Scalar Diffusion Research Articles

Arbitrary-Lagrangian-Eulerian finite volume IMEX schemes for the incompressible Navier-Stokes equations on evolving Chimera meshes

In this article we design a finite volume semi-implicit IMEX scheme for the incompressible Navier-Stokes equations on evolving Chimera meshes. We employ a time discretization technique that separates explicit and implicit terms, accommodating the multi-scale nature of the governing equations, which involve both time scales of diffusion and advection operators. The finite volume approach for both explicit and implicit terms allows to encode into the nonlinear flux the velocity of displacement of the Chimera mesh via integration on moving cells. The numerical solution is then projected onto the physically meaningful solution manifold of non-solenoidal fields that stems from the energy equation. To attain second-order time accuracy, we employ semi-implicit IMEX Runge-Kutta schemes. These novel schemes are combined with a fractional-step method, thus the governing equations are eventually solved using a projection method to satisfy the divergence-free constraint of the velocity field. The implicit discretization of the viscous terms allows the CFL-type stability condition for the maximum admissible time step to be only defined by the relative fluid velocity referred to the movement of the frame and not depending on the viscous terms. Communication between different grid blocks is enabled through compact exchange of information from the fringe cells of one mesh block to the field cells of the other block. The continuity of the solution is recovered in one-shot during the solution of the arising algebraic systems by not involving neither direct discretization of the differential operators on fringe cells nor an iterative Schwartz-type method. Free-stream preservation property, i.e. compliance with the Geometric Conservation Law (GCL), is respected at the order of the scheme. The accuracy and capabilities of the new numerical schemes are proved through an extensive range of test cases, demonstrating ability to solve relevant benchmarks in the field of incompressible fluids.

The Dual Approach to Optimal Control in the Coefficients of Nonlocal Nonlinear Diffusion

We derive the dual variational principle (principle of minimal complementary energy) for the nonlocal nonlinear scalar diffusion problem, which may be viewed as the nonlocal version of the p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p$$\\end{document}-Laplacian operator. We establish existence and uniqueness of solutions (two-point fluxes) as well as their quantitative stability, which holds uniformly with respect to the small parameter (nonlocal horizon) characterizing the nonlocality of the problem. We then focus on the nonlocal analogue of the classical optimal control in the coefficient problem associated with the dual variational principle, which may be interpreted as that of optimally distributing a limited amount of conductivity in order to minimize the complementary energy. We show that this nonlocal optimal control problem Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document}-converges to its local counterpart, when the nonlocal horizon vanishes.

Pityriasis rosea: dermoscopic features in Uganda.

The study aimed to describe the dermoscopic features of pityriasis rosea among patients attending the skin clinic at Mbarara Regional Referral Hospital. A hospital-based cross-sectional descriptive study conducted for a 6-month period in the skin clinic of MRRH in Southwestern Uganda. Data were collected from consecutively recruited patients using structured questionnaires. Patients with a clinical diagnosis of pityriasis rosea were examined using a dermoscope and subsequently sent for KOH and TPHA tests to rule out fungal skin infection and secondary syphilis, respectively, and then received routine care at the skin clinic. There were 54 patients with pityriasis rosea seen. Dermoscopy was done on a total of 162 lesions of which 19 were herald patches, 51 were truncal lesions, 52 on the extremities while 40 were on the face and neck regions. Common dermoscopic features consisted of a violaceous background noted in 145 (89.51%), white scales in 161 (99.38%), diffuse scale distribution in 57 (35.19%), perifollicular scale type in 61 (37.65%), and brown-dotted pigmentary changes in 66 (40.74%). Other unique findings noted in a few lesions were cloudy structures, petechial spots, erosions, and punched out pits. Most prevalent dermoscopic features included: a violaceous background, white scales, diffuse scale distribution, perifollicular scale type, brown-dotted pigmentary changes with no visible blood vessels nor follicular changes. Other unique less frequently seen findings were cloudy structures, petechial spots, erosions, and punched out pits.

Solving scalar reaction diffusion equations with cubic non-linearity having time-dependent coefficients by the wavelet method of lines

<abstract><p>This paper aims to conduct the numerical solutions of the scalar reaction diffusion model with cubic non-linearity having constant and time-dependent coefficients. The proposed method is hybrid in nature in which Haar wavelets are used to approximate the spatial derivatives and the Runge-Kutta (RK) routines are used to solve the resultant system of ordinary differential equations. We illustrate the applicability and efficiency of the proposed method by computing $ L_2 $, $ L_{\infty} $, and $ L_{rms} $ error estimates for various test models. The numerical accuracy and stability of the Haar wavelet-based method of lines for solving the scaler reaction-diffusion model provides further insight into the use of this scheme for model equations across various disciplines.</p></abstract>

Dynamical crossovers and correlations in a harmonic chain of active particles.

