Classical Diffusion Research Articles

Temporal methane variability in the water column of an area of seasonal coastal upwelling: A study based on a 12 year time series

Temporal distribution of dissolved CH4 was analysed in a zone of strong seasonal coastal upwelling off central Chile (36.5°S,73°W). Observations were taken from a twelve-year time series that included monthly sampling of the water at eight depths. CH4 concentration fluctuated between 1.75 and 100.9 nmol L-1 (or 67.11% and 3965% of saturation), with the highest levels at bottom waters, which increase as upwelling evolved. Three kind of CH4 profiles were identified; a classical diffusion–advection distribution, with bottom/surface CH4 concentration ratio > 2, was predominantly observed in ~ 54% of the all profiles and attributed to high CH4 production in the sediments during coastal upwelling season (austral spring-summer); a period of higher biological productivity, as well as in hypoxic/anoxic condition. In contrast, relatively homogeneous profiles (CH4 level ratio between bottom and surface depth < 2) was observed about ~ 46% of all profiles during periods of extreme vertical mixing (such as winter storms). Furthermore, irregular CH4 profile with superficial peaks occurring between the surface and 15–30 m depth was likely observed. These peaks indicated that local production rates exceed turbulent mixing rates, suggesting a rapid CH4 cycling due to microbial processes on the surface. Despite the fact that strong seasonality was observed in most oceanographic variables, according to favourable and non-favourable upwelling periods, only a weak seasonality was observed in CH4 content and its air-sea flux, the latter ranged from 1.27 to 47.02 µmol m−2 d-1 (mean ± SD: 10.94 ± 7.48). The annual weighted mean CH4 effluxes during upwelling (64%) and non-upwelling (36%) periods fluctuated from 1.66 to 6.22 mmol m−2 (mean ± SD: 3.40 ± 1.43), highlighting the importance of the continental shelf under the influence of coastal upwelling as a significant CH4 source toward the atmosphere.

Adsorption of CO2, N2 and CH4 on a Fe-based metal organic framework, MIL-101(Fe)-NH2

MIL-101(Fe)-NH2 was synthesized using solvothermal method to assess the selective adsorption of CO2 over N2 and CH4. The BET surface area of adsorbent sample was 915 m2.g-1. The adsorption capacities of CO2, N2 and CH4 on MIL-101(Fe)-NH2 at 4 MP and 298 K were achieved equal to 13, 3.8 and 5 mmol.g-1 respectively. Khan adsorption equilibrium model was applied to correlate the adsorption isotherms of pure gases. In addition to Khan model, the adsorption isotherm of CO2, which showed type II behavior, was also obtained by BET model as well as a newly presented hybrid model, which resulted in excellent agreement with the experimental data. Moreover, the selectivity of CO2 over N2 and CH4 was estimated by Ideal Adsorbed Solution Theory (IAST). Comparison of the achieved results from IAST method with experimental data verified the accuracy of this method in the lower pressure. The selectivity coefficient was about 2.2 for CO2 over N2 and CH4 at 16 bar. The achieved results from a classical micropore diffusion model showed that the diffusion coefficient of the pure gases was approximately constant with pressure. Moreover, the estimated values for diffusion time constants (DC/rC2 × 103) for CO2, N2 and CH4 were obtained equal to 1.178, 1.118, and 0.802 respectively. The adsorption kinetic data were also correlated with empirical models. Ultimately, the results showed that pseudo-nth order empirical model achieved the best agreement with the experimental data, and it can be successfully applied for kinetic modeling of gas adsorption by MIL-101(Fe)-NH2 MOF.

On possible applications of media described by fractional-order models in electromagnetic cloaking

The purpose of this paper is to open a scientific discussion on possible applications of media described by fractional-order (FO) models (FOMs) in electromagnetic cloaking. A 2-D cloak based on active sources and the surface equivalence theorem is simulated. It employs a medium described by FOM in communication with sources cancelling the scattered field. A perfect electromagnetic active cloak is thereby demonstrated with the use of a finite-difference time-domain method combined with a simulation algorithm of non-monochromatic wave propagation in the media described by FOM. The application of constitutive relations based on FOMs in Maxwell’s equations provides solutions which correspond to the results reported for the time-fractional diffusion-wave equation, which is non-relativistic, like the classical diffusion equation. This property is employed in the presented cloaking scheme for communication with active current sources around the cloak, which cancel the scattered field of an object inside the cloak. Although in the real world perfect invisibility is impossible to obtain due to the constraint of light speed, it is possible to obtain a perfect cloak in theoretical considerations by using FO formulation of electromagnetism. It is worth noticing that numerous literature sources experimentally confirm the existence of electromagnetic media described by FOMs; hence, the presented numerical results should hopefully stimulate further investigations related to applications of FOMs in electromagnetic cloaking.

