Advances in the kinetics of heat and mass transfer in near-continuous complex flows

doi:10.1007/s11467-023-1353-8

Front. Phys.

2024, Vol. 19

Issue (4) : 42500 https://doi.org/10.1007/s11467-023-1353-8

Advances in the kinetics of heat and mass transfer in near-continuous complex flows

Aiguo Xu^1,^2,³(

), Dejia Zhang^1,^4,⁵, Yanbiao Gan⁶

¹. National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009-26, Beijing 100088, China
². State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China
³. HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing 100871, China
⁴. State Key Laboratory for GeoMechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing 100083, China
⁵. National Key Laboratory of Shock Wave and Detonation Physics, Mianyang 621999, China
⁶. Hebei Key Laboratory of Trans-Media Aerial Underwater Vehicle, School of Liberal Arts and Sciences, North China Institute of Aerospace Engineering, Langfang 065000, China

Download: PDF(27331 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

The study of macro continuous flow has a long history. Simultaneously, the exploration of heat and mass transfer in small systems with a particle number of several hundred or less has gained significant interest in the fields of statistical physics and nonlinear science. However, due to absence of suitable methods, the understanding of mesoscale behavior situated between the aforementioned two scenarios, which challenges the physical function of traditional continuous fluid theory and exceeds the simulation capability of microscopic molecular dynamics method, remains considerably deficient. This greatly restricts the evaluation of effects of mesoscale behavior and impedes the development of corresponding regulation techniques. To access the mesoscale behaviors, there are two ways: from large to small and from small to large. Given the necessity to interface with the prevailing macroscopic continuous modeling currently used in the mechanical engineering community, our study of mesoscale behavior begins from the side closer to the macroscopic continuum, that is from large to small. Focusing on some fundamental challenges encountered in modeling and analysis of near-continuous flows, we review the research progress of discrete Boltzmann method (DBM). The ideas and schemes of DBM in coarse-grained modeling and complex physical field analysis are introduced. The relationships, particularly the differences, between DBM and traditional fluid modeling as well as other kinetic methods are discussed. After verification and validation of the method, some applied researches including the development of various physical functions associated with discrete and non-equilibrium effects are illustrated. Future directions of DBM related studies are indicated.

Keywords near-continuous flow non-equilibrium kinetics discrete Boltzmann method complex physical field analysis

Corresponding Author(s): Aiguo Xu

Issue Date: 29 February 2024

Cite this article:

Aiguo Xu,Dejia Zhang,Yanbiao Gan. Advances in the kinetics of heat and mass transfer in near-continuous complex flows[J]. Front. Phys. , 2024, 19(4): 42500.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1353-8
https://academic.hep.com.cn/fop/EN/Y2024/V19/I4/42500

Fig.1 (a) Sketch of the formation mechanism of KHI. (b) Sketch of the formation mechanism of RTI.

Fig.2 The mesoscale dilemma between macroscopic continuous and microscopic particle descriptions.

Fig.3 The three main steps of complex flow simulation research.

Fig.4 Schematic of phase space description method.

Fig.5 Schematic of several commonly used two-dimensional discrete velocity sets.

Fig.6 Schematic diagram of the application scopes of the Boltzmann equation, the original BGK model, and the BGK-like model in kinetic methods.

Fig.7 Phase space description methods: from non-conserved moments of

f − f (0)

to any set of system characteristics.

Fig.8 Schematic for application ranges of several physical models.

Year	Schemes for detecting and describing discrete/TNE behavior and effects

Before 2012	There was no significant difference in physical function between the two types of LBMs.
2012	Proposed to use non-conserved moments of $f − f (0)$ to detect and describe discrete/TNE states and effects, which is the starting point of current DBM method [73].
2015	Proposed to use the non-conserved moments of $f − f (0)$ as bases to open phase space, and use the distance from a state point to the origin to define the TNE strength of one perspective. This is the starting point of the phase space description method in DBM [74].
2018	Proposed to use the distance between two points in the phase space to describe the difference between two discrete/TNE states, and use the mean distance between two points in a given time interval to describe the difference of two kinetic processes [75].
2021	Extended the phase space method to describe any set of system features [76].
2022	Proposed the concept of non-equilibrium strength vector, each of whose components is one TNE strength of a perspective, to multi-perspective cross-locate the non-equilibrium strength of complex flow [61, 77].

Tab.1 Milestones in the development of DBM.

Fig.9 Kinetic moments that should keep value in various levels of DBM.

Fig.10 Flowchart for DBM simulation.

Fig.11 Two dimensions of the perspective of complex flow behavior research.

Fig.12 Schematic of discretization of particle velocity space. The velocity discretization in

x

direction is taken as example.

Fig.13 Comparison of DBM simulation and DSMC simulation of a shock structure. Reproduced with permission from Ref. [77].

Fig.14 Schematic of velocity slip and temperature jump in Knudsen layer.

Fig.15 Comparison between DBM simulation results and analytical solutions: slip velocity. Reproduced with permission from Ref. [92].

Fig.16 Comparison between DBM simulation results and analytical solutions: velocity difference profile. Reproduced from Ref. [94] with permission.

Fig.17 Comparison between DBM simulation results and analytical solutions: temperature difference profile. Reproduced with permission from Ref. [94].

Fig.18 The results of Couette flow at steady state: (a) velocity profiles, the symbols are DSMC data and the lines denote DBM results; (b) viscous shear stress profiles, the symbols denote DSMC data, the dashed line represents the Lattice ES-BGK results, and the solid line represents the DBM results. Reproduced with permission from Ref. [93].

Fig.19 Pressure-driven flow. (a) Schematic, and (b) DBM simulation results of velocity contour under different Kn numbers. Reproduced with permission from Ref. [94].

Fig.20 (a) Profiles of pressure

p (x)

along the central line under different Kn numbers. (b) Profiles of

u x

along the

y

direction under different Kn numbers. Reproduced with permission from Ref. [94].

Fig.21 Inverse reduced mass flow rate under various Knudsen numbers, in which including the results of DBM simulation, NS simulation and experiment. Reproduced with permission from Ref. [94].

Fig.22 Simulation results of non-equilibrium cavity flow in steady state. (a) Temperature contour. (b) Heat flow streamline. (c) Horizontal velocity distribution on the vertical centerline. (d) Vertical velocity distribution on the vertical centerline. Reproduced with permission from Ref. [93].

