Zeitschriftenartikel: „Mixing equations“

1

Brigham, W. E. „Mixing Equations in Various Geometries“. SPE Reservoir Engineering 1, Nr. 02 (01.03.1986): 203–8. http://dx.doi.org/10.2118/4585-pa.

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2

Blasone, M., P. Jizba und L. Smaldone. „Schwinger-Dyson equations and flavor mixing“. Journal of Physics: Conference Series 1071 (August 2018): 012003. http://dx.doi.org/10.1088/1742-6596/1071/1/012003.

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3

Łoskot, K., und R. Rudnicki. „Mixing and some integro-functional equations“. Aequationes Mathematicae 40, Nr. 1 (Dezember 1990): 78–82. http://dx.doi.org/10.1007/bf02112282.

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4

Kostić, Marko. „Hypercyclic and topologically mixing properties of abstract timefractional equations with discrete shifts“. Sarajevo Journal of Mathematics 9, Nr. 2 (November 2013): 257–69. http://dx.doi.org/10.5644/sjm.09.2.10.

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5

Eggl, Maximilian F., und Peter J. Schmid. „Shape optimization of stirring rods for mixing binary fluids“. IMA Journal of Applied Mathematics 85, Nr. 5 (14.05.2020): 762–89. http://dx.doi.org/10.1093/imamat/hxaa012.

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Abstract Mixing is an omnipresent process in a wide range of industrial applications, which supports scientific efforts to devise techniques for optimizing mixing processes under time and energy constraints. In this endeavour, we present a computational framework based on nonlinear direct-adjoint looping for the enhancement of mixing efficiency in a binary fluid system. The governing equations consist of the nonlinear Navier–Stokes equations, complemented by an evolution equation for a passive scalar. Immersed and moving stirrers are treated by a Brinkman penalization technique, and the full system of equations is solved using a Fourier-based pseudospectral approach. The adjoint equations provide gradient and sensitivity information which is in turn used to improve an initial mixing strategy, based on shape, rotational and path modifications. We utilize a Fourier-based approach for parameterizing and optimizing the embedded stirrers and consider a variety of geometries to achieve enhanced mixing efficiency. We consider a restricted optimization space by limiting the time for mixing and the rotational velocities of all stirrers. In all cases, non-intuitive shapes are found which produce significantly enhanced mixing efficiency.

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XUE, SHE-SHENG. „NEUTRINO MASSES AND MIXINGS“. Modern Physics Letters A 14, Nr. 39 (21.12.1999): 2701–8. http://dx.doi.org/10.1142/s0217732399002844.

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We propose a novel theoretical understanding of neutrino masses and mixings, which is attributed to the left–right symmetric feature of the regularized standard model at short distances. We try to explain the smallness of Dirac neutrino masses and the decoupling of the right-handed neutrino as a free particle. Neutrino masses and mixing angles are completely related to each other in the Schwinger–Dyson equations for their self-energy functions. The solutions to these equations and a possible pattern of masses and mixings are discussed.

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7

Hall, Kenneth R., Gustavo A. Iglesias-Silva und G. Ali Mansoori. „Quadratic mixing rules for equations of state“. Fluid Phase Equilibria 91, Nr. 1 (November 1993): 67–76. http://dx.doi.org/10.1016/0378-3812(93)85079-2.

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8

Kirkup, S. M., M. Wadsworth, D. G. Armour, R. Badheka und J. A. Van Den Berg. „Computational solution of the atomic mixing equations“. International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 11, Nr. 4 (Juli 1998): 189–205. http://dx.doi.org/10.1002/(sici)1099-1204(199807/08)11:4<189::aid-jnm301>3.0.co;2-a.

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9

Chitsaz, Mahzad, und Mani Fathali. „Effect of External Magnetic Field on Dynamics of Two-dimensional Isotropic Conducting Flow“. E3S Web of Conferences 95 (2019): 02003. http://dx.doi.org/10.1051/e3sconf/20199502003.

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In this article, the impact of external uniform magnetic field on the dynamic characteristics and mixing parameters of two-dimensional isotropic magnetohydrodynamic (MHD) flow is investigated. For this purpose, the direct numerical simulation (DNS) is applied to two-dimensional incompressible Navier-Stokes and magnetic induction equations by pseudo-spectral method. Governing equations are considered in the N-S vorticity equations to guarantee the incompressibility conditions and remove the pressure term from equations. The Results of the calculations show that the deformation of vortexes by external magnetic field reduces the mixing efficiency. It is also demonstrated that in MHD flow the energy is exchanged by Lorentz force between the flow and the magnetic field in such a way that the kinetic energy decreases and consequently mixing of the fluid is reduced. This energy transfer causes reduction of viscous dissipation of energy and mixing efficiency, despite increasing the total dissipated energy rate.

