Bestand wählen
Merken

# Statistical Mechanics Lecture 9

Embed Code
DVD bestellen

#### Automatisierte Medienanalyse

Beta
Erkannte Entitäten
Sprachtranskript
Stecher University the Vatican
remind you we will go on to do today is going to study the Ising model I was terribly unfair rising rest time that was I I looked it up and I was but somewhat basis isolated I Azinger failed to solve the model correctly or whatever not be correctly and thought it was a phase of phase transition the one-dimensional Ising model that would be totally inexcusable and that it is not exactly what happened was that bad he solved one-dimensional rising model correctly would be given to most thesis advisers a problem claims the famous physicist lines and he saw the correctly he realized it didn't have a phase transition but the basis of that he Our believed and wrote In his thesis that PIC model and indeed dimension does not have a phase transition that was that was that was incorrect although talk about that today we're not going to solve the higher dimensional rising models it too hard for us they are very hard but way will use an approximation method that physically very intuitive and was see that in higher dimensions sufficiently high damage there is a phase transition will talk about what their phase transition means our phase transition means a sudden change in the
properties of the system as you very for example will be the temperature arms but let's let's go slow what's taken steps when I go back to this simple example that we study last time we studied a problem in which they a collection of little magnets each magnate could be upward debt and it was an energy function and the energy function differed between often now that may arise again the energy of
a magnet winds up is different energy Magna went down we introduced a little variable called Cigna could be plus 1 minus 1 plus 1 minus 1 and we wrote an energy function I wrote last time as a magnetic moment new plans a magnetic field kind of thing which tells you whether the spinners up or down change notation this is too complicated New Times be they just come together and always come together so we might as just call the product 1 thing and will call the product J it it turns out that as a standard notation for what will be the ring later sold his college 80 with J. stands for a know I'm also will make it might it doesn't make a difference physics because there really is
just a redefinition of what you mean was open barrel here for the original energy favored down there changes signed it favors up but other than that the interchange of up and down there really is no different so that's the way I have now it will favor popular favor
signal positive because of signal positive energy is negative and of course lowering the energy is favorable lower energy is favorable especially at low low-temperature accidentally will we did is we studied a whole group of them we did some comminatory X the try calculate how many states Our with little in up little in inbound bowler could done something much I did that way just up to work to do it in some careful detail we do something else with already learned that you could always think of a subsystem as a system of being a small subsystem plus a heat bath and in that case the rest of the heat that is just what the theater's provides the brings 1 of these the equilibrium only could just focus on 1 of them we just focus on 1 spin the course of his long magnets and a that just assume that it is in the thermal equilibrium with its environment and environment being the rest of the in that case there would just focus on 1 is organized and we would write the partition function for 1 of them as being summation although the configurations I'm configurations are there don't seem easy tho configurations each other miners beta sirens J. them plus David J. Collins said white plaster figures as opposed to write economic is made at times the energy Barcelona calculate was sin the building near the is telling us whether it's up or down so that really just 2 terms when Turner soon up that gives us each of the beta J and turns donor fatigue reminders Baby Jane that's the partition function for just 1 the problem was my form of my this beta J. each the mind bigotry when we calculated it thinking of the whole system was 1 system memory and so we got we just got this can be and how however the Moors was we got factor like this each in Chile could really short circuit all of that stuff about come apart and just focus on 1 spend their time and their independent of each other whenever you have independent systems 5 Yucatan simply take a factor partition function factors into a factor for research I serve to each will spin River fact but that would concentrate on expanding benzene and happens to be twice the hyperbolic