- Alan Robinson added an answer:What is the fundamental difference between modulation instability(MI) and Four Wave Mixing (FWM)?Alan Robinson · 4D Optics
Kenneth Schepler's reference to Agrawal's book is worth following.
MI can be explained as a FWM process, but does not require that the input signal is pulsed. Instability is generally only seen in fibres with anomalous dispersion, where the phase mismatch due to chromatic dispersion is offset by the phase shift induced by self phase modulation (SPM) of the carrier.
Any amplitude modulation of the signal results in phase modulation via SPM. Simultaneously, fibre dispersion converts the newly-generated phase modulation to amplitude modulation. For anomalous dispersion, the converted amplitude modulation reinforces the original perturbation. The amplitude perturbation is amplified, with peak gain at modulation frequencies such that the rate of generation of phase modulation by SPM and the phase rotation by chromatic dispersion are exactly balanced. This can be described as phase matched four wave mixing in which the unmodulated optical carrier acts as a degenerate pump, and power is transferred to two equally spaced Stokes and anti-Stokes sidebands.
For fibres with normal dispersion (negative ps/nm/km), FWM between modulation sidebands and carrier still occurs, but the transfer of energy between carrier and sidebands oscillates along the fibre, with no exponential growth of amplitude modulation.
Following - Ankit Verma added an answer:What is the relation between FeO and Fe2O3 in steel-making slag?
Any empirical co-relations or method to link it with any physical measurable quantity will be appreciated.
Ankit Verma · IIT KharagpurYes. or some relation using the oxygen potential. The problem is that in literature we have plenty of data using FeO or FeO and FeO1.5 but in industrial data available has Fe total in their analysis. I may looking for something to bridge the gap.
Following - Adarsh. M. J. added an answer:Does god really exist? Or is it just a product of a weak mind?Our universe is entirely self-contained, natural selection is controlling our evolution,so the question is what role is there for "god" to play?Adarsh. M. J. · B.V. Bhoomaraddi College of Engineering and Technology (BVBCET)
People don't believe in GOD because they are good..... they do it thinking... if they believe in GOD.... gods going to make them good.!
Following - Doug Dykaar added an answer:Is there any Non-linear optical material whose change of refractive index with incident LASER intensity is high?For CS2 it is high but we find new material better than it.Doug Dykaar · DifTek Lasers, Inc.
Organics and Lithium Niobate will have low damage thresholds. Also be wary of large refractive index changes that are close absorption edges.
Following - Yesid Goyes added an answer:Is there any model or equation for ridge dynamics?
I have a 2D system, you can think of it as a 2D sheet. There is a formation of ridges in this sheet when it is given a constant in-plane pressure. I want to model the ridge dynamics. Is there any model, equation or theory for the ridge formation?
Yesid Goyes · Industrial University of SantanderTransport away from mid-ocean ridge by plate motion (Davis and Lister, 1974)
Davis, E.E., and Lister, C.R.B., 1974, Fundamentals of ridge crest topography. Earth and Planetary Science Letters 21(4): 405-13.
Following - Cyril Mechkov added an answer:How do we create virtual electrical elements in electronics? Are they really "elements" or circuits?
To build electronic circuits, first of all we need the natural electrical elements resistors, capacitors and inductors. However, in many cases we are not satisfied with the performance of these passive components and try to improve them in an artificial way. For this purpose, in electronics we have been inventing a variety of clever and sophisticated techniques to create artificial (synthetic, virtual) elements. The question is, "How do we make virtual elements?"
Like magicians, in electronics we convert the imperfect passive elements into perfect active "elements" (by applying the virtual ground configuration)... or we transform some element (a capacitor) into its dual (an inductor) by swapping the voltage across and the current through it (gyrators)... or we transmute the passive circuits into their opposite mirror doubles (negative impedance)... or we even create completely new electrical elements (memristors)... Thus, for some reasons, we frequently replace the natural electrical elements by their circuit equivalents - a gyrator, multiplier, memristor, negative resistor (capacitor, inductor...)
It is important to note that all these virtual "elements" (electronic circuits) emulate only particular properties (usually, the time behavior) of the genuine elements... they are not real, they are just an illusion...
Genuine elements. The general property of passive electrical elements is taking (consuming) energy from the input source; resistors dissipate this energy while capacitors and inductors store (accumulate, "steal") it. But how do they do it?
Let's assume the considered passive element is connected in series to the exciting voltage source. What does it do in this case? It subtracts a portion of voltage from the whole input voltage: the resistor "creates" an opposing voltage drop across itself while the capacitor and inductor "create" an opposing voltage (a kind of emf). Resistors do this by throwing out (dissipating) energy while capacitors and inductors do it by taking energy from the excitation source, accumulating it into itself and setting it against the input source. In the first case there is a voltage drop while in the second case there is a voltage (emf).
