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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 649 records · Page 36
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

First-principles elucidation of the effects of Al-doping on Li-ion diffusion in LiCoO 2

Al-doped garnet Li 7 La 3 Zr 2 O 12 solid-electrolyte and LiCoO 2 cathode are promising choices as catholyte materials in all solid-state Li batteries, however, interdiffusion of Al is commonly evident during high-temperature processing and electrochemical cycling. Furthermore, to address the impact of Al interdiffusion on Li + transport properties in LiCoO 2 , we carried out a systematic evaluation of Al doping on Li + diffusion barriers in LiCoO 2 using first-principles based methods. Following the monovacancy diffusion mechanism, Al-doping (primarily at the Co site) is found to improve Li diffusion kinetics in the LiCoO 2 lattice due to favorable CoO 6 octahedral distortion experienced at the transition states. However, when considering the previously established dominant divacancy diffusion mechanism, slower Li diffusion is generally expected. In addition, a broad variation of Li diffusion barriers is observed upon Al doping, which suggests the system may suffer from non-uniform Li incorporation and diffusion that adversely affects its rate capacity during cycling. In summary, this work highlights, for the rational design of catholyte of all solid-state batteries, special attention may need to be paid to address the potential impact of non-intentional doping induced during processing on the overall electrochemical performance of the catholyte.

Al-doped LiCoO2↗
DOE OSTI2020

Selective One-Dimensional 13 C– 13 C Spin-Diffusion Solid-State Nuclear Magnetic Resonance Methods to Probe Spatial Arrangements in Biopolymers Including Plant Cell Walls, Peptides, and Spider Silk

Two-dimensional (2D) and 3D through-space 13 C– 13 C homonuclear spin-diffusion techniques are powerful solid-state nuclear magnetic resonance (NMR) tools for extracting structural information from 13 C-enriched biomolecules, but necessarily long acquisition times restrict their applications. In this work, we explore the broad utility and underutilized power of a chemical shift-selective one-dimensional (1D) version of a 2D 13 C– 13 C spin-diffusion solid-state NMR technique. The method, which is called 1D dipolar-assisted rotational resonance (DARR) difference, is applied to a variety of biomaterials including lignocellulosic plant cell walls, microcrystalline peptide fMLF, and black widow dragline spider silk. 1D 13 C– 13 C spin-diffusion methods described here apply in select cases in which the 1D 13 C solid-state NMR spectrum displays chemical shift-resolved moieties. Furthermore, this is analogous to the selective 1D nuclear Overhauser effect spectroscopy (NOESY) experiment utilized in liquid-state NMR as a faster (1D instead of 2D) and often less ambiguous (direct sampling of the time domain data, coupled with increased signal averaging) alternative to 2D NOESY. Selective 1D 13 C– 13 C spin-diffusion methods are more time-efficient than their 2D counterparts such as proton-driven spin diffusion (PDSD) and dipolar-assisted rotational resonance. The additional time gained enables measurements of 13 C– 13 C spin-diffusion buildup curves and extraction of spin-diffusion time constants TSD, yielding detailed structural information. Specifically, selective 1D DARR difference buildup curves applied to 13 C-enriched hybrid poplar woody stems confirm strong spatial interaction between lignin and acetylated xylan polymers within poplar plant secondary cell walls, and an interpolymer distance of ~0.45–0.5 nm was estimated. Additionally, Tyr/Gly long-range correlations were observed on isotopically enriched black widow spider dragline silks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Polymer Chain Diffusion in All-Polymer Nanocomposites: Confinement vs Chain Acceleration

