The profile of the nozzle of a water cannon designed for maximal inflow velocity

Using the method of total counting, which is based on representing the conditions on the characteristics of the equations of gas dynamics as transfer equations and subsequent approximation of them over triangular grids, we obtain a numerical solution of the variational problem of profiling the nozzle of a water cannon so as to obtain the maximal inflow velocity. We confirm numerically an earlier conclusion reached theoretically that the optimal nozzle of a water cannon contains breaks. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 24, 1993, pp. 86–89.     

The mechanics of a powder-drive water jet

We consider the processes in a powder-drive pulse water jet in which the acceleration of the water shell occurs as the result of the energy from burning powder. The one-dimensional motion of the fluid is described in the nonstationary formulation, while the combustion of the powder is described in a quasistationary formulation. The barriers are assumed rigid. In a numerical solution that is presented we use the method of complete computation. For a specific structure of the cannon we give the results of numerical computations. We discuss a simplified approach for estimating the parameters of the apparatus. Four figures. Bibliography: 5 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 124–128.     

Inversion of adjunction for non-degenerate hypersurfaces

 We prove a precise inversion of adjunction formula for the log variety (ℂ ^{d +1},X), where X is a non-degenerate hypersurface. As a corollary, the minimal log discrepancies of non-degenerate normal hypersurface singularities are bounded by dimension. Received: 17 September 2002 / Revised version: 22 November 2002 Published online: 14 February 2003 Current address: DPMMS, CMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, England. e-mail: f.ambro@dpmms.cam.ac.uk Mathematics Subject Classification (2000): Primary 14B05; Secondary 14M25, 52B20     

Experimental study of quantum chaos with cold atoms

We investigate experimentally the quantum behavior of laser-cooled atoms in a pulsed standing wave, a system that is an atomic analog of the quantum kicked rotor. In particular, it may display the well-known phenomenon of “dynamical localization”, when the standing wave is driven periodically. Furthermore, we study some interesting properties of a quasi-periodically driven kicked rotor, which presents resonances that are shown to be sharper than the inverse of the driven–excitation duration, thus presenting a sub-Fourier character.     

Cam design by hyperbolic spline functions of fourth order

E-mail: kohaupt{at}tfh-berlin.de In this paper, cam design using splines is discussed. The splinesare of 4th order so as to guarantee the continuity of the valve-liftcurve up to the third derivative in order to obtain valves withbetter dynamic behaviour. First, ordinary polynomial splinesare investigated, and their limited potential in cam designis illustrated. Then, the reason for introducing the new hyperbolicsplines is explained, and their potential for cam design isshown. Finally, specific cam designs based on the new splinesare compared with cams developed by Kurz. It turns out thatspline cams are an interesting alternative to Kurz's designsince—in some cases—they show a better dynamic behaviourwhen compared with Kurz's cams. The spline cam has been employed,e.g. in the M103 engine of Mercedes-Benz.     

Fluid dynamics of an underwater electric discharge on the axis of a shell immersed in a fluid

We study the motion of a fluid during an electrical discharge on the axis of an elastic cylindrical shell immersed in the fluid. We estimate the influence of the parameters of the shell on the dynamics of a gasvapor chamber. We point out several properties of the computation of the pulsed flows in an infinite volume of fluid (the choice of the method of constructing the grid, the limitation of the computational region). We obtain the pressure distribution over space at large distances from the shell. We analyze the influence of the shell on the parameters of the flow in the interior and exterior regions. Four figures. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 120–126.     

