Scalar Diffusion Research Articles

Visualising and mapping historical networks of international diplomatic training

AbstractWhat might methodological approaches drawing on Geographical Information Systems (GIS) and Social Network Analysis (SNA) offer to sub‐disciplines in geography which have traditionally been dominated by qualitative and often micro‐scale research, such as historical or political geography? How might these approaches—often understood as opposing—be brought together to advance transnational research in particular? This article responds to these questions through a reflection on a recent project on the geopolitics of diplomatic training in the mid‐twentieth century. Building on the established use of biography to focus transnational analyses within a complex abundance of sources, the project complemented such close‐reading with computational methods of distant‐reading, able to analyse large datasets to produce prosopographies and network visualisations that help identify diffuse and larger scale political and geographical relationships. The article concludes with a consideration of how such methods might be effectively integrated in the historical or political geographer's toolkit.

A Case of Severe Erythroderma in a Patient with Pustular Psoriasis

Case Presentation: A patient with a known history of pustular psoriasis presented with sub-acute development of diffuse erythema and scaling of the skin with areas of exfoliation consistent with erythroderma. She was ill appearing and required admission and aggressive treatment with steroid-impregnated wet dressings, topical emollients, analgesics and systemic immunosuppressants. Discussion: Erythroderma is a dermatologic emergency characterized by diffuse erythema and scaling spanning >90% of skin surfaces and is associated with a mortality rate as high as 64%. It is initially a clinical diagnosis and needs to be recognized and aggressively treated expeditiously to improve chances of a good outcome.

Trichoscopic Evaluation of Focal Non-Cicatricial Alopecia in Egyptian Children

Introduction: Dermoscopy is a noninvasive diagnostic tool that allows the recognition of morphologic structures not visible to the naked eye. Trichoscopy is useful for the diagnosis and follow-up of hair and scalp disorders. Objective: The aim of the present study is to evaluate the causes of focal non-cicatricial alopecia in Egyptian children and to assess the importance of the trichoscope in the diagnosis of each disease. Methods: This study was done with 200 Egyptian children patients aged from 2 to 18 years who suffered from focal non-cicatricial alopecia. Clinical and dermoscopic evaluations were performed for all patients, and informed consent was obtained from their parents. Results: The most prevalent diagnoses were alopecia areata (42%) and tinea capitis (40.5%), followed by trichotillomania (8%) and tractional alopecia (7%). Congenital triangular alopecia (1.5%) and patchy androgenetic alopecia (1%) were less common. Trichoscopy revealed distinct features in alopecia areata cases, such as short vellus hair, exclamation mark hair, black dots, broken hair, pigtail hair and upright regrowing hair. The most common trichoscopic features of tinea capitis were comma hair, corkscrew hair, broken hair, bent hair, zigzag hair, morse code hair, perifollicular scaling, and diffuse scaling. These findings contribute to understanding the etiology and clinical presentation of childhood alopecia, facilitating accurate diagnosis and appropriate management. Conclusion: The routine use of dermoscopy in the clinical evaluation of scalp and hair disorders enhances diagnostic capabilities beyond simple clinical inspection. Dermoscopy reveals disease features that contribute to accurate diagnosis and improved management.

CNN for scalar-source distance estimation in grid-generated turbulence

Countermeasures against material leakage in industrial plants call for rapid leak source estimation techniques based on limited downstream information. Assuming that such scalar diffusion occurs in a turbulent environment, it is necessary to extract features from its instantaneous local concentration distribution and estimate the distance from the observation point to the source. To this end, we proposed an estimation method using a supervised deep learning of a convolutional neural network (CNN) and investigated its estimation performance in grid-generated turbulence fields. The grid turbulence fields were reproduced by direct numerical simulations at three Reynolds numbers (Re), and the CNN was trained using two-dimensional distribution images of passive scalars downstream. We confirmed that the images large enough to cover the spatial integral length scales of the scalar resulted in high estimation accuracy. For images with a coarsened brightness gradation, the small-scale feature of scalar fluctuations was lost, and the CNN attained a low estimation accuracy. By training the CNN with high-Re images, a high estimation accuracy was obtained, even for low-Re images. The opposite case (low-Re training and high-Re estimation) yielded low accuracy, where the CNN significantly underestimated the distance against the source. Based on these results, we discussed the generalizability and essential features to be learned by the CNN.

