Nonstationary normal waves in a thin,curved waveguide of variable cross section

The propagation of nonstationary normal waves in a thin waveguide with variable properties along its course is considered. Along space-time rays the eikonal and transport equations are integrated, and asymptotic formulas for these waves are obtained. It is observed that for some types of initial data the effect of overturning of a wave packet of a normal wave is possible.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 89, pp. 210–218, 1979.     

Body fitted link-cell algorithm for particulate flow simulation in curved pipeline domain

The link-cell (LC) algorithm is widely used in discrete element method (DEM) simulation, in order to increase computational efficiency. The common way is to divide the entire computational domain into a series of square sub-cells. A huge index matrix, Ω$\Omega$, is required to store the information of particles located in each of these sub-cells. However, most of these sub-cells are always empty for some anomalistic computational domain, such as particulate flow in a pipeline. These empty sub-cells also consume the limited memory bandwidth and lower the computational power. In order to reduce the size of the index matrix, a body fitted link-cell (BFLC) algorithm is established to identify the neighbors quickly. Furthermore, a simplified algorithm for simulation of two dimensional particulate flow in curved pipelines is presented. Lastly, an example is presented to validate the BFLC algorithm.     

Motion of a nonlinear viscoelastic liquid in cylindrical channels of triangular cross section

The problem of the nonrectilinear steady-state flow of a nonlinear viscoelastic liquid in cylindrical channels is considered. It is established that in channels whose cross sections form an equilateral triangle or an isosceles right-angled triangle there are six transverse currents (eddies) in a plane perpendicular to the main longitudinal flow. In cylinders with cross sections in the form of an arbitrary triangle there may be four or six eddies, depending on the shape of the triangle.     

Bounds for the first eigenvalue of the horizontal Laplacian in positively curved sub-Riemannian manifolds

We establish lower bounds for the first non-zero eigenvalue for the natural geometric sub-elliptic Laplacian operator defined on sub-Riemannian manifolds of step 2 that satisfy a positive curvature condition. The methods are very general and can be applied even when the sub-Riemannian geometry has considerable torsion.     

An analytical solution for free liquid sloshing in a finite-length horizontal cylindrical container filled to an arbitrary depth

A general series-type theoretical formulation based on the linearized potential theory, the method of separation of variables, and the translational addition theorem for cylindrical Bessel functions is developed to study three-dimensional natural sloshing in a partially filled horizontally-mounted circular cylindrical tank of finite span. Assuming time-harmonic variations, the potential solutions associated with the Symmetric/Antisymmetric (S/A) modes of free liquid surface oscillations are first analytically expanded as series of bounded spatial functions with unknown modal coefficients. The impenetrability conditions of the rigid end-plates along with the free surface dynamic/kinematic boundary condition are then imposed. The zero-normal-velocity requirement of the lateral tank boundary is subsequently applied by innovative use of Graf's translational addition theorem for modified cylindrical Bessel functions. After truncation, four independent sets of homogeneous algebraic equations are obtained that are then numerically worked out for the natural sloshing eigen-frequencies and free surface oscillation mode shapes. Extensive numerical data include the first thirty six longitudinal/transverse Antisymmetric/Symmetric (AA, SA, AS, SS) dimensionless sloshing frequencies, for a wide range of liquid fill depths and container span to radius ratios. Also, the influence of fill depth on the free surface oscillation mode shapes is addressed through selected 2D images. Comprehensive numerical simulations illustrate the strong effects of container length and liquid fill depth on the calculated sloshing frequencies. It is revealed that the frequency branches with the same transverse mode number form a cluster that progressively merge together amid the tank fill-depth limits as the tank span ratio increases. On the other hand, when the tank length substantially decreases, the number of “frequency cross-overs” between various frequency clusters at certain liquid fill depths considerably increases. Moreover, primary advantages of proposed methodology in comparison to other approximate/numerical methods are explicitly pointed out, convergence of solution is tested, and accuracy/reliability of the results is demonstrated by comparisons with available data.     

A Stokes-like system for natural convection in a horizontal annulus

A linear version of the most commonly used model for natural convection in the horizontal annulus is considered here. Also, its validity is estimated. The predicted average Nusselt number is exactly found by this method, and it depends only on the geometry.     

Motion correction of a statistically uncertain system under communication constraints

The problem of motion correction of a controlled system is considered. It is required to minimize a terminal functional under statistical uncertainty of the disturbance and incomplete information about the state of the system. Reachable sets of filtering and prediction equations are used; these sets are uniquely determined for a given time moment by the realizations of the observed signal and the chosen control. A modification of the correction problem under communication constraints is considered, in which the bounded capacity of the digital data transmission channel is taken into account. It is assumed that the object is equipped with a computing facility that can remember the measured information, process it with a high level of accuracy, transmit it, and receive encoded signals via communication channels. Signals in the form of words of bounded length consisting of integers come to the control and information processing center (CIPC) at discrete time moments. For simplicity, the communication channel is assumed to be noise- and delay-free. The encoding device in the communication channel is used for transmitting information about the measured parameters of the object to the CIPC and the control action from the CIPC to the object. At the CIPC, the information about the parameters is decoded and used for calculating the correction moments and optimal control. Relations between the reconstruction accuracy of the measured parameters and the optimal value of the functional are obtained as well as between the length of the transmitted word and the transmission frequency. Several results are exemplified.     

