Narrow Results

Over the last 25 years a lot of work has been undertaken on constructing continuum models for segregation of particles of different sizes. We focus on one model that is designed to predict segregation and remixing of two differently sized particle species. This model contains two dimensionless parameters: S_r, a measure of the segregation rate, and D_r, a measure of the strength of diffusion. These, in general, depend on both flow and particle properties and one of the weaknesses of the model is that these dependencies are not predicted. They have to be determined by either experiments or simulations.

We present steady-state, periodic, chute-flow simulations using the discrete particle method (DPM) for several bi-disperse systems with different size ratios. The aim is to determine one parameter in the continuum model, i.e. the segregation Péclet number (ratio of the segregation rate to diffusion, S_r/D_r) as a function of the particle size ratio.

Reasonable agreement is found; but, also measurable discrepancies are reported; mainly, in the simulations a thick pure phase of large particles is formed at the top of the flow. Additionally, it was found that the Péclet number increases linearly with the size ratio for low values, but saturates to a value of approximately 7.7.

This paper introduces and analyzes some models in the framework of mean field games (MFGs) describing interactions between two populations motivated by the studies on urban settlements and residential choice by Thomas Schelling. For static games, a large population limit is proved. For differential games with noise, the existence of solutions is established for the systems of partial differential equations of MFG theory, in the stationary and in the evolutive case. Numerical methods are proposed with several simulations. In the examples and in the numerical results, particular emphasis is put on the phenomenon of segregation between the populations.

Ripples or corrugations are common phenomena observed in unpaved roads in less developed countries or regions. They cause several damages in vehicles leading to increased maintenance and product costs. In this paper, we present a computational study about the so-called washboard roads. Also, we study grain segregation on unpaved roads. Our simulations have been performed by the Discrete Element Method (DEM). In our model, the grains are regarded as soft disks. The grains are subjected to a gravitational field and both translational and rotational movements are allowed. The results show that wheels’ of different sizes, weights and moving with different velocities can change corrugations amplitude and wavelength. Our results also show that some wavelength values are related to specific wheels’ speed intervals. Segregation has been studied in roads formed by three distinct grain diameters distribution. We observed that the phenomenon is more evident for higher grain size dispersion.

Segregation of granular particles affects the quality of end products in the pharmaceutical, chemical and food processing industries. Many researchers have worked on controlling the mechanical properties of granular particles to minimize segregation. In this paper, we studied different chute-related factors — inclination angle, friction, fill, channel geometry and base profile — and their effects on segregation. We conducted a small-scale experiment with chute inclined at different angles, and also numerical simulations performed using an open-source discrete element method (DEM) code — LIGGGHTS. We found the optimal condition for minimum segregation of a binary granular mixture. We concluded that segregation is minimized if the stream-wise velocity is low, for example, by keeping the chute at a low inclination $10^{\circ }$ and increasing the wall roughness to 0.14.

Ni-based monocrystal superalloy with fine dendrite, precise orientation and finally elevated service performance is required as turbine blades in advanced aeroengine. In this paper, the melt superheating treatment is carried out for DD3 single crystal superalloy during directional solidification processing. The thermal gradient of solidification interface remains constant for different melt superheating temperatures with the appropriate superheating treatment regulation. It is shown that with the melt superheating temperature increased from 1500°C to 1640°C and then to 1780°C respectively, both the primary and the secondary dendrite arms are obviously refined and the dendrite segregation ratios of Mo, W and Ti are reduced while the deviation angle of (001) crystal orientation can all be controlled within 5°. The dendrite structure refinement and the crystal orientation consistence should be attributed to the melt structure change and heredity which is caused by the superheating treatment.

In this paper, we study hyperbolic and parabolic nonlinear partial differential equation models, which describe the evolution of two intersecting pedestrian flows. We assume that individuals avoid collisions by sidestepping, which is encoded in the transition rates of the microscopic 2D model. We formally derive the corresponding mean-field models and prove existence of global weak solutions for the parabolic model. Moreover we discuss stability of stationary states for the corresponding one-dimensional model. Furthermore we illustrate the rich dynamics of both systems with numerical simulations.

In Schelling’s segregation model, agents of two ethnic groups reside in a regular grid and aim to live in a neighborhood that matches the minimum desired fraction of members of the same ethnicity. The model shows that observed segregation can emerge from people interacting under spatial constraints following homophily preferences. Even mild preferences can generate high degrees of segregation at the macro level. In modern, ethnically diverse societies, people might not define similarity based on ethnicity. Instead, shared tolerance towards ethnic diversity might play a more significant role, impacting segregation and integration in societies. With this consideration, we extend Schelling’s model by dividing the population of agents into value-oriented and ethnicity-oriented agents. Using parameter sweeping, we explore the consequences that the mutual adaptation of these two types of agents has on ethnic segregation, value segregation, and population density in the neighborhood. We examine for equally sized ethnic groups and for majority–minority conditions. The introduction of value-oriented agents reduces total ethnic segregation compared to Schelling’s original model, but the new value segregation appears to be more pronounced than ethnic segregation. Due to spillover effects, stronger ethnic homophily preferences lead not only to greater ethnic segregation, but also to more value segregation. Stronger value-orientation of the tolerant agents similarly leads to increased ethnic segregation of the ethnicity-oriented agents. Also, value-oriented agents tend to live in neighborhoods with more agents than ethnicity-oriented agents. In majority–minority settings, such effects appear to be more drastic for the minority than the majority ethnicity.

Residential segregation has played a central role in theories of minority entrepreneurship. This study integrates two theories in the extant literature on minorities and urban areas (spatial assimilation theory and labor market disadvantage theory); and tests a hypothesis on the self-employment likelihood of black Americans. Descriptive statistics indicate a negative relationship between black-white segregation and increasing socioeconomic status (SES), although blacks remain considerably residentially segregated from whites of similar SES. The model results indicate that, after controlling for a number of factors, segregation of high SES blacks and whites in a metropolitan area is associated with higher likelihood of black self-employment.

Atomic segregation in bimetallic clusters can influence the surface nucleation and also the structures of clusters. It is important to study the effect of atomic segregation on the structure. In this study, initial cooling temperatures were used to tune the atomic segregation ability. Molecular dynamics simulation with an embedded atom method was used to study the relationship between the structure and atomic segregation. It was found that the higher the initial cooling temperature, the more obvious the Ag atomic segregation. When the clusters cooled down from 800 K and 600 K, the clusters formed a mixed icosahedron due to the weak atomic segregation ability. When the initial cooling temperature is higher than 1200 K, all the Ag atoms segregated to the surface layer, the clusters formed a Pd–Ag-core–shell chemical ordering. For 1200 K initial temperature, the structure is decahedral. The clusters formed an fcc structure when the clusters cooled down from 2000 K, 1800 K, and 1500 K. When the clusters cooled down from 860 K and 900 K, not all the Ag atoms segregated to the surface layer, the clusters formed a core–shell chemical ordering with a mixed Pd–Ag core. But the structure of 860 K is twinned of icosahedron and decahedron and that of 900 K is decahedral. This means that the chemical orderings and structures were influenced by the atomic segregation.