Reconstruction of the three mechanical material constants of a lossy fluid-like cylinder from low-frequency scattered acoustic fieldsReconstruction des trois constants mécaniques matériels d'un cylindre fluide dissipatif à partir de champs acoustiques basses fréquences

The inverse medium problem for a circular cylindrical domain is studied using low-frequency acoustic waves as the probe radiation. To second order in k₀a (k₀ the wavenumber in the host medium, a the radius of the cylinder), only the first three terms (i.e., of orders 0, ?1 and +1) in the partial wave representation of the scattered field are non-vanishing. This enables the scattered field to be expressed algebraically in terms of the unknown material constants, i.e., the density ρ₁, and the real and imaginary parts of complex compressibility κ₁ of the cylinder. It is shown that these relations can be inverted to yield explicit, decoupled expressions for ρ₁ and κ₁ in terms of the totality of the far-zone scattered field. These expressions furnish accurate estimations of the material parameters provided the probe frequency is low and the radius of the cylinder is known very precisely. To cite this article: T. Scotti, A. Wirgin, C. R. Mecanique 332 (2004).     

三通管路管壁声传递损失测试方法

针对汽车进气系统三通管路的特点,提出了多通管路的管壁传递损失测试方法。并以某车型的双涡轮增压发动机进气三通管道为例,采用该方法评价其用塑料代替铝后的声学性能,主要以声传递损失来评价涡轮增压器噪声通过三通连接管路管壁的辐射和透射特性。测试过程中,三通管道的两个连接涡轮增压器端口分别用声源两次发声,靠近进气歧管端口采用两种不同反射末端,然后在每段管路布置两个压力场扬声器进行测试,并基于平面波分离入射波和反射波,同时在三通管道外用声功率半球面十点分布法自由场扬声器测试,经过3次测量来计算管道管壁的声传递损失。由于声传递损失是管道本身特性决定,所以该测试方法能够准确找出塑料件和金属件在不同频率的声学特性差异。而后,在声传递损失测试结果的基础上,结合近场声全息方法和波束形成原理进行声源识别,可知该三通管路材质改为塑料后主要噪声来自焊缝薄弱处的中高频透射声和管壁结构的低频辐射声。     

An inverse method to fast-track the calculation of phase diagrams for sonoluminescing bubbles

A sound driven air bubble can be transformed into an argon bubble emitting light pulses stably. The very foundation to investigate the sonoluminescing bubble is to accurately determine the ambient radius and gas composition in the interior. The conventional approach is to model the air-to-argon transformation process through a large number of bubble dynamics simulations to obtain the physical parameters of the ultimate argon bubble. In this paper, we propose a highly efficient method to pinpoint this information in a phase diagram. The method is based on the diffusive equilibrium for each species inside the bubble and derives the ambient radius and composition inversely. To calculate the former parameter, the bisection algorithm is employed to consecutively narrow down the searching range until the equilibria is approached. Afterward, several cycles of full dynamics simulations are conducted to refine the composition. The method is validated using published experimental data. The calculated ambient radii deviate from the test results by less than 1 μm, which falls within the margin of measurement error. The advantages of this method over the semi-analytical approach reported by Hilgenfeldt et al. [J. Fluid Mech. 365 (1998)] are also discussed. Our study provides a standard procedure to calculate the ambient radius and composition and is beneficial for the numerical simulation of sonoluminescing bubbles.     

Hydrophobically Associating Polyacrylamides Prepared by Inverse Suspension Polymerization: Synthesis,Characterization and Aqueous Solution Properties

Hydrophobically associating polyacrylamides (HAPAMs) were synthesized via inverse suspension polymerization using ammonium persulphate (APS)/tertramethylethylenediamine (TEMED) as the redox initiators, 2-methacryloyloxyethyl n-alkyl dimethyl ammonium bromide (DM-n, n = 8, 12, 16) as the hydrophobic comonomers. The structures of the copolymers were elucidated by FT-IR and ionic chromatographic analysis, respectively. The morphology and particle size of the resultant HAPAMs were characterized by scanning electronic microscope (SEM) and laser particle size analyzer, which revealed that spherical particles were formed and the particle size exhibited Gaussian distribution centered from 25 μ m to 162 μ m. Furthermore, the solution properties of the copolymers were studied with viscometry and the results showed that HAPAMs synthesized under optimal conditions exhibited an obvious viscosity enhancement in aqueous solution and excellent salt-tolerant capability in brine.     

二阶微分方程的逆特征值问题

运用渐近分析的方法及Rayleigh商原理,将Sturm-Liouville问题的Ambarzumyan定理推广到具有Neumann边界条件或拟周期边界条件的二阶微分方程情形.同时,获得了二阶向量微分方程的有关Ambarzumyan型结果.     

Carleman Estimates for the Schr(o)dinger Equation and Applications to an Inverse Problem and an Observability Inequality

The authors prove Carleman estimates for the Schr(o)dinger equation in Sobolev spaces of negative orders,and use these estimates to prove the uniqueness in the inverse problem of determining Lp-potentials.An L2-1evel observability inequality and unique continuation results for the Schr(o)dinger equation are also obtained.     

Actions of inverse semigroups arising from partial actions of groups

In this work we present a definition of crossed product for actions of inverse semigroups on C^∗-algebras, without resorting to covariant representations as done by Sieben in related work. We also show the existence of an isomorphism between the crossed product by a partial action of a group G and the crossed product by a related action of S(G), an inverse semigroup associated to G introduced by the first named author.     

Global uniqueness in an inverse problem for time fractional diffusion equations

Given $(M,g)$, a compact connected Riemannian manifold of dimension $d?2$, with boundary ?M, we consider an initial boundary value problem for a fractional diffusion equation on $(0,T)\times M$, $T>0$, with time-fractional Caputo derivative of order $\alpha \in (0,1)\cup (1,2)$. We prove uniqueness in the inverse problem of determining the smooth manifold $(M,g)$ (up to an isometry), and various time-independent smooth coefficients appearing in this equation, from measurements of the solutions on a subset of ?M at fixed time. In the “flat” case where M is a compact subset of ${\mathbb{R}}^d$, two out the three coefficients ρ (density), a (conductivity) and q (potential) appearing in the equation $\rho {?}_t^{\alpha }u?\mathrm{div}\left(a\mathrm{?}u\right)+qu=0$ on $(0,T)\times M$ are recovered simultaneously.     

The m-functions of discrete Schrödinger operators are sparse compared to those for Jacobi operators

We explore the sparsity of Weyl–Titchmarsh m-functions of discrete Schrödinger operators. Due to this, the set of their m-functions cannot be dense on the set of those for Jacobi operators. All this reveals why an inverse spectral theory for discrete Schrödinger operators via their spectral measures should be difficult. To obtain the result, de Branges theory of canonical systems is applied to work on them, instead of Weyl–Titchmarsh m-functions.