Nonlinear Volume Flow Control of a Variable Displacement Vane Pump

Variable displacement vane pumps are used for mid-pressure applications in a variety of systems. Due to their potential for power loss reduction they are most prominently featured in automotive applications. They provide a hydraulic consumer with varying levels of volume flow, depending on the eccentricity of the cam ring of the pump. Eccentricity control is typically achieved by means of hydraulic actuation. In this contribution, a model of a hydraulic aggregate featuring a VDVP with a nonlinear control technique based on input-output-linearization for volume flow tracking requirements is presented. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal control of dams

Assume that a dam has a capacity V. Its water input I={I_t, t ? [0, ∞)}], is assumed to be a diffusion process. The water is released at one of two rates 0 and M units of water per unit of time. The release rate is 0 until the water reaches level λ(0 < λ < V), when the water is released at rate M until it reaches level λ, (0 ≤ τ < λ). Once the level λ is reached, the release rate remains at zero until level λ is reached again, and the cycle is repeated. Under general cost structure, we discuss and review some of the most recent work in the area of optimal control of dams with release policies of the above type; we also discuss some new results and corrections to some existing results.     

Weak Galerkin finite element methods for electric interface model with nonhomogeneous jump conditions

In this paper, the weak Galerkin finite element method (WG-FEM) is applied to a pulsed electric model arising in biological tissue when a biological cell is exposed to an electric field. A fitted WG-FEM is proposed to approximate the voltage of the pulsed electric model across the physical media involving an electric interface (surface membrane), and heterogeneous permittivity and a heterogeneous conductivity. This method uses totally discontinuous functions in approximation space and allows the usage of finite element partitions consisting of general polygonal meshes. Optimal pointwise-in-time error estimates in L²-norm and H¹-norm are shown to hold for the semidiscrete scheme even if the regularity of the solution is low on the whole domain. Furthermore, a fully discrete approximation based on backward Euler scheme is analyzed and related optimal error estimates are derived.     

Study on optimal kinematic synthesis of cam profiles for engine valve trains

Kinematic cam profile synthesis for engine valve trains to satisfy the requirements of a large lift area and small acceleration magnitudes is a multi-objective optimization problem. This paper proposed that its Pareto optimal solution set is constructed with constant acceleration profiles. For the definite design of an engine valve train, its Pareto front is a function of the time durations of the positive and negative accelerations. The relationships of positive acceleration, negative acceleration, and lift area for a constant acceleration cam profile are analyzed, and the results are applied to discuss the characteristics of polynomial cam profiles.     

Optimal stormwater management with two dams: the dynamics of the pump–to–fill policy†

We consider the management of water in two connected dams. Stormwater generated by rainfall flows into a large capture dam and is subsequently pumped to a smaller supply dam. Recently it was shown that the twin objectives of minimizing overflow and maximizing the amount of demand met are both achieved by the pump-to-fill policy, in which as much water as possible is pumped each day from the capture dam to the supply dam without allowing the supply dam to overflow. We present a simplifying reparameterization for this case and study the dynamics of the system.     

Curvature analysis of roller-follower cam mechanisms

The equations related to the curvature analysis of the roller-follower cam mechanisms are presented for roller surfaces being revolution surface, hyperboloidal surface, and globoidal surface. These equations give the expressions of the meshing function, the limit function of the first kind, and the limit function of the second kind. Once these functions are known, the principal curvatures of the cam surface, the relative normal curvatures of contacting surfaces, and the condition of undercutting can be derived. Three particular cam mechanisms with hyperboloidal roller are illustrated and the numerical comparison between 2-D and 3-D cam is given.     

在凸轮CAD中交点的数学处理方法及算法

本文建立了凸轮廓线的数学模型.利用一个活动坐标系可以很方便地建立凸轮各段运动轨迹的连接方程,并可对尖点进行修改.文中详述了上述数学处理方法及算法.     

Local solvability of control systems with mixed constraints

We analyze the local solvability of a control system with mixed constraints and control constraints. We obtain a sufficient condition for the local solvability of the control system under the assumption of smoothness and 2-regularity of the mapping g specifying the mixed constraints. For the case in which the mapping g is not smooth, a sufficient condition for the local solvability is obtained under the assumption of coverability of g.     