Emergent fracton dynamics in a nonplanar dimer model

We study the late time relaxation dynamics of a pure $U(1)$ lattice gauge theory in the form of a dimer model on a bilayer geometry. To this end, we first develop a proper notion of hydrodynamic transport in such a system by constructing a global conservation law that can be attributed to the presence of topological solitons. The correlation functions of local objects charged under this conservation law can then be used to study the universal properties of the dynamics at late times, applicable to both quantum and classical systems. Performing the time evolution via classically simulable automata circuits unveils a rich phenomenology of the system's non-equilibrium properties: For a large class of relevant initial states, local charges are effectively restricted to move along one-dimensional 'tubes' within the quasi-two-dimensional system, displaying fracton-like mobility constraints. The time scale on which these tubes are stable diverges with increasing systems size, yielding a novel mechanism for non-ergodic behavior in the thermodynamic limit. We further explore the role of geometry by studying the system in a quasi-one-dimensional limit, where the Hilbert space is strongly fragmented due to the emergence of an extensive number of conserved quantities. This provides an instance of a recently introduced concept of 'statistically localized integrals of motion', whose universal anomalous hydrodynamics we determine by a mapping to a problem of classical tracer diffusion. We conclude by discussing how our approach might generalize to study transport in other lattice gauge theories.

Analysis of water droplet penetration in earth plasters using X-ray microtomography

Earth plasters are a very interesting solution for the coating of earthen construction, in terms of embodied energy, technical efficiency, while keeping the hygroscopic properties of the wall, unlike very little permeable coatings, as the cement-based ones. An experimental campaign has been conducted on several earth plasters which differs by their sand granulometry, earth origin and earth to sand ratio, leading to controlled surface topography and bulk properties. A novel X-ray microtomography technique adapted to such material has been relevant to observe directly the penetration of a water damping droplet inside the plaster with the 2D radiograph method, and enhance the understanding of the role of the surface and the bulk structure on it. A 3D scanning method was useful to understand the microstructure of the different samples and analyse their differences in terms of porosity. Two custom-made MATLAB codes have been developed in order to follow the droplet parameters inside the material, such as the spread, the penetration depth and the relative quantity of water along the time. Results show the consistent role of the surface topography on the water inertial penetration, while the penetration rate due to diffusion is directly linked to the bulk properties, and can be assimilated to a classic diffusion solution. The determination of the drying rate in the earth plasters highlights that the plasters which prevent the water to penetrate too deeply are also the ones which dry the slower, leading to a questioning on the role researched in an efficient coating material.

Design of risk assessment and decision support system for transportation of hazardous chemicals

According to the needs of risk assessment, path planning and emergency rescue of hazardous chemicals transportation, a risk assessment and decision support system of hazardous chemicals transportation was designed, including system structure, implementation process and main functions. The feasibility analysis of key technologies was carried out. This system took Geographic Information System (GIS) as the support platform, and integrated multi-source information such as hazardous chemicals, global positioning system (GPS), geographic environment, Meteorological information, etc. Based on classical pollution diffusion models and relevant domestic and foreign standards, the index system of transportation risk assessment was built. Then the quantitative index of risk assessment and the early warning sign could be given, and the hazard area of the chemical accident was determined. At last, this risk assessment and decision support system provided suggestions on route optimization for hazardous chemicals transport, which could be severed as scientific basis for emergency rescue and command decision.

