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1

Guo, J. H., Y. Li, and H. G. Shan. "A Two-Temperature Model for LBVs." Proceedings of the International Astronomical Union 2004, IAUS226 (September 2004): 506–10. http://dx.doi.org/10.1017/s1743921305001146.

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2

Kristoffel, N., P. Konsin, and T. Örd. "Two-band model for high-temperature superconductivity." La Rivista Del Nuovo Cimento Series 3 17, no. 9 (September 1994): 1–41. http://dx.doi.org/10.1007/bf02724515.

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3

Girard, R., J. B. Belhaouari, J. J. Gonzalez, and A. Gleizes. "A two-temperature kinetic model of SF6plasma." Journal of Physics D: Applied Physics 32, no. 22 (November 12, 1999): 2890–901. http://dx.doi.org/10.1088/0022-3727/32/22/311.

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4

d’Hueppe, A., M. Chandesris, D. Jamet, and B. Goyeau. "Coupling a two-temperature model and a one-temperature model at a fluid-porous interface." International Journal of Heat and Mass Transfer 55, no. 9-10 (April 2012): 2510–23. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.01.009.

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5

Saito, Masao. "Accuracy of Temperature Estimation by Two-dimensional Model." Thermal Medicine(Japanese Journal of Hyperthermic Oncology) 4, no. 3 (1988): 215–19. http://dx.doi.org/10.3191/thermalmedicine.4.215.

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6

Olynick, David P., and H. A. Hassan. "New two-temperature dissociation model for reacting flows." Journal of Thermophysics and Heat Transfer 7, no. 4 (October 1993): 687–96. http://dx.doi.org/10.2514/3.478.

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7

Sobolev, S. L. "Two-temperature discrete model for nonlocal heat conduction." Journal de Physique III 3, no. 12 (December 1993): 2261–69. http://dx.doi.org/10.1051/jp3:1993273.

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8

CAIAFA, C. F., and A. N. PROTO. "TEMPERATURE ESTIMATION IN THE TWO-DIMENSIONAL ISING MODEL." International Journal of Modern Physics C 17, no. 01 (January 2006): 29–38. http://dx.doi.org/10.1142/s0129183106008856.

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We present two new algorithms for the estimation of the temperature from a realization of a 2-D Ising model. The methods here introduced are based in the maximization of pseudo likelihood and on the minimum mean squared error (MSE) fit of the conditional probability function. We derive the analytical expressions of these estimators and also we include computational results comparing these new techniques with the traditional method. A very good performance in terms of the average absolute error and the average standard deviation is demonstrated through simulations in a 100 × 100 lattice in the ferromagnetic and antiferromagnetic cases. Summarizing, we have provided two new useful computational tools that allow us to measure the "virtual" temperature of an Ising like system.
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9

Layevskii, Yu M., and A. A. Kalinkin. "A two-temperature model of hydrate-bearing rock." Mathematical Models and Computer Simulations 2, no. 6 (November 14, 2010): 753–59. http://dx.doi.org/10.1134/s2070048210060104.

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10

Wang (王亮堯), Liang-Yao, Hsien Shang (尚賢), Ruben Krasnopolsky, and Tzu-Yang Chiang (江子揚). "A TWO-TEMPERATURE MODEL OF MAGNETIZED PROTOSTELLAR OUTFLOWS." Astrophysical Journal 815, no. 1 (December 7, 2015): 39. http://dx.doi.org/10.1088/0004-637x/815/1/39.

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11

Youssef, Hamdy M., and Nehal T. Mansour. "Mathematical Model of Two-Temperature Generalized Thermoelastic Diffusion." Advanced Science, Engineering and Medicine 11, no. 5 (May 1, 2019): 408–14. http://dx.doi.org/10.1166/asem.2019.2373.

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12

Lipowski, A. "Critical temperature in the two-layered Ising model." Physica A: Statistical Mechanics and its Applications 250, no. 1-4 (February 1998): 373–83. http://dx.doi.org/10.1016/s0378-4371(97)00551-7.

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13

Takizawa, M. "A two-temperature model of the intracluster medium." Advances in Space Research 25, no. 3-4 (January 2000): 621–24. http://dx.doi.org/10.1016/s0273-1177(99)00813-3.

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14

Takizawa, Motokazu. "A Two‐Temperature Model of the Intracluster Medium." Astrophysical Journal 509, no. 2 (December 20, 1998): 579–86. http://dx.doi.org/10.1086/306530.