We explore the dynamics of a tracer in an active particle harmonic chain, investigating the influence of interactions. Our analysis involves calculating mean-squared displacements (MSDs) and space-time correlations through Green's function techniques and numerical simulations. Depending on chain characteristics, i.e., different time scales determined by interaction stiffness and persistence of activity, tagged-particle MSDs exhibit ballistic, diffusive, and single-file diffusion (SFD) scaling over time, with crossovers explained by our analytic expressions. Our results reveal transitions in bulk particle displacement distributions from an early-time bimodal to late-time Gaussian, passing through regimes of unimodal distributions with finite support and negative excess kurtosis and longer-tailed distributions with positive excess kurtosis. The distributions exhibit data collapse, aligning with ballistic, diffusive, and SFD scaling in the appropriate time regimes. However, at much longer times, the distributions become Gaussian. Finally, we derive analytic expressions for steady-state static and dynamic two-point displacement correlations. We verify these from simulations and highlight the differences from the equilibrium results.

Research on the Dissemination Strategies of Traditional Culture in Anime Illustrations and Picture Books - Based on the Application of Information Diffusion Models

Abstract Animation illustrations and picture books themed on traditional culture play a crucial role in its dissemination. This paper analyzes the present scenario of traditional cultural transmission via these mediums and introduces an information diffusion model as the theoretical framework for subsequent questionnaire design and analysis. The model incorporates the theory of network dimensional force and information diffusion resistance to depict the diffusion process within cyberspace, accounting for the constraints imposed by information resistance. This results in a model that accurately mirrors the realities of the network environment. The study further examines the velocity and distortion in information diffusion, exploring the model’s diffusion scale and laws. In assessing the diffusion effectiveness through a questionnaire on cartoon illustrations and picture books, findings indicate a moderate inclination towards purchases, with average willingness and mean purchase values at 3.32 and 3.35, respectively. The analysis reveals that the pivotal factors affecting dissemination include content knowledge, thematic significance, and channel preferences, all scoring an average of 4 in terms of mean and median values. However, the overall satisfaction with the dissemination of traditional culture remains moderate among respondents. To enhance the dissemination effectiveness, it is imperative to advance the construction of conventional cartoon-quality illustrations and picture books, thereby fostering a more robust propagation of traditional culture.

Growth of Massive Molecular Cloud Filament by Accretion Flows. I. Slow-shock Instability versus Ambipolar Diffusion

The Herschel Gould Belt Survey showed that stars form in dense filaments in nearby molecular clouds. Recent studies suggest that massive filaments are bound by the slow shocks caused by accretion flows onto the filaments. The slow shocks are known to be unstable to corrugation deformation of the shock front. Corrugation instability could convert the accretion flow's ram pressure into turbulent pressure that influences the width of the filament, which, according to theory, determines the self-gravitational fragmentation scale and core mass. In spite of its importance, the effect of slow-shock instability on star-forming filaments has not been investigated. In addition, the linear dispersion relation obtained from ideal magnetohydrodynamics (MHD) analysis shows that the most unstable wavelength of shock corrugation is infinitesimally small. In the scale of dense filaments, the effect of ambipolar diffusion can suppress the instability at small scales. This study investigates the influence of ambipolar diffusion on the instability of the slow shock. We perform two-dimensional MHD simulations to examine the linear growth of the slow-shock instability, considering the effect of ambipolar diffusion. The results demonstrate that the most unstable scale of slow-shock instability is approximately 5 times the length scale of ambipolar diffusion ℓ AD calculated using post-shock variables, where ℓ AD corresponds to the scale where the magnetic Reynolds number for ambipolar diffusivity is unity.

