Mass Transport Method Research Articles

A dynamic mass transport method for Poisson-Nernst-Planck equations

A dynamic mass-transport method is proposed for approximately solving the Poisson–Nernst–Planck (PNP) equations. The semi-discrete scheme based on the JKO type variational formulation naturally enforces solution positivity and the energy law as for the continuous PNP system. The fully discrete scheme is further formulated as a constrained minimization problem, shown to be solvable, and satisfy all three solution properties (mass conservation, positivity and energy dissipation) independent of time step size or the spatial mesh size. Numerical experiments are conducted to validate convergence of the computed solutions and verify the structure preserving property of the proposed scheme.

An Optimal Mass Transport Method for Random Genetic Drift

We propose and analyze an optimal mass transport method for a random genetic drift problem driven by a Moran process under weak-selection. The continuum limit, formulated as a reaction-advection-diffusion equation known as the Kimura equation, inherits degenerate diffusion from the discrete stochastic process that conveys to the blow-up into Dirac-delta singularities hence brings great challenges to both the analytical and numerical studies. The proposed numerical method can quantitatively capture to the fullest possible extent the development of Dirac-delta singularities for genetic segregation on one hand, and preserves several sets of biologically relevant and computationally favored properties of the random genetic drift on the other. Moreover, the numerical scheme exponentially converges to the unique numerical stationary state in time at a rate independent of the mesh size up to a mesh error. Numerical evidence is given to illustrate and support these properties, and to demonstrate the spatio-temporal dynamics of random generic drift.

Micro-Shaping of Pure Aluminum by Intermittent Ultrasonic Oscillation Assisted Wire Electrochemical Micromachining with an Ultra-Low-Concentration Mixed Electrolyte

Sacrificial mandrels and micro-components made from pure aluminum have considerable application potential for fabricating terahertz micro-cavity components and for MEMS. Although WECMM has significant advantages in micro-shaping micro-components from difficult-to-machine materials, high-quality micro-shaping of pure aluminum has always been very challenging due to its extremely high chemical activity in an aqueous solution. This study analyzes the electrochemical characteristics of pure aluminum and the corresponding machining experiments by traditional WECMM in various electrolytes, and manufactures a high-quality micro-slit with a short machining path in the obtained ultra-low-concentration mixed electrolyte. However, in a continuous long-term WECMM with a long machining path, poor mass transport leads to the accumulation of bubbles around the machining area and the deposition of insoluble products on the wire surface that reduce the machining stability and machining accuracy. Therefore, a mass transport method of using intermittent ultrasonic oscillation is proposed. The principle was expounded, systematic comparative experiments demonstrated the effectiveness of this method in continuous long-time WECMM in improving the machining stability and machining accuracy. Finally, a rectangular mandrel of pure aluminum with a path length greater than 10,000 μm was fabricated. After dissolving the rectangular mandrel, a terahertz hollow-core rectangular waveguide micro-cavity was produced.

A mass transportation proof of the sharp one-dimensional Gagliardo–Nirenberg inequalities

The aim of this paper is to give a mass transportation proof for a full family of sharp Gagliardo–Nirenberg inequalities in dimension one. In fact, we shall establish a duality principle which derives this family of inequalities as a consequence. We also characterize all optimizers for these inequalities via the mass transportation method.

Multi-marginal optimal transport using partial information with applications in robust localization and sensor fusion

During recent decades, there has been a substantial development in optimal mass transport theory and methods. In this work, we consider multi-marginal problems wherein only partial information of each marginal is available, a common setup in many inverse problems in, e.g., remote sensing and imaging. By considering an entropy regularized approximation of the original transport problem, we propose an algorithm corresponding to a block-coordinate ascent of the dual problem, where Newton’s algorithm is used to solve the sub-problems. In order to make this computationally tractable for large-scale settings, we utilize the tensor structure that arises in practical problems, allowing for computing projections of the multi-marginal transport plan using only matrix-vector operations of relatively small matrices. As illustrating examples, we apply the resulting method to tracking and barycenter problems in spatial spectral estimation. In particular, we show that the optimal mass transport framework allows for fusing information from different time steps, as well as from different sensor arrays, also when the sensor arrays are not jointly calibrated. Furthermore, we show that by incorporating knowledge of underlying dynamics in tracking scenarios, one may arrive at accurate spectral estimates, as well as faithful reconstructions of spectra corresponding to unobserved time points.

