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Spectroscopy
Published in Michael B. Smith, A Q&A Approach to Organic Chemistry, 2020
These two parameters are inversely proportional, by the equation c = νλ, where c is the speed of light (3 × 108 m/sec). In general, a high frequency is related to a small wavelength. Which is higher in energy, infrared light or ultraviolet light?
Planar Virtual Sound Barriers
Published in Qiu Xiaojun, An Introduction to Virtual Sound Barriers, 2019
Unlike the surface control system, the half wavelength of the sound at f20 is flat for the boundary control systems when the interval between the secondary sources is small, and starts to increase when the interval is about 0.2 m (one or half the short side length of the opening). A small wavelength means a high frequency. The flat half wavelength of the sound at f20 with the small secondary source intervals indicates that there exists an upper-limit frequency that is the highest frequency at which the sound radiation can be effectively reduced with sufficient secondary sources.
CFD Modeling of Convection Flow in Pan Cooking
Published in Da-Wen Sun, Computational Fluid Dynamics in Food Processing, 2018
The value of the heat flux or heat generation, as the heat source, is required for the CFD analysis. Since the heat flux changes according to the heating conditions, it is necessary to measure the heat flux whenever the heating condition changes. However, if the heat generation in IH can be estimated using electromagnetic field analysis (EFA), the heat flux need not be measured. Thus, in IH, the heat generation distribution in the pan was estimated by EFA using commercial software (JMAG Studio, USA). CFD was customized by FORTRAN programming to introduce the heat generation into the CFD calculation. By a so-called skin effect, the high-frequency current or the electromagnetic field is limited to the surface of the conductor. In addition, since the boiling calculation was not possible with the software used at the time of the study (STORM/CFD2000), it was customized in FORTRAN programming by using the temperature recovery method as follows. The temperature fluctuation with the boiling point (Tb), ΔT = T − Tb, was calculated at each point in the pan. Thus, if ΔT > 0, the sensible heat over the boiling point was considered to be released as latent heat, and this heat was added to the energy conservation law. Nowadays, the features of available computer simulation software, such as COMSOL Multiphysics, enable simulation of these phenomena without additional customization works.
Modeling and Fabrication Aspects of Cu- and Carbon Nanotube-Based Through-Silicon Vias
Published in IETE Journal of Research, 2021
Tanu Goyal, Manoj Kumar Majumder, Brajesh Kumar Kaushik
It is noticed that the resistance of TSV increases with frequency due to skin effect. Skin effect arises when a high-frequency current flows close to the surface of conductor due to the formation of eddy currents. This results in the current penetration through the conductors when frequency is varied. When the frequency is high enough such that the skin depth is smaller than the radius of the circular via-holes, the current starts to distribute unevenly and becomes crowded at the surface of the conductor. Hence, the resistance and inductance effectively increase and reduce with frequency [10]. where RTSV0 and LTSV0 are resistance and inductance of vias at 500 MHz frequency [10]. The lossy characteristics Rsub can be modeled as The current induced in the substrate rises as a result of high frequency that consequently reduces substrate resistance Rsub(f). The primary issue with this model was that it measured the resistance and inductance of large TSV structures but did not correlate them with the physical dimensions and material characteristics. Moreover, the model incorrectly ignores the substrate and oxide parasitic.
Impact of Polymer Liners on Crosstalk Induced Delay of Different TSV Shapes
Published in IETE Journal of Research, 2022
Maya Chandrakar, Manoj Kumar Majumder
The “skin effect” refers to the phenomenon in which high-frequency current flows near to the surface of a conductor due to the development of eddy current. Skin depth is obtained to model the TSV and bump resistances ( and ) with a non-uniform current distribution at high frequencies. Therefore, and (mentioned in Equation (1)) can be expressed as
Continuum model of two-dimensional crystal lattice of metamaterials
Published in Mechanics of Advanced Materials and Structures, 2019
Yahong Zhou, Peijun Wei, Yueqiu Li, Li Li
The lattice waves in the 2D crystal lattice of metamaterial have two acoustic branches and two optic branches. A low frequency bandgap between the acoustic branches and the optic branches appears. In order to describe the dispersive and bandgap characteristics of metamaterial, the equivalent classical continuum model requires the frequency-dependent mass density. Near the resonant frequency, the mass density may become negative or even infinite. To avoid the introduction of negative mass density, some continuum models, including the multiple displacement continuum model, strain gradient continuum model and the nonlocal gradient continuum model, are considered. By comparing the dispersive relation predicted by these continuum models with that predicted by the crystal lattice model of metamaterial, some conclusions can be drawn as follows. The multidisplacement continuum model avoids the frequency-dependent mass density by introducing additional degrees of freedom of micromotion. The dispersive curves predicted by the multidisplacement continuum model are in good agreement with those predicted by the crystal lattice model of metamaterial only at long wavelength range (near qL = 0). At the high frequency range, the deviation increases gradually as the wavelength decreases gradually.In general, the gradient continuum model without consideration of nonlocal effects can improve the prediction of multiple displacement continuum model and expand the frequency range where the prediction of the gradient continuum model well fit the dispersive relation of the crystal lattice model of metamaterial. However, the third-order gradient continuum model exhibits unstable nature as the frequency increases gradually. The fifth-order gradient continuum model is always stable in the whole Brillouin zone.By taking the nonlocal effects into consideration, the nonlocal gradient continuum model shows unconditional stable in the whole Brillouin zone. Not only that, by selecting suitable nonlocal parameters a1 and b1, the nonlocal gradient continuum model can better represent the dispersive relation and the bandgap characteristics of the metamaterial than the other continuum models considered.