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Lozovatsky, I. D., und H. J. S. Fernando. „Mixing efficiency in natural flows“. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, Nr. 1982 (13.01.2013): 20120213. http://dx.doi.org/10.1098/rsta.2012.0213.

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It is argued that the mixing efficiency of naturally occurring stratified shear flows, γ = Rf /(1− Rf ), where Rf is the flux Richardson number, is dependent on at least two governing parameters: the gradient Richardson number Ri and the buoyancy Reynolds number Re b = ε / vN 2 . It is found that, in the range approximately 0.03< Ri <0.4, which spans 10 4 < Re b <10 6 , the mixing efficiency obtained via direct measurements of fluxes and property gradients in the stable atmospheric boundary layer and homogeneous/stationary balance equations of turbulent kinetic energy (TKE) is nominally similar to that evaluated using the scalar balance equations. Outside these Ri and Re b ranges, the commonly used flux-estimation methodology based on homogeneity and stationarity of TKE equations breaks down (e.g. buoyancy effects are unimportant, energy flux divergence is significant or flow is non-stationary). In a wide range, 0.002< Ri <1, the mixing efficiency increases with Ri , but decreases with Re b . When Ri is in the proximity of Ri cr ∼0.1–0.25, γ can be considered a constant γ ≈0.16–0.2. The results shed light on the wide variability of γ noted in previous studies.

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Dopazo, César, Luis Valiño und Norberto Fueyo. „Statistical Description of the Turbulent Mixing of Scalar Fields“. International Journal of Modern Physics B 11, Nr. 25 (10.10.1997): 2975–3014. http://dx.doi.org/10.1142/s0217979297001453.

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A formulation in terms of probability density function (PDF) transport equations is presented for inert and reactive scalar fields undergoing turbulen mixing. The PDF methodology is related to the classical moment equations. The hierarchy of PDF transport equations resembles the BBGKY equations in statistical mechanics. Closure hypothesis, approximating the molecular mixing term, are described and their predictions for simple systems are compared with direct numerical simulations (DNS). Solution algorithms in terms of Monte Carlo particles are also discussed.

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Knapp, Helmut, Albert Reichl und Stanley I. Sandler. „Analysis of Thermodynamic Model Equations: Mixing Rules in Cubic Equations of State“. Industrial & Engineering Chemistry Research 37, Nr. 8 (August 1998): 2908–16. http://dx.doi.org/10.1021/ie970762b.

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13

Kim, Jeong-Hoon. „Asymptotic theory of noncentered mixing stochastic differential equations“. Stochastic Processes and their Applications 114, Nr. 1 (November 2004): 161–74. http://dx.doi.org/10.1016/j.spa.2004.05.004.

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14

Veretennikov, A. Yu. „On polynomial mixing bounds for stochastic differential equations“. Stochastic Processes and their Applications 70, Nr. 1 (Oktober 1997): 115–27. http://dx.doi.org/10.1016/s0304-4149(97)00056-2.

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15

Fish, Alexander. „Solvability of linear equations within weak mixing sets“. Israel Journal of Mathematics 184, Nr. 1 (31.07.2011): 477–504. http://dx.doi.org/10.1007/s11856-011-0077-6.

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16

Papanicolaou, G. C., und W. Kohler. „Asymptotic theory of mixing stochastic ordinary differential equations“. Communications on Pure and Applied Mathematics 27, Nr. 5 (13.09.2010): 641–68. http://dx.doi.org/10.1002/cpa.3160270503.

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17

PODOSHVEDOV, SERGEY A. „STUDIES OF SOME PECULIARITIES OF NONLINEAR DYNAMICS OF FOUR-WAVE MIXING OF LIGHT WAVES PROPAGATING FORWARD IN LIQUID CRYSTAL ON THERMAL NONLINEARITY“. Journal of Nonlinear Optical Physics & Materials 08, Nr. 03 (September 1999): 403–18. http://dx.doi.org/10.1142/s021886359900028x.

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Evolution of four waves propagating forward in nematic liquid crystal is studied using Hamiltonian representation of initial equations describing the process. Here we extend theory of the four-wave mixing on thermal nonlinearity of nematic liquid crystal. All types of analytical solutions are found for these equations. The possibilities of observing of optical switching in this mixing are discussed.

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Emperhoff, Sophie, Matthias Eberl, Tim Dwertmann und Jürgen Wöllenstein. „On the Influence of Humidity on a Thermal Conductivity Sensor for the Detection of Hydrogen“. Sensors 24, Nr. 9 (24.04.2024): 2697. http://dx.doi.org/10.3390/s24092697.

