Particle Characterization by Projected Area Determination

The projected areas of non-spherical particles do not represent an unambiguous particle characteristic. Depending on the orientation towards a constant observational direction, different projected areas result. The spectrum of all projected area values of a particle, if determined representatively, gives the probability with which a certain value is obtained by a single measurement. In this work, the frequency distributions of different examples of test objects were both calculated and measured. The objects were a cube, a rectangular parallelepiped and also three model agglomerates consisting of spheres of the same size. Instead of just one projected area, during each measuring procedure three projected areas from three orthogonal directions can be obtained. A mean value is then calculated to reduce the ambiguity of the particle characteristic and enhance the resolution. A suitable measurement set-up is introduced. The results of calculation and measurement are compared for observation from just one direction and also simultaneous observation from three directions. The frequency distributions of the equivalent diameters of the particle projected areas show a characteristic trend of the total curve with remarkable properties. The simultaneous measurement of three values from mutually orthogonal directions and their mean value calculation result in a much narrower distribution. In this case, a non-sphericity factor can additionally be calculated, whose frequency distribution contains information in a characteristic manner about the degree to which the particle shape differs from a sphere.     

Improved modeling and solution methods for the multi-resource routing problem

This paper presents modeling and solution method improvements for the Multi-Resource Routing Problem (MRRP) with flexible tasks. The MRRP with flexible tasks is used to model routing and scheduling problems for intermodal drayage operations in which two resources (tractors and trailers) perform tasks to transport loaded and empty equipment. Tasks may be either well defined, in which both the origin and the destination of a movement are given, or flexible, in which the origin or the destination is chosen by the model. This paper proposes methods to effectively manage the number of options considered for flexible tasks (either feasible origins for a known destination or feasible destinations for a known origin). This modeling change generates sufficient options to allow for low-cost solutions while maintaining reasonable computational effort. We also propose a new solution method that uses randomized route generation. Computational results from test cases show that these changes improve the quality of solutions by at least 5% in the test cases as compared to methods from previous studies.     

Runge–Kutta Methods for Itô Stochastic Differential Equations with Scalar Noise

A general class of stochastic Runge–Kutta methods for Itô stochastic differential equation systems w.r.t. a one-dimensional Wiener process is introduced. The colored rooted tree analysis is applied to derive conditions for the coefficients of the stochastic Runge–Kutta method assuring convergence in the weak sense with a prescribed order. Some coefficients for new stochastic Runge–Kutta schemes of order two are calculated explicitly and a simulation study reveals their good performance.