Higher-order Transport Research Articles

Higher-order topological transport protected by boundary Chern number in phononic crystals

Topological pumps enable robust transports of topological states when the system parameters are varied in a cyclic process. The reported topological pumps are protected by the bulk topology. However, the exploration of topological pump protected by other mechanism remains elusive. Here we report our prediction and observation of higher-order topological pumps linked to the boundary topology, i.e., boundary Chern number. Based on such topological pump, the higher-order transports between the topological states of different dimensions (e.g., corner-edge-corner) are directly observed by spatial scanning of the sound field, and their topological robustness is observed in the paths with defects. Furthermore, modulated by the fundamental corner-edge-corner topological transport, topological splitting effects are unambiguously observed in our acoustic experiments. Our findings not only advance the research of the higher-order topological transports, but also offer good platforms to design unconventional devices.

Derivation of extended-OBurnett and super-OBurnett equations and their analytical solution to plane Poiseuille flow at non-zero Knudsen number

In this work, we analyse wall-bounded flows in the continuum to transition regime with the help of higher-order transport equations (super-set of the Navier–Stokes equation). Towards this, we incorporate second-order in Knudsen number accurate terms in the single-particle distribution function, and with this complete representation, we first derive the second-order accurate extended-OBurnett (EOBurnett) and third-order accurate super-OBurnett (SOBurnett) equations. We then demonstrate that these newly derived equations exhibit unconditional linear stability. We finally validate the equations by solving for plane Poiseuille flow and derive closed-form analytical solutions for the pressure and velocity fields. The pressure and velocity results thus obtained have been compared with direct simulation Monte Carlo (DSMC) data in the transition regime. The results from both the EOBurnett and SOBurnett equations are found to yield better agreement with DSMC data than that obtained from the Navier–Stokes equations. This improved agreement is attributed to the presence of additional terms in the proposed equations, which effectively capture the effect of the Knudsen layer near the wall. The obtained higher-order transport equations and the closed-form solution presented in this work are novel. The ability of the equations to describe the flow in the transition regime should form the basis for conducting further realistic analytical studies of wall-bounded flows in the future.

Thomson effect in thermionic refrigeration: Enhanced performance of graphene/2D-semiconductor/graphene heterostructure cooler

Two-dimensional (2D) materials and their heterostructures have been widely explored for high-performance energy conversion applications. The Thomson effect—a higher order transport process—plays an important role in thermoelectric devices, yet its effect on the performance of thermionic devices remains unknown thus far. Here, we investigate the performance of thermionic refrigeration in vertically stacked heterostructure (VHS) and laterally stitched heterointerface (LHS) composed of a graphene and a 2D semiconductor (i.e., MoS2 and WSe2) in the presence of the Thomson effect. Using a temperature-dependent Seebeck coefficient, we derived the analytical expressions of the cooling efficiency and the effective ZT. We shall show that the Thomson effect improves the coefficient of performance (COP) by up to 20%, particularly, in the case where the temperature difference between the cold and the hot electrodes is large. However, the Carnot efficiency decreases with the temperature difference. The overall COP is reduced by the Thomson effect. We calculate the COP in graphene/MoS2/graphene and graphene/WSe2/graphene VHS and LHS devices. We show that the LHS composed of WSe2 significantly outperforms the VHS and MoS2 counterpart. These findings provide an understanding of thermionic processes in the higher-order transport regime and shall offer insights into the design of novel 2D material heterostructure thermionic energy converters.

Effects of root litter traits on soil organic matter dynamics depend on decay stage and root branching order

Decaying roots contribute disproportionately to soil organic carbon (SOC) stocks in many ecosystems, yet few studies have examined the afterlife effects of root trait variability on the formation, stability and mineralization of SOC. In order to assess how root functional class (absorptive vs. transport) and mycorrhizal association (ectomycorrhizal vs. arbuscular mycorrhizal fungi) affect both formation and loss of SOC, we decayed lower-order absorptive (orders 1–2) and higher-order transport (orders 3–4) roots from six arbuscular mycorrhizal (AM) and six ectomycorrhizal (EcM) associated hardwood tree species in an isotopically distinct soil under laboratory conditions. We found that root litter effects on SOC differed significantly among root functional classes and mycorrhizal types. AM absorptive and transport roots (high in nitrogen and soluble compounds) contributed more to the formation of new mineral-associated organic carbon (MAOC), but also contributed to higher mineralization of native SOC (via priming effects). Moreover, absorptive AM roots formed MAOC gradually and rates saturated, whereas ECM roots formed MAOC more quickly, despite slower decay (via greater formation efficiency). Together, these findings demonstrate how different combinations of root traits might contribute to soil C balance, and that failure to account for the chemical and morphological heterogeneity of roots, as well their interactions with microbes over time, may lead to incorrect projections of SOC stocks and turnover.

