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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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All sources NASA NTRS DOE OSTI

DOE OSTI2020

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy–cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe–Salpeter methods, second-order Møller–Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE’s functionality, including excited-state methods, RPA and Green’s function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE’s current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE’s development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1992

Buckling of stiffened shells with random initial imperfections, thickness and boundary conditions

The paper proposes a method to predict the buckling load of stiffened, composite shells reliably, where besides the randomness of the initial geometric imperfections also a random variation of the wall thickness and the uncertainty of the precise edge conditions is included in the analysis. The introduction of the variability in the thickness from shell to shell, in an ensemble of nominally identical shells, produced by the same manufacturing procedure is motivated by the growing realization of the importance of thickness variations by composite shells. The probabilistic treatment of the boundary conditions is dictated by the fact that 'true', deterministically specified boundary conditions are unlikely to be realizable in practice.

Elishakoff, I.↗

DOE OSTI2015

Complex-energy approach to sum rules within nuclear density functional theory

The linear response of the nucleus to an external field contains unique information about the effective interaction, correlations governing the behavior of the many-body system, and properties of its excited states. To characterize the response, it is useful to use its energy-weighted moments, or sum rules. By comparing computed sum rules with experimental values, the information content of the response can be utilized in the optimization process of the nuclear Hamiltonian or nuclear energy density functional (EDF). But the additional information comes at a price: compared to the ground state, computation of excited states is more demanding. To establish an efficient framework to compute energy-weighted sum rules of the response that is adaptable to the optimization of the nuclear EDF and large-scale surveys of collective strength, we have developed a new technique within the complex-energy finite-amplitude method (FAM) based on the quasiparticle random- phase approximation. The proposed sum-rule technique based on the complex-energy FAM is a tool of choice when optimizing effective interactions or energy functionals. The method is very efficient and well-adaptable to parallel computing. As a result, the FAM formulation is especially useful when standard theorems based on commutation relations involving the nuclear Hamiltonian and external field cannot be used.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1980

Feasibility of quasi-random band model in evaluating atmospheric radiance

The use of the quasi-random band model in evaluating upwelling atmospheric radiation is investigated. The spectral transmittance and total band adsorptance are evaluated for selected molecular bands by using the line by line model, quasi-random band model, exponential sum fit method, and empirical correlations, and these are compared with the available experimental results. The atmospheric transmittance and upwelling radiance were calculated by using the line by line and quasi random band models and were compared with the results of an existing program called LOWTRAN. The results obtained by the exponential sum fit and empirical relations were not in good agreement with experimental results and their use cannot be justified for atmospheric studies. The line by line model was found to be the best model for atmospheric applications, but it is not practical because of high computational costs. The results of the quasi random band model compare well with the line by line and experimental results. The use of the quasi random band model is recommended for evaluation of the atmospheric radiation.

Tiwari, S. N.↗

NASA NTRS1991

Probabilistic fracture finite elements

The Probabilistic Fracture Mechanics (PFM) is a promising method for estimating the fatigue life and inspection cycles for mechanical and structural components. The Probability Finite Element Method (PFEM), which is based on second moment analysis, has proved to be a promising, practical approach to handle problems with uncertainties. As the PFEM provides a powerful computational tool to determine first and second moment of random parameters, the second moment reliability method can be easily combined with PFEM to obtain measures of the reliability of the structural system. The method is also being applied to fatigue crack growth. Uncertainties in the material properties of advanced materials such as polycrystalline alloys, ceramics, and composites are commonly observed from experimental tests. This is mainly attributed to intrinsic microcracks, which are randomly distributed as a result of the applied load and the residual stress.