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Thermal conductivity sensors face an omnipresent cross-influence through varying humidity levels in real-life applications. We present the results of investigations on the influence of humidity on a hydrogen thermal conductivity sensor and approaches for predicting the behavior of thermal conductivity towards humidity. A literature search and comparison of different mixing equations for binary gas mixtures were carried out. The theoretical results were compared with experimental results from three different thermal conductivity sensors with mixtures of water vapor in nitrogen. The mixing equations show a large discrepancy between each other. Some of the models predict a continuously decreasing thermal conductivity and some predict an increasing thermal conductivity for increasing levels of humidity. Our measurements indicate an increase in thermal conductivity followed by a decrease after reaching a peak value. It is shown that the measured behavior is reproducible with different sensors. Depending on the sensor, this corresponds to an error up to 2 vol.% in the measured hydrogen value. The measured behavior is consistent with only one of the three models. Compared to this model, our own sensor shows a maximum deviation of 1.4%. Mixing equations for gas mixtures must be chosen carefully, taking into consideration whether mixing partners include polar or non-polar molecules. Some simplified mixing equations cannot be used to calculate the thermal conductivity of water vapor in air or nitrogen.

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Bibek, Koirala, und Dhobi Saddam Husain. „Oscillation of neutrino in a vacuum with mixing flavor“. International Journal of Physics Research and Applications 5, Nr. 1 (04.08.2022): 018–26. http://dx.doi.org/10.29328/journal.ijpra.1001046.

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We developed multiple equations to observe the two and three flavors of neutrino oscillation with the mixing angle based on L/E=0.1 to 0.9 in this study. In different settings, the nature of the neutrino oscillation probability was discovered to be varied in different equations. The observation indicates increasing likelihood in one equation and decreasing probability in the other equations in two flavor oscillation neutrinos. To characterize the probability of neutrino oscillation, we use four distinct angles: 50, 100, 150, and 200. The probability of neutrino oscillation was determined to be highest at an angle of 150 degrees. However, with increasing mixing angles, the likelihood of oscillation increases on the basis of created equation (25) and decreases on the basis of equations (26) and (27) in the three-flavor neutrino oscillation. From generated equations (25) and (26) the maximum neutrino oscillation of probability is discovered at an angle of 150, however, from equation (27), the maximum probability is observed at 50. The greatest neutrino oscillation is found to be 0.9999 and the minimum is zero in all of these two and three flavors of oscillation.

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Koirala, Bibek, Saddam Husain Dhobi, Prakash Subedi, Milan Gurung, Kumar Teemilsina und Sharad Kumar Oli. „Oscillation of neutrino in a vacuum with mixing flavor“. Journal of Physics: Theories and Applications 7, Nr. 1 (27.03.2023): 17. http://dx.doi.org/10.20961/jphystheor-appl.v7i1.64492.

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We developed multiple equations to observe the two and three flavors of neutrino oscillation with the mixing angle based on L/E=0.1 to 0.9 in this study. In different settings, the nature of the neutrino oscillation probability was discovered to be varied in different equations. The observation indicates increasing likelihood in one equation and decreasing probability in the other equations in two flavor oscillation neutrinos. To characterize the probability of neutrino oscillation, we use four distinct angles: 5degree, 10 degree, 15degree , and 20degree . The probability of neutrino oscillation was determined to be highest at an angle of 15 degrees. However, with increasing mixing angles, the likelihood of oscillation increases on the basis of created equation (25) and decreases on the basis of equations (26) and (27) in the three-flavor neutrino oscillation. From generated equations (25) and (26) the maximum neutrino oscillation of probability is discovered at an angle of 15degree , however, from equation (27), the maximum probability is observed at 5degree . The greatest neutrino oscillation is found to be 0.9999 and the minimum is zero in all of these two and three flavors of oscillation.

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Ji, Yao, und A. V. Belitsky. „On Equations of Motion in Twist-Four Evolution“. International Journal of Modern Physics: Conference Series 37 (Januar 2015): 1560051. http://dx.doi.org/10.1142/s2010194515600514.

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Explicit diagrammatic calculation of evolution equations for high-twist correlation functions is a challenge already at one-loop order in QCD coupling. The main complication being quite involved mixing pattern of the so-called non-quasipartonic operators. Recently, this task was completed in the literature for twist-four nonsinglet sector. Presently, we elaborate on a particular component of renormalization corresponding to the mixing of gauge-invariant operators with QCD equations of motion. These provide an intrinsic contribution to evolution equations yielding total result in agreement with earlier computations that bypassed explicit analysis of Feynman graphs.

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Buttsworth, D. R. „Interaction of oblique shock waves and planar mixing regions“. Journal of Fluid Mechanics 306 (10.01.1996): 43–57. http://dx.doi.org/10.1017/s002211209600122x.

