During rapid solidification, solute may be incorporated into the solid phase at a concentration significantly different from that predicted by equilibrium thermodynamics. This process, known as solute trapping, leads to a progressive reduction in the concentration change across the interface as the solidification rate increases. Theoretical treatments of rapid solidification using traditional sharp-interface descriptions require the introduction of separately derived nonequilibrium models for the behavior of the interfacial temperature and solute concentrations. In contrast, phase-field models employ a diffuse-interface description and eliminate the need to specify interfacial conditions separately. While at low solidification rates equilibrium behavior is recovered, at high solidification rates nonequilibrium effects naturally emerge from these models. In particular, in a previous study we proposed a phase-field model of a binary alloy [A. A. Wheeler et al., Phys. Rev. E 47, 1893 (1993)] in which we demonstrated solute trapping. Here we show that solute trapping is also possible in a simpler diffuse interface model. We show that solute trapping occurs when the solute diffusion length $D_I/V$ is comparable to the diffuse interface thickness. Here $V$ is the interface velocity and $D_I$ characterizes the solute diffusivity in the interfacial region. We characterize the dependence of the critical speed for solute trapping on the equilibrium partition coefficient $k_E$ that shows good agreement with experiments by Aziz and co-workers [see M. J. Aziz, Metall. Mater. Trans. A 27, 671 (1996)]. We also show that in the phase-field model, there is a dissipation of energy in the interface region resulting in a solute drag, which we quantify by determining the relationship between the interface temperature and velocity.

Partial least squares discriminant analysis (PLS-DA) is a well-known technique for feature extraction and discriminant analysis in chemometrics. Despite its popularity, it has been observed that PLS-DA does not automatically lead to extraction of relevant features. Feature learning and extraction depends on how well the discriminant subspace is captured. In this paper, discriminant subspace learning of chemical data is discussed from the perspective of PLS-DA and a recent extension of PLS-DA, which is known as the locality preserving partial least squares discriminant analysis (LPPLS-DA). The objective is twofold: (a) to introduce the LPPLS-DA algorithm to the chemometrics community and (b) to demonstrate the superior discrimination capabilities of LPPLS-DA and how it can be a powerful alternative to PLS-DA. Four chemical data sets are used: three spectroscopic data sets and one that contains compositional data. Comparative performances are measured based on discrimination and classification of these data sets. To compare the classification performances, the data samples are projected onto the PLS-DA and LPPLS-DA subspaces, and classification of the projected samples into one of the different groups (classes) is done using the nearest-neighbor classifier. We also compare the two techniques in data visualization (discrimination) task. The ability of LPPLS-DA to group samples from the same class while at the same time maximizing the between-class separation is clearly shown in our results. In comparison with PLS-DA, separation of data in the projected LPPLS-DA subspace is more well defined.

To curb the spread of SARS-CoV-2 virus (COVID-19) in Malaysia, the government imposed a nationwide movement control order (MCO) from 18 March 2020 to 3 May 2020. It was enforced in four phases (i.e., MCO 1, MCO 2, MCO 3 and MCO 4). In this paper, we propose an initiative to assess the impact of MCO by using time-varying reproduction number (Rt). We used data from the Johns Hopkins University Centre for Systems Science and Engineering Coronavirus repository. Day 1 was taken from the first assumed local transmission of COVID-19. We estimated Rt by using the EpiEstim package and plotted the epidemic curve and Rt. Then, we extracted the mean Rt at day 1, day 5 and day 10 for all MCO phases and compared the differences. The Rt values peaked around day 43, which was shortly before the start of MCO 1. The means for Rt at day 1, day 5, and day 10 for all MCOs ranged between 0.665 and 1.147. The average Rt gradually decreased in MCO 1 and MCO 2. Although spikes in the number of confirmed cases were observed when restrictions were gradually relaxed in the later MCO phases, the situation remained under control with Rt values being stabilised to below unity level (Rt value less than one).

Dimensionality reduction plays a pivotal role in preparing high-dimensional data for classification and discrimination tasks by eliminating redundant features and enhancing the efficiency of classifiers. The effectiveness of a dimensionality reduction algorithm hinges on its numerical stability. When data projections are numerically stable, they lead to enhanced class separability in the lower-dimensional embedding, consequently yielding higher classification accuracy. This paper investigates the numerical attributes of dimensionality reduction and discriminant subspace learning, with a specific focus on Locality-Preserving Partial Least Squares Discriminant Analysis (LPPLS-DA). High-dimensional data frequently introduce singularity in the scatter matrices, posing a significant challenge. To tackle this issue, the paper explores two robust implementations of LPPLS-DA. These approaches not only optimize data projections but also capture more discriminative features, resulting in a marked improvement in classification accuracy. Empirical evidence supports these findings through numerical experiments conducted on synthetic and spectral datasets. The results demonstrate the superior performance of the proposed methods when compared to several state-of-the-art dimensionality reduction techniques in terms of both classification accuracy and dimension reduction.