So, we can emulate these passive elements by replacing them with some other elements producing the same opposing voltage (having an opposite to the input voltage polarity when travelling along the loop). Then, we can modify or even create mirror active (negative) "copies" of these passive elements by replacing them with sources producing the same but now "helping" voltage (having the same as the input voltage polarity when travelling along the loop). This is the main idea of the substitution and inverse substitution theorem perfectly considered by Prof. Lutz von Wangenheim in his work:
https://www.researchgate.net/file.PostFileLoader.html?id=540dd638d039b1ee348b458f&key=d62e286c-fe94-4019-b22b-4b550b6c8bfa* Emulating by (varying) voltage. First, we may replace the original elements by varying voltage sources and this is the most natural way of making emulated capacitors and inductors (as they behave as varying through time voltage sources). Op-amp gyrator, multiplying, memcapacitive and meminductive circuits do it in this way. In these circuits, the op-amp output voltage represents the voltage across the according capacitor or inductor.
In the case of the true negative resistor, the ordinary ohmic resistor is replaced again with a voltage source (exactly as in the case of gyrators and multipliers) but it has the same polarity as the input voltage source so that it adds an additional voltage to the input voltage. For example, the negative impedance converter with voltage inversion (VNIC) is a dynamic voltage source emulating a negative resistor by adding a voltage that is equal to the voltage drop across a real ohmic resistor.
It is interesting that we can change the properties of the ordinary constant voltage source by properly varying its voltage (as in the attached picture below).
The emulation by including an additional voltage source is the basis of the Miller theorem (see https://en.wikipedia.org/wiki/Miller_theorem#Applications).* Emulating by (varying) resistance. But a memristor can do the same by replacing the voltage by an equivalent voltage drop across a dynamic time-dependent resistor. Transistor gyrator and multiplying circuits do it in a similar way.
It is interesting that we can change the properties of the ordinary ohmic resistor by properly varying its resistance. A good example of this technique is the creation of the negative differential resistor:
https://en.wikibooks.org/wiki/Circuit_Idea/Negative_Differential_Resistance#General_considerations_about_creating_the_NDRSo, to emulate passive elements (to create virtual elements), we may replace the elements behaving as resistors with (properly varying) resistors, and elements behaving as sources - with (properly varying) sources. But it seems we can do it by swapping these correspondences - replacing the elements behaving as sources with resistors, and elements behaving as resistors with sources... Am I right? Please, discuss.
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I was inspired to ask this question mainly by the numerous discussions between me and Prof. Lutz von Wangenheim mostly in the questions below...
https://www.researchgate.net/post/Are_electrical_sources_elements_with_static_negative_impedance_If_so_is_there_any_benefit_from_this_concept
https://www.researchgate.net/post/Does_the_op-amp_in_all_the_inverting_circuits_with_negative_feedback_behave_as_a_negative_impedance_element_negative_resistor_capacitor_etc
https://www.researchgate.net/post/Does_the_amplifier_in_negative_feedback_systems_possess_negative_impedance?
...and especially, by his idea about the inverse substitution theorem (IST) proposed by him in the question below:
https://www.researchgate.net/post/Can_we_formulate_Kirchhoffs_laws_for_resistances_KRL_and_conductances_KGL_based_on_KVL_and_KCL/2
Cyril Mechkov · Technical University of Sofia8. Virtually current-inverted (negative) resistance (3-4). Finally, we can go too far enormously strengthening the modified Miller's idea...
Now, when you reach the point 3 (in the attached picture below), I begin "overopposing" you along the whole section 3-4. As usual, you are continuously increasing (make more positive) the voltage V_{IN} of the input voltage source from point 3 to point 4 so that its IV curve continues translating to the right. But now I am extremely vigorously increasing the voltage V_{O} so the composed V_{O}-R IV curve extremely quckly moves (translates) to the right as well. As a result, the operating point A slides down along the new IV curve of the inverted positive resistance that is inclined (folded up) to the right and has a negative slope. You have the illusion the resistance R has become true negative resistance dR_{3} < 0.
This idea is directly implemented in current-inversion negative impedance converters (INIC).
Following - Peter Christoph Minkowski added an answer:Do you agree with Stephen Hawking's recent conclusion that black holes don't exist?Black holes don't exist. I published this many years ago. Cantor's Universe doesn't allow the concept.
Stephen Hawking now came up with the same conclusion. Read: http://www.spektrum.de/news/es-gibt-keine-schwarzen-loecher/1222059
In my opinion he is right this time. What is your opinion? Was he right then or is he correct now?Peter Christoph Minkowski · Universität BernI suggest that no questions be encapsulate into a weblink , to consult on details attached to the question
Following - Ellis D. Cooper added an answer:Is logical independence of the square root of minus one a consequence of arithmetic's incompleteness?
