Diffusion Process Research Articles

Fulgide Derivatives as Photo-Switchable Coatings for Cathodes of Lithium Ion Batteries - A DFT Study.

Photo-switchable coatings for lithium ion batteries (LIB) can offer the possibility to control the diffusion processes from the electrode materials to the electrolyte and thus, for example, reducing the energy loss in the fully charged state. Fulgide derivatives, as known photo-switches, are investigated concerning their use as coating for vanadium pentoxide, a potential cathode material for LIB. With the help of Density Functional Theory calculations, two fulgide derivatives are characterized with respect to their photophysics, their aggregation behaviour on the cathode material and the ability to form self-assembled monolayers (SAM). Furthermore, the two states of the photo-switchable coating are tested with respect to lithium diffusion from the cathode material, passing the SAM and entering the electrolyte. We found a difference for the energy barriers depending on the state of the photo-switch, preferring its closed form. This behaviour can be used to prevent the loss of charge in batteries of portable devices.

Faedo-Galerkin method for the time-fractional reaction-diffusion model

This paper investigates a time-fractional reaction-diffusion equation characterized by a Caputo derivative of fractional order , incorporates non-local and memory effects that are essential for accurately modeling complex diffusion processes in such environments. These effects arise from the fractal nature of the media, which leads to anomalous diffusion behavior that cannot be adequately described by classical diffusion models. We start by giving a definition of a weak solution for this problem, ensuring that the solution satisfies the equation in a generalized sense. Subsequently, the Faedo-Galerkin method combined with compactness arguments is employed to establish the existence and uniqueness of the weak solution. This approach involves approximating the solution using a sequence of finite-dimensional functions and then passing to the limit to obtain the desired solution . Moreover, we establish the stability of these solutions, which is fundamental for understanding their behavior under varying conditions and ensuring the reliability of the model . Our findings contribute to a deeper understanding of anomalous diffusion phenomena in fractal media and provide a solid foundation for further research in this area.

Diffusion Models for Counterfactual Explanations

Counterfactual explanations have demonstrated promising results as a post-hoc framework to improve the explanatory power of image classifiers. Herein, this paper proposes DiME, a method that allows the generation of counterfactual images using the latest diffusion models. The proposed method uses a guided generative diffusion process to exploit the gradients of the target classifier to generate counterfactual explanations of the input instances. Furthermore, we examine present strategies for assessing spurious correlations and expand the assessment methods by presenting a novel measure, Correlation Difference, which is more efficient at detecting such correlations. The provided work includes a comprehensive ablation study and a thorough experimental validation demonstrating that the proposed algorithm outperforms previous state-of-the-art results on the CelebA, CelebAHQ and BDD100k datasets.

Power Laws and Logarithmic Oscillations in Diffusion Processes on Discrete Ultrametric Spaces

Power Laws and Logarithmic Oscillations in Diffusion Processes on Discrete Ultrametric Spaces

Modeling and analysis of uncertain Bass diffusion model driven by uncertain Liu process

The Bass diffusion model is one of the most influential models for predicting the diffusion of new products and technologies, but the diffusion process will be affected by some uncertain factors. Usually, such kinds of uncertain factors are characterized as stochastic processes. However, in many cases, this approach can lead to uncertain issues. Therefore, in this article, a Bass diffusion model that incorporates the uncertainty theory is studied. First, we present an uncertain Bass diffusion model where the uncertain disturbance is modeled as an uncertain Liu process. Then, the existence and uniqueness of the uncertain Bass diffusion model are analyzed. Moreover, the uncertain Bass diffusion model is solved by using the 99-α-Runge-Kutta method. Finally, we carry out a numerical simulation on the output of the integrated circuit industry in China by using uncertain differential equations and stochastic differential equations. The results show that modeling with uncertain differential equations is superior to using stochastic differential equations.

