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^-α with the exponent α>-1. This model is known to exhibit anomalous scaling of the mean-squared displacement (MSD) of the form ∼t^2/2+α and weak ergodicity breaking in the sense that ensemble averaged and time averaged MSDs do not converge. In this paper, we look at the extreme value statistics of this model and derive, for all α, the exact probability distributions of the maximum spatial displacement M(t) and arg-maximum t_m(t) (i.e., the time at which this maximum is reached) till duration t. In the second part of our paper, we analyze the statistical properties of the residence time t_r(t) and the last-passage time t_ℓ(t) and compute their distributions exactly for all values of α. Our study unravels that the heterogeneous version (α≠0) displays many rich and contrasting features compared to that of the standard Brownian motion (BM). For example, while for BM (α=0), the distributions of t_m(t),t_r(t), and t_ℓ(t) are all identical (á la "arcsine laws" due to Lévy), they turn out to be significantly different for nonzero α. Another interesting property of t_r(t) is the existence of a critical α (which we denote by α_c=-0.3182) such that the distribution exhibits a local maximum at t_r=t/2 for α less then α_c whereas it has minima at t_r=t/2 for α≥α_c. The underlying reasoning for this difference hints at the very contrasting natures of the process for α≥α_c and α less then α_c which we thoroughly examine in our paper. All our analytical results are backed by extensive numerical simulations.The extension of microfluidics to many bioassay applications requires the ability to work with non-Newtonian fluids. One case in point is the use of microfluidics with blood having different hematocrit levels. This work is the first part of a two-part study and presents the formation dynamics of blood droplets in a T-junction generator under the squeezing regime. In this regime, droplet formation with Newtonian fluids depends on T-junction geometry; however, we found that in the presence of the non-Newtonian fluid such as red blood cells, the formation depends on not only to the channel geometry, but also the flow rate ratio of fluids, and the viscosity of the phases. In addition, we analyzed the impact of the red blood cell concentration on the formation cycle. In this study, we presented the experimental data of the blood droplet evolution through the analysis of videos that are captured by a high-speed camera. During this analysis, we tracked several parameters such as droplet volume, spacing between droplets, droplet generation frequency, flow conditions, and geometrical designs of the T junction. Our analysis revealed that, unlike other non-Newtonian fluids, where the fourth stage exists (stretching stage), the formation cycle consists of only three stages lag, filling, and necking stages. Because of the detailed analysis of each stage, a mathematical model can be generated to predict the final volume of the blood droplet and can be utilized as a guide in the operation of the microfluidic device for biochemical assay applications; this is the focus of the second part of this study [Phys. Rev. E 105, 025106 (2022)10.1103/PhysRevE.105.025106].Hematite at room temperature is a weak ferromagnetic material. Its permanent magnetization is three orders smaller than for magnetite. Thus, hematite colloids allow us to explore a different physical range of particle interaction parameters compared to ordinary ferromagnetic particle colloids. In this paper we investigate a colloid consisting of hematite particles with cubic shape. We search for energetically favorable structures in an external magnetic field with analytical and numerical methods and molecular dynamics simulations and analyze whether it is possible to observe them in experiments. We find that energetically favorable configurations are observable only for short chains. Longer chains usually contain kinks which are formed in the process of chain formation due to the interplay of energy and thermal fluctuations as an individual cube can be in one of two alignments with an equal probability.The random Lotka-Volterra model is widely used to describe the dynamical and thermodynamic features of ecological communities. In this work, we consider random symmetric interactions between species and analyze the strongly competitive interaction case. We investigate different scalings for the distribution of the interactions with the number of species and try to bridge the gap with previous works. Our results show two different behaviors for the mean abundance at zero and finite temperature, respectively, with a continuous crossover between the two. We confirm and extend previous results obtained for weak interactions at zero temperature, even in the strong competitive interaction limit, the system is in a multiple-equilibria phase, whereas at finite temperature only a unique stable equilibrium can exist. Finally, we establish the qualitative phase diagrams and compare the species abundance distributions in the two cases.We analyze the interaction with uniform external fields of nematic liquid crystals within a recent generalized free energy posited by Virga and falling in the class of quartic functionals in the spatial gradients of the nematic director. We review some known interesting solutions, i.e., uniform heliconical structures, which correspond to the so-called twist-bend nematic phase and we also study the transition between this phase and the standard uniform nematic one. The twist-bend phase is further reproduced by three-dimensional simulations. Moreover, we find liquid crystal configurations, which closely resemble some novel, experimentally detected, structures called Skyrmion tubes. Skyrmion tubes are characterized by a localized cylindrically symmetric pattern surrounded by either twist-bend or uniform nematic phase. We study the equilibrium differential equations and find numerical solutions and analytical approximations.
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