In a formal arithmetical system, axiomatised under the field axioms, the square root of minus one is logically independent of axioms. This is proved using Soundness and Completeness Theorems together. This arithmetic is incomplete and is therefore subject to Gödel's Incompletenss Theorems. But can it be said that the logical independence of the square root of minus one, is a consequence of incompleteness?
Ellis D. Cooper · Endicott CollegeTO Steve Faulker -- The term "real numbers" refers to a mathematical structure that is generally agreed to (by professional and amateur mathematicians worldwide) to be a model of the continuum, which is NOT a mathematical structure, it is a mental model with certain intuitively understood properties. The mathematical structure is frequently constructed within one or the other axiomatic set theory. The first time I saw this was in a text by Patrick Suppes. The construction of the real numbers has also been carried out in a topos with additional structure, such as a natural numbers object. That is a terribly opaque way to do it, however. Dedekind's construction of the real numbers has been formalized, but the tower of constructions from whole numbers, to natural numbers, to integers, to rational numbers, and completion to the real numbers is well understood, and in more than one way. Take your pick.
Following - Marek Wojciech Gutowski added an answer:How do you know whether a perfect disc falls heads or tails?
If you have a perfect disc and flick it like a coin, how do you know which side came up? How can you know that statistically it is perfectly 50/50?
Marek Wojciech Gutowski · Institute of Physics of the Polish Academy of SciencesSteve, you simply don't know before you try infinitely many times. Even the symmetry argument seems suspected. Here is why:
Suppose you order your pupils to draw a square with edges oriented horizontally and vertically and with its vertices marked as "A", "B", "C", and "D", in this very order. Suppose they only make a vertex "A" visible. Can you tell what are the marks of other vertices? "A" is always visible in one of four possible locations, but marking may be clockwise or counterclockwise. From purely geometrical point of view both orientations are equally good, but I'm pretty sure that they need NOT to be equally likely among those pupils. Sorry to complicate your thoughts about mixed quantum states even more ...
Following - Ali BenMoussa added an answer:Is it necessary to plot the Norde function to extract the barrier height and series resistance?
See above.
Ali BenMoussa · Solar-Terrestrial Centre of Excellence (STCE)For the estimation of the barrier height (at least) you could use optical (photocurrent) or CV methods.
Following - Tomasz Kawalec added an answer:Is it possible to observe sustained interference pattern from two independent laser source?
Interference
Tomasz Kawalec · Marian Smoluchowski Institute of Physics, Jagiellonian UniversityIf you use typical lasers like He-Ne, you need something like 10^-8 s resolution to observe the fringes. If you take two lasers and introduce a relative stabilization by means on an electronic circuit than the fringes are visible for hours (however the lasers are not independent).
http://iopscience.iop.org/0143-0807/33/1/007/article
Following - Shalender Singh added an answer:What do you think of the discovery of CERN and INFN about the velocity of neutrinos? It seems that they run faster than lightNeutrinos run faster than light...Shalender Singh · Indian Institute of Technology Bombay
I do not know validity of CERN experiments but superluminal particles exists very much in everyday life but they come up a particles going into past. So an electron moving faster than light is actually shows up as going into past, which means like a positron.
The superluminal velocities are real and following paper gives a method to push electrons above the speed of light using existing accelerators and lab equipment: http://www.researchgate.net/publication/265643274_Extended_principle_of_relativity_beyond_speed_of_light_and_a_method_to_push_particles_beyond_the_speed_of_light
Existence of superluminal velocities and the ability to measure them are two different problems. A frame of reference going above the speed of light will transform into 2 different frames of reference, one going in negative time and other in positive time. For example as I propose in another paper (not yet here), if an electron is pushed above the speed of light it will behave like a positron, which is an electron going into past. Also I propose that all positrons are electrons going above the speed of light, which shows up as going into past. As you can see in this paper, the Doppler Effect of radiation generated from a superluminal frame of reference shows up as negative frequency radiation, which is equivalent to Left hand em wave in vacuum. This radiation finds matter mostly transparent and the only way to detect is the reduction of entropy when it passes through matter.