sign of beta J we did last time we got twice the hyperbolic costs the data Jr erased the number powers reached we took the logarithm of that which is interesting thing it's simply becomes a summer for example we energy which is just a derivative of the Library of Congress is nothing but some of the images of the individual healer concentrating on 1 the time and go warned that the time I will calculate exactly the same energy for it so let's calculate energy energy can be calculated as 1 always eat with a minus sign derivative of zany with respect day that this is the same as the derivative water the removal order of disease as well as and derivative observed OK so the Solheim a derivative of Z with respect the baby as a tool and they want to derivative of hyperbolic cosigned hyperbolic signed so we will get a hyperbolic signed a Bader times J. but they really have to differentiate argument of the call sign kosher the costs with respect the beta and that gives us some of the GATT no not yet we still have to abide by Ze until they get rid of this 2 0 here I look at it here Mr. Duchess numerical multiple Emilio and the partition function and on America multiples don't matter but now we see exactly why where defined by his with 2 Otis cancel an arrow get J. saying provided by car which is called J the hyperbolic end of this indeed an hour a day off there is a negative Jr you are we are yet it might be yes they are the dollar young so that the average energy are over spin and you can also ask what is the probability that the spinners out vs. down Wednesday average signals that thing which could take on the value plus 1 of my warm bore the average said Willie energy it minus J said this is the average energy that's pretty clear that the average stigma is just the same thing have the Jake so that's right that was 1st alright energy and this is the average energy and is now the average energy of 1 particle it's not the average energy of the whole system of a focus on and that's equal j hyperbolic tangent beta J. led the same thing and we could also talk about the average
Spain and the average spin or the average keep calling it should call the magnetization the average value of the Mr. Obama's of magnet that is just equal to Tianjin hyperbolic tangent of Jake OK this is where the leaders will it but there are only just drop picture of a hyperbolic tangent is a function which looks like now this is a hyperbolic agent X an X is rated JT so this is a hyperbolic tangent or beta J. a number we could have said they want to know why keeping J. could with it can't just something proportional to the inverse temperature these slope of the hyperbolic tangent over is 1 just has a unit slope over here and then asymptotically becomes flattened coastal constant namely 1 over here and minus 1 OK so think about what that if they beta is very very large that means low temperature and suppose Jay's is positive and beta Jerry His very large and positive way out he wants telling us is that the speedy will point up with probability very very close to 1 value 1 and the average of the Spain very close the 1 the only way to be close to 1 if only values of takeover reminds 1 1 knows where the average to be really close to 1 of 3rd the probability is almost exclusively for it to be up and that's what's going on out here I could also look at the negative axis beta we don't want to be negative use inverse temperature but taken be negative just corresponds putting others signed an order does is flip up and down so as you might expect what goes on her way out here when beta JT very negative Spain wants the point in the opposite direction Magnum wants a point in the opposite direction and that's all what's happening here otherwise the 2 sides are completely cement not as bad as the origin and nowhere is the origin here the Argentines beta J. equals 0 that means very high temperature their high-temperature baby is universe temperature high-temperature off the temperatures just constantly being kicked around and it overcomes the temperature just over condoms any bias for it to be up-or-down stormy averages just plain 0 OK so this was a very very simple system now will come to the next most complicated magnet it's the 1 that we talked about back to it the Ising model which and the one-dimensional Ising model which it is at at each point along a one-dimensional array is a stigma simmers Iraq that thing is that energy depends on the relationship between neighboring 1 energy is now summer now this is not the 1 particle energy This is the total energy enough recently we better keep in mind that this thing over here is the the energy of just 1 spared the whole thing OK now actually studying the whole shebang energy is the sum of all of them all the progress on neighbors Of course it on 8 times I plus 1 His jury each