Trapezoidal type inequalities for n-time differentiable functions

In this paper we consider the flow shop scheduling problems with the effects of learning and deterioration. In this model the processing times of a job is defined as a function of its starting time and position in a sequence. The scheduling objective functions are makespan and total completion time. We prove that even with the introduction of learning effect and deteriorating jobs to job processing times, some special flow shop scheduling problems remain polynomially solvable.     

Approximate analytical solutions for strong shocks with variable energy

Approximate analytical solutions are obtained for self-similar flows behind strong shocks with variable energy deposition or withdrawal at the wavefront in a perfect gas at rest with constant initial density. Numerical solutions are also obtained and the approximate solutions agree with these solutions. The effect of the adiabatic index on the solutions is investigated. The dependence of shock density ratio on the parameter characterizing the energy of the flow is studied. It is observed that the rate of deposition of energy at the wavefront decreases with increase of the parameter that specifies the total energy of the flow.     

Mise en position optimale de tores par rapport à un flot d'Anosov

Let Φ′ be an Anosov flow on a (non atoroidal) 3-manifoldM. We say that an incompressible torusT embedded inM admits an optimal position with respect to Φ′ if it is isotopic to a torus transverse to Φ′ outside a finite number of periodic orbits contained inT (there's an additional condition we dont's mention here). The first remark is that such an optimal position is quasi unique, i.e., we prove that if two tori in optimal position are homotopics inM, then they are homotopics along the flow. Then we give some sufficient condition for a torus admiting an optimal position. Eventually, we show that if a finite collection of disjoint tori is such that each torus admits an optimal position, then these optimal positions can be chosen disjoints one from each other.      

Research on permutation flow shop scheduling problems with general position-dependent learning effects

Machine learning exists in many realistic scheduling situations. This study focuses on permutation flow shop scheduling problems, where the actual processing time of a job is defined by a general non-increasing function of its scheduled position, i.e., general position-dependent learning effects. The objective functions are to minimize the total completion time, the makespan, the total weighted completion time, and the total weighted discounted completion time, respectively. To solve these problems, we present approximation algorithms based on the optimal permutations for the corresponding single machine scheduling problems and analyze their worst-case error bound.     

Some results of the worst-case analysis for flow shop scheduling with a learning effect

This article considers flow shop scheduling problems with a learning effect. By the learning effect, we mean that the processing time of a job is defined by a function of its position in a processing permutation. The objective is to minimize the total weighted completion time. Some heuristic algorithms by using the optimal permutations for the corresponding single machine scheduling problems are presented, and the worst-case bound of these heuristics are also analyzed.     

Scheduling jobs with a general learning effect model

The paper deals with machine scheduling problems with a general learning effect. By the general learning effect, we mean that the actual processing time of a job is not only a non-increasing function of the total weighted normal processing times of the jobs already processed, but also a non-increasing function of the job’s position in the sequence, where the weight is a position-dependent weight. We show that even with the introduction of a general learning effect to job processing times, some single machine scheduling problems are still polynomially solvable under the proposed model. We also show that some special cases of the flow shop scheduling problems can be solved in polynomial time.     

Bubble simulations with an interface tracking technique based on a partitioned fluid-structure interaction algorithm

Numerical techniques frequently used for the simulation of one bubble can be classified as interface tracking techniques and interface capturing techniques. Most of these techniques calculate both the flow around the bubble and the shape of the interface between the gas and the liquid with one code. In this paper, a rising axisymmetric bubble is simulated with an interface tracking technique that uses separate codes to determine the position of the gas-liquid interface and to calculate the flow around the bubble. The grid converged results correspond well with the experimental data.The gas-liquid interface is conceived as a zero-mass, zero-thickness structure whose position is determined by the liquid forces, a uniform gas pressure and surface tension. Iterations between the two codes are necessary to obtain the coupled solution of both problems and these iterations are stabilized with a fluid-structure interaction (FSI) algorithm. The flow around the bubble is calculated on a moving mesh in a reference frame that rises at the same speed as the bubble. The flow solver first updates the mesh throughout the liquid domain given a position of the gas-liquid interface and then calculates the flow around the bubble. It is considered as a black box with the position of the gas-liquid interface as input and the liquid forces on the interface as output. During the iterations, a reduced-order model of the flow solver is generated from the inputs and outputs of the solver. The solver that calculates the interface position uses this model to adapt the liquid forces on the gas-liquid interface during the calculation of the interface position.     

