Time-dependent Transport Research Articles

Ganymede's Radiation Cavity and Radiation Belts

AbstractWhile planetary radiation belts are all embedded within the low energy solar wind, Ganymede is in the unique situation of being surrounded by the energetic particles of Jupiter's magnetosphere. Here we study Ganymede's environment based the recent flyby of Juno, as well as through reanalysis of past measurements from the Galileo spacecraft. We find that Ganymede is surrounded by a radiation cavity with intensities that are lower compared to Jupiter. Particles are lost in the cavity due to absorption by Ganymede that is likely enhanced by scattering. In the core of the cavity we find radiation belts. Their intensities are comparable to Jupiter for ions but lower for electrons. The radiation belts form peaks in phase space density, which indicates that they cannot be produced through steady inward influx and accumulation of Jupiter particles. Other processes are needed such as local acceleration, or time dependent transport and loss processes.

Time-Dependent Charge Carrier Transport with Hall Effect in Organic Semiconductors for Langevin and Non-Langevin Systems.

The time-dependent charge carrier transport and recombination processes in low-mobility organic semiconductor diodes are obtained through numerical simulations using the finite element method (FEM). The application of a Lorentz force across the diode alters the charge transport process leading to the Hall effect. In this contribution, the Hall effect parameters, such as the Hall voltage and charge carrier concentration with varying magnetic fields, are computed for both Langevin and non-Langevin type recombination processes. The results indicate the charge carrier concentration within the diode for the Langevin system is about seven and fourteen times less while the maximum amount of extracted charge is nearly five and ten times less than that in the non-Langevin system of 0.01 and 0.001, respectively. The Hall voltage values obtained for the steady-state case are similar to the non-Langevin system of ββL=0.01. However, the values obtained for the Langevin and non-Langevin systems of ββL=1 and 0.001 exhibit anomalies. The implications of these findings advance the understanding of the charge transport and Hall effect measurements in organic semiconductors that underpins the device's performance.

Time-dependent chloride transport models for cracked concrete bridge decks under chloride attack

The aims for this study is to develop time-dependent models of chloride diffusion using the survey data of sixteen sites of cracked concrete bridge decks under the influence of chloride attack in form of de-icing salts. This is taken into account, because it is evident that the diffusion of chloride ions through cracked concrete is different from that of uncracked one. The developed models consist of two main models, containing 4 parameters for regression. From the development, the models of chloride diffusion can predict the content of chloride ions through cracked concrete bridge decks in an average sense. Based on the prediction by the developed models, the long-term content of chloride ions near cracked concrete surface is found lower than that near uncracked one, because those chloride ions penetrate deep inside bridge decks. Because of this penetration, the increase of chloride ions near the surface of cracked concrete bridge decks is slower than that of uncracked ones. Moreover, the comparison of the diffusion coefficient indicates that the diffusion of chloride ions through cracked concrete bridge decks is faster than that through uncracked one. Considering the crack-free condition of concrete bridge decks, the available critical value of chloride ions for concrete cracking of 2.0 kg/m3 tends to overestimate the initiation time of concrete cracking. However, the critical chloride value for concrete cracking is here recommended as no more than 0.355 kg/m3 for more conservative condition.

Theoretical Study for Carrier Transit Limited Performance of Gate-All-Around Si Nanowire Transistor by Time-Dependent Quantum Transport Simulation

Theoretically, the upper limit performance of nanoscale transistor should be limited by carrier transit time through the channel as the charge in channel cannot follow the gate voltage and the gate capacitance will show strong frequency dependence if the gate voltage varies faster than the carrier transit time. Currently, the operation frequency of nanoscale transistor is limited by the non-ideal factors such as parasitic effects, and it is far below the limit caused by carrier transit time. However, how good the transistor can be if one can minimize these non-ideal factors is still a problem, thus, it would be worth exploring its upper limit performance. In this article, time-dependent quantum transport simulation is performed to explore the carrier transit limited performance of the gate-all-around (GAA) Si nanowire transistor. By using the mode space approach, the 3-D time-dependent quantum transport equation is decoupled to a 2-D confinement problem and a 1-D transport problem, and then self-consistently solved with the Poisson’s equation. The transient characteristics of channel charge are investigated, and it shows the response time of channel charge is in the scale of 0.1 ps. The responses of channel charge and drain current to high-frequency gate voltages are simulated. The carrier transit limited performance including the frequency-dependent gate capacitance and transconductance, 3 dB bandwidth, and cutoff frequency, are calculated and discussed.

