Mass transfer is often the rate determining step for solid-liquid chemical reactions. Decrease of the concentration boundary layer thickness is essential to intensify the chemical reaction. Because the concentration boundary layer exists in the velocity boundary layer, force imposition in the concentration boundary layer by superimposing an electrical current and a magnetic field was proposed. Through, flow can be directly excited in the concentration boundary layer. The previous result indicates that by superimposing a DC current and a gradient magnetic field, the development of the concentration boundary layer was suppressed, because of a macro-scale flow excitation in the whole vessel. And by superimposing the gradient magnetic field with a modulate current, the development of the concentration boundary layer was further suppressed. This is because of the macro-scale flow enhancement and the excitation of a micro-scale flow near the solid-liquid interface. However, the mechanism for the micro-scale flow excitation has not been clarified. To clarify this, a uniform magnetic field was superimposed with the DC current or the modulate current. By this means, only the micro-scale flow was excited near the anode surface. The results found that the non-unform electromagnetic force distribution is the main reason for the micro-scale flow excitation.

In the paper, we develop some numerical schemes including finite difference scheme and finite volume scheme for the fractional Laplacian operator, and apply the resulted numerical schemes to solve some fractional diffusion equations. First, the fractional Laplacian operator can be characterized as the weak singular integral by a integral operator with zero boundary condition. Second, because of the solution of fractional diffusion equation is usually singular near the boundary, we apply finite difference scheme to discrete fractional Laplacian operator and fractional diffusion equation by fractional interpolation function. Moreover, it is find that the differential matrix of the above scheme is symmetric matrix, and strictly row-wise diagonally dominant in special fractional interpolation function. Third, we show finite volume scheme to discrete fractional diffusion equation by fractional interpolation function, and analyze the properties of differential matrix. Finally, the numerical experiments are given, and verify the correctness of theoretical results and the efficiency of the schemes.

In our latest studies with the help of the self-similar Ansatz we derived new type of 1 solutions for the regular diffusion equation which are much more complex than the well-known 2 Gaussian and error functions. These solutions contain additional Kummer’s M and Kummer’s U 3 functions with quadratic argument. In the present treaties we perform an analogous analysis for the 4 regular diffusion equation which has a complex diffusion coefficient. Formally, it is equivalent to 5 the free Schrödinger equation however it is far from being trivial how the solutions can be given 6 quantum mechanical interpretation. We investigate both the one dimensional Cartesian and the 7 spherical symmetric equations. We find solutions which fulfill the L2 integrability criteria therefore 8 might have quantum mechanical relevance in the future.

We investigate the innovational determinants of “Patent Applications” in Europe. We use data from the European Innovation Scoreboard-EIS of the European Commission for 36 countries in the period 2010-2019. We use Panel Data with Fixed Effects, Panel Data with Random Effects, Pooled OLS, WLS and Dynamic Panel. We found that the variables that have a deeper positive association with “Patent Applications” are “Human Resources” and “Intellectual Assets”, while the variables that show a more intense negative relation with Patent Applications are “Employment Share in Manufacturing” and “Total Entrepreneurial Activity”. A cluster analysis with the k-Means algorithm optimized with the Silhouette Coefficient has been realized. The results show the presence of two clusters. A network analysis with the distance of Manhattan has been performed and we find three different complex network structures. Finally, a comparison is made among eight machine learning algorithms for the prediction of the future value of the “Patent Applications”. We found that PNN-Probabilistic Neural Network is the best performing algorithm. Using PNN the results show that the mean future value of “Patent Applications” in the estimated countries is expected to decrease of -0.1%.

In this article we have estimated the value of “Opportunity Driven Entrepreneurship” in Europe. We use data from European Innovation Scoreboard-EIS of the European Commission for 36 countries in the period 2010-2019. We use Panel Data with Fixed Effects, Panel Data with Random Effects, WLS, Pooled OLS, and Dynamic Panel. Our results show that “Opportunity Driven Entrepreneurship” is positively associated, among others, to “Innovation Friendly Environment” and “Turnover Share Large Enterprises”, while it is negatively associated, among others, to “Sales Impacts” and “R&D Expenditure Business Sectors”.