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15

Čiegis, R., A. Dement’ev, and G. Jankevičiūtė. "Numerical analysis of the hyperbolic two-temperature model." Lithuanian Mathematical Journal 48, no. 1 (January 2008): 46–60. http://dx.doi.org/10.1007/s10986-008-0005-6.

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16

Ingersent, Kevin, and Barbara A. Jones. "Low-temperature physics of the two-impurity, two-channel Kondo model." Physica B: Condensed Matter 199-200 (April 1994): 402–5. http://dx.doi.org/10.1016/0921-4526(94)91850-3.

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17

TAMAYO, P., R. GUPTA, and F. J. ALEXANDER. "TWO-TEMPERATURE NON-EQUILIBRIUM ISING MODELS." International Journal of Modern Physics C 07, no. 03 (June 1996): 389–99. http://dx.doi.org/10.1142/s0129183196000338.

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We present results from a computational study of a class of 2D two-temperature non-equilibrium Ising models. In these systems the dynamics is a local competition of two equilibrium dynamics at different temperatures. We analyzed non-equilibrium versions of Metropolis, heat bath/Glauber and Swendsen-Wang dynamics and found strong evidence that some of these dynamics have the same critical exponents and belong to the same universality class as the equilibrium 2D Ising model.
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18

Martemyanov, Sergey M., and Alexei L. Maslov. "Two-Temperature Two-Dimensional Model of Underground Shale Heating by Electromagnetic Field." Advanced Materials Research 1040 (September 2014): 620–24. http://dx.doi.org/10.4028/www.scientific.net/amr.1040.620.

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A two-dimensional two-temperature model of shale stratum heating by high-frequency electromagnetic field is proposed. The heat exchange between solid rock and gas contained in pores is shown to significantly affect temperature field characteristics. The stratum gas filtration and reaction heat effects are taken into account as a first approximation.
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19

Hiramoto, Tatsumi. "Two-Temperature model of optically thick plasmas in lamps." JOURNAL OF THE ILLUMINATING ENGINEERING INSTITUTE OF JAPAN 75, Appendix (1991): 61. http://dx.doi.org/10.2150/jieij1980.75.appendix_61.

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20

Shavlov, A. V. "The ball-lightning model based on two-temperature plasma." Doklady Physics 55, no. 3 (March 2010): 109–14. http://dx.doi.org/10.1134/s1028335810030018.

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21

Sanmartín, J. R., R. Ramis, J. L. Montañés, and J. Sanz. "Two-electron temperature model of a laser-driven implosion." Physics of Fluids 28, no. 7 (1985): 2282. http://dx.doi.org/10.1063/1.865281.

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22

Furudate, Michiko, Satoshi Nonaka, and Keisuke Sawada. "Behavior of Two-Temperature Model in Intermediate Hypersonic Regime." Journal of Thermophysics and Heat Transfer 13, no. 4 (October 1999): 424–30. http://dx.doi.org/10.2514/2.6480.

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23

ÓDOR, GÉZA. "SELF-ORGANIZING, TWO-TEMPERATURE ISING MODEL DESCRIBING HUMAN SEGREGATION." International Journal of Modern Physics C 19, no. 03 (March 2008): 393–98. http://dx.doi.org/10.1142/s0129183108012212.

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A two-temperature Ising-Schelling model is introduced and studied for describing human segregation. The self-organized Ising model with Glauber kinetics simulated by Müller et al. exhibits a phase transition between segregated and mixed phases mimicking the change of tolerance (local temperature) of individuals. The effect of external noise is considered here as a second temperature added to the decision of individuals who consider a change of accommodation. A numerical evidence is presented for a discontinuous phase transition of the magnetization.
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24

Park, Chul. "Assessment of two-temperature kinetic model for ionizing air." Journal of Thermophysics and Heat Transfer 3, no. 3 (July 1989): 233–44. http://dx.doi.org/10.2514/3.28771.

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25

Yasumura, K. "Critical temperature of an anisotropic two-dimensional Potts model." Journal of Physics A: Mathematical and General 20, no. 14 (October 1, 1987): 4975–83. http://dx.doi.org/10.1088/0305-4470/20/14/034.

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26

Lecomte, Vivien, Zoltán Rácz, and Frédéric van Wijland. "Energy flux distribution in a two-temperature Ising model." Journal of Statistical Mechanics: Theory and Experiment 2005, no. 02 (February 24, 2005): P02008. http://dx.doi.org/10.1088/1742-5468/2005/02/p02008.

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27

Tzou, D. Y., M. N. O¨zis¸ik, and R. J. Chiffelle. "The Lattice Temperature in the Microscopic Two-Step Model." Journal of Heat Transfer 116, no. 4 (November 1, 1994): 1034–38. http://dx.doi.org/10.1115/1.2911439.