On the Effect of Scalar Flux Weighting of Linearly Anisotropic Scattering Matrices in Higher-Order Transport Calculations

Most of the codes available for homogenized group constant generation for deterministic transport calculations apply the approximation of scalar flux weighting during energy group condensation of higher-order anisotropic scattering matrices. In this paper, we point out the bias caused by scalar flux weighting of linearly anisotropic scattering matrices in the result of SP3 and S12 calculations. An infinite pin cell was homogenized with Serpent 2 and ERANOS ECCO to compare group constants with different energy group condensation options. Serpent 2 applies scalar flux while ERANOS ECCO performs current weighting of the linearly anisotropic scattering matrices. Three simple reactor models were built assuming different core sizes using standard rectangular assemblies with 15 ×15 fuel pins to analyze the effect of the various weighting options. Diffusion, SP3, and S12 calculations were performed for the three models using group constants generated with Serpent 2 and ERANOS ECCO. The effect of scalar flux weighting of linearly anisotropic scattering matrices in higher-order transport calculations is shown by comparing the decrease in reactivity due to the decreased reactor size and the assembly power distribution to reference results obtained with Serpent 2 Monte Carlo calculations. Analogous results were observed during the extension of our investigations to a VVER-440 benchmark and the Budapest University of Technology and Economics (BME) Training Reactor. We also studied the effect of increasing the number of groups in these examples. Neglecting higher than linearly anisotropic scattering and indirect application of diffusion coefficients in higher-order transport calculations is advised with few-group structures if angular flux-moment spectra-weighted higher-order scattering matrices cannot be generated. Although in few-group calculations, it can lead to more accurate higher-order transport solutions than applying scalar flux–weighted linearly anisotropic scattering matrices, by increasing the number of energy groups, the distorting effect of scalar flux weighting can also be decreased.

On the simulation of neutron noise induced by vibrations of fuel pins in a fuel assembly

Vibrations of fuel assemblies are an important issue in the safe operation of nuclear reactors, because they can challenge the integrity of the fuel with potential for radioactive releases. Reactor neutron noise-based techniques for monitoring vibrations are valuable for core diagnostic since they are not intrusive and make use of ordinary neutron flux measurements from ex-core and in-core detectors. The application of these techniques involves the solution of inverse problems that require numerical simulations capable of estimating the reactor neutron noise, given a model of the vibrations. For this purpose, several novel reactor neutron noise solvers have been developed in the CORTEX project using either Monte Carlo or deterministic methods, such as the discrete ordinates method, the method of characteristics, and the diffusion approximation. In the current work, these solvers have been scrutinized by computing the neutron noise induced by vibrations of one or multiple fuel pins in a simplified UOX fuel assembly benchmark, via proper variations of macroscopic neutron cross sections. The comparison of these neutron noise solutions obtained from the different methods shows novel insights into the simulation of neutron noise induced by mechanical vibrations, such as the challenges posed by the Monte Carlo method, the impact of the angular discretization on the application of the discrete ordinates method, and the accuracy of the diffusion approximation assessed via the higher-order neutron transport methods.

Hybrid finite-element-based numerical solution of the SP3 equations – SP3 solution of two- and three-dimensional VVER reactor problems

As a follow-up to the paper previously published by the authors detailing the hybrid finite element (HYBFEM) solution of the SP3 equations, in this paper, besides a semi-analytical solver verification with an analysis on the applied source fitting polynomial order, three-dimensional VVER-440, and VVER-1000 benchmarks are reproduced with the continuous Galerkin (CGFEM) and HYBFEM SP3 modules of the SPNDYN code. The effect of the applied axial nodalisation and radial element order on the calculation results is discussed. The HYBFEM solver extended with a discontinuity factor (DCF) calculation module based on Serpent 2 output parameters is verified on a two-dimensional VVER-1000 benchmark. The SPNDYN CGFEM and HYBFEM results show very good agreement. We also verify that by introducing DCFs in SP3 calculations, the reference transport solution can be reproduced with high accuracy. We highlight the effect of using scalar flux weighted linearly anisotropic scattering matrices in higher-order transport calculations.