The Sound Field of a Source That Executes in a Liquid Layer a Motion Represented as the Sum of a Subsonic Uniform Rectilinear Motion and a Periodic Motion. Exact (Explicit) Solutions

The problem on the sound field generated in a liquid layer by a moving point source that was turned on at a moment infinitely distant in the past is considered. Properties of the layer and the source under consideration are chosen in such a way that the solution of the problem can be constructed in the form of a triple series, separating variables in a moving coordinate system. The expressions obtained for the terms of this series (for normal waves) are not only exact but also explicit outside a neighborhood of the source in the sense that they are products of elementary and known functions of coordinates and time. Bibliography: 10 titles.     

Isentropic fluid dynamics in a curved pipe

In this paper we study isentropic flow in a curved pipe. We focus on the consequences of the geometry of the pipe on the dynamics of the flow. More precisely, we present the solution of the general Cauchy problem for isentropic fluid flow in an arbitrarily curved, piecewise smooth pipe. We consider initial data in the subsonic regime, with small total variation about a stationary solution. The proof relies on the front-tracking method and is based on [1].     

Maximum number of flows in a pipeline

Unconditional pipeline computers (UPC) are studied from the viewpoint of the possibility of processing independent flows of information on them. Necessary and sufficient conditions are obtained which the parameters of UPC must satisfy in order that the pipeline admit K>1 independent minimum flows. Uniqueness of these flows is proved, and an effective algorithm for finding them is set forth.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 139, pp. 22–40, 1984.     

Large Deviations of a Storage Process with Fractional Brownian Motion as Input

We study probabilities of large extremes of the storage process Y(t) = sup _t (X() - X(t) - c( - t)), where X(t) is the fractional Brownian motion. We derive asymptotic behavior of the maximum tail distribution for the process on fixed or slowly increased intervals by a reduction the problem to a large extremes problem for a Gaussian field.     

On the motion of fluid in a curved annulus

Résumé On considère l'écoulement d'un liquide incompressible dans un anneau pour determiner la réduction de l'écoulement à cause de la courbure de l'anneau.     

Two-dimensional curved fronts in a periodic shear flow

This paper is devoted to the study of traveling fronts of reaction-diffusion equations with periodic advection in the whole plane R². We are interested in curved fronts satisfying some “conical” conditions at infinity. We prove that there is a minimal speed c^∗ such that curved fronts with speed c exist if and only if c≥c^∗. Moreover, we show that such curved fronts are decreasing in the direction of propagation, that is, they are increasing in time. We also give some results about the asymptotic behaviors of the speed with respect to the advection, diffusion and reaction coefficients.     

Benefits of a truck appointment system on the service quality of inland transport modes at a multimodal container terminal

Container terminals pay more and more attention to the service quality of inland transport modes such as tucks, trains and barges. Truck appointment systems are a common approach to reduce truck turnaround times. This paper provides a tool to use the truck appointment system to increase not only the service quality of trucks, but also of trains, barges and vessels. We propose a mixed integer linear programming model to determine the number of appointments to offer with regard to the overall workload and the available handling capacity. The model is based on a network flow representation of the terminal and aims to minimize overall delays at the terminal. It simultaneously determines the number of truck appointments to offer and allocates straddle carriers to different transport modes. Numerical experiments, conducted on actual data, quantify the benefits of this combined solution approach. Discrete-event simulation validates the results obtained by the optimization model in a stochastic environment.     

The motion of a cylinder-rod system on a horizontal plane: Path controllability and closed-loop control

This work deals with the guidance and control of a system which is composed of a rolling cylinder and a controlled slender rod that is pivoted, through its center of mass, about the cylinder's center. Given a finite time interval [0, t_f], and let P₁ and P₂ be two points in the (X, Y)-plane. The problem dealt with here is to find a closed-loop control law for the cylinder-rod system such that:

• 1.(i) the cylinder center will move from P₁ to P₂ during [0, t_f] and will come to rest at P₂, and
• 2.(ii) the rod will rotate from an angle ψ21 to ψ22 during [0, t_f] and will stop to rotate at t = t_f.

By introducing the concept of path controllability, a closed-loop control law for the solution of the above-posed problem is proposed and its efficiency is demonstrated by solving numerically some examples.     

Optimization of pressure control in a gas pipeline

We consider the synthesis of an approximate optimal control for a gas transport system when state information is acquired at the points X₁,...,x_n of the interval 0 x during the entire control period 0 t . This means that the functions (t, x₁),...,(t, x_n) characterizing the state of the controlled system at the points X₁,...,x_n are known. The approximate optimal control is determined using this information. We solve the control optimization problem which, for a given deviation of the approximate optimal control from the optimum, produces a minimum-information approximate optimal control, i.e., a control determined by a formula with the least number of points x_i, and establishes the location of these points.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 63, pp. 118–123, 1987.