Fig.23 Comparison of

Δ 2, x x ∗

profile between DBM simulation results and analytical results. The three figures represent the cases of weak, medium, and strong TNE strength, respectively. The two symbols indicate the results of first-order and second-order DBM, respectively, with lines representing the analytical results at two TNE levels. Reproduced with permission from Ref. [77].

Fig.24 The DBM simulation results from different orders of DBM. Reproduced with permission from Ref. [77].

Fig.25 Comparison of

Δ 2, x x

profile between DBM simulation results and analytical results. Each row of the pictures show corresponds to cases with weak, moderate, and strong TNE strength, and each column corresponds to the results of D2V13, D2V15, and D2V30, respectively. In the figures, the circles represent results from DBM at various levels, the green lines and green points are results calculated from the first theoretical analysis, and red lines denote results obtained from the second theoretical analysis. Reproduced with permission from Ref. [65].

Fig.26 Evolution of spike amplitude. The red points in the picture are experimental results from Ref. [102], and blue line represent DBM results. Reproduced with permission from Ref. [100].

Fig.27 Snapshots of schlieren images of the interaction between a shock wave and a heavy-cylindrical bubble. The odd rows represent experimental results from Ref. [34] with permission, and the even rows are DBM simulation results. Numbers in the picture represent the time in μs. Reproduced with permission from Ref. [103].

Fig.28 Evolution curves of the characteristic scale of shock−bubble interaction. The lines indicate DBM simulation results and the symbols are experimental results extracted from Ref. [34]. Reproduced with permission from Ref. [103].

Fig.29 Comparison between DBM results and NS results of pressure profile at the line

y = 0.625 π

in simulation of Orszag−Tang magnetic turbulence. Reproduced with permission from Ref. [43].

Fig.30 (a) Profiles of the dimensionless mass flow rate with various rarefaction parameters under three different values of TMAC for the one-dimensional pressure driven flow through a microchannel. (b) Profiles of the dimensionless mass flow rate with rarefaction parameters for three different aspect ratios in the context of the two-dimensional pressure-driven flow through a microchannel. Reproduced with permission from Ref. [64].

Fig.31 Comparison of three entropy production rates in fluid systems of detonation problems with chemical reactions. Reproduced with permission from Ref. [90].

Fig.32 Contours of the two typical TNE quantities

| Δ 2 σ ∗ |

and

| Δ 3, 1 σ ∗ |

at three different moments. Reproduced with permission from Ref. [110].

Fig.33 Profiles of average TNE strength along the

y

direction. Reproduced with permission from Ref. [110].

Fig.34 Evolution curves of the quantity of global TNE strength. Reproduced with permission from Ref. [110].

Fig.35 Evolution curves of boundary length

L

and non-equilibrium strength

D

in non-isothermal phase separation process. Reproduced with permission from Ref. [111].

Fig.36 Evolution curves of several characteristic quantities in the phase separation process. Reproduced with permission from Ref. [112].

Fig.37 Evolution curves of average coalescence velocity

u ¯

and

Δ ¯ 2, x x ∗

. Reproduced with permission from Ref. [113].

Fig.38 Evolution curves of the average strength

D ¯ ∗

, average coalescence velocity

a ¯

, the slope of boundary length

d L / d t

, and

(∇ u : u) 0.5 ¯

. Reproduced with permission from Ref. [113].

Fig.39 Evolution curves of two TNE quantities (

D ¯ 2 ∗

and

D ¯ 3 ∗

) during the droplet collisions, where (a) represents the two droplets are fused together after the head-on collision, (b) indicates the two droplets are separated after collision. Reproduced with permission from Ref. [36].

Fig.40 Evolution curves of change rate of entropy production rate

d S ˙ NOMF / d t

, change rate of boundary length

d L / d t

, and bubble velocity

V bubble

. Reproduced with permission from Ref. [115].

Fig.41 Evolution curves of boundary length

L

and strength of NOEF

D 3, 1

in coupled RT-KHI system. These two figures correspond to the cases with different initial shear velocity. Reproduced with permission from Ref. [118].

Fig.42 Profiles of

Δ 2 ∗

and

Δ 4, 2 ∗

of plasma shock wave with different Ma numbers. Reproduced with permission from Ref. [119].

Fig.43 TNE effects of Orszag−Tang vortex problem. (a) Contour of total TNE strength at

t = 3

. (b) Evolution of four kinds of entropy production rates with time. Reproduced with permission from Ref. [43].

Fig.44 Evolution of global average TNE effects with different initial applied magnetic fields from

t = 0

to 500. Reproduced with permission from Ref. [43].

Fig.45 Evolution of entropy production rates from

t = 0

to 500 with magnetic fields ranging from 0.01 to 0.05. Reproduced with permission from Ref. [43].

Fig.46 Evolution of entropy production rates from

t = 0

to 500 with magnetic fields ranging from 0.10 to 0.30. Reproduced with permission from Ref. [43].

Fig.47 The sketch of the two-dimensional contours of actual distribution function in velocity space (

v r

v θ

) at rarefaction front, material interface, and shock front, respectively. Reproduced with permission from Ref. [121].

Fig.48 The three-dimensional contour graph of the actual distribution function in velocity space (

v r

v θ

) at rarefaction front, material interfaces, and shock fronts, respectively. Reproduced with permission from Ref. [121].

Fig.49 Profiles of four types of TNE quantities. Each column of the figure represent different TNE quantities, and each row indicate the case with various positions. Reproduced with permission from Ref. [121].

Fig.50 Contours of various TNE quantities at a typical moment during the RTI evolution. Reproduced with permission from Ref. [125].

Fig.51 Evolution curve of interface amplitude obtained from two kinds of tracking techniques. Reproduced with permission from Ref. [126].