Diagnosis and management of erythroderma; a systematic review

Erythroderma, a condition characterized by diffuse erythema and scaling covering at least 90 percent of the skin\'s surface, poses a serious and potentially life-threatening threat. This systematic study aimed to establish diagnosis and management guidelines for erythroderma. Following PRISMA guidelines, a comprehensive review was conducted using PubMed/Medline, Scopus, and Embase databases focusing on English-language articles from 2010 to 2023. From 279 studies, seven articles were included, mainly comprising surveys and analyses of national databases. Erythroderma, as a clinical sign, can manifest as a consequence of various cutaneous and systemic diseases, drug hypersensitivity reactions, and rarely, Sezary syndrome. In pediatric patients, the clinical presentation encompasses a spectrum of acquired and inherited diseases, including infections, inflammatory skin conditions, ichthyoses, and congenital immunodeficiencies. Diagnosing erythroderma proves challenging due to its syndromatic nature, presenting with nonspecific clinical features. Dermatologists must diligently seek cause-oriented clues, employing multiple biopsies to enhance diagnostic accuracy. Initial management should include nutritional expert evaluation, assessment of fluid imbalance, skin barrier maintenance, sedative anti-histamines, and exclusion of secondary bacterial infection. Given its life-threatening potential, erythroderma might necessitate hospitalization. This study provides valuable insights into the complexities of erythroderma diagnosis and highlights essential considerations for effective management.

Phase-field crystal modeling of graphene/hexagonal boron nitride interfaces.

Two-dimensional (2D) materials such as graphene and hexagonal boron nitride (h-BN) are an essential class of materials with enhanced structural and electronic properties compared to their bulk counterparts. The phase-field crystal (PFC) model can reach diffusive time scales to study nucleation, growth of crystallites, and relaxation of strain-driven 2D monolayers that are much larger in comparison to molecular dynamics (MD) and quantum mechanical density functional theory (QMDFT) methods while retaining atomic resolution. The model also naturally incorporates an atomic length scale and elastic and plastic deformations. We simulate the morphological transition of the crystal growth of various equilibrium crystal shapes. In this work, we generalize the one-mode PFC model to study the graphene/h-BN heterostructure interface by using conserved dynamics to describe the dynamics of the model. The model was used to find the equilibrium shape of the crystal of the h-BN crystal embedded in a graphene monolayer.

Poroviscoelastic relaxations and rate-dependent adhesion in gelatin.

Hydrogels, polymeric networks swollen with water, exhibit time/rate-dependent adhesion due to their poroviscoleastic constitution. In this study, we conducted probe-tack experiments on gelatin and investigated the influence of dwelling times and unloading rates on pull-off forces and work of adhesion. We utilized in situ contact imaging to monitor separation kinematics and interfacial crack velocities. We found that the crack velocities scaled nonlinearly with the unloading rate, in a power law with an exponent of 0.8 and were independent of dwelling time. At maximum unloading rates corresponding to subsonic interfacial crack speeds, we observed an order of magnitude enhancement in the apparent work of adhesion. The enhancement of adhesion and the crack velocities were related by a power law with an exponent of 0.39. The maximum vertical extension during unloading, a measure of crack opening, exhibited linear correlation with the enhancement of adhesion. Both correlations were in line with the rate-dependent work of fracture modeled for viscoelastic solids (e.g., Persson and Brener model). We explored the links between dwelling times corresponding to varying degrees of poroelastic diffusion and the adhesion. We found 40% additional enhancement in adhesion at the highest unloading rate. This enhancement is due to the unbalanced osmotic pressure, also known as the suction effect. The influence of dwelling times on adhesion was negligible for the interfacial cracks propagating slower than the diffusive time scales. These results identify viscoelastic relaxations as the dominant mechanism governing the rate-dependent enhancement of adhesion, and hence pave the way for tuning rate-dependent adhesion in soft multiphasic materials.

Brownian motion of soft particles near a fluctuating lipid bilayer.

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.