Transporter-mediated ecdysteroid trafficking across cell membranes: A novel target for insect growth regulators

Ecdysteroids are a class of steroid hormones in arthropods that control molting and metamorphosis through interaction with intracellular nuclear receptors. In contrast to the extensive literature describing their biosynthetic pathways and signaling components, little has been known about how these hormones are traveling into and out of the cells through lipid bilayers of the cell membranes. Recently, a series of studies conducted in the fruit fly Drosophila melanogaster revealed that membrane transporters have critical functions in trafficking ecdysteroids across cell membranes, challenging the classical simple diffusion model of steroid hormone transport. Here we summarize recent advances in our understanding of membrane transporters involved in ecdysteroid signaling in Drosophila, with particular focus on Ecdysone Importer (EcI) that is involved in ecdysteroid uptake in peripheral tissues. We then discuss the potential advantage of EcI blockers as a novel pest management tool as compared to classical insect growth regulators.

Classical and Quantum Models of Diffusion

The objective of the paper is twofold: first, to review the classical diffusion models and show the approximations at the origin of the parabolic character of the classical equations; second, to demonstrate a connection between the quantum and classical models of diffusion. As diffusion is inherently related to the motion of constituents, the consistent models are framed within the dynamics of mixtures. The derivation of diffusion equations is then determined based on the related, pertinent approximations.

Quantum transport in a combined kicked rotor and quantum walk system

We present a theoretical and numerical study of the competition between two opposite interference effects, namely interference-induced ballistic transport on one hand, and strong (Anderson) localization on the other. While the former effect allows for resistance free transport, the latter brings the transport to a complete halt. As a model system, we consider the quantum kicked rotor, where strong localization is observed in the discrete momentum coordinate. In this model, we introduce the ballistic transport in the form of a Hadamard quantum walk in that momentum coordinate. The two transport mechanisms are combined by alternating the corresponding Floquet operators. Extending the corresponding calculation for the kicked rotor, we estimate the classical diffusion coefficient for the combined dynamics. Another argument, based on the introduction of an effective Heisenberg time should then allow to estimate the localization time and the localization length. While this is known to work reasonably well in the kicked rotor case, we find that it fails in our case. While the combined dynamics still shows localization, it takes place at much larger times and shows much larger localization lengths than predicted. Finally, we combine the kicked rotor with other types of quantum walks, namely diffusive and localizing quantum walks. In the diffusive case, the localizing dynamics of the kicked rotor is completely canceled and we get pure diffusion. In the case of the localizing quantum walk, the combined system remains localized, but with a larger localization length.

Layer-by-layer anionic diffusion in two-dimensional halide perovskite vertical heterostructures.

Anionic diffusion in a soft crystal lattice of hybrid halide perovskites affects their stability, optoelectronic properties and the resulting device performance. The use of two-dimensional (2D) halide perovskites improves the chemical stability of perovskites and suppresses the intrinsic anionic diffusion in solid-state devices. Based on this strategy, devices with an enhanced stability and reduced hysteresis have been achieved. However, a fundamental understanding of the role of organic cations in inhibiting anionic diffusion across the perovskite-ligand interface is missing. Here we demonstrate the first quantitative investigation of the anionic interdiffusion across atomically flat 2D vertical heterojunctions. Interestingly, the halide diffusion does not follow the classical diffusion process. Instead, a 'quantized' layer-by-layer diffusion model is proposed to describe the behaviour of the anionic migration in 2D halide perovskites. Our results provide important insights into the mechanism of anionic diffusion in 2D perovskites and provide a new materials platform with an enhanced stability for heterostructure integration.

Kicked rotor with attosecond pulse train

The kicked rotor (KR) is one of the basic models in connection with chaos and quantum chaos. A possible application of an attosecond pulse train as a kicking field in the KR is theoretically examined for the first time. This version of the KR is denoted as an atto-KR. It seems to be the most realistic version of the KR because it takes into account the real form of the kicking field as it appears in the experiments. The atto-KR is investigated from the classical and the quantum aspects. In the classical case, a new map instead of the Chirikov standard map is proposed. It may be useful in appropriate experiments with the classical chaos. In the quantum case, the atto-KR gives satisfactory results. Phenomena such as dynamical localization and quantum resonances appear in the undisturbed form. It may be also used for examining the influence of the quantum effects on classical chaos and diffusion.

