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DOE OSTI2015

The bispectrum of matter perturbations from cosmic strings

We present the first calculation of the bispectrum of the matter perturbations induced by cosmic strings. The calculation is performed in two different ways: the first uses the unequal time correlators (UETCs) of the string network - computed using a Gaussian model previously employed for cosmic string power spectra. The second approach uses the wake model, where string density perturbations are concentrated in sheet-like structures whose surface density grows with time. The qualitative and quantitative agreement of the two gives confidence to the results. An essential ingredient in the UETC approach is the inclusion of compensation factors in the integration with the Green's function of the matter and radiation fluids, and we show that these compensation factors must be included in the wake model also. We also present a comparison of the UETCs computed in the Gaussian model, and those computed in the unconnected segment model (USM) used by the standard cosmic string perturbation package CMBACT. We compare numerical estimates for the bispectrum of cosmic strings to those produced by perturbations from an inflationary era, and discover that, despite the intrinsically non-Gaussian nature of string-induced perturbations, the matter bispectrum is unlikely to produce competitive constraints on a population of cosmic strings.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1987

Sorption compressor/mechanical expander hybrid refrigeration

Experience with Deep Space Network (DSN) ground-based cryogenic refrigerators has proved the reliability of the basic two-stage Gifford-McMahon helium refrigerator. A very long life cryogenic refrigeration system appears possible by combining this expansion system or a turbo expansion system with a hydride sorption compressor in place of the usual motor driven piston compressor. To test the feasibility of this system, a commercial Gifford-McMahon refrigerator was tested using hydrogen gas as the working fluid. Although no attempt was made to optimize the system for hydrogen operation, the refrigerator developed 1.3 W at 30 K and 6.6 W at 60 K. The results of the test and of theoretical performances of the hybrid compressor coupled to these expansion systems are presented.

Jones, J. A.↗

DOE OSTI2025

Flow-Driven Stretch Fluctuations Govern the Nonlinear Viscoelasticity of Elongating Associative Polymer Networks

We use nonequilibrium molecular dynamics simulations to verify recent tube-model predictions that associative polymer networks exhibit broad stretch fluctuations during elongational flow. Simulations further show that these fluctuating dynamics give rise to the rate-dependent extensional viscosity 𝜂 𝐸 measured in filament stretching experiments on H-bonding networks. Simulations model bivalent associative networks with a reactive bead-spring model for varying association strength and extensional strain rate. We observe that stretch fluctuations are driven by a new form of chain tumbling, where chains continually collapse and elongate as their associations break and reform within the advecting network. This produces a broad, nearly uniform distribution of chain stretch over a wide range of strain rates, manifesting as a rate-independent plateau in the extensional stress. Our results show that the nonlinear viscoelasticity of associative networks is dominated by large fluctuations in molecular response, which cannot be captured by current mean-field models.

biomimetic & bio-inspired materials↗

DOE OSTI2017

A numerical manifold method model for analyzing fully coupled hydro-mechanical processes in porous rock masses with discrete fractures

A numerical manifold method (NMM) model was developed for fully coupled analysis of hydro-mechanical (HM) processes in porous rock masses with discrete fractures. Using an NMM two-cover-mesh system of mathematical and physical covers, fractures are conveniently discretized by dividing the mathematical cover along fracture traces to physical cover, resulting in a discontinuous model on a non-conforming mesh. In this model, discrete fracture deformation (e.g. open and slip) and fracture fluid flow within a permeable and deformable porous rock matrix are rigorously considered. For porous rock, direct pore-volume coupling was modeled based on an energy-work scheme. For mechanical analysis of fractures, a fracture constitutive model for mechanically open states was introduced. For fluid flow in fractures, both along-fracture and normal-to-fracture fluid flow are modeled without introducing additional degrees of freedom. When the mechanical aperture of a fracture is changing, its hydraulic aperture and hydraulic conductivity is updated. At the same time, under the effect of coupled deformation and fluid flow, the contact state may dynamically change, and the corresponding contact constraint is updated each time step. Therefore, indirect coupling is realized under stringent considerations of coupled HM effects and fracture constitutive behavior transfer dynamically. To verify the new model, examples involving deformable porous media containing a single and two sets of fractures were designed, showing good accuracy. Finally, the model was applied to analyze coupled HM behavior of fractured porous rock domains with complex fracture networks under effects of loading and injection.

