What is Fundamental: Definition and 946 Discussions

Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action. A fundamental domain or fundamental region is a subset of the space which contains exactly one point from each of these orbits. It serves as a geometric realization for the abstract set of representatives of the orbits.
There are many ways to choose a fundamental domain. Typically, a fundamental domain is required to be a connected subset with some restrictions on its boundary, for example, smooth or polyhedral. The images of a chosen fundamental domain under the group action then tile the space. One general construction of fundamental domains uses Voronoi cells.

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  1. K

    Fundamental thermo systems problem

    1. Unit mass of a fluid at a pressure of 3 bar, and with a specific volume of 0.18 m3/kg, contained in a cylinder behind a piston expands reversibly to a pressure of 0.6 bar according to the law p = c/v2, where c is a constant. Calculate the work done during the process. 2. P1V1=P2V2 3. I know...
  2. J

    Fundamental frequency of an object with nonlinear stiffness.

    Hi all. It's been a few years since I've posted here, but it's remained a great go-to resource for me. Any time I have dealt with mechanical vibrations, the fundamental frequency was based on a constant stiffness. However, I have never encountered the subject of finding the fundamental...
  3. J

    Why Does Fundamental Freq Have Largest Amplitude?

    Please could somebody explain why the fundamental frequency always has the biggest amplitude in comparison to the rest of the harmonics?
  4. M

    What is the geometric interpretation of the fundamental theorem of calculus?

    hey pf! i'm trying to get a geometric understanding of the fundamental theorem: \int_a{}^{b}f'(x)dx=f(b)-f(a) basically, isn't the above just saying that if we add up a lot of slopes on a line at every point we will get the difference of the y values? thanks! feel free to add more or correct me
  5. N

    The fundamental forces and elementary particles at absolute zero

    We all know that there four fundamental forces in nature, viz. The gravitational force The electromagnetic force The strong nuclear force The weak nuclear force Now also we know that temperature of any system is the average kinetic energy possessed by the particles of the system Now...
  6. T

    Help with the fundamental forces.

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  7. M

    Fundamental theories are gauge theories

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  8. T

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  9. T

    Why is the Higgs Field not considered a fifth fundamental force?

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  10. J

    Fundamental theorem of calculus for surface integrals?

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  11. S

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  12. MarkFL

    MHB Solve Derivative of Integral with F(x) - SnowPatrol Yahoo Answers

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  13. M

    Fundamental Frequency of a nano scale oscillator (graphene)

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  14. shounakbhatta

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  15. I

    Calculating Fundamental Frequency and Overtone Frequency of a Stretched Wire

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  16. Q

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  17. S

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  18. N

    What are the fundamental methods of generating motion?

    I know that motion today is usually generated by - generating a varying magnetic field and varying it in relation to a fixed one - ccombusion engines Are there other "fundamental" approaches to generate motion, or is that pretty much it? Your input is appreciated, thanks!
  19. P

    How fundamental are functions, really?

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  20. T

    Need something better than Wiley Fundamental of Physics?

    I'm nearly done with my first semester of college as an electrical engineering student. I'm doing pretty well other than in my physics class which I am struggling. I'm maintaining around a C+ right now. While it's passing, I know I can do much better. The class is late at night and I can't...
  21. V

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  22. T

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  23. TrickyDicky

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  24. L

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  25. P

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  26. J

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  27. A

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  28. S

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  29. M

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  30. O

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  31. J

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  32. C

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  33. D

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  34. S

    Fundamental Theorem of Calculus - Variables x and t

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  35. Daaavde

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  36. R136a1

    Are Abelian fundamental groups always isomorphic in path connected spaces?

