Linear Diffusion Research Articles

Simulation of Mercury-Driven Diffusion Pumps for Torus Exhaust Pumping

A new, continuous pumping train has been proposed for the European demonstration fusion power plant (DEMO). Mercury-driven linear diffusion pumps (LDPs) are suggested for use as high-vacuum pumps in this pumping train. In this work, we validate a 2-D simulation framework based on the direct simulation Monte Carlo (DSMC) method with experimental data of a two-stage mercury-driven LDP that was operated at the Lawrence Livermore National Laboratory (LLNL) in the 1950s. The simulation setup and assumed boundary conditions are described and their appropriateness discussed. Numerical results are compared to available experimental data for four different positions of the upper nozzle pipe. We find acceptable agreement between experimental and numerical results for the air pumping speed. This validation paves the way for using the simulation framework as a design and optimization tool in the further development process of the DEMO LDPs.

Convergence and parameter estimation of the linear weighted-fractional self-repelling diffusion

Let B a , b be a weighted-fractional Brownian motion with Hurst indexes a and b such that a > − 1 and 0 < b < 1 ∧ ( 1 + a ) . In this paper, we consider the linear self-repelling diffusion d X t a , b = d B t a , b + ( θ ∫ 0 t ( X t a , b − X s a , b ) ds + ν ) dt with X 0 a , b = 0 , where θ > 0 , ν ∈ R are two real parameters. The process is an analogue of the linear self-interacting diffusion (Cranston and Le Jan, Math. Ann. 303 (1995), 87-93). We introduce its large time behaviors, and the behavior presents a recursive convergence which is quite different from the asymptotic behavior of stochastic differential equations without interacting drifts. As a related question, we also consider the asymptotic behaviors of the least squares estimations of θ and ν.

Well-posedness of the initial-boundary value problems for the time-fractional degenerate diffusion equations

This paper deals with the solving of initial-boundary value problems for the one-dimensional linear timefractional diffusion equations with time-degenerate diffusive coefficients t^β with β &gt; 1 − α. The solutions to initial-boundary value problems for the one-dimensional time-fractional degenerate diffusion equations with Riemann-Liouville fractional integral I^1−α_0+,t of order α ∈ (0, 1) and with Riemann-Liouville fractional derivative D^α_0+,t of order α ∈ (0, 1) in the variable, are shown. The solutions to these fractional diffusive equations are presented using the Kilbas-Saigo function Eα,m,l(z). The solution to the problems is discovered by the method of separation of variables, through finding two problems with one variable. Rather, through finding a solution to the fractional problem depending on the parameter t, with the Dirichlet or Neumann boundary conditions. The solution to the Sturm-Liouville problem depends on the variable x with the initial fractional-integral Riemann-Liouville condition. The existence and uniqueness of the solution to the problem are confirmed. The convergence of the solution was evidenced using the estimate for the KilbasSaigo function E_α,m,l(z) from and by Parseval’s identity.

Ultramicroelectrode Based Approaches to Diagnose Utility of Redox Electrolytes in Flow Batteries

The proposed redox electrolyte system, concentrated solutions of Keggin type silicotungstic acid (H4SiW12O40), have been tested using the microelectrode methodology to determine mass-transport (effectively diffusional) coefficients for charge propagation and homogeneous (electron self-exchange) rates of electron transfers. Silicotungstic acid (H4SiW12O40) acts as proton conductors, and undergoes fast, reversible, multi-electron electron transfers leading to the formation of highly conducting, mixed-valence (tungsten(VI,V) heteropoly blue) compounds. To develop useful electroanalytical diagnostic criteria, electroanalytical approaches utilizing ultramicrodisk electrodes have been adapted to characterization of redox electrolytes. Combination of two parallel ultramicroelectrode-based experiments performed under radial (long-term experiment; e.g., slow scan rate) and linear (short-term experiment; e.g., fast scan rate) diffusion conditions permits determination of both effective concentration of redox centers and transport (diffusion) coefficient parameters, which are crucial to evaluation of the utility of a redox electrolyte for charge storage.