Temporal variation of S-wave attenuation during the 2009 L'Aquila, Central Italy, seismic sequence

Summary We investigate temporal and spatial variations of the spectral decay parameter kappa (κ) before and after the April 6, 2009, L'Aquila earthquake (Mw 6.1), in central Italy. We analyzed foreshocks ten days before and aftershocks occurring ten days and six months after this main event. We select earthquakes with magnitudes Mw ≥ 3.2 registered by the seismic network of central Italy within a radius of 20 km from the epicenter of the L'Aquila mainshock and having hypocenter distances of less than 170 km. We separate near-source, along-path and near-site contributions of κ for each group of events and we detected temporal variations of this S-wave attenuation parameter. We find that ten days before the mainshock κ along the path has the lowest values, probably due to high tectonic stress accumulated, in agreement with previous investigations performed with other techniques, then κ increases during the main event and remains constant during the first ten days of aftershocks. The aftershocks that occurred six months after show an increase in the regional attenuation probably due to the tectonic stress released during the main shock and the earlier aftershocks. From the spatial point of view, ten days before the principal event the foreshocks located to the south show an increase in the near-source attenuation towards the northeast, in the direction of the mainshock. These spatial variations of κ may be related to the presence of crustal fluids near the rupture area, as evidenced by other previous studies. The first ten days of aftershocks that concentrate around the main earthquake have high near-source κ, and those located north of the main rupture have lower values. These observations are consistent with previous investigations that show variations of elastic and anisotropic crustal properties during the L'Aquila earthquake sequence due to dilatancy and fluid diffusion processes within the nucleation zone. We conclude that temporal variations of the spectral decay parameter κ provide important clues for the earthquake cycle in central Italy.

Contrasting Supply Dynamics of Dissolved Iron and Nitrate Shape the Biogeography of Nutrient‐Limiting Conditions in the North Pacific

AbstractThe North Pacific is known with iron limitation for phytoplankton growth in the subarctic region and nitrogen limitation in the subtropical gyre. Although the growth rate of phytoplankton is determined by the concentration of limiting nutrient, the supply ratio of iron to nitrogen is suggested to be essential to this biogeographic pattern. However, the underlying dynamics determining the ratio remain largely unknown. We investigated mechanisms of dissolved iron (dFe) and nitrate (NO3−) transport to the euphotic zone of the North Pacific using an eddy‐resolvable biogeochemical model. We show that lateral advection and atmospheric deposition are dominant drivers for dFe transport, resulting in high Fe:N supply ratio in both subarctic and subtropical regions. Conversely, significant vertical supplies of NO3− through upwelling and diffusion processes markedly reduce the supply ratio in the subarctic region. These dynamics combined lead to high Fe:N supply ratio in the gyre and low ratio in the subarctic, ultimately driving high nitrogen fixation condition in the gyre and the iron‐limited phytoplankton growth condition in the subarctic region.

Density‐Aware Diffusion Model for Efficient Image Dehazing

AbstractExisting image dehazing methods have made remarkable progress. However, they generally perform poorly on images with dense haze, and often suffer from unsatisfactory results with detail degradation or color distortion. In this paper, we propose a density‐aware diffusion model (DADM) for image dehazing. Guided by the haze density, our DADM can handle images with dense haze and complex environments. Specifically, we introduce a density‐aware dehazing network (DADNet) in the reverse diffusion process, which can help DADM gradually recover a clear haze‐free image from a haze image. To improve the performance of the network, we design a cross‐feature density extraction module (CDEModule) to extract the haze density for the image and a density‐guided feature fusion block (DFFBlock) to learn the effective contextual features. Furthermore, we introduce an indirect sampling strategy in the test sampling process, which not only suppresses the accumulation of errors but also ensures the stability of the results. Extensive experiments on popular benchmarks validate the superior performance of the proposed method. The code is released in https://github.com/benchacha/DADM.