1	S. Tsien H.. Superaerodynamics, mechanics of rarefied gases. J. Aeronaut. Sci., 1946, 13(12): 653 https://doi.org/10.2514/8.11476
2	Thomson W.. Hydrokinetic solutions and observations. Lond. Edinb. Dublin Philos. Mag. J. Sci., 1871, 42(281): 362 https://doi.org/10.1080/14786447108640585
3	L. F. Helmholtz H.. On discontinuous movements of fluids. Monatsberichte der Königlichen Preussische Akademie der Wissenschaften zu Berlin, 1868, 36: 337
4	Rayleigh R., Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density, Proceedings of the London Mathematical Society s1‒14, pp 170–177 (1882)
5	I. Taylor G.. The instability of liquid surfaces when accelerated in a direction perpendicular to their planes (I). Proc. R. Soc. Lond. A, 1950, 201(1065): 192 https://doi.org/10.1098/rspa.1950.0052
6	D. Richtmyer R.. Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Math., 1960, 13(2): 297 https://doi.org/10.1002/cpa.3160130207
7	E. Meshkov E.. Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn., 1972, 4(5): 101 https://doi.org/10.1007/BF01015969
8	X. Liu Y., F. Wang L., G. Zhao K., Y. Li Z., F. Wu J., H. Ye W., J. Li Y.. Thin-shell effects on nonlinear bubble evolution in the ablative Rayleigh–Taylor instability. Phys. Rev. Lett., 2022, 29(8): 082102
9	X. Liu Y., Chen Z., F. Wang L., Y. Li Z., F. Wu J., H. Ye W., J. Li Y.. Dynamic of shock–bubble interactions and nonlinear evolution of ablative hydrodynamic instabilities initialed by capsule interior isolated defects. Phys. Plasmas, 2023, 30(4): 042302 https://doi.org/10.1063/5.0137856
10	Lan K.. Dream fusion in octahedral spherical hohlraum. Matter Radiat. Extrem., 2022, 7(5): 055701 https://doi.org/10.1063/5.0103362
11	H. Chen Y., C. Li Z., Cao H., Q. Pan K., W. Li S., F. Xie X., Deng B., Q. Wang Q., R. Cao Z., F. Hou L., S. Che X., Yang P., J. Li Y., A. He X., Xu T., G. Liu Y., L. Li Y., M. Liu X., J. Zhang H., Zhang W., L. Jiang B., Xie J., Zhou W., X. Huang X., Y. Huo W., L. Ren G., Li K., D. Hang X., Li S., L. Zhai C., Liu J., Y. Zou S., K. Ding Y., Lan K.. Determination of laser entrance hole size for ignition-scale octahedral spherical hohlraums. Matter Radiat. Extrem., 2022, 7(6): 065901 https://doi.org/10.1063/5.0102447
12	Lan K., Dong Y., Wu J., Li Z., Chen Y., Cao H., Hao L., Li S., Ren G., Jiang W., Yin C., Sun C., Chen Z., Huang T., Xie X., Li S., Miao W., Hu X., Tang Q., Song Z., Chen J., Xiao Y., Che X., Deng B., Wang Q., Deng K., Cao Z., Peng X., Liu X., He X., Yan J., Pu Y., Tu S., Yuan Y., Yu B., Wang F., Yang J., Jiang S., Gao L., Xie J., Zhang W., Liu Y., Zhang Z., Zhang H., He Z., Du K., Wang L., Chen X., Zhou W., Huang X., Guo H., Zheng K., Zhu Q., Zheng W., Y. Huo W., Hang X., Li K., Zhai C., Xie H., Li L., Liu J., Ding Y., Zhang W.. First inertial confinement fusion implosion experiment in octahedral spherical Hohlraum. Phys. Rev. Lett., 2021, 127(24): 245001 https://doi.org/10.1103/PhysRevLett.127.245001
13	M. Qiao X., Lan K.. Novel target designs to mitigate hydrodynamic instabilities growth in inertial confinement fusion. Phys. Rev. Lett., 2021, 126(18): 185001 https://doi.org/10.1103/PhysRevLett.126.185001
14	B. Gan Y., G. Xu A., C. Zhang G., J. Li Y.. Lattice Boltzmann study on Kelvin–Helmholtz instability: Roles of velocity and density gradients. Phys. Rev. E, 2011, 83(5): 056704 https://doi.org/10.1103/PhysRevE.83.056704
15	D. Lin C., G. Xu A., C. Zhang G., H. Luo K., J. Li Y.. Discrete Boltzmann modeling of Rayleigh–Taylor instability in two-component compressible flows. Phys. Rev. E, 2017, 96(5): 053305 https://doi.org/10.1103/PhysRevE.96.053305
16	Chen F., G. Xu A., C. Zhang G.. Collaboration and competition between Richtmyer–Meshkov instability and Rayleigh–Taylor instability. Phys. Fluids, 2018, 30(10): 102105 https://doi.org/10.1063/1.5049869
17	Chen F., G. Xu A., D. Zhang Y., B. Gan Y., B. Liu B., Wang S.. Effects of the initial perturbations on the Rayleigh–Taylor–Kelvin–Helmholtz instability system. Front. Phys., 2022, 17(3): 33505 https://doi.org/10.1007/s11467-021-1145-y
18	Chen L., L. Lai H., D. Lin C., M. Li D.. Specific heat ratio effects of compressible Rayleigh–Taylor instability studied by discrete Boltzmann method. Front. Phys., 2021, 16(5): 52500 https://doi.org/10.1007/s11467-021-1096-3
19	Zhang G., G. Xu A., J. Zhang D., J. Li Y., L. Lai H., M. Hu X.. Delineation of the flow and mixing induced by Rayleigh–Taylor instability through tracers. Phys. Fluids, 2021, 33(7): 076105 https://doi.org/10.1063/5.0051154
20	F. Li Y., L. Lai H., D. Lin C., M. Li D.. Influence of the tangential velocity on the compressible Kelvin–Helmholtz instability with non-equilibrium effects. Front. Phys., 2022, 17(6): 63500 https://doi.org/10.1007/s11467-022-1200-3
21	Lai H., Lin C., Gan Y., Li D., Chen L.. The influences of acceleration on compressible Rayleigh–Taylor instability with non-equilibrium effects. Comput. Fluids, 2023, 266(15): 106037 https://doi.org/10.1016/j.compfluid.2023.106037
22	D. Lin C., H. Luo K., B. Gan Y., P. Liu Z.. Kinetic simulation of nonequilibrium Kelvin–Helmholtz instability. Commum. Theor. Phys., 2019, 71(1): 132 https://doi.org/10.1088/0253-6102/71/1/132
23	D. Lin C., H. Luo K., G. Xu A., B. Gan Y., L. Lai H.. Multiple-relaxation-time discrete Boltzmann modeling of multicomponent mixture with non-equilibrium effects. Phys. Rev. E, 2021, 103(1): 013305 https://doi.org/10.1103/PhysRevE.103.013305