The formation and post-formation processes of vortex rings discharged from laminar starting jets

Motivated by biological systems, vortex rings can enhance the propulsive efficiency in industrial systems. To study the vortex properties during the formation and post-formation stages, impulsively starting jets are investigated by simulations. The effects of the stroke ratio and nozzle geometry are studied at a fixed jet Reynolds number of 2500. The stroke ratio at the formation number is found to be not enough to produce a vortex ring with maximum circulation. The stroke ratio is suggested to be about twice as large as the formation number. An alternative criterion based on the circulation ratio is proposed to describe the onset of pinch-off. This criterion states that the pinch-off would start when the vortex ring attains about 80% of the total jet circulation. During the formation stage, the scaling laws for vortex trajectories and circulation are proposed for continuous formation. By combining the suggested scaling relations and Saffman's velocity formula, the evolution of non-dimensional energy can be predicted. During the post-formation stage, the scaling laws for vortex properties (e.g., the vortex ring diameter, translational velocity, and circulation) are found to be independent of both the nozzle configuration and the vortex Reynolds number. On the grounds of the invariance of impulse in vortex decay, the scaling laws of vortex motion are derived for the non-dimensional energy, circulation, and diffusivity scale of the vortex core. In consequence, the normalized energy and circulation found in experiments can be successfully derived from the similarity model for both nozzle configurations.

Diffusion-weighted MR image analysis based on gamma distribution model for differentiating benign and malignant brain tumors.

Considering the invasiveness of the biopsy method, we attempted to evaluate the ability of the gamma distribution model using magnetic resonance imaging images to stage and grade benign and malignant brain tumors. A total of 42 patients with malignant brain tumors (including glioma, lymphoma, and choroid plexus papilloma) and 24 patients with benign brain tumors (meningioma) underwent diffusion-weighted imaging using five b-values ranging from 0 to 2000 s/mm2 with a 1.5 T scanner. The gamma distribution model is expected to demonstrate the probability of water molecule distribution based on the apparent diffusion coefficient. For all tumors, the apparent diffusion coefficient, shape parameter (κ), and scale parameter (θ) were calculated for each b-value. In the staging step, the fractions (ƒ1, ƒ2, ƒ3) expected to reflect the intracellular, and extracellular diffusion and perfusion were investigated. Diffusion <1 × 10-4 mm2/s (ƒ1), 1 × 10-4 mm2/s < Diffusion > 3 × 10-4 mm2/s (ƒ2), and Diffusion >3 × 10-4 mm2/s (ƒ3); in the grading step, fractions were determined to check heavily restricted diffusion. Diffusion lower than 0.3 × 10-4 mm2/s (ƒ11). Diffusion lower than 0.5 × 10-4 mm2/s (ƒ12). Diffusion lower than 0.8 × 10-4 mm2/s (ƒ13). The findings were analyzed using nonparametric statistics and receiver operating characteristic curve diagnostic performance. Gamma model parameters (κ, ƒ1, ƒ2, ƒ3) showed a satisfactory difference in differentiating meningioma from glioma. For b value = 2000 s/mm2, ƒ1 had a better diagnostic performance than κ and apparent diffusion coefficient (sensitivity, 88%; specificity, 68%; P < .001). The best diagnostic performance was related to ƒ3 in b = 2000 s/mm2 (area under the curve = 0.891, sensitivity = 83%, specificity = 80%, P < .001). In the grading step, ƒ12 (area under the curve = 0.870, sensitivity = 92%, specificity = 72%, P < .001) had the best diagnostic performance in differentiating high-grade from low-grade gliomas with b = 2000 s/mm2. The findings of our study highlight the potential of using a gamma distribution model with diffusion-weighted imaging based on multiple b-values for grading and staging brain tumors. Its potential integration into routine clinical practice could advance neurooncology and improve patient outcomes through more accurate diagnosis and treatment planning.