58 GEOSCIENCES↗

DOE OSTI2018

Chemical controls on the propagation rate of fracture in calcite

Calcite (CaCO 3 ) is one of the most abundant minerals in the Earth’s crust, and it is susceptible to subcritical chemically-driven fracturing. Understanding chemical processes at individual fracture tips, and how they control the development of fractures and fracture networks in the subsurface, is critical for carbon and nuclear waste storage, resource extraction, and predicting earthquakes. Chemical processes controlling subcritical fracture in calcite are poorly understood. We demonstrate a novel approach to quantify the coupled chemical-mechanical effects on subcritical fracture. The calcite surface was indented using a Vickers-geometry indenter tip, which resulted in repeatable micron-scale fractures propagating from the indent. Individual indented samples were submerged in an array of aqueous fluids and an optical microscope was used to track the fracture growth in situ. The fracture propagation rate varied from 1.6 × 10 -8 m s -1 to 2.4 × 10 -10 m s -1 . The rate depended on the type of aqueous ligand present, and did not correlate with the measured dissolution rate of calcite or trends in zeta-potential. We postulate that chemical complexation at the fracture tip in calcite controls the growth of subcritical fracture. Previous studies indirectly pointed to the zeta-potential being the most critical factor, while our work indicates that variation in the zeta-potential has a secondary effect.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Numerical analysis of soot emissions from gasoline-ethanol and gasoline-butanol blends under gasoline compression ignition conditions

In the present work, computational fluid dynamics (CFD) simulations of a single-cylinder gasoline compression ignition (GCI) engine were performed to investigate the impact of blending two biofuels, ethanol and n-butanol, with gasoline on the trade-off between combustion phasing and soot emissions under low load conditions. Here, in order to represent market gasoline (RD5-87), a four-component toluene primary reference fuel (TPRF) + ethanol (ETPRF) surrogate (with 20% ethanol by mole; E20) was formulated using a neural network based octane predictor such that the surrogate had the same ethanol content, Research Octane Number (RON) and Octane Sensitivity (S). In addition, a novel skeletal kinetic mechanism for ETPRF and TPRF + n-butanol (BTPRF) blends, incorporating polycyclic aromatic hydrocarbon (PAH) chemistry, was developed. A three-dimensional (3D) engine CFD formulation employing the skeletal mechanism, adaptive mesh refinement (AMR), finite-rate chemistry approach, and hybrid method of moments (HMOM) was adopted to capture the in-cylinder combustion phenomena and soot emissions. The engine CFD model was validated against RD5-87 experimental data for a broad range of start-of-injection (SOI) timings (-21/-27/-36/-45 crank angle degrees (CAD) after top-dead center (aTDC)), with respect to in-cylinder pressure, heat release rate, combustion phasing, and soot emissions. The closed-cycle simulation results were analyzed to elucidate the non-monotonic trend of soot emissions versus SOI timing: SOI-36 > SOI-45 > SOI-21 > SOI-27. Thereafter, the validated CFD model was employed to simulate the combustion of a gasoline-ethanol blend with 45% (by mole) ethanol (E45) and a gasoline-butanol blend with 45% (by mole) n-butanol (B45) under the same operating conditions to study the effects of fuel composition and SOI timing on combustion phasing and soot emissions. The sooting propensity followed the trend: B45 > E20 > E45 at all SOI timings. Overall, it was observed that the autoignition propensity was primarily related to fuel chemistry. On the other hand, sooting propensity showed strong coupling with both fuel chemistry and physical properties, with greater impact of fuel physical properties at advanced SOI timings.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2016

AREA 2: Novel Materials for Robust Repair of Leaky Wellbores in CO 2 Storage Formations

