Mixing Definition and 298 Threads

In mathematics, mixing is an abstract concept originating from physics: the attempt to describe the irreversible thermodynamic process of mixing in the everyday world: mixing paint, mixing drinks, industrial mixing, etc.
The concept appears in ergodic theory—the study of stochastic processes and measure-preserving dynamical systems. Several different definitions for mixing exist, including strong mixing, weak mixing and topological mixing, with the last not requiring a measure to be defined. Some of the different definitions of mixing can be arranged in a hierarchical order; thus, strong mixing implies weak mixing. Furthermore, weak mixing (and thus also strong mixing) implies ergodicity: that is, every system that is weakly mixing is also ergodic (and so one says that mixing is a "stronger" notion than ergodicity).

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  1. A

    Change in Entropy for Mixing of Two Liquids

    Homework Statement You mix 1 liter of water at 20°C with 1 liter of water at 80°C. Set up an equation to find the change in entropy for one of the volumes of liquid in terms of initial temperature (T1) and the temperature after the two volumes of water mixed (T2) Homework Equations...
  2. S

    How Do You Write the Neutrino Mixing Matrix Us from Equations 3 and 4?

    Please look at equation 3 and 4 of this paper http://arxiv.org/abs/0707.2481v1 I am facing problem to write the matrix Us Can anybody help me to write the complete matrix?
  3. trollcast

    Mixing bracket types when writing solutions?

    Is it okay to mix the types of brackets you use when writing out a solution to help make it a bit clearer? For example: If I was completeing the square with: $$ 3x^{2} + 5x -2 = 0 $$ I would factor out the 3 onto square brackets like this: 3 \left[x^{2} + \frac{5}{3}x - \frac{2}{3} \right]...
  4. M

    How do I determine the 'other stuff' in DE mixing problems?

    I am having major problems understanding these types of questions, where you will have water and in will be chemicals mixing at a certain rate, and coming out of another tube at a rate, and then the question is to find out certain things, concentration at a time or whatever. My question, the...
  5. C

    Differential Equation Mixing Problem

    Homework Statement Suppose the clean water of a stream flows into Lake Alpha, then into Lake Beta, and then further downstream. The in and out flow for each lake is 200 liters per hour. Lake Alpha contains 500 thousand liters of water, and Lake Beta contains 400 thousand liters of water. A...
  6. N

    Calculating Mixing Ratio of Hydroxyl Radicals at Sea Level

    A typical global concentration of hydroxii radicals (OH) is about 10^6 moleculues/cm^3. What is the mixing ratio corresponding to this concentration at sea level P = 10^5 Pa and T=298 K? Using the previous equations derived earlier ndOH= (P*Av/R*T)*COH (ndOH*R*T/(P*Av) ) = COH (10^6...
  7. P

    Singlet/Triplet state mixing question

    Hey guys! I am trying to show how singlet and triplet states mix via spin-orbit coupling, but I am having some trouble. I've gotten most of the way through, but I am stuck on how an operator works. Sadly, I think my poor basis in quantum is going to show right here. My starting point...
  8. D

    Mixing of substances of different temperature with change of state

    Two questions: 1.1. Homework Statement Steam at 100 °C is pumped into an insulating pot containing a mixture of ice and water at 0°C. There are 0.4kg of ice and 1.6kg of water in the pot. Assume there is no heat lost to the surroundings, how much steam (in kg) is needed so that all ice is just...
  9. R

    Mixing Two Gases: How to Calculate Combined Volumetric Flow Rate?

    Hi I'm working on a project where I have a two flow controller controlling the volumetric flow rate (in the order of 0.01-0.1ml/min) of two different gases. The gases are mixed together and I'm wondering if there's a way to figure out the exiting volumetric flow rate of the combined flow and...
  10. L

    Stimulated generation of superluminal light pulses via four-wave mixing (NIST)

    Concerning this paper: Stimulated generation of superluminal light pulses via four-wave mixing. I have two questions: 1) How can we check that information cannot be propagated faster than light with this system? 2) What is the meaning of the last sentense of this paper: Thanks
  11. M

    What is the outcome of mixing these two chemicals

    At work we use; Powder Bleach, ACTIVE INGREDIENT: Sodium Dochloroisocyanurate and A cleaning agent, ACTIVE INGREDIENT: Sodium Dodecylbenzene sulfonate These two chemicals are to be used separately but we have the sudden rumour that when mixed in a mop bucket it is significantly more...
  12. R

