Design and Performance of Family of Diffusing Scrolls with Mixed-flow Impeller and Vaneless Diffuser
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Results for “Diffusion equations”
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Energetic particle transport in relativistic flows
A discussion is given of pitch angle dependent and diffusive transport equations for cosmic rays applicable for both special relativistic and general relativistic flows, derived from the relativistic Boltzmann equation. As an example of particle transport in a curved spacetime we give a pitch angle dependent transport equation appropriate for radial accretion onto a Schwarzschild black hole. The roles of fluid shear, acceleration and compression on the energy changes of particles in the diffusive transport equations are emphasized. Also discussed are special flows (e.g. rigidly rotating flows) associated with a Killing vector for which a constant of the motion of the particles can be identified, and for which simplified transport equations can be constructed.
Webb, G. M.↗
Transformed Fourier and Fick equations for the control of heat and mass diffusion
We review recent advances in the control of diffusion processes in thermodynamics and life sciences through geometric transforms in the Fourier and Fick equations, which govern heat and mass diffusion, respectively. We propose to further encompass transport properties in the transformed equations, whereby the temperature is governed by a three-dimensional, time-dependent, anisotropic heterogeneous convection-diffusion equation, which is a parabolic partial differential equation combining the diffusion equation and the advection equation. We perform two dimensional finite element computations for cloaks, concentrators and rotators of a complex shape in the transient regime. We precise that in contrast to invisibility cloaks for waves, the temperature (or mass concentration) inside a diffusion cloak crucially depends upon time, its distance from the source, and the diffusivity of the invisibility region. However, heat (or mass) diffusion outside cloaks, concentrators and rotators is unaffected by their presence, whatever their shape or position. Finally, we propose simplified designs of layered cylindrical and spherical diffusion cloaks that might foster experimental efforts in thermal and biochemical metamaterials.
36 MATERIALS SCIENCE↗
A simple Boltzmann transport equation for ballistic to diffusive transient heat transport
Developing simplified, but accurate, theoretical approaches to treat heat transport on all length and time scales is needed to further enable scientific insight and technology innovation. Using a simplified form of the Boltzmann transport equation (BTE), originally developed for electron transport, we demonstrate how ballistic phonon effects and finite-velocity propagation are easily and naturally captured. We show how this approach compares well to the phonon BTE, and readily handles a full phonon dispersion and energy-dependent mean-free-path. This study of transient heat transport shows (i) how fundamental temperature jumps at the contacts depend simply on the ballistic thermal resistance, (ii) that phonon transport at early times approach the ballistic limit in samples of any length, and (iii) perceived reductions in heat conduction, when ballistic effects are present, originate from reductions in temperature gradient. Importantly, this framework can be recast exactly as the Cattaneo and hyperbolic heat equations, and we discuss how the key to capturing ballistic heat effects is to use the correct physical boundary conditions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Integrated surface/subsurface permafrost thermal hydrology: Model formulation and proof-of-concept simulations
The need to understand potential climate impacts and feedbacks in Arctic regions has prompted recent interest in modeling of permafrost dynamics in a warming climate. A new fine-scale integrated surface/subsurface thermal hydrology modeling capability is described and demonstrated in proof-of-concept simulations. The new modeling capability combines a surface energy balance model with recently developed three-dimensional subsurface thermal hydrology models and new models for nonisothermal surface water flows and snow distribution in the microtopography. Surface water flows are modeled using the diffusion wave equation extended to include energy transport and phase change of ponded water. Variation of snow depth in the microtopography, physically the result of wind scour, is also modeled heuristically with a diffusion wave equation. The multiple surface and subsurface processes are implemented by leveraging highly parallel community software. Fully integrated thermal hydrology simulations on the tilted open book catchment, an important test case for integrated surface/subsurface flow modeling, are presented. Fine-scale 100-year projections of the integrated permafrost thermal hydrological system on an ice wedge polygon at Barrow Alaska in a warming climate are also presented. Finally, these simulations demonstrate the feasibility of microtopography-resolving, process-rich simulations as a tool to help understand possible future evolution of the carbon-rich Arctic tundra in a warming climate.
