A new approach to hyperbolic inverse problems

We present a modification of the BC-method in the inverse hyperbolic problems. The main novelty is the study of the restrictions of the solutions to the characteristic surfaces instead of the fixed time hyperplanes. The main result is that the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely determines the coefficients of the self-adjoint hyperbolic operator up to a diffeomorphism and a gauge transformation. In this paper we prove the crucial local step. The global step of the proof will be presented in the forthcoming paper.Comment: We corrected the proof of the main Lemma 2.1 by assuming that potentials A(x),V(x) are real value

Inverse Scattering for Gratings and Wave Guides

We consider the problem of unique identification of dielectric coefficients for gratings and sound speeds for wave guides from scattering data. We prove that the "propagating modes" given for all frequencies uniquely determine these coefficients. The gratings may contain conductors as well as dielectrics and the boundaries of the conductors are also determined by the propagating modes.Comment: 12 page

Formation of hot tear under controlled solidification conditions

Aluminum alloy 7050 is known for its superior mechanical properties, and thus finds its application in aerospace industry. Vertical direct-chill (DC) casting process is typically employed for producing such an alloy. Despite its advantages, AA7050 is considered as a "hard-to-cast" alloy because of its propensity to cold cracking. This type of cracks occurs catastrophically and is difficult to predict. Previous research suggested that such a crack could be initiated by undeveloped hot tears (microscopic hot tear) formed during the DC casting process if they reach a certain critical size. However, validation of such a hypothesis has not been done yet. Therefore, a method to produce a hot tear with a controlled size is needed as part of the verification studies. In the current study, we demonstrate a method that has a potential to control the size of the created hot tear in a small-scale solidification process. We found that by changing two variables, cooling rate and displacement compensation rate, the size of the hot tear during solidification can be modified in a controlled way. An X-ray microtomography characterization technique is utilized to quantify the created hot tear. We suggest that feeding and strain rate during DC casting are more important compared with the exerted force on the sample for the formation of a hot tear. In addition, we show that there are four different domains of hot-tear development in the explored experimental window-compression, microscopic hot tear, macroscopic hot tear, and failure. The samples produced in the current study will be used for subsequent experiments that simulate cold-cracking conditions to confirm the earlier proposed model.This research was carried out within the Materials innovation institute (www.m2i.nl) research framework, project no. M42.5.09340

High-Density Genotypes of Inbred Mouse Strains: Improved Power and Precision of Association Mapping.

Human genome-wide association studies have identified thousands of loci associated with disease phenotypes. Genome-wide association studies also have become feasible using rodent models and these have some important advantages over human studies, including controlled environment, access to tissues for molecular profiling, reproducible genotypes, and a wide array of techniques for experimental validation. Association mapping with common mouse inbred strains generally requires 100 or more strains to achieve sufficient power and mapping resolution; in contrast, sample sizes for human studies typically are one or more orders of magnitude greater than this. To enable well-powered studies in mice, we have generated high-density genotypes for ∼175 inbred strains of mice using the Mouse Diversity Array. These new data increase marker density by 1.9-fold, have reduced missing data rates, and provide more accurate identification of heterozygous regions compared with previous genotype data. We report the discovery of new loci from previously reported association mapping studies using the new genotype data. The data are freely available for download, and Web-based tools provide easy access for association mapping and viewing of the underlying intensity data for individual loci

Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow

We compute the sum of the positive Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow. The computation is based on the analytic Riemann-Roch Theorem and uses a comparison of determinants of flat and hyperbolic Laplacians when the underlying Riemann surface degenerates.Comment: Minor corrections. To appear in Publications mathematiques de l'IHE

Data and videos for ultrafast synchrotron X-ray imaging studies of metal solidification under ultrasound.

The data presented in this article are related to the paper entitled 'Ultrafast synchrotron X-ray imaging studies of microstructure fragmentation in solidification under ultrasound' [Wang et al., Acta Mater. 144 (2018) 505-515]. This data article provides further supporting information and analytical methods, including the data from both experimental and numerical simulation, as well as the Matlab code for processing the X-ray images. Six videos constructed from the processed synchrotron X-ray images are also provided

Understanding the highly dynamic phenomena in ultrasonic melt processing by ultrafast synchrotron x-ray imaging

In this paper, we present some highlighted findings from our recent research on real-time and in situ studies of the fundamentals of ultrasonic melt processing, including (1) ultrasonic bubble implosion, oscillation in liquid and semi-liquid (semi-solid) metals and their interactions with the growing solidifying phases; (2) enhanced acoustic metal flow and their impact on the liquid-solid metal interface. The real time experimental phenomena were interpreted with the aid of calculating the propagation of acoustic pressure in liquid metals using the Helmholtz equation and bubble wall pressure and velocity profile during bubble oscillation using the classical Gilmore model. The research provides unambiguous real-time evidence and robust theoretical interpretation in elucidating the dominant mechanisms of microstructure fragmentation and refinement in solidification under ultrasound

Effect of water temperature and induced acoustic pressure on cavitation erosion behaviour of aluminium alloys

Data availability: The raw/processed data required to reproduce these findings are available from the corresponding author on request.Copyright © 2023 The Author(s). Cavitation erosion is a major challenge for marine and fluid machinery systems. This study investigated the erosion performance of two as-cast aluminium alloys exposed to acoustic cavitation in water at temperatures of 10–50 °C and those were then compared with an extruded wrought alloy tested specifically at the temperature of maximum erosion. The results showed that the as-cast A380 alloy displayed exceptional resistance to cavitation erosion, with the lowest mass loss and surface roughness. This finding suggests that the as-cast A380 alloy is a suitable choice for lightweight, high-performance components in applications where cavitation resistance is critical.This work was financially sponsored by the PAAM (grants EP/W006774/1, EP/W00593X/1 and EP/W006154/1), UltraMelt2 (grants EP/R011001/1, EP/R011095/1 and EP/R011044/1) and EcoUltra2D (grants EP/R031401/1, EP/R031665/1, EP/R031819/1, EP/R031975/1) projects funded by the UK Engineering and Physical Sciences Research Council (EPSRC)

In situ synchrotron x-ray study of ultrasound cavitation and its effect on solidification microstructures

Considerable progress has been made in studying the mechanism and effectiveness of using ultrasound waves to manipulate the solidification microstructures of metallic alloys. However, uncertainties remain in both the underlying physics of how microstructures evolve under ultrasonic waves, and the best technological approach to control the final microstructures and properties. We used the ultrafast synchrotron X-ray phase contrast imaging facility housed at the Advanced Photon Source, Argonne National Laboratory, US to study in situ the highly transient and dynamic interactions between the liquid metal and ultrasonic waves/bubbles. The dynamics of ultrasonic bubbles in liquid metal and their interactions with the solidifying phases in a transparent alloy were captured in situ. The experiments were complemented by the simulations of the acoustic pressure field, the pulsing of the bubbles, and the associated forces acting onto the solidifying dendrites. The study provides more quantitative understanding on how ultrasonic waves/bubbles influence the growth of dendritic grains and promote the grain multiplication effect for grain refinement