A sweep-based low-rank method for the discrete ordinate transport equation

The dynamical low-rank (DLR) approximation is an efficient technique to approximate the solution to matrix differential equations. Recently, the DLR method was applied to radiation transport calculations to reduce memory requirements and computational costs. This work extends the low-rank scheme for the time-dependent radiation transport equation in 2-D and 3-D Cartesian geometries with discrete ordinates discretization in angle (SN method). The reduced system that evolves on a low-rank manifold is constructed via the “unconventional” basis update & Galerkin integrator to avoid a substep that is backward in time, which could be unstable for dissipative problems. The resulting system preserves the information on angular direction by applying separate low-rank decompositions in each octant where angular intensity has the same sign as the direction cosines. Then, transport sweeps and source iteration can efficiently solve this low-rank-SN system. The numerical results in 2-D and 3-D Cartesian geometries demonstrate that the low-rank solution requires less memory and computational time than solving the full rank equations using transport sweeps without losing accuracy.

Extension of the energetic particle transport kick model in TRANSP to multiple fast ion species

Alfvénic instabilities (AEs) are well known to cause enhanced transport of energetic particles (EPs) in fusion devices. Most studies until now have focused on characterizing and understanding AE stability in single-species plasmas heated by neutral beams (NB), where deuterium is typically used as both main plasma species and NB fuel. As the fusion community moves toward fusion reactors that target burning plasma conditions, such as ITER, the single-species picture breaks down. Burning plasmas, which will use a mix of deuterium and tritium (DT) as main fuel, also feature the presence of several supra-thermal fusion products such as alpha particles, protons, helium isotopes and high-energy tritium ions. This work presents the extension of the EP transport kick model implemented in the TRANSP time-dependent tokamak transport code to study the combined effect of multiple EP species on AE stability and, in turn, the response of different EP species to plasma instabilities in terms of their redistribution and losses. Further validation of the enhanced model is planned based on experimental results expected from the JET DT campaign scheduled for 2021, in preparation for ITER plasmas and beyond.

Accurate solutions to time dependent transport problems with a moving mesh and exact uncollided source treatments

To find benchmark quality solutions to time dependent Sntransport problems, we develop a numerical method in a Discontinuous Galerkin (DG) framework that utilizes time dependent cell edges, called a moving mesh, and an uncollided source treatment. The moving mesh and uncollided source treatment is devised to circumvent discontinuities in the solution and better realize the potential of the DG method to converge on smooth problems. The resulting method achieves spectral convergence on smooth problems. When applied to problems with discontinuity-inducing sources, our combined method returns a significantly better solution than the standard DG method. On smooth problems, we observe spectral convergence even in problems with wave fronts. In problems where the angular flux is inherently non-smooth, we do not observe high-order of convergence when compared with static meshes, but there is a quantitative reduction in error of nearly three orders of magnitude.

Time-dependent transport in graphene Mach-Zender interferometers

Graphene nanoribbons provide an ideal platform for electronic interferometry in the Integer Quantum Hall regime. Here, we solve the time-dependent four-component Schroedinger equation for single carriers in graphene and expose several dynamical effects of the carrier localization on their transport characteristics in pn junctions. We simulate two kinds of Mach-Zender Interferometers (MZI). The first is based on Quantum Point Contacts and is similar to traditional GaAs/AlGaAs interferometers. As expected, we observe Aharonov-Bohm oscillations and phase averaging. The second is based on Valley Beam Splitters, where we observe unexpected phenomena due to the intersection of the Edge Channels that constitute the MZI. Our results provide further insights into the behavior of graphene interferometers. Additionally, they highlight the operative regime of such nanodevices for feasible single-particle implementations.

