Fluid sensing using microcantilevers: From physics-based modeling to deep learning

In-situ measurements of the viscosity and density of small volumes of liquids are required in several industrial applications. MEMS sensors deploying vibrating microstructures constitute an attractive alternative given the significant impact of the surrounding liquid on their dynamic behavior. In this work, we combine physics-based modeling approaches and deep learning techniques to simultaneously estimate the density and viscosity of liquids from the resonance frequencies and quality factors of immersed microcantilevers. The physics-based model is first validated by comparing the simulated resonance frequencies and quality factors of immersed microcantilevers to those obtained from experiments conducted on a large variety of liquids. Then, we use the simulations results to train deep neutral networks to learn the mapping from the data space to the parameter space. The deep learning method shows high prediction accuracy provided that there is enough independent input data, shows no bias in the predicted values, and provides the results instantaneously. The optimal accuracy in the estimation of the liquid viscosity and density is achieved when the first resonance frequency and corresponding quality factor are used as inputs.     

Photothermal response of polymer microcantilever with metal coating in fluids

Cantilever beams are used as sensors in a great variety of applications. It is a promising research to study the vibration characteristics of microcantilever for biological and chemical detections. In this paper, a (a a) theoretical model was used to calculate the photothermal vibration frequency spectra of coating polymer microcantilever, which immersed in fluids and excited by an intensity-modulated laser beam. The comparison was made among the response of vibration in different fluids. Theoretical analysis demonstrated that a great distortion occurred to the vibration frequency spectra due to the high density and viscosity of liquids. In addition, it can be concluded from theoretical calculation that the coating has significant effect on the dynamic response of microcantilever.     

A level set approach for computing discontinuous solutions of Hamilton-Jacobi equations

We introduce two types of finite difference methods to compute the L-solution and the proper viscosity solution recently proposed by the second author for semi-discontinuous solutions to a class of Hamilton-Jacobi equations. By regarding the graph of the solution as the zero level curve of a continuous function in one dimension higher, we can treat the corresponding level set equation using the viscosity theory introduced by Crandall and Lions. However, we need to pay special attention both analytically and numerically to prevent the zero level curve from overturning so that it can be interpreted as the graph of a function. We demonstrate our Lax-Friedrichs type numerical methods for computing the L-solution using its original level set formulation. In addition, we couple our numerical methods with a singular diffusive term which is essential to computing solutions to a more general class of HJ equations that includes conservation laws. With this singular viscosity, our numerical methods do not require the divergence structure of equations and do apply to more general equations developing shocks other than conservation laws. These numerical methods are generalized to higher order accuracy using weighted ENO local Lax-Friedrichs methods as developed recently by Jiang and Peng. We verify that our numerical solutions approximate the proper viscosity solutions obtained by the second author in a recent Hokkaido University preprint. Finally, since the solution of scalar conservation law equations can be constructed using existing numerical techniques, we use it to verify that our numerical solution approximates the entropy solution.

     

反平面剪切动态扩展裂纹尖端的弹-粘塑性场

采用Bingham弹性-粘塑性模型对反平面剪切动态扩展裂纹尖端的应力应变场进行了渐近分析．给出了适当的位移模式、推导了渐近方程并且给出了数值解．分析和计算表明对于低粘性情况,裂纹尖端场具有对数奇异性．对于高粘性情况,裂纹尖场具有幂奇异性A·D2对于临界情况,两种奇异性可以相互转换．揭示了粘性在裂纹尖端场研究中的重要作用．     

Exact approaches for lifetime maximization in connectivity constrained wireless multi-role sensor networks

In this paper, we consider the duty scheduling of sensor activities in wireless sensor networks to maximize the lifetime. We address full target coverage problems contemplating sensors used for sensing data and transmit it to the base station through multi-hop communication as well as sensors used only for communication purposes. Subsets of sensors (also called covers) are generated. Those covers are able to satisfy the coverage requirements as well as the connection to the base station. Thus, maximum lifetime can be obtained by identifying the optimal covers and allocate them an operation time. The problem is solved through a column generation approach decomposed in a master problem used to allocate the optimal time interval during which covers are used and in a pricing subproblem used to identify the covers leading to maximum lifetime. Additionally, Branch-and-Cut based on Benders’ decomposition and constraint programming approaches are used to solve the pricing subproblem. The approach is tested on randomly generated instances. The computational results demonstrate the efficiency of the proposed approach to solve the maximum network lifetime problem in wireless sensor networks with up to 500 sensors.     

