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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

Streptococcus pneumoniae HtrA is a dynamic and monomeric virulence factor capable of forming larger oligomeric complexes

Abstract High‐temperature requirement A (HtrA) proteases are a conserved family of serine proteases central to protein quality control and bacterial virulence. While Gram‐negative and human HtrAs are structurally well studied, Gram‐positive homologs remain essentially uncharacterized. Here, we present the first integrated structural and mechanistic analysis of a Gram‐positive HtrA, from Streptococcus pneumoniae , a virulence factor essential for adhesion and infection in vivo. Proteomic profiling of an htrA knockout and cleavage assays demonstrate that S. pneumoniae HtrA is required for protein quality control, with the PDZ domain mediating substrate recognition. Biochemically, S. pneumoniae HtrA exists exclusively as a monomer in solution, a striking divergence from canonical trimeric HtrAs that we show is shared with other Gram‐positive homologs. NMR analyses reveal that the monomer dynamically samples open and closed conformations, while cryo‐EM of a catalytic mutant identifies a hexamer stabilized by a unique LoopA–PDZ interaction. Together, these findings define S. pneumoniae HtrA as a dynamic monomer with interdomain coupling between its protease and PDZ domains, establishing Gram‐positive HtrAs as a mechanistically divergent subgroup within the HtrA family.

Lee, Eunjeong [Department of Biochemistry and Mole↗
DOE OSTI2025

Imaging Bias‐Driven Domain Wall Motion With Scanning Oscillator Piezoresponse Force Microscopy

Understanding ferroelectric domain wall dynamics at the nanoscale across a broad range of timescales requires measuring domain wall position under different applied electric fields. The success of piezoresponse force microscopy (PFM) as a tool to apply local electric fields at different positions and imaging their changing position, together with the information obtained from associated switching spectroscopies has fueled numerous studies of the dynamics of ferroelectric domains to determine the impact of intrinsic parameters such as crystalline order, defects and pinning centers, as well as boundary conditions such as environment. However, the investigation of sub-coercive reversible domain wall vibrational modes requires the development of new tools that enable visualizing domain wall motion under varying applied fields with high temporal and spatial resolution while also accounting for spurious electrostatic effects. Here, scanning oscillator piezoresponse force microscopy extends the investigation of domain wall dynamics to new regimes, providing direct visualization of domain wall position as a function of an external electric field that varies in time and location. In conclusion, this enables studying the energetics of field-driven ferroelectric domain wall motion, which is shown to obey a thermally activated flow regime in the millisecond timescale.

Piezoresponse Force Microscopy↗
DOE OSTI2020

Higher-derivative corrections to entropy and the weak gravity conjecture in Anti-de Sitter space

We compute the four-derivative corrections to the geometry, extremality bound, and thermodynamic quantities of AdS-Reissner-Nordström black holes for general dimensions and horizon geometries. We confirm the universal relationship between the extremality shift at fixed charge and the shift of the microcanonical entropy, and discuss the consequences of this relation for the Weak Gravity Conjecture in AdS. The thermodynamic corrections are calculated using two different methods: first by explicitly solving the higher-derivative equations of motion and second, by evaluating the higher-derivative Euclidean on-shell action on the leading-order solution. In both cases we find agreement, up to the addition of a Casimir energy in odd dimensions. We derive the bounds on the four-derivative Wilson coefficients implied by the conjectured positivity of the leading corrections to the microcanonical entropy of thermodynamically stable black holes. These include the requirement that the coefficient of Riemann-squared is positive, meaning that the positivity of the entropy shift is related to the condition that c – a is positive in the dual CFT. We discuss implications for the deviation of η/s from its universal value and a potential lower bound.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Uncertainty amplification due to density/refractive index gradients in background-oriented schlieren experiments