Liu, W. K.↗

DOE OSTI2012

Packing microstructure and local density variations of experimental and computational pebble beds

In pebble bed type nuclear reactors the fuel is contained in graphite pebbles, which form a randomly stacked bed with a non-uniform packing density. These variations can influence local coolant flow and power density and are a possible cause of hotspots. To analyse local density variations computational methods are needed that can generate randomly stacked pebble beds with a realistic packing structure on a pebble-to-pebble level. We first compare various properties of the local packing structure of a computed bed with those of an image made using computer aided X-ray tomography, looking at properties in the bulk of the bed and near the wall separately. Especially for the bulk of the bed, properties of the computed bed show good comparison with the scanned bed and with literature, giving confidence our method generates beds with realistic packing microstructure. Results also show the packing structure is different near the wall than in the bulk of the bed, with pebbles near the wall forming ordered layers similar to hexagonal close packing. Next, variations in the local packing density are investigated by comparing probability density functions of the packing fraction of small clusters of pebbles throughout the bed. Especially near the wall large variations in local packing fractions exists, with a higher probability for both clusters of pebbles with low (<0.6) and high (>0.65) packing fraction, which could significantly affect flow rates and, together with higher power densities, could result in hotspots. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2017

Comparative effectiveness of coronary CT angiography vs stress cardiac imaging in patients following hospital admission for chest pain work-up: The Prospective First Evaluation in Chest Pain (PERFECT) Trial

Background: Because the frequency of cardiac event rates is low among chest pain patients following either performance of coronary CT angiography (CCTA) or stress testing, there is a need to better assess how these tests influence the central management decisions that follow from cardiac testing. The present study was performed to assess the relative impact of CCTA vs stress testing on medical therapies and downstream resource utilization among patients admitted for the work-up of chest pain. Methods: The admitted patients were randomized in a 1:1 ratio to either cardiac imaging stress test or CCTA. Primary outcomes were time to discharge, change in medication usage, and frequency of downstream testing, cardiac interventions, and cardiovascular re-hospitalizations. We randomized 411 patients, 205 to stress testing, and 206 to CCTA. Results: There were no differences in time to discharge or initiation of new cardiac medications at discharge. At 1 year follow-up, there was no difference in the number of patients who underwent cardiovascular downstream tests in the CCTA vs stress test patients (21% vs 15%, P = .1) or cardiovascular hospitalizations (14% vs 16%, P = .5). However, there was a higher frequency of invasive angiography in the CCTA group (11% vs 2%, P = .001) and percutaneous coronary interventions (6% vs 0%, P < .001). Conclusions: Randomization of hospitalized patients admitted for chest pain work-up to either CCTA or to stress testing resulted in similar discharge times, change in medical therapies at discharge, frequency of downstream noninvasive testing, and repeat hospitalizations. However, a higher frequency of invasive coronary angiography and revascularization procedures were performed in the CCTA arm. (ClinicalTrials.gov number, NCT01604655.)

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2024

Machine learning in materials research: Developments over the last decade and challenges for the future

The number of studies that apply machine learning (ML) to materials science has been growing at a rate of approximately 1.67 times per year over the past decade. In this review, I examine this growth in various contexts. First, I present an analysis of the most commonly used tools (software, databases, materials science methods, and ML methods) used within papers that apply ML to materials science. The analysis demonstrates that despite the growth of deep learning techniques, the use of classical machine learning is still dominant as a whole. It also demonstrates how new research can effectively build upon past research, particular in the domain of ML models trained on density functional theory calculation data. Next, I present the progression of best scores as a function of time on the matbench materials science benchmark for formation enthalpy prediction. In particular, a dramatic improvement of 7 times reduction in error is obtained when progressing from feature-based methods that use conventional ML (random forest, support vector regression, etc.) to the use of graph neural network techniques. Finally, I provide views on future challenges and opportunities, focusing on data size and complexity, extrapolation, interpretation, access, and relevance.