24	B. Gan Y., G. Xu A., C. Zhang G., D. Lin C., L. Lai H., P. Liu Z.. Nonequilibrium and morphological characterizations of Kelvin–Helmholtz instability in compressible flows. Front. Phys., 2019, 14(4): 43602 https://doi.org/10.1007/s11467-019-0885-4
25	F. Chen W.W. Zhao W., Moment Equations and Numerical Methods for Rarefied Gas Flows, Beijing: Science Press, 2017 (in Chinese)
26	H. Li Z., P. Peng A., X. Zhang H., G. Deng X.. Numerical study on the gas-kinetic high-order schemes for solving Boltzmann model equation. Sci. China Phys. Mech. Astron., 2011, 54(9): 1687 https://doi.org/10.1007/s11433-011-4440-8
27	Karniadaskis G.Beskok A.Aluru N., Microflows and Nanoflows: Fundamentals and Simulation, New York: Springer-Verlag, 2005
28	Keerthi A., K. Geim A., Janardanan A., P. Rooney A., Esfandiar A., Hu S., A. Dar S., V. Grigorieva I., J. Haigh S., C. Wang F., Radha B.. Ballistic molecular transport through two-dimensional channels. Nature, 2018, 558(7710): 420 https://doi.org/10.1038/s41586-018-0203-2
29	López Quesada G., Tatsios G., Valougeorgis D., Rojas-Cárdenas M., Baldas L., Barrot C., Colin S.. Design guidelines for thermally driven micropumps of different architectures based on target applications via kinetic modeling and simulations. Micromachines (Basel), 2019, 10(4): 249 https://doi.org/10.3390/mi10040249
30	Kavokine N., R. Netz R., Bocquet L.. Fluids at the nanoscale: From continuum to subcontinuum transport. Annu. Rev. Fluid Mech., 2021, 53(1): 377 https://doi.org/10.1146/annurev-fluid-071320-095958
31	Jiang X., A. Siamas G., Jagus K., G. Karayiannis T.. Physical modelling and advanced simulations of gas–liquid two-phase jet flows in atomization and sprays. Prog. Eenerg. combust., 2010, 36(2): 131 https://doi.org/10.1016/j.pecs.2009.09.002
32	C. Ding J., Si T., J. Chen M., G. Zhai Z., Y. Lu X., S. Luo X.. On the interaction of a planar shock with a three-dimensional light gas cylinder. J. Fluid Mech., 2017, 828: 289 https://doi.org/10.1017/jfm.2017.528
33	Liang Y., G. Zhai Z., S. Luo X.. Interaction of strong converging shock wave with SF6 gas bubble. Sci. China Phys. Mech. Astron., 2018, 61(6): 064711 https://doi.org/10.1007/s11433-017-9151-6
34	C. Ding J., Liang Y., J. Chen M., G. Zhai Z., Si T., S. Luo X.. Interaction of planar shock wave with three-dimensional heavy cylindrical bubble. Phys. Fluids, 2018, 30(10): 106109 https://doi.org/10.1063/1.5050091
35	S. Luo X., Li M., C. Ding J., G. Zhai Z., Si T.. Nonlinear behaviour of convergent Richtmyer–Meshkov instability. J. Fluid Mech., 2019, 877: 130 https://doi.org/10.1017/jfm.2019.610
36	D. Zhang Y., G. Xu A., J. Qiu J., T. Wei H., H. Wei Z.. Kinetic modeling of multiphase flow based on simplified Enskog equation. Front. Phys., 2020, 15(6): 62503 https://doi.org/10.1007/s11467-020-1014-0
37	L. Jiang Z.H. Teng H., Gaseous Detonation Physics and Its Universal Framework Theory, Singapore: Springer, 2022
38	P. Wang J.B. Yao S., Principle and Technology of Continuous Detonation Engine, Beijing: Science Press, 2018 (in Chinese)
39	Xiao J., Liu P., X. Wang C., W. Yang G.. External field-assisted laser ablation in liquid: An efficient strategy for nanocrystal synthesis and nanostructure assembly. Prog. Mater. Sci., 2017, 87: 140 https://doi.org/10.1016/j.pmatsci.2017.02.004
40	G. Rinderknecht H., A. Amendt P., C. Wilks S., Collins G.. Kinetic physics in ICF: Present understanding and future directions. Plasma Phys. Contr. Fusion, 2018, 60(6): 064001 https://doi.org/10.1088/1361-6587/aab79f
41	Vidal F., P. Matte J., Casanova M., Larroche O.. Ion kinetic simulations of the formation and propagation of a planar collisional shock wave in a plasma. Phys. Fluids B Plasma Phys., 1993, 5(9): 3182 https://doi.org/10.1063/1.860654
42	Bond D., Wheatley V., Samtaney R., I. Pullin D.. Richtmyer–Meshkov instability of a thermal interface in a two-fluid plasma. J. Fluid Mech., 2017, 833: 332 https://doi.org/10.1017/jfm.2017.693
43	H. Song J.G. Xu A.Miao L.Chen F.P. Liu Z. F. Wang L.F. Wang N.Hou X., Plasma kinetics: Discrete Boltzmann modelling and Richtmyer–Meshkov instability, Phys. Fluids 36, 016107(2023)
44	L. Yao P., B. Cai H., X. Yan X., S. Zhang W., Du B., M. Tian J., H. Zhang E., W. Wang X., P. Zhu S.. Kinetic study of transverse electron-scale interface instability in relativistic shear flows. Matter Radiat. Extrem., 2020, 5(5): 054403 https://doi.org/10.1063/5.0017962
45	B. Cai H., X. Yan X., L. Yao P., P. Zhu S.. Hybrid fluid–particle modeling of shock-driven hydrodynamic instabilities in a plasma. Matter Radiat. Extrem., 2021, 6(3): 035901 https://doi.org/10.1063/5.0042973
46	K. Agarwal R., Y. Yun K., Balakrishnan R.. Beyond Navier–Stokes: Burnett equations for flows in the continuum-transition regime. Phys. Fluids, 2001, 13(10): 3061 https://doi.org/10.1063/1.1397256
47	K. Kundu P.M. Cohen I.Dowling D., Fluid Mechanics, 4th Ed., Ch. 13, pp 537–601, Oxford: Elsevier Academic Press, 2008
48	J. Zhou H., Zhang Y., C. Ouyang Z.. Bending and base-stacking interactions in double-stranded DNA. Phys. Rev. Lett., 1999, 82(22): 4560 https://doi.org/10.1103/PhysRevLett.82.4560
49	Y. Zhang X., Boccaletti S., G. Guan S., H. Liu Z.. Explosive synchronization in adaptive and multilayer networks. Phys. Rev. Lett., 2015, 114(3): 038701 https://doi.org/10.1103/PhysRevLett.114.038701