The mechanism of higher-order structure formation and transport function of amino acid transporter super-complexes

The mechanism of higher-order structure formation and transport function of amino acid transporter super-complexes

Laminar-turbulent transition in Taylor-Couette flow from a molecule dependent transport equation

In this Letter, a previously utilized higher-order momentum transport equation obtained using a projection-perturbation formalism from the most general equation of classical transport for the N-particle distribution function, the Liouville equation, is applied to the Taylor-Couette flow, e.g. fluid flow enclosed between two concentric cylinders where the inner cylinder is rotating with some constant speed and the outer cylinder is stationary. The results of the numerical simulation of azimuthal velocity profiles are analyzed to see how an initial laminar velocity profile evolves in time into a velocity profile characteristic for turbulent flow. Although the experiments were not very accurate, they all point to the near uniformity of the velocity profiles in turbulent regime in the central region of the annulus. Using the time evolution of the velocity profiles, we further investigate possibility of observing double phase transition from a laminar to turbulent regime.

Revealing strong correlations in higher-order transport statistics: A noncrossing approximation approach

We present a method for calculating the full counting statistics of a nonequilibrium quantum system based on the propagator noncrossing approximation (NCA). This numerically inexpensive method can provide higher order cumulants for extended parameter regimes, rendering it attractive for a wide variety of purposes. We compare NCA results to Born-Markov quantum master equations (QME) results to show that they can access different physics, and to numerically exact inchworm quantum Monte-Carlo data to assess their validity. As a demonstration of its power, the NCA method is employed to study the impact of correlations on higher order cumulants in the nonequilibrium Anderson impurity model. The four lowest order cumulants are examined, allowing us to establish that correlation effects have a profound influence on the underlying transport distributions. Higher order cumulants are therefore demonstrated to be a proxy for the presence of Kondo correlations in a way that cannot be captured by simple QME methods.

Measurement of the third-order transport coefficient in N2 and its effect on the longitudinal diffusion coefficient measured from the arrival-time spectra of an electron swarm

Arrival-time spectra (ATS) of an electron swarm in N2 from 50 Td to 700 Td (1 Td = 10−17 Vcm2) were measured by double-shutter drift tube, and then the first Townsend ionization coefficient, mean-arrival-time drift velocity, longitudinal diffusion coefficient, and longitudinal third-order transport coefficient were obtained from the measured ATS. This is the first successful measurement of the third-order transport coefficient in a gas. Furthermore, we went back to an expression of the longitudinal diffusion coefficient in terms of the α parameter, which is the electron transport coefficient derived from ATS, and then demonstrated that the third-order and higher-order electron transport coefficients, which are traditionally ignored in the electron swarm experiment, should be considered to obtain the longitudinal diffusion coefficient properly at moderate and high reduced electric fields.

Strong shock as a stringent test for Onsager-Burnett equations.

A new set of thermodynamically consistent Onsager-Burnett equations [Singh, Jadhav, and Agrawal, Phys. Rev. E 96, 013106 (2017)2470-004510.1103/PhysRevE.96.013106] has recently been derived. In this work, we subject these equations to a severe test case of strong shock (Mach number = 134) for a dilute gas system composed of hard-sphere molecules. The numerical results of OBurnett equations for conserved and nonconserved variables are compared against the molecular dynamics and direct simulation Monte Carlo results available in the literature. With no tweaking of the equations in any way, we establish several fundamental aspects of OBurnett equations which other higher-order continuum theories like Burnett and Grad equations lack. In particular, evidence is put forward for smooth shock structures, the existence of heteroclinic trajectory, and positive entropy generation inside the shock at all Mach numbers. With respect to shock profiles of hydrodynamic variables, it is observed that OBurnett equations significantly improve upon the results of Navier-Stokes equations. Further comparison with regularized 13 (R13) equations at lower Mach numbers shows that OBurnett equations capture the more rarefied upstream part better than the R13 equations. These evidences suggest that the OBurnett equations are accurate and form a reliable set of higher-order transport equations. Further, it should now be possible to describe the complex structure of the shock wave correctly, even at a very large Mach number.

Semi-analytical methods for SP3 equations solver verification including third-order scattering anisotropy

Although diffusion theory is still the most widely applied deterministic method in reactor physics calculations, due to the increasing complexity of material composition and geometric structures in today's reactor design, and as a result of rapid development of computational technologies, neutronics codes based on higher-order transport approximations and advanced numerical approaches are becoming widespread. One promising alternative of diffusion theory is the simplified spherical harmonics (SPN) method. Since Gelbard heuristically proposed an approximate form of the multidimensional spherical harmonics equations, firm theoretical substantiation and – quite recently – generalization of the theory have been elaborated, thus several neutron physics code are being developed based on its application. In this paper, semi-analytical solutions of the steady-state, one-group SP3 equations are presented for homogeneous slab, cylindrical and spherical geometries assuming up to third-order scattering anisotropy. The developed methods are applied for preliminary verification of a finite-element-based SP3 solver developed by the authors.

