In the past ten years much work has been undertaken on developing mixture theory continuum models to describe kinetic sieving-driven size segregation. We propose an extension to these models that allows their application to bidisperse flows over inclined channels, with particles varying in density and size. Our model incorporates both a recently proposed explicit formula for how the total pressure is distributed among different species of particles, which is one of the key elements of mixture theory-based kinetic sieving models, and a shear rate-dependent drag. The resulting model is used to predict the range of particle sizes and densities for which the mixture segregates. The prediction of no segregation in the model is benchmarked by using discrete particle simulations, and good agreement is found when a single fitting parameter is used which determines whether the pressure scales with the diameter, surface area or volume of the particle.

Over the last 12 years, numerous new theoretical continuum models have been formulated to predict particle segregation in the size-based bidisperse granular flows over inclined channels. Despite their presence, to our knowledge, no attempts have been made to compare and contrast the fundamental basis upon which these continuum models have been formulated. In this paper, firstly, we aim to illustrate the difference in these models including the incompatible nomenclature which impedes direct comparison. Secondly, we utilise (i) our robust and efficient in-house particle solver MercuryDPM, and (ii) our accurate micro-macro (discrete to continuum) mapping tool called coarse-graining, to compare several proposed models. Through our investigation involving size-bidisperse mixtures, we find that (i) the proposed total partial stress fraction expressions do not match the results obtained from our simulation, and (ii) the kinetic partial stress fraction dominates over the total partial stress fraction and the contact partial stress fraction. However, the proposed theoretical total stress fraction expressions do capture the kinetic partial stress fraction profile, obtained from simulations, very well, thus possibly highlighting the reason why mixture theory segregation models work for inclined channel flows. However, further investigation is required to strengthen the basis upon which the existing mixture theory segregation models are built upon.

Micro-macro transition methods can be used to, both, calibrate and validate continuum models from discrete data obtained via experiments or simulations. These methods generate continuum fields such as density, momentum, stress, etc., from discrete data, i.e. positions, velocity, orientations and forces of individual elements. Performing this micro-macro transition step is especially challenging for non-uniform or dynamic situations. Here, we present a general method of performing this transition, but for simplicity we will restrict our attention to two-component scenarios. The mapping technique, presented here, is an extension to the micro-macro transition method, called coarse-graining, for unsteady two-component flows and can be easily extended to multi-component systems without any loss of generality. This novel method is advantageous; because, by construction the obtained macroscopic fields are consistent with the continuum equations of mass, momentum and energy balance. Additionally, boundary interaction forces can be taken into account in a self-consistent way and thus allow for the construction of continuous stress fields even within one element radius of the boundaries. Similarly, stress and drag forces can also be determined for individual constituents of a multicomponent mixture, which is critical for several continuum applications, e.g. mixture theory-based segregation models. Moreover, the method does not require ensemble-averaging and thus can be efficiently exploited to investigate static, B Deepak R. Tunuguntla steady and time-dependent flows. The method presented in this paper is valid for any discrete data, e.g. particle simulations, molecular dynamics, experimental data, etc.; however, for the purpose of illustration we consider data generated from discrete particle simulations of bidisperse granular mixtures flowing over rough inclined channels. We show how to practically use our coarse-graining extension for both steady and unsteady flows using our open-source coarse-graining tool MercuryCG. The tool is available as a part of an efficient discrete particle solver MercuryDPM (www.MercuryDPM. org).

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Evaluating bias, fairness, and social impact in monolingual language models is a difficult task. This challenge is further compounded when language modeling occurs in a multilingual context. Considering the implication of evaluation biases for large multilingual language models, we situate the discussion of bias evaluation within a wider context of social scientific research with computational work. We highlight three dimensions of developing multilingual bias evaluation frameworks: (1) increasing transparency through documentation, (2) expanding targets of bias beyond gender, and (3) addressing cultural differences that exist between languages. We further discuss the power dynamics and consequences of training large language models and recommend that researchers remain cognizant of the ramifications of developing such technologies.

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