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1. Hierarchically Coupled Ornstein–Uhlenbeck Processes for Transient Anomalous Diffusion

   https://doi.org/10.3390/physics6020042  

   Wang, Jingyang; Voulgarakis, Nikolaos K (June 2024, Physics)

   The nonlinear dependence of the mean-squared displacement (MSD) on time is a common characteristic of particle transport in complex environments. Frequently, this anomalous behavior only occurs transiently before the particle reaches a terminal Fickian diffusion. This study shows that a system of hierarchically coupled Ornstein–Uhlenbeck equations is able to describe both transient subdiffusion and transient superdiffusion dynamics, as well as their sequential combinations. To validate the model, five distinct experimental, molecular dynamics simulation, and theoretical studies are successfully described by the model. The comparison includes the transport of particles in random optical fields, supercooled liquids, bedrock, soft colloidal suspensions, and phonons in solids. The model’s broad applicability makes it a convenient tool for interpreting the MSD profiles of particles exhibiting transient anomalous diffusion. 

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2. A distributed‐order fractional diffusion equation with a singular density function: Analysis and approximation

   https://doi.org/10.1002/mma.9087  

   Yang, Zhiwei; Wang, Hong (January 2023, Mathematical Methods in the Applied Sciences)

   We prove the well‐posedness and smoothing properties of a distributed‐order time‐fractional diffusion equation with a singular density function in multiple space dimensions, which could model the ultraslow subdiffusion processes. We accordingly derive a finite element approximation to the problem and prove its optimal‐order error estimate. Numerical results are presented to support the mathematical and numerical analysis. 

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3. Brownian motion of soft particles near a fluctuating lipid bilayer

   https://doi.org/10.1063/5.0182499  

   Sheikh, S; Lonetti, B; Touche, I; Mohammadi, A; Li, Z; Abbas, M (December 2023, The Journal of Chemical Physics)

   The dynamics of a soft particle suspended in a viscous fluid can be changed by the presence of an elastic boundary. Understanding the mechanisms and dynamics of soft–soft surface interactions can provide valuable insights into many important research fields, including biomedical engineering, soft robotics development, and materials science. This work investigates the anomalous transport properties of a soft nanoparticle near a visco-elastic interface, where the particle consists of a polymer assembly in the form of a micelle and the interface is represented by a lipid bilayer membrane. Mesoscopic simulations using a dissipative particle dynamics model are performed to examine the impact of micelle’s proximity to the membrane on its Brownian motion. Two different sizes are considered, which correspond to ≈10−20nm in physical units. The wavelengths typically seen by the largest micelle fall within the range of wavenumbers where the Helfrich model captures fairly well the bilayer mechanical properties. Several independent simulations allowed us to compute the micelle trajectories during an observation time smaller than the diffusive time scale (whose order of magnitude is similar to the membrane relaxation time of the largest wavelengths), this time scale being hardly accessible by experiments. From the probability density function of the micelle normal position with respect to the membrane, it is observed that the position remains close to the starting position during ≈0.05τd (where τd corresponds to the diffusion time), which allowed us to compare the negative excess of mean-square displacement (MSD) to existing theories. In that time range, the MSD exhibits different behaviors along parallel and perpendicular directions. When the micelle is sufficiently close to the bilayer (its initial distance from the bilayer equals approximately twice its gyration radius), the micelle motion becomes quickly subdiffusive in the normal direction. Moreover, the temporal evolution of the micelle MSD excess in the perpendicular direction follows that of a nanoparticle near an elastic membrane. However, in the parallel direction, the MSD excess is rather similar to that of a nanoparticle near a liquid interface. 

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4. Scalable level-wise screening experiments using locating arrays

   https://doi.org/10.1080/00224065.2023.2220973  

   Akhtar, Yasmeen; Zhang, Fan; Colbourn, Charles J; Stufken, John; Syrotiuk, Violet R (October 2023, Journal of Quality Technology)

   Alternative design and analysis methods for screening experiments based on locating arrays are presented. The number of runs in a locating array grows logarithmically based on the number of factors, providing efficient methods for screening complex engineered systems, especially those with large numbers of categorical factors having different numbers of levels. Our analysis method focuses on levels of factors in the identification of important main effects and two-way interactions. We demonstrate the validity of our design and analysis methods on both well-studied and synthetic data sets and investigate both statistical and combinatorial properties of locating arrays that appear to be related to their screening capability. 

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5. Splice Variants of Superoxide Dismutases in Rice and Their Expression Profiles under Abiotic Stresses

   https://doi.org/10.3390/ijms22083997  

   Saini, Ajay; Rohila, Jai S.; Govindan, Ganesan; Li, Yong-Fang; Sunkar, Ramanjulu (April 2021, International Journal of Molecular Sciences)

   null (Ed.)

   The superoxide dismutases (SODs) play vital roles in controlling cellular reactive oxygen species (ROS) that are generated both under optimal as well as stress conditions in plants. The rice genome harbors seven SOD genes (CSD1, CSD2, CSD3, CSD4, FSD1, FSD2, and MSD) that encode seven constitutive transcripts. Of these, five (CSD2, CSD3, CSD4, FSD1, and MSD) utilizes an alternative splicing (AS) strategy and generate seven additional splice variants (SVs) or mRNA variants, i.e., three for CSD3, and one each for CSD2, CSD4, FSD1, and MSD. The exon-intron organization of these SVs revealed variations in the number and length of exons and/or untranslated regions (UTRs). We determined the expression patterns of SVs along with their constitutive forms of SODs in rice seedlings exposed to salt, osmotic, cold, heavy metal (Cu+2) stresses, as well as copper-deprivation. The results revealed that all seven SVs were transcriptionally active in both roots and shoots. When compared to their corresponding constitutive transcripts, the profiles of five SVs were almost similar, while two specific SVs (CSD3-SV4 and MSD-SV2) differed significantly, and the differences were also apparent between shoots and roots suggesting that the specific SVs are likely to play important roles in a tissue-specific and stress-specific manner. Overall, the present study has provided a comprehensive analysis of the SVs of SODs and their responses to stress conditions in shoots and roots of rice seedlings. 

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