Following - Shalender Singh added an answer:Can information travel faster than the speed of light by pushing and pulling something extended between 2 points?Let's say an iron rod connects the moon to earth, and a machine connected to one side pulls and pushs it a bit to transmit some message, then a computer connected to the other side read those pushes and pulls. So can we affirm that the information travelled instantaneously between these 2 computers?Shalender Singh · Indian Institute of Technology Bombay
The question is amazing and we cannot simplify or refute it by saying the rod is non-rigid OR the motion moves as molecular motion along the rod. Einstein never took those assumptions of elasticity of the matter OR motion as waves to deduce the special relativity. Let me answer your question as it is:
Assuming the rod is completely rigid and motion is in-fact matter translation (not wave transmission), still the rod motion will transfer at the speed of light. Why is that? Assume that the 2 different ends of the rod are in the inertial reference frames with 0 relative velocity. For a distance observer also at 0 speed w.r.t. to both, the act of pushing the rod from moon, which implies acceleration will create a space-time voxel around the rod, which will compress the space-time around start of the rod and this voxel will move at the speed of light along the rod (In 4D space-time it is a fixed bundle of trajectories of the space-time bend), expanding when the deceleration is applied to stop the rod. If the rod is accelerated and then just bought to a uniform velocity and never stopped, the rod will appear to be shorter as it shows up in the Lorentz transformation.
The reason Einstein described gravity and non-uniform motion as bend of space time was exactly because that. The space-time itself bends and warps, which means even the rigid bodies undergo transformation.
On the other hand superluminal velocities are real and following paper gives a method to push electrons above the speed of light using existing accelerators and lab equipment: http://www.researchgate.net/publication/265643274_Extended_principle_of_relativity_beyond_speed_of_light_and_a_method_to_push_particles_beyond_the_speed_of_light
Existence of superluminal velocities and the ability to measure them are two different problems. A frame of reference going above the speed of light will transform into 2 different frames of reference, one going in negative time and other in positive time. For example as I propose in another paper (not yet here), if an electron is pushed above the speed of light it will behave like a positron, which is an electron going into past. Also I propose that all positrons are electrons going above the speed of light, which shows up as going into past. As you can see in this paper, the Doppler Effect of radiation generated from a superluminal frame of reference shows up as negative frequency radiation, which is equivalent to Left hand em wave in vacuum. This radiation finds matter mostly transparent and the only way to detect is the reduction of entropy when it passes through matter.
Following - Cyril Mechkov added an answer:Are electrical sources elements with "static negative impedance"? If so, is there any benefit from this concept?
The negative impedance concept is so attractive that some authors try to bring it on even the most basic electrical elements as voltage and current sources. See as an example the work of this Wikipedian (although it seems his own creation, it is assembled entirely by else's thoughts extracted from reputable sources):
https://en.wikipedia.org/wiki/User:Chetvorno/work6#Negative_static_or_.22absolute.22_resistance
Also, this viewpoint was presented by Simone Orcioni in the question below:
https://www.researchgate.net/post/Does_the_op-amp_in_all_the_inverting_circuits_with_negative_feedback_behave_as_a_negative_impedance_element_negative_resistor_capacitor_etc
As far as I understand, this "negative resistance viewpoint at voltage sources" is the following. A voltage source is connected to a load (a resistor)... so the voltage V (V_{G} in he Simone's figure) across them and the current I through them are the same... and therefore the ratio V/I (the resistance) for each element is the same (see the first attached picture below)... Thus the resistor has a resistance R_{L} = V/I and the voltage source has a "negative resistance" R_{S} = V/-I = -R_{L}... so the sum of the two resistances (voltages, according to KVL) is zero... It sounds temptingly simple but...
In this arrangement, there is only one "main" voltage source and one resistor (the load)... and this is the possibly simplest electric circuit still from 19-th century - a source driving a load. But the popular belief is that "negative resistance" is a "supplemental" concept... It implies another (supplemental, "helping") voltage source (B_{H} in the second attached picture)... and this is not an ordinary constant but "dynamic" voltage source whose voltage is proportional to the current flowing through it (a 2-terminal current-to voltage converter)... and so it will act as a negative resistor with resistance -Ri. This negative resistance compensates another positive resistance Ri (e.g., the source internal resistance or the line resistance) thus giving as a result zero total resistance between the main source V_{IN} and the load R_{L}... and this 4-component circuit is reduced to the Simone's initial 2-component circuit (source and load)... The sense of this "trick" is that the unwanted resistance Ri (the voltage drop across it) is neutralized by an equivalent voltage:http://www.circuit-fantasia.com/circuit_stories/inventing_circuits/ser_nr_comp/ser_neg_res_comp.htm
If this supplemental voltage source was an ordinary constant voltage source, it would still compensate the voltage drop across Ri... but only for one value of the current; maybe because of that they name this kind of "negative resistance" with the name "static negative resistance". Really, it can compensate also the relatively steady voltage drop across a constant-voltage nonlinear resistor (diode, LED, Zener diode, etc)... but this is just another special case...
Note that, in contrast with an ordinary source, this exotic voltage source will not independently produce voltage if there is no input voltage V_{IN}; it starts acting after the main (input) voltage source begins increasing its voltage from zero.
