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Odd-diffusive systems, characterised by broken time-reversal and/or parity, have recently been shown to display counterintuitive features such as interaction-enhanced dynamics in the dilute limit. Here we extend the investigation to the high-density limit of an odd tracer embedded in a soft medium described by the Gaussian core model (GCM) using a field-theoretic approach based on the Dean–Kawasaki equation. Our analysis reveals that interactions can enhance the dynamics of an odd tracer even in dense systems. We demonstrate that oddness results in a complete reversal of the well-known self-diffusion ( D s ) anomaly of the GCM. Ordinarily, D s exhibits a non-monotonic trend with increasing density, approaching but remaining below the interaction-free diffusion, D 0 , ( D s < D 0 ) so that D s ↑ D 0 at high densities. In contrast, for an odd tracer, self-diffusion is enhanced ( D s > D 0 ) and the GCM anomaly is inverted, displaying D s ↓ D 0 at high densities. The transition between the standard and reversed GCM anomaly is governed by the tracer’s oddness, with a critical oddness value at which the tracer diffuses as a free particle ( D s ≈ D 0 ) across all densities. We validate our theoretical predictions with Brownian dynamics simulations, finding strong agreement between the them.

This paper introduces an advanced framework for accelerated processing of diffusion‐weighted imaging (DWI) data that utilizes an entire‐image modeling approach to optimize the estimation of diffusion parameters from DWIs by mapping input diffusion data to predicted signals and estimating parameter values via a stochastic gradient descent optimizer (Adam). To validate this approach, we applied this framework to diffusion basis spectrum imaging (DBSI) and analyzed in vivo human brain and ex vivo mouse brain DWIs. Results demonstrate significant improvements to computational speed and signal‐to‐noise ratio (SNR) in estimated parameter maps compared to standard DBSI. Our approach is applicable to any diffusion signal representation and enables rapid and reliable signal partitioning in complex microstructural environments, demonstrating the potential of this framework for future neuroimaging research. We introduce a new framework for accelerated processing of diffusion‐weighted imaging (DWI) data using a machine learning approach to optimize parameter estimation. We demonstrate that this new method, called DBSIpy, significantly improves computational speed and robustness to Rician noise compared to the standard DBSI method, with the improvements being generalizable to other DWI signal representations.

We consider a two-species simple exclusion process on a periodic lattice. We use the method of matched asymptotics to derive evolution equations for the two population densities in the dilute regime, namely a cross-diffusion system of partial differential equations for the two species’ densities. First, our result captures non-trivial interaction terms neglected in the mean-field approach, including a non-diagonal mobility matrix with explicit density dependence. Second, it generalises the rigorous hydrodynamic limit of Quastel (Commun Pure Appl Math 45(6):623–679, 1992), valid for species with equal jump rates and given in terms of a non-explicit self-diffusion coefficient, to the case of unequal rates in the dilute regime. In the equal-rates case, by combining matched asymptotic approximations in the low- and high-density limits, we obtain a cubic polynomial approximation of the self-diffusion coefficient that is numerically accurate for all densities. This cubic approximation agrees extremely well with numerical simulations. It also coincides with the Taylor expansion up to the second-order in the density of the self-diffusion coefficient obtained using a rigorous recursive method.

In this study, single-sided nuclear magnetic resonance (NMR) spectroscopy was used to detect the changes of axial and radial tangential moisture self-diffusion coefficient with diffusion time of Mongolian Scots pine (Pinus sylvestris var. mongolica). The result shows that, the self-diffusion coefficient values ranked as axial > radial > tangential. The axial self-diffusion coefficient exhibited free diffusion, averaging 2.0 × 10–9 m2/s, while radial and tangential directions showed restricted diffusion, decreasing with time. Based on the restricted diffusion theory, the results are as follows, radial and tangential tracheid surface-to-volume ratios (S/V) were approximately 203,000 ± 10,600/m and 265,000 ± 25,000/m, average size of lumen ends and pits 6.4 ± 0.33 μm and 6.2 ± 0.49 μm in radial and tangential direction respectively, tortuosity values τR = 3.96 ± 0.02 and τT = 6.59 ± 0.45. Combining S/V with the form factor (Fs) and the T2 relaxation mechanism yields the following results, average pore sizes for radial and tangential tracheids were 19.7 ± 1.44 μm and 15.09 ± 1.3 μm, cell water transverse surface relaxation rates were ρ2R = 0.103 ± 0.005 μm/ms and ρ2T = 0.082 ± 0.007 μm/ms. The pore size obtained above is within an acceptable range with the results of SEM. This study provides a systematic method for wood moisture self-diffusion analysis.

The hydration behavior of sugars varies from each other and examining the underlying mechanism is challenging. In this study, the hydration behavior of glucose, fructose, allulose (aka rare sugar), and sucrose have been explored using different Time Domain Nuclear Magnetic Resonance (TD-NMR) approaches (relaxation times, self-diffusion, and Magic Sandwich Echo (MSE)). For that purpose, the effects of different sugar concentrations (2.5%, 5%, 10%, 15%, 20%, 30%, and 40%) (w/v) and hydration at different times for 1 day were investigated by T2 relaxation times and self-diffusion coefficients. Crystallinity values of the solid and hydrated sugars were also determined with MSE. Change in T2 relaxation times with concentration showed that the fastest binding with water (parallel with the shortest T2 values) was observed for sucrose for all concentrations followed by glucose, fructose, and allulose. Furthermore, dependency of T2 relaxation times with hydration time showed that sucrose was the fastest in binding with water followed by glucose, fructose, and allulose. The study showed that allulose, one of the most famous rare sugars that is known to be a natural low-calorie sugar alternative, had the lowest interaction with water than the other sugars. TD-NMR was suggested as a practical, quick, and accurate technique to determine the hydration behavior of sugars.

