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At least 1,243 records · Page 69

Diffusion Blurring of GaAs Quantum Wells Grown at Low Temperature

The processes of the diffusion blurring of a periodic system of GaAs quantum wells separated by AlGaAs barriers are studied by photoluminescence spectroscopy. The system is grown by molecular-beam epitaxy at a low temperature (200°C) and additionally doped with Sb and P isovalent impurities. Postgrowth annealing at the temperature 750°C for 30 min induces an increase in the energy corresponding to the photoluminescence peak of the e1–hh1 exciton state in quantum wells because of blurring of the epitaxial GaAs/AlGaAs interfaces due to enhanced Al–Ga interdiffusion in the cation sublattice. For the Al concentration profile defined by linear diffusion into quantum wells, the Schrödinger equation for electrons and holes is solved. It is found that the experimentally observed energy position of the photoluminescence peak corresponds to the Al–Ga interdiffusion length 3.4 nm and to the effective diffusion coefficient 6.3 × 10{sup –17} cm{sup 2} s{sup –1} at the temperature 750°C. This value is found to be close to the corresponding value for GaAs quantum wells grown at low temperatures without additional doping with Sb and P impurities. From the results obtained in the study, it is possible to conclude that enhanced As–Sb and As–P interdiffusion in the anion sublattice only slightly influences the processes of Al–Ga interdiffusion in the cation sublattice.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Modeling and calculation of turbulent transport in free-shear flows

In this work the applicability of the combined bulk convection and gradient transport hypotheses for modeling turbulent diffusion is investigated. The resulting model equation, namely the one-equation model, is solved for free-shear flows by an implicit finite-difference method. Results indicate that significant improvements over previous models can be achieved with this new formulation of turbulent diffusion for both heat and momentum transport.

Biringen, S.↗

Mass loading and velocity diffusion models for heavy pickup ions at comet Grigg-Skjellerup

We compare model predictions of cometary water group ion densities and the solar wind slow down with measurements made by the Giotto Johnstone plasma analyzer implanted ion sensor at the encounter with comet Grigg-Skjellerup (G-S) on July 10, 1992. The observed slope of the ion density profile on approach to the comet is unexpectedly steep. Possible explanations for this are discussed. We present also a preliminary investigation of the quasilinear velocity-space diffusion of the implanted heavy ion population at G-S using a transport equation including souce, convection, adiabatic compression, and velocity diffusion terms. Resulting distributions are anisotropic, in agreement with observations. We consider theoretically the waves that may be generated by the diffusion process for the observed solar wind conditions. At initial ion injections, waves are generated at omega approximately Omega(sub i) the ion gyrofrequency, and lower frequencies are predicted for diffusion toward a bispherical shell.

Huddleston, D. E.↗

cDPD: A new dissipative particle dynamics method for modeling electrokinetic phenomena at the mesoscale

In this work, we develop a “charged” dissipative particle dynamics (cDPD) model for simulating mesoscopic electrokinetic phenomena governed by the stochastic Poisson-Nernst-Planck and the Navier-Stokes equations. In particular, the transport equations of ionic species are incorporated into the DPD framework by introducing extra degrees of freedom and corresponding evolution equations associated with each DPD particle. Diffusion of ionic species driven by the ionic concentration gradient, electrostatic potential gradient, and thermal fluctuations is captured accurately via pairwise fluxes between DPD particles. The electrostatic potential is obtained by solving the Poisson equation on the moving DPD particles iteratively at each time step. For charged surfaces in bounded systems, an effective boundary treatment methodology is developed for imposing both the correct hydrodynamic and electrokinetics boundary conditions in cDPD simulations. To validate the proposed cDPD model and the corresponding boundary conditions, we first study the electrostatic structure in the vicinity of a charged solid surface, i.e., we perform cDPD simulations of the electrostatic double layer and show that our results are in good agreement with the well-known mean-field theoretical solutions. Furthermore, we simulate the electrostatic structure and capacity densities between charged parallel plates in salt solutions with different salt concentrations. Moreover, we employ the proposed methodology to study the electro-osmotic and electro-osmotic/pressure-driven flows in a micro-channel. In the latter case, we simulate the dilute poly-electrolyte solution drifting by electro-osmotic flow in a micro-channel, hence demonstrating the flexibility and capability of this method in studying complex fluids with electrostatic interactions at the micro- and nano-scales.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Concurrent implicit spectral deferred correction scheme for low-Mach number combustion with detailed chemistry