Improved Dementia Prediction in Cerebral Small Vessel Disease Using Deep Learning-Derived Diffusion Scalar Maps From T1.

Cerebral small vessel disease is the most common pathology underlying vascular dementia. In small vessel disease, diffusion tensor imaging is more sensitive to white matter damage and better predicts dementia risk than conventional magnetic resonance imaging sequences, such as T1 and fluid attenuation inversion recovery, but diffusion tensor imaging takes longer to acquire and is not routinely available in clinical practice. As diffusion tensor imaging-derived scalar maps-fractional anisotropy (FA) and mean diffusivity (MD)-are frequently used in clinical settings, one solution is to synthesize FA/MD from T1 images. We developed a deep learning model to synthesize FA/MD from T1. The training data set consisted of 4998 participants with the highest white matter hyperintensity volumes in the UK Biobank. Four external validations data sets with small vessel disease were included: SCANS (St George's Cognition and Neuroimaging in Stroke; n=120), RUN DMC (Radboud University Nijmegen Diffusion Tensor and Magnetic Resonance Imaging Cohort; n=502), PRESERVE (Blood Pressure in Established Cerebral Small Vessel Disease; n=105), and NETWORKS (n=26), along with 1000 normal controls from the UK Biobank. The synthetic maps resembled ground-truth maps (structural similarity index >0.89 for MD maps and >0.80 for FA maps across all external validation data sets except for SCANS). The prediction accuracy of dementia using whole-brain median MD from the synthetic maps is comparable to the ground truth (SCANS ground-truth c-index, 0.822 and synthetic, 0.821; RUN DMC ground truth, 0.816 and synthetic, 0.812) and better than white matter hyperintensity volume (SCANS, 0.534; RUN DMC, 0.710). We have developed a fast and generalizable method to synthesize FA/MD maps from T1 to improve the prediction accuracy of dementia in small vessel disease when diffusion tensor imaging data have not been acquired.

Diffusive scaling limit of the Busemann process in last passage percolation

Diffusive scaling limit of the Busemann process in last passage percolation

On the Convergence of the Drainage Network with Branching

The Drainage Network is a system of coalescing random walks, exhibiting long-range dependence before coalescence, introduced by Gangopadhyay, Roy, and Sarkar [14]. Coletti, Fontes, and Dias [5] proved its convergence to the Brownian Web under diffusive scaling. In this work, we introduce a perturbation of the system allowing branching of the random walks with low probabilities varying with the scaling parameter. When the branching probability is inversely proportional to the scaling parameter, we show that this drainage network with branching consists of a tight family such that any weak limit point contains a Brownian Net. We conjecture that the limit is indeed the Brownian Net.

Impact of pathogenic variants of the Ras-mitogen-activated protein kinase pathway on major white matter tracts in the human brain.

