Scalar Diffusion Research Articles

Dermatitis Eksfoliatif Generalisata

Generalized exfoliative dermatitis, also known as erythroderma, is a skin disease with dermatological features in the form of diffuse erythema and scaling that affects more than 90% of the skin surface. This report describes the case of a 65 year old man who came with the main complaint, the skin all over his body felt itchy and peeling since approximately 2 years ago. The itching experienced by the patient worsens during hot weather/temperature, usually occurring during the day and night, but the itching experienced is more severe at night. The patient's complaints began with the appearance of redness on the skin in the left and right hand area, then spread to the chest area, groin/genital area, both legs, and throughout the body up to the head. Dermatological status examination revealed diffuse erythema macules accompanied by rough scales all over the body. The patient was diagnosed with generalized exfoliative dermatitis. In management, patients are given education to maintain skin moisture, avoid scratching the skin, and consume foods high in protein such as red meat. The pharmacological management given is in the form of corticosteroid drugs, antibiotics, proton pump inhibitors, antihistamines, and several topical drugs to reduce complaints of itching and peeling skin in patients.

Homogenization of a nonlinear reaction‐diffusion problem in a perforated domain with different size obstacles

AbstractIn this paper we consider a nonlinear reaction‐diffusion problem with low diffusion scales of order in a porous domain which periodically perforated by two different size obstacles. A nonlinear Neumann condition is prescribed on the boundaries of smaller obstacles, while a homogeneous Neumann condition is imposed on the other boundaries. Our aim is to derive the homogenized model as the small parameters tend to zero by using the method of three‐scale convergence and periodic reiterated unfolding operator. The final homogenized macroscopic model depends on three scales.

Macroscopic finite-difference scheme and modified equationsof the general propagation multiple-relaxation-time lattice Boltzmann model.

In this paper we first present the general propagation multiple-relaxation-time lattice Boltzmann (GPMRT-LB) model and obtain the corresponding macroscopic finite-difference (GPMFD) scheme on conservative moments. Then based on the Maxwell iteration method, we conduct the analysis on the truncation errors and modified equations(MEs) of the GPMRT-LB model and GPMFD scheme at both diffusive and acoustic scalings. For the nonlinear anisotropic convection-diffusion equation(NACDE) and Navier-Stokes equations(NSEs), we also derive the first- and second-order MEs of the GPMRT-LB model and GPMFD scheme. In particular, for the one-dimensional convection-diffusion equation(CDE) with the constant velocity and diffusion coefficient, we can develop a fourth-order GPMRT-LB (F-GPMRT-LB) model and the corresponding fourth-order GPMFD (F-GPMFD) scheme at the diffusive scaling. Finally, three benchmark problems, the Gauss hill problem, the CDE with nonlinear convection and diffusion terms, and the Taylor-Green vortex flow in two-dimensional space, are used to test the GPMRT-LB model and GPMFD scheme, and it is found that the numerical results not only are in good agreement with corresponding analytical solutions, but also have a second-order convergence rate in space. Additionally, a numerical study on one-dimensional CDE also demonstrates that the F-GPMRT-LB model and F-GPMFD scheme can achieve a fourth-order accuracy in space, which is consistent with our theoretical analysis.

Asymptotic preserving semi-Lagrangian discontinuous Galerkin methods for multiscale kinetic transport equations

We propose a new family of asymptotic preserving (AP) discontinuous Galerkin (DG) schemes for kinetic transport equations under a diffusive scaling. They are built upon a characteristics-based model reformulation proposed in Zhang et al. (2023) [27]. The reformulated model comprises a convection-diffusion-like equation for the macroscopic density and another evolution equation for the distribution function. We employ the equations in a weak form to enjoy the advantages of a DG method. We also leverage a semi-Lagrangian (SL) approach to achieve higher efficiency than a fully implicit scheme without loss of unconditional stability. A damping technique is introduced to control spurious numerical oscillations for high-order DG methods. We establish formal AP and Fourier stability analyses for fully discrete schemes in a linear scenario. Numerical experiments, covering one-dimensional to three-dimensional in space problems, confirm the accuracy, AP property, uniformly unconditional stability, and high parallel efficiency of the proposed methods.