    Hello everybody! So, I've learned that in a path connected space, all fundamental groups are isomorphic. Indeed, if ##\gamma## is a path from ##x## to ##y##, then we have an isomorphism of groups given by \Phi_\gamma : \pi_1(X,x)\rightarrow \pi_1(X,y): [f]\rightarrow [\overline{\gamma}]\cdot...
  37. SamRoss

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    As I understand it, a lot of what is taught about quantum mechanics are special techniques for solving problems. I'm not a physicist, so something like perturbation theory is not what I'm after. To be more specific, i would like to know the minimum that is necessary for "doing" quantum...
  38. L

    First Fundamental Form from tangent vectors

    Hi Appologies for formatting issues this is the first time I have submitted something to the forum. I have a pretty simple problem, I am just going through the derivation of the First Fundamental Form and I think I am missing something in the derivation. If we have a point x = (x1,x2)...
  39. T

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  40. V

    Questions about fundamental concepts

    I am confused about what I think should be the most basic concepts in quantum mechanics.. As far as I understood, a system that can be in only one of two states, can literally be only in one of those two states, right? So if I were to make a hypothetical measurement of the configuration of...
  41. P

    First Fundamental Theorem of Calculus

    Hi, I just learned about the First Fundamental theorem of calculus. From my understanding, it talks specifically about definite integrals. I was wondering if there is any sort of theorem that proves that the derivative of the indefinite integral of a function is equal to the function itself...
  42. A

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    Homework Statement Metric ansatz: ds^{2} = e^{\tilde{A}(\tilde{\tau})} d\tilde{t} - d\tilde{r} - e^{\tilde{C}(\tilde{\tau})} dΩ where: d\tilde{r} = e^{\frac{B}{2}} dr Homework Equations How to calculate second fundamental form and mean curvature from this metric? The Attempt at a...
  43. B

    Fundamental theorem in 2 dimensions.

    Hello I have heard that Greens, Stokes and the Divergence theorem is the equivalent of the fundamental theorem in multiple dimensions. But is there some way to show the result under: if F(x,y) = \int_{-\infty}^x\int_{-\infty}^yf(x^{*},y^{*})dx^{*}dy^{*} this implies that...
  44. S

    Constraints on possible fifth fundamental force

    Anyone read the article on this? http://phys.org/news/2013-06-precise-quantum-electrodynamics-constrain-fundamental.html I made an effort to read to arXiv paper, but I'm still working on my understanding of QFT, so I didn't get too much out of it.
  45. B

    Calculate fundamental overtone and length of tube

    Homework Statement It is observed that a tube open at both ends exhibits harmonics at 438 Hz, 584 Hz, and 730 Hz. A) Calculate the fundamental overtone of the tube. B) Calculate the length of the tube. Homework Equations L=lambda/2 x n, v = f x lambda The Attempt at a...
  46. L

    About fundamental social psychology

    I have always interested in psychology and never properly studied psychology in my life. But over the years I have learned about many things by learning about famous psychology experiments. However I cannot seem to get sufficient enough information to ‘understand’ human’s fundamental social...
  47. M

    Can one derive all of physics from the 5 fundamental force equations?

    If one knew the equations for the 5 fundamental forces, would that not explain the entirety of all physical phenomenon in the universe? (Presuming there were not undiscovered forces?) Or would something like quantum mechanics not be explainable via those interactions? Does the nature of the 5...
  48. adjacent

    Where does potential energy come from?

    Gravity pulls things down.Things then gain kinetic energy.When you lift something it has gravitational potential energy.I know that potential energy is transformed into kinetic but according to the law of conservation of energy, potential energy must also be transformed from some other type of...
  49. L

    Is the Universe able to evolve due to fundamental forces?

    I'm sorry if I posted this is the wrong section, but I was wondering if fundamental forces evolve? In other words, can universes evolve. Since stagnant ones eventually die out. And the successful ones produce black holes; transferring matter into a whole new beginning.
  50. J

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    I'm confused about the condition for spontaneity for the Helmholtz energy. My textbook (McQuarrie, "Physical Chemistry") derives the conditions as follows. We start with the combined law of thermodynamics: dU = δq + δw ≤ TdS – PdV since δq/T ≤ dS dU – TdS + PdV ≤ 0 For a process at...
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