Discrete Transport Research Articles

A disaggregate freight transport chain choice model for Europe

This paper presents the estimation of a discrete freight transport chain choice model for Europe, which was developed for the European Union as part of the Transtools 3 project. The model describes nine different multi- and single mode chain alternatives of which three can be either container or non-containerised, and it segments freight into dry bulk, liquid bulk, containers and general cargo. The model was estimated on the basis of disaggregate data at the shipment level (Swedish CFS and French ECHO data). Several transport costs specifications and nesting structures were tested and elasticities compared with reference literature. It was found that freight models are characterised by heterogeneity, non-linearity in transport costs and hence Value of Times and non-constant rates of substitution. Not taking these elements into account will have consequences for the evaluation of transport policies using the freight transport model.

Accuracy balancing for the simulation of gate-all-around junctionless nanowire transistors using discrete Wigner transport equation

We report the application of the discrete Wigner transport equation to the simulation of gate-all-around junctionless nanowire transistors (JLNWTs). We show that unphysical simulation results are obtained unless we pay attention to the accuracy balancing problem. An empirical criterion based on the subthreshold swing of the JLNWT is proposed for the accuracy balancing. Using this criterion, we investigate the characteristics of JLNWTs with the quantum effect fully considered.

Instability of dislocation fluxes in a single slip: Deterministic and stochastic models of dislocation patterning

We study a continuum model of dislocation transport in order to investigate the formation of heterogeneous dislocation patterns. We propose a physical mechanism which relates the formation of heterogeneous patterns to the dynamics of a driven system which tries to minimize an internal energy functional while subject to dynamic constraints and state dependent friction. This leads us to a novel interpretation which resolves the old 'energetic vs. dynamic' controversy regarding the physical origin of dislocation patterns. We demonstrate the robustness of the developed patterning scenario by considering the simplest possible case (plane strain, single slip) yet implementing the dynamics of the dislocation density evolution in two very different manners, namely (i) a hydrodynamic formulation which considers transport equations that are continuous in space and time while assuming a linear stress dependency of dislocation motion, and (ii) a stochastic cellular automaton implementation which assumes spatially and temporally discrete transport of discrete 'packets' of dislocation density which move according to an extremal dynamics. Despite the huge differences between both kinds of models, we find that the emergent patterns are mutually consistent and in agreement with the prediction of a linear stability analysis of the continuum model. We also show how different types of initial conditions lead to different intermediate evolution scenarios which, however, do not affect the properties of the fully developed patterns.

Electrical Behavior and Electron Transfer Modulation of Nickel–Copper Nanoalloys Confined in Nickel–Copper Nitrides Nanowires Array Encapsulated in Nitrogen‐Doped Carbon Framework as Robust Bifunctional Electrocatalyst for Overall Water Splitting

AbstractProbing robust electrocatalysts for overall water splitting is vital in energy conversion. However, the catalytic efficiency of reported catalysts is still limited by few active sites, low conductivity, and/or discrete electron transport. Herein, bimetallic nickel–copper (NiCu) nanoalloys confined in mesoporous nickel–copper nitride (NiCuN) nanowires array encapsulated in nitrogen‐doped carbon (NC) framework (NC–NiCu–NiCuN) is constructed by carbonization‐/nitridation‐induced in situ growth strategies. The in situ coupling of NiCu nanoalloys, NiCuN, and carbon layers through dual modulation of electrical behavior and electron transfer is not only beneficial to continuous electron transfer throughout the whole system, but also promotes the enhancement of electrical conductivity and the accessibility of active sites. Owing to strong synergetic coupling effect, such NC–NiCu–NiCuN electrocatalyst exhibits the best hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) performance with a current density of 10 mA cm−2 at low overpotentials of 93 mV for HER and 232 mV for OER, respectively. As expected, a two‐electrode cell using NC–NiCu–NiCuN is constructed to deliver 10 mA cm−2 water‐splitting current at low cell voltage of 1.56 V with remarkable durability over 50 h. This work serves as a promising platform to explore the design and synthesis of robust bifunctional electrocatalyst for overall water splitting.