All-polymer nanocomposites, in which soft, polymer-based nanoparticles are dispersed in the polymer matrix, have received great interest lately due to their potential use in a range of applications, including drug delivery and self-healing materials. However, the impact of this new class of nanoparticles on the dynamics of a linear polymer matrix in an all-polymer nanocomposite is still largely unknown. In this work, we report that the addition of polystyrene soft nanoparticles accelerates the diffusion of high molecular weight linear PS chains over a range of nanoparticle loadings. Our results show that at nanoparticle loadings below 1%, the diffusion of the linear matrix increases, presumably via a constraint release mechanism. At loadings above 1%, the increase in diffusion is mitigated by confinement effects of the nanoparticles. Thus, the response of these all-polymer nanocomposites is dominated by the balance of entropic confinement of the chain, which slows diffusion and a constraint release mechanism that speeds up the diffusion. However, the diffusion of the linear chain in the all-polymer nanocomposite is faster than that of the same chain in the melt at all loadings, diverging from the behavior of most nanocomposites with hard, impenetrable nanoparticles. Thus, the mechanism that accelerates the chain diffusion dominates in these systems. This behavior is unusual and fundamentally different than what has been reported for nanocomposites with hard inorganic nanoparticles, indicating that new perspectives are needed for these materials where the control of loading can either accelerate or decelerate the dynamics of the matrix in a distinctive manner.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Using Active Learning to Rapidly Develop Machine Learned Diffusion Coefficients of CO 2 Conversion Reagents in Metal–Organic Frameworks

Here, we used a combined molecular dynamics/active learning (AL) approach to create machine learning models that can predict the diffusion coefficient of epichlorohydrin and chloropropene carbonate, the reactant and product of a common CO 2 cycloaddition reaction, in metal–organic frameworks (MOFs). Nanoporous MOFs are effective catalysts for the cycloaddition of CO 2 to epoxides. The diffusion rates within nanoporous catalysts can control the rate of reaction as the reactants and products must diffuse to the active sites within the MOF and then out of the nanoporous material for reusability. However, the diffusion process is routinely ignored when searching for new materials in catalytic applications. Here we verified improvement during the AL process by consistently tracking metrics on the same groups of MOFs to ensure consistency. Metal identity was found to have little impact on diffusion rates, while structural features like pore limiting diameter act as a threshold where a minimum value is needed for high diffusion rates. We identified the MOFs with the highest epichlorohydrin and chloropropene carbonate diffusion coefficients which can be used for further studies of reaction energetics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Molecular dynamics simulations of hydrogen diffusion in aluminum

In this study, hydrogen diffusion impacts the performance of solid-state hydrogen storage materials and contributes to the embrittlement of structural materials under hydrogen-containing environments. In atomistic simulations, the diffusion energy barriers are usually calculated using molecular statics simulations where a nudged elastic band method is used to constrain a path connecting the two end points of an atomic jump. This approach requires prior knowledge of the “end points”. For alloy and defective systems, the number of possible atomic jumps with respect to local atomic configurations is tremendous. Even when these jumps can be exhaustively studied, it is still unclear how they can be combined to give an overall diffusion behavior seen in experiments. Here we describe the use of molecular dynamics simulations to determine the overall diffusion energy barrier from the Arrhenius equation. This method does not require information about atomic jumps, and it has additional advantages, such as the ability to incorporate finite temperature effects and to determine the pre-exponential factor. As a test case for a generic method, we focus on hydrogen diffusion in bulk aluminum. We find that the challenge of this method is the statistical variation of the results. However, highly converged energy barriers can be achieved by an appropriate set of temperatures, output time intervals (for tracking hydrogen positions), and a long total simulation time. Our results help elucidate the inconsistencies of the experimental diffusion data published in the literature. The robust approach developed here may also open up future molecular dynamics simulations to rapidly study diffusion properties of complex material systems in multidimensional spaces involving composition and defects.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Influences of Hydrogen Bonding-Based Stabilization of Bolaamphiphile Layers on Molecular Diffusion within Organic Nanotubes Having Inner Carboxyl Groups