site and you multiply was spin by the spin the magnitude of the of the value of its neighbor will also put a J there Vijay is just a numerical constant which I'm so sorry introduced works with private and also that upon assigned their at the energy the minus signs means that if they lose them being Parra you want a lower the energy as much as possible the new law the energy by having them all parallel if all parallel the product of the spins is all equal plus 1 and with be minus sign that I included here with lower and used to make them more Harare also have an effect but plus J but that imagine them on the ground state the system or the grounds state of the system like the ground-state will have the lowest energy will have them all lined up but on which direction up or there is have similar saying they have the same energy or opts or back now will happen if we she signed on Jane the Rose may get plus chasing mice my plus 1 is really a different system now it's really the same system and all you have to do to see if the same system Mr. redefined every others by changing its signed on every other spins were due called up you know called them to redefine the variable and they would you find out is the ground-state once they have them or impact harrow up there Arab family but it's really mathematically an identical system and again in Europe to state this article could be up which cases wound down which cases will be up which faces will be down or the opposite so it's a it's mathematically identical a young guy dead volume Azinger bruises and plays Michael 3 of that it day but then online calculators the usual thing a calculator friend the partition function best friend the petition function and what is that that's e minus some early summer willing to be something all bull possible configuration a movies could be up there and that's a huge sums it up do it summer the minus J some nations in my eyes I 1 that looks terrible look very hard Our hope said Mr. must something here the temperature begin burst temperature is beta dash or did she is no external bowlers it is the latest in a long line of thought we could do it with an external magnet to its to discuss that at some point before the moment no external magnetic and this is a problem with 1 of them look at this 1st organizer question that we connect I would like to know the
possibilities and parallel array of that would tell you nothing about any individual spin unless you knew the first one was up you know the first one is up and you know new 1 billion no signature was suppose also known you want you till then you know what's in the and faxing the 3 will just be new 1 mutual why is that it knew what was up knew what kind of new to to square 1 signature was plus or minus 1 multiplying it by itself is you want and you find out of sync new 1 kinds mutual Soviet known you want and you know you to you know the 1st obviously if you not amused for all of the links between you know all the spin and has no redundancy there's no bubble camping as long as you know that at 1st and is up and his no double counting is equally good to know the newest which lives speak on the bonds between the as it is not themselves but that's very useful why because state energy is just made up out of these bonds variables on meaning beyond the relationship between neighbors so His all account like we can write that this energy is just as some although the bomb call them the bottom of the neighboring bonds some older bonds 1st bonds 2nd 1 notices 1 fueled by are particles but some of the bonds of new fight Nova words but also some alive but Cisco so I knew why the world's 1st Mon variables 2nd variable himself times by his jail we don't when that is multiplying anything anymore it's just the individual bonds and the individual bonds are all independent no relationships between them as long as you know that that 1st is up no relationship between and among them fans it is as good to know you as it is the the novel Ucon substitute you could write you could write you could substitute the song over Spain's substitute for the sum of the values of the barn where the possible values of the bonds plus 1 minus 1 now it's plus 1 if they're lying and minus 1 of their entire life so I can write this as that of the sum of spin some of the some of the bond variables the miners JT data Collins the now in fact tell you that prices why is it twice that and that get physical was found that her food yield partition function the other the other thing is to remember if the number of the magnets is very logical that much but we should remember that 1 fewer bonds and spit of those met this has now reduced to exactly this problem except that I have really accept new in this year His called have some over coupled individual Barton and has exactly the same form as the partition