We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

http://nathan.instras.com/documentDB/paper-69.pdf

Porous silicon: a quantum sponge structure for silicon based optoelectronics

流体力学杂志“Journal of Fluid Mechanics”由剑桥大学教授George Batchelor在1956年5月创办，在国际流体力学界享有很高的学术声望，被公认为是流体力学最著名的学术刊物之一，2005年的影响因子为2．061，雄居同类期刊之首．在它创刊50周年之际，2006年5月JFM出版了第554卷的纪念特刊，其中刊登了现任主编（美国西北大学S．H．Davis教授和英国剑桥大学T．J．Pedley教授）合写的述评：“Editorial：JFM at50”，以JFM为背景，从独特的视角对近50年来流体力学的发展进行了简明的回顾和展望，并归纳了一系列非常有启发性的有趣统计数字．2006年7月21日在剑桥大学应用数学和理论物理研究所（DAMTP）举行了创刊50周年的庆祝会．下午2点，JFM的新老编辑和来宾会聚一堂，Pedley教授致开幕词，其后是5个精彩的报告：The mysterious rattleback and its fluid counterpart（Keith Moffatt），Developments in shear instabilities（Patrick Huerre），Falling clouds（Elisabeth Guazzelli），Ecotectural fluid mechanics（Paul Linden），The success of JFM（Herbert Huppert），最后由Davis教授致闭幕词．

Journal of Fluid Mechanics创刊50周年

Theory of the electrochemical impedance of anomalous diffusion

The fifth-generation mobile initiative, 5G, is a tremendous and collective effort to specify, standardize, design, manufacture, and deploy the next cellular network generation. 5G networks will support demanding services such as enhanced Mobile Broadband, Ultra-Reliable and Low Latency Communications and massive Machine-Type Communications, which will require data rates of tens of Gbps, latencies of few milliseconds and connection densities of millions of devices per square kilometer. This survey presents the most significant use cases expected for 5G including their corresponding scenarios and traffic models. First, the paper analyzes the characteristics and requirements for 5G communications, considering aspects such as traffic volume, network deployments, and main performance targets. Secondly, emphasizing the definition of performance evaluation criteria for 5G technologies, the paper reviews related proposals from principal standards development organizations and industry alliances. Finally, well-defined and significant 5G use cases are provided. As a result, these guidelines will help and ease the performance evaluation of current and future 5G innovations, as well as the dimensioning of 5G future deployments.

/pdf/a-survey-on-5g-usage-scenarios-and-traffic-models-2n74ncu4n6.pdf

A Survey on 5G Usage Scenarios and Traffic Models

We have measured the frequency dependence of the conductivity and the dielectric constant of various samples of porous Si in the regime 1 Hz-100 kHz at different temperatures. The conductivity data exhibit a strong frequency dependence. When normalized to the dc conductivity, our data obey a universal scaling law, with a well-defined crossover, in which the real part of the conductivity sigma' changes from an sqrt(omega) dependence to being proportional to omega. We explain this in terms of activated hopping in a fractal network. The low-frequency regime is governed by the fractal properties of porous Si, whereas the high-frequency dispersion comes from a broad distribution of activation energies. Calculations using the effective-medium approximation for activated hopping on a percolating lattice give fair agreement with the data.

Hopping transport on a fractal: ac conductivity of porous silicon.

Wireless Mesh Networks WMNs have emerged as a key technology for the next generation of wireless networking. Instead of being another type of ad-hoc networking, WMNs diversify the capabilities of ad-hoc networks. Several protocols that work over WMNs include IEEE 802.11a/b/g, 802.15, 802.16 and LTE-Advanced. To bring about a high throughput under varying conditions, these protocols have to adapt their transmission rate. This paper proposes a scheme to improve channel conditions by performing rate adaptation along with multiple packet transmission using packet loss and physical layer condition. Dynamic monitoring, multiple packet transmission and adaptation to changes in channel quality by adjusting the packet transmission rates according to certain optimization criteria provided greater throughput. The key feature of the proposed method is the combination of the following two factors: 1 detection of intrinsic channel conditions by measuring the fluctuation of noise to signal ratio via the standard deviation, and 2 the detection of packet loss induced through congestion. The authors show that the use of such techniques in a WMN can significantly improve performance in terms of the packet sending rate. The effectiveness of the proposed method was demonstrated in a simulated wireless network testbed via packet-level simulation.

