A sharp condition for existence of an inertial manifold

It is shown that a perturbation argument that guarantees persistence of inertial (invariant and exponentially attracting) manifolds for linear perturbations of linear evolution equations applies also when the perturbation is nonlinear. This gives a simple but sharp condition for existence of inertial manifolds for semi-linear parabolic as well as for some nonlinear hyperbolic equations. Fourier transform of the explicitly given equation for the tracking solution together with the Plancherel's theorem for Banach valued functions are used.     

Water cavitation of hydrogels

Using the cavitation rheology (CR) technique developed in our labs, we show that fluids with negligible interfacial tensions with a surrounding material can be used to induce an elastic, cavitation instability in that material. We do this by changing the cavitation media from air, which was demonstrated to induce cavitation at the tip of a syringe needle in previous studies, to water, which has a negligible surface tension with the surrounding poly(vinyl alcohol) hydrogel material. In this case, the critical pressure in which this instability occurs can be directly related to the elastic modulus of the surrounding network and is shown to be nearly independent of length scale. This independence of size scale has important implications in the use of CR for the characterization of mechanical properties from molecular to macroscopic length scales. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1423–1427, 2010     

A Stokes model with cavitation for the numerical simulation of hydrodynamic lubrication

We present a cavitation model based on the Stokes equation and formulate adaptive finite element methods for its numerical solution. A posteriori error estimates and adaptive algorithms are derived, and numerical examples illustrating the theory are supplied, in particular with comparison to the simplified Reynolds model of lubrication. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical simulation of the unsteady behaviour of cavitating flows

A 2D numerical model is proposed to simulate unsteady cavitating flows. The Reynolds‐averaged Navier–Stokes equations are solved for the mixture of liquid and vapour, which is considered as a single fluid with variable density. The vapourization and condensation processes are controlled by a barotropic state law that relates the fluid density to the pressure variations. The numerical resolution is a pressure‐correction method derived from the SIMPLE algorithm, with a finite volume discretization. The standard scheme is slightly modified to take into account the cavitation phenomenon. That numerical model is used to calculate unsteady cavitating flows in two Venturi type sections. The choice of the turbulence model is discussed, and the standard RNG k–εmodel is found to lead to non‐physical stable cavities. A modified k–εmodel is proposed to improve the simulation. The influence of numerical and physical parameters is presented, and the numerical results are compared to previous experimental observations and measurements. The proposed model seems to describe the unsteady cavitation behaviour in 2D geometries well. Copyright © 2003 John Wiley & Sons, Ltd.     

平面应变条件下孔洞化不稳定性问题研究

考虑平面应变条件下，由一类推广的幂次neo—Hookean材料组成的内部分布温度场的圆柱体在轴向和径向载荷作用下的孔洞化不稳定性问题，研究中发现当材料参数满足一定的条件时，存在着一个载荷临界值，当外加载荷大于该临界值时，圆柱体中心将出现一个圆柱形的孔洞，即发生了孔洞化不稳定性现象并详细讨论了温度和材料参数对孔洞化极限载荷的影响。     

拟周期时滞耗散半线性波方程的惯性流形

本文研究了具有拟周期外力作用的时滞波方程解的长时间性态,利用斜积半流方法,在扩展相空间中将非自治系统提升成自治系统,利用算子半群理论及Lyapunov-Perron方法在一定的谱间隙条件和充分小的时滞假设下,证明了拟周期半线性时滞波方程惯性流形的存在性.     

Sonocrystallization of polycarbonate melts

In this paper, we showed the simplified continuous process to crystallize the polycarbonate (PC) melts using sonocrystallization which is based on ultrasonic cavitation and ‘hot spot’ theory. High power ultrasonic wave was introduced to crystallize the PC prepolymers which is generally used for solid‐state polymerization (SSP) to obtain the ultra‐high molecular weight PCs. The structure and properties of PC treated with ultrasonic wave such as torque changes and crystallinities were studied. The experimental results showed that ultrasonic wave could improve the crystallinities of PCs and sonication time was proportional to their crystallinity. This is attributed to the decrease of the specific volume and the resulting shrinkage is compensated by a flux of a polymer melt toward the crystallization front. Torque data were collected directly from the Haake internal mixer and crystallinities were evaluated from differential scanning calorimeter (DSC). This process is an environmentally benign process so that no additional solvents or treatments are needed and will be very useful in the conventional solid‐state process which is used industrially. Copyright © 2007 John Wiley & Sons, Ltd.     