54 ENVIRONMENTAL SCIENCES↗
Viscosities, diffusion coefficients, and mixing times of intrinsic fluorescent organic molecules in brown limonene secondary organic aerosol and tests of the Stokes–Einstein equation
Viscosities and diffusion rates of organics within secondary organic aerosol (SOA) remain uncertain. Using the bead-mobility technique, we measured viscosities as a function of water activity ( a w ) of SOA generated by the ozonolysis of limonene followed by browning by exposure to NH 3 (referred to as brown limonene SOA or brown LSOA). These measurements together with viscosity measurements reported in the literature show that the viscosity of brown LSOA increases by 3–5 orders of magnitude as the a w decreases from 0.9 to approximately 0.05. In addition, we measured diffusion coefficients of intrinsic fluorescent organic molecules within brown LSOA matrices using rectangular area fluorescence recovery after photobleaching. Based on the diffusion measurements, as the a w decreases from 0.9 to 0.33, the average diffusion coefficient of the intrinsic fluorescent organic molecules decreases from 5.5 × 10 - 9 to 7.1 × 10 - 13 cm 2 s -1 and the mixing times of intrinsic fluorescent organic molecules within 200 nm brown LSOA particles increases from 0.002 to 14 s. These results suggest that the mixing times of large organics in the brown LSOA studied here are short ( < 1 h) for a w and temperatures often found in the planetary boundary layer (PBL). Since the diffusion coefficients and mixing times reported here correspond to SOA generated using a high mass loading ( ~1000 µ g m -3 ), biogenic SOA particles found in the atmosphere with mass loadings ≤10 µ g m -3 are likely to have higher viscosities and longer mixing times (possibly 3 orders of magnitude longer). These new measurements of viscosity and diffusion were used to test the accuracy of the Stokes–Einstein relation for predicting diffusion rates of organics within brown LSOA matrices. The results show that the Stokes–Einstein equation gives accurate predictions of diffusion coefficients of large organics within brown LSOA matrices when the viscosity of the matrix is as high as 10 2 to 10 4 Pa s. These results have important implications for predicting diffusion and mixing within SOA particles in the atmosphere.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium
The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
The diffusion approximation versus the telegraph equation for modeling solar energetic particle transport with adiabatic focusing. I. Isotropic pitch-angle scattering
The diffusion approximation to the Fokker-Planck equation is commonly used to model the transport of solar energetic particles in interplanetary space. In this study, we present exact analytical predictions of a higher order telegraph approximation for particle transport and compare them with the corresponding predictions of the diffusion approximation and numerical solutions of the full Fokker-Planck equation. We specifically investigate the role of the adiabatic focusing effect of a spatially varying magnetic field on an evolving particle distribution. Comparison of the analytical and numerical results shows that the telegraph approximation reproduces the particle intensity profiles much more accurately than does the diffusion approximation, especially when the focusing is strong. However, the telegraph approximation appears to offer no significant advantage over the diffusion approximation for calculating the particle anisotropy. The telegraph approximation can be a useful tool for describing both diffusive and wave-like aspects of the cosmic-ray transport.
79 ASTRONOMY AND ASTROPHYSICS↗
Numerical prediction of fiber orientation in injection-molded short-fiber/thermoplastic composite parts with experimental validation
Numerical prediction of the fiber orientation in the short-glass fiber (GF) reinforced polyamide 6 (PA6) composites with the fiber weight concentration of 30%, 50%, and 70% manufactured by the injection molding process is presented. And the fiber orientation was also directly observed and measured through X-ray computed tomography. During the injection molding process of the short-fiber/thermoplastic composite, the fiber orientation is produced by the flow states and the fiber-fiber interaction. Folgar and Tucker equation is the well known for modeling the fiber orientation in a concentrated suspension. They included into Jeffrey’s equation a diffusive type of term by introducing a phenomenological coefficient to account for the fiber-fiber interaction. Our developed model for the fiber-fiber interaction was proposed by modifying the rotary diffusion term of the Folgar-Tucker equation. This model was presented in a conference paper of the 29{sup th} International Conference of the Polymer Processing Society published by AIP conference proceeding. For modeling fiber interaction, the fiber dynamic simulation was introduced in order to obtain a global fiber interaction coefficient, which is sum function of the fiber concentration, aspect ratio, and angular velocity. The fiber orientation is predicted by using the proposed fiber interaction model incorporated into a computer aided engineering simulation package C-Mold. An experimental program has been carried out in which the fiber orientation distribution has been measured in 100 x 100 x 2 mm injection-molded plate and 100 x 80 x 2 mm injection-molded weld by analyzed with a high resolution 3D X-ray computed tomography system XVA-160α, and calculated by X-ray computed tomography imaging. The numerical prediction shows a good agreement with experimental validation. And the complex fiber orientation in the injection-molded weld was investigated.
