We consider the electromagnetic (EM) perturbative effects produced by the high-frequency gravitational waves (HFGWs) in the GHz band in a special EM resonance system, which consists of fractal membranes, a Gaussian beam (GB) passing through a static magnetic field.It is predicted, under the synchroresonance condition, coherence modulation of the HFGWs to the preexisting transverse components of the GB produces the transverse perturbative photon flux (PPF),which has three novel and important properties: (1)The PPF has maximum at a longitudinal symmetrical surface of the GB where the transverse background photon flux (BPF) vanishes; (2) the resonant effect will be high sensitive to the propagating directions of the HFGWs; (3) the PPF reflected or transmitted by the fractal membrane exhibits a very small decay compared with very large decay of the much stronger BPF. Such properties might provide a new way to distinguish and display the perturbative effects produced by the HFGWs. We also discuss the high-frequency asymptotic behavior of the relic GWs in the microwave band and the positive definite issues of their energy-momentum pseudo-tensor .

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A coupling system between Gaussian type-microwave photon flux, static magnetic field and fractal membranes (or other equivalent microwave lenses) can be used to detect high-frequency gravitational waves (HFGWs) in the microwave band. We study the signal photon flux, background photon flux and the requisite minimal accumulation time of the signal in the coupling system. Unlike pure inverse Gertsenshtein effect (G-effect) caused by the HFGWs in the GHz band, the the electromagnetic (EM) detecting scheme (EDS) proposed by China and the US HFGW groups is based on the composite effect of the synchro-resonance effect and the inverse G-effect. Key parameters in the scheme include first-order perturbative photon flux (PPF) and not the second-order PPF; the distinguishable signal is the transverse first-order PPF and not the longitudinal PPF; the photon flux focused by the fractal membranes or other equivalent microwave lenses is not only the transverse first-order PPF but the total transverse photon flux, and these photon fluxes have different signal-to-noise ratios at the different receiving surfaces. Theoretical analysis and numerical estimation show that the requisite minimal accumulation time of the signal at the special receiving surfaces and in the background noise fluctuation would be ∼ 10 3 − 10 5 seconds for the typical laboratory condition and parameters of h r.m.s. ∼ 10 −26 − 10 −30 at 5GHz with bandwidth ∼1Hz. In addition, we review the inverse G-effect in the EM detection of the HFGWs, and it is shown that the EM detecting scheme based only on the pure inverse G-effect in the laboratory condition would not be useful to detect HFGWs in the microwave band. PACS numbers: 04.30Nk, 04.25Nx, 04.30Db, 04.80Nn a

This book provides a solid foundation to a number of important topics in mathematics of interest to science and engineering students. The authors' approach is simple and direct, the emphasis being on the analytical structure and applications of the material. The text is virtually self-contained, assuming only that the student has received a good basic course in ancillary mathematics. Each chapter contains a large number of worked examples, and concludes with problems for solution, with answers given in the back of the book. There is no comparable text that covers this material in such a concise form. This book will be of great value to undergraduates in physics, chemistry, theoretical biology, and in all engineering disciplines, as a source book of advanced mathematical methods, and also to postgraduate students as a revision text.

Under most models of the early universe evolution, high-frequency gravitational waves (HFGWs) were produced. They are referred to as “relic” high-frequency gravitational waves or HFRGWs and their detection and measurement could provide important information on the origin and development of our Universe – information that could not otherwise be obtained. So far three instruments have been built to detect and measure HFRGWs, but so far none of them has achieved the required sensitivity. This paper concerns another detector, originally proposed by Baker in 2000 and patented, which is based upon a recently discovered physical effect (the Li effect); this detector has accordingly been named the “Li-Baker detector.” The detector has been a joint development effort by the P. R. China and the United States HFGW research teams. A rigorous examination of the detector’s performance is important in the ongoing debate over the value of attempting to construct a Li-Baker detector and, in particular, an accurate prediction of its sensitivity in the presence of significant noise will decide whether the Li-Baker detector will be capable of detecting and measuring HFRGWs. The potential for useful HFRGW measurement is theoretically confirmed