36 MATERIALS SCIENCE↗

DOE OSTI2011

Volumetric-Modulated Arc Therapy for Stereotactic Body Radiotherapy of Lung Tumors: A Comparison With Intensity-Modulated Radiotherapy Techniques

Purpose: To demonstrate the potential of volumetric-modulated arc therapy (VMAT) compared with intensity-modulated radiotherapy (IMRT) techniques with a limited number of segments for stereotactic body radiotherapy (SBRT) for early-stage lung cancer. Methods and Materials: For a random selection of 27 patients eligible for SBRT, coplanar and noncoplanar IMRT and coplanar VMAT (using SmartArc) treatment plans were generated in Pinnacle{sup 3} and compared. In addition, film measurements were performed using an anthropomorphic phantom to evaluate the skin dose for the different treatment techniques. Results: Using VMAT, the delivery times could be reduced to an average of 6.6 min compared with 23.7 min with noncoplanar IMRT. The mean dose to the healthy lung was 4.1 Gy for VMAT and noncoplanar IMRT and 4.2 Gy for coplanar IMRT. The volume of healthy lung receiving >5 Gy and >20 Gy was 18.0% and 5.4% for VMAT, 18.5% and 5.0% for noncoplanar IMRT, and 19.4% and 5.7% for coplanar IMRT, respectively. The dose conformity at 100% and 50% of the prescribed dose of 54 Gy was 1.13 and 5.17 for VMAT, 1.11 and 4.80 for noncoplanar IMRT and 1.12 and 5.31 for coplanar IMRT, respectively. The measured skin doses were comparable for VMAT and noncoplanar IMRT and slightly greater for coplanar IMRT. Conclusions: Coplanar VMAT for SBRT for early-stage lung cancer achieved plan quality and skin dose levels comparable to those using noncoplanar IMRT and slightly better than those with coplanar IMRT. In addition, the delivery time could be reduced by {<=}70% with VMAT.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2013

Toward Fully Automated Multicriterial Plan Generation: A Prospective Clinical Study

Purpose: To prospectively compare plans generated with iCycle, an in-house-developed algorithm for fully automated multicriterial intensity modulated radiation therapy (IMRT) beam profile and beam orientation optimization, with plans manually generated by dosimetrists using the clinical treatment planning system. Methods and Materials: For 20 randomly selected head-and-neck cancer patients with various tumor locations (of whom 13 received sequential boost treatments), we offered the treating physician the choice between an automatically generated iCycle plan and a manually optimized plan using standard clinical procedures. Although iCycle used a fixed “wish list” with hard constraints and prioritized objectives, the dosimetrists manually selected the beam configuration and fine tuned the constraints and objectives for each IMRT plan. Dosimetrists were not informed in advance whether a competing iCycle plan was made. The 2 plans were simultaneously presented to the physician, who then selected the plan to be used for treatment. For the patient group, differences in planning target volume coverage and sparing of critical tissues were quantified. Results: In 32 of 33 plan comparisons, the physician selected the iCycle plan for treatment. This highly consistent preference for the automatically generated plans was mainly caused by the improved sparing for the large majority of critical structures. With iCycle, the normal tissue complication probabilities for the parotid and submandibular glands were reduced by 2.4% ± 4.9% (maximum, 18.5%, P=.001) and 6.5% ± 8.3% (maximum, 27%, P=.005), respectively. The reduction in the mean oral cavity dose was 2.8 ± 2.8 Gy (maximum, 8.1 Gy, P=.005). For the swallowing muscles, the esophagus and larynx, the mean dose reduction was 3.3 ± 1.1 Gy (maximum, 9.2 Gy, P<.001). For 15 of the 20 patients, target coverage was also improved. Conclusions: In 97% of cases, automatically generated plans were selected for treatment because of the superior quality. Apart from the improved plan quality, automatic plan generation is economically attractive because of the reduced workload.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2013

Is There a Dose-Response Relationship for Heart Disease With Low-Dose Radiation Therapy?