Sharp adaptive and pathwise stable similarity testing for scalar ergodic diffusions

Sharp adaptive and pathwise stable similarity testing for scalar ergodic diffusions

An Electrical Parameter Characterizing Solute Heterogeneity: The Mixing Factor M

AbstractQuantitative estimates of hydrological state variables using electrical or electromagnetic geophysical methods are systematically biased by overlooked heterogeneity below the spatial scale resolved by the method. We generalize the high‐salinity asymptotic limit of electrical conduction in porous media at the continuous (e.g., Darcy) scale, by introducing a new petrophysical parameter, the mixing factor M, which accounts for the effect of fluid conductivity heterogeneity on the equivalent electrical conductivity tensor; it is expressed in terms of the volume‐average of the product of mean‐removed fluid conductivity and electric fields. We investigate the behavior of M for static and evolving fluid conductivity scenarios. Considering 2‐D ergodic log‐normal random fields of fluid conductivity, we demonstrate, in absence of surface conductivity, that observing the components of the M‐tensor allows univocally determining the variance and anisotropy of the field. Further, time‐series of the M‐tensor under diffusion‐limited mixing allows distinguishing between different characteristic temporal scales of diffusion, which are directly related to the initial integral scales of the salinity field. Under advective‐diffusive transport and for a pulse injection, the time‐series of M have a strong dependence on the Péclet number. Since M is defined in the absence of surface conductivity, we investigate how to correct measurements for surface conductivity effects. The parameter M provides conceptual understanding about the impact of saline heterogeneity on electrical measurements. Further work will investigate how it can be incorporated into hydrogeophysical inverse formulations and interpretative frameworks.

Nuclear quantum effects on the vibrational dynamics of the water-air interface.

We have applied path-integral molecular dynamics simulations to investigate the impact of nuclear quantum effects on the vibrational dynamics of water molecules at the water-air interface. The instantaneous fluctuations in the frequencies of the O-H stretch modes are calculated using the wavelet method of time series analysis, while the time scales of vibrational spectral diffusion are determined from frequency-time correlation functions and joint probability distributions. We find that the inclusion of nuclear quantum effects leads not only to a redshift in the vibrational frequency distribution by about 120 cm-1 for both the bulk and interfacial water molecules but also to an acceleration of the vibrational dynamics at the water-air interface by as much as 35%. In addition, a blueshift of about 45 cm-1 is seen in the vibrational frequency distribution of interfacial water molecules compared to that of the bulk. Furthermore, the dynamics of water molecules beyond the topmost molecular layer was found to be rather similar to that of bulk water.

Towards the understanding of convective dissolution in confined porous media: thin bead pack experiments, two-dimensional direct numerical simulations and physical models

We consider the process of convective dissolution in a homogeneous and isotropic porous medium. The flow is unstable due to the presence of a solute that induces a density difference responsible for driving the flow. The mixing dynamics is thus driven by a Rayleigh–Taylor instability at the pore scale. We investigate the flow at the scale of the pores using Hele-Shaw type experiment with bead packs, two-dimensional direct numerical simulations and physical models. Experiments and simulations have been specifically designed to mimic the same flow conditions, namely matching porosities, high Schmidt numbers and linear dependency of fluid density with solute concentration. In addition, the solid obstacles of the medium are impermeable to fluid and solute. We characterise the evolution of the flow via the mixing length, which quantifies the extension of the mixing region and grows linearly in time. The flow structure, analysed via the centreline mean wavelength, is observed to grow in agreement with theoretical predictions. Finally, we analyse the dissolution dynamics of the system, quantified through the mean scalar dissipation, and three mixing regimes are observed. Initially, the evolution is controlled by diffusion, which produces solute mixing across the initial horizontal interface. Then, when the interfacial diffusive layer is sufficiently thick, it becomes unstable, forming finger-like structures and driving the system into a convection-dominated phase. Finally, when the fingers have grown sufficiently to touch the horizontal boundaries of the domain, the mixing reduces dramatically due to the absence of fresh unmixed fluid. With the aid of simple physical models, we explain the physics of the results obtained numerically and experimentally. The solute evolution presents a self-similar behaviour, and it is controlled by different length scales in each stage of the mixing process, namely the length scale of diffusion, the pore size and the domain height.