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An analysis for predicting the interaction of a steady oblique shock wave and a planar mixing region is presented. Specifically, an equation for the shock curvature was obtained from the shock wave and isentropic wave difference equations which govern the shock transmission within a region of varying Mach number. The effects of nonuniform gas composition within the mixing region were assessed using a similar treatment; however, the wave equations were expanded in terms of a varying ratio of specific heats instead of a varying Mach number. An expression for the shock-induced vorticity due to velocity and density gradients within the mixing region was also obtained. This expression provides a means of estimating the possible mixing augmentation induced in various shock wave-mixing region interactions. When the velocity and density gradients within the mixing region oppose each other, it is demonstrated that the pre-shock vorticity may be attenuated by the shock. Applications of the analysis are discussed with reference to specific examples involving mixing augmentation and shock oscillation.

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Hernández Cervantes, Daniel, P. Amparo López-Jiménez, José Antonio Arciniega Nevárez, Xitlali Delgado Galván, Martín Rubén Jiménez Magaña, Modesto Pérez-Sánchez und José de Jesús Mora Rodríguez. „Incomplete Mixing Model at Cross-Junctions in Epanet by Polynomial Equations“. Water 13, Nr. 4 (09.02.2021): 453. http://dx.doi.org/10.3390/w13040453.

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In Water Distribution Networks (WDN), the water quality could become vulnerable due to several operational and temporal factors. Epanet is a hydraulic and water quality simulation software, widely used, to preserve the control of chemical disinfectants in WDN among other capabilities. Several researchers have shown that the flow mixing at Cross-Junctions (CJs) is not complete as Epanet assumes for the cases of two contiguous inlets and outlets. This paper presents a methodology to obtain the outlet concentrations in CJs based on experimental scenarios and a validated Computational Fluid Dynamics (CFD) model. In this work, the results show that the Incomplete Mixing Model (IMM) based on polynomial equations, represents in a better way the experimental scenarios. Therefore, the distribution of the concentration could be in different proportions in some sectors of the network. Some comparisons were made with the complete mixing model and the Epanet-Bulk Advective Mixing (BAM), obtaining relative errors of 90% in some CJs.

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Kuo, T. K., und S. H. Chiu. „Flavor Mixing and the Permutation Symmetry among Generations“. Advances in High Energy Physics 2020 (07.01.2020): 1–8. http://dx.doi.org/10.1155/2020/2491897.

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In the standard model, the permutation symmetry among the three generations of fundamental fermions is usually regarded to be broken by the Higgs couplings. It is found that the symmetry is restored if we include the mass matrix parameters as physical variables which transform appropriately under the symmetry operation. Known relations between these variables, such as the renormalization group equations, as well as formulas for neutrino oscillations (in vacuum and in matter), are shown to be covariant tensor equations under the permutation symmetry group.

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Mahammedi, Abdelkader, Naas Toufik Tayeb, Kwang-Yong Kim und Shakhawat Hossain. „Mixing Enhancement of Non-Newtonian Shear-Thinning Fluid for a Kenics Micromixer“. Micromachines 12, Nr. 12 (30.11.2021): 1494. http://dx.doi.org/10.3390/mi12121494.

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In this work, a numerical investigation was analyzed to exhibit the mixing behaviors of non-Newtonian shear-thinning fluids in Kenics micromixers. The numerical analysis was performed using the computational fluid dynamic (CFD) tool to solve 3D Navier-Stokes equations with the species transport equations. The efficiency of mixing is estimated by the calculation of the mixing index for different cases of Reynolds number. The geometry of micro Kenics collected with a series of six helical elements twisted 180° and arranged alternately to achieve the higher level of chaotic mixing, inside a pipe with a Y-inlet. Under a wide range of Reynolds numbers between 0.1 to 500 and the carboxymethyl cellulose (CMC) solutions with power-law indices among 1 to 0.49, the micro-Kenics proves high mixing Performances at low and high Reynolds number. Moreover the pressure losses of the shear-thinning fluids for different Reynolds numbers was validated and represented.

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Derksen, H., und D. Masser. „Linear equations over multiplicative groups, recurrences, and mixing I“. Proceedings of the London Mathematical Society 104, Nr. 5 (29.01.2012): 1045–83. http://dx.doi.org/10.1112/plms/pdr040.

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27

Seeger, Benjamin. „Scaling limits and homogenization of mixing Hamilton-Jacobi equations“. Communications in Partial Differential Equations 46, Nr. 1 (24.10.2020): 165–99. http://dx.doi.org/10.1080/03605302.2020.1831020.

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Mäkinen, J., und N. Gustavsson. „Estimating proportions in geochemical mixing equations by Chebyshev's method“. Applied Geochemistry 14, Nr. 1 (Januar 1999): 85–90. http://dx.doi.org/10.1016/s0883-2927(98)00027-4.

