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. M

    What is the life (in cycles) for a hydraulic cylinder

    Does anyone know how many cycles (extend / retract) that a hydraulic cylinder should be able to do before needing repair? The specifics for the cylinder are that there is minimal (almost none) low frequency and low amplitude pulsing of pressure. The cylinder will cycle once every 5 minutes...
  2. T

    Products of disjoint cycles. Explanation please.

    Hey all, Currently trying to revise products of disjoint cycles. I am struggling to get my head around the idea however. Its strange, i can generate disjoint cycles easily however i can't quite see the product of cycles. Mabye I've missed something. eg of what i don't quite get. What is...
  3. N

    Temperature change and Milankovitch cycles

    According to Milankovitch cycles, is the Earth in a warming, stable, or cooling period ?
  4. B

    Carnot's cycle and a-like cycles

    Hello, Lately I encountered thermodynamics. And all that world is very new to me, gas expansion etc etc. I recently learned about Carnot's cycle. IT has 2 isotherms and 2 adiabatic processes. Now, I understand what those processes in separation mean. Adiabatic processes don't...
  5. U

    Thermodynamic cycles and their analysis

    Homework Statement 1. In Air compressor cycles, the work done is calculated by integrating vdp and not pdv(like we'd do in otto cycle or any other thermodynamic cycle)...why? 2. In Rankine cycle. we calculate work done by making use of enthalpy calculations whereas in brayton cycle and...
  6. G

    Conjugation of Cycles in Permutation Groups: Proving the Property with Examples

    Homework Statement show that if ##(x_1 x_2 ... x_k)## is a cycle in ##S_n## ( ##k \leq n## ) and ##\pi## is any permutation in ##S_n## then ##\pi (x_1 x_2 ... x_k) \pi ^{-1} = ( \pi(x_1) \pi(x_2) ... \pi(x_k) )## Homework Equations The Attempt at a Solution firstly is this...
  7. N

    Carnot cycles in thermodynamics

    Homework Statement A heat engine operates in a Carnot cycle between 75.0°C and 353°C. It absorbs 21000 J of energy per cycle from the hot reservoir. The duration of each cycle is 2.00 s. Homework Equations W=Qc-Qh, W=-P change in temperature The Attempt at a Solution I attempted to...
  8. D

    What are the other types of geothermal cycles aside from dry, binary

    What are the other types of geothermal cycles aside from dry, binary and flash?
  9. H

    Mastering Cycle Conjugation: Essential Homework Tips and Strategies

    Homework Statement Homework Equations The Attempt at a Solution I honestly do not know how to start this.
  10. Y

    Where Can We Find Limit Cycles in Practical Machines?

    Where we can find Limit Cycles Phenomena in Practice, I mean in which class of machines?
  11. J

    Engine Cycles: Otto, Diesel and Carnot

    Problem / Question 1)Study the engine cycles for the Otto cycle, Diesel cycle, the Carnot cycle and the standard air cycle. Explain the principles of how they work why they are different and the benefits and disadvantages of each of the systems. I have wrote about the otto cycle...
  12. S

    Can an AC Water Well Pump Handle 50Hz Cycles for Use in Africa?

    I am new here and I am not really sure where to post this question. I am also not an Engineer, so general language would be appreciated. I sell Water Well Pumps at my location and on the Internet among other things. Today I had a call from a Man who wanted a Pump that was going to Africa. He...
  13. B

    Geometric Example of Torsion Cycles and Relative Cycles (in Homology)

    Hi, Everybody: I am trying to understand torsion and relative cycles in a more geometric way; I think I understand some of the machinery behind relative cycles (i.e., the LES, and the induced maps.), and I understand that by ,e .g., Poincare duality, in order to have torsion in...
  14. M

    Prove Odd Length Cycle u2 is Also a Cycle

    Homework Statement Show that for any cycle of odd length, u, then u2 is a cycle as well. Homework Equations The Attempt at a Solution I looked at examples of it and it does work them but I am unsure of how to generalize it.
  15. B

    How do I express an element in a matrix of s8 as a product of disjoint cycles?