Identifying diffusive length scales in one-dimensional Bose gases

In the hydrodynamics of integrable models, diffusion is a subleading correction to ballistic propagation. Here we quantify the diffusive contribution for one-dimensional Bose gases and find it most influential in the crossover between the main thermodynamic regimes of the gas. Analysing the experimentally measured dynamics of a single density mode, we find diffusion to be relevant only for high wavelength excitations. Instead, the observed relaxation is solely caused by a ballistically driven dephasing process, whose time scale is related to the phonon lifetime of the system and is thus useful to evaluate the applicability of the phonon bases typically used in quantum field simulators.

A general fourth-order mesoscopic multiple-relaxation-time lattice Boltzmann model and its macroscopic finite-difference scheme for two-dimensional diffusion equations

In this work, we first develop a general mesoscopic multiple-relaxation-time lattice Boltzmann (MRT-LB) model for the two-dimensional diffusion equation with the constant diffusion coefficient and source term, where the D2Q5 (five discrete velocities in two-dimensional space) lattice structure is considered. Then we exactly derive the corresponding macroscopic finite-difference scheme of the MRT-LB model. Additionally, we also propose a proper MRT-LB model for the diffusion equation with a linear source term, and obtain a macroscopic six-level finite-difference scheme. After that, we conduct the accuracy and stability analysis on the finite-difference scheme and the mesoscopic MRT-LB model, and find that at the diffusive scaling, both of them can achieve a fourth-order accuracy in space based on the Taylor expansion. The stability analysis also shows that they are both unconditionally stable. Finally, some numerical experiments are conducted, and the numerical results are also consistent with our theoretical analysis.

Spatial Confinement of Co Nanoparticles in N-Doped Carbon Nanorods for Wastewater Purification via CaSO3 Activation.

Spatial confinement of organic pollutants and reactive oxygen species (e.g., SO4•- and •OH) with ultrashort lifetime inside the scale of chemical theoretical diffusion could provide a greatly promising strategy to overcome the limitation of mass transfer in the heterogeneous Fenton-like oxidation process. Herein, we first reported spatial confinement of cobalt nanoparticles in N-doped carbon nanorods (Co-NCNRs), by encapsulating Co nanoparticles into N-doped carbon nanorods, in activating CaSO3 for antibiotic degradation. Compared to Na2SO3 and NaHSO3, CaSO3 could slowly and persistently discharge SO32- due to its low solubility, thus avoiding the depletion of the generated SO3•- and •OH under the high concentration of sulfite ions. Fully physical characterizations confirmed that the 3D hydrogel was mostly transformed into the nanorod structure of Co-NCNRs at 550 °C. Co atoms were successfully nanoconfined into N-doped carbon nanorods, which contributes to mass transfer and prevents the agglomeration of Co nanoparticles, thus enhancing its catalytic activity and stability in activating CaSO3 for water decontamination. The catalytic performance, kinetic research, influences of inorganic anions, pH, and degradation mechanism of chlortetracycline degradation catalyzed by the Co-NCNRs/CaSO3 system have been studied in detail. This work not only proposed a facile method for synthesis of nanoconfined catalyst but also provided an excellent Co-NCNRs/CaSO3 system for wastewater treatment.