We present a parallel multi-implicit time integration scheme for the advection-diffusion-reaction systems arising from the equations governing low-Mach number combustion with complex chemistry. Here, our strategy employs parallelisation across the method to accelerate the serial Multi-Implicit Spectral Deferred Correction (MISDC) scheme used to couple the advection, diffusion, and reaction processes. In our approach, the diffusion solves and the reaction solves are performed concurrently by different processors. Our analysis shows that the proposed parallel scheme is stable for stiff problems and that the sweeps converge to the fixed-point solution at a faster rate than with serial MISDC. We present numerical examples to demonstrate that the new algorithm is high-order accurate in time, and achieves a parallel speedup compared to serial MISDC.

97 MATHEMATICS AND COMPUTING↗

Combustion Of Moving Droplets And Of Droplets Suspended Within A Convective Environment: Transient Numerical Results

The problem considered is that of a single-component liquid fuel (n-heptane) droplet undergoing evaporation and combustion in a hot, convective, low pressure, zero-gravity environment of infinite expanse. For a moving droplet, the relative velocity (U(sub infinity)) between the droplet and freestream is subject to change due to the influence of the drag force on the droplet. For a suspended droplet, the relative velocity is kept constant. The governing equations for the gas-phase and the liquid-phase consist of the unsteady, axisymmetric equations of mass, momentum, species (gas-phase only) and energy conservation. Interfacial conservation equations are employed to couple the two phases. Variable properties are used in the gas- and liquid-phase. Multicomponent diffusion in the gas-phase is accounted for by solving the Stefan-Maxwell equations for the species diffusion velocities. A one-step overall reaction is used to model the combustion. The governing equations are discretized using the finite volume and SIMPLEC methods. A colocated grid is adopted. Hyperbolic tangent stretching functions are used to concentrate grid points near the fore and aft lines of symmetry and at the droplet surface in both the gas- and liquid-phase. The discretization equations are solved using the ADI method with the TDMA used on each line of the two alternating directions. Iterations are performed within each time-step until convergence is achieved. The grid spacing, size of the computational domain and time-step were tested to ensure that all solutions are independent of these parameters. A detailed discussion of the numerical model is given.

Gogos, George↗

Loss and Isotopic Fractionation of Alkali Elements during Diffusion-Limited Evaporation from Molten Silicate: Theory and Experiments

Moderately volatile elements (MVEs) are variably depleted in planetary bodies, reflecting the imprints of nebular and planetary processes. Among MVEs, Na, K, and Rb are excellent tracers for unraveling the history of MVE depletion in planetary bodies because they have similar geochemical behaviors but can be chemically fractionated by evaporation and condensation processes. Furthermore, K and Rb are amenable to high-precision isotopic analyses, which can help constrain the conditions of evaporation and condensation. To quantitatively understand why Na, K, and Rb are depleted in planetary bodies, we have carried out vacuum evaporation experiments from basaltic melt at 1200 and 1400 °C to study their evaporation kinetics and isotopic fractionations. We chose this composition because it is relevant to evaporation from small differentiated planetesimals. The Rb isotopic compositions of the evaporation residues were measured by multicollector inductively coupled plasma mass spectrometry (MC-ICPMS), and the K isotopic compositions were measured along profiles across the residues by secondary ion mass spectrometry (SIMS). In the 1400 °C run products, we found that the concentrations of both K and Rb in the run products decreased from core to rim, which was accompanied by a heavy K isotope enrichment near the surface. This indicates that, in this run, evaporation was limited by diffusion. To use those data quantitatively, we derive analytical equations that describe the evaporation rate and isotopic fractionation associated with diffusion-limited evaporation from a sphere, slab, and cylinder in transient and quasi-steady state regimes. This model is used to tease out the roles that diffusive transport in the melt and evaporation at the melt/gas interface play in setting the elemental depletion and isotopic composition of the residue. Under our experimental conditions, volatility decreases in the order of Na, Rb, and K. Using our experimental results in a thermodynamic model, we have estimated the product γΓ of activity coefficients × evaporation coefficients of Na, Rb, and K. The measured isotopic compositions of the residues are well explained using Rayleigh distillations, whereby the relative volatilities of K and Rb isotopes are given by the square root of their masses. We use our results and previously published data to predict how K and Rb could have been lost as a function of temperature, melt composition, oxygen fugacity, and saturation degree relevant to Vesta’s building blocks. We find that the K and Rb depletions, K/Rb elemental fractionation, and δ 41 K and δ 87 Rb isotopic fractionations of Vesta (as sampled by howardite-eucrite-diogenite (HED) meteorites) are best explained by evaporation of submillimeter size objects for 0.1-10 years at moderate temperatures (~1050 °C) in a medium ~98.8% saturated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On the generation of 'strong' magnetic fields