This paper reports molecular diffusion behavior in two bolaamphiphile-based organic nanotubes having inner carboxyl groups with different inner dimeters (10 and 20 nm) and wall structures, COOH-ONT 10nm and COOH-ONT 20nm , using imaging fluorescence correlation spectroscopy (imaging FCS). Here, the results were compared to those previously obtained in a similar nanotube with inner amine groups (NH 2 -ONT 10nm ). COOH-ONT 10nm , as with NH 2 -ONT 10nm , were formed from a rolled bolaamphiphile layer incorporating triglycine moieties, whereas COOH-ONT 20nm consisted of four stacks of triglycine-free bolaamphiphile layers. Imaging FCS measurements were carried out for anionic sulforhodamine B (SRB), zwitterionic/cationic rhodamine B (RB) and cationic rhodamine-123 (R123) diffusing within ONTs (1–9 µm long) at different pH (3.4–8.4) and ionic strengths (1.6–500 mM). Diffusion coefficients (D) of these dyes in the ONTs were very small (0.01–0.1 µm 2 /s), reflecting the significant contributions of molecule-nanotube interactions to diffusion. The D of SRB was larger at higher pH and ionic strength, indicating the essential role of electrostatic repulsion that was enhanced by the deprotonation of the inner carboxyl groups. Importantly, the D of SRB was virtually independent of nanotube inner diameter and wall structure, indicating the diffusion of the hydrophilic molecule was controlled by short timescale adsorption/desorption processes onto the inner surface. In contrast, pH effects on D were less clear for relatively hydrophobic R123 and RB, suggesting the significant contributions of non-Coulombic interactions. Interestingly, the diffusion of these molecules in COOH-ONT 20nm was slower than in COOH-ONT 10nm . Slower diffusion in COOH-ONT20nm was attributable to relatively efficient partitioning of the hydrophobic dyes into the bolaamphiphile layers, which was reduced in COOH-ONT 10nm due to the stabilization of its layer by polyglycine-II-type hydrogen bonding networks. These results show that, by tuning the bolaamphiphile structures and their intermolecular interactions, unique environments can be created within the nanospaces for enhanced molecular separations and reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Simulations and Experiments Reveal Effect of Nanopores on Helium Diffusion in Quartz

The diffusion properties of noble gases in minerals are widely used to reconstruct the thermal histories of rocks. In this work, we combine density functional theory (DFT) calculations with laboratory experiments to investigate controls on helium diffusion in quartz. DFT calculations for perfect α-quartz predict substantially lower activation energies and frequency factors for helium diffusion than observed in laboratory experiments, especially in the [001] direction. These results imply that no helium could be retained in quartz at Earth surface temperatures, which conflicts with observations of partial cosmogenic 3 He retention over geologic time scales. Here, we implement a model of helium diffusion in α-quartz modulated by nanopore defects that disrupt energetically favorable diffusion pathways. In this model, we find that laboratory-determined diffusivities can be most closely reproduced when a helium atom encounters ~70 nanopore sites per million interstitial sites. The results of our model indicate that diffusion of helium in natural quartz, like other noble gases in other minerals, can be significantly modulated by extended defects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Modeling the Ionic Strength Effect on Diffusion in Clay. The DR-A Experiment at Mont Terri

Solute diffusion in compacted clays depends on ionic strength through its control on the thickness of the electrical double layer (EDL) on the charged clay surfaces. In the DR-A field experiment (Mont Terri, Switzerland), synthetic porewater was circulated through a borehole for 189 days, leading to the out-diffusion of a variety of tracers into the Opalinus Clay. The borehole solution was then replaced with a higher-salinity solution for an additional 540 days, leading to the diffusion of Cs + , Ca 2+ , Mg 2+ , and Sr 2+ back into the borehole and to an increase in the out-diffusion of anions (I - , Br - ) and 3 H. The experimental results were interpreted using the CrunchClay code, which includes a mean electrostatic potential model for the EDL. The EDL corresponds to a second continuum in addition to bulk electrically neutral porewater. Species-specific diffusion (Nernst-Planck equation) occurs through both domains. A 1D radial model considered a single pore diffusion coefficient (Dp = 10-9 m2/s) for cations and 3H in the bulk porosity, and a smaller D p (3 × 10 -10 m 2 /s) for anions. Dp values in the EDL were smaller (10 -11 m 2 /s), except for Cs + and K + (5 × 10 -10 and 2 × 10 -10 m 2 /s, respectively). The model reproduced well the experimental results and showed the capability to consider temporal changes in geochemical conditions affecting the transport and retention of potentially important radionuclide contaminants (e.g., 137 Cs + , 90 Sr 2+ , 129 I - ) in underground geological nuclear waste repositories. Finally, coupled multicomponent diffusion together with the electrostatic properties of the charged surfaces are essential in the development of predictive models for ion transport in clays.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Highly Effective GeNi Alloy Contact Diffusion Barrier for BiSbTe Long-Term Thermal Exposure