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28

IWATA, Koji. "OS0202 A temperature dependent two-surface cyclic plasticity model." Proceedings of the Materials and Mechanics Conference 2009 (2009): 138–40. http://dx.doi.org/10.1299/jsmemm.2009.138.

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29

Dik, I. G., and A. V. Tolstykh. "Two-temperature model for the ignition of porous systems." Combustion, Explosion, and Shock Waves 29, no. 6 (November 1993): 663–67. http://dx.doi.org/10.1007/bf00786845.

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30

Groll, Andreas, Brenda López-Cabrera, and Thilo Meyer-Brandis. "A consistent two-factor model for pricing temperature derivatives." Energy Economics 55 (March 2016): 112–26. http://dx.doi.org/10.1016/j.eneco.2015.12.020.

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31

SINGH, NAVINDER. "TWO-TEMPERATURE MODEL OF NONEQUILIBRIUM ELECTRON RELAXATION: A REVIEW." International Journal of Modern Physics B 24, no. 09 (April 10, 2010): 1141–58. http://dx.doi.org/10.1142/s0217979210055366.

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The present paper is a review of the phenomena related to nonequilibrium electron relaxation in bulk and nano-scale metallic samples. The workable Two-Temperature Model (TTM) based on Boltzmann–Bloch–Peierls kinetic equation has been applied to study the ultra-fast (femto-second) electronic relaxation in various metallic systems. The advent of new ultra-fast (femto-second) laser technology and pump-probe spectroscopy has produced wealth of new results for micro- and nano-scale electronic technology. The aim of this paper is to clarify the TTM, conditions of its validity and nonvalidity, its modifications for nano-systems, to sum-up the progress, and to point out open problems in this field. We also give a phenomenological integro-differential equation for the kinetics of nondegenerate electrons that goes beyond the TTM.
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32

Inaba, K., A. Koga, S. Suga, and N. Kawakami. "Zero-temperature phase diagram of two dimensional Hubbard model." Journal of Physics: Conference Series 150, no. 4 (March 1, 2009): 042066. http://dx.doi.org/10.1088/1742-6596/150/4/042066.

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33

Ohguchi, Yasutomo, and Tetsuro Murakami. "Nonequilibrium Argon Induction Plasmas by a Two-Temperature Model." Journal of the Physical Society of Japan 55, no. 6 (June 15, 1986): 1931–35. http://dx.doi.org/10.1143/jpsj.55.1931.

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34

Leuning, R. "Temperature dependence of two parameters in a photosynthesis model." Plant, Cell & Environment 25, no. 9 (August 15, 2002): 1205–10. http://dx.doi.org/10.1046/j.1365-3040.2002.00898.x.

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35

Craco, Luis. "Finite-temperature properties of the two-orbital Anderson model." Journal of Physics: Condensed Matter 11, no. 44 (October 20, 1999): 8689–95. http://dx.doi.org/10.1088/0953-8984/11/44/307.

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36

Christensen, B. H., K. Vestentoft, and P. Balling. "Short-pulse ablation rates and the two-temperature model." Applied Surface Science 253, no. 15 (May 2007): 6347–52. http://dx.doi.org/10.1016/j.apsusc.2007.01.045.

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37

Kirpichnikov, A. P. "Two-temperature channel model of a direct current arc." Soviet Physics Journal 33, no. 7 (July 1990): 619–24. http://dx.doi.org/10.1007/bf00899115.

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38

Schram, R. P. C., and G. H. Wegdam. "Fast and slow sound in the two-temperature model." Physica A: Statistical Mechanics and its Applications 203, no. 1 (February 1994): 33–52. http://dx.doi.org/10.1016/0378-4371(94)90030-2.

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39

Chen, J. K., D. Y. Tzou, and J. E. Beraun. "A semiclassical two-temperature model for ultrafast laser heating." International Journal of Heat and Mass Transfer 49, no. 1-2 (January 2006): 307–16. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2005.06.022.

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40

Triola, Christopher. "Model comparisons for two-temperature plasma equations of state." Physics of Plasmas 29, no. 11 (November 2022): 112705. http://dx.doi.org/10.1063/5.0110725.