IMO the word "resistor"/"negative resistor" has the meaning of something that resists/"helps" the current flowing through it... so it implies some initial current produced by another (main, input) voltage source... Therefore, this main source is simply a source, not a negative resistor... and maybe this viewpoint is just a misconseption as many others in the field of negative impedance phenomena?
I would add here also the questions asked by Lutz Wangenheim: "Does it make sense to interpret this scenario as a connection of a positive and a negative resistance of the same value? More than that, are voltage and current directions of the voltage source in accordance with the DEFINIONS of a negative resistance? If this would be true, we could treat each voltage source in each circuit as a negative resistance, couldn´t we?"Cyril Mechkov · Technical University of SofiaFinally, I have asked the extremely interesting question about how to create virtual electrical elements in electronics:
https://www.researchgate.net/post/How_do_we_create_virtual_electrical_elements_in_electronics_Are_they_really_elements_or_circuits
Following - Cyril Mechkov added an answer:Does the op-amp in all the inverting circuits with negative feedback behave as a negative impedance element (negative "resistor", "capacitor", etc)?In all the op-amp inverting circuits (transimpedance amplifier, inverting integrator and differentiator, diode log and antilog converters, etc.), the op-amp compensates the voltage drop across the passive element (e.g., a resistor as in the attachment below) connected between the op-amp output and inverting input by adding an equivalent "mirror" voltage in series:
https://en.wikibooks.org/wiki/Circuit_Idea/Voltage_Compensation
As a result, the same current flows through the two elements - the resistor and the op-amp output, and the same voltage appears across them; so, they process the same energy and they have the same impedance. But while the first of them is a passive element that consumes energy (voltage) from the input voltage source, the second is an active element that adds the same energy (voltage) to the input voltage source. Then, if the first element has a "positive" resistance, the second element will show a negative resistance!
https://en.wikibooks.org/wiki/Circuit_Idea/Voltage_Compensation#Negative_impedance_viewpoint_at_voltage_compensation
So, we can conclude that in all the op-amp inverting circuits, the combination of the op-amp and the power supply actually acts as an element with negative impedance that neutralizes the positive impedance of the element connected between the output and the inverting input. As a result, the whole combination of the "positive" element (the resistor R in the picture) and negative element (the supplied op-amp) behaves just as... a piece of wire with zero impedance!
From this negative impedance viewpoint, in the circuit of a capacitive integrator the op-amp is a "negative capacitor" producing the voltage Vc, in a diode log converter - a "negative diode" producing the voltage Vf, etc.
It is interesting to compare this negative "resistor" with the true negative resistance circuit (voltage-inversion negative impedance converter - VNIC)...
https://en.wikibooks.org/wiki/Circuit_Idea/Revealing_the_Mystery_of_Negative_ImpedanceCyril Mechkov · Technical University of SofiaFinally, I have asked the extremely interesting question about how to create virtual electrical elements in electronics:
https://www.researchgate.net/post/How_do_we_create_virtual_electrical_elements_in_electronics_Are_they_really_elements_or_circuits
Following - Jean-Luc Dion added an answer:Advice suggestions or references for sonication?I'm trying to get a handle on how factors such as power (watts), frequency (kHz) and sonication medium (water) affect sonication of my samples (often nanoparticles or antibodies). Has anyone done research on what power/frequency is suitable for biological applications or the effect of ultrasonication on the same?Jean-Luc Dion · Université du Québec à Trois-Rivières
Voir cet article :
http://www.deepdyve.com/lp/elsevier/contamination-free-high-capacity-converging-waves-sonoreactors-for-the-owNjRuNMUf
Following - Ahmed Hesham added an answer:Non-dimensional analysis of physical systems?
What are the limitations and assumption made in Buckingham Pi Theorem for non dimensional analysis. Comment on the accuracy over Rayleigh’s method
Ahmed Hesham · Ain Shams UniversityRead this about Rayligh's method:
http://books.google.com.eg/books?id=Q6iflrgVaWcC&pg=PA69&dq=Rayleigh%E2%80%99s+method+non+dimensional+analysis&hl=en&sa=X&ei=Ni0YVLzsB5CTuASYroK4Ag&ved=0CCsQ6AEwAzgK#v=onepage&q=Rayleigh%E2%80%99s%20method%20non%20dimensional%20analysis&f=falseFollowing - Nicolas Chamel added an answer:What is the difference between infinite and finite nuclear matter?
Which place use both, explain briefly. Is there any connection with compact stars?