A GeNi alloy diffusion barrier for contacts on bismuth antimony telluride is proposed. Multiple gold contact diffusion barriers were tested at different thermal aging conditions in air and reducing atmospheres. Among all diffusion barriers, the GeNi alloy barrier shows the best performance for bulk samples with no substantial degradation of the contact resistance, no contact color change, and no change of thermoelectric properties. We observed D Au–GeNi = (9.8 ± 2.7) × 10 –20 m 2 /s within the GeNi alloy barrier, which is 4 times smaller than D Au–BiSbTe . The presence of the initial Ge layer also proves to be effective in reducing nickel diffusion yielding D Ni–BiSbTe = (8.57 ± 0.49) × 10 –19 m 2 /s. During GeNi alloy formation, Ge diffusion into BiSbTe produces GeTe, which apparently blocks the van der Waals gaps eliminating Au and Ni fast diffusion pathways. Thermal aging of BiSbTe nanowires shows that Au and Ni diffusion degrades the thermoelectric power factor, whereas the GeNi alloy barrier sample is mostly preserved. The GeNi alloy barrier is a reliable solution to long-term thermal applications of BiTe-based materials.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Fast Diffusion of Ultrarelativistic Electrons in the Outer Radiation Belt: 17 March 2015 Storm Event

Inward radial diffusion driven by ULF waves has long been known to be capable of accelerating radiation belt electrons to very high energies within the heart of the belts, but more recent work has shown that radial diffusion values can be highly event-specific, and mean values or empirical models may not capture the full significance of radial diffusion to acceleration events. Here we present an event of fast inward radial diffusion, occurring during a period following the geomagnetic storm of 17 March 2015. Ultrarelativistic electrons up to ~8 MeV are accelerated in the absence of intense higher-frequency plasma waves, indicating an acceleration event in the core of the outer belt driven primarily or entirely by ULF wave-driven diffusion. We examine this fast diffusion rate along with derived radial diffusion coefficients using particle and fields instruments on the Van Allen Probes spacecraft mission.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Reduction of phosphorus diffusion in germanium by fluorine implantation

The control of phosphorus (P) diffusion in germanium (Ge) is essential for the realisation of ultrashallow n-type junctions in Ge. This work reports a detailed study of the effect of fluorine (F) co-implantation on P diffusion in Ge. P and F profiles were characterized by secondary ion mass spectroscopy. The ion implantation damage was investigated using cross sectional transmission electron microscopy. It is shown that F co-implantation reduces the implanted P profile width and reduces both intrinsic and extrinsic P diffusion in Ge. A defect mediated mechanism for the strong influence of F co-implantation on P diffusion in Ge is proposed and invokes the formation of F{sub n}V{sub m} clusters in the F-amorphized Ge layer. A fraction of these F{sub n}V{sub m} clusters decorate the interstitial type end-of-range defects in the re-grown Ge layer and the rest react during re-growth with interstitial germanium atoms diffusing back from the amorphous crystalline interface. The Ge vacancies are then annihilated and mobile interstitial F is released and out diffuses from the surface. This results in a re-grown Ge layer which has a low vacancy concentration and in which the P diffusion rate is reduced. These results open the way to the realization of enhanced Ge n-type devices.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Tungsten diffusion in silicon

Two doses (10{sup 13} and 10{sup 15} cm{sup −2}) of tungsten (W) atoms were implanted in different Si(001) wafers in order to study W diffusion in Si. The samples were annealed or oxidized at temperatures between 776 and 960 °C. The diffusion profiles were measured by secondary ion mass spectrometry, and defect formation was studied by transmission electron microscopy and atom probe tomography. W is shown to reduce Si recrystallization after implantation and to exhibit, in the temperature range investigated, a solubility limit close to 0.15%–0.2%, which is higher than the solubility limit of usual metallic impurities in Si. W diffusion exhibits unusual linear diffusion profiles with a maximum concentration always located at the Si surface, slower kinetics than other metals in Si, and promotes vacancy accumulation close to the Si surface, with the formation of hollow cavities in the case of the higher W dose. In addition, Si self-interstitial injection during oxidation is shown to promote W-Si clustering. Taking into account these observations, a diffusion model based on the simultaneous diffusion of interstitial W atoms and W-Si atomic pairs is proposed since usual models used to model diffusion of metallic impurities and dopants in Si cannot reproduce experimental observations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Diffusion and spectroscopy of water and lipids in fully hydrated dimyristoylphosphatidylcholine bilayer membranes