Analysis of Population Control Techniques for Time-Dependent and Eigenvalue Monte Carlo Neutron Transport Calculations

An extensive study of population control techniques (PCTs) for time-dependent and eigenvalue Monte Carlo (MC) neutron transport calculations is presented. We define PCT as a technique that takes a censused population and returns a controlled, unbiased population. A new perspective based on an abstraction of particle census and population control is explored, paving the way to improved understanding and application of the concepts. Five distinct PCTs identified from the literature are reviewed: simple sampling, splitting-roulette (SR), combing (CO), modified combing, and duplicate-discard (DD). A theoretical analysis of how much uncertainty is introduced to a population by each PCT is presented. Parallel algorithms for the PCTs, applicable for both time-dependent and eigenvalue MC simulations, are proposed. The relative performance of the PCTs based on run time and tally mean error or standard deviation is assessed by solving time-dependent and eigenvalue test problems. It is found that SR and CO are equally the most performing techniques, closely followed by DD.

Efficient reduced order model based on the proper orthogonal decomposition for time-dependent MOC calculations

ABSTRACT An efficient reduced order model (ROM) for time-dependent transport calculations using the method of characteristics (MOC) is proposed. In the present ROM, the flux distributions and the net neutron currents between the adjacent unstructured mesh regions are taken from the MOC solution. Then, the coefficient matrices for the MOC-equivalent diffusion equation are reconstructed from them. The proper orthogonal decomposition (POD) is applied for the MOC-equivalent diffusion equation to reduce the degree of freedoms (DOFs) using the orthogonal bases obtained by the singular value decomposition (SVD) for the sampled MOC solution. The accuracy and computation time of the present ROM are verified in the C5G7-TD 2D benchmark problem. The calculation results show that the present ROM enables us approximately 5000–6000 times faster computation than the full order model (FOM) for kinetic calculations itself in the present calculation condition. The present method can be substituted as real-time simulations without the spatial homogenization when typical flux distributions and the net neutron currents of a target problem can be precalculated.

VITAS: A multi-purpose simulation code for the solution of neutron transport problems based on variational nodal methods

Existing neutronic whole-core simulation codes are problem-oriented. With the advancement of computer technology and the development of complicated micro-nuclear reactors, there is a pressing need to create solution methods with broad applicability and the ability to accommodate more complex, high-fidelity, unstructured geometries. This necessity motivates the development of a neutron transport code that can adapt to different types of nuclear reactors. This work describes the code design and theoretical model of VITAS, a multi-purpose simulation code for handling steady-state and time-dependent neutron transport problems. This code incorporates algorithms and models inside a unified variational nodal framework based on the second-order neutron transport equation. The most recent version of VITAS employs the isotropic scattering approximation and permits arbitrary spatial and angular refinement. VITAS is compatible with Cartesian geometry, hexagonal geometry, triangular geometry, and Cartesian geometry with finite element subdivisions in the radial direction (Cartesian-FE). The three-dimensional modeling can be performed by axially extruding the two-dimensional mesh. Users can choose the mesh type and expansion order on-demand for optimal computational efficiency.In this paper, VITAS is validated using benchmark problems, i.e., the TAKEDA3 benchmark and the transient LMW benchmark with Cartesian homogenized geometry, the C5G7 and C5G7-TD exercises with Cartesian-FE geometry, the TAKEDA4 benchmark and the Buckner and Stewart benchmark with hexagonal-z homogenized geometry, and the Dodds benchmark with cylindrical-z geometry described by triangular-z unstructured meshes. The space-angle truncation is extensively examined to demonstrate the asymptotic convergence behavior with p- and h-refinement. The results indicate that VITAS has the potential to become a versatile toolset for solving a variety of nuclear reactor problems.

Benchmarks for Infinite Medium, Time Dependent Transport Problems with Isotropic Scattering

The widely used AZURV1 transport benchmarks package provides a suite of solutions to isotropic scattering transport problems with a variety of initial conditions. Most of these solutions have an initial condition that is a Dirac delta function in space; as a result these benchmarks are challenging problems to use for verification tests in computer codes. Nevertheless, approximating a delta function in simulation often leads to low orders of convergence and the inability to test the convergence of high-order numerical methods. While there are examples in the literature of integration of these solutions as Green’s functions for the transport operator to produce results for more easily simulated sources, they are limited in scope and briefly explained. For a sampling of initial conditions and sources, we present solutions for the uncollided and collided scalar flux to facilitate accurate testing of source treatment in numerical solvers. The solution for the uncollided scalar flux is found in analytic form for some sources. Since integrating the Green’s functions is often nontrivial, discussion of integration difficulty and workarounds to find convergent integrals is included. Additionally, our uncollided solutions can be used as source terms in verification studies, in a similar way to the method of manufactured solutions.

