Folding characterization in conservative chaotic fluid flows

We study transport of passive scalar fields in a bidimensional incompressible chaotic fluid flow. For a spatially smooth velocity field with impulsive perturbations, the model is described by a randomized standard mapping. We numerically investigate passive scalar field transport for given initial concentration distributions and their dependence on the nonlinearity and noise amplitude. We show that space and time concentration histograms are determined by the underlying mechanism of stretching and folding. Moreover, to characterize this process we introduce a parameter, the average derivative of a tracer line length, which shows interesting scale properties.     

Local well‐posedness for the ideal incompressible density‐dependent viscoelastic flow

In this paper, we study the ideal incompressible density‐dependent Oldroyd model in . We establish local in time existence and uniqueness of solutions for the ideal incompressible density‐dependent Oldroyd model. Copyright © 2014 John Wiley & Sons, Ltd.     

Maximizing profit of a food retailing chain by targeting and promoting valuable customers using Loyalty Card and Scanner Data

In this paper, we set up a House of Profit Model, an approach of maximizing profit of a food retailing chain by targeting and promoting valuable customers. Our model combines

• •segmentation analysis of households using Loyalty Card and Scanner Data,
• •price and promotion elasticity analysis,
• •simulation of effects of pricing and promotion,
• •price and promotion optimization to maximize profit.

These components are well-known in the literature and each of them has received considerable independent study. However, in this study we combine each of these components into one consistent, application-orientated model. We then demonstrate using panel data that the combination has a synergic effect on the efficiency of estimation and the maximization of profit (e.g., price and promotion elasticity estimation is improved by conducting it within market segments rather than across an entire hetereogeneous population). These estimates are further improved by incorporating “pass through”—a functional relationship between a retailer’s unit prices and unit costs.     

Incompressibility of tori transverse to Axiom A flows

We prove that a torus transverse to an Axiom A vector field that does not exhibit sinks, sources or null homotopic periodic orbits on a closed irreducible -manifold is incompressible. This strengthens the works of Brunella (1993), Fenley (1995), and Mosher (1992).

     

Mobile geometric graphs: detection, coverage and percolation

We consider the following dynamic Boolean model introduced by van den Berg et al. (Stoch. Process. Appl. 69:247–257, 1997). At time 0, let the nodes of the graph be a Poisson point process in ${\mathbb{R}^d}$ with constant intensity and let each node move independently according to Brownian motion. At any time t, we put an edge between every pair of nodes whose distance is at most r. We study three fundamental problems in this model: detection (the time until a target point—fixed or moving—is within distance r of some node of the graph); coverage (the time until all points inside a finite box are detected by the graph); and percolation (the time until a given node belongs to the infinite connected component of the graph). We obtain precise asymptotics for these quantities by combining ideas from stochastic geometry, coupling and multi-scale analysis.     

A new look at a smart polling model

We analyze a Markovian smart polling model, which is a special case of the smart polling models studied in the work of Boon et al. (Queueing Syst 66:239–274, 2010), as well as a generalization of the gated M / M / 1 queue considered in Resing and Rietman (Stat Neerlandica 58:97–110, 2004). We first derive tractable expressions for the stationary distribution (when it exists) as well as the Laplace transforms of the transition functions of this polling model—while further assuming the system is empty at time zero—and we also present simple necessary and sufficient conditions for ergodicity of the smart polling model. Finally, we conclude the paper by briefly explaining how these techniques can be used to study other interesting variants of this smart polling model.     

On the blow-up criterion of strong solutions for the MHD equations with the Hall and ion-slip effects in {\mathbb{R}^{3}}

In this paper, we establish a blow-up criterion of strong solutions to the 3D incompressible magnetohydrodynamics equations including two nonlinear extra terms: the Hall term (quadratic with respect to the magnetic field) and the ion-slip term (cubic with respect to the magnetic field). This is an improvement of the recent results given by Fan et al. (Z Angew Math Phys, 2015).     

A cognitive hierarchy model of behavior in the action commitment game

We apply the cognitive hierarchy model of Camerer et al. (Q J Econ 119(3):861–898, 2004)—where players have different levels of reasoning—to Huck et al. (Games Econ Behav 38:240–264, 2002) discrete version of Hamilton and Slutsky (Games Econ Behav 2:29–46, 1990) action commitment game—a duopoly with endogenous timing of entry. We show that, for an empirically reasonable average number of thinking steps, the model rules out Stackelberg equilibria, generates Cournot outcomes including delay, and outcomes where the first mover commits to a quantity higher than Cournot but lower than Stackelberg leader. We show that a cognitive hierarchy model with quantal responses can explain the most important features of the experimental data on the action commitment game in (2002). In order to gauge the success of the model in fitting the data, we compare it to a noisy Nash model. We find that the cognitive hierarchy model with quantal responses fits the data better than the noisy Nash model.     

Large-time behavior of solutions to the equations of a viscous polytropic ideal gas

We study Lagrangian systems with symmetry under the action of a constant generalized force in the direction of the symmetry field. After Routh's reduction, such systems become nonautonomous with Lagrangian quadratic in time. We prove the existence of solutions tending to an orbit of the symmetry group as t± . As an example, we study doubly asymptotic solutions for the Kirchhoff problem of a heavy rigid body in an infinite volume of incompressible ideal fluid performing a potential motion.Supported by GNFM and by MURST (40%: «Equazioni di evoluzione...»).Supported by Russian Foundation of Basic Research and by INTAS.     