SOD‐diffusion: Salient Object Detection via Diffusion‐Based Image Generators

AbstractSalient Object Detection (SOD) is a challenging task that aims to precisely identify and segment the salient objects. However, existing SOD methods still face challenges in making explicit predictions near the edges and often lack end‐to‐end training capabilities. To alleviate these problems, we propose SOD‐diffusion, a novel framework that formulates salient object detection as a denoising diffusion process from noisy masks to object masks. Specifically, object masks diffuse from ground‐truth masks to random distribution in latent space, and the model learns to reverse this noising process to reconstruct object masks. To enhance the denoising learning process, we design an attention feature interaction module (AFIM) and a specific fine‐tuning protocol to integrate conditional semantic features from the input image with diffusion noise embedding. Extensive experiments on five widely used SOD benchmark datasets demonstrate that our proposed SOD‐diffusion achieves favorable performance compared to previous well‐established methods. Furthermore, leveraging the outstanding generalization capability of SOD‐diffusion, we applied it to publicly available images, generating high‐quality masks that serve as an additional SOD benchmark testset.

An image encryption algorithm for colour images based on a cellular neural network and the Chua's chaotic system

In the internet era, image encryption technology plays a crucial role in ensuring the security of image information. Aiming at the problem that low-dimensional chaotic encryption has a relatively small key space and is vulnerable to chosen-plain attacks, this paper proposed a novel colour image block encryption algorithm based on the cellular neural network and the Chua's chaotic system. Firstly, the plain is separated into three primary colours. And Fourier transform is applied to achieve optical transformation, generating six chaotic sequences iteratively. Secondly, the chaotic sequences were combined in pairs. And then combined with the plain to form three sequences, which were used in the diffusion process. Finally, the improved Chua's chaotic system is used to scramble the image. Both diffusion and scrambling are performed synchronously during encryption. Through the above operation, we get the final colour encrypted picture. The experimental results show that the algorithm has excellent encryption effect and can resist common attacks.

Simulation of Total Harmonic Distortion of Solid Oxide Fuel Cells for Carbon Deposition Detection

Abstract Identifying the degradation mechanisms at the early stage of operation is important for the long-term operation of solid oxide fuel cells (SOFCs). Compared to conventional methods, total harmonic distortion analysis (THDA) can significantly reduce the test time for identifying performance degradation during SOFC operation. In this study, a one-dimensional transient elementary reaction kinetic model of an SOFC fueled with syngas is developed. The model incorporates the coupling effect of elementary chemical and electrochemical reactions, the electrode microstructure, the charge and mass transport processes, and the detailed evolution reaction of surface adsorbed carbon. A THDA simulation calculation method was developed and applied to determine the failure mode of anode carbon deposition. The amplitude, duration, and harmonic number of the perturbation signal are determined to improve fault detection for THDs. The results show that the use of THD can not only detect carbon accumulation behavior at the early stage of SOFC operation but also distinguish the specific degradation mechanism caused by carbon deposition: the hindered SOFC charge transfer reaction can be detected in the frequency range of 100-4000 Hz, and the hindered gas diffusion process inside the anode can be detected in the frequency range of 0.01-10 Hz.

Acceleration of Diffusion in Ab Initio Nanoreactor Molecular Dynamics and Application to Hydrogen Sulfide Oxidation.

The computational description of chemical reactivity can become extremely complex when multiple different reaction products and intermediates come into play, forming a chemical reaction network. Therefore, computational methods for the automated construction of chemical reaction networks have been developed in the last decades. One of these methods, ab initio nanoreactor molecular dynamics (NMD), is based on external forces enhancing reactivity by e.g., periodically compressing the system and allowing it to relax. However, during the relaxation process, a significant simulation time is required to allow energy to dissipate and molecules to diffuse, making this part of the NMD simulation computationally intensive. This work aims to improve NMD by accelerating the diffusion process in the relaxation phase. We systematically investigate the speedup of reaction discovery gained by diffusion acceleration, leading to a factor of up to 28 in discovery frequency. Diffusion-accelerated nanoreactor molecular dynamics (DA-NMD) is then used to construct a reaction network of hydrogen sulfide oxidation under atmospheric conditions, where reactions are automatically detected by a change in the bond order and bond distance. A reaction network of 108 molecular species and 399 elementary reactions was constructed starting from hydrogen sulfide, hydroxy radicals, and molecular oxygen covering a broad variety of sulfur-oxygen chemistry and oxidation states of the sulfur atom ranging from -II to +VI.