Regularized optimal transport and the rot mover's distance

This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a m...

Analysis of Spatial Discretization Error Estimators Implemented in ARES Transport Code for SN Equations

The discrete ordinates method (SN) is one of the mainstream methods for neutral particle transport calculations. Assessing the quality of the numerical solution and controlling the discrete error are essential parts of large-scale high-fidelity simulations of nuclear systems. Three error estimators, a two-mesh estimator, a residual-based estimator, and a dual-weighted residual estimator, are derived and implemented in the ARES transport code to evaluate the error of zeroth-order spatial discretization for SN equations. The difference in scalar fluxes on coarse and fine meshes is adopted to indicate the error in the two-mesh method. To avoid zero residual in zeroth-order discretization, angular fluxes within one cell are reconstructed by Legendre polynomials. The error is estimated by inverting the discrete transport operator using the estimated directional residual as an anisotropic source. The inner product of the forward directional residual and the adjoint angular flux is employed to quantify the error in quantities of interest which can be denoted by a linear functional of forward angular flux. Method of Manufactured Solutions (MMS) is adopted to generate analytical solutions for SN equation with scattering and the determined true error is used to evaluate the effectivity of these estimators. Promising results are obtained in the numerical results for both homogeneous and heterogeneous cases. The larger error region is well captured and the average effectivity index for the local error estimation is less than unity. For the series test problems, the estimated goal quantity error can be contained within an order of magnitude around the exact error.

Mesh-free RBF collocation method to solve the multi-group SN neutron transport equation in arbitrary domains

Generally for numerical solution of the differential equations the mesh generation process is a major problem in classical mesh-based methods, especially in irregular domains. Contrary to the meshed based methods, Mesh Free (MFree) methods have been developed to avoid mesh generation. In the MFree methods a set of scattered nodes is used without requiring any mesh grid. So in this work the application of MFree collocation method is examined to solve SN neutron transport equation. The MFree collocation method uses the formulation of strong form which is truly mesh less method. Since MFree method is flexible for distributing arbitrary and irregular nodes, this method can be easily applied for high heterogeneous nuclear reactor problems with complicated geometry. To validate the proposed method some test problems including regular and irregular geometries have been modeled. Our results show that the mesh free collocation method can be used for discrete ordinate neutron transport equation as an efficient and accurate method without hardness and limitations of the mesh-based methods like finite element method.

Topological Disk Mesh Morphing Based on Area-Preserving Parameterization

Mesh morphing is a technique which gradually deforms a mesh into another one. Mesh parameterization, a powerful tool adopted to establish the one-to-one correspondence map between different meshes, is of great importance in 3D mesh morphing. However, current parameterization methods used in mesh morphing induce large area distortion, resulting in geometric information loss. In this paper, we propose a new morphing approach for topological disk meshes based on area-preserving parameterization. Conformal mapping and Mobius transformation are computed firstly as rough alignment. Then area preserving parameterization is computed via the discrete optimal mass transport map. Features are exactly aligned through radial basis functions. A surface remeshing scheme via Delaunay refinement algorithm is developed to create a new mesh connectivity. Experimental results demonstrate that the proposed method performs well and generates high-quality morphs.

Discrete Fractional Derivative Based Computational Model to Describe Dynamics of Bed-Load Transport

Bed-load transport in natural rivers exhibits nonlinear dynamics with strong temporal memory (i.e., retention due to burial) and/or spatial memory (i.e., fast displacement driven by turbulence). Nonlinear bed-load transport is discrete in nature due to the discontinuity in the sediment mass density and the intermittent motion of sediment along river beds. To describe the discrete bed-load dynamics, we propose a discrete spatiotemporal fractional advection-dispersion equation (D-FADE) without relying on the debatable assumption of a continuous sediment distribution. The new model is then applied to explore nonlinear dynamics of bed-load transport in flumes. Results show that, first, the D-FADE model can capture the temporal memory and spatial dependency characteristics of bed-load transport for sediment with different sizes. Second, fine sediment particles exhibit stronger super-diffusive features, while coarse particles exhibit significant subdiffusive properties, likely due to the size-selective memory impact. Third, sediment transport with an instantaneous source exhibits stronger history memory and weaker spatial nonlocality, compared to that with a continuous source (since a smaller number of particles might be blocked or buried relatively easier). Hence, the D-FADE provides a strict computational model to quantify discrete bed-load transport, whose nonlinear dynamics can be sensitive to particle sizes and source injection modes, both common in applications.

