Linear Transport Research Articles

A Transport Theory Route to the Dirac Equation

Starting from the similarity between the spherical harmonics approximation of order one to the linear transport equation (usually referred as P 1 approximation) and the Klein-Gordon equation of the quantum physics, an extended set of equations is introduced, which is proved to be equivalent to the Dirac equation with imaginary mass. Conversely, when a real mass is restored into the extended P 1 system, a new equation is obtained, whose solutions are superposition of the spinors for a spin particle and the corresponding antiparticle.

QLBT: a linear Boltzmann transport model for heavy quarks in a quark-gluon plasma of quasi-particles

We develop a new heavy quark transport model, QLBT, to simulate the dynamical propagation of heavy quarks inside the quark-gluon plasma (QGP) created in relativistic heavy-ion collisions. Our QLBT model is based on the linear Boltzmann transport (LBT) model with the ideal QGP replaced by a collection of quasi-particles to account for the non-perturbative interactions among quarks and gluons of the hot QGP. The thermal masses of quasi-particles are fitted to the equation of state from lattice QCD simulations using the Bayesian statistical analysis method. Combining QLBT with our advanced hybrid fragmentation-coalescence hadronization approach, we calculate the nuclear modification factor R_mathrm {AA} and the elliptic flow v_2 of D mesons at the Relativistic Heavy-Ion Collider and the Large Hadron Collider. By comparing our QLBT calculation to the experimental data on the D meson R_mathrm {AA} and v_2, we extract the heavy quark transport parameter hat{q} and diffusion coefficient D_mathrm {s} in the temperature range of 1-4~T_mathrm {c}, and compare them with the lattice QCD results and other phenomenological studies.

Spectral stabilization of linear transport equations with boundary and in-domain couplings

In this work, the problem of stabilization of general systems of linear transport equations with indomain and boundary couplings is investigated. It is proved that the unstable part of the spectrum is of finite cardinal. Then, using the pole placement theorem, a linear full state feedback controller is synthesized to stabilize the unstable finite dimensional part of the system. Finally, by a careful study of semigroups, we prove the exponential stability of the closed-loop system. As a by product, the linear control constructed before is saturated and a fine estimate of the basin of attraction is given.

Rapid linear transport infrastructure development in the Carpathians: A major threat to the integrity of ecological connectivity for large carnivores

The development of sustainable transport is a key challenge in societies where there is an accelerated need for socio-economic development. This is the case for seven countries from central and south-eastern Europe that share the Carpathian Mountains. The challenge of developing sustainable transport requires transdisciplinary, or at least cross-sectoral cooperation, between the transport development and nature conservation sectors. Such cooperation is not in the culture of the Carpathian countries, which together host some of the most remarkable biodiversity values in Europe, including the largest populations of brown bear, grey wolf and Eurasian lynx. The overall length of motorways in these countries more than quintupled in the last 30 years and the rapid expansion of Linear Transport Infrastructure (LTI) continues at exacerbating rates. The rich biodiversity habitats are being fragmented and the concept of ecological connectivity is poorly understood and implemented by the national authorities. Ecological networks for large carnivores are not defined nor officially recognised in the Carpathian countries, with little exceptions. The legislation is not consistent across the strands of ecological connectivity and is not harmonised between the countries to effectively support transnational conservation efforts. Thus, the critical intersections between planned or even existing LTI and ecological corridors for large carnivores cannot be identified, in most cases leading to increasing habitat fragmentation and isolation of wildlife populations in the region. We summarised all this key context-related information for the Carpathians in relation to LTI development and ecological connectivity. To counteract this trend in the Carpathian ecoregion, we propose a set of recommendations to: improve and harmonise the legislation; develop and endorse methodologies for designating ecological corridors; address the cumulative impact on ecological connectivity; define other threats on landscape permeability; improve stakeholder engagement, cooperation and communication; develop comprehensive and transparent biodiversity and transport databases; monitor wildlife and transport for implementing most appropriate mitigation measures and strategies; build capacity to address the issue of sustainable transportation; and foster transnational cooperation and dialogue. Bringing these elements together will support the design of ecological networks in a way that considers the needs and location of both current and future habitats and contribute to efforts to address the climate crisis. These specific recommendations are relevant also for other areas of the world facing similar problems as the Carpathians.