Here, we theoretically analyze the effect of density/refractive index gradients on the measurement precision of background-oriented schlieren (BOS) experiments by deriving the Cramer–Rao lower bound (CRLB) for the 2D centroid estimation process. A model is derived for the diffraction limited image of a dot viewed through a medium containing density gradients that includes the effect of the experimental parameters such as the magnification and f-number. It is shown using the model that nonlinearities in the density gradient field lead to blurring of the dot image. This blurring amplifies the effect of image noise on the centroid estimation process, leading to an increase in the CRLB and a decrease in the measurement precision. The ratio of position uncertainties of a dot in the reference and gradient images is shown to be a function of the ratio of the dot diameters and dot intensities. We termed this parameter the amplification ratio (A F ), and a methodology for reporting position uncertainties in tracking-based BOS measurements is proposed. The theoretical predictions of the dot position estimation variance from the CRLB are compared to ray tracing simulations, and agreement is obtained. The uncertainty amplification is also demonstrated on experimental BOS images of flow induced by a spark discharge, where it is seen that regions of high amplification ratio correspond to regions of density gradients. This analysis elucidates the dependence of the position uncertainty on density and refractive index gradient-induced distortion parameters, provides a methodology for accounting its effect on uncertainty quantification and provides a framework for optimizing experiment design.

42 ENGINEERING↗
DOE OSTI2022

Relationships between Cloud Droplet Spectral Relative Dispersion and Entrainment Rate and Their Impacting Factors

Cloud microphysical properties are significantly affected by entrainment and mixing processes. However, it is unclear how the entrainment rate affects the relative dispersion of cloud droplet size distribution. Previously, the relationship between relative dispersion and entrainment rate was found to be positive or negative. To reconcile the contrasting relationships, the Explicit Mixing Parcel Model is used to determine the underlying mechanisms. When evaporation is dominated by small droplets, and the entrained environmental air is further saturated during mixing, the relationship is negative. However, when the evaporation of big droplets is dominant, the relationship is positive. Whether or not the cloud condensation nuclei are considered in the entrained environmental air is a key factor as condensation on the entrained condensation nuclei is the main source of small droplets. However, if cloud condensation nuclei are not entrained, the relationship is positive. If cloud condensation nuclei are entrained, the relationship is dependent on many other factors. High vertical velocity, relative humidity of environmental air, liquid water content, and low droplet number concentration are more likely to cause the negative relationship since new saturation is easier to achieve by evaporation of small droplets. Further, the signs of the relationship are not strongly affected by the turbulence dissipation rate, but the higher dissipation rate causes the positive relationship more significant for a larger entrainment rate. A conceptual model is proposed to reconcile the contrasting relationships. This work enhances the understanding of relative dispersion and lays a foundation for the quantification of entrainment-mixing mechanisms.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Biofluid-based staging of Alzheimer’s disease

Recently, conceptual systems for the in vivo staging of Alzheimer’s disease (AD) using fluid biomarkers have been suggested. Thus, it is important to assess whether available fluid biomarkers can successfully stage AD into clinically and biologically relevant categories. In the TRIAD cohort, we explored whether p-tau217, p-tau205 and NTA-tau (biomarkers of early, intermediate and late AD pathology, respectively) have potential for biofluid-based staging in cerebrospinal fluid (CSF; n = 219) and plasma (n = 150), and compared them in a paired CSF and plasma subset (n = 76). Our findings suggest a good concordance between biofluid staging and underlying pathology when classifying amyloid-positivity into three categories based on neurofibrillary pathology: minimal/non-existent (p-tau217 positive), early-to-intermediate (p-tau217 and p-tau205 positivity), and advanced tau tangle deposition (p-tau217, p-tau205 and NTA-tau positive), as indexed by tau-PET. Discordant cases accounted for 4.6% and 13.3% of all CSF and plasma measurements respectively (9.2% and 11.8% in paired samples). Notably, CSF- and plasma-based staging matched one another in 61.7% of the cases, while approximately 32% of the remaining participants were one to three biofluid stages higher in CSF as compared to plasma. Overall, these exploratory results suggest that biofluid staging of AD holds potential for offering valuable insights into underlying AD hallmarks and disease severity. However, its applicability beyond molecular characterization at research settings has yet to be demonstrated.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Understanding the role of negative charge in the scaffold of an artificial enzyme for CO 2 hydrogenation on catalysis

