studiot

If you want to understand all this, we need to start back 250 years before Christ, when a Greek gentleman made his famous utterance about Archimedes Principle. The interesting thing is that the importance of AP, in this context, was not enunciated until after Relativity, after QM and after Godel in 1936 when Terzaghi introduced the notion of 'effective stress'. So I am going to ask if you understand the notions of contact force, contact stress, and the classification into direct (also called normal) force and stress and (not indirect or abnormal) but tangential or shear force and shear stress, Liquid mechanical behavious is controlled by shear stress, as is soil and rock mechanics in regard to failures such as landslip, avalanche, slope stability and so on. Soils break due to shear failure in almost every case. If you are not sure about any of the terms please ask and I will include the necessary explanations in my next post. Conceptually it really is quite a simple subject ( mathematicians can always make it more hairy than it really needs to be) High stress is just not necessary. Did you manage to access the full paper by any chance ?

That's true. In fairness both mica and talc occur more often as minerals in some rock eg granite. The result of granite weathering creates many small mineral flakes that go twoards the clay soil. The South West batholith granite is vey coarse grained which leads to easy breakdown and the fine china clays of Cornwall and coarser clays in Devon. Somerset has a completely different geology with the sedimentary clays, sandstones and mudstones the result of run off from the edge of a former continental margin. There are almost no igneous rocks in Somerset an exmoore is sedimentary, unlike Dartmoor, Bodmin and the other cornish moors. Known examples of liquid fracture under gravity. Now contrast this with the behaviour of separation drops (fractured water stream) from a dipping/slow running tap

The difference is that clay is a soil, mica and talc are rocks. Clay has its peculiar properties due to a complex (electrostatic) interaction between soil water and the clay minerals, whcih carry charges. Graphite sheets themselves are of course basically electrically neutral, although intersheet forces are Van Der Waals electrostatic.

I think the authors of the paper talk about stress regimes, rather than velocity regimes. They also seem to limit their definition of breakage or fracture to what happens with metals. But the real world is a heck of a lot more complex than solid, liquid or gas. So is a carbon fibre fishing rod a solid ? How about a four by two piece of 'solid' oak ? (Why do the americans insist on two by four?) Both are fibrous, not crystalline. But what about soil ? The mechanics of soil and its response to stress depends upon load sharing between the granular solid particles and soil pore water. @exchemist mentions bitumen. There is the bitumen drop test, an experiment that has being going for nearly 100 years. Then there is Griffith's theory of strength and fracture and J E Gordon's experiments with alleged flows of old window glass. @paulsutton Yes graphite can be considered as a stack of monolayers of carbon. In fact I know of 4 allotropic forms of carbon viz Diamond, Graphite, Amorphous (soot, coke, charcoal, etc) and Buckeyballs. There are also many potentialy infinite planar lattices of aluminosilicate materials. Some of these make up the clay minerals group with characteristic clay failure modes and the atterberg limits test.

+1 No I disagree about an abrupt change in a velocity profile defining fracture as the object/material may be stationary, but still break or not as the case may be. However I do agree that the motion of the object is a condition to be taken into account, as with the marine breaker I mentioned, where the top of a wave is travelling faster than the retarded bottom, although there may be a smooth rather than an abrupt variation in the velocity profile.

Thank you for the extra links. Unfortunately the second is paywalled to me. There is, however a useful abstract, that does not uses better technical language like fractures, not breaks. I have however been reconsidering the subject. A question arises as to what is meant by 'breaks' ? Detachment of part of the body of material or just (nonelastic) deformation? Both of these phenomena can be observed simply by going down to the sea shore and watching the waves roll in. The results are not called breakers for nothing. But the abstract implies something rather different. Forced flow in a tube or pipe, with perhaps a nozzle, with a slow moving highly viscous material. It is possible they were counting the rate of drop formation (detachment). Many materials are tested in this way.