Scheduling data transfers in a network and the set scheduling problem

In this paper we consider the online ftp problem. The goal is to service a sequence of file transfer requests given bandwidth constraints of the underlying communication network. The main result of the paper is a technique that leads to algorithms that optimize several natural metrics, such as max-stretch, total flow time, max flow time, and total completion time. In particular, we show how to achieve optimum total flow time and optimum max-stretch if we increase the capacity of the underlying network by a logarithmic factor. We show that the resource augmentation is necessary by proving polynomial lower bounds on the max-stretch and total flow time for the case where online and offline algorithms are using same-capacity edges. Moreover, we also give polylogarithmic lower bounds on the resource augmentation factor necessary in order to keep the total flow time and max-stretch within a constant factor of optimum.     

A comparison of the flow around a flexible and a non-flexible airfoil for flapping wing propulsion

The flow around flapping airfoils is evaluated using the Stereoscopic Particle Image Velocimetry (PIV) technique. Resulting from the measurements is the distribution of the turbulent shear stress. This serves as an indicator for the position of transition from laminar to turbulent flow. The distributions were compared for both a flapping non–flexible airfoil and a flexible airfoil. It was determined that there are differences between the flow around the flexible and the non–flexible airfoils. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Worst-case analysis for flow shop scheduling problems with an exponential learning effect

A real industrial production phenomenon, referred to as learning effects, has drawn increasing attention. However, most research on this issue considers only single machine problems. Motivated by this limitation, this paper considers flow shop scheduling problems with an exponential learning effect. By the exponential learning effect, we mean that the processing time of a job is defined by an exponent function of its position in a processing permutation. The objective is to minimize one of the four regular performance criteria, namely, the total completion time, the total weighted completion time, the discounted total weighted completion time, and the sum of the quadratic job completion times. We present heuristic algorithms by using the optimal permutations for the corresponding single-machine scheduling problems. We also analyse the worst-case bound of our heuristic algorithms.     

Worst-case behavior of simple sequencing rules in flow shop scheduling with general position-dependent learning effects

A real industrial production phenomenon, referred to as learning effects, has drawn increasing attention. However, most research on this issue considers only single machine problems. Motivated by this limitation, this paper considers flow shop scheduling problems with a general position-dependent learning effects. By the general position-dependent learning effects, we mean that the actual processing time of a job is defined by a general non-increasing function of its scheduled position. The objective is to minimize one of the five regular performance criteria, namely, the total completion time, the makespan, the total weighted completion time, the total weighted discounted completion time, and the sum of the quadratic job completion times. We present heuristic algorithms by using the optimal permutations for the corresponding single machine scheduling problems. We also analyze the worst-case bound of our heuristic algorithms.     

Coverage Maximization with Autonomous Agents in Fast Flow Environments

This work examines the cooperative motion of a group of autonomous vehicles in a fast flow environment. The magnitude of the flow velocity is assumed to be greater than the available actuation to each agent. Collectively, the agents wish to maximize total coverage area defined as the set of points reachable by any agent within T time. The reachable set of an agent in a fast flow is characterized using optimal control techniques. Specifically, this work addresses the complementary cases where the static flow field is smooth, and where the flow field is piecewise constant. The latter case arises as a proposed approximation of a smooth flow that remains analytically tractable. Furthermore, the techniques used in the piecewise constant flow case enable treatment for obstacles in the environment. In both cases, a gradient ascent method is derived to maximize the total coverage area in a distributed fashion. Simulations show that such a network is able to maximize the coverage area in a fast flow.     

Convex mean curvature flow with a forcing term in direction of the position vector

A smooth, compact and strictly convex hypersurface evolving in ℝ ⁿ⁺¹ along its mean curvature vector plus a forcing term in the direction of its position vector is studied in this paper. We show that the convexity is preserving as the case of mean curvature flow, and the evolving convex hypersurfaces may shrink to a point in finite time if the forcing term is small, or exist for all time and expand to infinity if it is large enough. The flow can converge to a round sphere if the forcing term satisfies suitable conditions which will be given in the paper. Long-time existence and convergence of normalization of the flow are also investigated.     

