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At least 289 records · Page 16

Hamiltonian systems, Toda lattices, solitons, Lax pairs on weighted Z -graded graphs

In this study, we consider discrete one-dimensional nonlinear equations and present the procedure of lifting them to Z -graded graphs. We identify conditions that allow one to lift one-dimensional solutions to solutions on graphs. In particular, we prove the existence of solitons for static potentials on graded fractal graphs. We also show that even for a simple example of a topologically interesting graph, the corresponding non-trivial Lax pairs and associated unitary transformations do not lift to a Lax pair on the Z -graded graph.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Complex field reversal dynamics in nanomagnetic systems

Nanomagnetic materials, built from thin, patterned films of ferromagnetic materials, began as analogues to frustrated magnetism. Their low energy of operation and emergent properties make them strong candidates for physics-based devices. A recent model of how nanomagnetic domains flip, the Glauber mean-field model, is used here to understand how systems of nanomagnets evolve when opposed by external field. This reversal can be expressed in an analytical form in the case of one-dimensional chains and trees at zero temperature, where the cascade of spin flips gives rise to harmonic power spectra. Finally, the same cascades in two and three dimensions form fractal field reversal clusters whose shape depends on the strength of the field and the tuning of interactions between nanomagnets.

36 MATERIALS SCIENCE↗

Scaling in nature: from DNA through heartbeats to weather

The purpose of this report is to describe some recent progress in applying scaling concepts to various systems in nature. We review several systems characterized by scaling laws such as DNA sequences, heartbeat rates and weather variations. We discuss the finding that the exponent alpha quantifying the scaling in DNA in smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the scaling exponent alpha is smaller during sleep periods compared to wake periods. We also discuss the recent findings that suggest a universal scaling exponent characterizing the weather fluctuations.

Review↗

Statistical mechanics in biology: how ubiquitous are long-range correlations?

The purpose of this opening talk is to describe examples of recent progress in applying statistical mechanics to biological systems. We first briefly review several biological systems, and then focus on the fractal features characterized by the long-range correlations found recently in DNA sequences containing non-coding material. We discuss the evidence supporting the finding that for sequences containing only coding regions, there are no long-range correlations. We also discuss the recent finding that the exponent alpha characterizing the long-range correlations increases with evolution, and we discuss two related models, the insertion model and the insertion-deletion model, that may account for the presence of long-range correlations. Finally, we summarize the analysis of long-term data on human heartbeats (up to 10(4) heart beats) that supports the possibility that the successive increments in the cardiac beat-to-beat intervals of healthy subjects display scale-invariant, long-range "anti-correlations" (a tendency to beat faster is balanced by a tendency to beat slower later on). In contrast, for a group of subjects with severe heart disease, long-range correlations vanish. This finding suggests that the classical theory of homeostasis, according to which stable physiological processes seek to maintain "constancy," should be extended to account for this type of dynamical, far from equilibrium, behavior.

Non-NASA Center↗

Multifractality in human heartbeat dynamics

There is evidence that physiological signals under healthy conditions may have a fractal temporal structure. Here we investigate the possibility that time series generated by certain physiological control systems may be members of a special class of complex processes, termed multifractal, which require a large number of exponents to characterize their scaling properties. We report on evidence for multifractality in a biological dynamical system, the healthy human heartbeat, and show that the multifractal character and nonlinear properties of the healthy heart rate are encoded in the Fourier phases. We uncover a loss of multifractality for a life-threatening condition, congestive heart failure.

Non-NASA Center↗

Generalized Levy-walk model for DNA nucleotide sequences

We propose a generalized Levy walk to model fractal landscapes observed in noncoding DNA sequences. We find that this model provides a very close approximation to the empirical data and explains a number of statistical properties of genomic DNA sequences such as the distribution of strand-biased regions (those with an excess of one type of nucleotide) as well as local changes in the slope of the correlation exponent alpha. The generalized Levy-walk model simultaneously accounts for the long-range correlations in noncoding DNA sequences and for the apparently paradoxical finding of long subregions of biased random walks (length lj) within these correlated sequences. In the generalized Levy-walk model, the lj are chosen from a power-law distribution P(lj) varies as lj(-mu). The correlation exponent alpha is related to mu through alpha = 2-mu/2 if 2 < mu < 3. The model is consistent with the finding of "repetitive elements" of variable length interspersed within noncoding DNA.

