Blob algebra and two-color Soergel calculus

In 2003, Martin and Woodcock noticed a connection between the representation theory of the blob algebra and the Kazhdan–Lusztig polynomials associated with the infinite dihedral group. However, no conceptual explanation for this coincidence has yet been provided. In this study, a possible explanation of this phenomenon is suggested by enunciating a conjecture that relates the endomorphism algebra of Bott–Samelson bimodules to certain subalgebras of the blob algebra obtained by idempotent truncation. Evidence supporting this conjecture is provided.     

Self-similar point vortices and confinement of vorticity

This papers deals with the large time behavior of solutions of the incompressible Euler equations in dimension 2. We consider a self-similar configuration of point vortices which grows like the square root of the time. We study the confinement properties of a blob of vorticity initially located around the first point vortex and moving in the velocity field produced by itself and by the other point vortices. We find a su?cient condition on the point vortices such that the vorticity stays confined around the first point vortex at a rate better than the square root of the time. The relevance to the large time behavior of the Euler equations is discussed.     

Convergence of vortex methods for weak solutions to the 2-D euler equations with vortex sheet data

We prove the convergence of vortex blob methods to classical weak solutions for the two-dimensional incompressible Euler equations with initial data satisfying the conditions that the vorticity is a finite Radon measure of distinguished sign and the kinetic energy is locally bounded. This includes the important example of vortex sheets. The result is valid as long as the computational grid size h does not exceed the smoothing blob size ε, i.e., h/ε ≦ C.. ©1995 John Wiley & Sons, Inc.     

A computational study of the error in the vortex method associated with discontinuous vorticity

We investigate computationally the error computed by the vortex method for a discontinuous patch of vorticity. Specifically, the computed velocity and vorticity of an elliptical path of constant vorticity, known as the Kirchhoff ellipse, are compared to the analytic velocity and vorticity. The error in the velocity and the vorticity for the Kirchhoff ellipse as computed by the vortex method is presented. This error is studied as a function of the aspect ratio of the ellipse, the blob function, the spacing between the centers of the computational elements, and the blob radius. Both the error at the initial time and the error after three revolutions of the ellipse are discussed. © 1996 John Wiley & Sons, Inc.     

Supply chain dynamic configuration as a result of new product development

This study considers supply chain network configuration in an innovative environment while the new product development (NPD) will affect the supply chain configuration (SCC). The time of new product introduction has a significant effect on the market performance while it has an effect on the supply chain configuration. Supplier integration into the new product introduction is the key parameter for successfully new product introduction, which may contribute to supply chain reconfiguration. Consequently By considering the new product development concept, we may face with dynamic supply chain configuration during a planning horizontal time. In this study, a new model is presented to consider the dynamic configuration of a supply chain by developing new products. In the proposed model, the dynamic configuration of a supply chain and the new product launching time is optimized simultaneously. The proposed model considers production, sales and transportation planning for the entire supply chain in order to achieve an integrative and efficient supply as well. Then some numerical analyses have been done to show the applicability of the proposed model. The results show that the new product development has a significant effect on the configuration of supply chain.     

THE VORTEX BLOB METHOD AS A SECOND-GRADE NON-NEWTONIAN FLUID

We show that a certain class of vortex blob approximations for ideal hydrodynamics in two dimensions can be rigorously understood as solutions to the equations of second-grade non-Newtonian fluids with zero viscosity and initial data in the space of Radon measures M (R ²). The solutions of this regularized PDE, also known as the isotropic Lagrangian averaged Euler or Euler-α equations, are geodesics on the volume preserving diffeomorphism group with respect to a new weak right invariant metric. We prove global existence of unique weak solutions (geodesics) for initial vorticity in M (R ²) such as point-vortex data, and show that the associated coadjoint orbit is preserved by the flow. Moreover, solutions of this particular vortex blob method converge to solutions of the Euler equations with bounded initial vorticity, provided that the initial data is approximated weakly in measure, and the total variation of the approximation also converges. In particular, this includes grid-based approximation schemes as are common in practical vortex computations.     

Modelling the capillary locking of point defects in nematic liquid crystals

DEDICATED TO JERRY ERIKSEN: It has long been known that the equilibrium configuration withminimum energy of a nematic liquid crystal within a cylindersubject to homeotropic conditions on the lateral boundary isescaped along the axis of the cylinder, and there is no singularityof the orientation field. So problems of explaining the presenceof point defects in capillary tubes and of exploring their stabilityarise. There is enough evidence to believe that the menisciplay a central role in preventing the orientation field arounda point defect from unwinding towards the escaped configuration.We propose a variational model which describes how a point defectinteracts with a meniscus. This interaction fades away at afinite distance. When active, it is two-sided, being repulsiveat first and then attractive when the defect comes closer tothe centre of curvature of the meniscus. Thus, when a defectis enclosed between two menisci they can become antagonists,so that there is a metastable equilibrium position where thedefect could be locked in.     

Simultaneous determination of capacities and load in parallel M/M/1 queues

In this paper, we address an analytical model to simultaneously determine the processing capacity and load assigned to each processor in a multiple processor configuration within the framework of M/M/1 queues. A queueing optimization model is formulated as a nonlinear programming problem having linear constraints. We then propose an optimization algorithm that utilizes the special structure of the problem. To illustrate the applicability of our method, a small sample system has been solved.     