Time-Dependent Measurements of Shale's Compressive Strength When Contacting Ionic Solutions.

Time-dependent measurements of uniaxial compressive strength, and ionic and water transport were conducted to analyze the alteration of shale’s strength, as a function of time, when exposed to aqueous solutions. Results showed that the compressive strength of shale is time-dependent, and it relies highly on water activity and ionic concentration differences between shale and aqueous solutions. Data obtained from this work showed that time-dependent water and ion transport into shale correlated well with compressive strength measurements. It was revealed that initial water extraction by osmosis strengthened shale until ions and their associated water clouds invaded shale causing reduction in its strength. It is quite possible that water flow by diffusion osmosis may have counteracted water flow by chemical osmosis rendering ionic diffusion as the primary regulator on shale strength alteration. Furthermore, it was found that alteration of compressive strength when it interacted with aqueous solutions could be adequately explained within the confines of chemical osmosis, ionic diffusion, and diffusion osmosis. Data suggests that the impact of chemical osmosis on compressive strength is observed earlier than ionic diffusion and diffusion osmosis. Data also showed that potassium ions seem to contribute to the enhancement of the compressive strength of shale.

Application of stiffness confinement method within variational nodal method for solving time-dependent neutron transport equation

The stiffness confinement method (SCM) is implemented in the variational nodal method (VNM) framework to solve time-dependent multi-group neutron transport equations. With frequency-transform, the time-dependent neutron equation is decoupled from the precursor equation and transformed into a dynamic eigenvalue problem which can be solved with the in-house VNM code VITAS. An improved time-source iteration method within the VNM-SCM framework is proposed to accelerate constructing response matrices and reduces memory usage. Based on the VNM-SCM scheme, the kinetics module of VITAS is developed for the Cartesian and hexagonal-z geometry and verified by several benchmark problems.Numerical results demonstrate that VNM-SCM can perform accurate and efficient transient calculations with large time-step sizes. For the two-dimensional TWIGL benchmark, the VNM-SCM produces a maximum core power error of -0.57% with the time-step size of 20 ms. For the three-dimensional LMW benchmark, the VNM-SCM results in a maximum core power error of 0.95% with the time-step size of 2 s. The VNM-SCM also yields an accurate neutron flux prediction for the hexagonal-z geometry problem. In addition, the effect of the angular expansion is investigated systematically. Examinations with the three-dimensional LMW benchmark display an error reduction in the core power error from 0.131% to 0.011% from P1 to P3 interfacial angular expansion, with a substantial computing time increase of 6.14 hours. The study indicates that the high-order angular expansion significantly increases the computing time but contributes little to the accuracy of the core power. Besides, it was found that the initial steady-state calculation dominates the shape error of the flux in the transient calculation.

Advances in analytical solutions for time-dependent solute transport model

Advances in analytical solutions for time-dependent solute transport model

An efficient collocation method for long-time simulation of heat and mass transport on evolving surfaces

This paper presents an efficient collocation method which combines the generalized finite difference method (GFDM) with the Krylov deferred correction (KDC) method for the long-time simulation of heat and mass transport on evolving surfaces. The KDC method utilizes a pseudo-spectral-type temporal collocation formulation to discretize the time-dependent surface heat and mass transport equation in each time marching step, where the time derivatives at the collocation points are introduced as the new unknown variables. A low-order time marching scheme is then applied as an effective preconditioner in the Jacobian-Free Newton-Krylov framework to decouple the spatial surface PDEs at different collocation nodes. Each decoupled surface PDE is then solved by the meshless GFDM, where both the continuous-form evolving surfaces defined by parametric equations and discretized-form evolving surfaces composed of point clouds are considered in the GFDM spatial discretization. Numerical experiments show that the combined GFDM-KDC solver is a promising numerical scheme for long-time evolution simulation of heat and mass transport on intractable evolving surfaces.