Cellulose being the most widely available biopolymer on Earth is attracting significant interest from the industry and research communities. While molecular simulations can be used to understand fundamental aspects of cellulose nanocrystal self-assembly, a model that can perform on the experimental scale is currently missing. In our study we develop a supra coarse-grained (sCG) model of cellulose nanocrystal which aims to bridge the gap between molecular simulations and experiments. The sCG model is based on atomistic molecular dynamics simulations and it is developed with the force-matching coarse-graining procedure. The validity of the model is shown through comparison with experimental and simulation results of the elastic modulus, self-diffusion coefficients and cellulose fiber twisting angle. We also present two representative case studies, self-assembly of nanocrystal during solvent evaporation and simulation of a chiral nematic phase ordering. Finally, we discuss possible future applications for our model.Graphic abstract

Increasing biodiesel production poses a significant challenge in managing its primary byproduct, bioglycerol. Advancements in production techniques have markedly enhanced bioglycerol potential applications across various sectors, including as cosolvent in industrial formulations. In the context of ecosustainable formulation design, this study addresses the self‐aggregation of rhamnolipids, biosurfactants with a wide range of physicochemical and biological activities, in bioglycerol aqueous mixtures, studied by integrating surface tension and NMR self‐diffusion measurements. Preliminary analysis of the properties of water–bioglycerol mixtures indicates that bioglycerol impurities (mainly potassium acetate) have only a small effect on surface tension and no discernible effect on bulk properties such as density, viscosity, and refractive index. The aggregation of rhamnolipids is unaffected by bioglycerol at concentrations up to 40–50 wt%. At higher cosolvent levels, the cmc increases and the micellar size decreases, an indirect effect of the decreasing polarity of the medium. These results provide the basic knowledge to promote the exploration of rhamnolipids and bioglycerol as valuable ingredients in formulations for various applications. Bioglycerol, the primary byproduct of biodiesel production, has the potential to be valorized as a cosolvent in industrial formulations. Surface tension and self‐diffusion data reveal that rhamnolipid self‐aggregation in water is poorly affected by the addition of bioglycerol up to very high concentrations. These results demonstrate that biosurfactants and bioglycerol are suitable ingredients in ecofriendly product design.

By using the concepts of Kronecker sum and Kronecker product, the matrix form of decoupling method is proposed to analyze the Turing instability of the equilibria for a memristive cellular neural networks under the zero-flux boundary conditions. It is shown that Turing instability can never occur at the zero equilibrium nor at the non-zero equilibrium for the self-diffusion case, while Turing instability may occur at the non-zero equilibrium for the cross-diffusion case. Furthermore, the local stability of the non-zero equilibrium determined by system parameters is studied. Finally, several numerical simulations are given. This matrix form of decoupling method can be extended to study memristive cellular neural networks with other boundary conditions.

Numerical simulation can provide detailed understanding of mass transport within complex structures. For this purpose, numerical tools are required that can resolve the complex morphology and consider the contribution of both convection and diffusion. Solving the Navier–Stokes equations alone, however, neglects self - diffusion. This influences the simulated displacement distribution of flow especially in porous media at low Péclet numbers (Pe < 16) and in near-wall regions where diffusion is the dominant mechanism. To address this problem, this study uses μCT-based computational fluid dynamics (CFD) simulations in OpenFOAM coupled with the random-walk particle tracking (PT) module disTrackFoam and cross-validated experimentally using pulsed-field gradient (PFG) nuclear magnetic resonance (NMR) measurements of gas flow within open-cell foams (OCFs). The results of the multi-scale simulations—with a resolution of 130–190 µm—and experimental PFG NMR data are compared in terms of diffusion propagators, which are microscopic displacement distributions of gas flows in OCFs during certain observation times. Four different flow rates with Péclet numbers in the range of 0.7–16 are studied in the laminar flow regime within 10 and 20 PPI OCFs, and axial dispersion coefficients were calculated. Cross-validation of PFG NMR measurements and CFD-PT simulations revealed a very good matching with integral differences below 0.04%, underpinning the capability of both complementary methods for multi-scale transport analysis.

Containerless measurements of the thermophysical properties density, viscosity, and self-diffusion by electromagnetic- (EML) and electrostatic levitation (ESL) are compared. The development history of the two techniques is briefly traced. The levitation principles and the measurement techniques for the properties considered are discussed. In the case of the density, data measured by both techniques are available for a liquid NiTi alloy. The results agree within a systematic error of ± 1 %. The data measured in EML exhibit a significant larger scatter. Viscosity data cannot be measured in ground-based electromagnetic levitation, so the comparison is carried out for a NiB alloy investigated in ESL and a classical viscometer. Good agreement was found as well. No significant difference is observed in self-diffusion data of various systems between different levitation techniques.