Dermoscopy findings of the axilla of women with frontal fibrosing alopecia

AbstractBackgroundFrontal fibrosing alopecia (FFA) is a form of inflammatory and cicatricial alopecia, presenting concomitantly with rarefaction of eyebrows and body hair. However, the involvement of body hair in FFA is still poorly investigated.ObjectivesTo compare the dermoscopy findings of axillary hairs in a group of women with FFA with a group of women without FFA.MethodsAn observational case‐control study was carried out on the dermoscopic findings of the axillary hair in this group of patients with FFA compared to a group of women without FFA, matched by age groups and skin phototypes.ResultsThirty women with a clinical and histopathological diagnosis of FFA were included in the study. Dermoscopy of the axilla in patients with FFA revealed the presence of axillary hair in 93.3% and all patients had hairless follicular openings. More than one wire per follicular ostium was observed in 70% of the patients and variability in the diameter of the hairs in 83.3% of the cases. Regarding dermoscopic inflammatory signs, a peripillary brownish halo was present in 83.3% of patients, peripillary scaling in 56.7%, diffuse scaling in 63.3% and pigmented network of the epidermis in 73.3% of the cases. When comparing the dermoscopic findings of the axilla of cases with controls, the chance of occurrence of brownish peripillary halos between cases was higher than double the chance of occurrence of these halos among controls (OR = 2.7; 95% CI: 1.1−7.6; p = 0.029). The rest of variables were not statistically associated with the FFA.ConclusionsDermoscopy of the axilla in patients with FFA revealed that brownish peripillary halos may be a diagnostic clue for FFA in the axillary region. The dermoscopy findings found in the present study allow characterizing the axillary involvement of patients with FFA and recognize the dermoscopic differences with other dermatoses involving this location.

Vectorial finite-difference-based lattice Boltzmann method: Consistency, boundary schemes and stability analysis

In this paper we propose a vectorial finite-difference-based lattice Boltzmann method (FD-LBM), which unifies several different numerical schemes for the incompressible Navier–Stokes equations. By using the Maxwell iteration, we analyze the consistency under the diffusive scaling. In the situation that the widely used bounce-back or “anti-bounce-back” boundary schemes are not applicable, a new boundary scheme is developed to accompany the vectorial method. It is shown that the scheme has second-order accuracy when the boundary is located at the middle of two neighboring lattice nodes. We also prove the numerical stability of the vectorial method on periodic domains and the vectorial method together with the boundary scheme on bounded domains. Several numerical experiments for 2D & 3D flow problems with straight and curved boundaries validate the stability and accuracy of the vectorial LBM with the proposed boundary scheme.

Fast-reaction limit of reaction–diffusion systems with nonlinear diffusion

In this paper, we present an approach to characterizing fast-reaction limits of systems with nonlinear diffusion, when there are either two reaction–diffusion equations, or one reaction–diffusion equation and one ordinary differential equation, on unbounded domains. Here, we replace the terms of the form [Formula: see text] in usual reaction–diffusion equation, which represent linear diffusion, by terms of form [Formula: see text], representing nonlinear diffusion. We prove the convergence in the fast-reaction limit [Formula: see text] that is determined by the unique solution of a certain scalar nonlinear diffusion problem.

Flexible Bayesian Inference for Diffusion Processes using Splines

We introduce a flexible method to simultaneously infer both the drift and volatility functions of a discretely observed scalar diffusion. We introduce spline bases to represent these functions and develop a Markov chain Monte Carlo algorithm to infer, a posteriori, the coefficients of these functions in the spline basis. A key innovation is that we use spline bases to model transformed versions of the drift and volatility functions rather than the functions themselves. The output of the algorithm is a posterior sample of plausible drift and volatility functions that are not constrained to any particular parametric family. The flexibility of this approach provides practitioners a powerful investigative tool, allowing them to posit a variety of parametric models to better capture the underlying dynamics of their processes of interest. We illustrate the versatility of our method by applying it to challenging datasets from finance, paleoclimatology, and astrophysics. In view of the parametric diffusion models widely employed in the literature for those examples, some of our results are surprising since they call into question some aspects of these models.

Exploring solute-defect interactions in nanosized palladium hydrides across multiple time scales

We employ two different atomistic methods to investigate solute-defect interactions in nanosized palladium–hydrogen (Pd–H) systems across multiple time scales. The first method, referred to as Diffusive Molecular Dynamics (DMD), focuses on capturing hydride phase transformation and the evolution of solute-induced lattice defects over a diffusive time scale. The second method, Molecular Dynamics (MD), provides more detailed insights into atomic movements and lattice relaxation over the time scale of thermal vibrations. These two methods are connected with MD simulations initialized using statistical measures of microscopic variables obtained from DMD at different H/Pd ratios. Our study demonstrates that DMD effectively captures the propagation of an atomistically sharp hydride phase boundary as well as the dynamics of solute-induced misfit dislocations and stacking faults. While the H-concentrated phase leads to a reduction in the vibrational energy, the presence of stacking faults locally increases the vibrational energy of both Pd and H atoms. Furthermore, the MD simulation results align with DMD in terms of equilibrium potential energy, the preservation of hydride phase boundary, and the spatial distribution of stacking faults. We thoroughly characterize the lattice crystalline structures in four key regions of the particle. We observe a preference for H atoms to occupy tetrahedral interstitial sites near stacking faults due to the lower stacking fault energies provided by these sites within the H-concentrated phase.