Microscopic structure and dynamics of water and lipids in a fully hydrated dimyristoylphosphatidylcholine phospholipid lipid bilayer membrane in the liquid-crystalline phase have been analyzed with all-atom molecular dynamics simulations based on the recently parameterized CHARMM36 force field. The diffusive dynamics of the membrane lipids and of its hydration water, their reorientational motions as well as their corresponding spectral densities, related to the absorption of radiation, have been considered for the first time using the present force field. In addition, structural properties such as density and pressure profiles, a deuterium-order parameter, surface tension, and the extent of water penetration in the membrane have been analyzed. Molecular self-diffusion, reorientational motions, and spectral densities of atomic species reveal a variety of time scales playing a role in membrane dynamics. The mechanisms of lipid motion strongly depend on the time scale considered, from fast ballistic translation at the scale of picoseconds (effective diffusion coefficients of the order of 10{sup −5} cm{sup 2}/s) to diffusive flow of a few lipids forming nanodomains at the scale of hundreds of nanoseconds (diffusion coefficients of the order of 10{sup −8} cm{sup 2}/s). In the intermediate regime of sub-diffusion, collisions with nearest neighbors prevent the lipids to achieve full diffusion. Lipid reorientations along selected directions agree well with reported nuclear magnetic resonance data and indicate two different time scales, one about 1 ns and a second one in the range of 2–8 ns. We associated the two time scales of reorientational motions with angular distributions of selected vectors. Calculated spectral densities corresponding to lipid and water reveal an overall good qualitative agreement with Fourier transform infrared spectroscopy experiments. Our simulations indicate a blue-shift of the low frequency spectral bands of hydration water as a result of its interaction with lipids. We have thoroughly analyzed the physical meaning of all spectral features from lipid atomic sites and correlated them with experimental data. Our findings include a “wagging of the tails” frequency around 30 cm{sup −1}, which essentially corresponds to motions of the tail-group along the instantaneous plane formed by the two lipid tails, i.e., in-plane oscillations are clearly of bigger importance than those along the normal-to-the plane direction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Oxygen and nitrogen diffusion in α-hafnium from first principles

We use a combination of density functional theory and multistate diffusion formalism to analyze the diffusion of oxygen and nitrogen in technologically important hafnium metal. Comparing the local density approximation and the Perdew-Burke-Ernzerhof version of the generalized gradient approximation, we find that a better description of the hafnium lattice in the latter results in the correct sequence of stable and transition states for oxygen interstitials leading to essentially quantitative agreement with experiment. For oxygen diffusion, we find an isotropic temperature-dependent diffusion coefficient of D=0.082e{sup −2.04/k{sub B}T}cm{sup 2}s{sup −1} utilizing interstitial sites with hexahedral and octahedral coordination. For the diffusivity of nitrogen, we find that an additional stable interstitial site, the crowdion site, exists and that the diffusion coefficient is D=0.15e{sup −2.68/k{sub B}T}cm{sup 2}s{sup −1}. Our results also reproduce the experimental observation that nitrogen diffusivity is lower than that of oxygen in hafnium.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Density functional theory calculations of stability and diffusion mechanisms of impurity atoms in Ge crystals

Ge-based substrates are being developed for applications in advanced nano-electronic devices because of their higher intrinsic carrier mobility than Si. The stability and diffusion mechanism of impurity atoms in Ge are not well known in contrast to those of Si. Systematic studies of the stable sites of 2nd to 6th row element impurity atoms in Ge crystal were undertaken with density functional theory (DFT) and compared with those in Si crystal. It was found that most of the impurity atoms in Ge were stable at substitutional sites, while transition metals in Si were stable at interstitial sites and the other impurity atoms in Si were stable at substitutional sites. Furthermore, DFT calculations were carried out to clarify the mechanism responsible for the diffusion of impurity atoms in Ge crystals. The diffusion mechanism for 3d transition metals in Ge was found to be an interstitial-substitutional diffusion mechanism, while in Si this was an interstitial diffusion mechanism. The diffusion barriers in the proposed diffusion mechanisms in Ge and Si were quantitatively verified by comparing them to the experimental values in the literature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Computer simulation of grain boundary self-diffusion in aluminum