Equilibrium solutions to generalized motion by mean curvature

In this paper we consider viscosity equilibria to the mean curvature level set flow with a Dirichlet condition. The main result shows that almost every level set of an equilibrium solution is analytic off of a singular set of Hausdorff dimension at most n − 8 and that these level sets are stationary and stable with respect to the area functional. A key tool developed is a maximum principle for solutions to obstacle problems where the obstacle consists of (viscosity) minimal surfaces. Convergence to equilibrium as t → ∞ is also established for the associated initial-boundary value problem.     

Geometric properties of solutions of Hamilton-Jacobi equations

The method of moving parallel planes, previously used for elliptic and parabolic PDE, is adapted to study solutions of the Cauchy problem for Hamilton-Jacobi equations. This is possible in the framework of the theory of viscosity solutions, using the comparison theorem for such solutions as a kind of maximum principle. One of the main results states that if the initial data are nonnegative and compact supported, the Hamiltonian radial and the level sets expanding, then the level sets become asymptotically spherical as t → ∞, the convergence taking place in the Lipschitz norm.     

A LEVEL SET APPROACH TO SEMICONTINUOUS VISCOSITY SOLUTIONS FOR CAUCHY PROBLEMS

A level set formulation is presented to characterize a maximal solution of the Cauchy problem for the Hamilton-Jacobi equation with semicontinuous initial data in an explicit way. No convexity assumptions on Hamiltonians are imposed. The solution proposed in the present paper is interpreted as the level set of an auxiliary problem and called an L-solution. It turns out that our L-solution is consistent with a classical discontinuous viscosity solution and a bitateral viscosity solution. Moreover, our L-solution is unique and enjoy the comparison principle. The condition that initial data is really attained is also discussed.     

A convergent scheme for a non local Hamilton Jacobi equation modelling dislocation dynamics

We study dislocation dynamics with a level set point of view. The model we present here looks at the zero level set of the solution of a non local Hamilton Jacobi equation, as a dislocation in a plane of a crystal. The front has a normal speed, depending on the solution itself. We prove existence and uniqueness for short time in the set of continuous viscosity solutions. We also present a first order finite difference scheme for the corresponding level set formulation of the model. The scheme is based on monotone numerical Hamiltonian, proposed by Osher and Sethian. The non local character of the problem makes it not monotone. We obtain an explicit convergence rate of the approximate solution to the viscosity solution. We finally provide numerical simulations.This work has been supported by funds from ACI JC 1041 “Mouvements d’interfaces avec termes non-locaux”, from ACI-JC 1025 “Dynamique des dislocations” and from ONERA, Office National d’Etudes et de Recherches. The second author was also supported by the ENPC-Région Ile de France.     

Maximizing system lifetime in wireless sensor networks

One of the most critical issues in wireless sensor networks is represented by the limited availability of energy on network nodes; thus, making good use of energy is necessary to increase network lifetime. In this paper, we define network lifetime as the time spanning from the instant when the network starts functioning properly, i.e., satisfying the target level of coverage of the area of interest, until the same level of coverage cannot be guaranteed any more due to lack of energy in sensors. To maximize system lifetime, we propose to exploit sensor spatial redundancy by defining subsets of sensors active in different time periods, to allow sensors to save energy when inactive. Two approaches are presented to maximize network lifetime: the first one, based on column generation, must run in a centralized way, whereas the second one is based on a heuristic algorithm aiming at a distributed implementation. To assess their performance and provide guidance to network design, the two approaches are compared by varying several network parameters. The column generation based approach typically yields better solutions, but it may be difficult to implement in practice. Nevertheless it provides both a good benchmark against which heuristics may be compared and a modeling framework which can be extended to deal with additional features, such as reliability.     