The potential leakage of hydrocarbon fluids or CO 2 out of subsurface formations through wells with fractured cement or debonded microannuli is a primary concern in oil and gas production and CO 2 storage. The presence of fractures in a cement annulus with apertures on the order of 10–300 microns can pose a significant leakage danger with effective permeability in the range of 0.1–1 mD (millidarcy). Leakage pathways with small apertures are often difficult to repair using conventional oilfield cement, thus a low-viscosity sealant that can be easily placed into these fractures while providing an effective seal is desired. The development of a novel application using pH-triggered polymeric sealants could potentially be the solution to plugging these fractures and that was the research aim of this study. The application is based on the transport and reaction of a low-pH poly(acrylic acid) polymer through fractures in strongly alkaline cement. The pH-sensitive microgels viscosify upon neutralization with cement to become highly swollen gels with substantial yield stress that can block fluid flow. Experiments in a cement fracture determined the effects of the viscosification and gel deposition via real-time visual observation and measurements of pressure gradient and effluent pH. While the pH-triggered gelling mechanism and rheology measurements of the neutralized polymer gel show promising results, the polymer solution in contact with cement undergoes an undesirable reaction known as polymer syneresis. Syneresis is caused by the release of calcium cation from cement that collapses the polymer network. Syneresis produces an unstable calcium-precipitation byproduct that is detrimental to the strength and stability of the gel in place. As a result, gel-sealed leakage pathways that subjected to various degrees of syneresis often failed to hold back pressures. Several chemicals were studied to inhibit polymer syneresis and tested for pretreatment of cement cores to remove calcium and prevent syneresis during polymer placement. A chelating agent, sodium triphosphate (Na 5 P 3 O 10 ), was found to successfully eliminate syneresis without compromising the injectivity of polymer solution during placement. Polymer gel strength is determined by recording the maximum holdback pressure gradients during liquid breakthrough tests after various periods of pretreatment and polymer shut-in time. Cores pretreated with Na 5 P 3 O 10 successfully held up to an average of 80 psi/ft, which is significantly greater than the expected threshold value of about 0.1-5 psi/ft required to prevent flow in a typical CO 2 leakage scenario. The use of such inexpensive, pH-triggered poly-acrylic acid polymer allows long-term robust seal of leaky wellbores under high pH conditions.

01 COAL, LIGNITE, AND PEAT↗

NASA NTRS2014

Combinatorial Multidomain Mesoporous Chips and a Method for Fractionation, Stabilization, and Storage of Biomolecules

A new fractionation device shows desirable features for exploratory screening and biomarker discovery. The constituent MSCs may be tailored for desired pore sizes and surface properties and for the sequestration and enrichment of extremely low abundant protein and peptides in desired ranges of the mass/charge spectrum. The MSCs are effective in yielding reproducible extracts from complex biological samples as small as 10 microliter in a time as short as 30 minutes. They are inexpensive to manufacture, and allow for scaled up production to attain the simultaneous processing of a large number of samples. The MSCs are multiplexed, label-free diagnostic tools with the potential of biological recognition moiety modification for enhanced specificity. The MSCs may store, protect and stabilize biological fluids, enabling the simplified and cost-effective collection and transportation of clinical samples. The MSC-based device may serve as a diagnostic tool to complement histopathology, imaging, and other conventional clinical techniques. The MSCs mediated identification of disease-specific protein signatures may help in the selection of personalized therapeutic combinations, in the real-time assessment of therapeutic efficacy and toxicity, and in the rational modulation of therapy based on the changes in the protein networks associated with the prognosis and the drug resistance of the disease.

Ferrari, Mauro↗

NASA NTRS1990

Advanced systems engineering and network planning support

The objective of this task was to take a fresh look at the NASA Space Network Control (SNC) element for the Advanced Tracking and Data Relay Satellite System (ATDRSS) such that it can be made more efficient and responsive to the user by introducing new concepts and technologies appropriate for the 1997 timeframe. In particular, it was desired to investigate the technologies and concepts employed in similar systems that may be applicable to the SNC. The recommendations resulting from this study include resource partitioning, on-line access to subsets of the SN schedule, fluid scheduling, increased use of demand access on the MA service, automating Inter-System Control functions using monitor by exception, increase automation for distributed data management and distributed work management, viewing SN operational control in terms of the OSI Management framework, and the introduction of automated interface management.