We rediscuss the nature of magnetic field generation in astrophysical systems. We show that as a result of ineffective three-dimensional turbulent diffusion in the presence of strong azimuthal magnetic fields, the standard dynamo equations are not likely to provide a reasonable description of magnetic dynamos in systems such as late-type stars and galaxies. Instead, we propose a new set of dynamo equations, which take into account the modifications of turbulent diffusion by strong magnetic fields.

Vainshtein, S. I.↗

Mathematical model and calculation algorithm of micro and meso levels of separation process of gaseous mixtures in molecular sieves

In the given article, the main thermodynamic aspects of the issue of modeling diffusion transfer in molecular sieves have been formulated. Dissipation function is used as a basic notion. The differential equation, connecting volume flow with the change of the concentration of catchable component has been derived. As a result, the expression for changing the concentration of the catchable component and the coefficient of membrane detecting has been received. As well, the system approach to describing the process of gases separation in ultra porous membranes has been realized and micro and meso-levels of mathematical modeling have been distinguished. The non-ideality of the shared system is primarily taken into consideration at the micro-level and the departure from the diffusion law of Fick has been taken into account. The calculation method of selectivity considering fractal structure of membranes has been developed at the meso level. The calculation algorithm and its software implementation have been suggested.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Simulations of neutron noise in the research reactor AKR-2: comparison between a discrete ordinates and a diffusion-based method

A diffusion-based and a discrete ordinates method are used to simulate a neutron noise experiment in the research reactor AKR-2 at the Technical University in Dresden, Germany. The AKR-2 reactor provides an interesting case for the comparison between the two methods because it is characterized by large heterogeneities and regions with low macroscopic neutron cross-sections. For the calculations, the same spatial discretization and the same set of two-energy macroscopic neutron cross-sections with isotropic scattering are used. Significant discrepancies between the diffusion-based and discrete ordinates methods are found in regions of the systems where the diffusion approximation is expected to be inaccurate in reproducing characteristics of the static neutron flux and neutron noise. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Equation-free and variable free modeling for complex/multiscale systems. Coarse-grained computation in science and engineering using fine-grained models

The work explored the linking of modern developing machine learning techniques (manifold learning and in particular diffusion maps) with traditional PDE modeling/discretization/scientific computation techniques via the equation-free methodology developed by the PI. The result (in addition to several PhD degrees, two of them by CSGF Fellows) was a sequence of strong developments - in part on the algorithmic side, linking data mining with scientific computing, and in part on applications, ranging from PDE discretizations to molecular dynamics and complex network dynamics.

97 MATHEMATICS AND COMPUTING↗

Mass Changes the Diffusion Coefficient of Particles with Ligand-Receptor Contacts in the Overdamped Limit

Inertia does not generally affect the long-time diffusion of passive overdamped particles in fluids. Yet a model starting from the Langevin equation predicts a surprising property of particles coated with ligands that bind reversibly to surface receptors: heavy particles diffuse more slowly than light ones of the same size. We show this by simulation and by deriving an analytic formula for the mass-dependent diffusion coefficient in the overdamped limit. We estimate the magnitude of this effect for a range of biophysical ligand-receptor systems, and find it is potentially observable for tailored micronscale DNA-coated colloids.

97 MATHEMATICS AND COMPUTING↗

Direct Measurement of Diffusion Coefficients: Evidence for Diffusive Stochastic Heating in Collisionless Plasmas