Noonan syndrome and neurofibromatosis type 1 are genetic conditions linked to pathogenic variants in genes of the Ras-mitogen-activated protein kinase signalling pathway. Both conditions hyper-activate signalling of the Ras-mitogen-activated protein kinase pathway and exhibit a high prevalence of neuropsychiatric disorders. Further, animal models of Noonan syndrome and neurofibromatosis type 1 and human imaging studies show white matter abnormalities in both conditions. While these findings suggest Ras-mitogen-activated protein kinas pathway hyper-activation effects on white matter, it is unknown whether these effects are syndrome-specific or pathway-specific. To characterize the effect of Noonan syndrome and neurofibromatosis type 1 on human white matter's microstructural integrity and discern potential syndrome-specific influences on microstructural integrity of individual tracts, we collected diffusion-weighted imaging data from children with Noonan syndrome (n = 24), neurofibromatosis type 1 (n = 28) and age- and sex-matched controls (n = 31). We contrasted the clinical groups (Noonan syndrome or neurofibromatosis type 1) and controls using voxel-wise, tract-based and along-tract analyses. Outcomes included voxel-wise, tract-based and along-tract fractional anisotropy, axial diffusivity, radial diffusivity and mean diffusivity. Noonan syndrome and neurofibromatosis type 1 showed similar patterns of reduced fractional anisotropy and increased axial diffusivity, radial diffusivity, and mean diffusivity on white matter relative to controls and different spatial patterns. Noonan syndrome presented a more extensive spatial effect than neurofibromatosis type 1 on white matter integrity as measured by fractional anisotropy. Tract-based analysis also demonstrated differences in effect magnitude with overall lower fractional anisotropy in Noonan syndrome compared to neurofibromatosis type 1 (d = 0.4). At the tract level, Noonan syndrome-specific effects on fractional anisotropy were detected in association tracts (superior longitudinal, uncinate and arcuate fasciculi; P < 0.012), and neurofibromatosis type 1-specific effects were detected in the corpus callosum (P < 0.037) compared to controls. Results from along-tract analyses aligned with results from tract-based analyses and indicated that effects are pervasive along the affected tracts. In conclusion, we find that pathogenic variants in the Ras-mitogen-activated protein kinase pathway are associated with white matter abnormalities as measured by diffusion in the developing brain. Overall, Noonan syndrome and neurofibromatosis type 1 show common effects on fractional anisotropy and diffusion scalars, as well as specific unique effects, namely, on temporoparietal-frontal tracts (intra-hemispheric) in Noonan syndrome and on the corpus callosum (inter-hemispheric) in neurofibromatosis type 1. The observed specific effects not only confirm prior observations from independent cohorts of Noonan syndrome and neurofibromatosis type 1 but also inform on syndrome-specific susceptibility of individual tracts. Thus, these findings suggest potential targets for precise, brain-focused outcome measures for existing medications, such as MEK inhibitors, that act on the Ras-mitogen-activated protein kinase pathway.

Vibrational frequency fluctuations of poly(N,N-diethylacrylamide) in the vicinity of coil-to-globule transition studied by two-dimensional infrared spectroscopy and molecular dynamics simulations.

Poly(N,N-diethylacrylamide) (PdEA), one of the thermoresponsive polymers, in aqueous solutions has attracted much attention because of its characteristic properties, such as coil-to-globule (CG) transition. We performed two-dimensional infrared spectroscopy and molecular dynamics (MD) simulations to understand the hydration dynamics in the vicinity of the CG transition at the molecular level via vibrational frequency fluctuations of the carbonyl stretching modes in the side chains of PdEA. Furthermore, N,N-diethylpropionamide, a repeating monomer unit of PdEA, is also investigated for comparison. From decays of the frequency-frequency time correlation functions (FFTCFs) of the carbonyl stretching modes, we consider that inhomogeneity of the hydration environments originates from various backbone configurations of PdEA. The degree of the inhomogeneity depends on temperature. Hydration water molecules near the carbonyl groups are influenced by the confinements of the polymers. The restricted reorientation of the embedded water, the local torsions of the backbone, and the rearrangement of the whole structure contribute to the slow spectral diffusion. By performing MD simulations, we calculated the FFTCFs and dynamical quantities, such as fluctuations of the dihedral angles of the backbone and the orientation of the hydration water molecules. The simulated FFTCFs match well with the experimental results, indicating that the retarded water reorientations via the excluded volume effect play an important role in the vibrational frequency fluctuations of the carbonyl stretching mode. It is also found the embedded water molecules are influenced by the local torsions of the backbone structure within the time scales of the spectral diffusion.

Sequence programmable nucleic acid coacervates.