First let me say thank you Paul for bringing this to our attention. +1 However the linked article seems more like the hyped up writings of a sensationalist journalist, than an august Professor. What is meant, for instance, by pulling a liquid apart ? or by breaking a liquid ? The classification into solids, liquids and gases was known 100 years ago to be seriously simplistic and unable to describe the behaviour of most materials in the real world. A good question to ask is what causes solids to break ? In fact solids have several different breakage mechanisms available, including one where the solid cannot break at all as it is so confined. So a second good question is what gives them their strength ? A third one might be what is a solid ? A pile of dry sand or wheatgrain follows the laws of fluid mechanics. What about a tube of toothpaste ? All these issues and many more are largely ignored by physicists, but taken up by Rheologists, Chemists, Pharmacists, Geologists and others. There is significant modern research into the properties of monomolecular layers. So where would you like to start ?

Well the word 'constitution' relates to 'what is' rather than 'what is not'. So the US constitution is based on the principle that certain rights are available to US citizens. Other rights or priviledges are not guaranteed, but are not necessarily forbidden. England has the Magna Carta which is a very primitive guarantess of some rights for some people only. It is often summarised by lawyers that The english 'Constitution' says " You may do/have anything not specifically forbidden by Law" The US constitution say "You may only do what it allows in the Constitution" Neither is summary is totally true but it does contrast the philosophy behind the difference. And the differences are becoming more and more blurred as time goes on. Applied to the English Language it is clear that you cannot found an language 'authority' on what is not', but you can on 'what is'.

Well I don't often link to other discussion sites, and I only found that one because I needed to fix a mobile phone, that was apparantly out of battery. A replacement battery didn't fix it, so I looked for the ideas presented in that discussion concerning the charging circuitry and a loose ribbon cable. In the event there was no ribbon cable, the micro usb was firmly soldered onto the one piece mainboard. However disassembly and reassembly brought the old battery and system back to life. But it still did not like the replacement battery - allegedy the same type number. Interestingly when I tested the new and old batteries off load they both showefd 4.1 volts - a bit high for the nominal 3.7v. ~As I said there were many lesson for those who read the discussion, not least the need to keep Li-ion batteries topped up every few months. My usage of portable power tools is diminished these days and rather intermittent and I do find the discipline prolongs active life PAL for those who rember the dogfood adververts.

Following a mobile phone charging issue I came across this intriguing discussion thread on reviving dead batteries and or devices. It starts off with a phone but goes not to rechargeable tools (drill, chainsaws etc) https://www.ukworkshop.co.uk/threads/how-i-charged-an-old-removable-mobile-phone-battery.146855/ I'm sure we could all learn something from this, for example DeWalt device battery terminal

Very subtle. +1

Yes I agree they are the same construction with different notation. This is exactky what I mean by a plethora of notation.

You don't actually have to post in a thread to 'vote', which is why I originally responded as I did for I did not then know who it was. The mods can see who voted what, of course.

Here is a good (polite) way to contradict someone.

Here is an excerpt from the Times of India that contradicts your statement. The Times of India6 animals that live without a heart and still survive in...We usually think of the heart as something every animal needs– pumping blood, carrying oxygen, and keeping the body alive. It’s seen as one of the most essential organs. But nature often breaks the ru

Judging by this and your other recent threads you are following some scheme connecting formal logic and maths. Both disciplines suffer from a plethora of notation, this may help. If you wish to contradict someone, my expectation would be to follow the bald negation with a proper mathematical substantiation of your own claim.

There has been continued interest in this subject since the days of Cantor and Poincare. Here are a couple of recent papers. One note of interest is confirming that the 1 in the naturals is the same as the 1 in the reals or the integers for those who widh to be strictly pedantic. Realnum_RMJ-2015-45-3-737.pdf acampo-real.pdf

Yes all constructions of R are isomorphic, I think at the current count there are more than 10 different ones. The only real issue about this is do you include the number zero in the naturals ? I don't see the downvote as justified, so I have added a balancing +1