42 ENGINEERING↗
Temperature Quenching and Fluorescence Depolarization of Carbon Nanodots Obtained via Paraffin Pyrolysis
A temperature effect on fluorescence intensity and polarization of a colloidal system of carbon nanodots in glycerol under linearly polarized pumping conditions is studied. Nanodots are obtained via pyrolysis of paraffin in nanopores of a mesoporous silica. An increase in temperature leads to quenching of nanodots fluorescence, and activation energy of the quenching process is assessed. An experimental relationship between the linear fluorescence polarization and temperature is described by the Levshin–Perrin equation, which takes into account the rotational diffusion of luminescent particles (fluorophores) in a liquid matrix. The size of fluorophores is noticeably smaller than that of carbon nanodots according to the Levshin–Perrin model. A difference between the dimensions of the fluorophore and the nanodot indicates that the small atomic groups responsible for luminescence of the nanodot possess high segmental mobility.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Particle acceleration and reconnection in the solar wind
An emerging paradigm for the dissipation of magnetic turbulence in the supersonic solar wind is via localized quasi-2D small-scale magnetic island reconnection processes. An advection-diffusion transport equation for a nearly isotropic particle distribution describes particle transport and energization in a region of interacting magnetic islands [1; 2]. The dominant charged particle energization processes are 1) the electric field induced by quasi-2D magnetic island merging, and 2) magnetic island contraction. The acceleration of charged particles in a “sea of magnetic islands” in a super-Alfvénic flow, and the energization of particles by combined diffusive shock acceleration (DSA) and downstream magnetic island reconnection processes are discussed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Chaotic dynamics and diffusion in a piecewise linear equation
Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Bremsstrahlung gamma rays from light dark matter
We discuss the often-neglected role of bremsstrahlung processes on the interstellar gas in computing indirect signatures of Dark Matter (DM) annihilation in the Galaxy, particularly for light DM candidates in the phenomenologically interesting O(10) GeV mass range. Especially from directions close to the Galactic Plane, the γ-ray spectrum is altered via two effects: directly, by the photons emitted in the bremsstrahlung process by energetic electrons which are among the DM annihilation byproducts; indirectly, by the modification of the same electron spectrum, due to the additional energy loss process in the diffusion-loss equation (e.g. the resulting inverse Compton emission is altered). We quantify the importance of the bremsstrahlung emission in the GeV energy range, showing that it is sometimes the dominant component of the γ-ray spectrum. We also find that, in regions in which bremsstrahlung dominates energy losses, the related γ-ray emission is only moderately sensitive to possible large variations in the gas density. Still, we stress that, for computing precise spectra in the (sub-)GeV range, it is important to obtain a reliable description of the Galaxy gas distribution as well as to compute self-consistently the γ-ray emission and the solution to the diffusion-loss equation. For example, these are crucial issues to quantify and interpret meaningfully γ-ray map 'residuals' in the inner Galaxy.
79 ASTRONOMY AND ASTROPHYSICS↗
Numerical Analysis of Liquid Metal MHD Flow and Heat Transfer for Open-Surface Li Divertor in FNSF
Within the ongoing U.S.-based program on the development of liquid metal plasma-facing components, numerical simulations and analyses are performed to address the feasibility of the open-surface Li divertor. In the previous scoping studies (Smolentsev, 2021), heat-removal capabilities of the divertor were assessed using a simplified flow model for a slug-type velocity profile and constant flow thickness. Here, new analyses take into account forces acting on the flowing Li layer. Three reduced-order mathematical models are applied under the conditions of the U.S. Fusion Nuclear Science Facility (FNSF) to access magnetohydrodynamic (MHD) flow development effects, velocity distribution, and surface waves: 1) fully developed MHD flow; 2) quasi-2-D developing MHD flow; and 3) multiphase MHD flow. The obtained results for MHD flows and the surface heat flux computed with the plasma code scrape-off layer plasma simulation for ITER (SOLPS-ITER) are then used as input data to compute the temperature distribution in the divertor by solving the convection–diffusion energy equation.