Transport of neutral solutes in a viscoelastic solvent through a porous microchannel

We study the effect of viscoelasticity on the transportation of neutral solutes through a porous microchannel. The underlying transport phenomenon, modelled using the simplified Phan-Thien-Tanner constitutive equation, is actuated by the combined influence of pressure gradient and electroosmosis. Here, we obtain the closed form solution for the velocity distribution inside the flow domain and calculate the concentration profiles of the neutral solutes within the mass transport boundary layer by invoking the similarity solution approach. To establish the efficacy of viscoelastic solvents in the transportation of neutral solutes, which may find relevance in transdermal drug delivery applications, here we show the variations in the local solute concentration, the length averaged solute concentration at the wall, and the Sherwood number with the viscoelastic parameter. The present study infers that the shear-thinning nature of the viscoelastic fluid enhances the convective mass transfer as well as the permeation rate in the porous membranes. A complex interplay between the fluid rheology and the porous structure of the walls influenced by the electrochemistry at the interfacial scale modulates the mass transfer boundary layer of neutral solutes, implicating an effective method of mass transport in transdermal drug delivery applications.

Sharp Gagliardo–Nirenberg Trace Inequalities via Mass Transportation Method and Their Affine Versions

Exploiting the mass transportation method, we prove a dual principle which implies directly the sharp Gagliardo–Nirenberg trace inequalities which was recently proved by Bolley et al. (Int Math Res Not, 2017, https://doi.org/10.1093/imrn/rny111). Moreover, we determine all optimal functions for these obtained sharp Gagliardo–Nirenberg trace inequalities. This settles a question left open in Bolley et al. (Int Math Res Not, 2017, https://doi.org/10.1093/imrn/rny111). Finally, we use the sharp Gagliardo–Nirenberg trace inequality to establish their affine versions (i.e. the sharp affine Gagliardo–Nirenberg trace inequalities) which generalize a recent result of De Napoli et al. (Math Ann 370:287–308, 2018). It was shown that the affine versions are stronger and imply the sharp Gagliardo–Nirenberg trace inequalities. We also determine all extremal functions for the sharp affine Gagliardo–Nirenberg trace inequalities.

Stability and perturbations of countable Markov maps**Dedicated to the memory of Bernd O Stratmann

Let T and , , be countable Markov maps such that the branches of converge pointwise to the branches of T, as . We study the stability of various quantities measuring the singularity (dimension, Hölder exponent etc) of the topological conjugacy between and T when . This is a well-understood problem for maps with finitely-many branches, and the quantities are stable for small ε, that is, they converge to their expected values if . For the infinite branch case their stability might be expected to fail, but we prove that even in the infinite branch case the quantity is stable under some natural regularity assumptions on and T (under which, for instance, the Hölder exponent of fails to be stable). Our assumptions apply for example in the case of Gauss map, various Lüroth maps and accelerated Manneville–Pomeau maps when varying the parameter α. For the proof we introduce a mass transportation method from the cusp that allows us to exploit thermodynamical ideas from the finite branch case.

Chapter 52 - Selective brain hypothermia

Selective brain hypothermia is a powerful concept for neuroprotection that has been successfully investigated in a variety of animal models of global and focal ischemia. Its major advantages over systemic hypothermia include rapid induction of cooling, ability to achieve profound target brain temperatures, organ-selective cooling, and temperature control. Clinical systems and devices are available or are currently under development that utilize conductive (surface-cooling pads, closed-loop catheters), convective (transnasal coolant delivery), or mass and energy transport (cold intra-arterial infusion) methods to achieve and maintain selective brain hypothermia. The "ideal" brain-cooling system that is characterized by rapid cooling to profound hypothermia, its ability to maintain selective cooling over several days, and is noninvasive in nature, remains unrealistic. Instead, systems may be identified by their distinct advantages to meet a specific need in the care of a patient. This involves the consideration of the timing of ischemic injury (preischemic, intraischemic, postischemic), extent of ischemic damage (excitotoxicity, inflammation, necrosis, edema), and type and setting of therapeutic intervention (intensive care, interventional therapy, surgery). The successful translation of these systems into clinical practice will depend on smart engineering, safety and efficacy, and usability in current clinical work flow.