NASA Discipline Number 14-10↗

Override of spontaneous respiratory pattern generator reduces cardiovascular parasympathetic influence

We investigated the effects of voluntary control of breathing on autonomic function in cardiovascular regulation. Variability in heart rate was compared between 5 min of spontaneous and controlled breathing. During controlled breathing, for 5 min, subjects voluntarily reproduced their own spontaneous breathing pattern (both rate and volume on a breath-by-breath basis). With the use of this experimental design, we could unmask the effects of voluntary override of the spontaneous respiratory pattern generator on autonomic function in cardiovascular regulation without the confounding effects of altered respiratory pattern. Results from 10 subjects showed that during voluntary control of breathing, mean values of heart rate and blood pressure increased, whereas fractal and spectral powers in heart rate in the respiratory frequency region decreased. End-tidal PCO2 was similar during spontaneous and controlled breathing. These results indicate that the act of voluntary control of breathing decreases the influence of the vagal component, which is the principal parasympathetic influence in cardiovascular regulation.

NASA Discipline Cardiopulmonary↗

Analysis of Retinal Vascular Branching in Human Subjects Undergoing 70-Day Head-Down Tilt by NASAs VESGEN Software

Significant risks for visual impairment were discovered recently in astronauts following spaceflight, especially after long-duration missions. We hypothesize that microgravity-induced fluid shifts result in pathological changes within the retinal vasculature that precede visual and other ocular impairments. We therefore are analyzing retinal vessels in healthy subjects before and after head-down tilt (HDT), a ground-based microgravity analog with NASA's VESsel GENeration Analysis (VESGEN) software. Methods. Spectralis® infrared (IR) fundus images were collected from both eyes of 6 subjects before and after 70 days of bed rest at 6 degree HDT (NASA Campaign 11). For our retrospective study, branching patterns in arterial and venous trees are mapped by VESGEN into vessel branching generations (Gx) that are quantified by parameters such as densities of vessel length (Lv), area (Av), number (Nv) and fractal dimension (Df) as described previously for diabetic retinopathy (IOVS 51(1):498). Results are further assigned by VESGEN into groups of large (G1-3), medium (G4-6) and small (G≥7) vessels. Results. All subjects remained asymptomatic throughout duration of HDT. To date, we have analyzed one IR image from each of the 12 eyes. Interestingly, two groups of the masked study population identified by VESGEN are distinguished by the presence or absence of small veins (G≥7). For example, L≥7 and Av≥7 are 2.7+/-1.3 E-4 px/px2 and 7.2+/-3.6 E-4 px2/px2 in 6 retinas, but 0 in the other 6 retinas. Nonetheless, the space-filling properties of the entire venous trees were remarkably uniform by all parameters, such as Df = 1.56+/-0.02 for 6 retinas with G≥7 and 1.55+/-0.02 for retinas without G≥7. No small arteries (G≥7) were detected. Conclusions. For our preliminary masked analysis, two groups of venous trees with and without small veins (G≥7) were clearly revealed by VESGEN. Upon completing all images and unmasking the subject status of before and after HDT, we will determine whether differences in the presence or absence of small veins are important correlates, and perhaps reliable predictors, of other ocular and physiological adaptations to prolonged head-down tilt and microgravity. Clinical methods for examining adaptive microvascular remodeling in the retina to microgravity space flight are not currently established.

Fractal↗

Galvanic Transformation Dynamics in Heterostructured Nanoparticles

Corrosion is a significant problem for the stability of structural metals and potentially for functional nanomaterials in operating environments. When two metals with different electrochemical potentials form a junction, galvanic corrosion occurs, resulting in the sacrificial dissolution of the metal with a higher oxidation potential (lower electrode potential). In this report it is shown that bimetallic hetero-nanostructures composed of phase-segregated metals undergo galvanic corrosion in aqueous environments. Such selective etching of the sacrificial metal in heterojunction particles leads to the formation of unusual and kinetically stabilized half-spheroid particles. By using a fluid cell and in situ scanning transmission electron microscopy, a two-stage corrosion process can be observed where the Cu experiences a fractal breakdown before the Ag corrodes due to the lack of a protective oxide layer. However, when treated with a mild Ar plasma, the stability of these structures against corrosion is enhanced due to the conversion of the amorphous native oxide to a denser, thin layer of CuO on the Cu surface. Taken together, this work highlights the importance of considering the effects of galvanic corrosion on the stability of multicomponent nanoparticles, and it shows how mass transport in a nanoscale system is influenced by redox processes.

