New exact traveling wave solutions for the Klein–Gordon–Zakharov equations

AbstractBased on the extended hyperbolic functions method, we obtain the multiple exact explicit solutions of the Klein–Gordon–Zakharov equations. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for u and n, (b) the solitary wave solutions of kink-type for u and bell-type for n, (c) the solitary wave solutions of a compound of the bell-type and the kink-type for u and n, (d) the singular traveling wave solutions, (e) periodic traveling wave solutions of triangle function types, and solitary wave solutions of rational function types. We not only rederive all known solutions of the Klein–Gordon–Zakharov equations in a systematic way but also obtain several entirely new and more general solutions. The variety of structures of the exact solutions of the Klein–Gordon–Zakharov equations is illustrated

A model of riots dynamics: shocks, diffusion and thresholds

We introduce and analyze several variants of a system of differential equations which model the dynamics of social outbursts, such as riots. The systems involve the coupling of an explicit variable representing the intensity of rioting activity and an underlying (implicit) field of social tension. Our models include the effects of exogenous and endogenous factors as well as various propagation mechanisms. From numerical and mathematical analysis of these models we show that the assumptions made on how different locations influence one another and how the tension in the system disperses play a major role on the qualitative behavior of bursts of social unrest. Furthermore, we analyze here various properties of these systems, such as the existence of traveling wave solutions, and formulate some new open mathematical problems which arise from our work

Picosecond amplification and absorption in the XeCl laser

Imperial Users onl

Protection of Future Electricity Systems

The electrical energy industry is undergoing dramatic changes: massive deployment of renewables, increasing share of DC networks at transmission and distribution levels, and at the same time, a continuing reduction in conventional synchronous generation, all contribute to a situation where a variety of technical and economic challenges emerge. As the society’s reliance on electrical power continues to increase as a result of international decarbonisation commitments, the need for secure and uninterrupted delivery of electrical energy to all customers has never been greater. Power system protection plays an important enabling role in future decarbonized energy systems. This book includes ten papers covering a wide range of topics related to protection system problems and solutions, such as adaptive protection, protection of HVDC and LVDC systems, unconventional or enhanced protection methods, protection of superconducting transmission cables, and high voltage lightning protection. This volume has been edited by Adam Dyśko, Senior Lecturer at the University of Strathclyde, UK, and Dimitrios Tzelepis, Research Fellow at the University of Strathclyde

Study and development of turbofan nacelle modifications to minimize fan-compressor noise radiation. Volume 2 - Acoustic lining development, 1 May 1967 - 1 November 1969

Development of acoustic lining for turbofan nacelle modification to minimize fan compressor noise radiatio

Assessing blood brain barrier dynamics or identifying or measuring selected substances, including ethanol or toxins, in a subject by analyzing Raman spectrum signals

A non-invasive method for analyzing the blood-brain barrier includes obtaining a Raman spectrum of a selected portion of the eye and monitoring the Raman spectrum to ascertain a change to the dynamics of the blood brain barrier.Also, non-invasive methods for determining the brain or blood level of an analyte of interest, such as glucose, drugs, alcohol, poisons, and the like, comprises: generating an excitation laser beam at a selected wavelength (e.g., at a wavelength of about 400 to 900 nanometers); focusing the excitation laser beam into the anterior chamber of an eye of the subject so that aqueous humor, vitreous humor, or one or more conjunctiva vessels in the eye is illuminated; detecting (preferably confocally detecting) a Raman spectrum from the illuminated portion of the eye; and then determining the blood level or brain level (intracranial or cerebral spinal fluid level) of an analyte of interest for the subject from the Raman spectrum. In certain embodiments, the detecting step may be followed by the step of subtracting a confounding fluorescence spectrum from the Raman spectrum to produce a difference spectrum; and determining the blood level and/or brain level of the analyte of interest for the subject from that difference spectrum, preferably using linear or nonlinear multivariate analysis such as partial least squares analysis. Apparatus for carrying out the foregoing methods are also disclosed

Silicon photonic modulators for PAM transmissions

High-speed optical interconnects are crucial for both data centers and high performance computing systems. High power consumption and limited device bandwidth have hindered the move to higher optical transmission speeds. Integrated optical transceivers in silicon photonics (SiP) using pulse-amplitude modulation (PAM) are a promising solution to increase data rates. In this paper, we review recent progress in SiP for PAM transmissions. We focus on materials and technologies available CMOS-compatible photonics processes. Performance metrics of SiP modulators and crucial considerations for high-speed PAM transmissions are discussed. Various driving strategies to achieve optical PAM signals are presented. Some of the state-of-the-art SiP PAM modulators and integrated transmitters are reviewed