A stochastic framework for modeling random-sized batch arrivals of sediment particles into open channel flows

Arrivals of sediment particles into open channel flows are typically simulated deterministically. However, there are random quantities of sediment particles brought into the open channel by natural phenomena such as rainfalls, landslides, mudflows, and dam breaches. As such, sediment particles may arrive at channel flow at random times in probabilistic quantities. Such arrival processes of sediment particles cannot be fully described without using probability. A stochastic framework that can account for the arrivals of random-sized batches of sediment particles into receiving waters is proposed. In this work, the random-sized batch arrival process of sediment particles is introduced to evaluate comprehensively the effects of particle arrival patterns, including random occurrences and random quantities of incoming sediment particles, on particle transport rates and sediment concentrations. Random arrivals are simulated as a Poisson process and the number of sediment particles in each arriving batch is described by a stochastic process that is specified in terms of binomially distributed random variables herein. The stochastic diffusion particle tracking model is used to simulate random trajectories of moving particles. Particle deposition and resuspension processes are considered. A probabilistic description of discrete sediment transport based on ensemble statistics of sediment concentrations and transport rates is presented. Simulation results are validated with experimental observations. Finally, time-dependent risks (i.e., probability of exceeding a pre-established turbidity standard with respect to time) are provided for decision makers to have a more comprehensive assessment for water quality management.

Geant4-DNA track-structure simulations for gold nanoparticles: The importance of electron discrete models in nanometer volumes.

Gold nanoparticles (GNPs) are known to enhance the absorbed dose in their vicinity following photon-based irradiation. To investigate the therapeutic effectiveness of GNPs, previous Monte Carlo simulation studies have explored GNP dose enhancement using mostly condensed-history models. However, in general, such models are suitable for macroscopic volumes and for electron energies above a few hundred electron volts. We have recently developed, for the Geant4-DNA extension of the Geant4 Monte Carlo simulation toolkit, discrete physics models for electron transport in gold which include the description of the full atomic de-excitation cascade. These models allow event-by-event simulation of electron tracks in gold down to 10eV. The present work describes how such specialized physics models impact simulation-based studies on GNP-radioenhancement in a context of x-ray radiotherapy. The new discrete physics models are compared to the Geant4 Penelope and Livermore condensed-history models, which are being widely used for simulation-based NP radioenhancement studies. An ad hoc Geant4 simulation application has been developed to calculate the absorbed dose in liquid water around a GNP and its radioenhancement, caused by secondary particles emitted from the GNP itself, when irradiated with a monoenergetic electron beam. The effect of the new physics models is also quantified in the calculation of secondary particle spectra, when originating in the GNP and when exiting from it. The new physics models show similar backscattering coefficients with the existing Geant4 Livermore and Penelope models in large volumes for 100keV incident electrons. However, in submicron sized volumes, only the discrete models describe the high backscattering that should still be present around GNPs at these length scales. Sizeable differences (mostly above a factor of 2) are also found in the radial distribution of absorbed dose and secondary particles between the new and the existing Geant4 models. The degree to which these differences are due to intrinsic limitations of the condensed-history models or to differences in the underling scattering cross sections requires further investigation. Improved physics models for gold are necessary to better model the impact of GNPs in radiotherapy via Monte Carlo simulations. We implemented discrete electron transport models for gold in Geant4 that is applicable down to 10eV including the modeling of the full de-excitation cascade. It is demonstrated that the new model has a significant positive impact on particle transport simulations in gold volumes with submicron dimensions compared to the existing Livermore and Penelope condensed-history models of Geant4.