function for road would be simple a magnet remember now mule does not stand for the value of the magnet that stems from relationship between the 2 neighbors but still we know the partition function there it is saying they placed cost data a baseless revenue from its twice this however were extra factor to 1 outside of it quite twice cuspated Jake and now let me put in the thing which I didn't put here which was if I have a lot of spin this case raised me and Al so this is now the number of bonds which is the same as the number of magnets minus 1 minus 1 OK so are you with me or is 1st with hit by itself is not Ferreira at last 1 both are some you there is some clear this way but about yet if my some are back 5 the workers of course that the other large eaters push us there rare that some remember that some next fall just streets of Prague right so this is just a year some of each individual box that arises In a separate best some for each 1 by lawyers for each 1 them on of the editors of some of these walls that is the product of the nominal each in letter dated individually but the factor there fewer words if you have trouble seeing exactly why factor I think the door is still write it down restating To mark the right back
not and neighbors but the particular spent at this point the average spin at Massey Energy of 1 particular spin sitting in the back of the field of all the others is called mean-field approximation need not being in the sense Of the SPD but being In sense of average and field now being the field experience by 1 spin In the field of all the others so this is energy of this particular spin over here and now what we can do it it is due the partition function of that 1 state and that we don't even need to do the partition function we'll the partition function exactly the same calculation we build Blix said instead of writing JTU we will write to these times Jerry exactly the same calculation was here except every place we saw Jay and the upper calculations will have to be cleansed today so I can immediately write down what the average a committee that I can immediately right there and that the average of this this 1 over here but call Sigma bubble for a minute the double bar indicates that I'm talking about what its average band is just going to be but there are not going to be beta Jerry it's gonna be beta arms tool b Javed from sir mama with said I say every place that J. we should stick to DJ not every place were C. J we should stick this whole thing to be kind signal this over here is moving in the background always others and others all constitute a constant field that we just called we so this is going to be the average of despair as hyperbolic tangent of tool D. J Mama if I thank you off Tools beta B. J signal right over again but could news but here as clear they were noble body average of this particular span is going to be hyperbolic tangent of tool Bader D. J I'm simmer water now this mean-field approximation is also sometimes called self consistent field approximation oneself consist of self-consistent because hopefully self-consistent because this Spain over here is no different than all the others it's just 1 of the many spends in the system and of all of these have an average equal Mama the physical and torsion would require that you would say that the 1 here also has the same thing that's got to do with translation invariant do with that everyone was really the same as every other 1 for big sample and follow the self-consistent approximate self-consistent field theory is to say signal bar single double Mars if the when equation we equation its Irma Morris to equation a little their world could cultural mobile workers not moral over we've had since I've I put the bright Kanaranzi it to indicate that this was a constant OK it's a constant with proportional to be immersed temperature but yes purposes yes this is inside the Brackett said mama's inside the bracket so this is an implicit equation for similar Martin who are solid this this fall this equation would apply Richard but when there when variable almost the that all there not not finishing left 0 . 