In the work study the process of self-diffusion in symmetric tilt grain boundaries (GB) with the axes misorientation [100], [110] and [111]. The research was carried out by the methods of computer simulation The objects of the research are the three GB of common and special type for each axis misorientation. The angles of misorientation of the common GB is amounted to 10°, 30° and 50°. The simulation was performed by the method of molecular dynamics in the temperature range from 600 to 1000 K, with an interval of 50 K. For research on the direction jumps atoms were built tracks the movement of atoms in the process of self-diffusion. The calculations have shown, that for all of GB is characterized by pronounced anisotropy of the jumps at low temperatures (< 700K). At temperatures near to the melting point directions of the jumps are isotropic only for three GB (Θ=30°[100], Θ=50=[100] and Σ5(013)[100]). For other GB such as [100] and [110] remains priority direction of diffusion along the nuclei GB dislocations. Arrenius curves have from one to three linear plots with different tilt. Change the tilt of Arrenius dependences testifies to the change in the mechanism of self-diffusion. The parameters of grainboundary self-diffusion were determined The activation energy of grainboundary diffusion in 4–5 times lower than the energy of activation of a volume self-diffusion of aluminum (about 200 KJ/mol). The minimum value of activation energy has GB 10° with the axis misorientation [100] (10,15 KJ/mol), maximum (104.12 Kj/mol) - a special GB Σ11(113)

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Accurate and absolute diffusion measurements of Rhodamine 6G in low-concentration aqueous solutions by the PGSE-WATERGATE sequence

A pulsed field gradient spin-echo nuclear magnetic resonance (NMR) sequence with solvent suppression (PGSE-WATERGATE) was applied to accurately measure the diffusion coefficients of Rhodamine 6G (Rh6G) in low-concentration aqueous solutions. Three samples with Rh6G concentrations of C{sub Rh6G} = 1, 4.5, and 25 μM were investigated. The precise determination of the diffusion coefficients in this low-concentration range was made possible by using a cryogenically cooled NMR probe and by the effective solvent suppression of the PGSE-WATERGATE sequence. The present results bridge the gap between diffusion data measured by fluorescence correlation spectroscopy in the single molecule limit and diffusivities obtained by pulsed field gradient NMR (PFG-NMR) without solvent suppression at higher concentrations. To further extend the concentration range, the diffusion coefficient of Rh6G was also measured on a sample with C{sub Rh6G} = 410 μM by PFG-NMR. The overall concentration dependence of the Rh6G diffusion at 25 °C is discussed in terms of dimerization of the Rh6G molecules. The concentration-dependent monomer/dimer proportion is deduced from the diffusion data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Submodels of model of nonlinear diffusion in the inhomogeneous medium involving absorption

We study the five-parameter model, describing the process of nonlinear diffusion in an inhomogeneous medium in the presence of absorption, for which the differential equation of the model admits a continuous Lie group of transformations, acting on the set of its solutions. We found six submodels of the original model of nonlinear diffusion, with different symmetry properties. Of these six submodels, the five submodels with transient absorption, for which the absorption coefficient depends on time according to a power law, represent the greatest interest with a mathematical point of view and with the point of view of physical applications. For each of these nonlinear submodels, we obtained formulas for producing new solutions that contain arbitrary constants, and we found all invariant submodels. All essentially distinct invariant solutions describing these invariant submodels are found in an explicit form or are reduced to finding the solution of nonlinear integral equations. The presence of the arbitrary constants in the integral equations that determine these solutions provide new opportunities for analytical and numerical study of boundary value problems for the received submodels and, thus, for the original model of nonlinear diffusion. For the received invariant submodels, we studied diffusion processes for which at the initial moment of the time at a fixed point is specified as a concentration and its gradient or as a concentration and its velocity. Solving of boundary value problems describing these processes is reduced to the solving of nonlinear integral equations. We established the existence and uniqueness of solutions of these boundary value problems under some additional conditions. The obtained results can be used to study the diffusion of substances, diffusion of conduction electrons and other particles, diffusion of physical fields and propagation of heat in inhomogeneous medium, and also to study a turbulence (Leith model, differential approximation to wave turbulence)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