Nature uses bottom-up self-assembly to build structures with remarkable complexity and functionality. Understanding how molecular-scale interactions translate to macroscopic properties remains a major challenge and requires systems that effectively bridge these two scales. Here, we generate DNA and RNA liquids with exquisite programmability in their material properties. Nucleic acids are negatively charged, and in the presence of polycations, they may condense to a liquid-like state. Within these liquids, DNA and RNA retain sequence-specific hybridization abilities. We show that intermolecular hybridization in the condensed phase cross-links molecules and slows down chain dynamics. This reduced chain mobility is mirrored in the macroscopic properties of the condensates. Molecular diffusivity and material viscosity scale with the intermolecular hybridization energy, enabling precise sequence-based modulation of condensate properties over orders of magnitude. Our work offers a robust platform to create self-assembling programmable fluids and may help advance our understanding of liquid-like compartments in cells.

Glymphatic system dysfunction in mood disorders: Evaluation by diffusion magnetic resonance imaging

The glymphatic system, an expansive cerebral waste-disposal network, harbors myriad enigmatic facets necessitating elucidation of their nexus with diverse pathologies. Murine investigations have revealed a relationship between the glymphatic system and affective disorders. This study aimed to illuminate the interplay between bipolar disorder and the glymphatic system. Fifty-eight individuals afflicted with bipolar disorder were identified through meticulous psychiatric assessment. These individuals were juxtaposed with a cohort of 66 comparably aged and sex-matched, mentally stable subjects. Subsequent analysis entailed the application of covariance analysis to evaluate along with the perivascular space (ALPS) index, a novel magnetic resonance imaging method for assessing brain interstitial fluid dynamics via diffusion tensor imaging within the bipolar and control cohorts. We also evaluated the correlation between the ALPS index and clinical parameters, which included the Hamilton Depression scale scores, disease duration, and other clinical assessments. Moreover, partial correlation analyses, incorporating age and sex as covariates, were performed to investigate the relationships between the ALPS index and clinical measures within the two cohorts. A noteworthy adverse correlation was observed between the ALPS index and illness duration. A free-water imaging analysis revealed a substantial elevation in the free-water index within the white-matter tracts, prominently centered on the corpus callosum, within the bipolar cohort relative to that in the control group. In analogous cerebral regions, a conspicuous affirmative correlation was observed between the free-water–corrected radial diffusivity and depression rating scales. Our results showed that the protracted course of bipolar disorder concomitantly exacerbated glymphatic system dysregulation.

Vanishing self-diffusivity in Ginibre interacting Brownian motions in two dimensions

AbstractWe prove that the tagged particles of infinitely many Brownian particles in $$ {\mathbb {R}} ^2$$ R 2 interacting via a logarithmic (two-dimensional Coulomb) potential with inverse temperature $$ \beta = 2 $$ β = 2 are sub-diffusive. The associated unlabeled diffusion is reversible with respect to the Ginibre random point field, and the dynamics are thus referred to as the Ginibre interacting Brownian motion. If the interacting Brownian particles have interaction potential $$ \Psi $$ Ψ of Ruelle class and the total system starts in a translation invariant equilibrium state, then the tagged particles are always diffusive if the dimension $$ d$$ d of the space $$ {\mathbb {R}}^{d} $$ R d is greater than or equal to two. That is, the tagged particles are always non-degenerate under diffusive scaling. Our result is, therefore, contrary to known results. The Ginibre random point field has various levels of geometric rigidity. Our results reveal that the geometric property of infinite particle systems affects the dynamical property of the associated stochastic dynamics.

Scalar curvature for metric spaces: Defining curvature for quantum gravity without coordinates

Geometrical properties of spacetime are difficult to study in nonperturbative approaches to quantum gravity like causal dynamical triangulations (CDT), where one uses simplicial manifolds to define the gravitational path integral, instead of Riemannian manifolds. In particular, in CDT one only relies on two mathematical tools, a distance measure and a volume measure. In this paper, we define a notion of scalar curvature, for metric spaces endowed with a volume measure or a random walk, without assuming nor using notions of tensor calculus. Furthermore, we directly define the Ricci scalar, without the need of defining and computing the Riemann or the Ricci tensor . For this, we make use of quantities, like the surface of a geodesic sphere, or the return probability of scalar diffusion processes, that can be computed in these metric spaces, as in a Riemannian manifold, where they receive scalar curvature contributions. Our definitions recover the classical results of scalar curvature when the sets are Riemannian manifolds. We propose two methods to compute the scalar curvature in these spaces, and we compare their features in natural implementations in discrete spaces. The defined generalized scalar curvatures are easily implemented on discrete spaces, like graphs. We present the results of our definitions on random triangulations of a 2D sphere and plane. Additionally, we show the results of our generalized scalar curvatures on the quantum geometries of 2D CDT, where we find that all our definitions indicate a flat ground state of the gravitational path integral. Published by the American Physical Society 2024