An initial evaluation of the thermodynamic or kinetic separation performance of cation-exchanged LTA zeolites for mixtures of propane and propylene

Adsorptive separation of propylene (C3H6) and propane (C3H8) may represent an energy-efficient alternative to conventional cryogenic distillation. In this perspective, a set of zeolitic adsorbents of LTA type structure (pure-silica zeolite (Si-LTA) and cation- (Na+, 33% of Li+, 50% of Mg2+ and 50% of Ca2+) containing zeolites) were prepared, then characterized using various techniques such as PXRD, gas adsorption measurement, TGA, XRF, SEM and EDX mapping. Thanks to an in-house manometric dosing setup coupled with a Tian-Calvet type microcalorimeter, the pure gas adsorption isotherms and their corresponding differential enthalpies of adsorption were measured at 303 K and for pressures up to 5 bar. To fit those adsorption data, the dual-site Langmuir was selected as the best fit model, and by using the Ideal Adsorbed Solution Theory (IAST), thermodynamic selectivities were determined. The mass transfer constants were also estimated by fitting, separately, the Linear Driving Force (LDF) and isothermal micropore diffusion models to adsorption kinetic curves, thus allowing kinetic type selectivities to be calculated. The combination of those selectivities reveals that the thermodynamic separation of C3H6 from C3H8 is highly favorable on CaNa-LTA, followed by its MgNa-LTA counterpart with IAST selectivities around 15 and 5, respectively. On the other hand, the monovalent cationic zeolites (i.e., Na- and LiNa-LTA) show a predominance of steric effects. Also, except for Si-LTA which shows a moderate kinetic separation, the studied materials are potential candidates, in the following order CaNa- > MgNa- > LiNa- > Na-LTA, for the separation of C3H6 from C3H8 by adsorption-based technologies.

The Influence of Plastic Barriers on Aerosol Infection Risk during Airport Security Checks

Plastic barriers physically separate queuing passengers in airport security check areas as a measure against aerosol transmission. However, this may create “canyons” that interfere with the existing ventilation design: potentially inhibiting airflow, concentrating exhaled viruses, and exacerbating aerosol transmission risk. Accordingly, this study investigated the transmission implications of installing plastic barriers in a security check area with computational fluid dynamics (CFD). Two air distribution schemes were modeled: one with linear air supply diffusers aligned vertically to (Case 1) and another with diffusers parallel with (Case 2) the orientation of partitions. The drift-flux model was used to calculate the spread of viral bioaerosols with 5 µm in diameter; then the Wells–Riley equation was applied to assess aerosol transmission risk for SARS-CoV-2. According to simulation results, in Case 1, installing plastic barriers resulted in relatively small changes in volume with a high infection risk of 1% or greater in the breathing zone within the first 25 min. However, in Case 2, using plastic barriers resulted in the continuous increase in this volume within the first 25 min while this volume was near zero if without plastic barriers. In conclusion, installing plastic barriers needs careful consideration because they do not reduce the risk of airborne SARS-CoV-2 transmission and might even exacerbate it without localized ventilation and air cleaning.

Asymptotic stability problem of predator–prey system with linear diffusion

Abstract As the primary killer of health, the class of infectious diseases is the greatest threat to humanity. At present, international methods of studying the large-scale spatial transmission of sudden infectious diseases from the perspective of dynamics can be divided into two categories. On the one hand, top international biomedical and medical teams discuss the restraining effects of some prevention and control strategies on infectious diseases, such as smallpox, malaria, hand, foot and mouth disease and pandemic influenza, from the perspective of pragmatism. On the other hand, researchers in theoretical physics and network science tend to use compound population network models to explore the internal dynamic mechanism of spatial transmission of infectious diseases. This paper establishes a Lotka–Volterra dispersal predator–prey system in a patchy environment. It shows the existence of model boundary equilibria and asymptotic stability under an appropriate condition. This paper adopts the method of global Lyapunov function and the results of graph theory. We also consider a predator–prey dynamical model in a patchy environment, where the prey and predator individuals in each compartment can travel among n patches.

Particular flows and attracting sets

In this commentary, I expand on the analysis of the recent article "How particular is the physics of the Free Energy Principle?" by Aguilera et al. by studying the flow fields of linear diffusions, and particularly the rotation of their attracting sets in the presence of different types of solenoidal coupling. This analysis sheds new light on previous claims made in the FEP literature (and contested in the target article) that the internal dynamics of stochastic systems can be cast performing a gradient flow on variational free energy, and thus endowed with an inferential interpretation, i.e., as if internal states are performing inference about states external to the system. I express general agreement with the target article's statement that the marginal flow of internal states does not point along variational free energy gradients evaluated at the most likely internal state (i.e., the conditional mode). However, in this commentary I focus on the flow of particular states (internal and blanket states) and their variational free energy gradients, and show that for a wide but restricted class of solenoidal couplings, the average flow of these systems point along variational free energy gradients. This licenses a different but perhaps stronger re-description of the flow of particular states as performing inference, which importantly holds at arbitrary points in state space, not just at the conditional modes.