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DERKSEN, H., und D. MASSER. „Linear equations over multiplicative groups, recurrences, and mixing III“. Ergodic Theory and Dynamical Systems 38, Nr. 7 (02.05.2017): 2625–43. http://dx.doi.org/10.1017/etds.2016.137.

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Given an algebraic $\mathbf{Z}^{d}$-action corresponding to a prime ideal of a Laurent ring of polynomials in several variables, we show how to find the smallest order $n+1$ of non-mixing. It is known that this is determined by the non-mixing sets of size $n+1$, and we show how to find these in an effective way. When the underlying characteristic is positive and $n\geq 2$, we prove that there are at most finitely many classes under a natural equivalence relation. We work out two examples, the first with five classes and the second with 134 classes.

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Konstandin, Thomas, Tomislav Prokopec, Michael G. Schmidt und Marcos Seco. „MSSM electroweak baryogenesis and flavour mixing in transport equations“. Nuclear Physics B 738, Nr. 1-2 (März 2006): 1–22. http://dx.doi.org/10.1016/j.nuclphysb.2005.11.028.

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31

Odasso, Cyril. „Exponential Mixing for the 3D Stochastic Navier–Stokes Equations“. Communications in Mathematical Physics 270, Nr. 1 (01.12.2006): 109–39. http://dx.doi.org/10.1007/s00220-006-0156-4.

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Hopf, Katharina, und José L. Rodrigo. „Aggregation equations with fractional diffusion: Preventing concentration by mixing“. Communications in Mathematical Sciences 16, Nr. 2 (2018): 333–61. http://dx.doi.org/10.4310/cms.2018.v16.n2.a2.

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Masser, D. W. „Mixing and linear equations over groups in positive characteristic“. Israel Journal of Mathematics 142, Nr. 1 (Dezember 2004): 189–204. http://dx.doi.org/10.1007/bf02771532.

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Derksen, H., und D. Masser. „Linear equations over multiplicative groups, recurrences, and mixing II“. Indagationes Mathematicae 26, Nr. 1 (Januar 2015): 113–36. http://dx.doi.org/10.1016/j.indag.2014.08.002.

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Souza, Leonardo S., Ernesto P. Borges und Fernando L. P. Pessoa. „q-Quadratic mixing rule for cubic equations of state“. Chemical Engineering Science 132 (August 2015): 150–58. http://dx.doi.org/10.1016/j.ces.2015.04.022.

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Axt, V. M., A. Stahl, E. J. Mayer, P. Haring Bolivar, S. Nüsse, K. Ploog und K. Köhler. „Four-wave-mixing theory beyond the semiconductor Bloch equations“. physica status solidi (b) 188, Nr. 1 (01.03.1995): 447–56. http://dx.doi.org/10.1002/pssb.2221880142.

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Hui, Qian, Song Xiuling, Zhang Xuedi, Yang Chao und Li Peiyue. „Calculation of pH Values for Mixed Waters“. E-Journal of Chemistry 8, Nr. 2 (2011): 657–64. http://dx.doi.org/10.1155/2011/391396.

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Mixing of waters with different compositions is a common phenomenon. The pH of mixed water can be calculated by introducing charge neutrality equation into the equations for equilibrium distribution calculation of species in water. In this paper, the equations thus obtained were solved by golden section method. To verify the calculation method, laboratory experiments were done for three sets of mixing water. The results showed the calculated pH values are in good agreement with measured ones.

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Boocock, C., und D. Tsiklauri. „Enhanced phase mixing of torsional Alfvén waves in stratified and divergent solar coronal structures – Paper I. Linear solutions“. Monthly Notices of the Royal Astronomical Society 510, Nr. 2 (04.12.2021): 1910–22. http://dx.doi.org/10.1093/mnras/stab3535.

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ABSTRACT We derive a corrected analytical solution for the propagation and enhanced phase mixing of torsional Alfvén waves, in a potential magnetic field with exponentially divergent field lines, embedded in a stratified solar corona. Further we develop a code named TAWAS that calculates the analytic solution describing torsional Alfvén waves using idl software language. We then use TAWAS to demonstrate that both our correction to the analytic solution and the inclusion of wave reflection have a significant impact on Alfvén wave damping. We continue to utilize TAWAS by performing a parameter study in order to identify the conditions under which enhanced phase mixing is strongest. We find that phase mixing is the strongest for high frequency Alfvén waves in magnetic fields with highly divergent field lines and without density stratification. We then present a finite difference solver, Wigglewave, which solves the linearized evolution equations for the system directly. Comparing solutions from TAWAS and Wigglewave we see that our analytical solution is accurate within the limits of the WKB approximation but under-reports the wave damping, caused by enhanced phase mixing, beyond the WKB limit. Both TAWAS and Wigglewave solve the linearized governing equations and not the complete non-linear magnetohydrodynamics (MHD) equations. Paper II will consider simulations that solve the full MHD equations including important non-linear effects.

