One-dimensional Diffusion Research Articles

Fast Color Image Encryption Algorithm Based on DNA Coding and Multi-Chaotic Systems

At present, there is a growing emphasis on safeguarding image data, yet conventional encryption methods are full of numerous limitations. In order to tackle the limitations of conventional color image encryption methodologies, such as inefficiency and insufficient security, this paper designs an expedited encryption method for color images that uses DNA coding in conjunction with multiple chaotic systems. The encryption algorithm proposed in this paper is based on three-dimensional permutation, global scrambling, one-dimensional diffusion and DNA coding. First of all, the encryption algorithm uses three-dimensional permutation algorithms to scramble the image, which disrupts the high correlation among the image pixels. Second, the RSA algorithm and the SHA-256 hashing algorithm are utilized to derive the starting value necessary for the chaotic system to produce the key. Third, the image is encrypted by using global scrambling and one-dimensional diffusion. Finally, DNA coding rules are used to perform DNA computing. The experimental results indicate that the encryption scheme exhibits a relatively weak inter-pixel correlation, uniform histogram distribution, and an information entropy value approaching eight. This shows that the proposed algorithm is able to protect the image safely and efficiently.

Numerical Solution of External Boundary Conditions Inverse Multilayer Diffusion Problems

The present study is concerned with the numerical solution of external boundary conditions in inverse problems for one-dimensional multilayer diffusion, using the difference method. First, we formulate multispecies parabolic problems with three types of Dirichlet–Neumann–Robin internal boundary conditions that apply at the interfaces between adjacent layers. Then, using the symmetry of the diffusion operator, we prove the well-posedness of the direct (forward) problem in which the coefficients, the right-hand side, and the initial and boundary conditions are given. In inverse problems, instead of external boundary conditions of the first and the last layers, point observations of the solution within the entire domain are posed. Rothe’s semi-discretization of differential problems combined with a symmetric exponential finite difference solution for elliptic problems on each time layer is proposed to develop an efficient semi-analytical approach. Next, using special solution decomposition techniques, we numerically solve the inverse problems for the identification of external boundary conditions. Numerical test examples are discussed.

Linked Data-Driven, Physics-Based Modeling of Pumping-Induced Subsidence with Application to Bangkok, Thailand.

Research into land subsidence caused by groundwater withdrawal is hindered by the availability of measured heads, subsidence, and forcings. In this paper, a parsimonious, linked data-driven and physics-based approach is introduced to simulate pumping-induced subsidence; the approach is intended to be applied at observation well nests. Time series analysis using response functions is applied to simulate heads in aquifers. The heads in the clay layers are simulated with a one-dimensional diffusion model, using the heads in the aquifers as boundary conditions. Finally, simulated heads in the layers are used to model land subsidence. The developed approach is applied to the city of Bangkok, Thailand, where relatively short time series of head and subsidence measurements are available at or near 23 well nests; an estimate of basin-wide pumping is available for a longer period. Despite the data scarcity, data-driven time series models at observation wells successfully simulate groundwater dynamics in aquifers with an average root mean square error (RMSE) of 2.8 m, relative to an average total range of 21 m. Simulated subsidence matches sparse (and sometimes very noisy) land subsidence measurements reasonably well with an average RMSE of 1.6 cm/year, relative to an average total range of 5.4 cm/year. Performance is not good at eight out of 23 locations, most likely because basin-wide pumping is not representative of localized pumping. Overall, this study demonstrates the potential of a parsimonious, linked data-driven, and physics-based approach to model pumping-induced subsidence in areas with limited data.

Inverse coefficient problems for one-dimensional time-fractional diffusion equations

We prove the uniqueness in determining a spatially varying zeroth-order coefficient of a one-dimensional time-fractional diffusion equation by initial value and Cauchy data at one end point of the spatial interval.

Recognizing microbial manganese reduction in lacustrine carbonate and its linkage to terrestrial biogeochemical processes

Carbonate authigenesis, the in situ precipitation of carbonate minerals within the sediment porewaters, is a key pathway for carbonate deposition and plays a crucial role in global biogeochemical cycles. Heterotrophic microorganisms are essential in regulating authigenic carbonate formation, primarily through the consumption of organic matter. Although bacterial manganese reduction is known to influence the formation of rhodochrosite and dolomite, its role in limestone deposition is unclear. Here, we present a systematic investigation of mixed calcareous siliciclastic rocks from a Paleogene freshwater lake to identify the formation of authigenic carbonate, decode the role of microbial Mn reduction, and understand the microbial response to ancient lacustrine environmental changes. The positive correlation between carbonate fraction in bulk samples (Carb%) and Mn content in carbonate minerals (Mncarb) suggests that carbonate precipitation is stimulated by Mn2+ enrichment. The dissimilarity between Mncarb and Fecarb, along with the synergic variations of Mncarb and diagenetic indicators, support an authigenic rather than a hydrogenetic origin for the carbonates. Using a one-dimensional diffusion–advection-reaction model, we quantify the impact of Mn reduction on promoting carbonate precipitation. Furthermore, correlations between Pcarb and other values–positive with the chemical index alteration (CIA), negative with Mncarb, and none with TOC–suggest that nitrogen availability, regulated by continental weathering, is likely the primary factor limiting both the primary productivity and the bacterial reduction intensity at the study site. Overall, this study uncovers the role of microbial Mn reduction in stimulating authigenic carbonate precipitation, and reveals the modulation mechanism of Mn-reducing microorganisms in an ancient lake. These findings shed new light on the authigenic limestone formation mechanisms and provide a new perspective on interpreting the authigenic impacts on carbonate chemistry.