Nicolas Chamel · Université Libre de BruxellesAlthough most neutron stars are supposed to be made of neutrons, protons, electrons and muons, these particles are present in very different phases: the outermost past of the star is made of atomic nuclei arranged in a crystal lattice. At densities exceeding about ten thousand times that of ordinary matter, atoms are fully ionised by the pressure and become progressively more neutron rich with increasing depth. At some point, neutrons "drip out" of nuclei. The inner region of the crust therefore consists of neutron-proton clusters coexisting with free neutrons and electrons. As the density attains about half that found in heavy nuclei, the crust dissolves into a uniform mixture of nucleons and electrons. Muons appear at higher densities. Other particles may also be present in the core of the most massive neutron stars.
Following - Peter Benjamin added an answer:Is it possible to calculate the escape velocity in a classical system of three equal mass particles?
The classical three body system is not uniformly solvable (unlike the quantum mechanical equivalent) and hence there are chaotic regimes. Is it, however, possible to calculate a minimum system kinetic energy below which none of the particles will escape, as opposed to solving for the entire three body dynamics?
Peter Benjamin · Harvey Mudd College@Robert: Thanks for the URL of the 13 new solutions. Wonderful stuff. Good to have confirmed the circular orbits (stable if undisturbed, but not likely to be found in real life - see below). The figure 8 solution is new for me.
@Robert: Thanks for the URL of a 2005 book with 23 pages of explicit math detailing the many possibilities. Of course, any 'worthy' real life 3 body problem would start with an assumption two bodies are already orbiting each other, and the third comes in from infinity, or closer. The assumption one could set the initial conditions as pre-existing orbits, is for thought experiments only.
@Bejo: I agree, upon one or more of these conditions: the radius of the 3 bodies is zero, and/or they can collide at the center, and/or roll, friction free, against each other. Some would not call that orbiting. Their mass is much less than black holes.
Following - Robert Shuler added an answer:Are Fermat and Wilson behind Pythagoras in Nature?
Does any one have a view on the possiblity that Fermat's and Wilson's Theorem might be the background cause of Pythagoras all around us?
Robert Shuler · NASAI stumbled across this question and find the Pythagorean aspect interesting and understand the relation to Fermat's LAST theorem. But in reading about Wilson's theorem, it appears related only to Fermat's LITTLE theorem, which seems to me to have nothing to do with the LAST theorem.
While waiting for clarification I'll venture my opinion. I have thought about the occurrences of Pythagorean related formula extensively, especially in relativity theory. They occur in the Pythagorean form, which is the power 2 form of the Fermat LAST theorem, regardless of the dimensionality of the problem. Therefore, I do not think there is a relation. It is only coincidence that the power 2 is integer solvable. I have not seen any need for integers in any of these applications, which further supports my conclusion.
Following - Sergio Pissanetzky added an answer:What has been the biggest scientific injustice, fraud or intellectual illegality that you know?One of the most known is the cold fusion that Fleischmann and Pons claimed to find in 1989 a chemical reaction at room temperature, which had an implicit nuclear reaction produced at tens of millions of degrees at normal conditions. Their experiment involved electrolysis of heavy water at on the surface of palladium electrode and very soon it was rejected by most of the scientific community. But in spite of that the University of Utah financed one great project on this issue and also Japan opened one program from 1992 till 1997 as other countries. How can it be possible with all the presumed filters fail on such a basic knowledge?
Another famous one is Woo Suk cloning human cells in 2005 and making a good publication in Science. Do you know of more recent ones in your own country?Sergio Pissanetzky · University of Houston - Clear LakeDaniel, Can you get Melanie Mitchell's book "Complexity: A guided tour"? Melanie is with the famous Santa Fe Institute, so one must assume she knows what she's talking about. Go to Chapter 17 "The mystery of scaling." Check also p. 269 "The unresolved mystery of power laws." These mysteries have not been solved. Much less the mysteries of emergence, self-organization, brain function, adaptation, intelligence, semantics, etc etc. Organized physics is trying to get away very easily: "It's not physics."
So here is my message: It is physics, but there is currently no theory of physics that can solve any of these problems. A whole new fundamental theory is needed, and it's got to be one of physics. Unfortunately, it needs information, not spacetime and matter as its most basic working hypothesis. There are many arguments. I'll just list a few:
(1) I am showing one. Take causality as a principle, represent it with causal pairs, find the groupoid and calculate the new causal set. Repeat. There you have the fractals and the power laws. And the scaling, that Melanie can't find. They all are in causality. A general property of nature. There is nothing else in the theory, no heuristics, no assumptions, the fractals are there. That easy. All quantitative.
(2) Neuroscience alone cannot do it. There are millions of papers being published, but no single person can comprehend them. They will continue doing their rat research for ever, they will never get it right. They need physics to pitch in. Conversely, it is nothing less than an obligation of physics to help. Because if they don't, diseases like autism, Alzheimer's, dementia, will never be understood.
