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Purpose: In marine and ocean engineering area, some underwater cylindrical shell structures or vehicles may approach a free surface (water surface) or a rigid wall (seabed). The existence of the free surface or rigid wall makes the surrounding fluid around the structure an acoustic half-space, causing that the vibroacoustic characteristics of the shell may have much difference from those in an infinite fluid field. In this study, the far-field acoustic radiation of a finite cylindrical shell with an arbitrary, time-harmonic surface velocity distribution positioned within an acoustic semi-space is studied. Methods: The Fourier transform method is utilized to express acoustical pressure in the wavenumber domain, and the acoustic boundary effect is considered through the use of the Graf’s addition theorem and the image approach. Then, the relationship between acoustical pressure and the normal velocity on the structure surface is established in the wavenumber domain. Finally, the far-field acoustical pressure could be expressed by the stationary phase method approximately. Results: The accuracy of the present approach is verified by contrast with the boundary element method. It could be observed that there are many similarities between the directivity of the far-field acoustical pressure of the cylindrical shell and the acoustical dipole due to the interference of sound waves. For the case of a rigid wall boundary, a similar interference phenomenon also exists. Conclusions: The present method has the advantages of simpleness and fewer calculations; it can be utilized to rapidly predict the far-field acoustical pressure in an acoustic half-space. Besides, after discussing the multiple scattering effects between the acoustic boundary and the shell, a simpler physical model is successfully put forward to resolve the far-field acoustical pressure of an inclined shell within an acoustic semi-space, assuming that the distance between the shell and the acoustical boundary is larger than a certain value (five-time radiuses in the present study).

The thermal bonding method is an advanced processing technology, which can bond a variety of polymer sheets on request. This work aims to analyze the effect of applied loading, heating temperature and duration on the depth loss of the PMMA microfluidic chip after bonding. Several experiments were designed by us and the results were analyzed by orthogonal experimental method. Finally optimal applied loading, heating temperature and duration were obtained and in the optimal case, the bonded microfluidic chip has small depth loss and enough strength.

We investigate theoretically quantum scattering of two distinguishable photon wave packets from a Ξ-type three-level atom in a one-dimensional waveguide. The quantum state of scattered photons is solved analytically, and the solution indicates how the two photons become strongly correlated after the scattering. We determine the two-photon reflection and transmission properties, and analyze the quantum entanglement between the scattered photons. In particular, we show that the degree of entanglement can be enhanced by decreasing the spectral width of the incident photon wave packets. [ABSTRACT FROM AUTHOR]

It is well known that singularities are inherent to parallel manipulators and have serious influence on their properties. It is desired that the motion uncertainty caused by the singularity should be avoided in the design and operation stages. The singularity distribution hypersurface shows the relations among the pose components at the singular points, but it is difficult to be utilized in predicting the motion certainty through checking and controlling the lengths of input parameters. In this article, taking a 3-RPR parallel manipulator as an example, and considering the clearances existing in the joints and the deformations of the input actuating cylinders under external loads, the maximal singularity-free distribution of input parameters is investigated. While the input parameters are located within the space enveloped by the maximal singularity-free distribution surfaces, the manipulator can bear the required external loads and give out a certain motion at the neighbourhood of singular points. Based on this kind of the maximal singularity-free distribution of input parameters, the singularity can be avoided both in the early design stage by assigning the input parameters into a suitable region and in the operation state through controlling and monitoring the values of the input parameters.

In view of structure-borne sound, vibrational power flow analysis is investigated for damaged beam structures. In this paper, the damage is modelled as a joint of a local spring. The damage point transfer matrix and the beam element transfer matrix are deduced, then the relations of the vibrational power flow, the position and the characteristic size of the damage are obtained combined with periodic structure theory. Based on the theoretical analysis and measurement results, the damage can be diagnosed in the next work.

Abstract.: In practice, finding mixed cells in certain polyhedral subdivisions plays a dominating role when a polyhedral homotopy is employed to approximate all isolated zeros of polynomial systems. This paper gives a new algorithm for the mixed cell computation via a new formulation of the underlying linear programming problems. Numerical results show that the algorithm provides a major advance in the speed of computation with much less memory requirements.

In [4] a conjecture concerning the connectivity of mixed cells of subdivisions for Minkowski sums of polytopes was formulated. This conjecture was, in fact, originally proposed by Pedersen [3]. It turns out that a positive confirmation of this conjecture can substantially speed up the algorithm for the ``dynamical lifting'' developed in [4]. In the mean time, when the polyhedral method is used for solving polynomial systems by homotopy continuation methods [2], the positiveness of this conjecture also plays an important role in the efficiency of the algorithm. Very unfortunately, we found that this conjecture is inaccurate in general. In Section 1 a counterexample is presented for a general subdivision. In Section 2 another counterexample shows that even restricted to ``regular'' subdivisions induced by liftings, this conjecture still fails to be true.

Summary Most systems ofn polynomial equations inn unknowns arising in applications aredeficient, in the sense that they have fewer solutions than that predicted by the total degree of the system. We introduce the random product homotopy, an efficient homotopy continuation method for numerically determining all isolated solutions of deficient systems. In many cases, the amount of computation required to find all solutions can be made roughly proportional to the number of solutions.

The power flow analysis for a floating raft isolation system consisting of constrained damped beams is completed by using the Green function, an analytical method instead of the traditional mobility approach. The transmitted power flow from a harmonic force excitation to the foundation beams via an isolator–raft beam–isolator system is calculated. Some important structural parameters that influence the transmitted power flow are discussed. The conclusions provide a theoretical basis for vibration control in engineering.