Locating Sources in Multiplex Networks for Linear Diffusion Systems

Accurately locating sources with limited resources plays an important role in suppressing and even predicting the spread of harmful information. Due to the existence of the coupling between layers, compared with simplex networks, many studies have revealed that multiplex networks present many interesting phenomena. However, almost all the works involved in source(s) localization concentrate on simplex networks, while it is unclear how the coupling strength between layers of a multiplex network affects source(s) localization. Here we focus on a linear diffusion process and propose a general framework of multiple sources localization in multiplex networks with minimum measurements by combining the observability theory and compressed sensing theory. One surprise finding is that, for undirected two-layer networks with fully coupling between layers, the messengers placed at the same layer is sufficient to accurately locate all the sources. Different from simplex networks, the diffusion coefficients of linear diffusion process in multiplex networks can affect the minimum number of messengers. Simulation results from various network structures show that the minimum number of messengers is fewer when the coupling strength between layers is higher. Besides, we find the larger the network size the fewer measurements are required for sources localization. We further provide simulations from synthetic networks and one real network demonstrates our framework of sources localization is robust against small amount of data, noise and the coupling strength between layers.

Asymptotic Behavior on a Linear Self-Attracting Diffusion Driven by Fractional Brownian Motion

Let BH={BtH,t≥0} be a fractional Brownian motion with Hurst index 12≤H&lt;1. In this paper, we consider the linear self-attracting diffusion: dXtH=dBtH+σXtHdt−θ∫0tXsH−XuHdsdt+νdt with X0H=0, where θ&gt;0 and σ,ν∈R are three parameters. The process is an analogue of the self-attracting diffusion (Cranston and Le Jan, Math. Ann.303 (1995), 87–93). Our main aim is to study the large time behaviors. We show that the solution t−σθHXtH−X∞H converges in distribution to a normal random variable, as t tends to infinity, and obtain two strong laws of large numbers associated with the solution XH.

Inverting passive margin stratigraphy for marine sediment transport dynamics over geologic time

AbstractPassive margin stratigraphy contains time‐integrated records of landscapes that have long since vanished. Quantitatively reading the stratigraphic record using coupled landscape evolution and stratigraphic forward models (SFMs) is a promising approach to extracting information about landscape history. However, there is no consensus about the optimal form of simple SFMs because there has been a lack of direct tests against observed stratigraphy in well‐constrained test cases. Specifically, the extent to which SFM behaviour over geologic space and timescales should be governed by local (downslope sediment flux depends only on local slope) versus nonlocal (sediment flux depends on factors other than local slope, such as the history of slopes experienced along a transport pathway) processes is currently unclear. Here, we develop a nonlocal, nonlinear SFM that incorporates slope bypass and long‐distance sediment transport, both of which have been previously identified as important model components but not thoroughly tested. Our model collapses to the local, linear model under certain parameterizations such that best‐fit parameter values can indicate optimal model structure. Comparing 2‐D implementations of both models against seven detailed seismic sections from the Southeast Atlantic Margin, we invert the stratigraphic data for best‐fit model parameter values and demonstrate that best‐fit parameterizations are not compatible with the local, linear diffusion model. Fitting observed stratigraphy requires parameter values consistent with important contributions from slope bypass and long‐distance transport processes. The nonlocal, nonlinear model yields improved fits to the data regardless of whether the model is compared against only the modern bathymetric surface or the full set of seismic reflectors identified in the data. Results suggest that processes of sediment bypass and long‐distance transport are required to model realistic passive margin stratigraphy and are therefore important to consider when inverting the stratigraphic record to infer past perturbations to source regions.

A new and efficient approach for solving linear and nonlinear time-fractional diffusion equations of distributed order

A new and efficient approach for solving linear and nonlinear time-fractional diffusion equations of distributed order

An explicit method for the self-interacting diffusion driven by fractional Brownian motion under global Lipschitz conditions

The linear self-interacting diffusion driven by fractional Brownian motion is approximated by an explicit numerical scheme in this paper. The present method’s mean-square convergence is investigated, and the order of convergence is established to be 1. To demonstrate the performance of the suggested method, a numerical simulation is performed.