Numerical simulation of deuterium retention in tungsten under ELM-like conditions

Retention of hydrogen isotopes (HI) in plasma-facing components (PFCs) is a crucial process influencing the operation of a fusion device. The dynamics of HI retention is mainly determined by irradiation conditions of PFCs. These conditions can change due to the onset of fast transient events, such as edge-localised modes (ELMs). The development of ELMs results in repetitive short-term plasma bursts on PFCs, affecting the exposure regime. In this work, the effect of ELM-like loads on the fuel retention is numerically analysed using a one-dimensional diffusion model, implemented in the FESTIM code. As a representative simulation case, the deuterium (D) retention in tungsten (W) is considered with the geometry and inter-ELM exposure conditions relevant for large fusion devices. Temporal dependencies of heat and particle fluxes during intra-ELM stages are accounted for by applying the free-streaming model for an ELM filament transport. The simulations were conducted for three inter-ELM exposure regimes with various properties of transient loads, D trapping sites, and D recombination rates. Compared to the ELM-free irradiation, the onset of transients is shown to mainly reduce the D retention rate because of significant material heating induced by the arrival of energetic ELMy particles. This relative difference can decrease if the material is characterised by strong trapping sites or limited desorption from a surface. The findings also demonstrate that additional heating during transients provides conditions for a faster D migration into the bulk. In addition, we discuss the possibility of using ELM-average loads to obtain quick assessments of the D content. The approach is shown to be applicable for the case of small ELMs and is used to derive the analytical expressions for the D distribution in W within the steady-state approximation.

Differential dynamics specify MeCP2 function at nucleosomes and methylated DNA.

Methyl-CpG-binding protein 2 (MeCP2) is an essential chromatin-binding protein whose mutations cause Rett syndrome (RTT), a severe neurological disorder that primarily affects young females. The canonical view of MeCP2 as a DNA methylation-dependent transcriptional repressor has proven insufficient to describe its dynamic interaction with chromatin and multifaceted roles in genome organization and gene expression. Here we used single-molecule correlative force and fluorescence microscopy to directly visualize the dynamics of wild-type and RTT-causing mutant MeCP2 on DNA. We discovered that MeCP2 exhibits distinct one-dimensional diffusion kinetics when bound to unmethylated versus CpG methylated DNA, enabling methylation-specific activities such as co-repressor recruitment. We further found that, on chromatinized DNA, MeCP2 preferentially localizes to nucleosomes and stabilizes them from mechanical perturbation. Our results reveal the multimodal behavior of MeCP2 on chromatin that underlies its DNA methylation- and nucleosome-dependent functions and provide a biophysical framework for dissecting the molecular pathology of RTT mutations.

Numerical analysis of a class of penalty discontinuous Galerkin methods for nonlocal diffusion problems

In this paper, we consider a class of discontinuous Galerkin (DG) methods for one-dimensional nonlocal diffusion (ND) problems. The nonlocal models are integral equations that are widely used in describing many physical phenomena with long-range interactions. The ND problem is the nonlocal analog of the classic diffusion problem, and the nonlocality disappears as the interaction radius (horizon) vanishes, then the ND problem recovers the classic diffusion problem. Under certain conditions, the exact solution to the ND problem may contain discontinuities, and this is one of the properties of the ND problem that sets it apart from the classic diffusion problem. It is natural to adopt the DG method to compute the ND problems since the DG method shows its great advantages in resolving problems with discontinuities in the computational fluid dynamics in the past several decades. Based on \cite{DuCAMC2020}, we construct the DG methods with different penalty terms, and the proposed DG methods have their local counterparts as the horizon vanishes. This indicates the proposed methods will converge to the existing DG schemes as the horizon vanishes, which is crucial to obtain the {\it asymptotic compatibility}. Rigorous proofs are provided to demonstrate the stability, error estimates, and asymptotic compatibility of the proposed DG schemes. To see the nonlocal diffusion effect, we also consider the time-dependent convection-diffusion problems with nonlocal diffusion. We conduct several numerical experiments, including accuracy tests and Burgers' equation with nonlocal diffusion, and various horizons are taken to show the good performance of the proposed algorithm and validate the theoretical findings.