The research results conducted on binderless tungsten carbide (WC) ceramics obtained by Spark Plasma Sintering (SPS) of WC powders with different average particle sizes (0.095, 0.8, 3 μm) are presented. Nonuniform distribution of crystalline phases and microstructure of the WC ceramics was studied using layer-by-layer XRD analysis and SEM. Surface layers of the WC-based ceramics are characterized by nonuniform distribution of W2C crystalline phase and grain sizes, including the appearance of abnormally large grains. Thickness of the nonuniform layer was at least 50 μm. The effect under study is associated with an intense carbon diffusion from graphite foil. On the one hand, this contributed to a decrease in the intensity of W2C phase particle formation, which is transformed into α-WC phase due to the carbon. On the other hand, it caused abnormal grain growth in the layer where the carbon diffused. The obtained value of the carbon diffusion depth exceeds the values known from the literature (up to 1 μm in the case of volume diffusion even at temperature of 2370℃ and exposure time of ~ 60 h). The use of boron nitride (BN) as a protective coating on graphite mold parts did not prevent the formation of nonuniform layer on the ceramic surface.

As part of a comprehensive research on eco-friendly processing techniques, the influence of heat treatment environment on the case-hardening of AISI 1018 steel using pulverized cassava leaf was studied. The process was carried out at two different temperatures (850˚C and 950˚C) and under three environmental conditions: (Process 1) the control experiment, was carried out in air only, (Process 2) the medium comprised of pulverized cassava leaves, and (Process 3) the combination of pulverized cassava leaves plus barium carbonate (BaCO3) as an energizer (CBC mixture). Vickers microhardness testing and scanning electron microscopy were used to evaluate the effect of processing environment on case hardening of the steel. As expected, regardless of the processing temperature, Process 1 resulted in little or no hardening of the steel surface. However, notable case hardening occurred when steel specimens were subjected to either Process 2 or Process 3. Furthermore, the inclusion of barium carbonate in Process 3 significantly enhanced the case hardening effectiveness of the cassava leaf as it pertains to rate and maximum hardness achieved. Maximum enhancement was observed at 950oC. After 1 hour, the increase in hardness were 160% and 280%, for Process 2 and Process 3, respectively. Upon increasing the processing time to 5 hours, the increase in hardness due to Process 2 was raised to 254%, while that of Process 3 remained at approximately 280%. Diffusivity of AISI 1018 was calculated using the microhardness data. Diffusivity was highest in Process 2 samples with values of 1.568 x 10-9 m2/s at 850°C and 1.893 x 10-9 m2/s at 950 °C.

In this paper a combined Laplace transform (LT) and boundary element method (BEM) is used to find numerical solutions to problems of anisotropic functionally graded media which are governed by the transient diffusion-convection-reaction equation. First, the variable coefficients governing equation is reduced to a constant coefficients equation. Then, the Laplace-transformed constant coefficients equation is transformed a boundary-only integral equation. Using a BEM, the numerical solutions in the frame of Laplace transform may then be obtained from this integral equation. Then the solutions are inversely transformed numerically using the Stehfest formula. Some problems considered are those of compressible or incompressible flow, and of media which are quadratically, exponentially and trigonometrically graded materials. The results obtained show that the analysis used to transform the variable coefficients equation into the constant coefficients equation is valid, and the mixed LT-BEM is easy to implement for obtaining the numerical solutions. The numerical solutions are verified by showing their accuracy and steady state. For symmetric problems, the symmetry of solutions is also justified. Moreover, the effect of the anisotropy and inhomogeneity of the material on the solutions are also shown, as to suggest that it is important to take the anisotropy and inhomogeneity into account when doing experimental studies.

Colorectal liver metastases (CRLM) patients combined with hepatic lymph node metastases was a negative prognostic factor associated with outcomes. Up to now, there was still lack of a reliable method to identify the status of hepatic lymph nodes. The aim of this study was to investigate the predictive ability of mono-exponential, bi-exponential, and stretched-exponential diffusion-weighted imaging (DWI) models to distinguish between benign and malignant hepatic lymph nodes in CRLM patients who underwent neoadjuvant chemotherapy prior to surgery. In total, 97 CRLM patients with pathologically proved hepatic lymph node status were included. Various quantitative parameters, including the apparent diffusion coefficient (ADC) from mono-exponential model, D, D*, and f derived from intravoxel incoherent motion (IVIM) model, as well as DDC and α from stretched-exponential model (SEM), were measured. Multivariate analysis revealed that the pre- treatment DDC value and the short diameter of the largest lymph node after treatment were independent predictors of metastatic hepatic lymph nodes. A nomogram combining these two factors demonstrated excellent performance in distinguishing between benign and malignant lymph nodes in CRLM patients, with an area under the curve (AUC) of 0.873. Therefore, the nomogram can serve as a preoperative assessment tool for determining the status of hepatic lymph nodes and aiding in the decision-making process for surgical treatment in CRLM patients.

