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Three-dimensional short-crested water waves are known to host harmonic resonances (HRs). Their existence depends on their sporadicity versus their persistency. Previous studies, using a unique yet hybrid solution, suggested that HRs exhibit sporadic instability, with the domain of instability exhibiting a bubble-like structure which experiences a loss of stability followed by a re-stabilization. Through the calculation of their complete multiple solution structures and normal forms, we discuss the particular harmonic resonance (2,6). The (2,6) resonance was chosen, not only because it is of lower order, and thus more likely to be significant, but also because it is representative of a fully developed three-dimensional water wave field. Its appearance, growth rate and persistency are discussed. On our converged solutions, we show that, at an incidence angle for which HR (2,6) occurs, the associated superharmonic instability is no longer sporadic. It was also found that the multiple solution operates a subcritical pitchfork bifurcation, so regardless of the value of the control parameter, the wave steepness, a stable branch of the solution always exists. As a result, the analysis reveals two competing processes that either provoke and enhance HRs, or inhibit their appearance and development.
The study applies a two-dimensional adaptive mesh refinement (AMR) method to estimate the coordinates of the locations of the centre of vortices in steady, incompressible flow around a square cylinder placed within a channel. The AMR method is robust and low cost, and can be applied to any incompressible fluid flow. The considered channel has a blockage ratio of $1/8$. The AMR is tested on eight cases, considering flows with different Reynolds numbers ($5\le Re\le 50$), and the estimated coordinates of the location of the centres of vortices are reported. For all test cases, the initial coarse meshes are refined four times, and the results are in good agreement with the literature where a very fine mesh was used. Furthermore, this study shows that the AMR method can capture the location of the centre of vortices within the fourth refined cells, and further confirms an improvement in the estimation with more refinements.
Complicated option pricing models attract much attention in financial industries, as they produce relatively better accurate values by taking into account more realistic assumptions such as market liquidity, uncertain volatility and so forth. We propose a new hybrid method to accurately explore the behaviour of the nonlinear pricing model in illiquid markets, which is important in financial risk management. Our method is based on the Newton iteration technique and the Fréchet derivative to linearize the model. The linearized equation is then discretized by a differential quadrature method in space and a quadratic trapezoid rule in time. It is observed through computations that the accurate solutions for the model emerge using very few grid points and time elements, compared with the finite difference method in the literature. Furthermore, this method also helps to avoid consideration of the convergence issues of the Newton approach applied to the nonlinear algebraic system containing many unknowns at each time step if an implicit method is used in time discretization. It is important to note that the Fréchet derivative supports to enhance the convergence order of the proposed iterative scheme.
This chapter focuses on experimental techniques in the micro/nanoscale thermal radiation. The contents in the chapter are divided into two parts based on either far- or near-field measurement. The contents mainly involve far-field Fourier transform infrared microscopes, near-filed scanning thermal microscopy, and near-field thermal radiation instrument. We will review some outstanding experiments performed by different research groups for measuring the properties of micro/nanoscale thermal radiation. This chapter can be served as a guideline for researchers to design the experimental setups.
These years, we have witnessed great progress in manipulating radiative properties of thermal radiation, including angular, spectral, and polarized responses, via tailoring the light–matter interaction by taking advantages of designed nanostructures, metamaterials or metasurfaces, novel 2D materials, or even anisotropic materials. This chapter will review and give a detailed introduction of several manipulating mechanisms based on different types of materials, giving a comprehensive view of recent progress of radiative property engineering.
This chapter will focus on some important theories in micro/nanoscale thermal radiation, which are the basis of this area and become the fundamentals of other chapters in the books. The contents mainly involve electromagnetic wave theory, fluctuation dissipation theorem, and near-field thermal radiation. Brief derivation, solving the process and analysis method will be presented.
This chapter will cover a variety of methods, especially numerical methods of rigorous coupled-wave analysis and finite-difference time-domain solution. These methods are widely used in solving the problems of the micro/nanoscale thermal radiation. It is important and will give students hands-on experience in numerical simulations.
With the great development of theory, experiment, and manipulation of micro/nanoscale thermal radiation, several advanced applications emerge and show promising prospects in high-efficiency energy harvest/conversion such as angular/spectral selective or wideband absorber, thermophotovoltaics, or heat management implements such as radiative cooling, thermal camouflage, cloaking, and illusion. This chapter will give a brief introduction of these state-of-art technologies on the basis of theory of micro/nanoscale thermal radiation.
In this chapter, a summary of numerical algorithms solving the radiative transfer equation (RTE) is presented. These algorithms could be roughly classified into two categories. The one is ray-tracing methods, including the Zone method, Monte Carlo method, and discrete transfer method. The stochastic approach of Monte Carlo codes is widely used, since its flexible applicability to arbitrary multidimensional configurations. The others are methods based on the discretization of the differential form of RTE, including the spherical harmonics method, discrete ordinates method, and finite volume method.
At micro/nanoscale, the general principles of the thermal radiation are failed to solve or explain the majority of radiative problems or phenomena. This chapter will first point out the limitations and reasons of the general principles of thermal radiation by introducing a typical example. Then, some basic concepts, including the role of energy carriers such as photons, electrons, and phonon will be introduced first, followed by the brief introduction of the corresponding governing equations and the influence mechanism in radiative properties. Next, we would like to give a fundamental framework and chart review from macro- to nanoscalethermal radiation, aiming to make the relation and difference between macro- and nanothermal radiation more distinct. Finally, the development of micro/nanoscale thermal radiation in the last decades will be summarized as well.
The radiative transfer equation (RTE) is the governing equation of radiation propagation in participating media, which plays a central role in the analysis of radiative transfer in gases, semitransparent liquids and solids, porous materials, and particulate media, and is important in many scientific and engineering disciplines. This chapter will give a detailed introduction of the RTE. The microphysical derivation and the physical meaning of the relating quantities will be given. Besides, the relationship between the RTE and Maxwell’s equation will also be discussed and deduced as well, to build a comprehensive understanding of the RTE.
Thermal radiation is a ubiquitous aspect of nature, and this subject has developed for several centuries. In order to build a framework of macroscale thermal radiation, this chapter will give brief introductions of some fundamental theories and definitions of basic concepts of thermal radiation, such as blackbody radiation, radiative interactions at a surface, and radiative exchange between two or more surfaces. Besides, gas radiation as an important direction of thermal radiation will be introduced, including the molecular radiation theory, some gas spectral models, and some useful results in engineering applications.
Macrothermal radiation theory and analysis methods have been widely used in several real applications, such as heat transfer processes in the industrial boiler, radiant heat exchanger design, solar-thermal conversion in solar power plants, and so on. This chapter will cover the applications associated with macrothermal properties control, and some typical application examples will be given, hoping to offer a guidance in engineering applications.