Here, we have approached the construction of an artificial enzyme by employing a robust protein scaffold, lactococcal multidrug resistance regulator, LmrR, providing a structured secondary and outer coordination spheres around a molecular rhodium complex, [Rh I (P Et2 N gly P Et2 ) 2 ] - . Previously, we demonstrated a 2–3 fold increase in activity for one Rh-LmrR construct by introducing positive charge in the secondary coordination sphere. In this study, a series of variants was made through site-directed mutagenesis where the negative charge is located in the secondary sphere or outer coordination sphere, with additional variants made with increasingly negative charge in the outer coordination sphere while keeping a positive charge in the secondary sphere. Placing a negative charge in the secondary or outer coordination sphere demonstrates decreased activity by a factor of two compared to the wild-type Rh-LmrR. Interestingly, addition of positive charge in the secondary sphere, with the negatively charged outer coordination sphere restores activity. Vibrational and NMR spectroscopy suggest minimal changes to the electronic density at the rhodium center, regardless of inclusion of a negative or positive charge in the secondary sphere, suggesting another mechanism is impacting catalytic activity, explored in the discussion.

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

Microbial abundances and carbon use under ambient temperature or experimental warming in a southern boreal peatland

Abstract Organic peat soils occupy relatively little of the global land surface area but store vast amounts of soil carbon in northern latitudes where climate is warming at a rapid pace. Warming may result in strong positive feedbacks of carbon loss and global climate change driven by microbial processes if warming alters the balance between primary productivity and decomposition. To elucidate effects of warming on the microbial communities mediating peat carbon dynamics, we explored the abundance of broad microbial groups and their source of carbon (i.e. old carbon versus more recently fixed photosynthate) using microbial lipid analysis (δ 13 C PLFA) of peat samples under ambient temperatures and before/after initiation of experimental peat warming (+ 2.25, + 4.5, + 6.75, and + 9 °C). This analysis occurred over a profile to 2 m depth in an undrained, ombrotrophic peat bog in northern Minnesota. We found that the total microbial biomass and individual indicator lipid abundances were stratified by depth and strongly correlated to temperature under ambient conditions. However, under experimental warming, statistically significant effects of temperature on the microbial community were sporadic and inconsistent. For example, 3 months after experimental warming the relative abundance of Gram-negative bacterial indicators across depth combined and > 50 cm depth and Gram-positive bacterial indicators at 20–50 cm depth showed significant positive relationships to temperature. At that same timepoint, however, the relative abundance of Actinobacterial indicators across depth showed a significant negative relationship to temperature. After 10 months of experimental warming, the relative abundance of fungal biomarkers was positively related to temperature in all depths combined, and the absolute abundance of anaerobic bacteria declined with increasing temperature in the 20–50 cm depth interval. The lack of observed response in the broader microbial community may suggest that at least initially, microbial community structure with peat depth in these peatlands is driven more by bulk density and soil water content than temperature. Alternatively, the lack of broad microbial community response may simply represent a lag period, with more change to come in the future. The long-term trajectory of microbial response to warming in this ecosystem then could either be direct, after this initial lag time, or indirect through other physical or biogeochemical changes in the peat profile. These initial results provide an important baseline against which to measure long-term microbial community and carbon-cycling responses to warming and elevated CO 2 .

Felice, Mark↗
DOE OSTI2022

Analytical methods for superresolution dislocation identification in dark-field X-ray microscopy

In this work, we develop several inference methods to estimate the position of dislocations from images generated using dark-field X-ray microscopy (DFXM)—achieving superresolution accuracy and principled uncertainty quantification. Using the framework of Bayesian inference, we incorporate models of the DFXM contrast mechanism and detector measurement noise, along with initial position estimates, into a statistical model coupling DFXM images with the dislocation position of interest. We motivate several position estimation and uncertainty quantification algorithms based on this model. We then demonstrate the accuracy of our primary estimation algorithm on synthetic realistic DFXM images of edge dislocations in single-crystal aluminum. We conclude with a discussion of our methods’ impact on future dislocation studies and possible future research avenues.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Shifts in belowground processes along a temperate forest edge