Purpose: To quantify cardiac radiation therapy (RT) exposure using sensitive measures of cardiac dysfunction; and to correlate dysfunction with heart doses, in the setting of adjuvant RT for left-sided breast cancer. Methods and Materials: On a randomized trial, 32 women with node-positive left-sided breast cancer underwent pre-RT stress single photon emission computed tomography (SPECT-CT) myocardial perfusion scans. Patients received RT to the breast/chest wall and regional lymph nodes to doses of 50 to 52.2 Gy. Repeat SPECT-CT scans were performed 1 year after RT. Perfusion defects (PD), summed stress defects scores (SSS), and ejection fractions (EF) were evaluated. Doses to the heart and coronary arteries were quantified. Results: The mean difference in pre- and post-RT PD was −0.38% ± 3.20% (P=.68), with no clinically significant defects. To assess for subclinical effects, PD were also examined using a 1.5-SD below the normal mean threshold, with a mean difference of 2.53% ± 12.57% (P=.38). The mean differences in SSS and EF before and after RT were 0.78% ± 2.50% (P=.08) and 1.75% ± 7.29% (P=.39), respectively. The average heart Dmean and D95 were 2.82 Gy (range, 1.11-6.06 Gy) and 0.90 Gy (range, 0.13-2.17 Gy), respectively. The average Dmean and D95 to the left anterior descending artery were 7.22 Gy (range, 2.58-18.05 Gy) and 3.22 Gy (range, 1.23-6.86 Gy), respectively. No correlations were found between cardiac doses and changes in PD, SSS, and EF. Conclusions: Using sensitive measures of cardiac function, no clinically significant defects were found after RT, with the average heart Dmean <5 Gy. Although a dose response may exist for measures of cardiac dysfunction at higher doses, no correlation was found in the present study for low doses delivered to cardiac structures and perfusion, SSS, or EF.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2013

Effects of Respiratory Motion on Passively Scattered Proton Therapy Versus Intensity Modulated Photon Therapy for Stage III Lung Cancer: Are Proton Plans More Sensitive to Breathing Motion?

Purpose: To quantify and compare the effects of respiratory motion on paired passively scattered proton therapy (PSPT) and intensity modulated photon therapy (IMRT) plans; and to establish the relationship between the magnitude of tumor motion and the respiratory-induced dose difference for both modalities. Methods and Materials: In a randomized clinical trial comparing PSPT and IMRT, radiation therapy plans have been designed according to common planning protocols. Four-dimensional (4D) dose was computed for PSPT and IMRT plans for a patient cohort with respiratory motion ranging from 3 to 17 mm. Image registration and dose accumulation were performed using grayscale-based deformable image registration algorithms. The dose–volume histogram (DVH) differences (4D-3D [3D = 3-dimensional]) were compared for PSPT and IMRT. Changes in 4D-3D dose were correlated to the magnitude of tumor respiratory motion. Results: The average 4D-3D dose to 95% of the internal target volume was close to zero, with 19 of 20 patients within 1% of prescribed dose for both modalities. The mean 4D-3D between the 2 modalities was not statistically significant (P<.05) for all dose–volume histogram indices (mean ± SD) except the lung V5 (PSPT: +1.1% ± 0.9%; IMRT: +0.4% ± 1.2%) and maximum cord dose (PSPT: +1.5 ± 2.9 Gy; IMRT: 0.0 ± 0.2 Gy). Changes in 4D-3D dose were correlated to tumor motion for only 2 indices: dose to 95% planning target volume, and heterogeneity index. Conclusions: With our current margin formalisms, target coverage was maintained in the presence of respiratory motion up to 17 mm for both PSPT and IMRT. Only 2 of 11 4D-3D indices (lung V5 and spinal cord maximum) were statistically distinguishable between PSPT and IMRT, contrary to the notion that proton therapy will be more susceptible to respiratory motion. Because of the lack of strong correlations with 4D-3D dose differences in PSPT and IMRT, the extent of tumor motion was not an adequate predictor of potential dosimetric error caused by breathing motion.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2014

Perceptions of Radiation Oncologists and Urologists on Sources and Type of Evidence to Inform Prostate Cancer Treatment Decisions