Weighted Error Estimates for Transient Transport Problems Discretized Using Continuous Finite Elements with Interior Penalty Stabilization on the Gradient Jumps

In this paper we consider the semi-discretization in space of a first order scalar transport equation. For the space discretization we use standard continuous finite elements with a stabilization consisting of a penalty on the jump of the gradient over element faces. We recall some global error estimates for smooth and rough solutions and then prove a new local error estimate for the transient linear transport equation. In particular we show that for the stabilized method the effect of non-smooth features in the solution decay exponentially from the space time zone where the solution is rough so that smooth features will be transported unperturbed. Locally the L2-norm error converges with the expected order O(h^{k+frac 12}), if the exact solution is locally smooth. We then illustrate the results numerically. In particular we show the good local accuracy in the smooth zone of the stabilized method and that the standard Galerkin fails to approximate a solution that is smooth at the final time if underresolved features have been present in the solution at some time during the evolution.

A low rank tensor representation of linear transport and nonlinear Vlasov solutions and their associated flow maps

We propose a low-rank tensor approach to approximate linear transport and nonlinear Vlasov solutions and their associated flow maps. The approach takes advantage of the fact that the differential operators in the Vlasov equation are tensor friendly, based on which we propose a novel way to dynamically and adaptively build up low-rank solution basis by adding new basis functions from discretization of the PDE, and removing basis from an SVD-type truncation procedure. For the discretization, we adopt a high order finite difference spatial discretization and a second order strong stability preserving multi-step time discretization. We apply the same procedure to evolve the dynamics of the flow map in a low-rank fashion, which proves to be advantageous when the flow map enjoys the low rank structure, while the solution suffers from high rank or displays filamentation structures. Hierarchical Tucker decomposition is adopted for high dimensional problems. An extensive set of linear and nonlinear Vlasov test examples are performed to show the high order spatial and temporal convergence of the algorithm with mesh refinement up to SVD-type truncation, the significant computational savings of the proposed low-rank approach especially for high dimensional problems, the improved performance of the flow map approach for solutions with filamentations.

The Effect of Various Dose Normalization Strategies When Implementing Linear Boltzmann Transport Equation Dose Calculation for Lung Stereotactic Body Radiation Therapy Planning

PurposeTo explore implications of various plan normalizations when implementing a linear Boltzmann transport equation solver dose calculation algorithm (LBTE) for lung stereotactic body radiation therapy (SBRT). Methods and MaterialsEighty-seven plans originally calculated with a convolution-superposition algorithm (CS) were recalculated with LBTE and normalized in 3 ways: prescription covering 95% of planning target volume (PTV), 99% of internal target volume (ITV), and keeping the original planned PTV coverage. Effect on delivered dose after implementing the new algorithm was quantified using change in total monitor units for each renormalization strategy. Treatment planning system–reported changes in PTV, ITV, and organ at risk (OAR) doses were also quantified, along with the feasibility of LBTE plans to meet institutional OAR planning objectives. ResultsLBTE renormalization resulted in monitor unit increases of 7.0 ± 8.8%, 0.31 ± 5.8%, and 7.9 ± 8.6% when normalizing to the PTV D95%, ITV D99%, and planned coverage, respectively. When normalizing to PTV D95%, the LBTE reported increased PTV and ITV D1% (Gy) relative to CS (median, 3.4% and 3.2%, respectively), and normalizing to ITV D99% showed a median 1.9% decrease. For LBTE plans, reported OAR doses were increased when normalizing to PTV D95% or planned coverage (median chest wall V30 Gy [cc] increase of 0.85 and 1.7 cc, respectively) and normalizing to ITV D99% resulted in decreased dose (median chest wall V30 Gy [cc] decrease of 1.8 cc). LBTE plans normalized to PTV D95% showed inferior ability to meet the OAR objectives, but reoptimizing kept the objectives manageable while maintaining PTV coverage. ConclusionsWhen transitioning from CS to LBTE dose calculation for lung SBRT, maintaining a PTV coverage-based normalization generally results in increased dose delivered relative to CS and increased reported target and OAR dose. In cases where PTV normalization results in unacceptably high doses to targets or OARs, normalizing based on ITV coverage can be considered to maintain similar target dose as CS.