    Thermodynamics: Calculating Entropy Change for Mixing Streams

    Homework Statement http://img401.imageshack.us/img401/6641/problem2t.jpg The Attempt at a Solution I'm not sure how to approach this problem. I know of this equations for when they reach thermal equilibrium: T_f = \frac{C_1 T_{1,i} + C_2T_{2,i}}{C_1+C_2} And this for entropy change...
  13. B

    Mixing Tank, Differential Equations Problem

    Homework Statement a larg tank is filled with 500 gals of water with 400lbs of salt. pure water is pumped into the tank at a rate of 3gal/min. the well mixed solution is pumped out at a rate of 7 gal/min. I need help finding the Differential Homework Equations The Attempt at a...
  14. C

    Mixing He, O, Ge, N and U: What Could Happen?

    What would be the result of mixing helium, oxygen, germanium, nitrogen and uranium?
  15. E

    Calculating ΔS for Mixing H20 and D20 Solutions

    Homework Statement For both H20 and D20: Cp = 75.5 J/mole-k for the liquid Cp = 37.8 J/mole-k for the solid ΔHfus=6.01 kJ/mole. Liquid H20 and D20 form an ideal solution. a) One mole of liquid H20 at 10 C is mixed with four moles of LIQUID D20 at 0 C in an insulated...
  16. L

    Osmosis and entropy/free energy and mixing.

    I sometimes have trouble with the concept of entropy being a driving force for work being done. For example, during osmosis you can raise the level of water on one side of a semipermeable membrane (i.e. do work) because the free energy of the system is minimized if there is a flow of solvent...
  17. L

    Stark effect, mixing state of 2s and 2p

    hi all, can anyone help me understanding what is the meaning of the mixing state of 2p and 2s? thanks in advance. when an electron in n=2 sate in a hydrogen atom, experience a external em field, then the degenerate states split into 3 classes, which are: 1/sqrt2( 210 + 200 ) with higher...
  18. C

    Mixing chamber with multiple inlets

    Hi I was wondering if someone could help me with this question. Question 4 uploaded in picture. Ok, so far this is what I have found Pipe 1: m1=2kg/s P1=1000kpa T1=100 C h1=334.82kJ/kg Pipe 2: sat-liquid T2=60 C P2= 1000kpa h2=291.36KJ/kg Outlet: sat vapor P3=1000kpa V=20...
  19. T

    Mixing water tempretures and flow rates

    Have a work related problem here, tried all afternoon to find a formula but no luck so far Heres the problem. I have a tap supplying water at 41°c and at a flow rate of 0.17 l/s. The tap is connected to a Termostatic Mixing Valve (TMV) with a hot and cold water supply. The hot water is...
  20. T

    Thermostatic Mixing Valve: Flow Rates and Energy Conservation

    Heres the problem. I have a tap supplying water at 41°c and at a flow rate of 0.17 l/s. The tap is connected to a Termostatic Mixing Valve (TMV) with a hot and cold water supply. The hot water is at 60°c and the cold water is being supplied at 10°c. What are the flow rates for the hot...
  21. A

    How to calculate entropy of mixing in 2-d systems

    Hello physics forums, I am writing a paper and I am wondering how to calculate the entropy of mixing in a two dimensional system. I am sure that entropy increases with mixing in a two dimensional system, but I do not know what equation to use. Would I just use the same equation as for 3-d...
  22. D

    Why can the mixing of acids and bases be dangerous

    I tried googling this topic and basically all I could find was sites saying they neutralise each other - I know that. But why is it that when you mix say a drop of pH 14 solution with a lot of pH 1 solution that they react rather violently and the acid sprays everywhere? If someone could maybe...
  23. Spinnor

    Mechanical system with simlar phyysics of neutrion flavor mixing.

    Mechanical system with similar physics of neutrino flavor mixing. Pull one mass down while holding the others at their rest positions. Now let them all go. See system here (don't know how to add images): https://picasaweb.google.com/andyeverett57/August282011 Sorry for the spelling in the...
  24. D

    Entropy of Mixing for Two Ideal Gases at Different Temperatures

    Homework Statement Two monatomic ideal gases are separated in a container by an impermeable wall, with volumes V_{1} and V_{2}, temperatures T_{1} and T_{2}, number of atoms N_{1} and N_{2}, and both are at the same, constant pressure P. The wall is then removed, and the pressure is continued...
  25. M

    Neutrino mixing matrix: Can it be derived?