Purpose: To perform a national survey of radiation oncologists and urologists about the type of resources used and the level of evidence needed to change clinical practice in localized prostate cancer. Methods and Materials: From a random sample, 1422 physicians were mailed a survey assessing the types of information used and what level of evidence could alter their clinical practice in prostate cancer. Multivariable logistic regression models were used to identify differences in physician characteristics for each outcome. Results: Survey response rates were similar for radiation oncologists and urologists (44% vs 46%; P=.46). Specialty-specific journals represented the most commonly used resource for informing the clinical practice for radiation oncologists (65%) and urologists (70%). Relative to radiation oncologists, urologists were less likely to report utilizing top-tier medical journals (25% vs 39%; adjusted odds ratio [OR] 0.50; P=.01) or cancer journals (22% vs 51%; adjusted OR 0.50; P<.001) but more likely to rely on clinical guidelines (46% vs 38%; adjusted OR 1.6; P=.006). Both radiation oncologists and urologists most commonly reported large randomized, clinical trials as the level of evidence to change treatment recommendations for localized prostate cancer (85% vs 77%; P=.009). Conclusions: Both specialties rely on their own specialty-specific journals and view randomized, clinical trials as the level of evidence needed to change clinical practice. Our study provides a context on meaningful ways of disseminating evidence for localized prostate cancer.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2015

Double-Blind, Placebo-Controlled Pilot Study of Processed Ultra Emu Oil Versus Placebo in the Prevention of Radiation Dermatitis

Purpose: The purpose of this single-institution pilot study was to evaluate the feasibility and safety of an oil-based skin agent, Ultra Emu Oil, on skin-related toxicity in patients undergoing radiation therapy to the breast or chest wall. Methods and Materials: Patients were randomized 2:1 in a double-blind fashion and were instructed to apply processed Ultra Emu Oil or placebo (cottonseed oil) twice daily during the course of radiation therapy. The oils were applied before the third fraction and continued for 6 weeks after completion of treatment. The primary endpoint was the area under the curve (AUC) of Skindex-16 scale scores over time. Secondary outcomes included maximum grade of radiation dermatitis using the Common Terminology Criteria (CTC) for Adverse Events (CTCAE 3.0), the Skin Toxicity Assessment Tool, quality of life (QOL) measured by Linear Analogue Self-Assessment, and a symptom experience diary (SED). Results: In all, 42 of 45 patients completed the study and were evaluable. The median times to peak rash, skin redness, peeling, and skin swelling were weeks 6, 6, 7, and 7, respectively as measured by the SED. The Skindex AUC scores tended to be lower in emu oil patients than in placebo patients (mean total AUC 7.2 vs 10.4, respectively). This trend was also seen in all the Skindex subdomains. The overall QOL was slightly better in the emu oil group but remained stable throughout the study for both arms. Peak CTC toxicity occurred at week 6. Patients using emu oil appeared slightly worse on maximum CTC grade, but the difference was not significant. Conclusions: This pilot study confirmed the safety of oil-based skin treatments during radiation therapy and suggests a trend for reduced skin toxicity for patients receiving emu oil. A larger study is needed to evaluate the efficacy of emu oil in reducing radiation dermatitis in patients receiving breast radiation.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2023

Factors influencing mode choice of adults with travel-limiting disability

Introduction: Despite the plethora of research devoted to analyzing the impact of disability on travel behavior, not enough studies have investigated the varying impact of social and environmental factors on the mode choice of people with disabilities that restrict their ability to use transportation modes efficiently. This research gap can be addressed by investigating the factors influencing the mode choice behavior of people with travel-limiting disabilities, which can inform the development of accessible and sustainable transportation systems. Additionally, such studies can provide insights into the social and economic barriers faced by this population group, which can help policymakers to promote social inclusion and equity. Method: This study utilized a Random Parameters Logit model to identify the individual, trip, and environmental factors that influence mode selection among people with travel-limiting disabilities. Here, using the 2017 National Household Travel Survey data for New York State, which included information on respondents with travel-limiting disabilities, the analysis focused on a sample of 8,016 people. In addition, climate data from the National Oceanic and Atmospheric Administration were integrated as additional explanatory variables in the modeling process. Results: The results revealed that people with disabilities may be inclined to travel longer distances walking in the absence of suitable accommodation facilities for other transportation modes. Furthermore, people were less inclined to walk during summer and winter, indicating a need to consider weather conditions as a significant determinant of mode choice. Moreover, low-income people with disabilities were more likely to rely on public transport or walking. Conclusion: Based on this study’s findings, transportation agencies could design infrastructure and plan for future expansions that is more inclusive and accessible, thus catering to the mobility needs of people with travel-limiting disabilities.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2020