36 MATERIALS SCIENCE↗

X‐ray characterization of three possible edible oleogelators: Experiment and theory

Abstract Three oleogelator molecules (Triacontane (TC), Stearic acid (SA), and Behenyl Lignocerate (BL)) were studied individually, in pairs, or all together to make an oleogel using triolein as the oil. WAXS, SAXS and USAXS were used to elucidate the solid structures from angstroms to a few micrometers. A two‐dimensional mapping of atomic positions for each molecule was carried out to understand the crystalline multilayer structures formed. We assumed that the molecules were rigidly extended and that they underwent no significant (hindered) rotations so that the free energy is determined by the Lennard‐Jones interactions of closely packed multilayers. TC molecules were predicted to form a tilt angle of , yielding a SAXS line at Å ─1 , in acceptable agreement with the measured . For SA crystals (predicted) yielding a SAXS line at compared to (observed). No mixed crystals were observed for any pair of molecules or when all three were used. USAXS data showed that SA forms large nanocrystals compared to TC and BL. All three combinations of molecular pairs showed basic scatterers smaller or similar to those of individual molecules. The theory presented here, together with the experimental results, showed why no mixed crystals are formed from two or all three molecules. Data from the USAXS region suggested that, when using all three molecules, a more compact fractal structure was obtained, compared with those if one or two of the molecules were used.

Chemistry↗

Heterogeneity of soil structure and fertility during desertification of alpine grassland in northwest Sichuan

Abstract The variations of soil structure and soil physical–chemical properties in the process of alpine grassland desertification were revealed, and the indicators of grassland desertification were put forward in order to deepen the understanding of the law of degradation succession and development of alpine grassland. It was used to provide scientific basis for ecological restoration and improvement of ecological service function of alpine grassland. With severe desertification alpine grassland as the core in the Hongyuan County, Tibetan Qiang Autonomous Prefecture of Ngawa, Sichuan Province, China, along both the directions of wetland and arid grassland, the heterogeneity of soil structure and soil fertility in both directions was studied by the analysis of the mean weight diameter (MWD), geometric mean diameter (GMD), >0.25 mm aggregate content ( R 0.25 ), fractal dimension ( D ), soil bulk density, soil moisture content, and soil nutrients. Our results showed that MWD, GMD, and R 0.25 all gradually increased, but the D decreased with the reduction in the degree of desertification in the arid grassland and wetland, resulting in the strong stability of soil structure. The decreasing rate of the D in the direction of arid grassland was faster than that of wetland. Therefore, soil structure stability and erosion resistance in the direction of arid grassland were stronger than that of wetland soil; the D had different response to aggregates with different particle sizes. The aggregate less than 0.25 mm ( r = 0.981, P < 0.01) and 1–2 mm ( r = −0.79, P < 0.01) had the largest responses in the direction of the arid grassland and wetland, respectively; the aggregate more than 1 mm and 1–2 mm can be used as indicators to evaluate desertification of the soil in the direction of the arid grassland and wetland, respectively. The higher the content of the indicating aggregates, the weaker the degree of the desertification.

Ma, Li↗

Report on the AAPM grand challenge on deep generative modeling for learning medical image statistics

Abstract Background The findings of the 2023 AAPM Grand Challenge on Deep Generative Modeling for Learning Medical Image Statistics are reported in this Special Report. Purpose The goal of this challenge was to promote the development of deep generative models for medical imaging and to emphasize the need for their domain‐relevant assessments via the analysis of relevant image statistics. Methods As part of this Grand Challenge, a common training dataset and an evaluation procedure was developed for benchmarking deep generative models for medical image synthesis. To create the training dataset, an established 3D virtual breast phantom was adapted. The resulting dataset comprised about 108 000 images of size 512 512. For the evaluation of submissions to the Challenge, an ensemble of 10 000 DGM‐generated images from each submission was employed. The evaluation procedure consisted of two stages. In the first stage, a preliminary check for memorization and image quality (via the Fréchet Inception Distance [FID]) was performed. Submissions that passed the first stage were then evaluated for the reproducibility of image statistics corresponding to several feature families including texture, morphology, image moments, fractal statistics, and skeleton statistics. A summary measure in this feature space was employed to rank the submissions. Additional analyses of submissions was performed to assess DGM performance specific to individual feature families, the four classes in the training data, and also to identify various artifacts. Results Fifty‐eight submissions from 12 unique users were received for this Challenge. Out of these 12 submissions, 9 submissions passed the first stage of evaluation and were eligible for ranking. The top‐ranked submission employed a conditional latent diffusion model, whereas the joint runners‐up employed a generative adversarial network, followed by another network for image superresolution. In general, we observed that the overall ranking of the top 9 submissions according to our evaluation method (i) did not match the FID‐based ranking, and (ii) differed with respect to individual feature families. Another important finding from our additional analyses was that different DGMs demonstrated similar kinds of artifacts. Conclusions This Grand Challenge highlighted the need for domain‐specific evaluation to further DGM design as well as deployment. It also demonstrated that the specification of a DGM may differ depending on its intended use.