Grad's Second Problem and Its Solution Within the Framework of Burnett Hydrodynamics

Abstract In his seminal work, Grad not only derived 13 moment equations but also suggested two problems to check his derived equations. These problems are highly instructive as they bring out the character of the equations by examining their solutions to these problems. In this work, we propose Grad's second problem as the potential benchmark problem for checking the accuracy of different sets of higher-order transport equations. The problem definition can be stated as: examination of steady-state solution for a gas at rest in infinite domain upon application of a one-dimensional heat flux. With gas at rest (no bulk velocity), the interest lies in obtaining the solution for pressure and temperature. The problem is particularly interesting with respect to the solution for pressure when Maxwell and hard-sphere molecules are considered. For Maxwell molecules, it is well known that the exact normal solution of Boltzmann equation gives uniform pressure with no stresses in the flow domain. In the case of hard-sphere molecules, direct simulation Monte Carlo (DSMC) results predict nonuniform pressure field giving rise to stresses in the flow domain. The simplistic nature of the problem and interesting results for pressure for different interaction potentials makes it an ideal test problem for examining the accuracy of higher-order transport equations. The proposed problem is solved within the framework of Burnett hydrodynamics for hard-sphere and Maxwell molecules. For hard-sphere molecules, it is observed that the Burnett order stresses do not become zero; they rather give rise to a pressure gradient in a direction opposite to that of temperature gradient, consistent with the DSMC results. For Maxwell molecules, the numerical solution of Burnett equations predicts uniform pressure field and one-dimensional temperature field, consistent with the exact normal solution of the Boltzmann equation.

Finite element solution of the time-dependent SP3 equations using an implicit integration scheme

Abstract A coupled thermal-hydraulics and reactor physics code system is being developed at the Institute of Nuclear Techniques of the Budapest University of Technology and Economics based on a higher-order transport approximation, the simplified spherical harmonics theory. The advantage of this method is that with a small increase in computational demand, it provides additional accuracy compared to diffusion theory. Besides - due to the fact that the multi-group SP3 and diffusion equations have a mathematically similar form - it requires minimal effort to implement an SP3 solution algorithm to an existing diffusion code. This paper focuses on an algorithm developed by the authors which applies Galerkin weighted residual method for spatial and theta method for time discretization. Results of two-group kinetic SP3 calculations performed with the SPNDYN code are also presented for various one-dimensional perturbations taking into account the delayed neutron precursor balance equations as well. The flexible nature of the SP3 equations makes the developed code a good starting point for more realistic dynamic calculations in the future.

(3+1)D Quasiparticle Anisotropic Hydrodynamics for Ultrarelativistic Heavy-Ion Collisions.

We present the first comparisons of experimental data with phenomenological results from (3+1)D quasiparticle anisotropic hydrodynamics (aHydroQP). We compare particle spectra, average transverse momentum, and elliptic flow. The dynamical equations used for the hydrodynamic stage utilize aHydroQP, which naturally includes both shear and bulk viscous effects. The (3+1)D aHydroQP evolution obtained is self-consistently converted to hadrons using anisotropic Cooper-Frye freeze-out. Hadron production and decays are modeled using a customized version of therminator 2. In this first study, we utilized smooth Glauber-type initial conditions and a single effective freeze-out temperature T_{FO}=130 MeV with all hadronic species in full chemical equilibrium. With this rather simple setup, we find a very good description of many heavy-ion observables.

Non-equilibrium of charged particles in swarms and plasmas—from binary collisions to plasma effects

In this article we show three quite different examples of low-temperature plasmas, where one can follow the connection of the elementary binary processes (occurring at the nanoscopic scale) to the macroscopic discharge behavior and to its application. The first example is on the nature of the higher-order transport coefficient (second-order diffusion or skewness); how it may be used to improve the modelling of plasmas and also on how it may be used to discern details of the relevant cross sections. A prerequisite for such modeling and use of transport data is that the hydrodynamic approximation is applicable. In the second example, we show the actual development of avalanches in a resistive plate chamber particle detector by conducting kinetic modelling (although it may also be achieved by using swarm data). The current and deposited charge waveforms may be predicted accurately showing temporal resolution, which allows us to optimize detectors by adjusting the gas mixture composition and external fields. Here kinetic modeling is necessary to establish high accuracy and the details of the physics that supports fluid models that allows us to follow the transition to streamers. Finally, we show an example of positron traps filled with gas that, for all practical purposes, are a weakly ionized gas akin to swarms, and may be modelled in that fashion. However, low pressures dictate the need to apply full kinetic modelling and use the energy distribution function to explain the kinetics of the system. In this way, it is possible to confirm a well established phenomenology, but in a manner that allows precise quantitative comparisons and description, and thus open doors to a possible optimization.