Modeling Nanoconfinement Effects Using Active Learning

Predicting the spatial configuration of gas in nanopores of is relevant in applications such as fluid flow forecasting and hydrocarbon reserves estimation. For example, shale reservoirs have suffered from computationally intractable multiscale problems, since fluid properties such as viscosity, density, and adsorption must be calculated by using expensive molecular dynamics (MD) simulations within each nanopore, whereas flow through these connected nanopores must be simulated at the micrometer scale. We utilize machine learning techniques to quickly and accurately model nanoscale confinement effects as an important step toward bridging the nano and micro scales. Our workflow is based on building and training physics-based deep-neural-networks models by learning from a database of MD calculations. The model accounts for the adsorption phenomenon by predicting the statistical distribution of gas inside nanopores. Because large databases of MD calculations are expensive to create, we investigate active learning (AL) as a data set construction strategy. In this workflow, new data are selected based on the model uncertainty via the query-by-committee approach. We show that our workflow obtains accurate models that generalize to real scanning electron microscopy geometries with 1/10th of the number of MD calculations required vs random data set generation. Our method enables the possibility of modeling nanoconfinement effects at the mesoscale, where complex connected sets of nanopores affect flow.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Functionalized Graphene via a One-Pot Reaction Enabling Exact Pore Sizes, Modifiable Pore Functionalization, and Precision Doping

Functionalizing graphene with exact pore size, specific functional groups, and precision doping poses many significant challenges. Current methods lack precision and produce random pore sizes, sites of attachment, and amounts of dopant, leading to compromised structural integrity and affecting graphene’s applications. In this work, we report a strategy for the synthesis of functionalized graphitic materials with modifiable nanometer-sized pores via a Pictet–Spengler polymerization reaction. This one-pot, four-step synthesis uses concepts based on covalent organic frameworks (COFs) synthesis to produce crystalline two-dimensional materials that were confirmed by PXRD, TEM measurements, and DFT studies. These new materials are structurally analogous to doped graphene and graphene oxide (GO) but, unlike GO, maintain their semiconductive properties when fully functionalized.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2012

Effect of Spatial Concentration Fluctuations on Effective Kinetics in Diffusion-Reaction Systems

The effect of spatial concentration fluctuations on reaction of two solutes, A+B$\rightarrow$C, is considered. In the absence of fluctuations, concentration of solutes decays as $A_{det}=B_{det} \sim t^{-1}$. Contrary to this, experimental and numerical studies suggest that concentrations decay significantly slower. Existing theory suggests $t^{-d/4}$ scaling in the asymptotic regime ($d$ is the dimensionality of the problem). Here we study the effect of fluctuations using the classical diffusion-reaction equation with random initial conditions. Initial concentrations of the reactants are treated as correlated random fields. We use the method of moment equations to solve the resulting stochastic diffusion-reaction equation and obtain a solution for the average concentrations that deviates from $\sim t^{-1}$ to $\sim t^{-d/4}$ behavior at time $t^*$. Finally, we derive analytical expressions for the time $t^*$ as a function of Damk\"{o}hler number and the coefficient of variation of the initial concentration. Our analytical results support earlier explanations of the deviation of average concentrations from $A_{det}=B_{det} \sim t^{-1}$ behavior, which attributed this change of scaling to the creation of isolated {\it islands} of A and B.

uncertainty quantification, stochastic differentia↗