Walters, David H.↗

NASA NTRS2000

Efficient Use of Distributed Systems for Scientific Applications

Distributed computing has been regarded as the future of high performance computing. Nationwide high speed networks such as vBNS are becoming widely available to interconnect high-speed computers, virtual environments, scientific instruments and large data sets. One of the major issues to be addressed with distributed systems is the development of computational tools that facilitate the efficient execution of parallel applications on such systems. These tools must exploit the heterogeneous resources (networks and compute nodes) in distributed systems. This paper presents a tool, called PART, which addresses this issue for mesh partitioning. PART takes advantage of the following heterogeneous system features: (1) processor speed; (2) number of processors; (3) local network performance; and (4) wide area network performance. Further, different finite element applications under consideration may have different computational complexities, different communication patterns, and different element types, which also must be taken into consideration when partitioning. PART uses parallel simulated annealing to partition the domain, taking into consideration network and processor heterogeneity. The results of using PART for an explicit finite element application executing on two IBM SPs (located at Argonne National Laboratory and the San Diego Supercomputer Center) indicate an increase in efficiency by up to 36% as compared to METIS, a widely used mesh partitioning tool. The input to METIS was modified to take into consideration heterogeneous processor performance; METIS does not take into consideration heterogeneous networks. The execution times for these applications were reduced by up to 30% as compared to METIS. These results are given in Figure 1 for four irregular meshes with number of elements ranging from 30,269 elements for the Barth5 mesh to 11,451 elements for the Barth4 mesh. Future work with PART entails using the tool with an integrated application requiring distributed systems. In particular this application, illustrated in the document entails an integration of finite element and fluid dynamic simulations to address the cooling of turbine blades of a gas turbine engine design. It is not uncommon to encounter high-temperature, film-cooled turbine airfoils with 1,000,000s of degrees of freedom. This results because of the complexity of the various components of the airfoils, requiring fine-grain meshing for accuracy. Additional information is contained in the original.

Taylor, Valerie↗

NASA NTRS2017

Numerical Modeling of an Integrated Vehicle Fluids System Loop for Pressurizing a Cryogenic Tank

This paper presents a numerical model of the pressurization loop of the Integrated Vehicle Fluids (IVF) system using the Generalized Fluid System Simulation Program (GFSSP). The IVF propulsion system, being developed by United Launch Alliance to reduce system weight and enhance reliability, uses boiloff propellants to drive thrusters for the reaction control system as well as to run internal combustion engines to develop power and drive compressors to pressurize propellant tanks. NASA Marshall Space Flight Center (MSFC) conducted tests to verify the functioning of the IVF system using a flight-like tank. GFSSP, a finite volume based flow network analysis software developed at MSFC, has been used to support the test program. This paper presents the simulation of three different test series, comparison of numerical prediction and test data and a novel method of presenting data in a dimensionless form. The paper also presents a methodology of implementing a compressor map in a system level code.

LeClair, A. C.↗

NASA NTRS1993

A concurrent hybrid Navier-Stokes/Euler approach to fluid dynamic computations

We present a methodology for the numerical simulation of flow fields by the simultaneous application of two distinct approaches to computational aerodynamics. We compute the three dimensional flow field of a missile at moderate angle of attack by dividing the flow field into two regions: a region near the surface where we use a structured grid and a Navier Stokes solver, and a region farther away from the surface where we utilize an unstructured grid and an Euler solver. The two solvers execute as independent UNIX processes either on the same machine or on two machines. The solvers communicate data across their common interfaces within the same machine or over the network. The computations indicate that extensively separated flow fields can be computed without significant distortion by combining viscous and inviscid solvers.

Tavella, Domingo A.↗

DOE OSTI2019

Experimental and Theoretical Investigation of the Ion Conduction Mechanism of Tris(adiponitrile)perchloratosodium, a Self-Binding, Melt-Castable Crystalline Sodium Electrolyte

Sodium perchlorate (NaClO4) crystallizes with adiponitrile (ADN) as a 1:3 solvate to produce (ADN) 3 NaClO 4 , a solid electrolyte for sodium ion conduction. The solid possesses high thermal stability (up to 150 °C) and the ability to be melt-cast (T m = 81 °C). The pressed solid has a high ionic conductivity of 2.2 × 10 –4 S cm –1 at room temperature with a low activation barrier for ion conduction of 22 kJ mol –1 . The high conductivity is the result of low-affinity ion-conduction channels in the bulk based on the X-ray crystal structure, and by low grain-boundary resistance and possibly a grain-boundary percolating network due to a fluidlike nanoliquid layer between the grains, observable by scanning electron microscopy and differential scanning calorimetry. When the liquid nanolayer is rinsed away or removed by excessive drying, the bulk room temperature ionic conductivity is 4 × 10 –5 S cm –1 , activation energy for ionic conduction for an organic solid is 37 kJ mol –1 , and the sodium ion transference number is 0.71. Scanning electron microscopy and classical molecular dynamics simulations suggest that these cocrystals form a fluid layer of ADN at the surface, which facilitates the Na+ ion migration between the grains. Finally, density functional theory calculations are consistent with the possibility of ion conduction via a solvent–anion coordinated transition state through vacancy defects in the three symmetry-equivalent ion channels along separate directions, suggesting the possibility of ionic conductivity in three dimensions.