A two-layer Fe-Cr-Al-Zr surface alloy was synthesized on a zirconium substrate by magnetron sputtering and subsequent low-energy high-current electron-beam (LEHCEB) processing. Thicknesses of the top Fe69Cr20Al11 (at.%) relatively large-grained (~1 µm) and transition Fe-Zr Cr-Al amorphous layers were about 0.7 and 0.6 µm, respectively. In turn, the amorphous layer consisted of two Fe64–54Zr8–22Cr21–17Al8–7 and Fe40–16Zr42–78Cr12–4Al6–2 (at.%) sublayers, differing in both zirconium and iron concentrations in wide ranges, which were separated by another nanocrystalline interlayer. The Fe-Cr-Al-Zr surface alloy serve as a diffusion barrier, preventing interaction of the zirconium substrate with oxygen from an environment. It was thermally stable up to ≈1173 K.

This article focuses on the analysis of dynamics emerging in a Network of Hodgkin-Huxley Reaction-Diffusion equations. The network is forced with three external periodic stimulus input. A synchronization phenomenon is observed.

Using analysis methods such as Rutherford backscattering Spectrometry, scanning electron microscopy, X-ray diffraction, and Raman spectroscopy, the diffusion behavior of iodine in micro/nano-porous graphite under high-temperature conditions was studied. The results indicate that iodine diffusion leads to the contraction of graphite microcrystals, a decrease in interlayer spacing, and an increase in defect density, resulting in a reduction in microcrystal size. Upon diffusion of iodine out of iodine-loaded graphite, the microcrystal size of the graphite increases, the interlayer spacing appears to return to the initial state, and the defect density decreases. By comparing the iodine diffusion performance of nanoporous graphite G400 and G450 with microporous graphite G500, it was determined that nanoporous graphite exhibits better inhibition of iodine diffusion compared to microporous graphite. Studying the diffusion behavior of iodine in micro/nano-porous graphite has significant academic significance and engineering value for the screening, design, and performance optimization of nuclear graphite.

In a previous paper, we solved the partial differential equation of Mullins problem in the case of the evaporation-condensation in electronic devices and gave an exact solution relative to the geometric profile of the grain boundary grooving when materials are submitted to thermal and mechanical solicitation and fatigue effect. In this new research, new modelling of the grain groove profile was proposed and new analytical expressions of the groove profile, the derivative and the groove depth were obtained in the case of diffusion in thin polycrystalline films by the resolution of the fourth differential equation formulated by Mullins that supposed 〖y'〗^2≪1. The obtained analytical solution gave more accurate information on the geometric characteristics of the groove that were necessary to study the depth and the width of the groove. These new findings will open a new way to study with more accuracy the problem of the evaporation-condensation combined to the diffusion phenomenon on the material surfaces with the help of the analytical solutions.

The paradigm of molecular communications is applied to the concrete case for delivering electrically charged nanoparticles to tumor. Once them have been injecetd in blood it is expecetd an optimal outcome as to reduce toxicity and minimal dispersion of drugs in the blood stream. With a fraction of nanoparticles arrives to surface of tumor, the scattered part of injected ones can minimize the success of scheme of drug delivery. In this paper is presented a theory based at the sequence electrodynamics-diffusion-Bayes theorem. The resulting probability of Bayes at the end of sequence, might be telling us that dynamical processes based in the injection of electrically charged nanoparticles might be dictated by stochastic formalism more that biochemical approaches by which makes impossible to know the success or fail of drug delivery dynamics. Illustrations demonstrating the transition of a linear to nonlinear scenario are presented

TThis paper delves into the extension and characterization of radial positive definite functions into non-integer dimensions. We provide a thorough investigation by employing the Riemann-Liouville fractional integral and fractional Caputo derivatives, enabling a comprehensive understanding of these functions. Additionally, we introduce a secondary characterization based on the Bernstein characterization of completely monotone functions. The practical significance of our study is showcased through an examination of the positivity of the fundamental solution of the space-fractional Bessel diffusion equation, highlighting the real-world applicability of the developed concepts. Through this work, we contribute to the broader understanding of radial positive definite functions and their utility in diverse mathematical and applied contexts.