There's nothing transient about a whip antenna transmitting or receiving CW. I think you have misunderstood my intentions anyway. The OP has admitted that the circuit as show serves no useful purpose, and it is also unclear whether the resistors R1 and R2 are the battery internal series resistors or not. Either way the three resistors are the only way power can be dissipated by this circuit, ideal voltage sources dissipate zero power. Therefore the input power must equal the resistive dissipation in the three resistors and his defining equation is a figment. I have tried to widen the discussion to something that comes a little closer to the real world, by discussing load lines. The configuration is actually very important in the electrical power industry where it appears as the parallel connection of generators. When the sources are alternating there are phase and other changes to consider. Further Sherwood's description of the circuit he shows specifically states that Kirchoff is not obeyed at switchon, and explains why. Equally you say that Kirchoff's laws are obeyed at every point. A small issue here as one is a loop law, not a point law,

Kirchoff's laws are a very convenient fiction in a similar way to centrifugal force and other imaginary forces such as such as virtual work. They work in the right circumstances, in that they produce the same answer as calculations with models more aligned to physical reality. Here is a short extract from the late Professor Shercliff's excellent book 'Vector Fields' - Cambridge University Press. J A Shercliff was Dean of Engineering and Applied Maths at Warwick, after leafing a distinguished early career in Magento Hydro Dynamics at Cambridge, Oxford and the UKEA Sorry for the integrals, j is current and q is charge.

I asked you three questions but you only answered one of them. I asked all three for good reasons, because it is no use being clever with maths if you are either using the wrong model or do not properly understand the 'correct' model. That is why I asked if this is electrical engineering or mathematical modelling. It should be remembered that the electrical symbols you have employed refer to perfect or ideal components. So both voltage sources are ideal. Do you understand the significance of that ? Equally all three resistors are ideal. But what do you imagine R1 (10 ohms) , and R2 (20ohms) actually are ? An electrical engineer would immediately say they are the internal series resistances of real world sources. This makes a difference to how the circuit and the model operate. I also asked why would anyone connect two batteries like this. Well they wouldn't because neither 5 volt nor 10 volt batteries actually exist. But here is a real world electrical engineering situation where one might. We have a nominal 1.5 volt battery that is somewhat discharged to 1.4 volts and we wish to boost its performance by adding in parallel a smaller but fresh 1.5 cell we have in the cupboard. The resultant voltage will never reach 1.5 volts but will be greater than 1.4 volts, which may be sufficient for our purposes. For calculation purposes assume the larger, but discharged battery has an internal resistance of 0.1 ohms and the smaller fresh battery has an internal resistance of 0.2 ohms. Such a parallel combination of batteries would then be used to supply a load RL which would be R3 (30 ohms) in your model circuit. At this point I owe you an apology since I misread you initial post that sought a nonlinear programming approach and thought you meant a linear programming solution. In point of fact an electrical engineer could perform a linear programming exercise on my battery problem, based on load lines which in this case are indeed straight lines. By drawing or calculating a load line for each battery, a load line for the parallel combination can be deduced to find the terminal voltage and thus the currents flowing in the loops. It is necessary to understand the action of an ideal voltage source and the concept of its terminal voltage. Addendum You should be very wary of Kirchoff's Laws are they are actually a rather convenient fiction. This was known as the famous crisis in the history of electromagnetic theory and was resolved in Maxwell in the 1860s. Consider a single wire that is not connected in one end and explain why Kirchoff predicts that zero current can flow into and out of this wire. For without such current radio transmission would simply not work.

There is of course a perfectly satisfactory way of defining multiplication as the result of repeated addition, if subtraction is also allowed. What is more difficult to get round is multip[lication by a fraction. The completion or lack of it of the operation also dependes upon the domain you are working in. Addition is complete in the natural numbers, but subtraction is only compete in the integers. In any axiomatic system axioms are used to deduce or prove theorems. It may be posssible to substitute some or all theorems for axioms, so providing an different but equivalent set.

Surely this statement cannot be right. Say there are G axioms and axiom G is found to be provable from the other axioms A to F. Unless the proof of G is independent of one or more axioms, say B, how does this lead to an inconsistent set ?

If you want ordered pairs, you need the Cartesin product a A with itself. The pairing subsets in the product space then provide one way to define a relation.

You will also find Tare in many places today for instance on modern digitql scales. When making bread I put the mixing bowl on the scales and press the Tare function to 'zero things before adding the ingredients.