This paper deals with the existence and the asymptotic behavior of discontinu- ous traveling wave entropy solutions for a modified Allen-Cahn model, in which, the usual Ficken-based model for phase transition is repla...This paper deals with the existence and the asymptotic behavior of discontinu- ous traveling wave entropy solutions for a modified Allen-Cahn model, in which, the usual Ficken-based model for phase transition is replaced with a more physical model with nonSn- ear diffusive flux. The discontinuous traveling waves correspond to the discontinuous phase transition phenomena.展开更多
Jumping from place to place, replicating food, biological or mechanical parts or beaming up somebody, may not be fiction, rather an issue of practical implementation as shall be observed in this paper. Devices like tr...Jumping from place to place, replicating food, biological or mechanical parts or beaming up somebody, may not be fiction, rather an issue of practical implementation as shall be observed in this paper. Devices like transporter, food replicators or warp drive intrigue our imagination. This paper is intended to show that Jump drive is an issue of coordinate transformation. Changing location from planet X to planet Y does not necessarily require travelling a distance D connecting between the two planets. The theoretical knowledge of changing the location from coordinate X to coordinate Y exists;we do that in signal processing, but, we have not yet developed such a machine. The present paper shows the feasibility of jump drive;however, much work needs to be done on the implementation.展开更多
基金supported by the Program for New Century Excellent Talents in University of the Ministry of Education(NCET-13-0804)NSFC(11471127,11371153)+7 种基金Guangdong Natural Science Funds for Distinguished Young Scholar(2015A030306029)the Excellent Young Teachers Program of Guangdong ProvinceSpecial support program of Guangdong Provincesupported by the Innovation Project of Graduate School of South China Normal University(2016lkxm70)the High-Level University Developments Innovation Project of Graduate School of South China Normal University(2016YN05)the Top-Notch Graduate Foundation of South China Normal University(2016028)supported by the Fundamental Research Funds for the Central Universities(2017BQ109)China Postdoctoral Science Foundation(2017M610517)
文摘This paper deals with the existence and the asymptotic behavior of discontinu- ous traveling wave entropy solutions for a modified Allen-Cahn model, in which, the usual Ficken-based model for phase transition is replaced with a more physical model with nonSn- ear diffusive flux. The discontinuous traveling waves correspond to the discontinuous phase transition phenomena.
文摘Jumping from place to place, replicating food, biological or mechanical parts or beaming up somebody, may not be fiction, rather an issue of practical implementation as shall be observed in this paper. Devices like transporter, food replicators or warp drive intrigue our imagination. This paper is intended to show that Jump drive is an issue of coordinate transformation. Changing location from planet X to planet Y does not necessarily require travelling a distance D connecting between the two planets. The theoretical knowledge of changing the location from coordinate X to coordinate Y exists;we do that in signal processing, but, we have not yet developed such a machine. The present paper shows the feasibility of jump drive;however, much work needs to be done on the implementation.