50	H. Tang G., Bi C., Zhao Y., Q. Tao W.. Thermal transport in nano-porous insulation of aerogel: Factors, models and outlook. Energy, 2015, 90: 701 https://doi.org/10.1016/j.energy.2015.07.109
51	C. Zong Z., C. Deng S., J. Qin Y., Wan X., H. Zhan J., K. Ma D., Yang N.. Enhancing the interfacial thermal conductance of Si/PVDF by strengthening atomic couplings. Nanoscale, 2023, 15(40): 16472 https://doi.org/10.1039/D3NR03706A
52	N. Yang L., S. Yang B., W. Li B.. Enhancing interfacial thermal conductance of an amorphous interface by optimizing the interfacial mass distribution. Phys. Rev. B, 2023, 108(16): 165303 https://doi.org/10.1103/PhysRevB.108.165303
53	Zhao H.. Identifying diffusion processes in one-dimensional lattices in thermal equilibrium. Phys. Rev. Lett., 2006, 96(14): 140602 https://doi.org/10.1103/PhysRevLett.96.140602
54	Li Y., Y. Shen X., H. Wu Z., Y. Huang J., X. Chen Y., S. Ni Y., P. Huang J.. Temperature-dependent transformation thermotics: From switchable thermal cloaks to macroscopic thermal diodes. Phys. Rev. Lett., 2015, 115(19): 195503 https://doi.org/10.1103/PhysRevLett.115.195503
55	Wang Z., C. Fu W., Zhang Y., Zhao H.. Wave-turbulence origin of the instability of anderson localization against many-body interactions. Phys. Rev. Lett., 2020, 124(18): 186401 https://doi.org/10.1103/PhysRevLett.124.186401
56	B. Li N., Ren J., Wang L., Zhang G., Hänggi P., W. Li B.. Phononics: Manipulating heat flow with electronic analogs and beyond. Rev. Mod. Phys., 2012, 84(3): 1045 https://doi.org/10.1103/RevModPhys.84.1045
57	Wang L., H. He D., B. Hu B.. Heat conduction in a three-dimensional momentum-conserving anharmonic lattice. Phys. Rev. Lett., 2010, 105(16): 160601 https://doi.org/10.1103/PhysRevLett.105.160601
58	Zhao L., L. Wang C., Liu J., H. Wen B., S. Tu Y., W. Wang Z., P. Fang H.. Reversible state transition in nanoconfined aqueous solutions. Phys. Rev. Lett., 2014, 112(7): 078301 https://doi.org/10.1103/PhysRevLett.112.078301
59	Maasilta I., J. Minnich A.. Heat under the microscope. Phys. Today, 2014, 67(8): 27 https://doi.org/10.1063/PT.3.2479
60	G. Chen S., Nonequilibrium Statistical Mechanics, Beijing: Science Press, 2010 (in Chinese)
61	G. Xu A.D. Zhang Y., Complex Media Kinetics, Beijing: Science Press, 2022 (in Chinese)
62	H. Li J.Wei G.Wang W.Yang N.H. Liu X. M. Wang L.F. He X.W. Wang X.W. Wang J.Kwauk M., From Multiscale Modeling to Meso-Science: A Chemical Engineering Perspective, Berlin: Springer-Verlag, 2013
63	L. Huang W., H. Li J., P. Edwards P.. Mesoscience: exploring the common principle at mesoscales. Natl. Sci. Rev., 2018, 5(3): 321 https://doi.org/10.1093/nsr/nwx083
64	D. Zhang Y., Wu X., B. Nie B., G. Xu A., Chen F., Wei R.. Lagrangian steady-state discrete Boltzmann model for non-equilibrium flows at micro–nanoscale. Phys. Fluids, 2023, 35(9): 092008 https://doi.org/10.1063/5.0166488
65	B. Gan Y., G. Xu A., L. Lai H., Li W., L. Sun G., Succi S.. Discrete Boltzmann multi-scale modelling of non-equilibrium multiphase flows. J. Fluid Mech., 2022, 951: A8 https://doi.org/10.1017/jfm.2022.844
66	L. Tien C.. Molecular and microscale transport phenomena: A report on the 2nd US Japan Joint Seminar, Santa Barbara, California, 7−10 August, 1996. Microscale Thermophys. Eng., 1997, 1(1): 71 https://doi.org/10.1080/108939597200458
67	M. McCoy B., Advanced Statistical Mechanics, Oxford: Oxford university press, 2010
68	D. Lee T., N. Yang C.. Statistical theory of equations of state and phase transitions. II. Lattice gas and Ising model. Phys. Rev., 1952, 87(3): 410 https://doi.org/10.1103/PhysRev.87.410
69	Succi S., The Lattice Boltzmann Equation: For Fluid Dynamics and Beyond, Oxford: Oxford University Press, 2001
70	L. He Y.Wang Y.Li Q., Lattice Boltzmann Method: Theory and Applications, Beijing: Science Press, 2009 (in Chinese)
71	L. Guo Z.Shu C., Lattice Boltzmann Method and its Applications in Engineering, Beijing: World Scientific Publishing, 2013
72	B. Huang H.C. Sukop M.Y. Lu X., Multiphase Lattice Boltzmann Methods: Theory and Application, John Wiley & Sons, 2015
73	G. Xu A., C. Zhang G., B. Gan Y., Chen F., J. Yu X.. Lattice Boltzmann modeling and simulation of compressible flows. Front. Phys., 2012, 7(5): 582 https://doi.org/10.1007/s11467-012-0269-5
74	G. Xu A., D. Lin C., C. Zhang G., J. Li Y.. Multiple relaxation-time lattice Boltzmann kinetic model for combustion. Phys. Rev. E, 2015, 91(4): 043306 https://doi.org/10.1103/PhysRevE.91.043306
75	G. Xu A.C. Zhang G.D. Zhang Y.B. Gan Y., Discrete Boltzmann modeling of nonequilibrium effects in multiphase flow, Presentation at the 31st International Symposium on Rarefied Gas Dynamics, see also FLOWS: Physics & Beyond, 1001 (2018)
76	G. Xu A.H. Song J.Chen F.Xie K.J. Ying Y., Modeling and analysis methods for complex fields based on phase space, Chinese Journal of Computational Physics 38(6), 631 (2021) (in Chinese)
77	J. Zhang D., G. Xu A., D. Zhang Y., B. Gan Y., J. Li Y.. Discrete Boltzmann modeling of high-speed compressible flows with various depths of non-equilibrium. Phys. Fluids, 2022, 34(8): 086104 https://doi.org/10.1063/5.0100873
78	D. Zhang Y., Modeling and research of non-equilibrium flows and multi-phase flows: Based on discrete Boltzmann method, Nanjing: Nanjing University of Science & Technology, 2019 (in Chinese)
79	B. Gan Y., G. Xu A., C. Zhang G., D. Zhang Y., Succi S.. Discrete Boltzmann trans-scale modeling of highspeed compressible flows. Phys. Rev. E, 2018, 97(5): 053312 https://doi.org/10.1103/PhysRevE.97.053312
