Transport Problems Research Articles

Minimum Cost Pathfinding Algorithm for the Determination of Optimal Paths under Airflow Constraints

Pathfinding algorithms allow for the numerical determination of optimal paths of travel across many applications. These algorithms remain poorly defined for additional consideration of outside parameters, such as fluid flow, while considering contaminant transport problems. We have developed a pathfinding algorithm based on the A* search algorithm which considers the effect of fluid flow behaviors in two dimensions. This search algorithm returns the optimal path between two points in a setting containing impermeable boundaries, allowing for a computational approach to the determination of the most likely path of travel for contaminants or hazards of concern due to fluid flow. This modified A* search algorithm has applications in the statistical modeling of airborne contamination distributions, providing a relative estimate of the statistical relationship between two points in an underground mine’s ventilation system. This method provides a significant improvement to the spatial resolution of minimum-cost path methods currently in use in mine ventilation network software.

Unveiling Pakistan's transport problems: a call to safeguard public health.

Public transportation is an important mode of transportation in developing countries like Pakistan since it is accessible and convenient. But there are also serious health hazards associated with it, especially when it comes to the transmission of infectious diseases including COVID-19, TB, and Haemophilus influenzae. Worldwide transportation systems are vulnerable, as the COVID-19 pandemic has shown, underscoring the necessity for study and mitigating measures. The danger of disease transmission is increased in Pakistan by crowded metropolitan areas, inadequate sanitation, and low health awareness. In addition, congested public transportation and inadequate ventilation lead to reduced air quality and elevated stress levels among commuters. Comprehensive actions are needed to address these health hazards, such as promoting physical distance, improving cleanliness, enforcing traffic safety laws, and implementing policy changes that support sustainable transportation. Community involvement and advocacy are critical in campaigning for safer and more sustainable transportation networks. Pakistan can enhance public health outcomes and reduce the health hazards linked to public transportation by giving priority to these measures.

Uzbekistan and BRICS: cooperation and prospects

Uzbekistan’s cooperation with the BRICS countries is very important owing, first, to the growing economic power of the group members and, second, to its role in the qualitative transformation of the global South development scenarios. It should involve joint efforts based on contacts with regional partners, rather than competition, in order to strengthen balanced and inclusive economic growth, improve international competitiveness of the BRICS economies and achieve development levels comparable with those of advanced Western economies. The present paper uses statistical data on foreign economic relations of Uzbekistan and is based on content and comparative analysis of the main indicators related to exports and imports of the goods and services necessary for economic development of the partner countries. Presenting the results of Uzbekistan’s interaction with the BRICS countries, it identifies the main difficulties these countries are faced with, suggests ways of resolving them and outlines possible strategies for cooperation between Uzbekistan and the BRICS countries. This cooperation will help increase trade turnover, which will benefit all the parties involved. At the same time, it may cause serious problems in regional transport, logistics and financing. The paper also considers the BRICS countries’ links with other Central Asian countries.

Moment-SoS methods for optimal transport problems

Most common optimal transport (OT) solvers are currently based on an approximation of underlying measures by discrete measures. However, it is sometimes relevant to work only with moments of measures instead of the measure itself, and many common OT problems can be formulated as moment problems (the most relevant examples being Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p$$\\end{document}-Wasserstein distances, barycenters, and Gromov–Wasserstein discrepancies on Euclidean spaces). We leverage this fact to develop a generalized moment formulation that covers these classes of OT problems. The transport plan is represented through its moments on a given basis, and the marginal constraints are expressed in terms of moment constraints. A practical computation then consists in considering a truncation of the involved moment sequences up to a certain order, and using the polynomial sums-of-squares hierarchy for measures supported on semi-algebraic sets. We prove that the strategy converges to the solution of the OT problem as the order increases. We also show how to approximate linear quantities of interest, and how to estimate the support of the optimal transport map from the computed moments using Christoffel–Darboux kernels. Numerical experiments illustrate the good behavior of the approach.