Durability of epoxy and vinyl ester polymers in wet, seawater, and seawater sea sand concrete environments: Molecular dynamics simulations

Epoxy and vinyl ester (VE) deteriorate under harsh environmental conditions typical of marine and offshore applications. Enhancing their performance requires a deeper understanding of their molecular-level interactions with these environments. This study uses molecular dynamics simulations to investigate the behavior of epoxy and VE under dry, wet, Na2SO4, NaCl, NaOH, KOH, and simulated seawater sea sand concrete (SWSSC) pore solution environments. The effect of temperatures ranging from 300 K to 368 K was also explored. Key parameters, such as radial distribution function, hydrogen bond dynamics, diffusion coefficients of water molecules and ions, swelling ratio, and glass transition temperature (Tg), were analyzed. Results show that epoxy is more sensitive to environmental effects than VE. In the dry state, three types of hydrogen bonds (H-bonds) were identified, with 64 % of the hydroxyl (OH) group involved in epoxy and 34 % in VE. As temperature increases, polymer chain interactions weaken, leading to a decrease in H-bonds, with epoxy showing a faster decline. Absorbed water molecules accumulate near the polymer polar sites, particularly at the OH groups, breaking some polymer-polymer H-bonds and forming new ones with the polymer polar sites. The hydrogen atoms of most absorbed water molecules orient away from the OH group, creating binding sites for water clustering through water-water H-bonds, leading to plasticization and potential hydrolytic degradation. Ions increase the number of polymer-water H-bonds, significantly decreasing polymer-polymer H-bonds (by 59.22 % for epoxy and 51.52 % for VE in SWSSC), thus accelerating material deterioration. Free volume distribution and dynamics, the transition between bound and free water, hydrogen bond dynamics, as well as ion hydration and dehydration collectively influence the water diffusion process in the polymer networks. Ion species diffuse much slower than water molecules, with epoxy showing higher permeability to Cl- and OH- compared to VE. Glass transition temperature (Tg) of both polymers is sensitive to environmental exposure, with epoxy being more affected. The detrimental effect on Tg is ranked as SWSSC > KOH > NaOH > NaCl > Na2SO4 > Wet. These findings provide new nanoscale insights into the interactions between polymers and SWSSC environments, offering a foundation for accurately predicting the durability of polymer-reinforced SWSSC.

Overcoming the Limitation of Ionomers on Mass Transport and Pt Activity to Achieve High-Performing Membrane Electrode Assembly.

The membrane electrode assembly (MEA) is one of the critical components in proton exchange membrane fuel cells (PEMFCs). However, the conventional MEA cathode with a covered-type catalyst/ionomer interfacial structure severely limits oxygen transport efficiency and Pt activity, hardly achieving the theoretical performance upper bound of PEMFCs. Here, we design a noncovered catalyst/ionomer interfacial structure with low proton transport resistance and high oxygen transport efficiency in the cathode catalyst layer (CL). This noncovered interfacial structure employs the ionomer cross-linked carbon particles as long-range and fast proton transport channels and prevents the ionomer from directly covering the Pt/C catalyst surface in the CL, freeing the oxygen diffusion process from passing through the dense ionomer covering layer to the Pt surface. Moreover, the structure improves oxygen transport within the pores of the CL and achieves more than 20% lower pressure-independent oxygen transport resistance compared to the covered-type structure. Fuel-cell diagnostics demonstrate that the noncovered catalyst/ionomer interfacial structure provides exceptional fuel-cell performance across the kinetic and mass transport-limited regions, with 77% and 67% higher peak power density than the covered-type interfacial structure under 0 kPagauge of oxygen and air conditions, respectively. This alternative interfacial structure provides a new direction for optimizing the electrode structure and improving mass-transport paths of MEA.