Dynamic transport characteristics of side-coupled double-quantum-impurity systems

A systematic study is performed on time-dependent dynamic transport characteristics of a side-coupled double-quantum-impurity system based on the hierarchical equations of motion. It is found that the transport current behaves like a single quantum dot when the coupling strength is low during tunneling or Coulomb coupling. For the case of only tunneling transition, the dynamic current oscillates due to the temporal coherence of the electron tunneling device. The oscillation frequency of the transport current is related to the step voltage applied by the lead, while temperature T, electron–electron interaction U and the bandwidth W have little influence. The amplitude of the current oscillation exists in positive correlation with W and negative correlation with U. With the increase in coupling t 12 between impurities, the ground state of the system changes from a Kondo singlet of one impurity to a spin singlet of two impurities. Moreover, lowering the temperature could promote the Kondo effect to intensify the oscillation of the dynamic current. When only the Coulomb transition is coupled, it is found that the two split-off Hubbard peaks move upward and have different interference effects on the Kondo peak at the Fermi surface with the increase in U 12, from the dynamics point of view.

Resilience assessment of railway networks: Combining infrastructure restoration and transport management

During railways operations, unplanned events might occur which can result in rail traffic being heavily impacted. The paper proposes a passenger-centred resilience assessment for disruption scenarios which consist of multiple simultaneous disruptions. It combines train traffic operations, passenger flows and network restoration. To evaluate resilience, an optimization-based approach has been developed for solving the new infrastructure restoration and transport management (IRTM) problem. Additionally, this approach develops mitigation plans for the best infrastructure restoration and traffic recovery and it captures the time-dependent transport network performance during disruptions. The approach is general with respect to types of disruptions, and can be applied for evaluation against short disruptions (1–2 h) as well as more substantial ones (multiple days or weeks). The performance of the proposed approach has been demonstrated on a Dutch railway network. Furthermore, the resilience of the system is assessed against the critical infrastructure disruption scenarios in the network. This optimization-based approach shall enable decision makers to quantify accurately impacts of multiple disruptions by considering the created inconveniences to passengers in the railway operation due to these disruptions.

Relative importance of parameters controlling scour at bridge piers using the new toolbox ScourAPP

The new toolbox ScourApp is presented and applied for analysis of the complex interactions between local scour and sediment deposition at bridges during floods and to determine the relative importance of the controlling parameters on scour depth. ScourApp represents the time-dependent sediment transport processes through modern empirical formulations to compute the evolution of scour depth at a bridge pier. Results show that the mathematical model reproduces observed scour depths with high accuracy and confirm that ScourApp is a suitable tool for scour analysis. The model parameters controlling the time dependent scour depth were the equilibrium scour depth, and two constants representing the effects of pier geometry, flow and sediment. Sensitivity analysis showed that all three scour model parameters exhibited a nearly linear relation with the final scour depth. Moreover, results considering sediment deposition obtained for the Rapel Bridge showed that scour depths are highly sensitive to the sediment supply rate. ScourApp is recommended in scour assessment for bridge planning, design, management, and forensic analysis, as well as for engineering education.

Approximate model and algorithms for precast supply chain scheduling problem with time-dependent transportation times

This paper focuses on the precast supply chain scheduling problem with time-dependent transportation time to minimise the total weighted tardiness (PSCSP_TDT |TWT). In the problem, an order sequence and several job sequences are to be determined simultaneously. At first, through in-depth analysis of problem structure and real data from a precast manufacturer, we approximate the problem into a three-stage order scheduling problem by combining the seven production stages into one differentiation stage, and then explore some useful properties of the schedules for the approximate problem. Subsequently, to solve the small instances for the PSCSP_TDT |TWT, we propose an approximate model-based hybrid dynamic programming and heuristic (AMHDPH) and obtain a lower bound as a by-product of the algorithm. For dealing with medium-or large instances, with considering the complexity of the problem, we propose four approximate model-based hybrid iterated greedy (AMHIG) algorithms by integration of constructive heuristics, structural properties of solutions, an iterated greedy, and a correction heuristic. Comprehensive computational results show that the AMHDPH generates tight lower bounds for small instances and solves the most of small instances to optimality within 60 seconds. Whereas the best AMHIG generates feasible solutions with an average optimality gap below 5 percent for around 70 percent instances.