A flux-based moving mesh method applied to solving the Poisson–Nernst–Planck equations

The moving mesh method is one of the important adaptive mesh methods which is practically useful when the mesh size and overall resolution are provided and fixed as seen in many engineering computations. We employ a moving mesh technique combined with a finite element method (FEM) to solve a widely-used charged carrier transport model, the Poisson–Nernst–Planck (PNP) equations, the solutions of which often have boundary or internal layers and sharp interfaces when the convection is dominated. Considering that flux is a significant physical quantity in designing stable and accurate numerical algorithm for transport problems such as the PNP system, we start from a relatively general functional and propose a flux-based monitor function and an adaptive step size-controlling algorithm for guiding the mesh movement in the FEM solution of the PNP equations. The numerical results illustrate that the moving mesh method is effectively addressing challenges arising from solution singularities and the convection-dominated effects. It also shows that the moving mesh finite element method we propose exhibits superior performance compared to both the traditional moving mesh finite element method and fixed mesh finite element method in some scenarios. Furthermore, it demonstrates better adherence to the physical properties of energy dissipation inherent in the PNP equation.

Stochastic simulation of exciton transport in semiconductor heterostructures

Abstract Stochastic simulation algorithm for solving exciton transport in a 3D layered semiconductor heterostructure is developed. The problem is governed by a transient drift-diffusion-recombination equation with Dirichlet and Neumann mixed boundary conditions. The semiconductor is represented as an infinite multilayer of finite thickness along the transverse coordinate z. The multilayer is composed by a set of sublayers of different materials so that the excitons have different diffusion and recombination coefficients in each layer. Continuity of solutions and fluxes at the plane interfaces between layers are imposed. The stochastic simulation algorithm solves the transport problem by tracking exciton trajectories in accordance with the probability distributions represented through the Green function of the problem in each sublayer. The method is meshless, the excitons jump only over the plane boundaries of the layers. This explains the high efficiency of the method. Simulation results for transport problems with different mixed boundary conditions are presented.

Deriving Landauer's formula by using the master equation approach

We revisit the problem of two-terminal transport of non-interacting Fermi particles in a mesoscopic device. First, we generalize the transport problem by taking into consideration relaxation processes in contacts (which are characterized by the contact self-thermalization rate γ) and then solve it by using the master equation approach. In the limit the obtained results are shown to reproduce those of the Landauer theory. Thus, the presented analysis proves correspondence between the Landauer and master equation approaches to quantum transport —a problem which has been waiting for a solution for decades.

Corrosion maps: Stability and composition diagrams for corrosion problems in CO2 transport

We present a Pourbaix-like graphical approach to assess the corrosive nature of impure CO2 streams for carbon capture and storage purposes. The effects of critical N- and S-containing impurities is evaluated. The model behind the approach assumes that chemical equilibrium is established, with some kinetic effects accommodated. The input is the composition of the stream (total quantity of S, N, H and O) and the output is the equilibrium composition (speciation). Comparison with experimental data shows that the content of acids in the CO2 stream upon reaching chemical equilibrium is a strong indicator of the corrosiveness of a given mixture.

Wind and rainfall erosion energy in large sediment generating and coarse sediment class areas of the middle Yellow river

Joint action by strong winds and high-intensive rainfall leads to serious soil erosion problems in large sediment generating and coarse sediment class areas of the middle Yellow River. Investigating the variation of trend and alternating wind and rainfall energy is an important prerequisite for controlling regional sediment transport problems. We calculated the wind and rainfall erosion energies by using the aerodynamic energy and rainfall kinetic energy formulas. The Mann-Kendall (MK) trend test and Theil-Sen approach were used to analyze the spatial-temporal variation and alternation of joint erosion energy during the last 40 years (1979–2018). The results show the following. 1) Wind erosion energy increased and rainfall erosion energy decreased. However, the former is larger than the latter. 2) The dominant erosive energy varies for different seasons. Wind erosive energy dominates in spring, and rainfall erosive energy dominates in summer. 3) There is a regular wind-rainfall-wind alternation of erosive energy. The wind-rainfall energies were alternately distributed in May–July and the rainfall-wind energies were alternately distributed in September–December. Furthermore, the dominant time of rainfall erosive energy decreased when wind erosive energy increased. The results can help decision makers to develop soil erosion control strategies to reduce soil erosion when it occurs in wind and water staggered areas.