1 finnish after occasional anywhere from my 1 more prepared so the quiet have solved wishes to play got so 4 rare angle threat saying he had not bathing you're wearing a bright that access by either side of the border of patient back talk of war talk about that no you're there is always a dark years later the velocity dimensions and one-dimensional and two-dimensional for 3 three-dimensional sex race whatever it is still the EAS got a day hired man got a next nearest neighbors a work of saying directions gone they are here chart so we picked the particularly predicted particular situation and studied as a function of dimension we could study is a function of the nature of 2nd nearest neighbor couplings 3rd nearest neighbor couplings always things is just 1 way of making this spin how a lot of nearest neighbors the physics of high dimensions not something we realize in the laboratory we all we want to prove something about a system global hard we can get our hands on it but we can go to some limit where becomes much easier are we probe that in the limit we haven't proved it for the physical case of interest but at least we can prove that somewhere between in this case one-dimensional and a 100 thousand dimensions of certain new kind of behavior happens that was present in 1 dimension once we see how that works we can then ask Where does the change happen in this case it happens between 1 and 2 OK but this is a nice simple example where you could see what happens physically without having a solid told a medical problem with these very large OK so let's try the solve this equation the 1st thing to do
is to change variables I know you hate to change variables Her but there are those of the reasons can't show all complicated things I want complicated things here at that time so I'm not saying told beta DJ is a number 2 beta DJ their own numbers for our purposes right now is just the number I'm going to change variables so that 2 beta DJ Prime said Nevada is itself a variable McCalla White recalled and on the left side was not the right side the right side is just why divided by 2 data from D J. pick now the solve this equation and is going to graph both sides and see where they intersect crews way to solve the equations does draws a graph on both sides and see where they intersect Ms. is white this vertical axis it just parents' potential white and Is it can't function not the left-hand side is a linear function of everything else in here instead of calling his beta let's take 1 over it the temperature in the numerator its temperature OK so let's plot the right the left hand side of different values of the temperature to another color and plotted for different values of the temperature 1st of all let's go the very high temperature and very high temperature this is a very steep function Of course he is a large number so how big large temperatures may depend on B but eventually you get a large enough temperature that the slope of this side is large so we go to some very large temperature and a slope crying and there's not only section except the intersection of white equals 0 the the only possible answer to the self-consistent field theory is that white people say robber was why why is proportional to the average of so we learned 1st of all there's very high temperatures that the average of Sigma must be 0 as expected that I surprised when now following a temperature as you'll all the temperature me slope of this curve decreases there is a point where the slope is actually equaled the 1 and the red line here is clear engine with him ends and the Pinto a lovely idea tangent cheer with that happens when slope that happens when the temperature about when temperatures although twice d J. is equal the 1 that's when the slope or when the temperatures twice B. J something happened temperature is equal to twice B. J. when you go beyond that is now some new solutions so as you get past warned you've could be over here just as this line a rogue states still is a gift past Loeb 1 who is now solutions alone here there's also a solution over here and then he ever let's let's assume the GAO's positive just To be acrylic Jay is positive so we only interested in the right hand side here now that the solutions and the no solutions y it is not equal to 0 and therefore are the average signatures not equal to 0 another words the system has all move on global average of Spain's point they all the same direction and that's the phenomenon on magnetization what happens here is called a phase transition beyond that point net magnetization average magnetization average you that just permeates the whole system forever my wait a minute when you say hole but what about the solution how I know that the right solution was the 1 the origin for any value of the constants red curve does intersect the black fervidly origin so how I know which 1 is right at which although calculation comparable good tonight maybe next time we're going to end this problem a key little magnetic field the biases system discovered that has little magnetic field will tell us that we should be on this French on this branch of the solution and not a buoy conceive another way let's go 0 temperature 0 temperature is way out of here we know what to expect at 0 temperature 0 temperature we expect online we expect everybody toll line and so we expect these call locked into a parallel configuration was way out here everybody alive and has to lower the temperature is sliding along those lines until you get to the transition