(3) Big Data cannot do it. They have the same problem of exceeding the capacity of the human mind to comprehend that mountain of data. The Internet of Things is at a standstill because they can't recognize images. Artificial Intelligence has been paralyzed for 60 years and they just don't know what else to do.
(4) Funding. As the Standard Model is finished, funding for research in physics dwindles.But that for Neuroscience grows. People want to understand the brain! Multi-billion dollar projects are on the way in US and Europe, but they will fail to achieve their goals but they are not equipped to do it, and worse, they don't even realize the nature of the problem. Because understanding the brain is Physics! Not Neuroscience. And there is money, ready for physics research.
(5) What happened to Physics? Where is the spirit? Physics is about enquiry, research, finding what nobody has found. Or is it a stereotype: "It must be spacetime and matter, or it is not physics."
(6) I gave the examples already, fractals and power laws. I also solved several problems, for example: Newton 2nd law from measurements, Euler equations for the rotating body from measurements, object-oriented programming from a problem statement, a prediction now confirmed of a power law for dendrite trees in the brain, more recently I solved the famous P=NP problem for discrete optimization. All published, the last one is on its way.
What are they waiting to jump right in? Because it is too easy? They don't believe me because it is too easy? And they are leaving me alone to fight this entire battle? Is this an unjustice or what? You see, we are back at square 1. But don't worry, it is just not physics.
Following - F. Caballero-Briones added an answer:What is the range of values for Urbach Energy for SnS thin film?I would appreciate a detailed calculation process.F. Caballero-Briones · National Polytechnic Institute-CICATA Altamira
The procedure mentioned by Manohar to calculate Urbach tail parameter in ZnS films is essentially correct, although the original question was about SnS. The values of Urbach tail parameter are dependent on the origin of the tail, for example, dislocation density, presence of active electrical/optical impurities including self doping for example by S vacancies, lack or increase of crystallinity and so on. You can do the calculations for Urbach parameter for your SnS samples by the suggested procedure and try to relate the values you get with the structure, the electrical behavior, composition and so on. Find a detailed treatment on the origin of Urbach tails in semiconductors in the following papers. We also have a couple of papers where the aforementioned correlations of Urbach parameter with impurities, microstructure, carrier density were made.
Following - Stephen Crothers added an answer:Can somebody solve the next problem by using only general relativity?We have two absolutely equal masses m1=m2=m that are in a distance r12=r21=r away each other. The masses are in rest in the laboratory frame. According to General Relativity (GR) each mass leads to a space time curvature and creates a kind of 'dent' in spacetime, see for example next Figure: http://upload.wikimedia.org/wikipedia/commons/2/22/Spacetime_curvature.png Since both masses are equal and there exist not any other reason which can distinguish one from the other, then the 'dent' of each mass is absolutely the same as the 'dent' of the other mass. So, according to GR, no motion will be produced, because otherwise we have to suppose that the two masses are not identical or our laboratory is not unbiased for one of them. But, due to Cavedish experiment: http://en.wikipedia.org/wiki/Cavendish_experiment we know that a force between m1 and m2 is certainly being developed. So, can somebody solve the problem of attracting m1 <-> m2 (Cavendish) inside the frame of GR? ============= Technical details ============= m1=m2=1 Kg, r12=r21=r=1 m Suggested structure of the solution process: --------------------------------------------------------- 1)Solve for each mass m1,m2 the next sub-problem: -->Solve Gmn=[(8 pi G)/(c^2)]*Tmn where T^{00}=rho/(c^2)=1 kg/m^3 / (c^2) and other T^{ij}=0, with the mass distribution arbitrarily chosen and not having any kind of known symmetry (: no spherical or other common geometrical symmetry, just arbitrary - the only assumption is that the two bodies are identical - 'twins' ). 2)Find the geodesic that object#2 has to follow due to the space time curvature produced by object#1. 3)Find the geodesic that object#1 has to follow due to the space time curvature produced by object#2. 4)Give the results and tell us what will finally be done. 5)Evaluate the theory, the effort and the results.Stephen Crothers · Alpha Institute of Advanced Study
Dear Readers,
I thank Professor Gerardus ‘t Hooft, Nobel Laureate, Editor-in-Chief Foundations in Physics, for drawing much attention to my work on black hole theory, big bang cosmology, and General Relativity, on his personal website; and for providing me thereby with the opportunity to critique in detail by means of the following paper:
General Relativity: In Acknowledgement Of Professor Gerardus ‘t Hooft, Nobel Laureate
http://vixra.org/abs/1409.0072
Stephen J. Crothers
Following - Abdul Kayum added an answer:What are the current trends in image processing regarding entropy based methods/theories for thresholding?Multilevel threshold.Abdul Kayum · Tezpur University
Multilevel Thresholding using Bacterial foraging optimization by maximizing Kapur's function. You can refer to this paper.