Enhanced diffusion and universal Rouse-like scaling of an active polymer in poor solvent

Enhanced diffusion and universal Rouse-like scaling of an active polymer in poor solvent

Coupled Simultaneous Evolution of Policy, Enterprise Innovation Awareness, and Technology Diffusion in Multiplex Networks

This study comprehensively examines the coupling effect of government policies, enterprise behavior, and existing technology on the diffusion of innovative technology. Utilizing multiplex network theory, a multiplex network model is constructed to couple policy incentives, enterprise innovation consciousness, and technology diffusion. Both global- and local-order parameters are introduced to characterize the interaction mechanisms between new and old technologies. By employing the microscopic Markov chain approach (MMCA), the threshold for technology diffusion is derived, theoretically revealing the mechanisms behind the diffusion of innovative technology. Considering the heterogeneity of enterprises, a numerical simulation is conducted on a scale-free network. The results indicate that, as the intensity of policy incentives increases, the threshold for technology diffusion decreases, promoting the spread of innovative technology. Additionally, the coupling relationship between existing technology and innovative technology influences the diffusion scale of the latter. The innovation behavior of enterprises further facilitates the adoption and dissemination of innovative technology.

Vortical structures and passive scalar transport in starting process of annular purging jet

The evolution of vortical structures and passive scalar transport in the starting process of annular purging jets are numerically investigated by large eddy simulation. Three flow configurations with different nozzle-to-plate distances at a fixed radius ratio of 0.71 and the Reynolds number of 13 750 are simulated. The numerical results are validated against documented experimental data. Three stages during the evolution are proposed based on instantaneous flow visualizations and assessed by calculating the circulation changes of the annular jets and vortex rings. The vortical structures are identified to understand the three-dimensional characteristics. The entrainment process is analyzed focusing on the passive scalar transport in the flow fields and is correlated with the cleaning performance of annular purging jets. The flow structures dominate the process of scalar mixing, especially the inner and outer vortex rings. The large-scale motions of trailing jets cause the intermittent events of scalar transport. During the starting process, the cleaning performance is better with a smaller nozzle-to-plate distance, while the cleaning efficiency may reach the optimum at a moderate distance. The cleaning process is limited by the scalar diffusion and entrainment process. These findings highlight the significance of flow structures for effective cleanness of temperature and contaminations in the purging systems.

Green technology diffusion model and simulation considering enterprise technology absorption capacity

ABSTRACT The diffusion and wide application of green technologies are important means to achieve climate change mitigation. Concerning the green technology absorption capacity and technology diffusion willingness of enterprises, this paper divided enterprises into four categories, constructed a green technology diffusion model and analysed the equilibrium point and stability of the model. Then, we studied the diffusion process and laws of green technology through simulation experiments. The results show that in the green technology diffusion system, the basic regeneration number is the key factor in determining the equilibrium state of green technology diffusion. The disease-free equilibrium point of the green technology diffusion system is globally asymptotically stable, and the endemic equilibrium point is locally asymptotically stable. In order to improve the speed and scale of green technology diffusion, it is necessary to create green technology diffusion sources through multiple channels, improve enterprise technology absorption capacity through multiple methods, and enhance enterprise green technology diffusion willingness at multiple levels.

A model for drift velocity mediated scalar eddy diffusivity in homogeneous turbulent flows

A model for drift velocity mediated scalar eddy diffusivity in homogeneous turbulent flows