Generation of short hard X-ray pulses of tailored duration using a M\"ossbauer source

We theoretically investigate a scheme for generations of single hard X-ray pulses of controllable duration in the range of 1 ns - 100 ns from a radioactive M\"ossbauer source. The scheme uses a magnetically perturbed $^{57}$FeBO$_3$ crystal illuminated with recoilless 14.4 keV photons from a radioisotope $^{57}$Co nuclide. Such compact X-ray source is useful for the extension of quantum optics to 10 keV energy scale which has been spotlighted in recent years. So far, experimental achievements are mostly performed in synchrotron radiation facilities. However, tabletop and portable hard X-ray sources are still limited for time-resolved measurements and for implementing coherent controls over nuclear quantum optics systems. The availability of compact hard X-ray sources may become the engine to apply schemes of quantum information down to the subatomic scale. We demonstrate that the present method is versatile and provides an economic solution utilizing a M\"ossbauer source to perform time-resolved nuclear scattering, to produce suitable pulses for photon storage and to flexibly generate X-ray single-photon entanglement.Comment: 8 pages, 6 figure

Influence of Curing Humidity on the Compressive Strength of Gypsum-Cemented Similar Materials

The analogous simulation experiment is widely used in geotechnical and mining engineering. However, systematic errors derived from unified standard curing procedure have been underestimated to some extent. In this study, 140 gypsum-cemented similar material specimens were chosen to study their curing procedure with different relative humidity, which is 10%–15%, 40%, 60%, and 80%, respectively. SEM microstructures and XRD spectra were adopted to detect the correlation between microstructures and macroscopic mechanical strength during curing. Our results indicated that the needle-like phases of similar materials began to develop in the early stage of the hydration process through intersecting with each other and eventually transformed into mat-like phases. Increase of humidity may inhibit the development of needle-like phases; thus the compressive strength changes more smoothly, and the time required for the material strength to reach the peak value will be prolonged. The peak strength decreases along with the increase of humidity while the humidity is higher than 40%; however, the reverse tendency was observed if the humidity was lower than 40%. Finally, we noticed that the material strength usually reaches the peak value when the water content continuously reduces and tends towards stability. Based on the above observation, a curing method determination model and experimental strength predication method for gypsum-cemented similar materials were proposed

Multiple positive solutions for functional dynamic equations on time scales

AbstractIn this paper, we study the following functional dynamic equation on time scales: {[Φ(uΔ(t))]∇+a(t)f(u(t),u(μ(t)))=0,t∈(0,T)T,u(t)=φ(t),t∈[−r,0)T,u(0)−B0(uΔ(0))=0,uΔ(T)=0, where Φ:R→R is an increasing homeomorphism and a positive homomorphism and Φ(0)=0. By using the well-known Leggett–Williams fixed point theorem, existence criteria for multiple positive solutions are established. An example is also given to illustrate the main results

Dark Matter Spike surrounding Supermassive Black Holes Binary and the nanohertz Stochastic Gravitational Wave Background

Recently, the NANOGrav, PPTA, EPTA and CPTA collaborations reported compelling evidence of the existence of the Stochastic Gravitational-Wave Background (SGWB). The amplitude and spectrum of this inferred gravitational-wave background align closely with the astrophysical predictions for a signal originating from the population of supermassive black-hole binaries. In light of these findings, we explore the possibility to detect dark matter spikes surrounding massive black holes, which could potentially impact the gravitational-wave waveform and modulate the SGWB. We demonstrate that the SMBH binary evolution induced by the combined effects of GW radiation and the dynamical friction of the dark matter spike exhibits detectable manifestations within the nHz frequency range of the SGWB.Comment: 5 pages, 1 figure. arXiv admin note: text overlap with arXiv:1408.3534 by other author

Positive Solutions for Third-Order p

We study the following third-order p-Laplacian functional dynamic equation on time scales: Φp(uΔ∇(t))∇+a(t)f(u(t),u(μ(t)))=0, t∈0,TT,  u(t)=φ(t),  t∈-r,0T,  uΔ(0)=uΔ∇(T)=0, and u(T)+B0(uΔ(η))=0. By applying the Five-Functional Fixed Point Theorem, the existence criteria of three positive solutions are established