Direct Nonlinear Optics Measurements Of Raman Gain In Bulk Glasses And Estimates Of Fiber Performance

The need for more bandwidth in communications has stimulated the search for new fiberizable materials with properties superior to fused silica which is the current state-of-the-art. One of the key properties is Raman gain by which a pump beam amplifies a signal beam of longer wavelength. An apparatus capable of directly measuring the spectral dependence and absolute magnitude of the material Raman gain coefficient using nonlinear optics techniques has been built. Using radiation from a 1064 nm Nd:YAG laser as the pump and from a tunable Optical Parametric Generator and Amplifier as the signal, the Raman gain spectrum was measured for different families of glass samples with millimeter thickness. A number of glass families were investigated. Tellurites with added oxides of tungsten, niobium, and thallium produced the largest Raman gain coefficients of any oxide family reported to date, typically 30-50 times higher than that of fused silica. On the other hand, phosphate families were found with spectrally broad Raman gain response, 5 times broader than fused silica and flat to [plus or minus] dB over the full spectral range in some compositions. Although the chalcogenides were found to photodamage easily, coefficients 50 - 80 times that of fused silica were measured. Finally, a numerical study was undertaken to predict the theoretical performance and noise properties of tellurite fibers for communications. Included in the computer modeling were linear loss; the interaction among multiple pumps and signals; forward and/or backward propagating pump beams; forward, backward and double Rayleigh scattering; noise properties of amplifiers; excess noise, etc. This led to a comparison of the optical signal-to-noise characteristics for Raman gain in a tellurite versus a silica fiber

Design and Construction of a Radio Frequency Plasma Device

We have constructed a radio frequency plasma device to study a wide range of phenomena including, power coupling between the plasma and the antenna and wave propagation. Our system includes a high vacuum chamber with mechanical and diffusion pumps, a radio frequency source magnetic field coils and a matching network

A MULTI-SCALE APPROACH TO FED-BATCH BIOREACTOR CONTROL

The rising energy costs, increased global competition in terms of both price and quality, and the need to make products in an environmentally benign manner have paved the way for the biological route towards manufacturing. Many of the products obtained by the biological route either cannot be produced, or are very difficult to obtain, by conventional manufacturing methods. Most of these products fall in the low volume/high value bracket, and it is estimated that the production of therapeutic proteins alone generated sales exceeding $25 billion in 2001. By increasing our understanding of these systems it may be possible to avoid some of the empiricism associated with the operation of (fed-)batch bioreactors. Considerable benefit, in terms of reduced product variability and optimal resource utilization could be achieved, and this work is a step in that direction.Biological reactors typically are governed by highly nonlinear behavior occuring on both a macroscopic reactor scale and a microscopic cellular scale. Reactions taking place at these scales also occur at different rates so that the bioreactor system is multi-scale both spatially and temporally. Since achievable controller performance in a model-based control scheme is dependent on the quality of the process model cite{mor89}, a controller based on a model that captures events occuring at both the reactor and cellular scales should provide superior performance when compared to a controller that employs a uniscale model. In the model considered for this work, the specific growth rate is used as a coupling parameter integrating the behavior of both scales. On the cellular level, flux distributions are used to describe cellular growth and product formation whereas a lumped-parameter reactor model provides the macroscopic process representation.The control scheme for the fed-batch bioreactor is implemented in two stages, and the substrate feed rate serves as the manipulated variable. Initially, a constrained optimal control problem is solved off-line, in order to determine the manipulated variable profile that maximizes the end of batch product concentration for the product of interest, while maintaining apre-specified, fixed final volume. The next step involves tracking of the optimal control trajectory, in closed-loop operation. The Shrinking Horizon Model Predictive Control (SHMPC) framework is used to minimize the projected deviations of the controlled variable from the specified trajectories. At every time step, the original nonlinear model is linearized and the optimization problem is formulated as a quadratic program, that includes constraints on the manipulated input and the final volume. Finally, the performance of the controller is evaluated, and strategies for disturbance compensation are presented. The results of this approach are presented for ethanol production in a baker's yeast fermentation case study