Keywords: Amorphous-precipitate, Nitride, Morphological stability, Diffusion, Internal stresses, Modelling, Simulation

: Broad-spectrum antifungal drug deployed for topical therapy, specific for onychomycosis, Itraconazole was used as the active pharmaceutical ingredient in a nail lacquer formulation1. The objective of the study was to optimize an antifungal nail lacquer, which when applied topically onto the dorsal surface of the nail plate would facilitate the transungual penetration of the drug. Itraconazole hydrochloride was synthesized to aid the formulation of the lacquers. The optimization involved comparing four different formulations of 1%w/w Itraconazole nail lacquers containing combinations of penetration enhancers (Urea, Salicylic acid, and Papain) based on their ability to facilitate diffusion of the drug through the nail plate over five days. The drug uptake was quantified by extracting the drug from the nail clippings and analyzing it. The tests conducted to account for the quality of the optimized formulation were drug content, spreadability, check for precipitation, and accelerated stability. The results demonstrated that the optimized 1%w/w Itraconazole nail lacquer contained 5%w/w Salicylic acid, 5 %w/w Papain, and 2.8% w/w Urea. The drug uptake from nail clippings was higher than the MIC90 for T. Rubrum strain, and the quality of the optimized lacquer was not compromised throughout three weeks2. The hypothesis stated that the inclusion of Salicylic acid, Papain, and Urea in an Itraconazole (1%w/w) nail lacquer would have the highest transungual penetration on application to the nail plate. In conclusion, the hypothesis was accepted, and the optimized lacquer passed the drug uptake evaluation and all quality control tests.

The service life of the reinforced concrete structure in the marine environment can be impaired significantly due to chloride-induced corrosion. However, how the chloride diffusion in pre-cracked concrete structures is affected by the hydrostatic pressure magnitude is poorly understood. This study experimentally examined the effect of hydrostatic pressure on the chloride diffusion in pre-cracked concrete. Cracks with five different widths, i.e., 20 μm, 40 μm, 60 μm, 80 μm, and 100 μm, were manually created using a splitting tensile apparatus respectively. The chloride diffusion in the concrete with a certain crack was then studied under four different hydrostatic pressures of 0 MPa, 0.1 MPa, 0.3 MPa, and 0.5 MPa. Experimental results show that the chloride diffusion in concrete with a crack greatly relies on both the hydrostatic pressure and the crack width. The chloride concentration increases as the hydrostatic pressure grows, particularly for the wider cracks with width ranging from 60 μm to 100 μm. Surprisingly, the hydrostatic pressure has a negligible effect on the chloride distribution in the concrete with a crack width no larger than 40 μm. Both the chloride diffusion coefficient and the surface chloride concentration of concrete increased gradually as the hydrostatic pressure increased. The experimental findings enrich our understanding of the behavior of pre-cracked concrete when exposed to chloride-induced corrosion at different depths of marine environments.

The focus of this paper is on analyzing the role and the choice of parameters in sociophysics diffusion models, by leveraging the potentialities of sociophysics from a mathematical programming perspective. We first present a generalised version of Galam’s opinion diffusion model (see, e.g. , ). For a given selection of the coefficients in our model, this proposal yields the original Galam’s model. The generalised model suggests guidelines for possible alternative selection of its parameters that allow to foster diffusion. Examples of the parameters selection process as steered by numerical optimisation, taking into account various objectives, are provided.

This paper constituted an extension of two previous studies concerning the mathematical development of the grain boundary grooving in polycrystalline thins films in the cases of the evaporation/condensation and diffusion taken separately. The thermal grooving processes are deeply controlled by the various mass transfer mechanisms of evaporation–condensation, surface diffusion, lattice diffusion, and grain boundary diffusion. This study proposed a new original analytical solution to the mathematical problem governing the grain groove profile in the case of simultaneous effects of evaporation-condensation and diffusion in polycrystalline thin films submitted to thermal and mechanical stress, and fatigue effects; by resolving the corresponding fourth-order partial differential equation ∂y∂t=C∂2y∂x2-B∂4y∂x4 obtained from the approximation y'2≪1. The comparison of the new solution to that of diffusion alone proved an important effect of the coupling of evaporation and diffusion on the geometric characteristics of the groove profile. A second analytical solution based on the series development was also proposed. It was proved that change of the boundary conditions of the grain grooving profile largely affected the different geometric characteristics of the groove profile.