Abstract Context Forests are increasingly fragmented, and as a result most forests in the United States are within one km of an edge. Edges change environmental conditions of the forest—especially radiation, roughness, temperature, and moisture—that can have consequences for plant productivity and ecosystem functions. However, edge effects on aboveground characteristics of plants and the environment are better understood relative to plant roots and soil in the belowground environment. Objectives Our main objectives were to determine if soil C pools and fluxes are higher at the edge relative to other landscape positions, and to understand how specific belowground processes contribute to bulk differences in pools and fluxes. Methods We measured environmental conditions, live and dead fine root traits, soil chemistry, and soil respiration along a 75 m transect from interior forest to meadow in Gaithersburg, MD. Results We observed differences in the soil chemical, biological and hydrological environment between the forest interior, edge and adjacent meadow. In some cases, the forest edge represented a mid-point in environmental or belowground characteristics between the forest interior and meadow ( e.g. , pH, C-to-N ratio [C:N], live fine root biomass, heterotrophic respiration), likely reflecting the change in litter type and quality associated with the transition from grass to woody species. In other cases, neighboring landscape positions were different from the forest edge, which was drier and had higher dead fine root biomass. Although soil C contents were not significantly different across landscape positions, there was a tendency towards higher average soil C content at the edge relative to other landscape positions, suggesting that increased C loss related to root decay and greater soil respiration at the edge relative to the forest interior may have been offset by increased C gain from high plant productivity and subsequent inputs to soil. Conclusions This research provides insight into how forest edge environments may differ from the interior and how concurrent processes above- and belowground may contribute to those differences.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Non-Markovian dynamics of open quantum system with memory

Highlights: • Non-Markovian master equation for open quantum system with power-law memory is proposed. • Non-Markovian dynamics of two-level quantum system with memory is described. • Solutions of non-Markovian quantum master equations are derived. • Complete positivity and bi-positivity in non-Markovian quantum dynamics with memory are described. • Exact solution of non-Markovian equations of system with memory is proposed. In this paper, non-Markovian generalization of master equation for open quantum system is proposed. Non-Markovian dynamics of two-level quantum system with memory and interaction with environment is described. To describe this system, the Gorini–Kossakowski–Sudarshan equation for open quantum states is generalized by taking into account power-law fading memory. The non-Markovian quantum processes with power-law memory are described by using integration and differentiation of non-integer orders. Complete positivity and bi-positivity in non-Markovian quantum dynamics with memory are described. An example of two-level quantum systems with power-law memory is suggested. Exact solution of the non-Markovian master equations of two-level open quantum systems with memory is derived.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Analysis of contrasting aerosol indirect effects in liquid water clouds over the northern part of Arabian Sea

The extensive daily statistics of aerosol properties, cloud properties, and their mutual correlations provide crucial information for better assessing future climate change. Here, in this paper, 14 years (2010–2023) of data from the Moderate Resolution Imaging Spectroradiometer (MODIS) are analyzed over the northern part of Arabian Sea (Latitude: 21°–25° N and Longitude: 62°–68° E) to assess the characteristics of aerosols and clouds and their relationships under different meteorological conditions. When aerosol optical depth (AOD) is less than ~0.7, the observations exhibit a positive correlation between AOD and cloud droplet effective radius (CDR) but negative correlations between AOD and cloud droplet number concentration (CDNC), between AOD and cloud optical depth (COD), between AOD and cloud liquid water path (CLWP), and between AOD and cloud geometrical thickness (H). The corresponding aerosol-cloud correlations change signs when the AOD values are larger than 0.7. However, the single folded positive AOD-cloud fraction (CF) relationship is observed in both AOD regimes. Similar correlations are also observed between precipitable water vapor (PWV) and CDR, CDNC, COD, H, CF and CLWP, together with a positive correlation between PWV and AOD. Further isolation of the environmental effects from aerosol effects by stratifying AOD and cloud data into different LTS and PWV bins shows that the signature of the well-known Twomey effect is observed under high LTS-high PWV conditions, while an opposite effect (anti-Twomey) is observed under low PWV conditions, regardless of LTS values. Additionally, negative correlations between AOD and COD, AOD and CLWP, and AOD and H are observed under low LTS, regardless of PWV conditions, with a slight positive correlation when AOD >0.4 under high LTS and PWV conditions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

