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在二维双向行人交通格子流体力学模型的基础上，提出了考虑次近邻行人相互作用进行行人流优化的行人交通格子流体力学模型.通过线性稳定性分析给出新模型的稳定性条件. 通过非线性分析得到描述交通堵塞密度波的改进的Korteweg-de Vries方程，并进行了数值模拟.
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关键词:
- 改进的Korteweg-de Vries方程 /
- 行人流 /
- 格子流体力学模型
Based on the lattice hydrodynamic model with bidirectional pedestrian flow, the lattice hydrodynamic model which considered the interaction of the next-nearest-neighbor pedestrians was proposed in this paper. By the linear stability analysis, the stability condition was obtained. By nonlinear analysis, the modified Korteweg-de Vries equation to describe the density wave of pedestrian congestion was given. Furthermore, numerical simulation was carried out to examine the performance of such a model and it shows consistency with the theoretical analysis results.[1] ［1］Chowdhury D, Santen L, Schadschneider A 2000 Phys. Rep. 329 199
[2] ［2］Helbing D 2001 Rev. Mod. Phys. 73 1067
[3] ［3］Nagatani T 2002 Rep. Prog. Phys. 65 1331
[4] ［4］Helbing D, Farkas I J, Vicsek T 2000 Phys. Rev. Lett. 84 1240
[5] ［5］Helbing D, Farkas I J, Vicsek T 2000 Nature 407 487
[6] ［6］Bohannon J 2005 Science 310 219
[7] ［7］Henderson L E 1971 Nature 229 381
[8] ［8］Helbing D, Molna′r P 1995 Phys. Rev. E 51 4282
[9] ［9］Muramatsu M, Irie T, Nagatani T 1999 Physica A 267 487
[10] ］Tajima Y, Nagatani T 2001 Physica A 292 545
[11] ］Tajima Y, Nagatani T 2002 Physica A 303 239
[12] ］Takimoto K, Tajima Y, Nagatani T 2002 Physica A 308 460
[13] ］Burstedde C, Klauck K, Schadschneider A, Zittarz J 2001 Physica A 295 507
[14] ］ Yue H, Shao C F, Yao Z S 2009 Acta Phys. Sin. 58 4523 (in Chinese)［岳昊、 邵春福、 姚智胜 2009 58 4523］
[15] ］Zhou J W, Kuan H, Liu M R, Kong L J 2009 Acta Phys. Sin. 58 3001 (in Chinese)［周金旺、 邝华、 刘慕仁、 孔令江 2009 58 3001］
[16] ］Kerner B S, Konhauser P 1993 Phys. Rev. E 48 2335
[17] ］Kurtze D A, Hong D C 1995 Phys. Rev. E 52 218
[18] ］Komatsu T S, Sasa S 1995 Phys. Rev. E 52 5574
[19] ］Muramatsu M, Nagatani T 1999 Phys. Rev. E 60 180
[20] ］Nagatani T 1998 Physica A 261 599
[21] ］Nagatani T 1999 Physica A 264 581
[22] ］Nagatani T 1999 Physica A 265 297
[23] ］Nagatani T 1999 Phys. Rev. E 59 4857
[24] ］Xue Y 2004 Acta Phys. Sin. 53 25 (in Chinese)［薛郁 2004 53 25］
[25] ］Tang T Q, Huang H J， Xue Y 2006 Acta Phys. Sin. 55 4026 (in Chinese)［唐铁桥、 黄海军、 薛郁 2006 55 4026］
[26] ］May A D 1990 Traffic Flow Fundamentals (New Jersey： Prentice Hall) p210
[27] ］Tian H H， Xue Y， He H D， Wei Y F， Lu W Z 2009 Physica A 388 2895
[28] ］Xue Y, Tian H H, He H D, Lu W Z, Wei Y F 2009 Eur. Phys. J. B 69 289
[29] ］Nagatani T, Nakanishi K 1998 Phys. Rev. E 57 6415
[30] ］Nagatani T 1998 Phys. Rev. E 58 4271
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[1] ［1］Chowdhury D, Santen L, Schadschneider A 2000 Phys. Rep. 329 199
[2] ［2］Helbing D 2001 Rev. Mod. Phys. 73 1067
[3] ［3］Nagatani T 2002 Rep. Prog. Phys. 65 1331
[4] ［4］Helbing D, Farkas I J, Vicsek T 2000 Phys. Rev. Lett. 84 1240
[5] ［5］Helbing D, Farkas I J, Vicsek T 2000 Nature 407 487
[6] ［6］Bohannon J 2005 Science 310 219
[7] ［7］Henderson L E 1971 Nature 229 381
[8] ［8］Helbing D, Molna′r P 1995 Phys. Rev. E 51 4282
[9] ［9］Muramatsu M, Irie T, Nagatani T 1999 Physica A 267 487
[10] ］Tajima Y, Nagatani T 2001 Physica A 292 545
[11] ］Tajima Y, Nagatani T 2002 Physica A 303 239
[12] ］Takimoto K, Tajima Y, Nagatani T 2002 Physica A 308 460
[13] ］Burstedde C, Klauck K, Schadschneider A, Zittarz J 2001 Physica A 295 507
[14] ］ Yue H, Shao C F, Yao Z S 2009 Acta Phys. Sin. 58 4523 (in Chinese)［岳昊、 邵春福、 姚智胜 2009 58 4523］
[15] ］Zhou J W, Kuan H, Liu M R, Kong L J 2009 Acta Phys. Sin. 58 3001 (in Chinese)［周金旺、 邝华、 刘慕仁、 孔令江 2009 58 3001］
[16] ］Kerner B S, Konhauser P 1993 Phys. Rev. E 48 2335
[17] ］Kurtze D A, Hong D C 1995 Phys. Rev. E 52 218
[18] ］Komatsu T S, Sasa S 1995 Phys. Rev. E 52 5574
[19] ］Muramatsu M, Nagatani T 1999 Phys. Rev. E 60 180
[20] ］Nagatani T 1998 Physica A 261 599
[21] ］Nagatani T 1999 Physica A 264 581
[22] ］Nagatani T 1999 Physica A 265 297
[23] ］Nagatani T 1999 Phys. Rev. E 59 4857
[24] ］Xue Y 2004 Acta Phys. Sin. 53 25 (in Chinese)［薛郁 2004 53 25］
[25] ］Tang T Q, Huang H J， Xue Y 2006 Acta Phys. Sin. 55 4026 (in Chinese)［唐铁桥、 黄海军、 薛郁 2006 55 4026］
[26] ］May A D 1990 Traffic Flow Fundamentals (New Jersey： Prentice Hall) p210
[27] ］Tian H H， Xue Y， He H D， Wei Y F， Lu W Z 2009 Physica A 388 2895
[28] ］Xue Y, Tian H H, He H D, Lu W Z, Wei Y F 2009 Eur. Phys. J. B 69 289
[29] ］Nagatani T, Nakanishi K 1998 Phys. Rev. E 57 6415
[30] ］Nagatani T 1998 Phys. Rev. E 58 4271
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