    Homework Statement Express the element in matrix A= 1,2,3,4,5,6,7,8 4,1,3,2,8,5,6,7 of s8 as a product disjoint cycles [b]2. Homework Equations [/b The Attempt at a Solution I pick a number say the first 1 and pu it in parenthises. (1, I multiply by the number in th...
  16. D

    Why has the Holocene temperature cycle deviated from previous cycles?

    Reading a lot about climate change over the past few years has lead me to a question. From looking at the available temperature charts for the past 450K years I have become curious about the lack of comment on the deviation for the last 12K years from previous periodic 124K year peak...
  17. K

    Proving t a^-1 = b: Permutations & Cycles Homework

    Homework Statement Let t be an element of S be the cycle (1,2...k) of length k with k<=n. a) prove that if a is an element of S then ata^-1=(a(1),a(2),...,a(k)). Thus ata^-1 is a cycle of length k. b)let b be any cycle of length k. Prove there exists a permutation a an element of S such that...
  18. 1

    3-cycle or a product of three cycles permutations

    Homework Statement Show that every element in A(n)= set of even permutations, for n> or equal to 3 can be expressed as a 3-cycle or a product of three cycles. Homework Equations 3-cycle = (_ _ _). a permutation is a function from a set A to A that is bijective. The Attempt at a...
  19. marcus

    Cycles of time-Penrose says his cyclic cosmology obeys thermodynamics.

    Cycles of time--Penrose says his cyclic cosmology obeys thermodynamics. Roger Penrose has devised a cyclic cosmology which he sees as not violating the second law of thermodynamics. There are several online videos of him lecturing about it. I'll get some links. I'm curious to know if others...
  20. K

    Alternatives to Rankine cycles

    I am plowing away through my ME curriculum and my intentions is to go into power engineering in some shape or form. I wanted to know if any research has gone into energy harvesting at a atomic level. I just wondered if any research has gone into alternative to a boiler and a turbine for...
  21. B

    Geometric description of (simplicial)homologous cycles

    Hi, everyone: I am trying to understand the geometric interpretation of two simplicial cycles being homologous to each other. Let C_k(X) be the k-th chain group in the simplicial complex X, and let c_k be a chain in C_k(X) The algebraic definition is clear: two...
  22. N

    Hamiltonian Systems: Showing Limit Cycles Impossible

    http://books.google.ca/books?id=Pd8-s6rOt_cC&pg=PA70&lpg=PA70&dq=%22show+that+in+a+hamiltonian+system+it+is+impossible+to+have+asymptotically%22&source=bl&ots=uJplwJKBPB&sig=4HBlny5uGifky2zfdNtWxDi-Uuo&hl=en&ei=yk6tS47hJJTssQOPvJmEDA&sa=X&oi=book_result&ct=result&resnum=1&ved=0CAkQ6AEwAA...
  23. K

    How Do You Calculate the Efficiency of a Heat Cycle in Thermodynamics?

    Homework Statement One mole of an ideal monatamic gas at an initial volume of 25L follows the cycle shown below. All the processes are quasistatic. Find the efficiency of the cycle. Homework Equations PV = nRT dQ (at constant volume) = Cv*dT dQ (at constant pressure) = Cp*dT W(isothermal)...
  24. K

    Permutations and cycles - linear algebra

    Homework Statement Let \rho \inSym(n), p be prime, r be the remainder when n is divided by p (so 0\leqr<p and n=qp+r for some integer q). 1. Show that \rho^p = \iota iff the cycles of \rho all have lengths 1 or p. 2. Show that if \rho^p = \iota then |Supp(\rho)| is a multiple of p and...
  25. F

    How Does Conjugation Affect Cycles in Permutations?

    Homework Statement Let P be a permutation of a set. Show that P(i1i2...ir)P-1 = (P(i1)P(i2)...P(ir))Homework Equations N/A The Attempt at a Solution Since P is a permutation, it can be written as the product of cycles. So I figured that showing that the above equation holds for cycles will...
  26. F

    Does the Product of Cycles Hold for Permutations?