A parameter-free and monolithic approach for multiscale simulations of flow, transport, and chemical reactions in porous media

Traditional approaches for transport in porous media rely on empirical hydrodynamic/transport parameters to quantify the interfacial exchange terms between fluid and solid, which leads to considerable uncertainties and also to a narrow application range of each method for realistic investigations of porous media. A parameter-free approach for flow, transport, and chemical reactions in porous media is presented in this paper. This approach adopts a novel, single-domain set of equations that are rigorously derived based on the elementary conservation laws describing the physical, continuous domain. The impact of the solid on nearby fluid being directly quantified in terms of the quantity to be solved, this avoids the introduction of empirical parameters. Various transport problems including external, conjugate, and reactive processes are properly formulated in this context, with the coupling between fluid and porous structures at different scales naturally solved in a monolithic manner. All these equations remain simple in terms of their numerical implementation, with solid structures represented by the porosity field on a background mesh. The application of the present method in both pore-scale and representative elementary volume (REV-scale) simulations are checked by performing a series of test cases, including interfacial momentum/heat/mass transport, conjugate heat/mass transfer, chemical reactions, and two practical applications containing reacting interfaces. An overall first-order convergence rate has been observed in both spatial and temporal accuracy tests.

Quantum genetic algorithm assisted high speed and precision pump-probe thermoreflectance characterization of micro-/nano-structures

The rapid and precise extraction of thermophysical properties remains an enormous challenge in pump-probe thermoreflectance, and quantum algorithms present significant potential for addressing thermal transport problems. This paper introduces an innovative application of the quantum genetic algorithm to the fitting of experimental data from pump-probe thermoreflectance. Initially, a physical model based on the thermal transmission matrix is developed to compute the heat transport of multilayer micro-/nano-structures. The quantum genetic algorithm is then employed for multiparameter optimization in the extraction of thermophysical properties and tested on three samples. Both simulation and experimental results demonstrate that the quantum genetic algorithm assisted pump-probe thermoreflectance, capable of extracting thermophysical properties with high precision in just one minute, is approximately 30 times faster than the conventional method and 10 times faster than the genetic algorithm. Furthermore, measurement sensitivity and algorithmic randomness are analyzed. The reasons behind the phenomenon of equivalent fitting results and the indication of non-convex optimization are also presented.

A relaxation viewpoint to Unbalanced Optimal Transport: Duality, optimality and Monge formulation

We present a general convex relaxation approach to study a wide class of Unbalanced Optimal Transport problems for finite non-negative measures with possibly different masses. These are obtained as the lower semicontinuous and convex envelope of a cost for non-negative Dirac masses. New general primal-dual formulations, optimality conditions, and metric-topological properties are carefully studied and discussed.

Multi-purpose pickup and delivery problem for combined passenger and freight transport

AbstractRecent advances in the development of modular transport vehicles allow deploying multi-purpose vehicles, which enable alternate transport of different demand types. In this study, we propose a novel variant of the pickup and delivery problem, the multi-purpose pickup and delivery problem, where multi-purpose vehicles are assigned to serve a multi-commodity flow. We solve a series of use case scenarios using an exact optimization algorithm and an adaptive large neighborhood search algorithm. We compare the performance of a multi-purpose vehicle fleet to a mixed fleet of single-purpose vehicles. Depending on cost parameters, our findings suggest that in certain scenarios, the total costs can be reduced by an average of 13% when multi-purpose vehicles are deployed, while at the same time reducing total vehicle trip duration and total distance traveled by on average 33% and 16%, respectively. The required fleet size can be reduced by 35% on average when operating multi-purpose vehicles. The results can be used by practitioners and policymakers to determine if the combined service of passenger and freight demand flows with multi-purpose vehicles in a given system will yield benefits compared to existing transport operations.

Modeling oxygen transport in the brain: An efficient coarse-grid approach to capture perivascular gradients in the parenchyma.