Near-field flow of submarines and ships advancing in a stable stratified fluid

A methodology is presented to predict density stratified flows in the near-field of naval vessels. The approach uses a single-phase level set method for the free surface, a dynamic overset technique to handle motions and controllers for self-propulsion and maneuvering. The density is solved with a higher-order transport equation coupled with momentum and mass conservation. Turbulence is implemented with a k−ε/k−ω based Delayed Detached Eddy Simulation (DDES) approach modified to add density gradients. Evaluation tests were performed for a two-dimensional square cavity, including grid and time step studies, and the stratified flow past a sphere, showing good agreement with available data. The stratified flow was studied for a self-propelled ship and a submarine. Density, velocity, pressure and turbulent quantities at the exit plane of the near-field contain a description of the relevant scales of the flow and can be used to compute the far-field stratified flow. It is shown that, as is the case of surface waves, the generation of internal waves requires energy that results in an increase in resistance. Moreover, the presence of a density interface against the hull results in a thickening of the boundary layer, just as in a solid/free surface juncture flow.

DYNAMICO-1.0, an icosahedral hydrostatic dynamical core designed for consistency and versatility

Abstract. The design of the icosahedral dynamical core DYNAMICO is presented. DYNAMICO solves the multi-layer rotating shallow-water equations, a compressible variant of the same equivalent to a discretization of the hydrostatic primitive equations in a Lagrangian vertical coordinate, and the primitive equations in a hybrid mass-based vertical coordinate. The common Hamiltonian structure of these sets of equations is exploited to formulate energy-conserving spatial discretizations in a unified way. The horizontal mesh is a quasi-uniform icosahedral C-grid obtained by subdivision of a regular icosahedron. Control volumes for mass, tracers and entropy/potential temperature are the hexagonal cells of the Voronoi mesh to avoid the fast numerical modes of the triangular C-grid. The horizontal discretization is that of Ringler et al. (2010), whose discrete quasi-Hamiltonian structure is identified. The prognostic variables are arranged vertically on a Lorenz grid with all thermodynamical variables collocated with mass. The vertical discretization is obtained from the three-dimensional Hamiltonian formulation. Tracers are transported using a second-order finite-volume scheme with slope limiting for positivity. Explicit Runge–Kutta time integration is used for dynamics, and forward-in-time integration with horizontal/vertical splitting is used for tracers. Most of the model code is common to the three sets of equations solved, making it easier to develop and validate each piece of the model separately. Representative three-dimensional test cases are run and analyzed, showing correctness of the model. The design permits to consider several extensions in the near future, from higher-order transport to more general dynamics, especially deep-atmosphere and non-hydrostatic equations.

ChemInform Abstract: Observing Magnetic Anisotropy in Electronic Transport Through Individual Single‐Molecule Magnets.

ChemInformVolume 46, Issue 23 Reviews ChemInform Abstract: Observing Magnetic Anisotropy in Electronic Transport Through Individual Single-Molecule Magnets. E. Burzuri, E. Burzuri Kavli Inst. Nanosci., Delft Univ. Technol., NL-2600 GA Delft, Neth.Search for more papers by this authorR. Gaudenzi, R. Gaudenzi Kavli Inst. Nanosci., Delft Univ. Technol., NL-2600 GA Delft, Neth.Search for more papers by this authorH. S. J. van der Zant, H. S. J. van der Zant Kavli Inst. Nanosci., Delft Univ. Technol., NL-2600 GA Delft, Neth.Search for more papers by this author E. Burzuri, E. Burzuri Kavli Inst. Nanosci., Delft Univ. Technol., NL-2600 GA Delft, Neth.Search for more papers by this authorR. Gaudenzi, R. Gaudenzi Kavli Inst. Nanosci., Delft Univ. Technol., NL-2600 GA Delft, Neth.Search for more papers by this authorH. S. J. van der Zant, H. S. J. van der Zant Kavli Inst. Nanosci., Delft Univ. Technol., NL-2600 GA Delft, Neth.Search for more papers by this author First published: 22 May 2015 https://doi.org/10.1002/chin.201523284AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume46, Issue23June, 2015 RelatedInformation