Dynamics behaviours of N-kink solitons in conformable Fisher–Kolmogorov–Petrovskii–Piskunov equation

PurposeThis manuscript is related to compute $N$-kink soliton solutions for conformable Fisher–Kolmogorov equation (CFKE) by using the generalized extended direct algebraic method (EDAM). The considered problem has important applications in mathematical biology and reaction diffusion processes. Also, the mentioned problem has significant applications in population dynamics. The fractional order conformable derivative has many features as compared to the other fractional order differential operators. For instance, the chain, product and quotient procedures do not satisfy by other fractional differential operators, but conformable operators obey the mentioned rules. Hence, we compute the soliton solutions for the mentioned problem and present its various dynamical behaviours graphically.Design/methodology/approachThe generalized EDAM is used in this article to examine the calculation of N-kink soliton solutions for the CFKE. In mathematical biology and reaction-diffusion processes, the topic under consideration holds great significance, especially when considering population dynamics.FindingsThe results highlight the benefits of utilising conformable derivatives in mathematical modelling and further our understanding of fractional differential equations and their applications.Research limitations/implicationsThe work focuses primarily on N-kink soliton solutions, which may limit the examination of alternative types of solutions (e.g., multi-soliton or periodic solutions) that might give new insights into the dynamics of the CFKE.Practical implicationsThe generated N N-kink soliton solutions can enhance mathematical models in biological contexts, notably in modelling population dynamics, disease propagation and ecological interactions, leading to better forecasts and interventions.Social implicationsPublic health initiatives can benefit from the understanding of disease transmission and intervention efficacy that comes from modelling population dynamics and reaction-diffusion processes.Originality/valueThe use of the generalized EDAM to obtain solutions for N-kink soliton problems is an innovative method for solving the conformable Fisher–Kolmogorov equation, demonstrating the power of this mathematical tool.

Partial stochastic resetting with refractory periods

Abstract The effect of refractory periods in partial resetting processes is studied. Under Poissonian partial resets, a state variable jumps to a value closer to the origin by a fixed fraction at constant rate, $x\to a x$. Following each reset, a stationary refractory period of arbitrary duration takes place. We derive an exact closed-form expression for the propagator in Fourier-Laplace space, which shows rich dynamical features such as connections not only to other resetting schemes but also to intermittent motion. For diffusive processes, we use the propagator to derive exact expressions for time dependent moments of $x$ at all orders. At late times the system reaches a non-equilibrium steady state which takes the form of a mixture distribution that splits the system into two subpopulations; trajectories that at any given time in the stationary regime find themselves in the freely evolving phase, and those that are in the refractory phase. In contrast to conventional resetting, partial resets give rise to non-trivial steady states even for the refractory subpopulation. Moments and cumulants associated with the steady state density are studied, and we show that a universal optimum for the kurtosis can be found as a function of mean refractory time, determined solely by the strength of the resetting and the mean inter-reset time. The presented results could be of relevance to growth-collapse processes with periods of inactivity following a collapse.

Multidimensional and Nonlinear Fractional Langevin Equations: Advancing the Theory in of Anomalous Diffusion

This paper presents a comprehensive theoretical analysis of fractional Langevin equations (FLEs) and their applications in modeling anomalous diffusion processes. We extend the classical FLE framework in several significant directions to address the complexities observed in various physical, biological, and social systems. First, we derive a multidimensional extension of the FLE, providing a robust tool for studying anomalous diffusion in higher-dimensional spaces. Second, we incorporate non-Gaussian Lévy α-stable noise into the FLE, enabling the description of systems characterized by heavy-tailed distributions and extreme events. Third, we develop a nonlinear variant of the FLE to model more intricate restoring forces and potential landscapes. Finally, we analyze a generalized FLE with different orders of fractional derivatives for the inertial and friction terms, offering a flexible framework capable of capturing a wider range of anomalous diffusion phenomena. For each extension, we prove the existence and uniqueness of solutions, derive the corresponding probability distributions, and analyze the scaling behavior of the mean squared displacement in the long-time limit. Our results demonstrate how these generalized FLEs can describe various regimes of anomalous diffusion, from subdiffusive to superdiffusive behavior. This work provides a unified theoretical foundation for understanding and modeling complex diffusive processes across diverse disciplines, paving the way for more accurate descriptions of systems exhibiting memory effects, non-Gaussian statistics, and multiscale dynamics.

