يعرض 1 - 10 نتائج من 402 نتيجة بحث عن '"wave propagation"', وقت الاستعلام: 1.29s تنقيح النتائج
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    المؤلفون: Baumstark, Julian, Jahnke, Tobias

    المصدر: ISSN: 2365-662X.

    الوصف: High-frequency wave propagation is often modelled by nonlinear Friedrichs systems where both the differential equation and the initial data contain the inverse of a small parameter ε, which causes oscillations with wavelengths proportional to $\varepsilon$ in time and space. A prominent example is the Maxwell–Lorentz system, which is a well-established model for the propagation of light in nonlinear media. In diffractive optics, such problems have to be solved on long time intervals with length proportional to $1/\varepsilon$. Approximating the solution of such a problem numerically with a standard method is hopeless, because traditional methods require an extremely fine resolution in time and space, which entails unacceptable computational costs. A possible alternative is to replace the original problem by a new system of PDEs which is more suitable for numerical computations but still yields a sufficiently accurate approximation. Such models are often based on the slowly varying envelope approximation or generalizations thereof. Results in the literature state that the error of the slowly varying envelope approximation is of $\cal{O}(\varepsilon)$. In this work, however, we prove that the error is even proportional to $\varepsilon^2$, which is a substantial improvement, and which explains the error behavior observed in numerical experiments. For a higher-order generalization of the slowly varying envelope approximation we improve the error bound from $\cal{O}(\varepsilon^2)$ to $\cal{O}(\varepsilon^3)$. Both proofs are based on a careful analysis of the nonlinear interaction between oscillatory and non-oscillatory error terms, and on a priori bounds for certain “parts” of the approximations which are defined by suitable projections. As an important technical tool we use an advantageous transformation of the coefficient functions which appear in the approximations.

    وصف الملف: application/pdf

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    الوصف: Soil moisture variation is complex and depends on a range of factors, which complicates the formulation of recommendations for GPR surveys. Low amounts of soil moisture produced GPR data of higher quality. However, precipitation rates as well as chronological sequence of precipitation/thawing processes and the GPR survey are of importance. Winter months can offer favorable conditions for GPR surveys if temperatures remain negative over a prolonged time period, allowing for frost to build in the ground. Results of the Borre Monitoring Project (BMP) are valid only for sites with similar settings as Borre; the monitoring approach, however, can be transferred to larger regions with more representative sites.

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    المؤلفون: Ulloa, Rafael Zamorano

    الوصف: Detailed electrodynamic descriptions of the fundamental workings of microwave heating devices are presented. We stress that all results come from Maxwell equations and the boundary conditions (BC). We analyze one by one the principal components of a microwave heater; the cooking chamber, the waveguide, and the microwave sources, either klystron or magnetron. The boundary conditions at the walls of the resonant cavity and at the interface air/surface of the food are given and show how relevant the BC are to understand how the microwaves penetrate the nonconducting, electric polarizable specimen. We mention the application of microwaving waste plastics to obtain a good H2 quantity that could be used as a clean energy source for other machines. We obtained trapped stationary microwaves in the resonant cavity and traveling waves in the waveguides. We show 3D plots of the mathematical solutions and agree quite well with experimental measurements of hot/cold patterns. Simulations for cylindrical cavities are shown. The radiation processes in klystrons and magnetrons are described with some detail in terms of the accelerated electrons and their trajectories. These fields are sent to the waveguides and feed the cooking chamber. Whence, we understand how a meal or waste plastic, or an industrial sample is microwave heated.