Sharp weighted isoperimetric and Caffarelli–Kohn–Nirenberg inequalities

Abstract Using the optimal mass transport method and a suitable quasi-conformal mapping, we study the sharp weighted isoperimetric, Sobolev, Gagliardo–Nirenberg and Caffarelli–Kohn–Nirenberg inequalities. The class of weight functions under consideration includes all nonnegative homogeneous weights satisfying a concavity condition that is equivalent to a usual curvature-dimension bound and the nonnegativity of a Bakry–Émery Ricci tensor. Though our densities are not radial in general, the optimizers are radially symmetric.

Simulation of Oxygen Transport Membranes for CPO Reactors in Small-scale Hydrogen or Syngas Production Applications

The proposed work aims at presenting a 1D finite volume steady state simulation model of an Oxygen Transport Membrane for Catalytic Partial Oxidation (OTM-CPO) reactor developed at the Group of Energy COnversion Systems (GECOS) at Politecnico di Milano. The model is able to simulate supported and unsupported perovskite-based reactive membranes by means of a lumped mass and energy transport method; the active ceramic layer is modelled throughout a generalised O2 permeation equation, which depends on the micro-structure characteristics and mixed-ion conduction properties of the material. The supporting porous structure is represented by a mass diffusion model dominated by gas-gas, porous and surface exchange transport processes. The model also includes a global chemical reaction kinetic mechanism of CPO on Rh-based catalysts. The model is applied to simulate the behaviour of a membrane reactor operated upstream the Hydrogen Transport Membrane for Methane Steam Reforming (HTM-MSR) installed at the Laboratory of Micro-Cogeneration (LMC) at Politecnico di Milano. The test bench is focused on testing fuel pre-processing systems for low temperature fuel cells (PEM) applications. The simulation object of this work would allow obtaining a feasibility assessment of the system and a preliminary design of the OTM-CPO reactor.

Morfizmy markowskie: zespolone podejście do wielowymiarowych kwantyli oparte o funkcje łącznikowe i zagadnienie transportowe

Our purpose is both conceptual and practical. On the one hand, we discuss the question which properties are basic ingredients of a general conceptual notion of a multivariate quantile. We propose and argue that the object “quantile” should be defined as a Markov morphism which carries over similar algebraic, ordering and topological properties as known for quantile functions on the real line. On the other hand, we also propose a practical quantile Markov morphism which combines a copula standardization and the recent optimal mass transportation method of Chernozhukov et al. (2015). Its empirical counterpart has the advantages of being a bandwidth-free, monotone invariant, a.s. consistent transformation. The proposed the approach gives a general and unified framework to quantiles and their corresponding depth areas, for both a continuous or a discrete multivariate distribution.

Mass transport in biological tissues: Comparisons between single- and dual-porosity models in the context of saline-infused Radiofrequency Ablation

Conventional method for modelling mass transport in biological tissues is based on the single-porosity (SP) model, which assumes a homogeneous pressure and concentration in the vasculature. Over the years, the dual-porosity (DP) model, which was originally derived for describing water flow in fractured rocks, has seen an increase in its application to describe flow in biological tissues. In DP models, two porous continua (the interstitium and the vasculature) co-exist within the same space. Flows in both continua are modelled explicitly, which allows for a more accurate representation of the hydraulic interaction between the interstitium and the vasculature. This raises the question on the validity and accuracy of the SP model for describing saline transport in biological tissues. This paper seeks to answer this question by performing a comparative study on the numerical predictions obtained using the SP and DP models in the context of saline-infused radiofrequency ablation (RFA). The results suggest that the SP model has a tendency to underestimate the saline penetration depth inside the tissue. Results from the present study are applicable only in the context of saline-infused radiofrequency ablation. They should not be generalized to other medical and biological applications, as comparison between the SP and DP models for these applications may yield observations that are different from those in the present study.