Mathematical modelling of layered contact mechanics of cam–tappet conjunction

The paper briefly introduces a fast converging mathematical model to predict the peculiarities of the non-conforming contact between an infinitely long cylinder and a coated elastic substrate. The proposed method is then integrated into a multi-physics analysis of the valve train system of a racing type internal combustion (IC) engine. Due to relatively high loads and speeds experienced, particularly in the cam–tappet contacts, hard wear resistant coatings are used, which greatly influence the contact mechanics performance. Results indicate that the layer thickness is the determining factor in contact characteristics, which alters during the cam cycle. Therefore, for optimal performance coatings of non-uniform thickness should ideally be applied to the circumference of the cam rather than the usual coating of the tappet surface with a given thickness.     

On the time optimization problem for two-dimensional control systems

We consider a time optimization problem for two-dimensional nonlinear control systems. For a constraint for the control vector u we take a convex polygon U. We obtain effective sufficient conditions under which the time-optimal control is equivalent in the Lebesgue sense to a piecewise constant control that has finitely many points of discontinuity and ranges in the set of vertices of U. We give examples illustrating the results.     

Erratum to “Time harmonic wave diffraction problems in materials with sign-shifting coefficients” [J. Comput. Appl. Math. doi:10.1016/j.cam.2009.08.041]

We mention here an error in the statement of the configurations that are covered by the theory of T-coercivity presented in the paper “Time harmonic wave diffraction problems in materials with sign-shifting coefficients” [J. Comput. Appl. Math. doi:10.1016/j.cam.2009.08.041].     

Modeling the spread of bird flu and predicting outbreak diversity

Avian influenza, commonly known as bird flu, is an epidemic caused by H5N1 virus that primarily affects birds like chickens, wild water birds, etc. On rare occasions, these can infect other species including pigs and humans. In the span of less than a year, the lethal strain of bird flu is spreading very fast across the globe mainly in South East Asia, parts of Central Asia, Africa and Europe. In order to study the patterns of spread of epidemic, we made an investigation of outbreaks of the epidemic in one week, that is from February 13–18, 2006, when the deadly virus surfaced in India. We have designed a statistical transmission model of bird flu taking into account the factors that affect the epidemic transmission such as source of infection, social and natural factors and various control measures are suggested. For modeling the general intensity coefficient f(r), we have implemented the recent ideas given in the article Fitting the Bill, Nature [R. Howlett, Fitting the bill, Nature 439 (2006) 402], which describes the geographical spread of epidemics due to transportation of poultry products. Our aim is to study the spread of avian influenza, both in time and space, to gain a better understanding of transmission mechanism. Our model yields satisfactory results as evidenced by the simulations and may be used for the prediction of future situations of epidemic for longer periods. We utilize real data at these various scales and our model allows one to generalize our predictions and make better suggestions for the control of this epidemic.     

Moment-free numerical integration of highly oscillatory functions

^** Email: s.olver{at}damtp.cam.ac.uk The aim of this paper is to derive new methods for numericallyapproximating the integral of a highly oscillatory function.We begin with a review of the asymptotic and Filon-type methodsdeveloped by Iserles and Nørsett. Using a method developedby Levin as a point of departure, we construct a new methodthat utilizes the same information as a Filon-type method, andobtains the same asymptotic order, while not requiring the computationof moments. We also show that a special case of this methodhas the property that the asymptotic order increases with theaddition of sample points within the interval of integration,unlike all the preceding methods whose orders depend only onthe endpoints.     

Optimal control of a large dam with compound Poisson input and costs depending on water levels

This paper studies a discrete model of a large dam where the difference between lower and upper levels, L, is assumed to be large. Passage across the levels leads to damage, and the damage costs of crossing the lower or upper level are proportional to the large parameter L. Input stream of water is described by compound Poisson process, and the water cost depends upon current level of water in the dam. The aim of the paper is to choose the parameters of output stream (specifically defined in the paper) minimizing the long-run expenses that include the damage costs and water costs. The present paper addresses the important question: How does the structure of water costs affect the optimal solution? We prove the existence and uniqueness of a solution. A special attention is attracted to the case of linear structure of the costs. As well, the paper contributes to the theory of state-dependent queueing systems. The inter-relations between important characteristics of a state-dependent queueing system are established, and their asymptotic analysis that involves analytic techniques of Tauberian theory and heavy traffic approximations is provided.