Time delay in the strong field limit for null and timelike signals and its simple interpretation

Gravitational lensing can happen not only for null signals but also timelike signals such as neutrinos and massive gravitational waves in some theories beyond GR. In this work we study the time delay between different relativistic images formed by signals with arbitrary asymptotic velocity v in general static and spherically symmetric spacetimes. A perturbative method is used to calculate the total travel time in the strong field limit, which is found to be a quasi-power series of the small parameter $$a=1-b_c/b$$ a = 1 - b c / b where b is the impact parameter and $$b_c$$ b c is its critical value. The coefficients of the series are completely fixed by the behaviour of the metric functions near the particle sphere $$r_c$$ r c and only the first term of the series contains a weak logarithmic divergence. The time delay $$\Delta t_{n,m}$$ Δ t n , m to the leading non-trivial order was shown to equal the particle sphere circumference divided by the local signal velocity and multiplied by the winding number and the redshift factor. By assuming the Sgr A* supermassive black hole is a Hayward one, we were able to validate the quasi-series form of the total time, and reveal the effects of the spacetime parameter l, the signal velocity v and the source/detector coordinate difference $$\Delta \phi _{sd}$$ Δ ϕ sd on the time delay. It is found that as l increases from 0 to its critical value $$l_c$$ l c , both $$r_c$$ r c and $$\Delta t_{n,m}$$ Δ t n , m decrease. The variation of $$\Delta t_{n+1,n}$$ Δ t n + 1 , n for l from 0 to $$l_c$$ l c can be as large as $$7.2\times 10^1$$ 7.2 × 10 1 [s], whose measurement then can be used to constrain the value of l. While for ultra-relativistic neutrino or gravitational wave, the variation of $$\Delta t_{n,m}$$ Δ t n , m is too small to be resolved. The dependence of $$\Delta t_{n,-n}$$ Δ t n , - n on $$\Delta \phi _{sd}$$ Δ ϕ sd shows that to temporally resolve the two sequences of images from opposite sides of the lens, $$|\Delta \phi _{sd}-\pi |$$ | Δ ϕ sd - π | has to be larger than a certain value, or equivalently if $$|\Delta \phi _{sd}-\pi |$$ | Δ ϕ sd - π | is small, the time resolution of the observatories has to be good.

Near Surface Velocity Estimation Using GPR Data: Investigations by Numerical Simulation, and Experimental Approach with AVO Response

The velocity of near-surface materials is one of the most important for Ground-Penetrating Radar (GPR). In the study, we evaluate the options for determining the GPR velocity to measure the accuracy of velocity approximations from the acquired GPR data at an experimental site in Hangzhou, China. A vertical profile of interval velocities can be estimated from each common mid-point (CMP) gather using velocity spectrum analysis. Firstly, GPR data are acquired and analyzed using the popular method of hyperbola fitting which generated surprisingly high subsurface signal velocity estimates while, for the same profile, the Amplitude variation with offset (AVO) analysis of the GPR data (using the same hyperbola fitting method) generate a more reasonable subsurface signal velocity estimate. Several necessary processing steps are applied both for CMP and AVO analysis. Furthermore, experimental analysis is conducted on the same test site to get velocities of samples based on dielectric constant measurement during the drilling process. Synthetic velocities generated by AVO analysis are validated by the experimental velocities which confirmed the suitability of velocity interpretations.

Causal hierarchy in modified gravity

We investigate the causal hierarchy in various modified theories of gravity. In general relativity the standard causal hierarchy, (key elements of which are chronology, causality, strong causality, stable causality, and global hyperbolicity), is well-established. In modified theories of gravity there is typically considerable extra structure, (such as: multiple metrics, aether fields, modified dispersion relations, Hořava-like gravity, parabolic propagation, etcetera), requiring a reassessment and rephrasing of the usual causal hierarchy. We shall show that in this extended framework suitable causal hierarchies can indeed be established, and discuss the implications for the interplay between “superluminal” propagation and causality. The key distinguishing feature is whether the signal velocity is finite or infinite. Preserving even minimal notions of causality in the presence of infinite signal velocity requires the aether field to be both unique and hypersurface orthogonal, leading us to introduce the notion of global parabolicity.