Quantifying oxygen diffusion during thermal degradation of combustible porous media

Oxygen diffusion controlled combustion occurs when local oxygen transport is slower than the chemistry, commonly found in porous combustible material or combustible material embedded within an inert porous medium. This mode of combustion, such as smouldering, can pose dangerous fire risks and also be harnessed in environmentally beneficial applications. However, the oxygen diffusion limitation is poorly understood in all contexts and persists as a key knowledge gap. Quantitative analysis of oxygen diffusion effects is therefore crucial for understanding the combustion behavior of combustible porous media and developing precise smouldering simulation models. In this paper, a reactive transport model incorporating both oxygen diffusion and chemical consumption was developed. Using coal as the model fuel, the impacts of key parameters on global mass loss during the one-dimensional diffusion combustion of coal samples were simulated and compared with TGA experiments conducted within a range of oxygen concentrations between 3–21%. Using this method, key kinetic and oxygen diffusion parameters were obtained within reasonable ranges by using a genetic algorithm optimization method. With these optimized parameters, the local oxygen distribution profiles in the samples at different inlet oxygen concentrations were simulated. The results indicate that oxygen diffusion can lead to large oxygen concentration differences within the coal samples, exceeding 63% of the inlet oxygen concentration. These oxygen differences can impact the local chemistry throughout the sample, and lead to fundamental errors in analyzing global kinetic analyses, if the transport effects are not considered. Altogether, this study delivers new insights into a potentially rate-limiting phenomenon that is relevant in progressing knowledge on many fire problems and engineering applications.

Characterization and optimization of waste Cucurbita maxima moschata lashes for biomass composite applications

In this paper, 5 % sodium hydroxide solution, mixed 20 % acetic acid and 5 % sodium chlorite solution, and 5 % silane coupling agent solution were successively used to soak the waste pumpkin (Cucurbita maxima moschata) lashes. Subsequently, FTIR, XRD, thermogravimetric analysis and other experimental methods were used to comprehensively characterize the properties of the discarded pumpkin lashes. On this basis, this work prepared cement mortar specimens with unadulterated pumpkin lashes, adulterated raw pumpkin lashes, and adulterated modified pumpkin lashes, and their residual mechanical properties were investigated after exposure to elevated temperatures. The experimental results indicate that the chemical modification utilized in this paper can increase the cellulose content of pumpkin lashes as well as reduce the proportion of amorphous components, and thus, improve the tensile strength, crystallinity index, grain size, thermal stability, and surface roughness of the samples. Meanwhile, the chemical treatment process can effectively reduce the water absorption and density of pumpkin lashes. The calculation outcomes of our thermal kinetics study showed that the apparent activation energies corresponding to the main pyrolysis stage of the treated pumpkin lashes were significantly enhanced. The one-dimensional diffusion model and the second-order model could better characterize the pyrolytic mechanism of the raw pumpkin lashes, while the mechanism was closer to the third-order model because of the chemical modification. Finally, the addition of chemically modified pumpkin lashes reduced the mass loss rate of cement mortar specimens at elevated temperatures while clearly increasing the residual strength of the specimens at 300 and 400 °C compared to those with referential pumpkin lashes.

ATEP: an advanced transport model for energetic particles

In this paper we report on the implementation and verification of a phase-space resolved energetic particle (EP) transport model. It is based on a first-principle theoretical framework, i.e. the system of non-linear gyrokinetic equations and the related transport equations. Its focus is primarily directed toward understanding the meso-scale character of EPs and its consequences. Compared to the conventional description of thermal radial transport via a one-dimensional radial diffusion equation, the newly developed model is three-dimensional using canonical constants-of-motion (CoM) variables. The model does not assume diffusive processes to be dominant a priori, instead the EP fluxes are self-consistently calculated and directly evolved in CoM space. We use the EP-Stability workflow and the HAGIS code to determine the phase space fluxes explicitly either in the limit of constant mode amplitudes or an energy-conserving quasi-linear model. As an application of the model the transport of neutral-beam-generated EPs due to a toroidal Alfvén eigenmode in an ITER plasma is investigated. As there are no sources and collisions taken into account so far (for an extension of the model see the companion paper (Meng et al 2024 Nucl. Fusion accepted)), the results cannot be considered as an exhaustive study, but rather as a practical demonstration of the conceptual framework on the way to a comprehensive reduced description of burning plasmas.