Statistics of the quantized microwave electromagnetic field in mesoscopic elements at low temperature

The quantum behavior of the electromagnetic field in mesoscopic elements is intimately linked to the quantization of the charge. In order to probe nonclassical aspects of the field in those elements, it is essential that thermal noise be reduced to the quantum level, i.e. to scales where kT ≲ hν. This is easily achieved in dilution refrigerators for frequencies of a few GHz, i.e. in the microwave domain. Several recent experiments have highlighted the link between discrete charge transport and discrete photon emission in simple mesoscopic elements such as a tunnel junction. Photocount statistics are inferred from the measurement of continuous variables such as the quadratures of the field.

A Multi-Objective Interpretation of Optimal Transport

This paper connects discrete optimal transport to a certain class of multi-objective optimization problems. In both settings, the decision variables can be organized into a matrix. In the multi-objective problem, the notion of Pareto efficiency is defined in terms of the objectives together with nonnegativity constraints and with equality constraints that are specified in terms of column sums. A second set of equality constraints, defined in terms of row sums, is used to single out particular points in the Pareto-efficient set which are referred to as “balanced solutions.” Examples from several fields are shown in which this solution concept appears naturally. Balanced solutions are shown to be in one-to-one correspondence with solutions of optimal transport problems. As an example of the use of alternative interpretations, the computation of solutions via regularization is discussed.

Visualizing endocytic recycling and trafficking in live neurons by subdiffractional tracking of internalized molecules.

Our understanding of endocytic pathway dynamics is restricted by the diffraction limit of light microscopy. Although super-resolution techniques can overcome this issue, highly crowded cellular environments, such as nerve terminals, can also dramatically limit the tracking of multiple endocytic vesicles such as synaptic vesicles (SVs), which in turn restricts the analytical dissection of their discrete diffusional and transport states. We recently introduced a pulse-chase technique for subdiffractional tracking of internalized molecules (sdTIM) that allows the visualization of fluorescently tagged molecules trapped in individual signaling endosomes and SVs in presynapses or axons with 30- to 50-nm localization precision. We originally developed this approach for tracking single molecules of botulinum neurotoxin type A, which undergoes activity-dependent internalization and retrograde transport in autophagosomes. This method was then adapted to localize the signaling endosomes containing cholera toxin subunit-B that undergo retrograde transport in axons and to track SVs in the crowded environment of hippocampal presynapses. We describe (i) the construction of a custom-made microfluidic device that enables control over neuronal orientation; (ii) the 3D printing of a perfusion system for sdTIM experiments performed on glass-bottom dishes; (iii) the dissection, culturing and transfection of hippocampal neurons in microfluidic devices; and (iv) guidance on how to perform the pulse-chase experiments and data analysis. In addition, we describe the use of single-molecule-tracking analytical tools to reveal the average and the heterogeneous single-molecule mobility behaviors. We also discuss alternative reagents and equipment that can, in principle, be used for sdTIM experiments and describe how to adapt sdTIM to image nanocluster formation and/or tubulation in early endosomes during sorting events. The procedures described in this protocol take ∼1 week.

A novel consistent and well-balanced algorithm for simulations of multiphase flows on unstructured grids

We discuss the development and assessment of a robust numerical algorithm for simulating multiphase flows with complex interfaces and high density ratios on arbitrary polygonal meshes. The algorithm combines the volume-of-fluid method with an incremental projection approach for incompressible multiphase flows in a novel hybrid staggered/non-staggered framework. The key principles that characterise the algorithm are the consistent treatment of discrete mass and momentum transport and the similar discretisation of force terms appearing in the momentum equation. The former is achieved by invoking identical schemes for convective transport of volume fraction and momentum in the respective discrete equations while the latter is realised by representing the gravity and surface tension terms as gradients of suitable scalars which are then discretised in identical fashion resulting in a balanced formulation. The hybrid staggered/non-staggered framework employed herein solves for the scalar normal momentum at the cell faces, while the volume fraction is computed at the cell centroids. This is shown to naturally lead to similar terms for pressure and its correction in the momentum and pressure correction equations respectively, which are again treated discretely in a similar manner. We show that spurious currents that corrupt the solution may arise both from an unbalanced formulation where forces (gravity and surface tension) are discretised in dissimilar manner and from an inconsistent approach where different schemes are used to convect the mass and momentum, with the latter prominent in flows which are convection-dominant with high density ratios. Interestingly, the inconsistent approach is shown to perform as well as the consistent approach even for high density ratio flows in some cases while it exhibits anomalous behaviour for other scenarios, even at low density ratios. Using a plethora of test problems of increasing complexity, we conclusively demonstrate that the consistent transport and balanced force treatment results in a numerically stable solution procedure and physically consistent results. The algorithm proposed in this study qualifies as a robust approach to simulate multiphase flows with high density ratios on unstructured meshes and may be realised in existing flow solvers with relative ease.

