not understand exactly what you mean here by "their natural state"?

Sorry for being not clear. Let me rephrase the question.

Are these species "sharply" defined? In other words, if one takes a large number of neutrons and measure the energies (is it equivalent to their speeds?) does that pdf be normal or multi-modal? If the latter, would it have finite number of modes?

[Amber G.]

I do not understand exactly what you mean here by "their natural state"?

Sorry for being not clear. Let me rephrase the question.

Are these species "sharply" defined? In other words, if one takes a large number of neutrons and measure the energies (is it equivalent to their speeds?) does that pdf be normal or multi-modal? If the latter, would it have finite number of modes?

I still do not understand exactly what you mean by "species". If one takes a large (well, not that large ) number of neutrons cars, it depends if they are in a parking lot or in a traffic jam on in a race track .. and also a fast car (say just came out from a highway) may slow down if it enters a traffic jam etc..

In one case, say neutrons in air (O2 or N2 nuclei) at room temperature (about 20C), has a mean (actual RMS) speed of about half a Km/sec. The distribution of velocity (or rather KE) follows MB distribution etc.. Neutrons, emitted by , say some decay, spent enough time in a moderator to "cool" down to room temperature will have energy about .02 eV. (distributed around this mean RMS value) and average speed, as said before (and if my calculations are correct - I don't remember all this, but it is very easy to calculate), is about 2Km/sec.

Neutron's coming out of U235 fission are much faster, if they get traffic jammed by water molecules (when these neutrons collide with water molecules.. they do loose some energy and they slow down..


As you can imagine it all depends a lot on reactor design.. type of moderator, type of fuel etc..

For example, an easy to understand paper for MIT reactor, can give better answer to your question..
http://web.mit.edu/joans/www/papers/neutrons.pdf

[member_22872]

AmberG ji/matrimC,

Could you please suggest me an elementary book on Topology for self study? where should I start? algebraic Topology? I read Reimann Geometry but it had been a while. I am not a mathematics major.

[Theo_Fidel]

\Start rant\
Downhill skiing now are we….

What happened to the claim of 66 km/sec is djinn power. I mean accusing a nuclear scientist Dr. Brownlee , a doctorate no less, with a dozen or so nuclear tests under his belt, of madrassa math and djinn power, what ever next…. …..And have the courtesy to accuse him directly by name BTW, it would show some integrity.

BTW ‘smart’ people, as opposed to us buddho’s … …please don’t hold back or anything…..

Also please don’t be economical with the truth. Verne’s problem was Gun powder or even dynamite. But with modern propulsion techniques it is very much possible to get to space. Orbit is impossible as the trajectory is incorrect without a course correction or some manner of slingshot maneuver. No Djinn power needed. This was the claim after all, and I quote…

Also, as said before, fairly simple (back of an envelop type) calculation can show that any steel plate of reasonable shape
can not be shot in the space from earth's surface (due to atmospheric drag) by shooting it off with an initial high velocity alone...

Note space, not moon as the latest downhill skiing moment says.

WRT plate the only claim made was on speed which the 'smart' people here misinterpreted as a bat. Almost everyone agrees it burnt up in the atmosphere but there is a non zero possibility that it could leave the atmosphere if certain configurations go right.

And again there was never any question of passengers of any sort. Only materials can be launched into outer space. Not sure why that silly idea is being dragged in here other than to be pedantic.

These sorts of bad/poorly thought thru posts are one reason why some well known mathematicians no longer post here. Also one reason why such technocrats are roundly panned and have lost weightage.

Again this what Dr Brownlee was accused of on BRF!!!

BTW, it seems that the this urban legend was some one's idea to claim Sputnik was not the first object in space.. (See for example this link: http://www.skepticblog.org/2011/12/15/u ... t-sputnik/. (Of course, there will always be a few people who will be ready to believe any thing ).To me the laughable part was some one to believe a claim that 66Km/sec was the "lower bound" because a high speed camera just had only one image in the frame or the "expert" said he saw the disk "flying as a bat" . (Other references talk about this). All this without giving any details about how, where, and what type of camera in 1950's could photograph, in a reliable way, something which will move more than 66 meter in a millisecond!, or where the expert was (near this nuke device) to see it as "flying as a bat"... or how did it was determined that it remained in one piece and not vaporized..etc..etc..

And this from a self confessed smart person as against all the buddho's who did the actual test and photographed the incident. By the way a lesson in American idioms also would be useful unless one is too smart for it.
/end rant/

BTW, there is quite a big difference between Harp type missiles (which is quite consistent with common sense) and 900 Kg mass flying with 6 types escape velocity. (The KE energy ratio is MORE THAN 1000!) (3.6Km (Mach 10-11)- harp is still about 1/3 of the escape velocity ... and even a few hundred Km range - which one can obviously see from Newton type calculations -- is nowhere close to shooting it into space (or even in earth's orbit) as N^3 says above..

[member_27873]

On the surface of it Topology is difficult subject I was told as student in intermediate class, it goes through so many slopes and is slippery to grasp, I recall.

In new science college there was one Dr. Shashuddin a PhD form US, in topology who used wear sherwani pyjama and often used to get lost thinking about surfaces. this was in late 1970s

[member_27873]

They are called bio markers

Why not microwave the cancer cells if we can know the resonant frequency?
Assuming the cancer cells have different mass, tissue density and shape in 3d

[Vayutuvan]

Venug, sorry I have no idea but please look for Dover paperback classics at amazon. I remember seeing one in that collection. They brought back several outofprint classics in inexpensive paperback editions.

[member_27873]

Venug Saar
I grew up with schaum series
So instinctively I googled for it. I remember in my younger days, I once peeped into it and was repelled by the subject. It's that repulsion that brought back my memory. Instead I got Laplace transformed
Good reviews as well in the same page


http://www.amazon.com/Schaums-Outline-G ... 0071763473

[member_22872]

matrimc, no problem saar. I will also look into Dover.

Yadagiri garu, Thanks, will also look into it. It is a very tough subject, but seems like a very interesting nevertheless. Poincare's Conjecture and Grigory Perelman's proof made me look it up.

[SaiK]

OT

[Vayutuvan]

venug, this book might fit your needs - got it from library from the new books section wanting to skim some of the topics in which I am interested - graph embeddings on surfaces and polytopes from topological POV.

Introduction to Topology and Geometry by Stahl and Stenson (ISBN 978-1-118-10810-9) Call no. 514 St14i 2013

Says it is suitable for a two sem UG course and some advanced theorems are proved only through informal argument. Looks like good book (to my non-topo eyes).

[Bade]

This thread is running too fast. Hopefully AmberG will keep everyone on a leash.