25 ENERGY STORAGE↗

DOE OSTI2018

Synthesis and Characterisation of Caesium Phosphomolybdate and Zirconium Molybdate found in the Highly Active Storage Tanks at Sellafield - 18154

Caesium phosphomolybdate (Cs{sub 3}PMo{sub 12}O{sub 40}.xH{sub 2}O, CPM) and zirconium molybdate (ZrMo{sub 2}O{sub 7}(OH){sub 2}.xH{sub 2}O, ZM) are two known fission products that precipitate out within the Highly Active Storage Tanks (HASTs) at Sellafield, potentially causing 'hot-spots' and blocking pipes. Currently, there is not enough behavioural understanding of these compounds present in the Highly Active Liquor (HAL) for effective Post Operational Clean Out (POCO) strategic planning. As the HASTs do not have an in situ monitoring system the behaviour of the HAL cannot be directly observed. Therefore, as with this research, non-radioactive simulants can be utilised to aid behavioural understanding to assist with the planning of future waste management programs. CPM, along with two different morphologies of ZM were characterised and compared to the common oxide particle material titanium dioxide (TiO{sub 2}). The study provides a detailed physical characterisation of the simulants including: particle shape, particle size, water content and crystal structure, along with zeta particle potential, suspension settling and compressive yield stress. CPM was found to be spheroidal in nature with a particle size of 275 nm and an x value of 13 H{sub 2}O which crystallises as a cubic lattice with space group Pn-3m. ZM was found to have a range of morphologies from cuboidal to wheat-sheaf, varying in size from 10 μm to 20 μm, with an x value of between 3 and 4 H{sub 2}O, which crystallise as a body-centred tetragonal lattice with space group I4{sub 1cd}. TiO{sub 2} used as a comparison simulant was found to be spheroidal in shape with particle size of 725 nm. The isoelectric points (IEPs) of the two ZM samples (ZM-A and ZM-B) with different morphologies were found to be pH 2.5, while for TiO{sub 2} it was pH 3.2. For CPM it could not be confidently identified due to its instability within the acidic environment. The settling rates and compressive yield stress of all simulants were tested in both water and 2 M nitric acid, conditions that replicate the HASTs. TiO{sub 2}, ZM-A and ZM-B all found settled faster in acid than in water. For CPM, slightly faster settling in acid was measured. For all samples it was found that as the particle concentration increased the settling rate decreased, which is a result of hindered settling. For compressive yield stress, similar trends were observed for CPM with little variation in its behaviour in acid and water, suggesting that the particles are highly aggregated in both fluids. For ZM samples little change in equilibrium volume fraction was measured with an increase in pressure (both acid and water). However, overall the sediment bed was denser in water, a result of the rapid settling in acid not allowing the non-spherical particles to pack in an ordered manner. It has been highlighted that both CPM and ZM within the acidic conditions of the HASTs, result in unstable and aggregated compounds, which settle quickly to form large open networks. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2019

A novel targeted plugging and fracture‐adaptable gel used as a diverting agent in fracturing

Abstract Diverting agents that could plug a targeted location and fill different shapes of fractures have attracted an increasing attention in the field of fracturing. In this study, a series of novel diverting agents were prepared by mixing aldehyde sodium alginate (ASA) and amino gelatin (AG) through a Schiff base reaction to form a primary network, polylactic acid (PLA) fibers were added to produce a 3D network, and Ca 2+ was mixed in as an ionic cross‐linking agent to strengthen the cross‐linking points. It was found that gelation time, swelling behavior, and mechanical performance could be controlled by varying the content of aldehyde groups and amino groups. Gelation time could be controlled in 1‐10 minutes. Plugging behavior and degradation tests demonstrated that the hydrogel could suit fractures with various shapes and plug effectively under high temperatures and pressures, and it could eventually become acidic fluid to help clean the wellbore. This novel ASA/AG/PLA hydrogel constitutes a promising environmentally friendly diverting agent in the application of diversion fracturing.