point here and beyond the transition lower temperature than the transition point the only solution was at the origin so that that's the nature of a phase transition which will talk about more but I think I won't try to do it tonight next time we will put it's pretty easy pretty easy from the point of magnetic field so they field have a whole lot of just with the only guaranteed is that sufficiently high dimension at work we know I see doesn't work for 1 an analyst said but it is mathematical beautiful sight cats want something most of it but both arms the court not to but took absolute 0 temperature 1st absolute 0 temperature everybody wants the line no it's around Madam writing the partition function as a sum of war all the configuration was how come we enumerate the configurations Starting with this configuration or normal by the number of spins of flipped relative to this configuration so we thought liberal in writing the partition function in writing partition function we would start this configuration Ito the miners Beta times of configuration at low-temperature starting at low temperatures this would be the dominant configuration and we raise the temperature will kind bid and some no configuration start to become poor could sample 1 Spain flipped let slip 1 spin In fact from withstood the same thing
said gap we constantly argument fear at 3 symbol OK was that it would cover can't function while a 8 dead they know what's left a suicide note left inside was the calculation of the average spin in the background field is a background field but we calculate the average In that back has report and they J. all policy the exact address what we did was we took this newly energy function calculated the average of city of stigma what do exactly the way we did before being inside this will bracket is just the number again this the number so we calculate the average spin unit in this expression for the energy and then we set that equal the average we we see we the calculational we get this number he can't wipers database that's got by saying do the spin over here feels neighbors you say you need to find out what it as equal I always prospered baby right there has why is still the same as it was before I might change the definition of white still to VGA services pinch of why plus beta but I don't know doesn't affect left inside inside the the to say yes why is exactly the same thing as it was before it is the average speed we calculated the average considered equal to the average right inside we did as statistical mechanics calculation of the average was storming the average a certain value on left them so I wasn't well OK but must be the average as was Kohlberg self-consistent approximation if he got Schiffer Caressa Westchester curve shift that that's exactly right where it should occur so let's say from Bader BE is positive that shifts curve backward Bucharest no curve and now withdraw the records the records original outside exactly the same as it was before the right side of the curve has just been shifted to left by how much I babies this gap year Our His beta be be here that we started the agenda saying curves but now there's no ambiguity about which solution we should take there is no solution at the origin or social origin if anymore alcohol only Rees points over here for positive jury proposal jury it Internet temperature OK so let's see what happens and temperature at infinite temperature this gets very close to vertical right no no no no 0 temperatures co-star example got into the temperature is his eye and are intersection is right over here and at that point wife is equal to 0 that data that Be that time the what that Eagles maybe those goes no no I would like to 0 temperature side with lots of adjusting yeah that yuck yuck yuck doesn't matter but not all brutal way we would do a lot temperature low temperature but a large temperature pockets beta goes 0 yes the curve of the curve shrinks back tops gap 1st out it was a L O free right but that are you sure she would have you write whatever happened is as point as shrink down here removed they here right so that she can not more the novel now we're of throwing out infinite temperature but and the temperature of random solve the solution the curve looks like the solution is found near here as you have made again smaller and smaller you find no magnetization as you should worry large temperature now as you move away from 0 can't write infinite temperature is seen only solutions lie on here no matter how small the boats got a small temperature small temperature you move his way back and research here and even as you go higher and higher temperatures you stay on the curve we stay on this point of the curve all the whole thing shrinks down here is no question of being stuck at this point all temperatures randomly