Monotone methods in counterparty risk models with nonlinear Black–Scholes-type equations

A nonlinear Black–Scholes-type equation is studied within counterparty risk models. The classical hypothesis on the uniform Lipschitz-continuity of the nonlinear reaction function allows for an equivalent transformation of the semilinear Black–Scholes equation into a standard parabolic problem with a monotone nonlinear reaction function and an inhomogeneous linear diffusion equation. This setting allows us to construct a scheme of monotone, increasing or decreasing, iterations that converge monotonically to the true solution. As typically any numerical solution of this problem uses most computational power for computing an approximate solution to the inhomogeneous linear diffusion equation, we discuss also this question and suggest several solution methods, including those based on Monte Carlo and finite differences/elements.

Optimal consumption, investment and life-insurance purchase under a stochastically fluctuating economy

We study the optimal consumption, investment and life-insurance purchase and selection strategies for a wage-earner with an uncertain lifetime with access to a financial market comprised of one risk-free security and one risky-asset whose prices evolve according to linear diffusions modulated by a continuous-time stochastic process determined by an additional diffusive nonlinear stochastic differential equation. The process modulating the linear diffusions may be regarded as an indicator describing the state of the economy in a given instant of time. Additionally, we allow the Brownian motions driving each of these equations to be correlated. The life-insurance market under consideration herein consists of a fixed number of providers offering pairwise distinct contracts. We use dynamic programming techniques to characterize the solutions to the problem described above for a general family of utility functions, studying the case of discounted constant relative risk aversion utilities with more detail.

L1 Method on Nonuniform Meshes for Linear Time-Fractional Diffusion Equations with Constant Time Delay

L1 Method on Nonuniform Meshes for Linear Time-Fractional Diffusion Equations with Constant Time Delay

Homogenization of a nonlinear elliptic system with a transport term in L 2

We consider the homogenization of a non-linear elliptic system of two equations related to some models in chemotaxis and flows in porous media. One of the equations contains a convection term where the transport vector is only in L 2 and a right-hand side which is only in L 1 . This makes it necessary to deal with entropy or renormalized solutions. The existence of solutions for this system has been proved in reference (Comm. Partial Differential Equations 45(7) (2020) 690–713). Here, we prove its stability by homogenization and that the correctors corresponding to the linear diffusion terms still provide a corrector for the solutions of the non-linear system.

Deviation properties for linear self-attracting diffusion process and applications

In this paper, we study explicitly the deviation properties, including the deviation inequalities and Cramér-type moderate deviations, for some quadratic functionals of linear self-attracting diffusion process. As applications, Cramér-type moderate deviations for the log-likelihood ratio process and drift parameter estimator are obtained. The main methods consist of the deviation inequalities and Cramér-type moderate deviations for multiple Wiener–Itô integrals, as well as the asymptotic analysis techniques.

Global classical solvability in a food metric chemotaxis system under zero boundary conditions at infinity

We consider the nutrient–chemotaxis model, derived by a food metric, on the real line. The model consists of the equation for the nutrient density of ordinary differential equation type and that for the microorganism density of parabolic type, in which the diffusion coefficient is singular at the zero nutrient density. We establish a global existence result of bounded classical solutions for a large class of initial data under zero boundary conditions at infinity. To this end, we propose a transformation related to the food metric that transforms the original system into a parabolic–hyperbolic system with linear diffusion. We obtain a proper global well-posedness result for the transformed system using standard estimates, including the heat kernel estimates. We convert this to the solution of the original equation via an inverse transformation.

Zero-contact angle solutions to stochastic thin-film equations

We establish existence of nonnegative martingale solutions to stochastic thin-film equations with quadratic mobility for compactly supported initial data under Stratonovich noise. Based on so-called alpha -entropy estimates, we show that almost surely these solutions are classically differentiable in space almost everywhere in time and that their derivative attains the value zero at the boundary of the solution’s support. From a physics perspective, this means that they exhibit a zero-contact angle at the three-phase contact line between liquid, solid, and ambient fluid. These alpha -entropy estimates are first derived for almost surely strictly positive solutions to a family of stochastic thin-film equations augmented by second-order linear diffusion terms. Using Itô’s formula together with stopping time arguments, Jakubowski’s modification of the Skorokhod theorem, and martingale identification techniques, the passage to the limit of vanishing regularization terms gives the desired existence result.