What is Cycles: Definition and 169 Discussions

In ecology and Earth science, a biogeochemical cycle is a pathway by which a chemical substance is turned over or moves through the biotic (biosphere) and the abiotic (lithosphere, atmosphere, and hydrosphere) compartments of Earth. There are biogeochemical cycles for the chemical elements calcium, carbon, hydrogen, mercury, nitrogen, oxygen, phosphorus, selenium, iron and sulfur; molecular cycles for water and silica; macroscopic cycles such as the rock cycle; as well as human-induced cycles for synthetic compounds such as polychlorinated biphenyls (PCBs). In some cycles there are reservoirs where a substance remains or is sequestered for a long period of time.

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  1. 0

    Check for Cycles in Undirected Graphs: O(|V|) Algorithm

    I'm just posting a random graph algorithm problem for discussion fodder, since another interesting graph algorithm post was removed due to a threatening-sounding title and lead-up. This is from Cormen, Leiserson, Rivest, & Stein, 22.4-3 (not a homework problem of any kind, just for fun--I had...
  2. E

    What is the significance of the sopfr function in these cycles?

    I posted this in another math forum, but have received no response: Let sopfr(n) be the sum of prime factors of n (see http://mathworld.wolfram.com/SumofPrimeFactors.html ). There have been observations that certain iterations involving the sopfr function seem to lead invariably to cycles...
  3. S

    Exploring the Expansive and Contractive Cycles of the Universe

    Hi guys, I've been working on a theory for a bit and am wondering what you guys think. So here it is: Summary The universe expands through the expansive era. Then it contracts through the contracton era. The universe contracts until it finally collides in the center of the universe. This...
  4. R

    Earth's Rotation: Day & Year Cycles

    Which way does the Earth rotate and why? I am talking about both of the rotations. Rotation for a day and a rotation for an year.
  5. R

    Is Cp Used Only for Processes with Flow Work in Power Cycles?

    do we use Cp just for processes with flow work or ther is anything more related with this, is my question thanks for ur help..
  6. B

    Help-higher order limit cycles

    Help. If anybody knows them beyond introductory level... i have a higher order system with a single fixed point. i chose such parameters that the fixed point is unstable. so it should either oscillate to infinity, or in this case it actually has a limit cycle. when running this system on the...
  7. C

    Powers of cycles? Orders of elements?

    When calculating powers of cycles, are there any easy steps to use in doing so? I mean...is there a typical relationship when calculating (123)^n? Also, is it safe to say that a ceratin n-cycle should have order n or n-1? I guess any explanation of orders for group elements would be...
  8. A

    Cycles of Matter: Carbon-Oxygen Cycle & Photosynthesis/Respiration

    In the carbon-oxygen cycle how does the process of photosynthesis and respiration interconnect? what pathways does a carbon atom go tom a fossil fuel to becoming a part of air that a person can exhale?
  9. Chi Meson

    Unbelievable Rainbow Phenomenon: 4 Cycles of Color!

    Last evening there was the perfect rainbow condition: A bright evening sun shining into a rainstorm just overhead. I went outside to see both complete arcs from horizon to horizon . THen... the inner rainbow (the most commonly seen rainbow, with red on the outside of the bow) looked odd...
  10. I

    Efficiency of an infinite series of Carnot cycles

    Dear people of Physics Forums, I would like to have your opinion about the following problem: Suppose we are interested to evaluate the average efficiency ( e ) of an infinite series of carnot cycles. The temperature of the hot reservoir of each carnot Cycle of the series, Ta, is at 990K, but...
  11. Oxymoron

    How Do Permutations and Conjugacy Classes Operate in Symmetric Groups?

    Question Let S_n be the symmetric group on n letters. (i) Show that if \sigma = (x_1,\dots,x_k) is a cycle and \phi \in S_n then \phi\sigma\phi^{-1} = (\phi(x_1),\dots,\phi(x_k)) (ii) Show that the congujacy class of a permutation \sigma \in S_n consists of all permutations in S_n...
  12. M

    Synchronized Cycles: Is There a Medical Explanation?

    This is a serious question. I'm not posting it to be vulgar or obsene. :confused: My sisters, our mother, and I are noticing that our monthly cycles are almost 100% in sync with each other. We thought this was pretty weird. Mainly because our cycles used to be at completely different times of...
  13. F

    How Do You Decompose a Random n-Cycle into 2-Cycles?

    can anyone explain me the technique to decompose a random n-cycle into a bucnh of 2 cycles. Thanks in advance.
  14. 2

    Investigating Solar Cycles and Their Effects

    I'd imagine this will get relegated to theory developement, but here goes anyways. Looking at some of the charts for solor cycles it's clear to see the 11 year cycle. But this cycle seems to grow stronger with every repeation. It then resets to a low point a starts again. Now, I admit, I know...
  15. S

    What is the concept of injection and surjection?

    Show that a 3 cycle(a,b,c) in Sn has order 3. Show that a product of disjoint transpositions (a,b)(c,d) in Sn has order 2. Find the order of (a,b)(x,y,z) in Sn, if this is a product of disjoint cycles. Apply this to tell the orders of all permutations in A4.
  16. T

    Attracting Heteroclinic Cycles.

    Hopefully this is a quick questions. I'm trying to describe what an attracting heteroclinic cycle is but not sure really how to describe it or what it means. I have a 3-dimensional population model x(t), y(t), z(t), which has a phase portrait that spirals from one equilibrium point to three...
  17. P

    Interactions Between Sedimentary, Igneous, and Tectonic Cycles

    The water and sedimentary cycles are interrelated in many ways, Would you please help me to identify the interactions between : sedimentary and tectonic, sedimentary and igneous, igneous and tectonic, water and tectonic ? Thank you very much in advance,
  18. P

    Could you please tell me their life cycles ? Does anyone of you work

    Could you please tell me their life cycles ? Does anyone of you work with worms daily ? I am sorry, i mean your research, your job ? Thank you very much
  19. Q

    How Does Infrared Data Transfer Work in Electronic Devices?

    I observed with several electronic devices (primarily romote controls) which use infrared light emitting diodes (IR-LEDs) to send data is that with some, if the LED is viewed closely and carefully enough you can see a red light flash when being used. I know that IR light is invisible, and I'm...
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