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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳俊全(Chiun-Chuan Chen) | |
| dc.contributor.author | Yen-Chi Lee | en |
| dc.contributor.author | 李彥奇 | zh_TW |
| dc.date.accessioned | 2021-06-15T16:23:48Z | - |
| dc.date.available | 2018-10-12 | |
| dc.date.copyright | 2015-10-12 | |
| dc.date.issued | 2015 | |
| dc.date.submitted | 2015-08-14 | |
| dc.identifier.citation | [1] S. Hiyama et al., Molecular communication, Journal-Institute of Electronics Information and Communication Engineers, 2006.
[2] I. F. Akyildiz, F. Brunetti, and C. Blzquez, Nanonetworks: A new communication paradigm, Computer Networks (Elsevier) Journal, vol. 52, no. 12, pp. 2260-2279, 2008. [3] M. Moore et al., A design of a molecular communication system for nanomachines using molecular motors, in Proceedings of the Fourth Annual IEEE International Conference on Pervasive Computing and Communications (PerCom06), 2006. [4] P. C. Yeh et al., A new frontier of wireless communication theory: diffusion-based molecular communications, IEEE Wireless Communications, vol. 19, no. 5, pp. 28-35, 2012. [5] R. Freitas, Nanomedicine, Volume I: Basic Capabilities, Landes Biosience, 1999. [6] A. W. Eckford, Achievable information rates for molecular communication with distinct molecules, Bio-Inspired Models of Network, Information and Computing Systems, 2007. [7] M. U. Mahfuz, D. Makrakis, and H. T. Mouftah, A comprehensive study of concentration-encoded unicast molecular communication with binary pulse transmission, IEEE Conference on Nanotechnology (IEEE-NANO), 2011. [8] B. Atakan, S. Galmes, and O. B. Akan, Nanoscale communication with molecular arrays in nanonetworks, IEEE Transactions on NanoBioscience, vol. 11, no. 2, pp. 149-160, 2012. [9] J. Crank, The Mathematics of Diffusion, Oxford: Clarendon Press, 1956. [10] B. Atakan and O. Akan, An information theoretical approach for molecular communications, Bio-Inspired Models of Network, Information and Computing Systems, 2007. [11] A. Einstein, On the movement of small particles suspended in a stationary liquid demanded by the molecular-kinetic theory of heat, Annalen der physik, vol. 17, pp. 549-560, 1905. [12] P. M orters and Y. Peres, Brownian motion, Vol. 30. Cambridge University Press, 2010. [13] K. Srinivas, A. Eckford, and R. Adve, Molecular communication in fluid media: The additive inverse Gaussian noise channel, IEEE Trans. Inf. Theory, vol. 58, no. 7, pp. 4678-4692, 2012. [14] J. L. Doob, Classical potential theory and its probabilistic counterpart, Springer-Verlag, 1984. [15] R. Nevanlinna, Analytic functions, Berlin: Springer, 1970. [16] R. Nevanlinna, Das harmonische Mass von Punktmengen und seine Anwendung in der Funktionentheorie, 8th Scand. Math. Congr., Stockholm, 1934. [17] S. Kakutani, On Brownian motion in n-space, Proc. Acad. Japan, 20, pp. 648-652, 1944. [18] E. B. Dynkin, Markov processes, Springer Berlin Heidelberg, 1965. [19] B. Oksendal, Stochastic differential equations. Springer Berlin Heidelberg, 2003. [20] L. Evans, Partial differential equations, American Mathematical Society, 1998. [21] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second, Springer, 1977. [22] A. D., Polyanin, Handbook of linear partial differential equations for engineers and scientists, CRC press, 2001. [23] A. N. Tikhonov and A. A. Samariskii, Equations of mathematical physics, Courier Corporation, 1990. [24] O.I. Marichev, Handbook of Integral Transforms of Higher Transcendental Functions, Theory and Algorithmic Tables, Chichester, Ellis Horwood, 1983. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/52699 | - |
| dc.description.abstract | Recent technology enables people to design tiny machines in nano-scale. These nanomachines bring us new applications in many fields, such as biomedical and military technology. Since the nano-scale devices have limited size and energy, molecular communication (MC) becomes a promising communication approach for nanonetworks. In this article, we propose a new molecular communication model that uses the particle position to carry information.
To analyze the position modulation system, we consider the integral kernel of the steady-state convection diffusion equation: △u+⃗v•∇u=0. With the help of the Green's function of the Helmholtz equation, the integral kernel of the steady-state convection-diffusion equation can be written in explicit form. There is a close relation between the integral kernel of steady-state convection-diffusion equation and Brownian motion with drift. We discuss in this article why the integral kernel can be interpreted as the hitting position distribution of a Brownian motion particle. With the hitting distribution, we derive the optimal detection rule for the proposed MC system, and analyze the bit error rate performance for the zero drift case. For the non-zero drift case, we derive an approximated representation for the detection boundary. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T16:23:48Z (GMT). No. of bitstreams: 1 ntu-104-R02221023-1.pdf: 818982 bytes, checksum: 41f671dc9ea26483df78d9835d84be93 (MD5) Previous issue date: 2015 | en |
| dc.description.tableofcontents | 1 Introduction......................................... 1
1.1 A Short Introduction to Molecular Communication.. 1 1.2 Harmonic Measure: A Link Between Probability and PDE Theory............................................. 3 2 A Relation Between Integral Kernel and First Hitting Position............................................... 4 2.1 The Dynkin Formula............................... 4 2.2 Finding First Hitting Position Distribution...... 5 3 Integral Kernel for Steady-State Convection-Diffusion Equation............................................... 8 3.1 Steady-State Convection-Diffusion Equation....... 8 3.2 The Helmholtz Equation........................... 9 3.3 Representation Formula for the Integral Kernel.. 10 4 Detection Problem for Binary Position Modulation.... 12 4.1 Detection for Zero Drift Case................... 12 4.2 Detection for Non-Zero Drift Case............... 15 Reference............................................. 19 | |
| dc.language.iso | en | |
| dc.subject | 分子通信 | zh_TW |
| dc.subject | 布朗運動 | zh_TW |
| dc.subject | 信號偵測 | zh_TW |
| dc.subject | 調變 | zh_TW |
| dc.subject | 對流擴散 | zh_TW |
| dc.subject | Brownian motion | en |
| dc.subject | Molecular communication | en |
| dc.subject | convection-diffusion | en |
| dc.subject | modulation | en |
| dc.subject | signal detection | en |
| dc.title | 對流擴散方程的積分核及其在分子通信上的應用 | zh_TW |
| dc.title | Integral Kernel of Steady-State Convection-Diffusion Equation and Its Application to Molecular Communication | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 103-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳宜良(I-Liang Chern),葉丙成(Ping-Cheng Yeh),夏俊雄(Chun-Hsiung Hsia),林太家(Tai-Chia Lin) | |
| dc.subject.keyword | 分子通信,對流擴散,布朗運動,調變,信號偵測, | zh_TW |
| dc.subject.keyword | Molecular communication,convection-diffusion,Brownian motion,modulation,signal detection, | en |
| dc.relation.page | 20 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2015-08-15 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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