temperature which is not infinite is only the solution of P matter how small you make temperatures Wong of the finite how large make the temperature of large or small the only solution was up here it is this year it now young but 1st calls by professional differed 4 of their or dueling capital of your it just where they they were hiding near while the 1st 3rd more than but had a bit of both however want you that worse still what is and of course but character of the heart of the heart disease that a it's yet not is thought to be an entity what do not what do just it is massive will white line now they were going intercept while so it there were also look at the place where across but it's getting more swarms of which no doubt through that it is not this was a that that worker by every year call and I say what is
at stanford . EBU
Basis <Elektrotechnik>
Kopfstütze
Besprechung/Interview
Modellbauer
Leitungstheorie
Greiffinger
Magnetisches Dipolmoment
Waffentechnik
Besprechung/Interview
Luftströmung
Reif
Magnetische Kraft
Magnet
Temperatur
Fass
Elektrisches Signal
Summer
Kraftfahrzeugexport
Sirene
Bergmann
Leistungssteuerung
Teilchen
Avro Arrow
Gasturbine
Kopfstütze
Speckle-Interferometrie
Multiplizität
Stunde
Kaltumformen
Gruppenlaufzeit
Tag
Rauschzahl
Elektronenschale
Magnetische Kraft
Übungsmunition
Spin
Werkzeug
Thermalisierung
Angeregtes Atom
Nassdampfturbine
Weiß
Kurzschlussstrom
Betazerfall
Mittwoch
Wärmequelle
Elektrisches Signal
Direkte Messung
Magnetisches Dipolmoment
Summer
Energiequelle
Grundzustand
Ruhestrom
Armaturenbrett
Leitungstheorie
Teilchen
Kette <Zugmittel>
Kopfstütze
Spiel <Technik>
Negativ <Photographie>
Speckle-Interferometrie
Flugbahn
Absoluter Nullpunkt
Rundstahlkette
Klangeffekt
Array
Konzentrator <Nachrichtentechnik>
Brennpunkt <Optik>
Gruppenlaufzeit
Impakt
Tag
Weltall
Rauschzahl
Gas
Telefon
Elektronenschale
Gleiskette
Druckkraft
Übungsmunition
Magnetische Kraft
Spin
Gleitsichtglas
Werkzeug
Angeregtes Atom
Burst
Gleichstrom
Flüssiger Brennstoff
Scheinbare Helligkeit
Betazerfall
Zementation <Metallurgie>
Synthesizer
Magnet
Temperatur
Potenzialausgleich
Wärmeaustauscher
Bombe
Parallelschaltung
Leisten
Satz <Drucktechnik>
Leistungssteuerung
Leitungstheorie
Kette <Zugmittel>
Biegen
Montag
Vorlesung/Konferenz
Array
Blasenkammer
Kaltumformen
Konzentrator <Nachrichtentechnik>
Pager
Pulsationsveränderlicher
Elektronenschale
Übungsmunition
Magnetische Kraft
Spin
Angeregtes Atom
Werkzeug
Jitter-Effekt
Jahreszeit
Jahr
Betazerfall
Supernova
Magnet
Temperatur
Elektrisches Signal
Direkte Messung
Bergmann
Hi-Fi
Schnittmuster
Chirp
Ruhestrom
Teilchen
Spiel <Technik>
Herbst
Reisewagen
Energielücke
Rundstahlkette
Kraft-Wärme-Kopplung
Lenkflugkörper
Telefon
Videotechnik
Gleichstrom
Summer
Bombe
Parallelschaltung
Hi-Fi
Konfektionsgröße
Fehlprägung
Satz <Drucktechnik>
Ruhestrom
Leitungstheorie
Kette <Zugmittel>
Kopfstütze
Spiel <Technik>
Winter
Speckle-Interferometrie
Rundstahlkette
Theodolit
Großkampfschiff
Pulsationsveränderlicher
Brennpunkt <Optik>
Rauschzahl
Telefon
Reif
Magnetische Kraft
Hall-Effekt
Übungsmunition
Spin
Schiffsklassifikation
Nassdampfturbine
Eisendraht
Gleichstrom
Römischer Kalender
Matrize <Drucktechnik>
Gummifeder
Scheinbare Helligkeit
Jahr
Lineal
Schreibstift
Initiator <Steuerungstechnik>
Frequenzsprungverfahren
Quantenfluktuation
Schalter
Temperatur
Magnet
Elektrisches Signal
Erwärmung <Meteorologie>
Begrenzerschaltung
Minute
Feldeffekttransistor
Edelgasatom
Schlauchkupplung
Marsmond
Fahrgeschwindigkeit
Herbst
Energielücke
Blasenkammer
Kaltumformen
Zugangsnetz
Stutzuhr
Emaillerie Alsacienne Strasbourg-Hoenheim
Waffentechnik
Tag
Maxwellsche Theorie
Ausschuss <Technik>
Übungsmunition
Spin
Werkzeug
Nassdampfturbine
Gleichstrom
Hintergrundstrahlung
Jahr
Betazerfall
Anstellwinkel
Temperatur
Gewicht
Potenzialausgleich
Elektrisches Signal
Schwimmer <Technik>
Drehen
Direkte Messung
Parallelschaltung
Bergmann
Erwärmung <Meteorologie>
Linearmotor
Energieniveau
Jacht
Ruhestrom
Minute
Leitungstheorie
Juni
Spiegelobjektiv
Fuß <Maßeinheit>
Schlicker
Vorlesung/Konferenz
Multiplizität
Theodolit
Kaltumformen
Stutzuhr
Pulsationsveränderlicher
Waffentechnik
Jeep
Maxwellsche Theorie
Flasche
Elektronenschale
Übungsmunition
Magnetische Kraft
Spin
Werkzeug
Angeregtes Atom
Weiß
Schwarzes Loch
Motor
Gleichstrom
Zylinderkopf
Buntheit
Betazerfall
Temperatur
Unterwasserfahrzeug
Messung
Direkte Messung
Kraftfahrzeugexport
Fehlprägung
Energieniveau
Störgröße
Ruhestrom
Satz <Drucktechnik>
Rasenmäher
Leitungstheorie
Trenntechnik
Boot
Vorlesung/Konferenz
Speise <Technik>
Energielücke
Kraftfahrzeugmechaniker
Großkampfschiff
Kraft-Wärme-Kopplung
Stutzuhr
Rotverschiebung
Elektronenschale
Magnetische Kraft
Spin
Angeregtes Atom
Tonbandgerät
Stuhl
Burst
Gleichstrom
Hintergrundstrahlung
Scheinbare Helligkeit
Jahr
Feldstecher
Magnet
Temperatur
Unterwasserfahrzeug
Computeranimation