Fourier Diffusion for Sparse CT Reconstruction.

Sparse CT reconstruction continues to be an area of interest in a number of novel imaging systems. Many different approaches have been tried including model-based methods, compressed sensing approaches, and most recently deep-learning-based processing. Diffusion models, in particular, have become extremely popular due to their ability to effectively encode rich information about images and to allow for posterior sampling to generate many possible outputs. One drawback of diffusion models is that their recurrent structure tends to be computationally expensive. In this work we apply a new Fourier diffusion approach that permits processing with many fewer time steps than the standard scalar diffusion model. We present an extension of the Fourier diffusion technique and evaluate it in a simulated breast cone-beam CT system with a sparse view acquisition.

Thermal and mechanical properties of AlSi7Mg matrix syntactic foams reinforced by Al2O3 or SiC particles in matrix

Materials with complex inner structure can be challenging to characterise in an effective way. The effective material parameters significantly depend on the structure, and thus on the interface properties. In the present paper, we focus on metal matrix syntactic foams, and we attempt to determine their effective thermal parameters. We supplement the results with their mechanical properties as well. For thermal characterisation, we use the heat pulse experiment to study their transient thermal response. We observed deviation from Fourier's law in multiple situations, and thus we propose an evaluation procedure for such experimental data using the Guyer–Krumhansl heat equation. We provide an iterative procedure to efficiently find the effective thermal diffusivity values provided by the Guyer–Krumhansl and Fourier equations based on the measured transient response. Furthermore, we studied the effective parameters, the specific heat, mass density, thermal conductivity and thermal diffusivity. We found that the standard estimations significantly overestimate the thermal conductivity. Furthermore, we propose a method for deducing a more reliable thermal diffusivity and thermal conductivity based on the transient temperature history, i.e., we propose to estimate Fourier's thermal diffusivity based on averaging the parameters of the Guyer-Krumhansl equation according to the observed diffusive time scales. We also found that for such metal matrix syntactic foams, even with knowing the constituents, the contact thermal resistance makes more challenging to provide a prior estimate for the effective thermal conductivity, but this difficulty can be resolved using proper effective thermal diffusivity values.

Squeezed Ensembles and Anomalous Dynamic Roughening in Interacting Integrable Chains.

It is widely accepted that local subsystems in isolated integrable quantum systems equilibrate to generalized Gibbs ensembles. Here, we identify a particular class of initial states in interacting integrable models that evade canonical generalized thermalization. Particularly, we demonstrate that in the easy-axis regime of the quantum XXZ chain, pure nonequilibrium initial states that lack magnetic fluctuations instead locally relax to squeezed generalized Gibbs ensembles governed by nonlocal equilibrium Hamiltonians, representing exotic equilibrium states with subextensive charge fluctuations that violate the self-affine scaling. At the isotropic point, we find exceptional behavior and explicit dependence on the initial state. Particularly, we find that relaxation from the Néel state is governed by extensive fluctuations and a superdiffusive dynamical exponent compatible with the Kardar-Parisi-Zhang universality. On the other hand, there are other nonfluctuating initial states that display diffusive scaling, e.g., a product state of spin singlets. Our predictions provide examples of anomalous quantum transport and fluctuations in strictly quantum states which can be directly tested in state-of-the-art cold atomic experimental settings.

Crystallization of Poly(l-lactic acid) on Water Surfaces via Controlled Solvent Evaporation and Langmuir-Blodgett Films.

Solvent evaporation is one of the most fundamental processes in soft matter. Structures formed via solvent evaporation are often complex yet tunable via the competition between solute diffusion and solvent evaporation time scales. This work concerns the polymer evaporative crystallization on the water surface (ECWS). The dynamic and two-dimensional (2D) nature of the water surface offers a unique way to control the crystallization pathway of polymeric materials. Using poly(l-lactic acid) (PLLA) as the model polymer, we demonstrate that both one-dimensional (1D) crystalline filaments and two-dimensional (2D) lamellae are formed via ECWS, in stark contrast to the 2D Langmuir-Blodgett monolayer systems as well as polymer solution crystallization. Results show that this filament-lamella biphasic structure is tunable via chemical structures such as molecular weight and processing conditions such as temperature and evaporation rate.