    Hi, When we consider the two neutrino mixing case, we have the matrix that converts between them as given below \begin{pmatrix} |v_{1}> \\ |v_{2}> \end{pmatrix} = \begin{pmatrix} cos\theta & sin\theta \\ -sin\theta & cos\theta\end{pmatrix}\begin{pmatrix} |v_{e}> \\ |v_{\mu}> \end{pmatrix}...
  26. D

    Can Mixing Different pH Indicators Broaden Detection Range in Spectrophotometry?

    As an experiment I was going to investigate the use of a spectrophotometre as a pH meter by using different chemical indicators which should change colour depending upon the pH of the substance. I know that indicators such as bromthymol blue only experience a distict change in colour over a pH...
  27. A

    Spontaneous parametric down-conversion: Should this be a three-wave mixing?

    Hi I am currently reading through a semiclassical approach to nonlinear optics. I learned about effects of second-order nonlinear optics like second harmonic generation and three wave mixing. I understand three-wave mixing as a process in which you send two (or three) monochromatic beams...
  28. R

    Help on Mixing solution from two tanks problem

    Two tanks, A and B, each contain 5K gal of water. To each tank 150 gal of a chemical should be added, but in error the entire 300 gal are poured into tank A. Pumps are set to work to circulate the liquid through the two tanks at the rate of 100 gal/min (a) How long will it take for tank A to...
  29. D

    Thermodynamics-psychrometry question, mixing two streams of warm moist air

    Homework Statement I'm trying to determine how to go about attacking this problem that I'm doing to I have 2 streams of air mixing, and I'm trying to find the temperature and relative humidity of the third stream. Stream 1: 2bar, 20C, 40%rh, and 1kg/s Stream 2: 1bar, 20C, 4kg/s So...
  30. J

    Design of a mixing box of different gases

    Hi guys, I am designing a mixing box for different gases. Here is my plan: I will use Acrylic panels with the dimension of 30cm x 30cm x30cm. Two 3/4 inch pipes feed inflows at flow rate of 1300 LPM in total. The outlet is an rectangular opening of 8cm x 8cm. How can I define the pressure inside...
  31. Z

    Electroweak Mixing: Hypercharge, Isospin & Photon/Z0

    In the GWS electroweak model, there are two fundamental charges: weak hypercharge and the third component of weak isospin (henceforth referred to as hypercharge and isospin respectively). The gauge boson of hypercharge is the B0, and those of isospin are the W+, W0, and W-. The B0 and W0 mix...
  32. W

    Thermodynamics - Simple mixing problem

    Homework Statement Liquid ammonia at 1.5 MPa, 20oC is mixed with saturated vapor ammonia at 1.5 MPa at equal flow rate. At the outlet, 1.3 MPa and quality of 0.85. Calculate the heat transfer per kilogram of ammonia exiting the mixer. Homework Equations The Attempt at a Solution I tried...
  33. PainterGuy

    Mixing 2nd and 6th groups' elements to semiconductor silicon

    Hi everyone, :smile: I was wondering why they only use 5th and 3rd groups elements to create n-type and p-type semiconductors respectively. Couldn't we mix 6th or 2nd groups' elements instead to make the semiconductors? What would happen if we do this? Perhaps elements of those groups will...
  34. V

    Flowing water temperature mixing

    Useless explanation text: I'm building a shower system that uses motors to manually turn valves to adjust the temperature based on what the user sets I'm trying to develop a way for the system to preemptively predict what the temperature will be so it doesn't just say "Open hot valve a...
  35. P

    Entropy of mixing, non-isolated system

    Homework Statement Take a container of volume V, which has two separated partitions, each with volume V/2. Each partition contains a gas of N molecules, with respectively mass \m_{a} and \(m_{b}\). The temperature in the partitions is equal to that of its surroundings, and energy exchange...
  36. PainterGuy

    What role does doping play in creating n-type and p-type semiconductors?

    hi everyone, when antimony is added to germanium, antimony's atoms make covalent bonds with germanium. antimony has five valence electrons and germanium has four. there would be total 4 covalent bonds each consisting of 2 electrons. this would mean that there would be one extra from each...
  37. X

    Mixing of two gasses. Find the temperature and pressure

    Homework Statement A rigid insulated tank is separated into two rooms by a stiff plate. Room A of 0.5 m3 contains air at 250 kPa, 300 K and room B of 1 m3 has air at 150 kPa, 1000 K. The plate is removed and the air comes to a uniform state without any heat transfer. Find the final pressure...
  38. S

    Creating a 'Heat Wave' Look Without Mixing

    Last night I experimented with glycerin, putting it in water to get the 'heat wave' look that results from a difference in refractive indexes. I forgot that glycerin is miscible in water, and after a little bit of agitation it all mixed into solution and the effect couldn't be seen anymore...
  39. P

    Mixing air how much water leaving?