A novel GEEC (Geometry, Energy, and Entropy Compatible) procedure applied to a staggered direct-ALE scheme for hydrodynamics

The simulation of transient compressible single-fluid flows, modeled by Euler’s classical equation, requires numerical schemes that comply with various stringent physical constraints such as thermodynamic consistency, robustness, and stability when shocks, large volume changes, and transport effects are present. For extreme conditions as encountered in defense applications, the present work introduces a novel generic GEEC (Geometry, Energy, and Entropy Compatible) procedure to derive physics-compatible numerical schemes with the following built-in properties: (i) geometric compatibility whereby volume variations (compressions and expansions) are taken into account consistently with advection relative to the grid; (ii) energetic compatibility whereby total energy is exactly conserved at discrete level for an accurate capture of shock levels and shock velocities, even if solving with primitive variables; and (iii) entropic compatibility whereby compliance with the second law of thermodynamics is ensured (here at least to second-order) – entropy must increase in general and must be conserved for isentropic flows.This novel generic GEEC procedure consists of a three-step mimicking derivation: (i) for a prescribed mass transport equation, a variational least action principle is used to generate the proper pressure forces in the discrete momentum evolution equation – thus ensuring a compatible exchange between kinetic and internal energies; – (ii) corrections are systematically performed on numerical residues in order to force conservation at discrete level up to round-off errors; and (iii) an artificial viscosity term is added as a pressure-like contribution in the evolution equations in order to capture shocks and to stabilize the scheme.As a proof of concept, this procedure is applied in the present work to produce a novel ALE (Arbitrary Lagrangian–Eulerian) compressible hydro-scheme with the following features: (i) a direct ALE formalism where mass, momentum, and energy transport fluxes are directly taken into account without separation in the discrete equations; (ii) continuity with “historic” Lagrangian solvers where velocity fields are space-and-time staggered; (iii) second-order accuracy in the Lagrangian limit; and as a consequence of the least action principle, (iv) a non-standard downwind formulation of the pressure gradient, dual of the upwind transport operator.Results on standard numerical test cases involving shocks and large deformations confirm the expected built-in properties of the scheme. In particular, the entropic compatibility leads to the preservation of entropy to second-order for isentropic flows, regardless of mesh motions and regardless of the first-order accuracy of the discrete mass transport equation. Indifference and versatility with respect to strenuous grid motion strategies are demonstrated in various situations – including supersonic shearing for new variants of Sod’s shock tube and Sedov’s blast wave – highlighting the advantages of the compatibility between velocity fields and volume variations in the presence of strong fluids advection.