Buoyancy-Driven Dissolution Instability in a Horizontal Hele-Shaw Cell.

The dissolution of minerals within rock fractures is fundamental to many geological processes. Previous research on fracture dissolution has highlighted the significant role of buoyancy-driven convection leading to dissolution instability. Yet, the pore-scale mechanisms underlying this instability are poorly understood primarily due to the challenges in experimentally determining flow velocity and concentration fields. Here, we integrate pore-scale simulations with theoretical analysis to delve into the dissolution instability prompted by buoyancy-driven convection in a radial horizontal geometry. Initially, we develop a pore-scale modeling approach incorporating gravitational effects, subsequently validating it through experiments. We then employ pore-scale numerical simulations to elucidate the 3D intricacies of flow-dissolution dynamics. Our findings reveal that a simple criterion can delineate the condition for the onset of buoyancy-driven dissolution instability. If the characteristic length falls below a critical threshold, dissolution remains stable. Conversely, exceeding this threshold leads to two distinct regimes: the unstable regime of the confined domain affected by the initial aperture and the unstable regime of the semi-infinite domain independent of the initial aperture where the instability is no longer influenced by the lower boundary. We demonstrate that the pore-scale mechanism for this instability is due to the concentration boundary layer attaining a gravitationally unstable critical thickness. Through theoretical analysis of this layer and the time scales of diffusion and advection, we establish a theoretical model to predict where the dissolution instability occurs. This model aligns closely with our numerical simulations and experimental data across diverse conditions. Our work improves the understanding of buoyancy-driven dissolution instability in radial horizontal geometry. It is also of practical significance in understanding cavity formation in karst hydrology and preventing leaks in geological CO2 storage.

Diffusive persistence on disordered lattices and random networks.

To better understand the temporal characteristics and the lifetime of fluctuations in stochastic processes in networks, we investigated diffusive persistence in various graphs. Global diffusive persistence is defined as the fraction of nodes for which the diffusive field at a site (or node) has not changed sign up to time t (or, in general, that the node remained active or inactive in discrete models). Here we investigate disordered and random networks and show that the behavior of the persistence depends on the topology of the network. In two-dimensional (2D) disordered networks, we find that above the percolation threshold diffusive persistence scales similarly as in the original 2D regular lattice, according to a power law P(t,L)∼t^{-θ} with an exponent θ≃0.186, in the limit of large linear system size L. At the percolation threshold, however, the scaling exponent changes to θ≃0.141, as the result of the interplay of diffusive persistence and the underlying structural transition in the disordered lattice at the percolation threshold. Moreover, studying finite-size effects for 2D lattices at and above the percolation threshold, we find that at the percolation threshold, the long-time asymptotic value obeys a power law P(t,L)∼L^{-zθ} with z≃2.86 instead of the value of z=2 normally associated with finite-size effects on 2D regular lattices. In contrast, we observe that in random networks without a local regular structure, such as Erdős-Rényi networks, no simple power-law scaling behavior exists above the percolation threshold.

Non-Gaussian anomalous diffusion of optical vortices.