金激光等离子体冕区电离态特性研究

 提出一种测量金激光等离子体电荷态分布与平均电离度的X射线光谱学诊断方法。该方法基于稳态碰撞-辐射近似，考虑电子离子直接碰撞激发与双电子复合两种激发态布居方式，建立了金M带5f-3d跃迁组辐射总强度与离子态分布的耦合方程。根据实验测量的金平面靶激光等离子体冕区辐射的5f-3d跃迁线系的强度分布，诊断得到了金激光等离子体的电荷态分布与平均电离度。此外，还分析了电子温度、电子密度以及双电子复合过程对电荷态分布及平均电离度诊断的影响，并将实验诊断结果与辐射流体力学理论模拟结果及离化平衡动力学计算结果进行了对比分析。结果表明：实验诊断结果与基于CRE近似的离化平衡动力学计算结果近似；当电子温度高于1.5 keV时，双电子复合过程对电离度的诊断结果影响较小。     

Cavitation-induced shock wave behaviour in different liquids

This paper follows our earlier work where a strong high frequency pressure peak has been observed as a consequence of the formation of shock waves due to the collapse of cavitation bubbles in water, excited by an ultrasonic source at 24 kHz. We study here the effects of liquid physical properties on the shock wave characteristics by replacing water as the medium successively with ethanol, glycerol and finally a 1:1 ethanol–water solution. The pressure frequency spectra obtained in our experiments (from more than 1.5 million cavitation collapsing events) show that the expected prominent shockwave pressure peak was barely detected for ethanol and glycerol, particularly at low input powers, but was consistently observed for the 1:1 ethanol–water solution as well as in water, with a slight shift in peak frequency for the solution. We also report two distinct features of shock waves in raising the frequency peak at MHz (inherent) and contributing to the raising of sub-harmonics (periodic). Empirically constructed acoustic pressure maps revealed significantly higher overall pressure amplitudes for the ethanol–water solution than for other liquids. Furthermore, a qualitative analysis revealed that mist-like patterns are developed in ethanol–water solution leading to higher pressures.     

The evolution of cavitation in narrow soft-solid wedge geometry mimicking periodontal and peri-implant pockets

In periodontology and implantology, laser-induced cavitation has not yet been used to treat biofilm-related problems. In this study we have checked how soft tissue affects the evolution of cavitation in a wedge model representing periodontal and peri-implant pocket geometry. One side of the wedge model was composed of PDMS mimicking soft periodontal or peri-implant biological tissue, the other side was composed of glass mimicking hard tooth root or implant surface, which allowed observations of the cavitation dynamics with an ultrafast camera. Different laser pulse modalities, PDMS stiffness, and irrigants were tested for their effect on the evolution of cavitation in the narrow wedge geometry. The PDMS stiffness varied in a range that corresponds to severely inflamed, moderately inflamed, or healthy gingival tissue as determined by a panel of dentists. The results imply that deformation of the soft boundary has a major effect on the Er:YAG laser-induced cavitation. The softer the boundary, the less effective the cavitation. We show that in a stiffer gingival tissues model, photoacoustic energy can be guided and focused at the tip of the wedge model, where it enables generation of secondary cavitation and more effective microstreaming. The secondary cavitation was absent in severely inflamed gingival model tissue, but could be induced with a dual-pulse AutoSWEEPS laser modality. This should in principle increase cleaning efficiency in the narrow geometries such as those found in the periodontal and peri-implant pockets and may lead to more predictable treatment outcomes.