Recent progresses in intravital imaging have enabled highly-resolved measurements of periarteriolar oxygen gradients (POGs) within the brain parenchyma. POGs are increasingly used as proxies to estimate the local baseline oxygen consumption, which is a hallmark of cell activity. However, the oxygen profile around a given arteriole arises from an interplay between oxygen consumption and delivery, not only by this arteriole but also by distant capillaries. Integrating such interactions across scales while accounting for the complex architecture of the microvascular network remains a challenge from a modelling perspective. This limits our ability to interpret the experimental oxygen maps and constitutes a key bottleneck toward the inverse determination of metabolic rates of oxygen. We revisit the problem of parenchymal oxygen transport and metabolism and introduce a simple, conservative, accurate and scalable direct numerical method going beyond canonical Krogh-type models and their associated geometrical simplifications. We focus on a two-dimensional formulation, and introduce the concepts needed to combine an operator-splitting and a Green's function approach. Oxygen concentration is decomposed into a slowly-varying contribution, discretized by Finite Volumes over a coarse cartesian grid, and a rapidly-varying contribution, approximated analytically in grid-cells surrounding each vessel. Starting with simple test cases, we thoroughly analyze the resulting errors by comparison with highly-resolved simulations of the original transport problem, showing considerable improvement of the computational-cost/accuracy balance compared to previous work. We then demonstrate the model ability to flexibly generate synthetic data reproducing the spatial dynamics of oxygen in the brain parenchyma, with sub-grid resolution. Based on these synthetic data, we show that capillaries distant from the arteriole cannot be overlooked when interpreting POGs, thus reconciling recent measurements of POGs across cortical layers with the fundamental idea that variations of vascular density within the depth of the cortex may reveal underlying differences in neuronal organization and metabolic load.

Distribution-on-distribution regression with Wasserstein metric: Multivariate Gaussian case

Distribution data refer to a data set in which each sample is represented as a probability distribution, a subject area that has received increasing interest in the field of statistics. Although several studies have developed distribution-to-distribution regression models for univariate variables, the multivariate scenario remains under-explored due to technical complexities. In this study, we introduce models for regression from one Gaussian distribution to another, using the Wasserstein metric. These models are constructed using the geometry of the Wasserstein space, which enables the transformation of Gaussian distributions into components of a linear matrix space. Owing to their linear regression frameworks, our models are intuitively understandable, and their implementation is simplified because of the optimal transport problem’s analytical solution between Gaussian distributions. We also explore a generalization of our models to encompass non-Gaussian scenarios. We establish the convergence rates of in-sample prediction errors for the empirical risk minimizations in our models. In comparative simulation experiments, our models demonstrate superior performance over a simpler alternative method that transforms Gaussian distributions into matrices. We present an application of our methodology using weather data for illustration purposes.

On the use of spherical harmonic approximations in nonclassical particle transport problems

Presented here is the application of the spherical harmonic expansion to the nonclassical transport equation to derive a system of equations for the nonclassical flux moments, namely nonclassical spherical harmonic approximations (NSHA). The nonclassical transport equation is a recently developed mathematical model that allows the modeling of transport problems wherein the particle flux does not undergo exponential attenuation. We employ a Spectral Approach technique to depict the nonclassical flux by expressing it as a truncated series of Laguerre polynomials with respect to the free-path variable s. This yields a system of equations for the nonclassical flux moments structured similarly to the classical PN equations. We show that the NSHA is reduced to the classical PN equation in a special case. Numerical results for slab-geometry test problems are given to verify the derivation.

On the Application of the Nyström Method to Two-Dimensional Neutral Particle Transport Problems in Heterogeneous Media

Over time, several methods were developed to deal with neutral particle transport problems. The interest in these problems is related to their wide range of applications, from neutron transport and heat transfer in nuclear reactors to radiative transfer in atmospheric clouds. Unlike the discrete ordinates or discrete ordinates–like methods, integral methods do not require discretization of angular variables. Instead, angular variables are completely eliminated by an integration procedure over the solid angle, which allows elimination of the ray effect. That said, this paper presents a new approach to estimate the scalar flux in two-dimensional fixed-source neutron transport problems in a heterogeneous medium, considering isotropic scattering and vacuum and reflective boundary conditions. Here, the Nyström method is combined with the singularity-subtraction technique to present an integral formulation for the scalar flux in a mesh grid over all regions of the domain. The iterative method of the Neumann series is used as an alternative to direct methods to solve the resulting system of equations generated from the domain discretization. Numerical results are given to verify the offered method.