This paper presents a numerical method for solving a two-dimensional subdiffusion equation with a Caputo fractional derivative. The problem considered assumes symmetry in both the equation’s solution domain and the boundary conditions, allowing for a reduction of the two-dimensional equation to a one-dimensional one. The proposed method is an extension of the fractional Crank-Nicolson method, based on the discretization of the equivalent integral-differential equation. To validate the method, the obtained results were compared with a solution obtained through Laplace transform. The analytical solution in the image of the Laplace transform was inverted using the Gaver-Wynn-Rho algorithm implemented in the specialized mathematical computing environment, Wolfram Mathematica. The results clearly show the mutual convergence of the solutions obtained by the two methods.

Polymer electrolyte was used as a medium for testing the performance of microband electrodes under conditions of linear diffusion. Cyclic voltammetry and chronoamperometry experiments were performed in such viscous medium, where diffusion rates are much slower than in fluid solutions. Confirmation of the existence of such conditions from the log i vs. log v or log i vs. log t relationships in the current equation always yielded values lower than the expected value of 0.5. This could indicate impure linear diffusion profile, i. e. some contribution from radial diffusion (edge effect). However, performing these tests in monomeric solvents of similar viscosities, such as glycerol or propylene glycol, gave the desired value of 0.5. These results lead to the conclusion that current equations which are based on Fick’s laws may not be applicable for polymer electrolytes, where various obstruction to diffusion make it a more complicated process than in monomeric solvents.

Predictions of mean values of statistical variables of large scale turbulent flow by the widely used basic k-ϵ model and a new fundamentally based model are verified against published results of Direct Numerical Simulations DNS of the Navier-Stokes equations. The verification concerns turbulent channel flow at shear Reynolds numbers of 950, 2000 and 104. The basic k-ϵ model is largely based on empirical formulations accompanied by calibration constants. This contrasts with the new model where descriptions of leading statistical quantities are based on the general principles of statistical turbulence at large Reynolds number. Predicted values of major output variables such as turbulent viscosity, diffusivity of passive admixture, temperature, and fluid velocities compare well with DNS in case of the new model. Significant differences are seen in case of the basic k-ϵ model.

The diffusion coefficient (D) is a key parameter characterizing gas transport in coal seams. Usually, the D is calculated from the desorption curve of particle coal, which cannot accurately reflect the diffusion characteristics under the stress constraint conditions of in-situ coal seams. In this paper, based on Fick's law of counter diffusion, different metamorphic deformed coals of medium and high coal rank are taken as the research object. The change laws of D under different confining pressure, gas pressure, and temperature conditions are tested and analyzed, and the influencing mechanisms on the D are discussed. The results show that the D of different metamorphic deformed coals decreases exponentially with the increase of confining pressure, and increases exponentially with the increase of gas pressure and temperature. There is a limit diffusion coefficient. The influence of confining pressure on the D is essentially determined by the change of effective stress, and the D has a negative effect of effective stress similar to permeability. The effect of gas pressure on the D involves two mechanisms, namely, mechanical and adsorption effects, which are jointly restricted by effective stress and coal particle shrinkage and expansion deformation. The effect of temperature on the D is mainly achieved by changing the root mean square speed and average free path of gas molecules. Under the same temperature and pressure conditions, the D increases first and then decreases with the increase of deformation degree, and the D of fragmented coal is the largest. Under similar deformation conditions, the D of high-rank anthracite is greater than that of medium-rank fat coal. It is considered that porosity is the key factor affecting the change of D in different metamorphic deformed coals.

For concrete structures exposed to offshore areas, chloride ion erosion is one of the main factors affecting the durability. It is crucial to evaluate chloride ion permeability resistance of concrete structures. In this article, a finite element simulation of the chloride ion diffusion process in concrete is conducted. A mass diffusion finite element model based on random aggregate approach is established to investigate the influence of aggregate, interface transition zone, and micro-cracks on chloride ion diffusion coefficients in concrete. The results show that the mass diffusion finite element analysis based on the exponential function model and power function model can effectively simulate the chloride ion diffusion process in concrete. In addition, the data reveal that coarse aggregate is the most important factor affecting chloride ion diffusivity in concrete. However, the interface transition zone significantly accelerates chloride ion diffusion in concrete. Moreover, this acceleration effect exceeds the barrier effect of aggregate.