Open questions in collisionless plasma dissipation can be addressed using space-based observations in different astrophysical environments, with implications for both astrophysical and laboratory plasma systems. We study a low-𝛽, highly imbalanced, sub-Alfvénic stream observed by Parker Solar Probe (PSP) to identify and distinguish between signatures of stochastic heating (SH) and resonant heating (RH) by parallel ion cyclotron waves (∥-ICWs). Prior work studying this stream [Trevor A. Bowen et al., Stochastic heating in the sub-Alfvénic solar wind, Phys. Rev. Lett. 135, 255201 (2025)] showed that the SH rate, accounting for intermittency, matched the amplitude of the local energy transfer (LET) rate, while the RH rate did not. This comparison relied on a number of assumptions regarding the nature of the diffusive process and the calculation of the LET rate. We introduce a novel technique of inverting the proton guiding center equation to empirically measure velocity-space diffusion coefficients using three-dimensional proton velocity distribution functions, from the ion electrostatic analyzer (the Solar Probe Analyzer for Ions) on PSP. Measured diffusion coefficients are used to determine phase-space heating rates, leading to a calculation of a fully kinetic heating rate independent of assumptions made in prior work. We show that scale-dependent analytic expressions for SH via noncoherent fluctuations match the empirical measurements from PSP data, provided that we account for intermittency in the heating calculation. In contrast, the derived heating rates for SH that accounts for the effects of the helicity barrier and heating rates for RH via ∥-ICWs do not peak in the same region of velocity space as the empirical measurements, nor do they reach the required magnitude. Our approach provides novel methodology to uniquely identify and constrain heating processes in collisionless plasmas and shows evidence of a Fokker-Planck-like diffusive process in the near-Sun solar wind.

Plasma kinetic theory↗

Numerical analysis and FORTRAN program for the computation of the turbulent wakes of turbomachinery rotor blades, isolated airfoils and cascade of airfoils

Turbulent wakes of turbomachinery rotor blades, isolated airfoils, and a cascade of airfoils were investigated both numerically and experimentally. Low subsonic and incompressible wake flows were examined. A finite difference procedure was employed in the numerical analysis utilizing the continuity, momentum, and turbulence closure equations in the rotating, curvilinear, and nonorthogonal coordinate system. A nonorthogonal curvilinear coordinate system was developed to improve the accuracy and efficiency of the numerical calculation. Three turbulence models were employed to obtain closure of the governing equations. The first model was comprised to transport equations for the turbulent kinetic energy and the rate of energy dissipation, and the second and third models were comprised of equations for the rate of turbulent kinetic energy dissipation and Reynolds stresses, respectively. The second model handles the convection and diffusion terms in the Reynolds stress transport equation collectively, while the third model handles them individually. The numerical results demonstrate that the second and third models provide accurate predictions, but the computer time and memory storage can be considerably saved with the second model.

Hah, C.↗

($\mathrm{INVITED}$)Counter-ion effect on the diffusion behavior of $\mathrm{Y}$b, $\mathrm{L}$u, and $\mathrm{N}$d ions in $\mathrm{YAG}$ transparent ceramics

The ability to fabricate additively manufactured laser waveguides with sharp dopant concentration interfaces is limited by diffusion of the dopants at the temperatures required to fully densify the material. Compositional analysis of bilayer samples, where each layer was either undoped YAG or YAG doped with Yb, Lu, or Nd, were fabricated such that all combinations were available for testing. Samples were fabricated at both 1750°C and 1850°C to determine the diffusion behavior of each dopant alone and also in the presence of a second dopant. It was found that the experimental concentration profiles exhibited both intragranular (bulk) and grain boundary contributions, and thus fitting to a complementary error function equation required the use of two diffusion coefficients. Nd always diffused further along grain boundaries than the other dopants, due in part to its small segregation coefficient in YAG. It is shown that the presence of Nd as a counter dopant inhibits intragranular diffusion of other dopants while enhancing their grain boundary diffusion. All the observed trends were attributed to a combination of intragranular lattice strain due to: dopant ions replacing yttrium substitutionally, the relative driving forces for the segregation of dopant ions to grain boundaries, and the ability of one dopant to affect the diffusion of a different dopant in the other direction to maintain charge neutrality.

36 MATERIALS SCIENCE↗

Dynamical derivation of momentum diffusion coefficients at collisions of relativistic charged particles

An expression has been obtained for the diffusion tensor of particles in the momentum space on the basis of the dynamics of particles motion. The general equations have been used to determine the rms momentum spread at collisions of relativistic charged particles at times shorter than the time of randomization of particles motion and at greater times when motion is completely random.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Comments on the reconnexion rate of magnetic fields.

The reconnection rate of magnetic fields is crucial in understanding the fields found in turbulent flows in the solar photosphere and in the galaxy, and in flare phenomena. The behavior of magnetic fields in the neighborhood of an X-type neutral point is examined. The treatment is kinematic specifying the velocity field v and constructing solutions to the hydromagnetic equation for B. The calculations demonstrate that the reconnection rate is controlled by the diffusion in the near neighborhood of the neutral point, and is not arbitrarily large, as has been suggested by similarity solutions of the complete field and fluid equations for vanishing diffusion.

Parker, E. N.↗