Adaptive Sending Rate Over Wireless Mesh Networks Using SNR

One of the extraordinary aspects of nonlinear wave evolution which has been observed as the spontaneous occurrence of astonishing and statistically extraordinary amplitude wave is called rogue wave. We show that the eigenvalues of the associated equation of nonlinear Schrodinger equation are almost constant in the vicinity of rogue wave and we validate that optical rogue waves are formed by the collision between quasi-solitons in anomalous dispersion fiber exhibiting weak third order dispersion.

Soliton's eigenvalue based analysis on the generation mechanism of rogue wave phenomenon in optical fibers exhibiting weak third order dispersion.

Optical “rogue” waves are rare and very high intensity pulses of light that occur in optical devices such as communication fibers. They appear suddenly and can cause transmission errors and damage in optical communication systems. Indeed, the physics governing their dynamics is very similar to “monster” or “freak” waves on the Earth’s oceans, which are known to harm shipping. It is therefore important to characterize rogue wave generation, dynamics and, if possible, predictability. Here we demonstrate a simple cascade mechanism that drives the formation and emergence of rogue waves in the generalized non-linear Schrodinger equation with third-order dispersion. This generation mechanism is based on inelastic collisions of quasi-solitons and is well described by a resonant-like scattering behaviour for the energy transfer in pair-wise quasi-soliton collisions. Our theoretical and numerical results demonstrate a threshold for rogue wave emergence and the existence of a period of reduced amplitudes — a “calm before the storm” — preceding the arrival of a rogue wave event. Comparing with ultra-long time window simulations of 3.865 × 106ps we observe the statistics of rogue waves in optical fibres with an unprecedented level of detail and accuracy, unambiguously establishing the long-ranged character of the rogue wave power-distribution function over seven orders of magnitude.

Rogue wave generation by inelastic quasi-soliton collisions in optical fibres

Purpose: The purpose of this paper is to investigate the use of 802.11e MAC to resolve the transmission control protocol (TCP) unfairness. Design/methodology/approach: The paper shows how a TCP sender may adapt its transmission rate using the number of hops and the standard deviation of recently measured round-trip times to address the TCP unfairness. Findings: Simulation results show that the proposed techniques provide even throughput by providing TCP fairness as the number of hops increases over a wireless mesh network (WMN). Research limitations/implications: Future work will examine the performance of TCP over routing protocols, which use different routing metrics. Other future work is scalability over WMNs. Since scalability is a problem with communication in multi-hop, carrier sense multiple access (CSMA) will be compared with time division multiple access (TDMA) and a hybrid of TDMA and code division multiple access (CDMA) will be designed that works with TCP and other traffic. Finally, to further improve network performance and also increase network capacity of TCP for WMNs, the usage of multiple channels instead of only a single fixed channel will be exploited. Practical implications: By allowing the tuning of the 802.11e MAC parameters that have previously been constant in 802.11 MAC, the paper proposes the usage of 802.11e MAC on a per class basis by collecting the TCP ACK into a single class and a novel congestion control method for TCP over a WMN. The key feature of the proposed TCP algorithm is the detection of congestion by measuring the fluctuation of RTT of the TCP ACK samples via the standard deviation, plus the combined the 802.11e AIFS and CWmin allowing the TCP ACK to be prioritised which allows the TCP ACKs will match the volume of the TCP data packets. While 802.11e MAC provides flexibility and flow/congestion control mechanism, the challenge is to take advantage of these features in 802.11e MAC. Originality/value: With 802.11 MAC not having flexibility and flow/congestion control mechanisms implemented with TCP, these contribute to TCP unfairness with competing flows. © Emerald Group Publishing Limited.

Marc A. Eberhard

Papers

Hopping transport on a fractal: ac conductivity of porous silicon.

Adaptive Sending Rate Over Wireless Mesh Networks Using SNR

Soliton's eigenvalue based analysis on the generation mechanism of rogue wave phenomenon in optical fibers exhibiting weak third order dispersion.

Rogue wave generation by inelastic quasi-soliton collisions in optical fibres

Implementing an adaptive TCP fairness while exploiting 802.11e over wireless mesh networks