    Homework Statement Let P be a permutation of a set. Show that P(i1i2...ir)B-1 = (P(i1)P(i2)...P(ir)) Homework Equations N/A The Attempt at a Solution Since P is a permutation, it can be written as the product of cycles. So I figured that showing that the above equation holds...
  27. R

    Supergalactic cluster waves and geological cycles

    In large scale surveys of the Universe there are found to be huge megawalls of galaxies. A 128 Mpc/h periodicity in galaxy redshifts is observed by Tom Broadhurst, Richard Ellis, David Koo and Alex Szalay, in Nature vol 343 p726. Some cosmologists have suggested that this might be some sort of...
  28. K

    At the end of these 100,000 year cycles of temperature, what causes

    at the end of these 100,000 year cycles of temperature, what causes the peak temperature to fall?
  29. C

    Hello. Needs help with disjoint cycles.

    Express as the product of disjoint cycles: a. (1,2,3)(4,5)(1,6,7,8,9)(1,5) b. (1,2)(1,2,3)(1,2) I now how to do in 2 row permutations, with right to - left. can anyone tell me , how to express it without transfer it into 2 row permutations. One more question, How do we find out it's...
  30. T

    Isobarric, Isochoric, Adiabatic cycles

    Homework Statement Ok, i have a cycle that goes from "a to b", via isobaric expansion, than from "b to c" vis isochoric decrease in pressure, and "c to a" via a adiabatic compression. Each occur under quasistatic conditions I just want to double check I've got the, changes in work, heat...
  31. A

    Cycles in a number-theoretic graph

    Consider the following graph: 1.) There are n vertices labeled 1...n. 2.) There exists an edge between vertices u and v iff label(u) | label(v) (the label of u divides the label of v). How many unique simple cycles does such a graph with n vertices contain? Note(s): The exact function...
  32. D

    Representing products as disjoint cycles

    Homework Statement Represent the following products as products of disjoint cycle. find the order of each product. Homework Equations a) (1234)(567)(261)(47) b) (12345)(67)(1357)(163) c) (14)(123)(45)(14) The Attempt at a Solution I've only attempted a) because I'm not sure...
  33. Mk

    Supernovae and solar cycles found in Ice Cores

    http://arxiv.org/abs/0902.3446 So apparently gamma rays from nearby supernovae produce nitrogen oxide in the atmosphere. The team took 122-meter-long cores from Dome Fuji station in Antarctica and found three nitrogen oxide spikes in the 11th century. They think they know what two of them are...
  34. C

    Entropy for reversible and irreversible cycles.

    I am confused about the entropy change for reversible and irreversible cycles. I know entropy is a state function, so for cycles, the entropy change within the system should be 0, since the process ends up in the same state as the beginning. So does this mean that the entropy change for the...
  35. N

    Continental drift: effect on climate cycles

    I'd be interested in any ideas or theories or references on how the location of the continents is thought to affect global warming and cooling cycles. I previously read somewhere that the current position of the continents would cause different net solar heat absorption/reflection than prior...
  36. X

    Question about permutation cycles

    If A is a cycle, and A=(1 4 5) (2 3 6). Is there a B such that BAB^-1=A^2. I found A^2=(1 5 4) (2 6 3), but I'm not really sure where to go from there.
  37. A

    Diesel, Otto and Dual Cycles

    I want to compare the Ideal Diesel, Otto and Dual cycles with constant specific heats. I am interested in knowing the relationship between r (compression) and nth (efficiency). I am unable to determine the common inputs to all three which can give me the efficiency for all the cycles. r with...
  38. D

    Two Closed Thermodynamic Cycles Conceptual Question

    Imagine processing the gas clockwise through Cycle 1 and then counterclockwise through Cycle 1. Compare these two processes on the basis of the heat energy transferred to the gas in the entire cycle. Choose the correct comparison symbol. Q_clockwise for Cycle 1 <,=,> Q_counterclockwise for...
  39. P