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When a plasma is generated in the laboratory, energy is often deposited preferentially into either the electrons or the ions, giving rise to a quasiequilibrium state in which the two species, electrons and ions, are well described by two effective temperatures, Te and Ti. Accurate hydrodynamic modeling of such a two-temperature plasma requires an equation of state that captures the relevant many-body physics without assuming a strict local thermodynamic equilibrium. Several models have been proposed within the literature, which extend conventional statistical approaches, each employing a different combination of assumptions for modifying the equilibrium equations. In this work, we compare the predictions for several models, presenting derivations of the internal energy and pressure for each microscopic model within a unified framework so that the assumptions of each model may be more easily compared to one another. We find that for sufficiently weak coupling, all models agree with one another. However, as the coupling strength is increased, the disagreement between the models becomes more pronounced. Moreover, the relative sizes of the corrections predicted by each model depend on which species has the higher temperature, Te > Ti vs Te < Ti.
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41

Akhmetov, Fedor, Nikita Medvedev, Igor Makhotkin, Marcelo Ackermann, and Igor Milov. "Effect of Atomic-Temperature Dependence of the Electron–Phonon Coupling in Two-Temperature Model." Materials 15, no. 15 (July 26, 2022): 5193. http://dx.doi.org/10.3390/ma15155193.

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Ultrafast laser irradiation of metals can often be described theoretically with the two-temperature model. The energy exchange between the excited electronic system and the atomic one is governed by the electron–phonon coupling parameter. The electron–phonon coupling depends on both, the electronic and the atomic temperature. We analyze the effect of the dependence of the electron–phonon coupling parameter on the atomic temperature in ruthenium, gold, and palladium. It is shown that the dependence on the atomic temperature induces nonlinear behavior, in which a higher initial electronic temperature leads to faster electron–phonon equilibration. Analysis of the experimental measurements of the transient thermoreflectance of the laser-irradiated ruthenium thin film allows us to draw some, albeit indirect, conclusions about the limits of the applicability of the different coupling parametrizations.
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42

Sangam, Afeintou, Élise Estibals, and Hervé Guillard. "Derivation and numerical approximation of two-temperature Euler plasma model." Journal of Computational Physics 444 (November 2021): 110565. http://dx.doi.org/10.1016/j.jcp.2021.110565.

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43

Hong, Sun-nan, and Hong Zhao. "Two Bio-Mass Model Incorporating Temperature Effect for “EBPR” Process." Proceedings of the Water Environment Federation 2010, no. 18 (January 1, 2010): 147–57. http://dx.doi.org/10.2175/193864710798130689.

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44

Kim, Beom Jun. "Finite-temperature resistive transition in the two-dimensionalXYgauge glass model." Physical Review B 62, no. 1 (July 1, 2000): 644–47. http://dx.doi.org/10.1103/physrevb.62.644.

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45

Mostaghimi, Javad, Pierre Proulx, and Maher I. Boulos. "A two‐temperature model of the inductively coupled rf plasma." Journal of Applied Physics 61, no. 5 (March 1987): 1753–60. http://dx.doi.org/10.1063/1.338073.

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46

Mukhopadhyay, S., R. Picard, S. Trostorff, and M. Waurick. "A note on a two-temperature model in linear thermoelasticity." Mathematics and Mechanics of Solids 22, no. 5 (December 8, 2015): 905–18. http://dx.doi.org/10.1177/1081286515611947.

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We discuss the so-called two-temperature model in linear thermoelasticity and provide a Hilbert space framework for proving well-posedness of the equations under consideration. With the abstract perspective of evolutionary equations, the two-temperature model turns out to be a coupled system of the elastic equations and an abstract ordinary differential equation (ODE). Following this line of reasoning, we propose another model which is entirely an abstract ODE. We also highlight an alternative method for a two-temperature model, which might be of independent interest.
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47

Szolnoki, Attila. "Stationary state in a two-temperature model with competing dynamics." Physical Review E 60, no. 2 (August 1, 1999): 2425–28. http://dx.doi.org/10.1103/physreve.60.2425.

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48

Ohguchi, Yasutomo, Takayoshi Satonaka, and Takenori Kaneko. "Nonequilibrium Hydrogen Plasmas in Microwave Fields by Two-Temperature Model." Japanese Journal of Applied Physics 24, Part 1, No. 3 (March 20, 1985): 317–23. http://dx.doi.org/10.1143/jjap.24.317.

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49

Sanmartín, J. R., R. Ramis, J. L. Montañés, and J. Sanz. "Erratum: ‘‘Two-electron temperature model of a laser-driven implosion’’." Physics of Fluids 29, no. 2 (1986): 597. http://dx.doi.org/10.1063/1.866027.

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50

Haule, K., J. Bonča, and P. Prelovšek. "Finite-temperature properties of the two-dimensional Kondo lattice model." Physical Review B 61, no. 4 (January 15, 2000): 2482–87. http://dx.doi.org/10.1103/physrevb.61.2482.

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