Following - Alexander Gagarin added an answer:Does Strontium Titanate dielectrics works at high frequency?
I am interested in the permittivity with respect frequency up to 10 gigahertz
Alexander Gagarin · Petersburg State Electrotechnical UniversityFerroelectric response (with spontaneous polarization, hysteresys loop and coercive voltage) is another question, of course. Actually SrTiO_{3} is virtual ferroelectric and in bulk form have no ferroelectric response. But in thin film form temperature peak of permittivity can be observed at about 50K (without bias voltage).
I hope we are talking about non-linear dielectric response of STO.
In our works we use SrTiO_{3} films grown by ion-plazma techology on Al_{2}O_{3} substrate (both polycrystalline alumina and monocrystalline R-cut sapphire) with or without bottom Pt conductive layer (for planar or sandwich capacitors). The films are textured with single-crystal blocks with sizes of (20. . . 40) nm and (100), (111), and (110) orientations normal to the substrate surface.
As for permeability... we have metal electrodes which have inductive response that exceeds any permeability effect in dielectric. But resonant frequency is about 30GHz for capacitors designed for 1GHz working frequency, so self-resonance can be neglected.
Following - Sibasish Dutta added an answer:What are the different positively charged capping agents available to cap silver and gold nanoparticles colloids?
To bind BSA (which is negatively charged) with gold and silver nanoparticles by electrostatic adsorption we need the surface of the nanoparticle( gold and silver) to be positively charged.
Sibasish Dutta · Tezpur UniversityThank you sudip sir for your answer
Following - Chao Shen added an answer:What is Rayleigh Taylor instability?
See above.
Chao Shen · National University of Defense Technologythank you guys
Following - James L Gole added an answer:How heavy atoms have strong spin orbit coupling?
We can say that in heavier atoms jj coupling occurs.. more spin spin interactions... but what cause those elements to undergo jj coupling motion? Can someone explain this at elementary level??
James L Gole · Georgia Institute of TechnologyManohar has given you a very reasonable simple explanation for the change from ls to jj coupling. I only would add that ls coupling and jj coupling are two limits. There are more complicated situations in between that require the use of more complex matrix solutions. A reasonably good description can be found in Griffiths Quantum Mechanics text. You can also go to any modern Atomic Physics text.
Following - Ulrich Mutze added an answer:Are differential equations the proper tool to describe reality?Newton introduced differential equations to physics, some 200 years ago. Later Maxwell added his own set. We also have Navier-Stokes equation, and of course - Schroedinger equation. All they were big steps in science, no doubts. But I feel uneasy, when I see, for example in thermodynamics,
differentiation with respect to the (discrete!) number of particles. That's clear abuse of a beautiful and well established mathematical concept - yet nobody complains or even raises this question. Our world seems discrete (look at STM images if you don't like XIX-th century Dalton's law), so perhaps we need some other mathematical tool(s) to describe it correctly? Maybe graph theory?@Lori
Where clear ideas are missing, we cry for paradigms.
Following - Francesco A. Raffa added an answer:Is magnetic force a conservative or non-conservative force?A conservative force is a force with the property that the work done in moving a particle between two points is independent of the taken path. Equivalently, if a particle travels in a closed loop, the net work done by a conservative force is zero (http://en.wikipedia.org/wiki/Conservative_force).
In case of a magnetic force, always the the work done in moving a charged particle between two points is equal to zero, because the magnetic force is always perpendicular to the velocity.Francesco A. Raffa · Politecnico di TorinoI found the whole debate very interesting. With reference to the comment of Bejo, I would like to submit the following remark: from analytical mechanics (as exposed, e.g., in Goldstein, "Classical Mechanics" and Lanczos, "The Variational Principles of Mechanics") one is led to assume that the Lorentz force on a single charge q(E+v \times B/c) is monogenic, i.e., it is derivable from a velocity-dependent potential U, which is a function of the particle velocity and of both scalar and vector potentials. Then the Lagrangian is L= T-U, while the conserved quantity is not T+U but the Hamiltonian of the system. Accordingly, one might state that the Lorentz force is "conservative" in this more general sense. Though this view is mathematically consistent, the physical nature of velocity-dependent potentials seems elusive.
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The standard text books say that MI and FWM are the different descriptions of the same phenomenon. These say that the MI is the temporal description of the breaking of a CW into pulses. The same thing when viewed in frequency domain manifests itself in the generation of symmetric sidebands around the pump and this is called FWM. But I have doubts regarding that when multiple FWM process is described, why the MI and FWM are treated differently?