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Yang-Soo Kim, Seung-Taek Oh und Jae-Hyun Lim. „The Control Method for Wavelength-Based CCT of Natural Light Using Warm/Cool White LED“. Proceedings of Engineering and Technology Innovation 25 (31.08.2023): 35–43. http://dx.doi.org/10.46604/peti.2023.12418.

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Reproducing circadian patterns of natural light through lighting requires technology that can control correlated color temperature (CCT) and short wavelength ratio (SWR) simultaneously. This study proposes a method for controlling wavelength-based CCT of natural light using LED light sources. First, the spectral power distribution (SPD) of each channel of the test lighting (two-channel LED lighting with warm white and cool white) is identified through actual measurement. Next, CCT and SWR are calculated based on the additive mixing of SPD using the mixing ratio from the measured SPD. Finally, the regression equations for mixing ratio-CCT and mixing ratio-SWR are derived through regression analysis. These equations are then utilized to implement a wavelength-based CCT control algorithm. For performance and evaluation purposes, natural light reproduction experiments were conducted, achieving a mean error of 94.5K for CCT and 1.5% for SWR.

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Wang, Haili, Changming Dong, Yongzeng Yang und Xiaoqian Gao. „Parameterization of Wave-Induced Mixing Using the Large Eddy Simulation (LES) (I)“. Atmosphere 11, Nr. 2 (15.02.2020): 207. http://dx.doi.org/10.3390/atmos11020207.

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Turbulent motions in the thin ocean surface boundary layer control exchanges of momentum, heat and trace gases between the atmosphere and ocean. However, present parametric equations of turbulent motions that are applied to global climate models result in systematic or substantial errors in the ocean surface boundary layer. Significant mixing caused by surface wave processes is missed in most parametric equations. A Large Eddy Simulation model is applied to investigate the wave-induced mixed layer structure. In the wave-averaged equations, wave effects are calculated as Stokes forces and breaking waves. To examine the effects of wave parameters on mixing, a series of wave conditions with varying wavelengths and heights are used to drive the model, resulting in a variety of Langmuir turbulence and wave breaking outcomes. These experiments suggest that wave-induced mixing is more sensitive to wave heights than to the wavelength. A series of numerical experiments with different wind intensities-induced Stokes drifts are also conducted to investigate wave-induced mixing. As the wind speed increases, the influence depth of Langmuir circulation deepens. Additionally, it is observed that breaking waves could destroy Langmuir cells mainly at the sea surface, rather than at deeper layers.

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Hsieh, Chang Yu, und An Shik Yang. „Mixing Enhancement of a Passive Micromixer by Applying Boundary Protrusion Structures“. Advanced Materials Research 74 (Juni 2009): 77–80. http://dx.doi.org/10.4028/www.scientific.net/amr.74.77.

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The purpose of this study is to examine the mixing behavior of two test fluids flowing via a passive micromixer with protruded structures arranged at the boundary of the mixer. In the analysis, the theoretical model was based on the three-dimensional conservation equations of mass, momentum and species concentration; whereas, the governing equations were numerically solved by using an iterative SIMPLEC algorithm to resolve flow/transport properties. The predicted mixing efficiency at different axial locations was compared with available measured results in the literature for code validation. Numerical experiments were extended to study the shape effect of boundary protrusion structures on mixing enhancement of a passive micromixer with diamond-shaped obstructions.

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Pinsky, M., A. Khain und A. Korolev. „Theoretical analysis of mixing in liquid clouds – Part 3: Inhomogeneous mixing“. Atmospheric Chemistry and Physics Discussions 15, Nr. 21 (04.11.2015): 30321–81. http://dx.doi.org/10.5194/acpd-15-30321-2015.

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Abstract. An idealized model of time-dependent mixing between cloud and non-cloud volumes is analyzed. Initial droplet size distribution (DSD) in cloud volume is assumed to be monodisperse. Both analytical investigation and parcel model investigation are used to study mixing processes and solve diffusion-evaporation equations. It is shown that the evolution of microphysical variables and the final equilibrium stage are unambiguously determined by two non-dimensional parameters. The first parameter, R, which is proportional to the ratio of the saturation deficit to the liquid water content in a cloud volume, determines whether the equilibrium stage is reached at 100 % relative humidity, or, rather, leads to a full evaporation of cloud droplets. The second parameter, Da, is the Damkölher number, which is equal to the ratio of the characteristic mixing time and phase relaxation time. This parameter (together with parameter R) determines whether mixing takes place according to a homogeneous or an inhomogeneous scenario. An analysis of the results obtained within a wide range of parameters R and Da is presented. It is shown that there is no pure homogeneous mixing, since the first stage of mixing is always inhomogeneous. Turbulent mixing between different volumes always starts as inhomogeneous and the mixing type can change during the mixing process. At any values of governing parameters, mixing leads to the formation of a tail of small droplets in the DSD and therefore to DSD broadening. The broadening depends onDa and the final DSD dispersion can be as large as 0.2 at large Da. The total duration of the mixing process varies from several to one hundred phase relaxation times, depending on R and Da. Delimitation between the types of mixing on the Da–R plane is carried out. The definitions of homogeneous and inhomogeneous mixings are reconsidered and clarified. The paper also compares the results of the current study with those obtained with classical mixing concepts.