A Reduced Basis Method for Radiative Transfer Equation

Linear kinetic transport equations play a critical role in optical tomography, radiative transfer and neutron transport. The fundamental difficulty hampering their efficient and accurate numerical resolution lies in the high dimensionality of the physical and velocity/angular variables and the fact that the problem is multiscale in nature. Leveraging the existence of a hidden low-rank structure hinted by the diffusive limit, in this work, we design and test the angular-space reduced order model for the linear radiative transfer equation, the first such effort based on the celebrated reduced basis method (RBM). Our method is built upon a high-fidelity solver employing the discrete ordinates method in the angular space, an asymptotic preserving upwind discontinuous Galerkin method for the physical space, and an efficient synthetic accelerated source iteration for the resulting linear system. Addressing the challenge of the parameter values (or angular directions) being coupled through an integration operator, the first novel ingredient of our method is an iterative procedure where the macroscopic density is constructed from the RBM snapshots, treated explicitly and allowing a transport sweep, and then updated afterwards. A greedy algorithm can then proceed to adaptively select the representative samples in the angular space and form a surrogate solution space. The second novelty is a least squares density reconstruction strategy, at each of the relevant physical locations, enabling the robust and accurate integration over an arbitrarily unstructured set of angular samples toward the macroscopic density. Numerical experiments indicate that our method is effective for computational cost reduction in a variety of regimes.

Iterated discretization error transport equations for laminar and turbulent flows

AbstractThe focus of this work is on discretization error estimation for finite‐volume schemes using iterated forms of the linear and nonlinear error transport equations. The accuracy of the discretization error estimates is studied by applying the error estimates as corrections to the primal problem and calculating the observed order of accuracy of the corrected solution. The test cases used in this work include two‐dimensional Cross Term Sinusoidal manufactured solutions for laminar flow and turbulent flow modeled by the Spalart–Allmaras and Menter's Shear Stress Transport model and a boundary layer manufactured solution for the Spalart–Allmaras model. The discretization error estimates of the linearized error transport equations and the nonlinear error transport equations are compared. Higher‐order accurate corrected solutions have been obtained which shows that the discretization error estimates are sufficiently accurate.

Nonlinear antidamping spin-orbit torque originating from intraband transport on the warped surface of a topological insulator

Motivated by recent experiments observing a large antidamping spin-orbit torque (SOT) on the surface of a three-dimensional topological insulator, we investigate the origin of the current-induced SOT beyond linear-response theory. We find that a strong antidamping SOT arises from intraband transitions in non-linear response, and does not require interband transitions as is the case in linear transport mechanisms. The joint effect of warping and an in-plane magnetization generates a non-linear antidamping SOT which can exceed the intrinsic one by several orders of magnitude, depending on warping parameter and the position of Fermi energy, and exhibits a complex dependence on the azimuthal angle of the magnetization. This nonlinear SOT provides an alternative explanation of the observed giant SOT in recent experiments.

Inhomogeneous linear responses and transport in armchair graphene nanoribbons in the presence of elastic scattering

Within linear-response theory we derive a response function that thoroughly accounts for the influence of elastic scattering and is valid beyond the long-wavelength limit. We use the theory to evaluate the polarization function and the conductivity in metallic armchair graphene nanoribbons in the Lindhard approximation for intra-band and inter-band transitions and for a relaxation time τ that is not constant. We obtain a logarithmic behaviour in the scattering-independent polarization function not only for intra-band transitions, as is usually the case for one-dimensional systems, but also for inter-band transitions. Modifying the screening wave vector and the impurity density in the long-wavelength limit strongly influences the relaxation time. In contrast, for large wave vectors, this modification leads to a conservative value of τ . We show that the imaginary part of the impurity-dependent conductivity varies with the wave vector while its scattering-independent part exists only for a single value of the wave vector.

True oxygen reduction capacity during photosynthetic electron transfer in thylakoids and intact leaves.