Numerical study of a particle separation method based on the Segré-Silberberg effect

Particles that are placed in a laminar pipe flow rotate and migrate transversally to a radial equilibrium position. This so called Segré-Silberberg effect is used in a new method for size separation of particles. The particles to be separated are placed in a pipe flow and subsequently enter an expansion chamber, where the flow is split and the particles are divided into two fractions. This paper reports the results of two-dimensional Euler-Lagrange simulations of the motion of neutrally-buoyant particles inside the expansion chamber. The simulation results agree well with experimental data on the separation and show that the Saffman force has a significant impact onto the particle trajectories. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of electromagnetic stirrer position on fluid flow and solidification in continuous casting mold

A computational study of the effect of stirrer position on fluid flow and solidification in a continuous casting billet mold with in-mold electromagnetic stirring has been carried out. The numerical investigation uses a full coupling method in which alternating magnetic field equations are solved simultaneously with the governing equations of fluid flow and heat transfer. An enthalpy-porosity technique is used for the solidification analysis while the magnetohydrodynamics technique is used for studying the fluid flow behavior under the electromagnetic field. The streamline, liquid fraction, and solid shell thickness at the mold wall have been predicted with and without EMS application at different positions along the length of the mold. Recirculation loops are seen to be formed above and below the stirrer position when fluid flow and electromagnetic field equations were solved, without incorporating the solidification model. Application of the solidification model interestingly resulted in the reduction of the size of the recirculation loops formed. The tangential component of velocity of the fluid near the solidification front, stirring intensity and the effective length of stirring below the stirrer decrease as the stirrer position is moved downwards. Significant changes in characteristics of solid shell formation like delay in initiation of solidification at the mold wall and formation of a gap in the re-solidified shell have been observed with change in stirrer position.     

Modeling duct flow by the R-function method

The article deals with a flow in the tube of rectangular cross-section with an inner circular cylindrical element. We use the numerical method basing on R-functions. This method is meshfree and therefore more efficient than the finite element method that requires remeshing when the geometry of problem is changed. The dependence of the flow on the diameter of the central cylinder and its position in the duct is investigated under constant pressure gradient. It was found that the resistance decreases if the inner element is moved from the center of the duct.     

Control of mechanical systems on Lie groups and ideal hydrodynamics

In contrast to the Euler–Poincaré reduction of geodesic flows of left- or right-invariant metrics on Lie groups to the corresponding Lie algebra (or its dual), one can consider the reduction of the geodesic flows to the group itself. The reduced vector field has a remarkable hydrodynamic interpretation: it is the velocity field for a stationary flow of an ideal fluid. Right- or left-invariant symmetry fields of the reduced field define vortex manifolds for such flows. Now we consider a mechanical system, whose configuration space is a Lie group and whose Lagrangian is invariant with respect to left translations on this group, and assume that the mass geometry f the system may change under the action of internal control forces. Such a system can also be reduced to a Lie group. Without controls, this mechanical system describes a geodesic flow of the left-invariant metric, given by the Lagrangian, and, therefore, its reduced flow is a stationary ideal fluid flow on the Lie group. The standard control problem for such system is to find the conditions under which the system can be brought from any initial position in the configuration space to another preassigned position by changing its mass geometry. We show that under these conditions, by changing the mass geometry, one can also bring one vortex manifold to any other preassigned vortex manifold. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 61, Optimal Control, 2008.     

The Calabi flow on Kähler Surfaces with bounded Sobolev constant (I)

We consider the formation of singularities along the Calabi flow by assuming the uniformly bounded Sobolev constants. On Kähler surfaces we prove that if curvature tensor is not uniformly bounded, then one can form a singular model called deepest bubble; such deepest bubble has to be a scalar flat ALE Kähler metric. In certain Kähler classes on toric Fano surfaces, the Sobolev constants are a priori bounded along the Calabi flow with small Calabi energy. We can also show in certain cases no deepest bubble can form along the flow. It follows that the curvature tensor is uniformly bounded and the flow exists for all time and converges to an extremal metric subsequently. To illustrate our results more clearly, we focus on an example on \({\mathbb{CP}^2}\) blown up three points at generic position. Our result also implies existence of constant scalar curvature metrics on \({\mathbb{CP}^2}\) blown up three points at generic position in the Kähler classes where the exceptional divisors have the same area.     

Laminar magnetohydrodynamic duct flow in the presence of a magnetic dipole

We study magnetohydrodynamic flow of a liquid metal in a straight duct. The magnetic field is produced by an exterior magnetic dipole. This basic configuration is of fundamental interest for Lorentz force velocimetry (LFV), where the Lorentz force opposing the relative motion of conducting medium and magnetic field is measured to determine the flow velocity. The Lorentz force acts in equal strength but opposite direction on the flow as well as on the dipole. We are interested in the dependence of the velocity on the flow rate and on strength of the magnetic field as well as on geometric parameters such as distance and position of the dipole relative to the duct. To this end, we perform numerical simulations with an accurate finite-difference method in the limit of small magnetic Reynolds number, whereby the induced magnetic field is assumed to be small compared with the external applied field. The hydrodynamic Reynolds number is also assumed to be small so that the flow remains laminar. The simulations allow us to quantify the magnetic obstacle effect as a potential complication for local flow measurement with LFV. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)