The radiation-induced optical absorption at 1.5-5.5 eV (up to the beginning of fundamental absorption) has been analyzed in CVD diamond disks exposed to 231-MeV 132Xe ions with four fluences from 1012 to 3.81013 cm-2. The 5-mm diameter samples (thickness 0.4 mm) were prepared by Diamond Materials, Freiburg (Germany), average grain size at growth site was around 80 m, the range of xenon ions was R= 11.5 m. The intensity of several bands grows with ion fluence thus confirming radiation-induced origin of the defects responsible for these bands. The recovery of radiation damage has been investigated via isochronal (stepwise) thermal annealing procedure up to 650°C, while all spectra were measured at room temperature. Based on these spectra, the annealing kinetics of several defects, in particular carbon vacancies (GR1 centers with a broad band 2 eV) and complementary C-interstitial-related defects ( 4 eV), as well as vacancies located nearby nitrogen substitutional atoms (narrow bands around 2.5 eV) have been constructed. The experimental kinetics have also been analyzed in terms of the diffusion-controlled bimolecular reactions. The migration energies of tentatively interstitial atoms (mobile components in recombination process) are obtained, their dependence on the irradiation fluences is discussed.

Abstract: Although experimental attempts to measure a single molecule/particle at room temperature or under physiological conditions without immobilization, for example on a surface, or without hydrodynamic flow have so far failed, this failure has given impetus to the underlying theory of Brownian motion towards its stochastic due to diffusion. Quantifying the thermodynamic jitter of molecules/particles inspires many and forms the theoretical basis of single-molecule/single-particle biophysics and biochemistry. For the first time, our simulation results for a live cell (cytoplasm) show that the tracks of individual single molecules are localized in Brownian motion, while there is fanning out in fractal diffusion (anomalous diffusion).

Cannabidiol (CBD) is a safe and non-psychotropic phytocannabinoid with a wide range of potential therapeutic antiinflamatory and antioxidant activity. Due to its lipophilicity, it is normally available dissolved in oily phases. The main aim of this work was to develop and characterize a new formulation of a microemulsion with a potential anti-inflammatory and antioxidant action for topical treatment of inflammatory skin disorders. The micro-emulsion system was obtained from a 20% CBD oil as hydrophobic phase, Labrasol/Plurol Oleique (1:1) as surfactant and cosurfactant (S/CoS) respectively and an aqueous vegetal extract obtained from S. ebulus L. ripe fruits, with a potential anti-oxidant and anti-inflammatory activity, as water phase. A pseudo-ternary phase diagram was elaborated, selecting an optimal proportion of 62% (S/CoS), 27% CBD oil and 11% water and, after testing its reproducibility, the aqueous phases were replaced by the vegetal hydrophilic extract. The defined systems were characterized in terms of conductivity, droplet size by laser scattering, compatibility of components by differential scanning calorimetry and rheological properties using a rotational rheometer. The designed microemulsion showed good stability and a slight pseudo-plastic behavior. The release properties of CBD from the oil phase and caffeic acid from the water phase of the microemulsion were studied by in vitro diffusion experiments using flow-through diffusion cells in comparison to a CBD oil and a microemulsion only with CBD as active substance. It was evidenced that the inclusion of the original oil in microemulsions did not provoke a significant modification of the release of CBD, incorporating the possibility of including hydrophilic active compounds in the formulation, stablishing an interesting strategy for the development of future formulations.

Being able to express broad families of equivariant or invariant attributed graph functions is a popular measuring stick of whether graph neural networks should be employed in practical applications. However, it is equally important to learn deep local minima of losses (i.e., with much smaller loss values than other minima), even when architectures cannot express global minima. In this work we introduce the architectural property of attracting GNN optimization trajectories to local minima as a means of achieving smaller losses. We take first steps in satisfying this property for losses defined over attributed undirected unweighted graphs with a novel architecture, called Universal Local Attractor (ULA). The latter refines each dimension of end-to-end trained node feature embeddings based on graph structure to track the optimization trajectories of losses satisfying some mild conditions. The refined dimensions are then linearly pooled to create predictions. We experiment on 10 tasks, from node classification to clique detection, on which ULA is comparable with or significantly outperforms popular alternatives of similar or greater theoretical expressive power.