80	Wu L., M. Reese J., H. Zhang Y.. Solving the Boltzmann equation deterministically by the fast spectral method: Application to gas microflows. J. Fluid Mech., 2014, 746: 53 https://doi.org/10.1017/jfm.2014.79
81	Yan B., G. Xu A., C. Zhang G., J. Ying Y., Li H.. Lattice Boltzmann model for combustion and detonation. Front. Phys., 2013, 8: 94 https://doi.org/10.1007/s11467-013-0286-z
82	D. Lin C., G. Xu A., C. Zhang G., J. Li Y.. Double distribution-function discrete Boltzmann model for combustion. Combust. Flame, 2016, 164: 137 https://doi.org/10.1016/j.combustflame.2015.11.010
83	D. Lin C., H. Luo K.. Mesoscopic simulation of nonequilibrium detonation with discrete Boltzmann method. Combust. Flame, 2018, 198: 356 https://doi.org/10.1016/j.combustflame.2018.09.027
84	D. Lin C., G. Xu A., C. Zhang G., J. Li Y.. Polar coordinate lattice Boltzmann kinetic modeling of detonation phenomena. Commum. Theor. Phys., 2014, 62(5): 737 https://doi.org/10.1088/0253-6102/62/5/18
85	D. Lin C.H. Luo K.L. Fei L.Succi S., A multicomponent discrete Boltzmann model for nonequilibrium reactive fows, Commum. Theor. Phys. 7(1), 14580 (2017)
86	D. Lin C.H. Luo K., MRT discrete Boltzmann method for compressible exothermic reactive flows, Comput. Fluids 166, 176 (2018)
87	D. Lin C., H. Luo K.. Discrete Boltzmann modeling of unsteady reactive flows with nonequilibrium effects. Phys. Rev. E, 2019, 99(1): 012142 https://doi.org/10.1103/PhysRevE.99.012142
88	D. Lin C., H. Luo K.. Kinetic simulation of unsteady detonation with thermodynamic nonequilibrium effects. Combust. Explos. Shock Waves, 2020, 56(4): 435 https://doi.org/10.1134/S0010508220040073
89	D. Lin C., L. Su X., D. Zhang Y.. Hydrodynamic and thermodynamic nonequilibrium effects around shock waves: Based on a discrete Boltzmann method. Entropy (Basel), 2020, 22(12): 1397 https://doi.org/10.3390/e22121397
90	D. Zhang Y., G. Xu A., C. Zhang G., M. Zhu C., D. Lin C.. Kinetic modeling of detonation and effects of negative temperature coefficient. Combust. Flame, 2016, 173: 483 https://doi.org/10.1016/j.combustflame.2016.04.003
91	M. Shan Y., G. Xu A., D. Zhang Y., F. Wang L., Chen F.. Discrete Boltzmann modeling of detonation: Based on the Shakhov model. Proc. Inst. Mech. Eng., C J. Mech. Eng. Sci., 2023, 237(11): 2517 https://doi.org/10.1177/09544062221096254
92	D. Zhang Y., G. Xu A., C. Zhang G., H. Chen Z.. Discrete Boltzmann method with Maxwell-type boundary condition for slip flow. Commum. Theor. Phys., 2018, 69(1): 77 https://doi.org/10.1088/0253-6102/69/1/77
93	D. Zhang Y., G. Xu A., C. Zhang G., H. Chen Z., Wang P.. Discrete Boltzmann method for non-equilibrium flows: Based on Shakhov model. Comput. Phys. Commun., 2019, 238: 50 https://doi.org/10.1016/j.cpc.2018.12.018
94	Zhang Y., Xu A., Chen F., Lin C., H. Wei Z.. Non-equilibrium characteristics of mass and heat transfers in the slip flow. AIP Adv., 2022, 12(3): 035347 https://doi.org/10.1063/5.0086400
95	Sone Y., Molecular Gas Dynamics: Theory, Techniques, and Applications, Springer Science & Business Media, 2007
96	Onishi Y., A rarefied gas flow over a flat wall, Bull. Univ. Osaka Prefect. Ser. A Eng. Nat. Sci. 22(2), 91 (1974)
97	S. Chen X., Dohm V., Schultka N.. Order-parameter distribution function of finite O(n) symmetric systems. Phys. Rev. Lett., 1996, 77(17): 3641 https://doi.org/10.1103/PhysRevLett.77.3641
98	J. Wagner A., M. Yeomans J.. Breakdown of scale invariance in the coarsening of phase-separating binary fluids. Phys. Rev. Lett., 1998, 80(7): 1429 https://doi.org/10.1103/PhysRevLett.80.1429
99	R. Swift M., R. Osborn W., M. Yeomans J.. Lattice Boltzmann simulation of nonideal fluids. Phys. Rev. Lett., 1995, 75(5): 830 https://doi.org/10.1103/PhysRevLett.75.830
100	M. Shan Y., G. Xu A., F. Wang L., D. Zhang Y.. Nonequilibrium kinetics effects in Richtmyer–Meshkov instability and reshock processes. Commum. Theor. Phys., 2023, 75(11): 115601 https://doi.org/10.1088/1572-9494/acf305
101	Latini M., Schilling O., S. Don W.. High-resolution simulations and modeling of reshocked single-mode Richtmyer–Meshkov instability: Comparison to experimental data and to amplitude growth model predictions. Phys. Fluids, 2007, 19(2): 024104 https://doi.org/10.1063/1.2472508
102	D. Collins B.W. Jacobs J., PLIF flow visualization and measurements of the Richtmyer–Meshkov instability of an air/SF6 interface, J. Fluid Mech. 464, 113 (2002)
103	J. Zhang D., G. Xu A., H. Song J., B. Gan Y., D. Zhang Y., J. Li Y.. Specific-heat ratio effects on the interaction between shock wave and heavy-cylindrical bubble: Based on discrete Boltzmann method. Comput. Fluids, 2023, 265: 106021 https://doi.org/10.1016/j.compfluid.2023.106021
104	S. Jiang G.L. Wu C., A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics, J. Comput. Phys. 150(2), 561 (1999)
105	H. Song J.G. Xu A.Miao L.G. Liao Y.W. Liang F. Tian F.Q. Nie M.F. Wang N., Entropy increase characteristics of shock wave/plate laminar boundary layer interaction, Acta Aeronautica et Astronautica Sinica 44(21), 528520 (2023) (in Chinese)
106	F. Liao S., B. Zhang W., Chen H., Y. Zou L., H. Liu J., X. Zheng X.. Atwood number effects on the instability of a uniform interface driven by a perturbed shock wave. Phys. Rev. E, 2019, 99(1): 013103 https://doi.org/10.1103/PhysRevE.99.013103