The impacts of building characteristics, social psychological and cultural factors on indoor environment quality productivity belief

Indoor environmental quality (IEQ) plays a key role in determining occupants' productivity at work; however, analyses of the interconnected factors among building physical, attitudinal, social and demographic components in one study are lacking. To fill this research gap, this study investigates these interconnected factors' influence on occupants’ IEQ-productivity belief, defined as a personal, subjective evaluation of the linkage between the impacts of five IEQ aspects (the quality of indoor temperature, air, natural and electric lighting, and acoustics) and productivity. A cross-sectional survey data was collected in university offices from six countries (Brazil, Italy, Poland, Switzerland, Taiwan and the U.S.). Results of multiple linear regression models indicate that IEQ satisfaction is the strongest positive predictor of the IEQ-productivity belief and this relationship is stronger in private offices. Country of residence is the second primary predictor. Several attitudinal-behavioral factors, including thermal comfort, perceived ease of controlling indoor environmental features, and attitudes toward sharing controls are all positively associated with IEQ-productivity belief. Interestingly, the level of control accessibility to light switches has the strongest impact as opposed to other controls. On the other hand, group norms and conformity intention are not significant predictors. Regarding demographics, men are more likely than women to perceive the IEQs to have positive impacts on their productivity, without considering other variables in the regression model; however, women are more likely than men to consider all IEQs as having positive impacts on productivity, after considering other variables. Furthermore, our findings provide suggestions for prioritizing wellness in the workplace since the early design stage.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2024

Visual feedback and guided balance training in an immersive virtual reality environment for lower extremity rehabilitation

Balance training is essential for physical rehabilitation procedures, as it can improve functional mobility and enhance cognitive coordination. However, conventional balance training methods may have limitations in terms of motivation, real-time objective feedback, and personalization, which a virtual reality (VR) setup may provide a better alternative. In this work, we present an immersive VR training environment for lower extremity balance rehabilitation with real-time guidance and feedback. The VR training environment immerses the user in a 3D ice rink model where a virtual coach (agent) leads them through a series of balance poses, and the user controls a trainee avatar with their own movements. Here we developed two coaching styles: positive-reinforcement and autonomous-supportive, and two viewpoints of the trainee avatar: first-person and third-person. The proposed environment was evaluated in a user study with healthy, non-clinical participants (n = 16, 24.4 ± 5.7 years old, 9 females). Our results show that participants showed stronger performance in the positive-reinforcement style compared to the autonomous-supportive style. Additionally, in the third-person viewpoint, the participants exhibited more stability in the positive-reinforcement style compared to the autonomous-supportive style. For viewpoint, participants exhibited stronger performance in the first-person viewpoint compared to third-person in the autonomous-supportive style, while they were comparable in the positive-reinforcement style. We observed no significant effects on the foot height and number of mistakes. Furthermore, we report the analysis of user performance with balance training poses and subjective measures based on questionnaires to assess the user experience, usability, and task load. The proposed VR balance training could offer an interactive, adaptive, and engaging environment and open new potential research directions for lower extremity rehabilitation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A novel method for quantifying irradiation damage in nuclear graphite using Raman spectroscopy

Raman spectroscopy has long been used in studying irradiation damage in carbon/graphite materials. It is however unclear if the measurements from different types of materials are directly comparable. Further, decoupling the contribution from irradiation temperature and fluence to the total damage in nuclear graphite possessing irradiation damage gradient is currently not readily feasible as it requires a complete set of test reactor irradiation experiments over the relevant temperature and fluence range. A novel methodology has therefore been proposed and developed to quantify total irradiation damage evolution at crystal level based on graphite Raman G-band position shift. Specifically, G-band positions derived from a large number of spectra collected from the fractured surface of microfine-grained POCO ZXF-5Q graphite possessing proton irradiation damage gradient were plotted with open literature Raman data on HOPG, BEPO (AXGP graphite), PCEA and IG-110 graphite as a function of dpa. The total damage level within 2σ beam radius in this POCO graphite was estimated to be equivalent to ~2–5 dpa at ~350–370 °C. Derived G-band positions were then mapped to the three-stage amorphization trajectory model indicating beam centre area has entered the second stage, i.e., transitioning from nanocrystalline graphite into amorphous carbon. G-band position relative shift (ΔG) curve with a ‘turn-around’ peak as a function of total damage can be used for in-service lifetime prediction. Importantly, the developed methodology has the potential to ‘unify’ total damage levels across different grades of nuclear graphite caused by ion, neutron and proton irradiation at different temperatures.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