An enhanced fourier neural operator surrogate for radioactive plume transport forecasting

Accurate real-time forecasts of atmospheric plume behavior are crucial for effective management of environmental release incidents. However, the computational demands of weather simulations and particle transport codes limit their applicability during emergencies. In this study, we employ a U-Net enhanced Fourier Neural Operator (U-FNO) to statistically emulate the calculations of the WSPEEDI dose forecasting numerical simulator, using pre-calculated ensemble simulations. The developed emulator is capable of effectively simulating any radioactive-release scenario and generating the time series of dose distribution in the environment 4000 times faster than the numerical simulator, while still maintaining high accuracy. It predicts the plume direction, extent, and dose-rate magnitudes using initial- and boundary-condition meteorological data as input. The speed and efficiency of this framework offers a powerful tool for swift decision-making during emergencies, facilitating risk-informed protective actions, evacuation execution, and zone delineation. Its application extends to various contaminant release and transport problems, and can be instrumental in engineering tasks requiring uncertainty quantification (UQ) for environmental risk assessment.

A Variational Surface-Evolution Approach to Optimal Transport over Transitioning Compact Supports with Domain Constraints

We examine the optimal mass transport problem in Rn between densities with transitioning compact support by considering the geometry of a continuous interpolating support boundary Γ in space-time within which the mass density evolves according to the fluid dynamical framework of Benamou and Brenier. We treat the geometry of this space-time embedding in terms of points, vectors, and sets in Rn+1=R×Rn and blend the mass density and velocity as well into a space-time solenoidal vector field W|Ω→Rn+1 over a compact set Ω⊂Rn+1. We then formulate a joint optimization for W and its support using the shaped gradient of the space-time surface Γ outlining the support boundary ∂Ω. This easily accommodates spatiotemporal constraints, including obstacles or mandatory regions to visit.

Information bottleneck-based Hebbian learning rule naturally ties working memory and synaptic updates.

Deep neural feedforward networks are effective models for a wide array of problems, but training and deploying such networks presents a significant energy cost. Spiking neural networks (SNNs), which are modeled after biologically realistic neurons, offer a potential solution when deployed correctly on neuromorphic computing hardware. Still, many applications train SNNs offline, and running network training directly on neuromorphic hardware is an ongoing research problem. The primary hurdle is that back-propagation, which makes training such artificial deep networks possible, is biologically implausible. Neuroscientists are uncertain about how the brain would propagate a precise error signal backward through a network of neurons. Recent progress addresses part of this question, e.g., the weight transport problem, but a complete solution remains intangible. In contrast, novel learning rules based on the information bottleneck (IB) train each layer of a network independently, circumventing the need to propagate errors across layers. Instead, propagation is implicit due the layers' feedforward connectivity. These rules take the form of a three-factor Hebbian update a global error signal modulates local synaptic updates within each layer. Unfortunately, the global signal for a given layer requires processing multiple samples concurrently, and the brain only sees a single sample at a time. We propose a new three-factor update rule where the global signal correctly captures information across samples via an auxiliary memory network. The auxiliary network can be trained a priori independently of the dataset being used with the primary network. We demonstrate comparable performance to baselines on image classification tasks. Interestingly, unlike back-propagation-like schemes where there is no link between learning and memory, our rule presents a direct connection between working memory and synaptic updates. To the best of our knowledge, this is the first rule to make this link explicit. We explore these implications in initial experiments examining the effect of memory capacity on learning performance. Moving forward, this work suggests an alternate view of learning where each layer balances memory-informed compression against task performance. This view naturally encompasses several key aspects of neural computation, including memory, efficiency, and locality.