When a real homotopy is used for solving a polynomial system with real coefficients, bifurcation of some of the homotopy paths at singular points is inevitable. The main result of this paper shows that, generically, the solution set of a real homotopy contains no singular point other than a finite number of quadratic turning points. At a quadratic turning point, the bifurcation phenomenon is quite simple. It consists of two bifurcation branches with their tangent vectors being perpendicular to each other.

The reactions of Zn-, Zn,Cd-, and Cd-thioneins with EDTA and apo-carbonic anhydrase have been studied. The ligand substitution reaction of zinc with EDTA is multiphasic, having both associative and dissociative components in the rate expression. The cadmium sites are about 2 orders of magnitude less reactive. In contrast, apo-carbonic anhydrase abstracts zinc from Zn-thionein and Zn,Cd-thionein in second-order processes that are 2-3 orders of magnitude more rapid than those involving EDTA and approach the rate for unligated Zn2+ with the apo-protein. In comparison with other zinc proteins, Zn-thionein contains unusually reactive metal sites, suggesting that this protein may be a physiological zinc transfer protein, able to donate zinc to zinc-requiring apo macromolecules.

By a deficient polynomial system of n polynomial equations in n unknowns we mean a system that has fewer solutions than that predicted by the total degree, or the Bézout number, of the system. If the system is m-homogeneous, the Bézout number can be considerably reduced. In this paper, we introduce a homotopy for numerically determining all isolated solutions of deficient m-homogeneous systems. The initial polynomial system Q is chosen which keeps the subschemes of $ H(x,t) = (1 - t)aQ(x) + tP(x)$t varies in [0, 1).

The eigenvalues of a matrix A are the zeros of its characteristic polynomial

Summary The homotopy method for solving systems of polynomial equations proposed by Li (also Morgan) is believed to be one of the simplest for computer implementation. It is shown here that the parameters of the homotopy can be chosen from an open and dense set such that all isolated solutions of polynomial systems can be obtained.

Summary The homotopy method can be used to solve eigenvalue-eigenvector problems. The purpose of this paper is to report the numerical experience of the homotopy method of computing eigenpairs for real symmetric tridiagonal matrices together with a couple of new theoretical results. In practice, it is rerely of any interest to compute all the eigenvalues. The homotopy method, having the order preserving property, can provide any specific eigenvalue without calculating any other eigenvalues. Besides this advantage, we note that the homotopy algorithm is to a large degree a parallel algorithm. Numerical experimentation shows that the homotopy method can be very efficient especially for graded matrices.

We say $ P:{L^1} \to {L^1}$ for $ f \geq 0$ $ \Vert Pf\Vert = \Vert f\Vert $. It is shown that any Markov operator $ P$ $ f \in {L^1}$ and $ \Vert f\Vert = 1$ $ {P^n}f \to \mathcal{F}$ $ n \to \infty $ $ \mathcal{F}$. It follows from this decomposition that $ {P^n}f$ .

Rat liver and horse kidney metallothioneins react with 5,5′-dithiobis-(2-nitrobenzoic acid) (Nbs2) to release 5-thio-2-nitrobenzoate and metal ions. The reactions are slow and exhibit biphasic kinetics with each process having an empirical rate law of the form: rate - k[RSM] X [Nbs2] + k'[RSM], where RSM represents mental-bound thiolate groups. The pseudo-first-order rates are insensitive to pH but are modified in guanidine hydrochloride solution. Rat liver metallothioneins of variable zinc, copper and cadmium composition react similarly and give observable thiol/total metal ratios in good agreement with stoichiometries of SH/(Cd + Zn) of 3 and SH/Cu of 1. A model complex cadmium-2,3-dimercaptopropanol, resembles the proteins in its reaction with Nbs2.

Online Oil debris detection is a complex and systemic issue that multiple requirements should be met for a practical application. When severe wear or tear happens, more accurate detection is needed for higher debris concentration. Aiming at promoting detection accuracy under the practical high debris concentration conditions, in this work, an experimental study is carried out to test the performance of an inductive oil debris detection method using a multi-channel sensor based on dual excitation sources with serial layout. Ferrous powders with different sizes and amounts are used for the experiment. Data processing methods including band-pass filter and anti-aliasing techniques are used for optimizing the estimation. The tested results indicate that the counting accuracy of coarse iron powder with 2.5 g/L concentration hydraulic oil at a flow rate of 40 L/min is higher than 85.8% and by data processing, the accuracy is promoted by 21.4% averagely.

Electric vehicle charging network develops rapidly, but now there is still lack of research about business value evaluation of electric vehicle charging network. This paper discusses the business value of electric vehicle charging network based on Internet of vehicles. By analyzing the business evaluation index, a three-dimensional value index system of the two business segments is set up from the aspects of economy, society and environmental benefits, which aimed at improving the business value of electric vehicle charging network.

Fluid cushioned porous sliders are useful in reducing the frictional resistance of moving objects. This paper studies the elliptic slider. After a transformation of variables, the Navier-Stokes equations reduce to a nonlinear two-point boundary-value problem. This boundary-value problem was solved by a homotopy-type method, which did not require a good initial approximation to the solution. The problem was solved for several Reynolds numbers and ellipse eccentricities. Lift and drag calculations show that an elliptic porous slider should be operated along the minor axis.