Selenium release kinetics and mechanism from Cordyceps sinensis exopolysaccharide-selenium composite nanoparticles in simulated gastrointestinal conditions

This work investigated selenium (Se) release kinetics and mechanism from exopolysaccharide-selenium nanoparticles (EPS-SeNPs, Se/EPS = 1/20, 1/1 and 4/3) in simulated gastric (SGF) and intestinal fluids (SIF) using kinetics models of Zero order, First order, Higuchi, Hixson-Crowell and Korsmeyer-Peppas. EPS-SeNPs showed an increase in size from 80–125 nm to 250–320 nm and more ambiguous boundary after gastrointestinal digestion. Se/EPS ratio and pH had significant influence on Se release. Se release kinetics from EPS-SeNPs (Se/EPS = 1/1 and 4/3 in SGF) followed a classical Fickian diffusion, in contrast to an erosion governed by macromolecular chains relaxation for Se/EPS = 1/20 in SIF. Se release from EPS-SeNPs (Se/EPS = 1/1 and 4/3 in SIF) was well-fitted to Korsmeyer-Peppas model and followed a non-Fickian mechanism controlled by both diffusion and erosion. Additionally, EPS-SeNPs (Se/EPS = 1/20) showed a low Se release after SGF digestion, but a high release after SIF digestion, suggesting its application in controlled release of Se-enriched supplements for Se-deficiency treatment.

The influence of density in population dynamics with strong and weak Allee effect

In this paper, we consider a reaction–diffusion model in population dynamics and study the impact of different types of Allee effects with logistic growth in the heterogeneous closed region. For strong Allee effects, usually, species unconditionally die out and an extinction-survival situation occurs when the effect is weak according to the resource and sparse functions. In particular, we study the impact of the multiplicative Allee effect in classical diffusion when the sparsity is either positive or negative. Negative sparsity implies a weak Allee effect, and the population survives in some domain and diverges otherwise. Positive sparsity gives a strong Allee effect, and the population extinct without any condition. The influence of Allee effects on the existence and persistence of positive steady states as well as global bifurcation diagrams is presented. The method of sub-super solutions is used for analyzing equations. The stability conditions and the region of positive solutions (multiple solutions may exist) are presented. When the diffusion is absent, we consider the model with and without harvesting, which are initial value problems (IVPs) and study the local stability analysis and present bifurcation analysis. We present a number of numerical examples to verify analytical results.

Signal Smoothing with Time-Space Fractional Order Model

Abstract The time-space fractional-order model (TSFOM) is a generation of the classical diffusion model which is an excellent smoothing method. In this paper, the fractional-order derivative in the model is found to have good performance for peak-preserving. To check the validity and performance of the model, some noisy signals are smoothed by some commonly used smoothing methods and results are compared with those of the proposed model. The comparison result shows that the proposed method outperforms the classical nonlinear diffusion model and some commonly used smoothing methods.

On the applicability of Schottky diffusion theory to non-ohmic cathode contact P3HT:PCBM bulk-hetero junction solar cell

The classical Schottky diffusion theory is applied to a non-ohmic cathode contact P3HT:PCBM bulk-heterojunction solar cell under the assumption of a p-type doped active region. Analytical expressions of the dark current density/voltage (JD/V) characteristic and the open-circuit voltage under illumination VOC are, thus, derived for this cell. They are validated with reference to a complete numerical simulation by the analysis of microelectronic and photonic structures-one-dimensional simulator. The Schottky diffusion theory is shown to be reasonably applicable to modeling the JD/V characteristic in the forward bias region within the range below the built-in voltage Vbi and in the complete reverse bias region. It is demonstrated that depending on the p-doping density NA and the hole mobility μh of the active region, VOC is linearly controlled by the Schottky barrier height φB.

Numerical implementation of the asymptotic theory for classical diffusion in heterogeneous media

Based on the asymptotic theory of impurity transport developed by one of the authors (P.S.K.), numerical calculations of the concentration for classical diffusion in heterogeneous media in one and two dimensions are performed. In parallel, for the same media, a direct numerical solution of the diffusion equation was carried out. The results of the two calculations are highly consistent with each other at asymptotically far distances from the impurity source. The computation time according to the asymptotic theory turned out to be two orders of magnitude less than the time required for direct calculations.