Anomalous diffusion of different particlelike entities, the deviation from typical Brownian motion, is ubiquitous in complex physical and biological systems. While optical vortices move randomly in evolving speckle fields, optical vortices have only been observed to exhibit pure Brownian motion in random speckle fields. Here we present direct experimental evidence of the anomalous diffusion of optical vortices in temporally varying speckle patterns from multiple-scattering viscoelastic media. Moreover, we observe two characteristic features, i.e., the self-similarity and the antipersistent correlation of the optical vortex motion, indicating that the mechanism of the observed subdiffusion of optical vortices can only be attributed to fractional Brownian motion (FBM). We further demonstrate that the vortex displacements exhibit a non-Gaussian heavy-tailed distribution. Additionally, we modulate the extent of subdiffusion, such as diffusive scaling exponents, and the non-Gaussianity of optical vortices by altering the viscoelasticity of samples. The discovery of the complex FBM but non-Gaussian subdiffusion of optical vortices may not only offer insight into certain fundamental physics, including the anomalous diffusion of vortices in fluids and the decoupling between Brownianity and Gaussianity, but also suggest a strong potential for utilizing optical vortices as tracers in microrheology instead of the introduced exogenous probe particles in particle tracking microrheology.

Scheduling in the High-Uncertainty Heavy Traffic Regime

We propose a model uncertainty approach to heavy traffic asymptotics that allows for a high level of uncertainty. That is, the uncertainty classes of underlying distributions accommodate disturbances that are of order 1 at the usual diffusion scale as opposed to asymptotically vanishing disturbances studied previously in relation to heavy traffic. A main advantage of the approach is that the invariance principle underlying diffusion limits makes it possible to define uncertainty classes in terms of the first two moments only. The model we consider is a single-server queue with multiple job types. The problem is formulated as a zero sum stochastic game played between the system controller, who determines scheduling and attempts to minimize an expected linear holding cost, and an adversary, who dynamically controls the service time distributions of arriving jobs and attempts to maximize the cost. The heavy traffic asymptotics of the game are fully solved. It is shown that an asymptotically optimal policy for the system controller is to prioritize according to an index rule, and for the adversary, it is to select distributions based on the system’s current workload. The workload-to-distribution feedback mapping is determined by a Hamilton–Jacobi–Bellman equation, which also characterizes the game’s limit value. Unlike in the vast majority of results in the heavy traffic theory and as a direct consequence of the diffusive size disturbances, the limiting dynamics under asymptotically optimal play are captured by a stochastic differential equation where both the drift and the diffusion coefficients may be discontinuous. Funding: R. Atar is supported by the Israeli Science Foundation [Grant 1035/20].

Optimization model of low-carbon technology adoption timing for coal power under decarbonization and flexibility demand: Empirical study in Beijing-Tianjin-Hebei region, China

Substituting renewable energy for coal power under the carbon neutrality goal is an inevitable path for power system transformation, while the high share of renewable energy leads to a rapid rise in system flexibility demand. Currently, coal-fired power is still one of the most economical and reliable large-scale flexible resources in China. Therefore, the issue of how to mitigate the conflict between cleanliness and flexibility for coal-fired power is urgent to be solved. Accordingly, this paper established an optimization framework for the retirement and technology adoption of coal-fired power units with high spatial-temporal resolution, and the regional carbon emission budget is estimated from a top-down perspective. Secondly, a dynamic carbon quota allocation method considering technological innovation and adoption is proposed. The carbon trading cost of the units is evaluated from a bottom-up perspective, to realize the interaction between the obligatory policy constraints of the top-level target and the flexible incentives of the market mechanism. Finally, the empirical analysis was conducted in the Beijing-Tianjin-Hebei region of China. The optimal solution achieved by proposed method results in a substantial 27% reduction in total costs while keeping the increase in carbon emissions below 3%. By analyzing the dynamic evolution path of coal and the scale of diffusion of multi-type technologies, the differences in the roles coal power assuming at various stages of decarbonization are discussed. The robustness of the model and the validity of the proposed method were verified by comparing the dynamic/static carbon quota allocation. Overall, this study provides an effective optimization model for investigating the low-carbon technology adoption timing for coal power in Beijing-Tianjin-Hebei region, and offers valuable insights for other coal-dominated emerging economies seeking for power system transformation roadmap in the forthcoming net-zero carbon age.