Dynamical symmetries in the non-equilibrium dynamics of the directed spherical model

The dynamical scaling and ageing in the relaxational dynamics of the quenched directed spherical model is analysed. The exact two-time correlation and response functions display new regimes of ballistic or anisotropic ballistic scaling, at larger distances than probed in the usual regime of diffusive scaling. The role of long-ranged initial correlations on the existence of these scaling regimes is clarified. Their dynamical symmetries are described in terms of extensions of the Schrödinger algebra appropriate to non-equilibrium dynamics in that the anisotropic ballistic scaling regime can be interpreted in terms of meta-Schrödinger invariance while the regime of isotropic ballistic scaling is meta-conformally invariant.

Convergent Evolution of Prehistoric Technologies: the Entropy and Diversity of Limited Solutions

Linking the likelihood of convergent evolution to the technologies’ complexity, this paper identifies the scales of technological diffusion and convergence, i.e., the evolving of structures that are similar, but not related to a common “ancestor.” Our study provides quantitative measures for understanding complexity and connectivity in technologies. The utility of our approach is exemplified through the case study of Cucuteni-Tripolye pottery kilns in Chalcolithic Southeastern Europe. The analysis shows that technological evolution has to be scaled to the “technologically important” (in quantitative terms) component parts, whose introduction shapes a ground for extinction and self-evolvement caused by the cascade effects along technological design structure. Similar technological solutions to the technological design structure engender the spread of similar devices in various locations. Surprisingly, such a broad distribution may be the result of relatively low internal diversity, rather than arising from higher efficiency. This gives some reasons for the underestimation of convergence as a mechanism for evolution of technology in current prehistoric archaeology.

Rigorous derivation of the Fick cross-diffusion system from the multi-species Boltzmann equation in the diffusive scaling

We present the arising of the Fick cross-diffusion system of equations for fluid mixtures from the multi-species Boltzmann equation in a rigorous manner in Sobolev spaces. To this end, we formally show that, in a diffusive scaling, the hydrodynamical limit of the kinetic system is the Fick model supplemented with a closure relation and we give explicit formulae for the macroscopic diffusion coefficients from the Boltzmann collision operator. Then, we provide a perturbative Cauchy theory in Sobolev spaces for the constructed Fick system, which turns out to be a dilated parabolic equation. We finally prove the stability of the system in the Boltzmann equation, ensuring a rigorous derivation between the two models.

PBPK Modeling of PAXLOVIDTM: Incorporating Rotamer Conversion Kinetics to Advanced Dissolution and Absorption Model

PAXLOVID™ is a combination medicine of nirmatrelvir tablets co-packaged with ritonavir tablets. Nirmatrelvir is a peptidomimetic inhibitor of SARS-CoV2 main protease (Mpro), developed for the treatment of COVID-19. Ritonavir is co-administered as a pharmacokinetics (PK) enhancer to inhibit CYP3A mediated metabolism increasing exposures of nirmatrelvir. In the solid form, nirmatrelvir exists in a stable single conformational state (ANTI form). However, nirmatrelvir exhibits atropisomerism in solution whereby upon dissolution the ANTI rotational isomer reversibly converts to another conformation state (SYN form). Nirmatrelvir rotamer conversion follows pseudo first order kinetics with a conversion half-life of approximately 15 min in aqueous solutions, which is on a similar time scale of diffusion mediated dissolution from the solid form. In vitro dissolution studies further indicated that rotamer conversion is one of the processes controlling nirmatrelvir dissolution. It was hypothesized that rotamer conversion kinetics would affect oral absorption of nirmatrelvir in vivo. Consequently, a physiologically based pharmacokinetic (PBPK) model for Paxlovid was developed in Simcyp™ using the advanced dissolution, absorption, and metabolism model (ADAM) by incorporating rotamer conversion kinetics to achieve a more mechanistic description of nirmatrelvir oral absorption. The results demonstrate that the established absorption model with rotamer kinetics adequately described observed clinical data from various nirmatrelvir doses, dosage forms, and dosing regimens. The predicted vs. observed AUCinf and Cmax ratios were within 2-fold. The model has been internally used to inform clinical studies and dose recommendations for pediatrics.