The rationale for the method of thermochemical processing of beet chips before extraction of sucrose

The objective of this thesis is to ensure utmost performance of the diffusion process by choosing the most effective components of chemical heat treatment of beet chips. Aqueous solutions of ammonia sulphates (NH4)2SO4, aluminium sulphate Al2(SO4)3, calcium sulphate CaSO4 have been considered as reagents to process chips. The classical diffusion process method has been used as a benchmarking option. It has been deduced from experiments that beet tissue treatment with solutions of the proposed reagents heated up to 73 ° C enables a high degree of cell plasmotosis, enhances its permeability and intensifies sucrose transfer to the extractant during heavy convectional leaching. The process is strongly enhanced if chips are treated with reagent solutions following electrochemical activation, which is confirmed by the study of the beet tissue fine structure after its various chemical heat treatments. Rational conditions of solution electrochemical activation for beet chips chemical heat treatment prior to extraction have been selected experimentally. 3 patents of the Russian Federation for the diffusion juice process have been obtained based on the results of the studies conducted.

3-D Gabor-based anisotropic diffusion for speckle noise suppression in dynamic ultrasound images.

Speckle noise contaminates medical ultrasound images, and the suppression of speckle noise is helpful for image interpretation. Traditional ultrasound denoising (i.e., despeckling) methods are developed on two-dimensional static images. However, one of the advantages of ultrasonography is its nature of dynamic imaging. A method for dynamic ultrasound despeckling is expected to incorporate both the spatial and temporal information in successive images of dynamic ultrasound and thus yield better denoising performance. Here we regard a dynamic ultrasound video as three-dimensional (3-D) images with two dimensions in the spatial domain and one in the temporal domain, and we propose a despeckling algorithm for dynamic ultrasound named the 3-D Gabor-based anisotropic diffusion (GAD-3D). The GAD-3D expands the classic two-dimensional Gabor-based anisotropic diffusion (GAD) into 3-D domain. First, we proposed a robust 3-D Gabor-based edge detector by capturing the edge with 3-D Gabor transformation. Then we embed this novel detector into the partial differential equation of GAD to guide the 3-D diffusion process. In the simulation experiment, when the noise variance is as high as 0.14, the GAD-3D improves the Pratt's figure of merit, mean structural similarity index and peak signal-to-noise ratio by 24.32%, 10.98%, and 6.51%, respectively, compared with the best values of seven other methods. Experimental results on clinical dynamic ultrasonography suggest that the GAD-3D outperforms the other seven methods in noise reduction and detail preservation. The GAD-3D is effective for dynamic ultrasound despeckling and may be potentially valuable for disease assessment in dynamic medical ultrasonography.

Exotic IMPATT Oscillator for Terahertz Thermography: Feasibility Studies in Hepatic Tumor Detection

Hepatic carcinoma is a major type of malignant tumor that needs a novel non-invasive/minimal invasive method for its early diagnosis. This paper for the first time reports a new scheme of diagnosis of hepatic tumor by studying the corresponding terahertz (THz) thermographs. A solid-state source of THz radiation (IMPact-ionisation avalanche transit time oscillator), capable of working at room temperature, is proposed in this paper and the THz non-linear characteristic of the device and system are studied through an in-house developed quantum modified classical drift diffusion simulator. The validity of the model is also established by comparing the results with experimental observations. The model includes temperature effects, quantum size effect, lattice phonon scatterings, and noise study. A COMSOL-based THz-thermograph model is further developed and a comparative analysis with those of microwave thermographs is reported. To the best of authors’ knowledge, this is the first report on studying the prospects of an exotic type non-invasive terahertz <p+-n-n+> radiation source for use in T-ray thermography studies of hepatic tumors detection with two sets of different radiation exposure.

Implementation of high-order, discontinuous Galerkin time stepping for fractional diffusion problems

The discontinuous Galerkin (DG) method provides a robust and flexible technique for the time integration of fractional diffusion problems. However, a practical implementation uses coefficients defined by integrals that are not easily evaluated. We describe specialized quadrature techniques that efficiently maintain the overall accuracy of the DG method. In addition, we observe in numerical experiments that known superconvergence properties of DG time stepping for classical diffusion problems carry over in a modified form to the fractional-order setting. doi: 10.1017/S1446181120000152