Particle trapping in multi-state quantum walk on a circle is studied. The timeaveraged probability distribution of a particle which moves four different lattice sites according to four internal states is calculated exactly. In contrast with “Hadamard walk” with only two internal states, the particle remains at the initial position with high probability. The time-averaged probability of finding ...

................................................................................................ 3 Introduction............................................................................................ 3 Part 1................................................................................................. 3 Diesel aerosol composition and structure................................................

a two-dimensional single particle finite element model was used to examine the effects of particle fragmental pattern on the average molecular weights, polymerization rate and particle overheating in heterogeneous ziegler-natta olefin polymerization. a two-site catalyst kinetic mechanism was employed together with a dynamic two-dimensional molecular species in diffusion-reaction equation. the i...

Aging of precipitation hardened alloys results in particle coarsening, which in turn affects the strength. In this study, the effect of particle size distribution on the strength of precipitation-hardened alloys was considered. To better represent real alloys, the particle radii were distributed using the Wagner and Lifshitz and Slyozov (WLS) particle size distribution theory. The dislocation m...

In this paper, we develop a multi-scale model to describe the particle growth in a fluidized bed reactor. Population balance model is presented to describe the dynamical behavior of particle size distribution. Stability analysis is derived to determine the control configuration for the complex particulate process. Inventory control strategy is applied to control the particle size distribution.

We summarize recent calculations concerning the evolution kernels of the two-particle B-meson distribution amplitudes φ + and φ − taking into account three-particle contributions, as well as the evolution kernel of the combination of three-particle distribution amplitudes Ψ A − Ψ V. We exploit these results to confirm constraints on φ + and φ − derived from the light-quark equation of motion.

We present in this paper a calculation of the average proton-nucleus inelasticity. Using an Iterative Leading Particle Model and the Glauber model we relate the leading particle distribution in nucleon-nucleus interactions with the respective one in nucleon-proton collisions. To describe the leading particle distribution in nucleon-proton collisions we use the Regge-Mueller formalism.

A conditional kinetic energy is defined in terms of the Wigner distribution. It is shown that this kinetic energy may become negative for negative Wigner distributions. A free particle wave packet with negative kinetic energy will spread in a nonclassical manner. 1 The Free Particle In classical statistical mechanics, a particle is described in terms of a nonnegative phase space distribution P ...

This paper mainly discusses the application of the particle swarm optimization in logistics distribution routing problems. Combining with the characteristics of logistics and distribution, it established a mathematical model of the distribution routing problem. Introducing three kinds of optimization strategies in the particle swarm optimization to optimize the particle swarm algorithm, constru...

Particle breakage in stirred vessels is usually modeled using population balance equations (PBEs) to describe the evolution in particle size with time. Although shape has a strong effect on the particle properties and hence the product quality, changes in the particle shape distribution are typically neglected. To account for changes in both size and shape simultaneously, a multivariate populat...