Radiology, Nuclear Medicine & Medical Imaging↗

Cover crops and poultry litter impact on soil structural stability in dryland soybean production in southeastern United States

Abstract This study explored the efficacy of soil aggregate indices in quantifying soil structural development, utilizing 5‐year field experiment data from the Southeastern United States. The experiment utilized a split‐plot design with cover crops (native vegetation as control, cereal rye (Secale cerealeL.), winter wheat (Triticum aestivum), hairy vetch (Vicia villosa), and mustard (Brassica rapa) plus cereal rye as the main factor and fertilizer source (no fertilizer as control, inorganic fertilizer with phosphorus, potassium, and elemental sulfur, and poultry litter) as the secondary factor. Aggregate size fractions were determined using the wet‐sieving method, and aggregate stability index (ASI), mean weight diameter (MWD), geometric mean diameter (GMD), and fractal dimension (FD) were calculated to assess soil structural stability. Main effects results indicated that cereal rye (55.11%) and poultry litter (50.97%) exhibited the highest ASI values. The highest MWD, GMD, and FD were observed under mustard plus cereal rye (1.187 mm), cereal rye (0.462 mm), and hairy vetch (2.573), respectively. Principal component analysis revealed that cover crops significantly improved soil aggregate structure and stability, overcoming limitations of sole fertilization practices. Regression analysis suggested that ASI, MWD, and GWD positively correlated with soil organic carbon, whereas FD negatively correlated with MWD, GMD, and ASI. Principal component analysis exhibited that FD decreased with increasing soil organic carbon, ASI, MWD, and GMD, demonstrating that lower FD values indicate enhanced soil aggregation and structure. Assessed indices, FD included, effectively gauged soil structural stability. These metrics should be prioritized in managerial decisions to support soil productivity and health in agricultural systems.

Agriculture↗

Self-organized criticality in multi-pulse gamma-ray bursts

The variability in multi-pulse gamma-ray bursts (GRBs) may help to reveal the mechanism of underlying processes from the central engine. To investigate whether the self-organized criticality (SOC) phenomena exist in the prompt phase of GRBs, we statistically study the properties of GRBs with more than 3 pulses in each burst by fitting the distributions of several observed physical variables with a Markov Chain Monte Carlo approach, including the isotropic energy E iso , the duration time T, and the peak count rate P of each pulse. Our sample consists of 454 pulses in 93 GRBs observed by the CGRO/BATSE satellite. The best-fitting values and uncertainties for these power-law indices of the differential frequency distributions are: α$^{d}_{E}$ = 1.54±0.09, α$^{d}_{T}$ = 1.82±$^{+0.14}_{0.15}$ and α$^{d}_{P}$ = 2.09$^{+0.18}_{–0.19}$, while the power-law indices in the cumulative frequency distributions are: α$^{c}_{E}$ = 1.44$^{+0.08}_{–0.10}$, α$^{c}_{T}$ = 1.75$^{+0.141}_{–0.13}$ and α$^{c}_{P}$ = 1.99$^{+0.16}_{–0.19}$. We find that these distributions are roughly consistent with the physical framework of a Fractal-Diffusive, Self-Organized Criticality (FD-SOC) system with the spatial dimension S = 3 and the classical diffusion β=1. The results of this study support that the jet responsible for the GRBs should be magnetically dominated and magnetic instabilities (e.g., kink model, or tearing-model instability) lead the GRB emission region into the SOC state.

79 ASTRONOMY AND ASTROPHYSICS↗

Single molecule characterization of anomalous transport in a thin, anisotropic film

Here, the diffusion of small, charged molecules incorporated in an anisotropic polyelectrolyte multilayers (PEMs) was tracked in three dimensions by combining single-molecule fluorescence localization (to characterize lateral diffusion) with Förster resonance energy transfer (FRET) between diffusing molecules and the supporting surface (to measure diffusion in the surface-normal direction). Analysis of the surface-normal diffusion required model-based statistical analysis to account for the inherently noisy FRET signal. Combining these distinct single-molecule methods, which are inherently sensitive to different length scales, permitted simultaneous characterization of severely anisotropic diffusion, which was more than three orders of magnitude slower in the surface-normal direction. We hypothesize that the anomalously slow surface-normal diffusion was related to the periodic distribution of charge in the PEM, which created electrostatic barriers. The motion was strongly subdiffusive, with anomalous temporal scaling exponents in lateral and normal directions, suggesting a connection to the transient, random fractal conformation of polymer chains in the film’s matrix.