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A. Al-Hemiri, Adil, und Sa’ad A. Fa’ek. „COMPUTATIONAL ANALYSIS OF THE MIXING ZONE IN THE COMBUSTION CHAMBER OF RAMJET“. Iraqi Journal of Chemical and Petroleum Engineering 9, Nr. 3 (30.09.2008): 27–32. http://dx.doi.org/10.31699/ijcpe.2008.3.4.

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A theoretical analysis of mixing in the secondary combustion chamber of ramjet is presented. Theoretical investigations were initiated to insight into the flow field of the mixing zone of the ramjet combustor and a computer program to calculate axisymmetric, reacting and inert flow was developed. The mathematical model of the mixing zone of ramjet comprises differential equations for: continuity, momentum, stagnation enthalpy, concentration, turbulence energy and its dissipation rate. The simultaneous solution of these equations by means of a finite-difference solution algorithm yields the values of the variable at all internal grid nodes.The results showed that increasing air mass flow (0.32 to 0.64 kg/s) increases the development of velocity profile due to the high turbulence generated resulting in very fast mixing and homogenous flow. And the occurrence of chemical reaction causes higher local temperature and composition resulting in faster development of the velocity profile

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Rauf, S., und J. A. Tataronis. „Resonant four-wave mixing of finite-amplitude Alfvén waves“. Journal of Plasma Physics 55, Nr. 2 (April 1996): 173–80. http://dx.doi.org/10.1017/s0022377800018766.

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Using the derivative nonlinear SchrÖdinger equation, resonant four-wave mixing of finite-amplitude Alfvén waves is explored in this paper. The evolution equations governing the amplitudes of the interacting waves and the conservation relations ale derived from the basic equation. These evolution equations are used to study parametric amplification and oscillation of two small-amplitude Alfvén waves due to two large-amplitude pump (Alfvén) waves. It is also shown that three pump waves can mix together to generate a low-frequency Alfven wave in a dissipative plasma.

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Yang, Da Yong. „Numerical Analysis of Micro-Mixing in Rough Microchannels“. Advanced Materials Research 189-193 (Februar 2011): 1452–55. http://dx.doi.org/10.4028/www.scientific.net/amr.189-193.1452.

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Understanding the micro-mixing of electroosmotic ﬂow is of both fundamental and practical signiﬁcance for the design and optimization of various microﬂuidic devices to control ﬂuid motion. In this paper, the governing equations of the micro-mixing in rough microchannels with rectangle surface roughness are solved using the finite element method and the effects of roughness height and space on mixing efficiency are investigated. The results indicate that the effects cannot be ignored and the mixing efficiency increases with the roughness element height and density.

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KUO, T. K. „RENORMALIZATION OF THE NEUTRINO MASS MATRIX“. Modern Physics Letters A 17, Nr. 36 (30.11.2002): 2355–60. http://dx.doi.org/10.1142/s0217732302009052.

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The renormalization group equations for the general 2 × 2, complex, neutrino mass matrix are shown to have exact, analytic solutions. Simple formulas are given for the physical mixing angle, mass ratio and intrinsic CP phase. We also establish a (complex) renormalization invariant relating these parameters. It is found that the mixing angle exhibits the resonance behavior. Also, the infrared fixed point corresponds to vanishing mixing angle and infinite mass hierarchy.

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Naunyka V. N. „Four-wave mixing by phase-amplitude holographic gratings in the photorefractive piezocrystal of 43m symmetry class“. Optics and Spectroscopy 132, Nr. 3 (2022): 356. http://dx.doi.org/10.21883/eos.2022.03.53557.2936-21.

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A system of coupled-wave equations for calculating the vector amplitudes of linearly polarized light waves at four-wave mixing by phase-amplitude holographic gratings in a cubic photorefractive semiconductor of an arbitrary cut belonging to the 43m symmetry class is presented. The dependences of the intensities of the polarization components of the reversed light wave on the orientation angle for GaAs crystal of (110)-cut are calculated on the basis of the numerical solution of the system of coupled-wave equations. The obtained dependences are compared with the known theoretical and experimental data. It is shown that the best agreement between the results of theoretical modeling and experimental data at calculating the counterpropagating four-wave mixing in GaAs crystal of (110)-cut is achieved if formation of several phase-amplitude holographic gratings is allowed, and the contribution of the photoelastic and inverse piezoelectric effects are taken into account together with absorption of the crystal. Keywords: four-wave mixing, photorefractive semiconductor, light wave, holographic grating, coupled wave equations.