    Can a permutation with non-disjoint cycles still be used to find its order?

    i am pretty sure it's true that to find the order of a permutation, you can find LCM of the length of the disjoint cycles... if you have a permutation that doesn't have disjoint cycles (i.e. like one with (1,3,6,8)(4,6)), then can you use the same method to find the order? I feel like I am...
  40. S

    Counting cycles in a permutation

    I'm trying to show that for two permutations f ang g in Sn, the number of disjoint cycles in fg is the same as the number of disjoint cycles in gf. I know that in general fg does not equal gf, but by working examples it seems like they always decompose into the same number of disjoint cycles...
  41. A

    Expressing as Product of Disjoint Cycles

    Homework Statement Express as the product of disjoint cycles: a. (1,2,3)(4,5)(1,6,7,8,9)(1,5) b. (1,2)(1,2,3)(1,2) The Attempt at a Solution a. (1, 2, 3) ( 4, 5, 6, 7, 8, 9) b. (1, 2, 3) These are the answers I got directly through the product. Would anybody be willing to check...
  42. D

    Sleep cycles, circadian rythms, etc

    On all those studies which took people and placed them in caves/prolonged darkness, it's known the body goes into a 25 hour "day/night cycle". But is that cycle itself roughly synced with the actual day and night (even when the person can't tell whether it's day or night outside), and if so, how...
  43. R

    Problem Dealing with Digit Cycles

    Not sure if cycle is the best word here.. Let k and b (both > 1) be such that b does not divide k-1 (with the exception that b may equal k-1). If n is the smallest power so that k^n is equivalent to 1 mod b (so n is the length of the digit cycle of 1/b in base k), then bn is the...
  44. Andre

    What Causes 430,000 Year Cycles in Paleocene Sea Level?

    We have discussed sea level yoyo's from the Pleistocene ice age of which it is suggested that it balances with the ice volume paced on the poles. So all of a sudden a study pops up (courtesy of the author), Dr Madeleine Briskin...
  45. R

    Independent Sets of Cycles proof Involves Combinations

    Homework Statement Let C_n Recalling our notation from class, we know that I_0(C_n) = 1 and I_1(C_n) = n. Prove that for k > 1, I_k(C_n)=\left(\frac{n}{k}\right)\left(\stackrel{n-k-1}{k-1}\right) Homework Equations I_k implies number of independent sets of size k C_n implies the cycle with...
  46. C

    What are the approximate costs for operations on common x86 chips?

    As a first step to optimizing code, I like to think about faster ways to do things. Algorithmic improvements are far better than minute improvements to code, or even use of inline assembly, in general. But most optimizations beyond common subroutine elimination and its ilk substitute...
  47. S

    Multiplying non-disjoint permutation cycles

    Maybe I'm just being dense, but I've been having issues with the multiplying non-disjoint permutation cycles (as you may have guessed from the topic title). Simple products like (1, 4, 5, 6)(2, 1, 5) [an example from my textbook], as well as in the opposite order. Mayhap that I'm tired...
  48. R

    What Are the Pros and Cons of Using Nitrogen vs Helium in PBMR Cooling?

    I would need help, if there is someone willing to help... Q: ·What are advantages and disadvantages of nitrogen as cooling gas in PBMR comparing with helium? ·On witch way is possible to increase power of Brayton cycle to act on compressor side and in the same time greatest pressure...
  49. M

    Cycles per instruction question, why different CPI when I change for loop order?

    Hello everyone, this is a computer science/computer engineering problem... I had the following file that multiplies 2 matrices together, with 100 elements and puts it into a 3rd 100 element matrix. Well I used Simple Scalar to anlayize the CPI generated by the code and it also records the miss...
  50. J

    Thermo Question - Fridge cycles

    Consider a 300 kJ/min refrigeration system that operates on an ideal vapor-compression cycle with refrigerant-134a as the working fluid. The refrigerant enters the compressor as saturated vapor at 140 kPa and is compressed to 800 kPa. Determine the (a) quality of the refrigerant at the end of...
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