36 MATERIALS SCIENCE↗

Onset dynamics of air-water menisci on rock fracture surfaces

Information on menisci dynamics and equilibrium contact angles, θ e , is needed for modeling multiphase flow of fluids in geologic formations. The wettability of fracture faces is relevant to applications such as waterflooding in enhanced oil recovery and evaluation of caprock integrity for geologic carbon sequestration. We investigated the vertical capillary rise of air-water menisci on exposed fracture faces for a sandstone, a shale, and three granites. The experimental design approximated that employed in the Wilhelmy plate method. Replicate fracture faces were prepared by fracturing cylindrical rock cores using the Brazilian method and splitting the fractured cores apart along their fracture planes. Meniscus onset was imaged from a cross-sectional perspective using dynamic neutron radiography, and quantified with change point analysis. An existing model for meniscus onset fitted the experimental data very well (median R 2 = 0.96). Capillary rise was typified by t 2/3 scaling (where t is time), followed by a constant equilibrium height, z e . The average time taken for the menisci to reach z e was 0.39 s, with no differences between rock types. The menisci achieved a greater vertical extent on the fracture faces of the sedimentary rocks as compared to those of the granites. Apparent θ e values were calculated from the best fit estimates of z e using the Wilhelmy plate equation for a smooth and planar vertical surface. Despite the fractal roughness of some of the fracture faces, there was a significant linear relationship (R 2 = 0.80) between the apparent θ e values and intrinsic θ e values measured on polished surfaces of the same rocks using the sessile drop method. The regression equation indicated the apparent θ e values were consistently greater than the intrinsic values. This overestimation may be due to averaging of pixels at the air-water-solid interface, a required step in the image analysis. Further exploration of the range of applicability and measurement accuracy of this proposed new technique would be valuable.

58 GEOSCIENCES↗

A Modeling framework for flocculated cohesive sediment transport in the current bottom boundary layer

Cohesive sediment transport, where its settling velocity is controlled by the flocculation process, is a crucial component in determining biochemical cycles, fate of pollutants, and morphodynamics in many aquatic ecosystems. In this study, a modeling framework is presented to investigate how flocculation influences cohesive sediment transport in the current bottom boundary layer in dilute conditions, consistent with the calibration range of the flocculation model. From a local analysis of floc dynamics in homogenous turbulence, we identify that the floc size distribution is mainly controlled by floc cohesion and yield strength. The uncertainty in fractal dimension plays a minor role for the floc size but it influences the resulting floc density and settling velocity. The transport analysis in the current boundary layer shows that the flocculation process alters the vertical distribution of the settling velocity and hence the sediment concentration with a strong dependence on cohesion, floc yield strength, and floc structure. When the flocs are more susceptible to breaking, a well-mixed concentration profile is obtained. In contrast, for flocs with higher cohesion or yield strength, higher concentration with a sharp gradient is observed close to the bed. Overall, the settling velocity exhibits a low vertical variability within 20 % of the depth-averaged value except near the bed. Further, this suggests that using a depth-averaged settling velocity yields acceptable predictions of the sediment concentration profiles, especially for flocs with lower cohesion.

54 ENVIRONMENTAL SCIENCES↗

Hinderance of C-S-H sheet piling during first drying using a shrinkage reducing agent: A SAXS study

The role of a shrinkage reducing agent (SRA) in the hardened cement paste during a first desorption process was investigated by measuring the small-angle X-ray scattering (SAXS). Fractal disc analysis and Guinier approximation were adopted to interpret the SAXS profiles. We experimentally confirmed that the presence of SRA molecules mitigated the piling of calcium-silicate hydrate (C-S-H) sheets, which could be monitored by the increase in the thickness of the disc, representing the agglomeration of C-S-H sheets. In addition, the basal spacing of C-S-H did not change during the drying. By contrast, the diameter of the discs monotonically decreased and showed a similar trend to that of samples lacking SRA. Based on these findings, we concluded that SRA molecules were on the surface of the C-S-H sheets and mitigated the piling, facilitating water removal from the C-S-H agglomeration in the RH range of 80–40%.

36 MATERIALS SCIENCE↗