Inverse modeling of thin layer flow cells for detection of solubility, transport and reaction coefficients from experimental data

Thin layer flow cells are used in electrochemical research as experimental devices which allow to perform investigations of electrocatalytic surface reactions under controlled conditions using reasonably small electrolyte volumes. The paper introduces a general approach to simulate the complete cell using accurate numerical simulation of the coupled flow, transport and reaction processes in a flow cell. The approach is based on a mass conservative coupling of a divergence-free finite element method for fluid flow and a stable finite volume method for mass transport. It allows to perform stable and efficient forward simulations that comply with important physical constraints, namely mass conservation and maximum principles for the involved species. In this context, several recent approaches to obtain divergence-free velocity approximations from finite element simulations are discussed. In order to perform parameter identification, the forward simulation method is coupled to standard optimization tools. After an assessment of the inverse modeling approach using hypothetical, but realistic data, first results of the identification of solubility and transport data for O2 dissolved in organic electrolytes are presented. A plausibility study for a more complex situation with surface reactions concludes the paper and shows possible extensions of the presented numerical tools.

A mass transportation approach for Sobolev inequalities in variable exponent spaces

In this paper we provide a proof of the Sobolev–Poincare inequality for variable exponent spaces by means of mass transportation methods, in the spirit of Cordero-Erausquin et al. (Adv Math 182(2):307–332, 2004). The importance of this approach is that the method is flexible enough to deal with different inequalities. As an application, we also deduce the Sobolev-trace inequality improving the result of Fan (J Math Anal Appl 339(2):1395–1412, 2008) by obtaining an explicit dependence of the exponent in the constant.

The Moser-Trudinger-Onofri inequality

This paper is devoted to results on the Moser-Trudinger-Onofri inequality, or Onofri inequality for brevity. In dimension two this inequality plays a role similar to the Sobolev inequality in higher dimensions. After justifying this statement by recovering the Onofri inequality through various limiting procedures and after reviewing some known results, we state several elementary remarks. We also prove various new results. We give a proof of the inequality using mass transportation methods (in the radial case), consistently with similar results for Sobolev's inequalities. We investigate how duality can be used to improve the Onofri inequality, in connection with the logarithmic Hardy-Littlewood-Sobolev inequality. In the framework of fast diffusion equations, we establish that the inequality is an entropy--entropy production inequality, which provides an integral remainder term. Finally we give a proof of the inequality based on rigidity methods and introduce a related nonlinear flow.

Predicting the transport process of indoor semi-volatile organic compounds via lattice Boltzmann method

In this paper, a model consisting of the lattice Boltzmann (LB) method for fluid flow and mass transport and the cellular automata probabilistic method employed for simulating the movement of airborne particles to predict the transport process of indoor semi-volatile organic compounds (SVOCs) is developed. This model is used to obtain the concentration distribution of the airborne di-2-ethylhexyl phthalate (DEHP), a typical SVOC, including the gas-phase DEHP and the particle-phase DEHP in the given indoor environment where the vinyl flooring is the only emission source. Research on the influence of airborne particles on the transport of indoor airborne DEHP is made through comparing concentration distribution of DEHP in the cases of different airborne particle mass concentration and diameter, respectively. The DEHP emission rate under different ventilation types is also studied. Simulation results show that the airborne particle concentration directly affects the indoor DEHP emission. The increase of the indoor airborne particle mass concentration or the decrease of the airborne particle diameter will both help reduce the gas phase DEHP concentration. The emission rate increases with the increase of the airborne particle concentration. The indoor DEHP pollution will be reduced when the air changes per hour (ACH) increases. In general, Comparing with the cross ventilation method, the displacement one is more beneficial to reduce indoor DEHP pollution.