Diffusion Cascades and Mutually Coupled Diffusion Processes

In this paper, we define and investigate a system of coupled regular diffusion equations in which each concentration acts as a driving term in the next diffusion equation. Such systems can be understood as a kind of cascade process which appear in different fields of physics like diffusion and reaction processes or turbulence. As a solution, we apply the time-dependent self-similar Ansatz method, the obtained solutions can be expressed as the product of a Gaussian and a Kummer’s function. This model physically means that the first diffusion works as a catalyst in the second diffusion system. The coupling of these diffusion systems is only one way. In the second part of the study we investigate mutually coupled diffusion equations which also have the self-similar trial function. The derived solutions show some similarities to the former one. To make our investigation more complete, different kinds of couplings were examined like the linear, the power-law, and the Lorentzian. Finally, a special coupling was investigated which is capable of describing isomerization with temporal decay.

Politico-Administrative Culture and Public Service Reform in Post-Independence Kazakhstan

Classical organizational management literature draws clear parallels between organizational culture and climate and effective use of power and influence as key to successful policy implementation of reforms in public sector organizations. On the other hand, the public policy literature, in particular, policy transfer as a strand within policy studies, emphasizes the role of the national context, more specifically, ‘facilitators’ and ‘constraints’ of ‘‘politico-administrative culture” within the national context, as crucial to understanding processes of transfer, convergence, and diffusion of public policy. There is a plethora of studies by Western scholars of public management who have successfully utilized these theoretical underpinnings to study the effectiveness of public service reforms in mature policy environments such as the UK, the US, Australia, New Zealand, and others. However, the public policy and comparative public management literature only offers a limited number of case studies from developing, middle-/upper-middle countries, which rely on concepts of organizational management in addition to narratives on the impact of policy learning from global doctrines, such as Weberianism, New Public Management (NPM), and New Public Governance (NPG), and national politics, on the implementation of administrative reforms in those contexts. Kazakhstan, as a resource-affluent post-Soviet country and a bastion of modernization and ‘open government’ in Central Asia or the Commonwealth of Independent States (CIS) in the post-Soviet era is a case in point. Based on ethnographic research consisting of interviews with elite academics, civil servants, and think-tank activists, as well as reviews of OECD and government strategy reports in Astana, the findings point to a potential abatement of the impact of context constraints such as large power distance and collectivist behavior by context facilitators such as those surrounding the use of ‘trilingualism’ and public diplomacy towards reforms in Kazakhstan particularly in recent years.

TempDiff: Enhancing Temporal‐awareness in Latent Diffusion for Real‐World Video Super‐Resolution

AbstractLatent diffusion models (LDMs) have demonstrated remarkable success in generative modeling. It is promising to leverage the potential of diffusion priors to enhance performance in image and video tasks. However, applying LDMs to video super‐resolution (VSR) presents significant challenges due to the high demands for realistic details and temporal consistency in generated videos, exacerbated by the inherent stochasticity in the diffusion process. In this work, we propose a novel diffusion‐based framework, Temporal‐awareness Latent Diffusion Model (TempDiff), specifically designed for real‐world video super‐resolution, where degradations are diverse and complex. TempDiff harnesses the powerful generative prior of a pre‐trained diffusion model and enhances temporal awareness through the following mechanisms: 1) Incorporating temporal layers into the denoising U‐Net and VAE‐Decoder, and fine‐tuning these added modules to maintain temporal coherency; 2) Estimating optical flow guidance using a pre‐trained flow net for latent optimization and propagation across video sequences, ensuring overall stability in the generated high‐quality video. Extensive experiments demonstrate that TempDiff achieves compelling results, outperforming state‐of‐the‐art methods on both synthetic and real‐world VSR benchmark datasets. Code will be available at https://github.com/jiangqin567/TempDiff