On the regularity of the pressure field of Brenier’s weak solutions to incompressible Euler equations

In this paper we improve the regularity in time of the gradient of the pressure field arising in Brenier’s variational weak solutions (Comm Pure Appl Math 52:411–452, 1999) to incompressible Euler equations. This improvement is necessary to obtain that the pressure field is not only a measure, but a function in . In turn, this is a fundamental ingredient in the analysis made by Ambrosio and Figalli (2007, preprint) of the necessary and sufficient optimality conditions for the variational problem by Brenier (J Am Mat Soc 2:225–255, 1989; Comm Pure Appl Math 52:411–452, 1999).     

Asymptotic spreading of KPP reactive fronts in incompressible space–time random flows

We study the asymptotic spreading of Kolmogorov–Petrovsky–Piskunov (KPP) fronts in space–time random incompressible flows in dimension d>1$d>1$. We prove that if the flow field is stationary, ergodic, and obeys a suitable moment condition, the large time front speeds (spreading rates) are deterministic in all directions for compactly supported initial data. The flow field can become unbounded at large times. The front speeds are characterized by the convex rate function governing large deviations of the associated diffusion in the random flow. Our proofs are based on the Harnack inequality, an application of the sub-additive ergodic theorem, and the construction of comparison functions. Using the variational principles for the front speed, we obtain general lower and upper bounds of front speeds in terms of flow statistics. The bounds show that front speed enhancement in incompressible flows can grow at most linearly in the root mean square amplitude of the flows, and may have much slower growth due to rapid temporal decorrelation of the flows.     

An orienteering model for the search and rescue problem

In this paper, we propose a new model for the search and rescue problem. We focus on the case of a single airborne search asset through a connected space and continuous time with a maximum travel time \(T\) . The intent is to maximize the detection of a cooperative target (search and rescue). The proposed model is based on the assumption of existing a priori information (e.g., result of information fusion process) to establish a spatial distribution of probability of containment in possible geographic locations. The possibility area is defined using a cut threshold on the probability of containment and the search path as well as the allocation of the level of effort to each region in the search space is obtained based on an orienteering model. We illustrate the application of the proposed model on an empirical example.     

A linear programming approach for determining optimal advertising policy

^** Email: wkc{at}maths.hku.hk In this paper, we propose a new advertising model which cancapture the advertising wear out phenomenon. The objective hereis to maximize overall sales. We show how to derive the optimalpulsation advertising strategy. The optimization problem canbe formulated as a linear programming problem. Closed-form optimalsolution can also be obtained under some conditions. We presentnumerical examples to illustrate the proposed model and applythe model to practical sales data.     

Global well-posedness of incompressible flow in porous media with critical diffusion in Besov spaces

In this paper we study the model of heat transfer in a porous medium with a critical diffusion. We obtain global existence and uniqueness of solutions to the equations of heat transfer of incompressible fluid in Besov spaces with 1?p?∞ by the method of modulus of continuity and Fourier localization technique.     

Incompressible pairwise incompressible surfaces in link complements

The central subject of studying in this paper is incompressible pairwise incompressible surfaces in link complements. Let L be a non-split prime link and let F be an incompressible pairwise incompressible surface in S~3 - L. We discuss the properties that the surface F intersects with 2-spheres in S~3 - L. The intersection forms a topological graph consisting of a collection of circles and saddle-shaped discs. We introduce topological graphs and their moves (R-move and S~2-move), and define the characteristic number of the topological graph for F∩S~2±. The characteristic number is unchanged under the moves. In fact, the number is exactly the Euler Characteristic number of the surface when a graph satisfies some conditions. By these ways, we characterize the properties of incompressible pairwise incompressible surfaces in alternating (or almost alternating) link complements. We prove that the genus of the surface equals zero if the component number of F∩S~2+(or F∩S~2-) is less than five and the graph is simple for alternating or almost alternating links. Furthermore, one can prove that the genus of the surface is zero if #(F) ≤8.     

Compositions of convex functions and fully linear models

Derivative-free optimization (DFO) is the mathematical study of the optimization algorithms that do not use derivatives. One branch of DFO focuses on model-based DFO methods, where an approximation of the objective function is used to guide the optimization algorithm. Proving convergence of such methods often applies an assumption that the approximations form fully linear models—an assumption that requires the true objective function to be smooth. However, some recent methods have loosened this assumption and instead worked with functions that are compositions of smooth functions with simple convex functions (the max-function or the \(\ell _1\) norm). In this paper, we examine the error bounds resulting from the composition of a convex lower semi-continuous function with a smooth vector-valued function when it is possible to provide fully linear models for each component of the vector-valued function. We derive error bounds for the resulting function values and subgradient vectors.     

On the mechanics of helical flows in an ideal incompressible nonviscous continuous medium

We find a general solution to the problem on the motion in an incompressible continuous medium occupying at any time a whole domain D ? R ³ under the conditions that D is an axially symmetric cylinder and the motion is described by the Euler equation together with the continuity equation for an incompressible medium and belongs to the class of helical flows (according to I.S. Gromeka’s terminology), in which sreamlines coincide with vortex lines. This class is constructed by the method of transformation of the geometric structure of a vector field. The solution is characterized in Theorem 2 in the end of the paper.     

Incompressible limit of all-time solutions to 3-D full Navier–Stokes equations for perfect gas with well-prepared initial condition

In this paper, we prove the incompressible limit of all-time strong solutions to the three-dimensional full compressible Navier–Stokes equations. Here the velocity field and temperature satisfy the Dirichlet boundary condition and convective boundary condition, respectively. The uniform estimates in both the Mach number \({\epsilon\in(0,\overline{\epsilon}]}\) and time \({t\in[0,\infty)}\) are established by deriving a differential inequality with decay property, where \({\overline{\epsilon}\in(0,1]}\) is a constant. Based on these uniform estimates, the global solution of full compressible Navier–Stokes equations with “well-prepared” initial conditions converges to the one of isentropic incompressible Navier–Stokes equations as the Mach number goes to zero.