Computational Study of Pump Turbine: Partial Load Operations

The performance of a pump-turbine under partial flow rates, 85%, 75%, and 65%, is studied using the LES model. The power signal, velocity, vorticity, and pressure field is presented over the blades and throughout the draft tube. Pressure fluctuations are probed at various locations over the wall of the draft tube. Examining the flow field in the blade region can provide further insights into the system performance. Flow-induced pressure fluctuations can disrupt system stability. For this turbine, a strong swirling region is observed around the draft tube walls, causing pressure fluctuations. The size and intensity of this region decrease with the flow rate. A vortex rope is present in all cases. At the design point, the strength is constant throughout the draft tube. However, at partial load, the rope is weakened along the draft tube. Between the region dominated by the vortex rope and the wall, there is a swirling shear layer, which moves closer to the wall as the flow rate decreases. Both the magnitude of pressure fluctuations at the wall and the pressure difference over the blade decrease with the flow rate. The decreased pressure differences over the blade represent less power produced, and the decline in fluctuation magnitude at the wall represents more system stability. For this turbine, there appears to be a trade-off between power and strength of pressure fluctuations.

Study on Doppler characteristics of underwater bistatic reverberation

Active sonar has two typical types of geometry configuration respectively named monostatic and bistatic like a radar system. In the monostatic scenario, co-located underwater transducers transmit and receive sound energy, while in a bistatic situation the transducers are physically separated. Both object detection and identification can be significantly enhanced through utilization of the additional dimension provided by a bistatic geometry. So, more people care about bistatic scattering characteristics of underwater objects as well as bistatic reverberation in recent years. In this paper, Doppler characteristics of bistatic reverberation generated by moving transmitter and receiver are studied. Theoretical formulism for receiving frequency of bistatic reverberation is derived in case of a tone signal being transmitted. Further analysis shows bistatic reverberation is more complicated than monostatic reverberation when Doppler is concerned. In monostatic case, the Doppler frequency shift of reverberation relates to centre frequency of the tone signal, velocity of the transmitter as well as the arriving direction. While in bistatic situation, it varies not only with the above factors, but also the locations, moving directions, velocities of both transmitter and receiver, and also the arriving time of the reverberation, which makes extraction and utilization of Doppler information more difficult.

Assessing Ground Penetrating Radar's Ability to Image Subsurface Characteristics of Icy Debris Fans in Alaska and New Zealand

Icy debris fans have recently been described as fan shaped depositional landforms associated with (or formed during) deglaciation, however, the subsurface characteristics remain essentially undocumented. We used ground penetrating radar (GPR) to non-invasively investigate the subsurface characteristics of icy debris fans (IDFs) at McCarthy Glacier, Alaska, USA and at La Perouse Glacier, South Island of New Zealand. IDFs are largely unexplored paraglacial landforms in deglaciating alpine regions at the mouths of bedrock catchments between valley glaciers and icecaps. IDFs receive deposits of mainly ice and minor lithic material through different mass-flow processes, chiefly ice avalanche and to a lesser extent debris flow, slushflow, and rockfall. We report here on the GPR signal velocity observed from 15 different wide-angle reflection/refraction (WARR) soundings on the IDFs and on the McCarthy Glacier; the effect of GPR antenna orientation relative to subsurface reflections; the effect of spreading direction of the WARR soundings relative to topographic contour; observed differences between transverse electric (TE) and transverse magnetic (TM) antenna polarization; and a GPR profile extending from the McCarthy Glacier onto an IDF. Evaluation of the WARR soundings indicates that the IDF deposits have a GPR signal velocity that is similar to the underlying glacier, and that the antenna polarization and orientation did not prevent identification of GPR reflections. The GPR profile on the McCarthy Glacier indicates that the shallowest material is layered, decreases in thickness down fan, and has evidence of brittle failure planes (crevasses). The GPR profile and WARR soundings collected in 2013 indicate that the thickness of the McCarthy Glacier is 82 m in the approximate middle of the cirque and that the IDF deposits transition with depth into flowing glacial ice.

Spectral Particularities of Femtosecond Optical Pulses Propagating in Dispersive Medium

We have proposed a refined solution of the wave equation for a dispersive medium without restriction on the duration of an optical pulse. We apply a series of elementary wave packages (EWP) to the representation of superwideband signals (fs pulse). We investigate peculiarities of the propagation of waves with low and high frequencies through the one-resonance medium. We show the existence of a “precursor” for fs optical pulses. We propose a formula for the optical signal velocity (OSV). Its value does not exceed the light velocity in vacuum. We have designed a method of adaptation of EWP-pulses to time-domain spectroscopy.