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Nazha, Marouan A. A., Hobina Rajakaruna und Roy J. Crookes. „An Effective Property, LHF-Type Model for Spray Combustion“. Journal of Engineering for Gas Turbines and Power 122, Nr. 2 (14.02.2000): 275–79. http://dx.doi.org/10.1115/1.483206.

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A mathematical model capable of describing the evaporation, mixing and burning characteristics of a confined reacting two-phase flow is presented. The flow field is described by solving the partial differential equations of continuity, momentum, and energy transport, together with the k-ε equations of turbulence. Evaporation is accounted for via a droplet evaporation sub-model which runs in parallel with the gas-phase solver exchanging data with it. Effective properties are calculated in each control volume and the property changes resulting from the evaporation are allowed to propagate according to the turbulent mixing model. Combustion follows the mixing process and is assumed to proceed to equilibrium. The model is validated against experimental results, and its applicability over a wide range of conditions is investigated. [S0742-4795(00)03002-7]

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Kaas, E., B. Sørensen, P. H. Lauritzen und A. B. Hansen. „A hybrid Eulerian–Lagrangian numerical scheme for solving prognostic equations in fluid dynamics“. Geoscientific Model Development 6, Nr. 6 (22.11.2013): 2023–47. http://dx.doi.org/10.5194/gmd-6-2023-2013.

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Abstract. A new hybrid Eulerian–Lagrangian numerical scheme (HEL) for solving prognostic equations in fluid dynamics is proposed. The basic idea is to use an Eulerian as well as a fully Lagrangian representation of all prognostic variables. The time step in Lagrangian space is obtained as a translation of irregularly spaced Lagrangian parcels along downstream trajectories. Tendencies due to other physical processes than advection are calculated in Eulerian space, interpolated, and added to the Lagrangian parcel values. A directionally biased mixing amongst neighboring Lagrangian parcels is introduced. The rate of mixing is proportional to the local deformation rate of the flow. The time stepping in Eulerian representation is achieved in two steps: first a mass-conserving Eulerian or semi-Lagrangian scheme is used to obtain a provisional forecast. This forecast is then nudged towards target values defined from the irregularly spaced Lagrangian parcel values. The nudging procedure is defined in such a way that mass conservation and shape preservation is ensured in Eulerian space. The HEL scheme has been designed to be accurate, multi-tracer efficient, mass conserving, and shape preserving. In Lagrangian space only physically based mixing takes place; i.e., the problem of artificial numerical mixing is avoided. This property is desirable in atmospheric chemical transport models since spurious numerical mixing can impact chemical concentrations severely. The properties of HEL are here verified in two-dimensional tests. These include deformational passive transport on the sphere, and simulations with a semi-implicit shallow water model including topography.

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50

Kaas, E., B. Sørensen, P. H. Lauritzen und A. B. Hansen. „A hybrid Eulerian Lagrangian numerical scheme for solving prognostic equations in fluid dynamics“. Geoscientific Model Development Discussions 6, Nr. 3 (18.07.2013): 3819–91. http://dx.doi.org/10.5194/gmdd-6-3819-2013.

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Abstract. A new hybrid Eulerian Lagrangian numerical scheme (HEL) for solving prognostic equations in fluid dynamics is proposed. The basic idea is to use an Eulerian as well as a fully Lagrangian representation of all prognostic variables. The time step in Lagrangian space is obtained as a translation of irregularly spaced Lagrangian parcels along downstream trajectories. Tendencies due to other physical processes than advection are calculated in Eulerian space, interpolated, and added to the Lagrangian parcel values. A directionally biased mixing amongst neighboring Lagrangian parcels is introduced. The rate of mixing is proportional to the local deformation rate of the flow. The time stepping in Eulerian representation is achieved in two steps: first a mass conserving Eulerian or semi-Lagrangian scheme is used to obtain a provisional forecast. This forecast is then nudged towards target values defined from the irregularly spaced Lagrangian parcel values. The nudging procedure is defined in such a way that mass conservation and shape preservation is ensured in Eulerian space. The HEL scheme has been designed to be accurate, multi-tracer efficient, mass conserving, and shape preserving. In Lagrangian space only physically based mixing takes place, i.e., the problem of artificial numerical mixing is avoided. This property is desirable in atmospheric chemical transport models since spurious numerical mixing can impact chemical concentrations severely. The properties of HEL are here verified in two-dimensional tests. These include deformational passive transport on the sphere, and simulations with a semi-implicit shallow water model including topography.

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