Reactive oxygen species (ROS) are generated in electron transport processes of living organisms in oxygenic environments. Chloroplasts are plant bioenergetics hubs where imbalances between photosynthetic inputs and outputs drive ROS generation upon changing environmental conditions. Plants have harnessed various site-specific thylakoid membrane ROS products into environmental sensory signals. Our current understanding of ROS production in thylakoids suggests that oxygen (O2) reduction takes place at numerous components of the photosynthetic electron transfer chain (PETC). To refine models of site-specific O2 reduction capacity of various PETC components in isolated thylakoids of Arabidopsis thaliana, we quantified the stoichiometry of oxygen production and consumption reactions associated with hydrogen peroxide (H2O2) accumulation using membrane inlet mass spectrometry and specific inhibitors. Combined with P700 spectroscopy and electron paramagnetic resonance spin trapping, we demonstrate that electron flow to photosystem I (PSI) is essential for H2O2 accumulation during the photosynthetic linear electron transport process. Further leaf disc measurements provided clues that H2O2 from PETC has a potential of increasing mitochondrial respiration and CO2 release. Based on gas exchange analyses in control, site-specific inhibitor-, methyl viologen-, and catalase-treated thylakoids, we provide compelling evidence of no contribution of plastoquinone pool or cytochrome b6f to chloroplastic H2O2 accumulation. The putative production of H2O2 in any PETC location other than PSI is rapidly quenched and therefore cannot function in H2O2 translocation to another cellular location or in signaling.

Addressing the gas kinetics Boltzmann equation with branching-path statistics.

This article proposes a statistical numerical method to address gas kinetics problems obeying the Boltzmann equation. This method is inspired by Monte Carlo algorithms used in linear transport physics, where virtual particles are followed backwards in time along their paths. The nonlinear character of gas kinetics translates, in the numerical simulations presented here, into branchings of the virtual particle paths. The obtained algorithms have displayed in the few tests presented here two noticeable qualities: (1) they involve no mesh and (2) they allow one to easily compute the gas density at rarefied places of the phase space, for example, at high kinetic energy.

Dissipative and Dispersive Properties of Finite Difference Schemes for the Linear Transport Equation on A 4 × 3 Metatemplate

Dissipative and Dispersive Properties of Finite Difference Schemes for the Linear Transport Equation on A 4 × 3 Metatemplate

Optimization of a multi-constraint transport problem using a heuristic approach

A Linear transport problem can be defined as the action of transporting products from "m origins" (or units) to "n destinations" (or customers) at the lowest cost. So the solution to a transportation problem is to organize the transportation in such a way as to minimize its cost. The objective of this paper is to determine the quantity sent from each source (origin) to each destination while minimizing transport costs. Achieving this objective requires a methodology which consists in deploying an algorithm whose purpose is the search for an optimal solution, based on an initial solution. The application is made on a factory producing mechanical parts.

Estimating linear mass transport coefficients in solid solutions via correlation splitting and a law of total diffusion

Directly computing linear mass transport coefficients in stochastic models entails integrating over time the equilibrium correlations between atomic displacements. Here, we show how to improve the accuracy of kinetic Monte Carlo simulations via correlation splitting and conditioning, which statistically amounts to estimating the mass transport coefficients through a law of total diffusion. We illustrate the approach with kinetic path sampling simulations of atomic diffusion in a random alloy model in which percolating solute clusters trap the mediating vacancy. There, Green functions serve to generate first-passage paths escaping the traps and to propagate the long-time dynamics. When they also serve to estimate mean-squared displacements via conditioning, colossal reductions of statistical errors are achieved.

Molecular and Photosynthetic Performance in the Yellow Leaf Mutant of Torreya grandis According to Transcriptome Sequencing, Chlorophyll a Fluorescence, and Modulated 820 nm Reflection.