High‐Pressure Enhanced Infusion: Influence of Process Parameters

AbstractHigh‐pressure processing (HPP) has been shown to enhance infusion of small‐size molecules into foods primarily because of cell membrane rupture. The enhanced infusion has been previously explained using increased effective diffusivity, which does not elucidate the actual mass transport mechanisms. This study evaluates and explains the role of transport processes and the influence of process parameters on enhanced infusion of antioxidants by HPP. Frozen‐thawed cranberries were infused with quercetin. A greater amount of quercetin (three times) was infused faster (18 times) in cranberries after HPP (100 MPa–551 MPa at 22C) compared with those infused at ambient conditions. While freeze‐thawing process ruptured cell membranes in cranberries, measured as cell permeability, there was no additional cell rupture after HPP. A similar degree of measured cell permeability before (0.48 ± 0.01) and after HPP (0.48 ± 0.04), and observed enhanced infusion under high‐pressure suggest that cell membrane permeabilization may not be the only cause for high–pressure‐assisted infusion.Practical ApplicationsConventional diffusion‐based mass transport methods currently used in the food industry are slow processes. In order to accelerate the process, this research investigates (1) the potential of high‐pressure processing (HPP) to enhance and accelerate infusion in cranberries and (2) the mechanisms operative during high–pressure‐assisted infusion. The present study was focused on understanding influence of process variables on extent of infusion and cell permeability. HPP significantly enhanced and accelerated infusion of quercetin in cranberries. Additionally, the commonly accepted explanation of cell permeabilization being the only cause for enhanced infusion under high pressure was not found to be operative in the current system of study. The success of this research can highlight the potential of HPP as an alternative technology that will be useful to the food industry to develop a broad class of nutrient infused food products.

High Pressure‐Enhanced Infusion in Fresh and Frozen‐Thawed Cranberries: A Comparative Study

AbstractHigh‐pressure processing (HPP) has been shown to enhance and accelerate infusion of molecules compared with osmosis‐driven diffusion. The primary cause for enhanced HPP infusion is attributed to cell membrane permeabilization. This study tests the validity of this commonly accepted mechanism by conducting HPP (100 MPa–551 MPa) infusion of quercetin into cranberries. Two systems used in this study were fresh cranberries, cells of which are intact, and frozen‐thawed cranberries, cells of which are permeabilized during freeze‐thaw process. Results showed that while fresh and frozen‐thawed cranberries had similar cell membrane permeability after HPP, twice as much quercetin was infused into fresh cranberries as compared with frozen‐thawed cranberries. If cell membrane permeability were the only cause of infusion, the amount of quercetin infused into cranberries in both systems should have been same. These results suggest that enhanced infusion caused by HPP is not just caused by cell permeabilization alone.Practical ApplicationsConventional diffusion based mass transport methods, currently used in the food industry for infusion, are slow processes. In order to accelerate the mass transport, this research investigated the potential of HPP to enhance and accelerate infusion in cranberries. The present study was focused on the comparison of infusion during HPP using fresh cranberries, cells of which were intact and frozen‐thawed cranberries, cells of which were permeabilized (with ruptured cell membranes) by freeze‐thaw process. Results showing increased infusion in fresh cranberries and similar cell permeability in both fresh and frozen‐thawed cranberries suggested that enhanced infusion during HPP was not caused only by cell permeabilization. This research opens new avenues for investigating additional mass transport mechanisms occurring during HPP, which will help develop accurate predictive mass transport models for HPP infusion processes.

A new approach to the local time stepping problem for scalar transport

A new scalar transport method is proposed to reduce computational time when a large number of scalars are transported in coupled hydrodynamic-ecosystem models. The new Local Mass Transport (LMT) method confines subtime transport computations to regions where the local Courant–Freidrichs–Lewy (CFL) number exceeds a given numerical stability criteria for a global (large) time step, but the method does not require either contiguous regions or special boundary algorithms between regions as used in previous Local Time Stepping (LTS) approaches. The new method uses conservative transport of mass rather than dissolved concentration. This approach allows different faces of a single grid cell to use different subtime steps. The new LMT method is further extended to include background filtering (LMTB) so that scalars below a pre-defined background concentration are ignored in transport calculations. This new approach can further reduce computational time where large regions are at or below an irrelevant background concentration. Both LMT and LMTB methods can be more computationally efficient than global subtime stepping.