107	Y. Zou L., Al-Marouf M., Cheng W., Samtaney R., C. Ding J., S. Luo X.. Richtmyer–Meshkov instability of an unperturbed interface subjected to a diffracted convergent shock. J. Fluid Mech., 2019, 879: 448 https://doi.org/10.1017/jfm.2019.694
108	Y. Zou L., Wu Q., Z. Li X.. Research progress of general Richtmyer–Meshkov instability. Sci. Sin. Phys. Mech. Astron., 2020, 50: 104702
109	M. Shan Y.G. Xu A.D. Zhang Y.F. Wang L. Wall-heating phenomena in shock wave physics: Physical or artificial? (in preparation)
110	J. Zhang D., G. Xu A., B. Gan Y., D. Zhang Y., H. Song J., J. Li Y.. Viscous effects on morphological and thermodynamic non-equilibrium characterizations of shock-bubble interaction. Phys. Fluids, 2023, 35(10): 106113 https://doi.org/10.1063/5.0172345
111	B. Gan Y., G. Xu A., C. Zhang G., Succi S.. Discrete Boltzmann modeling of multiphase flows: Hydrodynamic and thermodynamic non-equilibrium effects. Soft Matter, 2015, 11(26): 5336 https://doi.org/10.1039/C5SM01125F
112	D. Zhang Y., G. Xu A., C. Zhang G., B. Gan Y., H. Chen Z., Succi S.. Entropy production in thermal phase separation: A kinetic-theory approach. Soft Matter, 2019, 15(10): 2245 https://doi.org/10.1039/C8SM02637H
113	L. Sun G., B. Gan Y., G. Xu A., D. Zhang Y., F. Shi Q.. Thermodynamic nonequilibrium effects in bubble coalescence: A discrete Boltzmann study. Phys. Rev. E, 2022, 106(3): 035101 https://doi.org/10.1103/PhysRevE.106.035101
114	L. Sun G.B. Gan Y.G. Xu A.F. Shi Q., Droplet coalescence kinetics: Thermodynamic nonequilibrium effects and entropy production mechanism, arXiv: 2311.06546 (2023), Phys. Fluids (2024) (in press)
115	Chen J., G. Xu A., W. Chen D., D. Zhang Y., H. Chen Z.. Discrete Boltzmann modeling of Rayleigh–Taylor instability: Effects of interfacial tension, viscosity, and heat conductivity. Phys. Rev. E, 2022, 106(1): 015102 https://doi.org/10.1103/PhysRevE.106.015102
116	Q. Jia Y.G. Xu A.F. Wang L.W. Chen D., Study on Rayleigh−Taylor instability under variable acceleration: Based on discrete Boltzmann method, Beijing: Symposium on Interfacial Instability and Multi-media Turbulence, 2023 (in Chinese)
117	Chen J.G. Xu A.W. Chen D.D. Zhang Y.H. Chen Z., Kinetics of RT instability in van der Waals fluid: The influence of compressibility (in preparation)
118	Chen F., G. Xu A., D. Zhang Y., K. Zeng Q.. Morphological and non-equilibrium analysis of coupled Rayleigh–Taylor–Kelvin–Helmholtz instability. Phys. Fluids, 2020, 32(10): 104111 https://doi.org/10.1063/5.0023364
119	P. Liu Z., H. Song J., G. Xu A., D. Zhang Y., Xie K.. Discrete Boltzmann modeling of plasma shock wave. Proc. Inst. Mech. Eng., C J. Mech. Eng. Sci., 2023, 237(11): 2532 https://doi.org/10.1177/09544062221075943
120	H. Song J.Miao L.G. Xu A.Chen F.Li L. Hou X., Plasma kinetics: Transport and mixing characteristics induced by Kelvin–Helmholtz instability (in preparation)
121	D. Lin C., G. Xu A., C. Zhang G., J. Li Y., Succi S.. Polar-coordinate lattice Boltzmann modeling of compressible flows. Phys. Rev. E, 2014, 89(1): 013307 https://doi.org/10.1103/PhysRevE.89.013307
122	D. Zhang Y., G. Xu A., C. Zhang G., H. Chen Z., Wang P.. Discrete ellipsoidal statistical BGK model and Burnett equations. Front. Phys., 2018, 13(3): 135101 https://doi.org/10.1007/s11467-018-0749-3
123	L. Su X., D. Lin C.. Nonequilibrium effects of reactive flow based on gas kinetic theory. Commum. Theor. Phys., 2022, 74(3): 035604 https://doi.org/10.1088/1572-9494/ac53a0
124	L. Su X., D. Lin C.. Unsteady detonation with thermodynamic nonequilibrium effect based on the kinetic theory. Commum. Theor. Phys., 2023, 75(7): 075601 https://doi.org/10.1088/1572-9494/acd6dd
125	L. Lai H., Modeling and Simulation of Compressible Rayleigh-Taylor Instability by Discrete Boltzmann, Post-doctoral research report of Beijing Institute of Applied Physics and Computational Mathematics, 2015 (in Chinese)
126	L. Lai H., G. Xu A., C. Zhang G., B. Gan Y., J. Ying Y., Succi S.. Nonequilibrium thermohydrodynamic effects on the Rayleigh-Taylor instability in compressible flows. Phys. Rev. E, 2016, 94(2): 023106 https://doi.org/10.1103/PhysRevE.94.023106
127	G. Chen A., Study of shock detachment distance in rarefied flow field, Hefei: The 2nd National Conference on Shock Wave and Shock Tube, 2022 (in Chinese)
128	M. Bao W., Future aerospace technology development and aerodynamics challenges, Tianjin: The 2nd Aerodynamics Congress, 2023 (in Chinese)
129	S. Zhu G., Several encountered aerodynamic problems and progress in hypersonic flight, Tianjin: The 2nd Aerodynamics Congress, 2023 (in Chinese)
130	C. Ai B., Research on some problems of aerodynamics of space vehicle, Tianjin: The 2nd Aerodynamics Congress, 2023 (in Chinese)
131	G. Chen A.Wang J.H. Li Z.Q. Li Z.Tian Y. Y. Long Z., Velocity measurement investigation of rarefied flow field by pulse electron beam fluorescence technique, Phys. Gases 6(5), 67 (2021) (in Chinese)
132	Chen W.Y. Hu H.Wang L., Characterization method and measurement technique of thermodynamic non-equilibrium characteristics of high enthalpy flow field, Dalian: The 17th National Conference on Physics and Mechanics, 2023 (in Chinese)
133	M. Danehy P., Molecular based hypersonic nonequilibrium flow optical diagnosis (in Chinese, translated by Qifeng Chen) (to be published)
134	M. Danehy P.F. Bathel B.T. Johansen C.., et al.. Molecular Based Hypersonic Non-Equilibrium Flow Optical Diagnosis, AIAA Progress Series, 2013