Improved discrete nodal transport method for treating void regions

To solve neutron transport problems with void regions accurately and efficiently, the legacy discrete nodal transport method (DNTM) was improved in three-dimensional Cartesian geometry. Firstly, the efficient nodal-equivalent finite difference (NEFD) algorithm was modified, named M-NEFD, to directly treat the zero total cross section in the denominator for void nodes. Furthermore, an angle projection discrete-ordinates (APSN) method was proposed to combine with the NEFD algorithm, named APSN-NEFD, to treat the void regions without sweeping the void nodes one by one. Thirdly, the angular sweeps within one octant of both M-NEFD and APSN-NEFD were parallelized using OpenMP. Based on these improvements, a discrete-ordinates nodal transport code named NECP-HONESTY has been developed in three-dimensional Cartesian geometry. To test the performance of the method and the code, a fission-source problem with two small void regions and a fixed-source problem with one large void region were presented in this paper by comparing with the Monte Carlo method. It has been demonstrated by the numerical results that the improved DNTM can provide accurate eigenvalue and scalar flux, no matter directly sweeping the void nodes with M-NEFD or skipping the void regions with APSN. In addition, compared with M-NEFD, APSN-NEFD can efficiently reduce both computing time and storage requirement for problem with large void regions.

An automatic algorithm for generating seaborne transport pattern maps based on AIS

We provide an automatic algorithm proceeding from raw automatic identification system (AIS) data, through filters, highlighting vessel types, cargo, or regions, to discrete transport patterns, describing the geographic, directional, and total volume of transport. The designed algorithm automatically detects major ports or zones, where vessels are stationary and close to land, and groups them hierarchically in order to determine the end nodes in a transport matrix. In conjunction with vessel type, size, and draught information, the transport matrix is then used to compile transported tonnage and vessel count, to display as trade flows between nodes. In addition, by clicking on individual routes, the system also provides quantitative details, such as summed tonnage, or passing vessel counts. We use trades carried out by VLCC and Supramax bulk carriers as examples to demonstrate the results. The contribution of the research is threefold. First, we use AIS data to aggregate “real-time” trade flows. This substantially reduces latency from the traditional way of mapping flows and generating trade statistics. Second, the ability to visualize changes in seasonal or regional trading patterns enables economists and policy makers to monitor changes at a macro level. Finally, the ability to dripple down to the individual ship level allows commercial traders to monitor vessels or company performances, which provides valuable information in trading and decision-making.

Mesh-free method for numerical solution of the multi-group discrete ordinate neutron transport equation

The finite element method (FEM) is a widely-used method to solve neutron transport equation in an arbitrary domain, but in order to ensure the accuracy of solution a re-meshing process is often required and some regions of the domain need to be meshed with finer meshes and consequently the whole domain should be re-meshed again. To overcome this problem of the FEM we have applied Mesh Free (MFree) method for the solution of the neutron transport equation. In mesh free technique, there is no need to regenerate finer meshes to ensure the accuracy of the solution and only the number of nodes in local domains is increased. MFree method is flexible for distributing arbitrary and irregular nodes, therefore this method can be easily applied for high absorbent regions in the nuclear reactor problems. We have developed a program, named SNMF, which solves discrete ordinate neutron transport equation, using mesh free techniques based on Radial Point Interpolation Method (RPIM). To validate SNMF program some test problems have been modeled. For the first time, the application of MFree method is examined to solve neutron transport equation. Our results show that mesh free discrete ordinate method can be used as an efficient and accurate method to solve neutron transport equation without hardness and limitations of finite element methods.

The adaptive collision source method for discrete ordinates radiation transport

A novel collision source method has been developed to solve the Linear Boltzmann Equation (LBE) more efficiently by adaptation of the angular quadrature order. The angular adaptation method is unique in that the flux from each scattering source iteration is obtained, with potentially a different quadrature order used for each. Traditionally, the flux from every iteration is combined, with the same quadrature applied to the combined flux. Since the scattering process tends to distribute the radiation more evenly over angles (i.e., make it more isotropic), the quadrature requirements generally decrease with each iteration. This method allows for an optimal use of processing power, by using a high order quadrature for the first iterations that need it, before shifting to lower order quadratures for the remaining iterations. This is essentially an extension of the first collision source method, and is referred to as the adaptive collision source (ACS) method. The ACS methodology has been implemented in the 3-D, parallel, multigroup discrete ordinates code TITAN. This code was tested on a several simple and complex fixed-source problems. The ACS implementation in TITAN has shown a reduction in computation time by a factor of 1.5–4 on the fixed-source test problems, for the same desired level of accuracy, as compared to the standard TITAN code.