Mathieu equation with application to analysis of dynamic characteristics of resonant inertial sensors

In this paper, Mathieu equation is applied to analyze the dynamic characteristics of resonant inertial sensors. Unlike previous work, Mathieu equation is not just a differential equation and analyzes the stability of the transition curves, but become an important method in analyzing parametric resonant characteristics and approximate output of resonant inertial sensors. It is demonstrated that the mathematical model of resonant inertial sensors is described by Mathieu equation. The relevant Mathieu equation theory and dynamic characteristics analysis methods were proposed, which include both stability and dynamic linear output. Finally, theoretical and experimental analysis show that the correlation of the theoretical curve and the experimental result coincide so perfectly, which means proposed analysis methods for Mathieu equation could be used to analyze the dynamic output characteristic of resonant inertial sensors. The theoretical analyzing approach of Mathieu equation and experimental results of resonant inertial sensors are obtained, which provide an application area for Mathieu equation and a reference for the robust design for resonant inertial sensors.     

Approximation of General Facets by Regular Facets with Respect to Anisotropic Total Variation Energies and Its Application to Crystalline Mean Curvature Flow

We show that every bounded subset of a euclidean space can be approximated by a set that admits a certain vector field, the so‐called Cahn‐Hoffman vector field, that is subordinate to a given anisotropic metric and has a square‐integrable divergence. More generally, we introduce a concept of facets as a kind of directed sets, and show that they can be approximated in a similar manner. We use this approximation to construct test functions necessary to prove the comparison principle for viscosity solutions of the level set formulation of the crystalline mean curvature flow that were recently introduced by the authors. As a consequence, we obtain the well‐posedness of the viscosity solutions in an arbitrary dimension, which extends the validity of the result in the previous paper.© 2018 Wiley Periodicals, Inc.     

Rising bubble simulations using lattice Boltzmann method coupled with level set interface capturing

A multiphase Lattice Boltzmann (LB) scheme coupled with a level set interface capturing module is used for the simulation of multiphase flows, and in particular, rising bubbles under moderate and high density and viscosity ratios. We employ a consistent, robust discretization of the pressure forces which enables us to preserve stability and accuracy. The accuracy of the present scheme is shown to be competitive with that of the benchmark data from the finite element solutions in [3]. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Constrained optimization with stochastic feasibility regions applied to vehicle path planning

In real-time trajectory planning for unmanned vehicles, on-board sensors, radars and other instruments are used to collect information on possible obstacles to be avoided and pathways to be followed. Since, in practice, observations of the sensors have measurement errors, the stochasticity of the data has to be incorporated into the models. In this paper, we consider using a genetic algorithm for the constrained optimization problem of finding the trajectory with minimum length between two locations, avoiding the obstacles on the way. To incorporate the variability of the sensor readings, we propose a modified genetic algorithm, addressing the stochasticity of the feasible regions. In this way, the probability that a possible solution in the search space, say x, is feasible can be derived from the random observations of obstacles and pathways, creating a real-time data learning algorithm. By building a confidence region from the observed data such that its border intersects with the solution point x, the level of the confidence region defines the probability that x is feasible. We propose using a smooth penalty function based on the Gaussian distribution, facilitating the borders of the feasible regions to be reached by the algorithm.     

Nonlinear instability of Hele-Shaw flows with smooth viscous profiles

We rigorously derive nonlinear instability of Hele-Shaw flows moving with a constant velocity in the presence of smooth viscosity profiles where the viscosity upstream is lower than the viscosity downstream. This is a single-layer problem without any material interface. The instability of the basic flow is driven by a viscosity gradient as opposed to conventional interfacial Saffman-Taylor instability where the instability is driven by a viscosity jump across the interface. Existing analytical techniques are used in this paper to establish nonlinear instability.     

Homogenization of Navier-Stokes model: the dependence upon parameters

In this paper we continue earlier work [5], by studying the influence of the kinematic viscosity and of the external forces on the asymptotic behaviour of the Navier-Stokes model of fluid flow through a periodic structure as the characteristic length of the cell tends to zero. The main result is a new estimate of the specific restriction operator. It turns out that the energetic method works as long as the microscopic viscosity forces dominate over the inertial and external ones; at the macroscopic level we get the linear Darcy model. In the transition case, by a formal procedure, we obtain a non-linear law. The crucial parameter is the non-dimensional Galilean number.     