To study the photosynthetic energy mechanism and electron transfer in yellow leaves, transcriptomics combined with physiological approaches was used to explore the mechanism of the yellow leaf mutant Torreya grandis ‘Merrillii’. The results showed that chlorophyll content, the maximal photochemical efficiency of PSII (Fv/Fm), and the parameters related to the OJ phase of fluorescence (φEo, φRo) were all decreased significantly in mutant-type T. grandis leaves. The efficiency needed for an electron to be transferred from the reduced carriers between the two photosystems to the end acceptors of the PSI (δRo) and the quantum yield of the energy dissipation (φDo) were higher in the leaves of mutant-type T. grandis compared to those in wild-type leaves. Analysis of the prompt fluorescence kinetics and modulated 820 nm reflection showed that the electron transfer of PSII was decreased, and PSI activity was increased in yellow T. grandis leaves. Transcriptome data showed that the unigenes involved in chlorophyll synthesis and the photosynthetic electron transport complex were downregulated in the leaves of mutant-type T. grandis compared to wild-type leaves, while there were no observable changes in carotenoid content and biosynthesis. These findings suggest that the downregulation of genes involved in chlorophyll synthesis leads to decreased chlorophyll content, resulting in both PSI activity and carotenoids having higher tolerance when acting as photo-protective mechanisms for coping with chlorophyll deficit and decrease in linear electron transport in PSII.

A Forward Analytic Model of Neutron Time-of-Flight Signals for Inferring Ion Temperatures from MagLIF Experiments

A forward analytic model is required to rapidly simulate the neutron time-of-flight (nToF) signals that result from magnetized liner inertial fusion (MagLIF) experiments at Sandia’s Z Pulsed Power Facility. Various experimental parameters, such as the burn-weighted fuel-ion temperature and liner areal density, determine the shape of the nToF signal and are important for characterizing any given MagLIF experiment. Extracting these parameters from measured nToF signals requires an appropriate analytic model that includes the primary deuterium-deuterium neutron peak, once-scattered neutrons in the beryllium liner of the MagLIF target, and direct beamline attenuation. Mathematical expressions for this model were derived from the general-geometry time- and energy-dependent neutron transport equation with anisotropic scattering. Assumptions consistent with the time-of-flight technique were used to simplify this linear Boltzmann transport equation into a more tractable form. Models of the uncollided and once-collided neutron scalar fluxes were developed for one of the five nToF detector locations at the Z-Machine. Numerical results from these models were produced for a representative MagLIF problem and found to be in good agreement with similar neutron transport simulations. Twenty experimental MagLIF data sets were analyzed using the forward models, which were determined to only be significantly sensitive to the ion temperature. The results of this work were also found to agree with values obtained separately using a zero scatter analytic model and a high-fidelity Monte Carlo simulation. Inherent difficulties in this and similar techniques are identified, and a new approach forward is suggested.

Nonlinear magnetoresistivity in two-dimensional systems induced by Berry curvature

The band geometric properties of quantum materials play an elemental role in the linear and nonlinear transport of electrons. In this paper, we propose that the interplay of the Berry curvature, the orbital magnetic moment and the Lorentz force can induce a finite nonlinear resistivity in two dimensional systems in presence of a perpendicular magnetic field. The induced nonlinear magnetoresistivity scales linearly with the magnetic field and is purely quantum mechanical in origin. This novel transport signature can be used as an additional experimental probe for the geometric quantities in intrinsically time reversal symmetric systems.

Integrated urban transport infrastructure development: The role of digital social geo-communication in Hamburg's TEN-T improvement

The European Union's (EU) Trans-European transport network (TEN-T) policy transport policy strives for an integrated and sustainable transport development. The process can be regarded as an ongoing spatial governance process rather than a linear transport planning and project implementation. Transport developers increasingly regard information and communication technologies (ICT) as supportive in these collaborative processes and government use Public Participatory Geographic Information Systems (PPGIS). Many contextual factors, institutional and technological conditions are influencing the usage and results of the tools, there is still the need to understand their role in the spatial governance processes. Therefore, exemplified by Hamburg's TEN-T green corridor project, the following question will be investigated in the paper: how did the public and governmental actors interact when utilising (PPGIS) in Hamburg's (TEN-T) green corridor project? By the means of MAXQDA, a qualitative and mixed data analysis tool the contributions of the participants from the online participation, the consultant report that summarised the contribution and government's response been analysed (GovHam, 2020a). Furthermore, a theoretical spatial governance framework had been suggested that guided the analysis. The study shows that the selective process by authorities and consulting institutions decreases the potentials of (PPGIS) to create a deliberate and transparent discussion. Hence, the results confirm other studies, showing that the social geo- communication tools are mainly used to inform participants rather than engaging reflective learning.