Zhang, Yuyuan↗

DOE OSTI2012

Characterization of mechanical behavior of an epithelial monolayer in response to epidermal growth factor stimulation

Cell signaling often causes changes in cellular mechanical properties. Knowledge of such changes can ultimately lead to insight into the complex network of cell signaling. In the current study, we employed a combination of atomic force microscopy (AFM) and quartz crystal microbalance with dissipation monitoring (QCM-D) to characterize the mechanical behavior of A431 cells in response to epidermal growth factor receptor (EGFR) signaling. From AFM, which probes the upper portion of an individual cell in a monolayer of cells, we observed increases in energy dissipation, Young's modulus, and hysteresivity. Increases in hysteresivity imply a shift toward a more fluid-like mechanical ordering state in the bodies of the cells. From QCM-D, which probes the basal area of the monolayer of cells collectively, we observed decreases in energy dissipation factor. This result suggests a shift toward a more solid-like state in the basal areas of the cells. The comparative analysis of these results indicates a regionally specific mechanical behavior of the cell in response to EGFR signaling and suggests a correlation between the time-dependent mechanical responses and the dynamic process of EGFR signaling. This study also demonstrates that a combination of AFM and QCM-D is able to provide a more complete and refined mechanical profile of the cells during cell signaling. -- Highlights: Black-Right-Pointing-Pointer The EGF-induced cellular mechanical response is regionally specific. Black-Right-Pointing-Pointer The EGF-induced cellular mechanical response is time and dose dependent. Black-Right-Pointing-Pointer A combination of AFM and QCM-D provides a more complete mechanical profile of cells.

60 APPLIED LIFE SCIENCES↗

NASA NTRS2004

NASA Tech Briefs, March 2004

Topics covered include: 1) Advanced Signal Conditioners for Data-Acquisition Systems; 2) Downlink Data Multiplexer; 3) Viewing ISS Data in Real Time via the Internet; 4) Autonomous Environment-Monitoring Networks; 5) Readout of DSN Monitor Data; 6) Parallel-Processing Equalizers for Multi-Gbps Communications; 7) AIN-Based Packaging for SiC High-Temperature Electronics; 8) Software for Optimizing Quality Assurance of Other Software; 9) The TechSat 21 Autonomous Sciencecraft Experiment; 10) Software for Analyzing Laminar-to-Turbulent Flow Transitions; 11) Elastomer Filled With Single-Wall Carbon Nanotubes; 12) Modifying Ship Air-Wake Vortices for Aircraft Operations; 13) Strain-Gauge Measurement of Weight of Fluid in a Tank; 14) Advanced Docking System With Magnetic Initial Capture; 15) Blade-Pitch Control for Quieting Tilt-Rotor Aircraft; 16) Solar Array Panels With Dust-Removal Capability; 17) Aligning Arrays of Lenses and Single-Mode Optical Fibers; 18) Automatic Control of Arc Process for Making Carbon Nanotubes; 19) Curved-Focal-Plane Arrays Using Deformed-Membrane Photodetectors; 20) Role of Meteorology in Flights of a Solar-Powered Airplane; 21) Model of Mixing Layer With Multicomponent Evaporating Drops; 22) Solution-Assisted Optical Contacting; 23) Improved Discrete Approximation of Laplacian of Gaussian; 24) Utilizing Expert Knowledge in Estimating Future STS Costs; 25) Study of Rapid-Regression Liquefying Hybrid Rocket Fuels; and 26) More About the Phase-Synchronized Enhancement Method.

Source record↗

NASA NTRS1986

Group-kinetic theory of turbulence

The two phases are governed by two coupled systems of Navier-Stokes equations. The couplings are nonlinear. These equations describe the microdynamical state of turbulence, and are transformed into a master equation. By scaling, a kinetic hierarchy is generated in the form of groups, representing the spectral evolution, the diffusivity and the relaxation. The loss of memory in formulating the relaxation yields the closure. The network of sub-distributions that participates in the relaxation is simulated by a self-consistent porous medium, so that the average effect on the diffusivity is to make it approach equilibrium. The kinetic equation of turbulence is derived. The method of moments reverts it to the continuum. The equation of spectral evolution is obtained and the transport properties are calculated. In inertia turbulence, the Kolmogoroff law for weak coupling and the spectrum for the strong coupling are found. As the fluid analog, the nonlinear Schrodinger equation has a driving force in the form of emission of solitons by velocity fluctuations, and is used to describe the microdynamical state of turbulence. In order for the emission together with the modulation to participate in the transport processes, the non-homogeneous Schrodinger equation is transformed into a homogeneous master equation. By group-scaling, the master equation is decomposed into a system of transport equations, replacing the Bogoliubov system of equations of many-particle distributions. It is in the relaxation that the memory is lost when the ensemble of higher-order distributions is simulated by an effective porous medium. The closure is thus found. The kinetic equation is derived and transformed into the equation of spectral flow.

Tchen, C. M.↗