灰度图像复原的一种空间适应性向前向后扩散模型

该文考虑退化灰度图像复原问题. 首先, 作者利用时滞正则化方法定义退化图像去噪过程和去模糊过程之间的权重函数, 将激波过滤器边缘增强模型与水平集运动去噪模型相结合, 建立一种新的图像磨光增强偏微分方程. 然后, 证明该偏微分方程初值问题黏性弱解的存在唯一性. 最后, 给出该模型的部分数值算例.     

Direct Sturm–Liouville problem for surface Love waves propagating in layered viscoelastic waveguides

This paper presents theoretical model for shear-horizontal (SH) surface acoustic waves of the Love type propagating in lossy waveguides consisting of a lossy viscoelastic layer deposited on a lossless elastic half-space. To this end, a direct Sturm–Liouville problem that describes Love waves propagation in the considered viscoelastic waveguides was formulated and solved, what constitutes a novel approach to the state-of-the-art. To facilitate the solution of the complex dispersion equation, the Author employed an original approach that relies on the separation of its real and imaginary part. By separating the real and imaginary parts of the resulting complex dispersion equation for a complex wave vector k = k₀ + jα of the Love wave, a system of two real nonlinear transcendental algebraic equations for k₀ and α has been derived. The resulting set of two algebraic transcendental equations was then solved numerically. Phase velocity v_p and coefficient of attenuation α were calculated as a function of the wave frequency f, thickness of the surface layer h and its viscosity η₄₄. Dispersion curves for Love waves propagating in lossy waveguides, with a lossy surface layer deposited on a lossless substrate, were compared to those corresponding to Love surface waves propagating in lossless waveguides, i.e., with a lossless surface layer deposited on a lossless substrate. The results obtained in this paper are original and to some extent unexpected. Namely, it was found that: 1) the phase velocity v_p of Love surface waves increases as a function of viscosity η₄₄ of the lossy surface layer, and 2) the coefficient of attenuation α has a maximum as a function of thickness h of the lossy surface layer. The results obtained in this paper are novel and can be applied in geophysics, seismology and in the optimal design and development of viscosity sensors, bio and chemosensors.     

Piezoelectric control of flexible vibrations in rotating beams: An experimental study

Active control of flexible vibrations by distributed piezoelectric actuators and sensors plays an increasing role in engineering, especially in light-weight structures. Exemplarily, in this contribution a rotating beam is studied which can be found in many practical applications, e.g. as robot arms or flexible manipulators in production processes. It has been intensively shown in the literature that it is possible to completely suppress the flexible vibrations by an appropriate distribution of piezoelectric actuation strains. In order to compensate the inertial forces in the considered rotating beam, a complex distribution is obtained, such that a practical realisation would be very extensive. To overcome the problem, a discrete approximation by piezoelectric patches is applied. In order to find an optimal configuration for an experimental setup, and to investigate several control strategies, a numerical simulation model has been implemented based on Bernoulli-Euler beam theory. The numerical results are verified by an experimental set-up, in which 48 piezoelectric patches have been attached on a beam with rectangular hollow cross-section. Each patch can be used either as an actuator or a sensor. Additionally, strain gauges can be used as sensors. For monitoring, acceleration sensors are used. The control system is implemented within a dSpace environment. The results show a significant reduction of the flexible vibrations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Melting heat and mass transfer in stagnation point micropolar fluid flow of temperature dependent fluid viscosity and thermal conductivity at constant vortex viscosity

Steady mixed convection micropolar fluid flow towards stagnation point formed on horizontal linearly stretchable melting surface is studied. The vortex viscosity of micropolar fluid along a melting surface is proposed as a constant function of temperature while dynamic viscosity and thermal conductivity are temperature dependent due to the influence of internal heat source on the fluid. Similarity transformations were used to convert the governing equation into non-linear ODE and solved numerically. A parametric study is conducted. An analysis of the results obtained shows that the flow-field is influenced appreciably by heat source, melting, velocity ratio, variable viscosity and thermal conductivity.