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

State-of-the-art oriented review of CIRCUS

Mathematical procedures for CIRCUS, digital computer program which is based on built-in model library and is capable of time domain analysis of certain circuit

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

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

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

Ultrasonic processing of aluminium alloys above the liquidus: the role of Zr

© The Authors, 2020. Ultrasonic melt processing (USP) is gaining quite an interest in recent years due to the benefits of this technology to the melt quality and structure refinement. A number of mechanisms have been identified that govern the effects of USP at different stages of melt processing. Technologically it is advantageous to apply USP to the fluid melt rather than to a mushy solidifying alloy. In this case heterogeneous nucleation on available or activated/multiplied substrates is the main mechanism. Among these substrates, primary crystals of Al3Zr phase were shown to be potent and effective. This paper gives a review of the own research into the role of Al3Zr in structure refinement in various groups of Al alloys, from solid-solution type to hypereutectic. This overview includes the evidence of a possible eutectic reaction between Al and Al3Zr in Al-rich alloys, mechanisms of Al3Zr formation and refinement under USP (that enables these primary crystals to be active substrates for Al and some other primary phases), the role of USP in facilitating primary solidification of Al3Zr in the Al-Zr system, and the additional benefits of solute Ti presence. The paper is illustrated with the data obtained over the last 15 years of research led by the author.M2i (The Netherlands) for projects MC4.05215 and M11.5.11419 and EPSRC (The United Kingdom) for projects Ultra-Cast (Grant EP/L019884/1) and UltraMelt2 (Grant EP/R011095/1

Effect of V and N on the microstructure evolution during continuous casting of steel

Low Carbon (LC) steel is not expected to be sensitive to hot tearing and/or cracking while microalloyed steels are known for their high cracking sensitivity during continuous casting. Experience of the Direct Sheet Plant caster at Tata Steel in Ijmuiden (the Netherlands), seems to contradict this statement. It is observed that a LC steel grade has a high risk of cracking alias hot tearing, while a High Strength Low Alloyed (HSLA) steel has a very low cracking occurrence. Another HSLA steel grade, with a similar composition but less N and V is however very sensitive to hot tearing. An extreme crack results in a breakout. A previous statistical analysis of the breakout occurrence reveals a one and a half times higher possibility of a breakout for the HSLA grade compared to the LC grade. HSLA with extra N, V shows a four times smaller possibility of breakout than LC. This study assigns the unexpected effect of the chemical composition on the hot tearing sensitivity to the role of some alloying elements such as V and N as structure refiners.This research was carried out under project number M41.5.08320 within the framework of the Research Program of the Materials innovation institute M2i (www.m2i.nl)

A new Al-Zr-Ti master alloy for ultrasonic grain refinement of wrought and foundry aluminum alloys

A new grain refiner master alloy based on the Al-Zr-Ti system was prepared by salt assisted synthesis. 90% of Al3Zr particles in the master alloy were ranged between 1 and 13 μm. 80% reduction of grain size was observed with the addition of 0.2wt% Zr equivalent master alloy combined with ultrasonic treatment in an Al alloy. The new master alloy demonstrated 30% improvement in grain refinement efficiency compared to the one prepared by a conventional alloy route.The authors wish to acknowledge financial support from the ExoMet Project, which is co-funded by the European Commission in the 7th Framework Programme (contract FP7-NMP3-LA-2012-280421), by the European Space Agency and by the individual partner organisations