    I have a situation like this: Where C is a air stream from a pipe, and A is the sky. Droplet will be made, and there will be fog. Now I have to calculate the amount of water leaving the air. In my book I found this equation: Qwater = Qdry.air.C * (xA - xC) But do it have to be...
  40. P

    What does mixing under RG flow mean?

    what does "mixing under RG flow" mean? I'm trying to understand the language people use when they talk about RG flow. Here's what I understand: We have the RG flow equations governing the couplings' dependence on energy scale [tex]\mu {dg_i \over d\mu}=\beta(g_j)[\tex], and we can find the...
  41. C

    Differential Equations Mixing Problem (REVISED)

    1. Suppose we have two tanks, each with an inflow pipe and an outflow pipe and also connected to each other by pipes. At the start, tank A contains 40 gallons of clean water and Tank B contains 25 gallons of clean water. At t = 0 brine containing 0.5 lbs of salt per gallon begins to flow into...
  42. A

    Mixing gases to achieve desired ppm

    I have to mix 2 gases, Hydrogen and Nitrogen to achieve a constant flow of mixed gas with 100, 200... 1000 ppm of H2 in the mixture. I have mass flow meters to adjust the flow of each individual gas but how do I determine what they should read to achieve the desired ppm
  43. J

    Exploring the Mixing Paradox: Entropy Change

    Just learned about it recently, and I'm curious to understand more. The 'mixing' form of the paradox goes something like this: Imagine a box partitioned in the middle. The two partitions are the same volume. In each there is a gas, on one side labelled A, and on the other B. The are held at...
  44. M

    How much new entropy have you created by mixing the water

    Homework Statement In order to take a warm bath, you mix 50 liters of hot water at 55 degrees Celsius with 25 liters of cold water at 10 degrees Celsius, How much new entropy have you created by mixing the water Homework Equations S = Integral(Ti to Tf) (Cv / T) dT The Attempt...
  45. D

    Animating Mixing Tank with PID Controller for Fluid Flow Control

    I am working on an assignment which is based around studying and designing the control system for a tank which has two inlet flows and one outlet flow. For the purpose of what i am doing, i will be assuming that only one of the inlet flow rates changes. Part of the assignment requires me to...
  46. R

    Solving Mixing problems in calculus

    [b]1. A tank contains 2940 L of pure Water. A Solution that contains 0.08 kg of sugar per liter enters a tank at the rate 8 Liter/minute. The solution is mixed and drains from the tank at the same rate. Find the amount of sugar in the tank After t minutes
  47. H

    Differential Equations mixing sugar and water

    Homework Statement A tank contains 2860 L of pure water. A solution that contains 0.04 kg of sugar per liter enters a tank at the rate 5 L/min The solution is mixed and drains from the tank at the same rate. Find the amount of sugar in the tank after t minutes. Homework Equations...
  48. H

    How Do You Calculate Salt Concentration in a Leaky Stirred Tank Reactor?

    Homework Statement A stirred tank reactor that initially contains a volume V(0) = V_0 of water. Suppose that a stirred solution of salt at concentration S is pumped in at a rate of F_in = F litres/hr and the well-stirred mixture is pumped out at a slight faster rate of F_out = (F + f)...
  49. W

    Checking for interference equation - two wave mixing

    Homework Statement Not too sure if my problem falls under this category. Hope I have done all formatting correctly Basically I am seeking some confirmation on my maths derivation and would like to enquire why there is discrepancies when we expressed the result in Fourier Spectrum...
  50. D

    Linearizing a Nonlinear Mixing Tank System: Finding Steady-State Concentrations

    I have a problem to solve where i am required to linearise a nonlinear system. Basically, the system involves a mixing tank of height H(t) and cross section area A with two input streams with flow rates Q1(t) and Q2(t) with concentrations C1 and C2 of some species (concentrations are constant)...
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