A machine learning approach for increased throughput of density functional theory substitutional alloy studies

In this study, a machine learning-based technique is developed to reduce the computational cost required to explore large design spaces of substitutional alloys. The first advancement is based on a neural network (NN) approach to predict the initial position of minority and majority ions prior to DFT relaxation. The second advancement is to allow the NN to predict the total energy for every possibility minority ion position and select the most stable configuration in the absence of relaxing each trial minority configuration. A bismuth oxide materials system, (Bi x La y Yb z ) 2 MoO 6 , was used as the model system to demonstrate the developed methods and quantify the resulting computational speedup. Compared to a brute force method that requires the calculation of every permutation of minority configuration and subsequent DFT relaxation, a 1.3× speedup was realized if the NN predicted the initial configuration of ions prior to relaxation. Implementation of the second advancement allowed the NN to predict the total energy for all possible trial configurations and downselect the most stable configurations prior to relaxation, resulting in a speedup of approximately 37×. Validation was done by comparing position and energy between the NN and DFT predictions. A maximum position vector mean squared error (MSE) of 1.6 × 10 -2 and a maximum energy MSE of 2.3 × 10 -7 was predicted for the worst case configuration. This method demonstrates a significant computational speedup, which has the potential for even greater computational savings for larger compositional design spaces.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Machine learning reveals sequence-function relationships in family 7 glycoside hydrolases

Family 7 glycoside hydrolases (GH7) are among the principal enzymes for cellulose degradation in nature and industrially. These important enzymes are often bimodular, including a catalytic domain and carbohydrate binding module (CBM) attached via a flexible linker, and exhibit an active site that binds cello-oligomers of up to ten glucosyl moieties. GH7 cellulases consist of two major subtypes: cellobiohydrolases (CBH) and endoglucanases (EG). Despite the critical importance of GH7 enzymes, there remain gaps in our understanding of how GH7 sequence and structure relate to function. Here, we employed machine learning to gain data-driven insights into relationships between sequence, structure, and function across the GH7 family. Machine-learning models, trained only on the number of residues in the active-site loops as features, were able discriminate GH7 CBHs and EGs with up to 99% accuracy, demonstrating that the lengths of loops A4, B2, B3, and B4 strongly correlate with functional subtype across the GH7 family. Classification rules were derived such that specific residues at 42 different sequence positions each predicted the functional subtype with accuracies surpassing 87%. A random forest model trained on residues at 19 positions in the catalytic domain predicted the presence of a CBM with 89.5% accuracy. Our ML results recapitulate, as top-performing features, a substantial number of the sequence positions determined by previous experimental studies to play vital roles in GH7 activity. We surmise that the yet-to-be-explored sequence positions among the top-performing features also contribute to GH7 functional variation and may be exploited to understand and manipulate function.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

A series representation of the discrete fractional Laplace operator of arbitrary order

Although fractional powers of non-negative operators have received much attention in recent years, there is still little known about their behavior if real-valued exponents are greater than one. In this article, we define and study the discrete fractional Laplace operator of arbitrary real-valued positive order. Here a series representation of the discrete fractional Laplace operator for positive non-integer powers is developed. Its convergence to a series representation of a known case of positive integer powers is proven as the power tends to the integer value. Furthermore, we show that the new representation for arbitrary real-valued positive powers of the discrete Laplace operator is consistent with existing theoretical results.

97 MATHEMATICS AND COMPUTING↗