[1]	Yaofeng Li, Huilin Lai, Chuandong Lin, Demei Li. Influence of the tangential velocity on the compressible Kelvin−Helmholtz instability with nonequilibrium effects[J]. Front. Phys. , 2022, 17(6): 63500-.
[2]	Feng Chen, Aiguo Xu, Yudong Zhang, Yanbiao Gan, Bingbing Liu, Shuang Wang. Effects of the initial perturbations on the Rayleigh–Taylor–Kelvin–Helmholtz instability system[J]. Front. Phys. , 2022, 17(3): 33505-.
[3]	Lu Chen (陈璐), Huilin Lai (赖惠林), Chuandong Lin (林传栋), Demei Li (李德梅). Specific heat ratio effects of compressible Rayleigh–Taylor instability studied by discrete Boltzmann method[J]. Front. Phys. , 2021, 16(5): 52500-.
[4]	Yu-Dong Zhang, Ai-Guo Xu, Jing-Jiang Qiu, Hong-Tao Wei, Zung-Hang Wei. Kinetic modeling of multiphase flow based on simplified Enskog equation[J]. Front. Phys. , 2020, 15(6): 62503-.
[5]	Yan-Biao Gan, Ai-Guo Xu, Guang-Cai Zhang, Chuan-Dong Lin, Hui-Lin Lai, Zhi-Peng Liu. Nonequilibrium and morphological characterizations of Kelvin–Helmholtz instability in compressible flows[J]. Front. Phys. , 2019, 14(4): 43602-.
[6]	Ying-Xiang Zhen, Ming Yang, Rui-Ning Wang. Thermoelectricity in B₈₀-based single-molecule junctions: First-principles investigation[J]. Front. Phys. , 2019, 14(2): 23603-.
[7]	Zhao Deng (赵登),R. E. Waltz,Xiaogang Wang (王晓钢). Cyclokinetic models and simulations for high-frequency turbulence in fusion plasmas[J]. Front. Phys. , 2016, 11(5): 115203-.
[8]	Dazhi Xu,Jianshu Cao. Non-canonical distribution and non-equilibrium transport beyond weak system-bath coupling regime: A polaron transformation approach[J]. Front. Phys. , 2016, 11(4): 110308-110308.
[9]	Feng Chen, Ai-Guo Xu, Guang-Cai Zhang, Yong-Long Wang. Two-dimensional Multiple-Relaxation-Time Lattice Boltzmann model for compressible and incompressible flows[J]. Front. Phys. , 2014, 9(2): 246-254.
[10]	Wen-Zhi Zheng(郑文智), Yuan Liang(梁源), Ji-Ping Huang(黄吉平). Equilibrium state and non-equilibrium steady state in an isolated human system[J]. Front. Phys. , 2014, 9(1): 128-135.
[11]	Li-fang SONG (宋莉芳), Chun-hong JIANG (姜春红), Shu-sheng LIU (刘淑生), Cheng-li JIAO (焦成丽), Xiao-liang SI (司晓亮), Shuang WANG (王爽), Fen LI (李芬), Jian ZHANG (张箭), Li-xian SUN (孙立贤), Fen XU (徐芬), Feng-lei HUANG (黄风雷). Progress in improving thermodynamics and kinetics of new hydrogen storage materials[J]. Front. Phys. , 2011, 6(2): 151-161.
[12]	Haiping LIN (林海平), Janosch M. C. RAUBA, Kristian S. THYGESEN, Karsten W. JACOBSEN, Michelle Y. SIMMONS, Werner A. HOFER. First-principles modelling of scanning tunneling microscopy using non-equilibrium Green’s functions[J]. Front Phys Chin, 2010, 5(4): 369-379.
[13]	Jing NING (宁静), Xin SHEN (沈昕), Zi-yong SHEN (申自勇), Xing-yu ZHAO (赵兴钰), Shi-min HOU (侯士敏). First-principles calculation on the conductance of ruthenium-quasi cumulene-ruthenium molecular junctions[J]. Front. Phys. , 2009, 4(3): 398-402.

Viewed

Full text

Abstract

Cited

Shared

Discussed