Hele Shaw Flows with Time-Dependent Free Boundaries Involving Injection Through Slits

Consider the classical Hele Shaw situation with two parallel planes separated by a narrow gap. Suppose a Newtonian fluid to be injected into this gap through straight-line slits as well as, possibly, at isolated points. We are interested in predicting the plan-view of the resultant expanding blob, or blobs, of fluid. We show that the method of solution developed earlier for dealing with such problems when the injection is only at isolated points can be adapted to yield solutions in this more general situation.     

Numerical study of soliton-like surface configurations on a magnetic fluid layer in the Rosensweig instability

In the Rosensweig instability, a perpendicular, uniform magnetic field applied to a pool of magnetic fluid generates an ordered periodic pattern on the liquid–air interface when the field exceeds a critical threshold. Decreasing the field strength, a lower critical threshold is observed at which the developed pattern disappears. In this respect, the deformation of the free surface shows a hysteretic behaviour with changing field strength. Recently, in experiments, a novel soliton-like surface configuration has been generated within the hysteretic regime of the Rosensweig instability. The main objective of this paper is a numerical study of this new configuration by means of two models, an axisymmetric two-dimensional one and a fully three-dimensional one.     

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)     

Turbulent Entrainment in the Atmospheric Boundary Layer

Turbulent entrainment – the process by which turbulence inside of the atmospheric boundary layer entrains air from the free troposphere above it – has been investigated using direct numerical simulations in two configurations, one without a cloud and one with a cloud. With the first configuration, we have learned that the entrainment zone in a convective boundary layer growing into a linearly stratified troposphere is better described in terms of a two-layer structure, with different characteristic scales associated with each of the two sub-layers. With the second configuration, we have explained how wind shear across the entrainment zone capping a stratocumulus cloud can render evaporative cooling as important as radiative cooling in driving convective motions. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Vortex Methods for Initial Boundary Value Problems

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一类指数和函数的性质及其应用

对一类指数和函数的递推关系、积分公式、曲线的单峰形态等性质进行了讨论,证明了该函数为概率密度函数,并给出了该函数在等式证明、物质转化反应的微分方程模型等方面的应用.     

The Finite Cell Method for large deformation analysis

The Finite Cell Method (FCM) combines the fictitious domain approach with high-order finite elements and adaptive integration. For linear elastic problems with smooth solution, FCM has been shown to achieve exponential rates of convergence in energy norm, while its structured cell grid guarantees simple mesh generation irrespective of the geometric complexity involved. In this contribution, the FCM idea is combined with standard finite element technology for the solution of geometrically nonlinear problems. In particular, a modified FCM formulation is introduced, which resets the deformed configuration of the fictitious domain to the deformation-free reference configuration after each Newton iteration. Numerical experiments show that this intervention allows for stable nonlinear FCM analysis with very small values of the penalty parameter, while the accuracy of the geometrically nonlinear solution within the physical domain remains unaffected. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rayleigh-Taylor instability of compressible finitely conducting rotating fluid in the presence of a magnetic field

The character of the equilibrium of a non-viscous, compressible finitely conducting rotating fluid in the presence of a vertical magnetic field along the direction of gravitational field has been investigated. It is shown that the solution is characterised by a variational principle. Based on the existence of variational principle, an approximate solution has been derived for the case of a fluid having exponentially varying density in the vertical direction. Due to finite resistivity of the medium it is found that potentially stable or unstable configuration retains its character. Further the growth rate of disturbance has been obtained corresponding to short and long wavelengths and it is found that electrical resistivity suppresses the growth rate for large wavelengths but it increases the same for small wavelengths. It is further shown that magnetic field has a destabilizing influence for large wavelengths and a stabilizing influence for small wavelengths.     

Existence of equilibria in articulated bearings

The existence of equilibrium solutions for a lubricated system consisting of an articulated body sliding over a flat plate is considered. Though this configuration is very common (it corresponds to the popular tilting-pad thrust bearings), the existence problem has only been addressed in extremely simplified cases, such as planar sliders of infinite width. Our results show the existence of at least one equilibrium for a quite general class of (nonplanar) slider shapes. We also extend previous results concerning planar sliders.     

The Existence of Görtler Vortices in Separated Boundary Layers

The linear stability properties of Görtler vortices within a general separated boundary layer flow are addressed. There has been little previous theoretical work directed toward this problem and here we are able to characterize the important features of vortices over the complete wavenumber spectrum. This investigation complements earlier studies of vortices within an attached flow which demonstrated that there are three distinctive wavenumber régimes which together describe the most relevant possibilities for vortex behavior. In the first of these, at relatively small wavenumbers, the mode is inviscid in character; as the vortex wavenumber increases so the spatial amplification rate of the vortices increases until viscous effects become significant and the growth rate begins to diminish. As the wavenumber increases yet further so the vortex is completely stabilized. Here we discuss the corresponding structures which may exist within a separated flow and the most significant result we find is that the maximum growth rate of a mode in this type of flow is actually greater than that which occurs when the flow has not separated. In addition, the inviscid modes are shown to have a far more complicated configuration than within an attached boundary layer and, indeed, their structure can only be completely determined by implementation of numerical procedures.     

DEA based auctions

We discuss the design of a multi-dimensional procurement mechanism that combines Data Envelopment Analysis (DEA) and auction theory. The mechanism selects an agent to provide a project characterized by multiple attributes. The optimal configuration of the multiple attributes is settled endogenously by trading off the costs to the provider with the benefits to the acquirer. This is done within a context of asymmetric information and strategic behavior as well as possibly correlated costs. The mechanism makes it individually rational and incentive compatible to participate and reveal costs, and the outcome is socially optimal (allocatively efficient).