Smolentsev, Sergey↗
Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model
In this paper we present a time-parallel algorithm for the 3D neutrons calculation of a transient model in a nuclear reactor core. The neutrons calculation consists in numerically solving the time dependent diffusion approximation equation, which is a simplified transport equation. The numerical resolution is done with finite elements method based on a tetrahedral meshing of the computational domain, representing the reactor core, and time discretization is achieved using a θ-scheme. The transient model presents moving control rods during the time of the reaction. Therefore, cross-sections (piecewise constants) are taken into account by interpolations with respect to the velocity of the control rods. The parallelism across the time is achieved by an adequate use of the parareal in time algorithm to the handled problem. This parallel method is a predictor corrector scheme that iteratively combines the use of two kinds of numerical propagators, one coarse and one fine. Our method is made efficient by means of a coarse solver defined with large time step and fixed position control rods model, while the fine propagator is assumed to be a high order numerical approximation of the full model. The parallel implementation of our method provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch–Maurer–Werner benchmark.
97 MATHEMATICS AND COMPUTING↗
Development of a robust modeling tool for radiation-induced segregation in austenitic stainless steels
Irradiation-assisted stress corrosion cracking (IASCC) of austenitic stainless steels in Light Water Reactor (LWR) components has been linked to changes in grain boundary composition due to irradiation induced segregation (RIS). This work developed a robust RIS modeling tool to account for thermodynamics and kinetics of the atom and defect transportation under combined thermal and radiation conditions. The diffusion flux equations were based on the Perks model formulated through the linear theory of the thermodynamics of irreversible processes. Both cross and non-cross phenomenological diffusion coefficients in the flux equations were considered and correlated to tracer diffusion coefficients through Manning’s relation. The preferential atom-vacancy coupling was described by the mobility model, whereas the preferential atom-interstitial coupling was described by the interstitial binding model. The composition dependence of the thermodynamic factor was modeled using the CALPHAD approach. Detailed analysis on the diffusion fluxes near and at grain boundaries of irradiated austenitic stainless steels suggested the dominant diffusion mechanism for chromium and iron is via vacancy, while that for nickel can swing from the vacancy to the interstitial dominant mechanism. The diffusion flux in the vicinity of a grain boundary was found to be greatly influenced by the composition gradient formed from the transient state, leading to the oscillatory behavior of alloy compositions in this region. This work confirms that both vacancy and interstitial diffusion, and segregation itself, have important roles in determining the microchemistry of Fe, Cr, and Ni at irradiated grain boundaries in austenitic stainless steels.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Towards fully self-consistent optoelectronic simulation of planar devices
Photon recycling plays an important role in various optoelectronic devices, such as thin-film solar cells and intracavity double-diode structures presently studied for electroluminescent cooling. However, a complete description of photon recycling requires developing fully self-consistent simulation tools of photon and electronic charge transport in realistic device structures. In this paper, we describe a possible route towards such simulation tools in planar devices by combining the radiative transfer (RT) equation of photon transport with the drift-diffusion (DD) equations of electron and hole dynamics. We investigate the feasibility of the approach by selected proof-of-principle device studies. The results indicate that combining the RT and DD models not only yields the expected device characteristics, but also produces new insight into the pertinent local emission and absorption properties within the device structures. In particular, the model allows to accurately investigate how emission directivity and saturation affect the coupling coefficient in the double diode structures, showing that the main contribution to the coupling coefficient arises from the reflectivity of the top contact. For completeness, we also discuss how interference affects photon transport in resonant devices by an example calculation using the quantized fluctuational electrodynamics framework, paving way for self-consistent modeling tools that also account for wave-optical effects.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