Strongly quasi-mixing properties for one-dimensional diffusion processes with killing *

In this paper, we establish sufficient conditions for the existence of strongly (uniformly and exponentially) quasi-mixing limits of one-dimensional diffusion processes with killing. As a by-product, these conditions also ensure that the considered processes have strong quasi-ergodicity, strong fractional quasi-ergodicity and uniform mean-ratio quasi-ergodicity. Moreover, the quasi-ergodic speeds of these three quasi-ergodicities are also characterized.

Study on the UV FEL single-shot damage threshold of an Au thin film.

The damage threshold of an Au-coated flat mirror, one of the reflective optics installed on the FEL-2 beamline of the Dalian Coherent Light Source, China, upon far-UV free-electron laser irradiation is evaluated. The surface of the coating is characterized by profilometer and optical microscope. A theoretical approach of the phenomenon is also presented, by application of conventional single-pulse damage threshold calculations, a one-dimensional thermal diffusion model, as well as finite-element analysis with ANSYS.

Single-mode termination of phage transcriptions, disclosing bacterial adaptation for facilitated reinitiations.

Bacterial and bacteriophage RNA polymerases (RNAPs) have divergently evolved and share the RNA hairpin-dependent intrinsic termination of transcription. Here, we examined phage T7, T3 and SP6 RNAP terminations utilizing the single-molecule fluorescence assays we had developed for bacterial terminations. We discovered the phage termination mode or outcome is virtually single with decomposing termination. Therein, RNAP is displaced forward along DNA and departs both RNA and DNA for one-step decomposition, three-dimensional diffusion and reinitiation at any promoter. This phage displacement-mediated decomposing termination is much slower than readthrough and appears homologous with the bacterial one. However, the phage sole mode of termination contrasts with the bacterial dual mode, where both decomposing and recycling terminations occur compatibly at any single hairpin- or Rho-dependent terminator. In the bacterial recycling termination, RNA is sheared from RNA·DNA hybrid, and RNAP remains bound to DNA for one-dimensional diffusion, which enables facilitated recycling for reinitiation at the nearest promoter located downstream or upstream in the sense or antisense orientation. Aligning with proximity of most terminators to adjacent promoters in bacterial genomes, the shearing-mediated recycling termination could be bacterial adaptation for the facilitated reinitiations repeated at a promoter for accelerated expression and coupled at adjoining promoters for coordinated regulation.

Initial Boundary Value and Inverse Coefficient Problems for One-Dimensional Fractional Diffusion Equation in a Half-Line

Initial Boundary Value and Inverse Coefficient Problems for One-Dimensional Fractional Diffusion Equation in a Half-Line

Development of an Ecosystem Model Considering Sediment Redox Processes in Enclosed Water Bodies

This study investigates enclosed water bodies to understand the intricate interactions among physical, chemical, and biological processes. A one-dimensional model, integrating sediment and ecosystem components, was developed to analyze oxygen depletion, nutrient dynamics, and the influence of sediment organic matter on oxygen concentrations due to stratification. Oxygen and nutrient concentrations were derived by combining results from a one-dimensional vertical diffusion model with the ecosystem model. The dissolution, adsorption, and desorption of inorganic substances in bottom mud react differently under anaerobic and aerobic conditions, necessitating separate formulations for reduction and oxidation reactions in the bottom mud model. In Lake Biwa, Japan’s largest lake, dissolved oxygen levels have decreased despite regulatory efforts since the 1970s, prompting an investigation into the causes of oxygen-depleted water masses. The model was thus applied to examine oxygen consumption in Lake Biwa’s deep sediments, shedding light on anoxia in enclosed water bodies. This study emphasizes the significance of bottom sediments in water quality models and their implications for ecosystems. Furthermore, the adaptive nature of this model allows for its application in various water bodies, including freshwater reservoirs, lakes, and saltwater bays.

Impact of resin molecular weight on drying kinetics and sag of coatings

Coating performance is influenced by factors inherent to formulation design and processing conditions. Understanding the complex interplay of these attributes enables for mitigating defects, such as sag, which is a gravity-driven phenomenon that impacts the aesthetic and functionality of a coating. The work herein investigates the impact of resin molecular weight and solvent choice on the drying kinetics and sag velocity in polymer films. These films, ranging in thickness from ~60 μm to ~120 μm were formulated with 45 % by weight polymer resin in one of two solvent packages with different relative evaporation rates (RER). Gravimetry was initially used to track drying rate and a one-dimensional diffusion model was utilized to compute the apparent solvent diffusivity. In addition, the film thickness was tracked with optical profilometry. Results from these measurements showed that for fixed molecular weight the drying rate increased by approximately two-fold for the high RER solvent, whereas the apparent diffusivity tended to increase with increasing polymer molecular weight. Films formulated from higher molecular weight resins had greater initial viscosities and thicknesses for identical draw down blade clearance. By extension, the higher apparent diffusivities at greater molecular weights were attributed to effects of prolonged evaporation times for the thicker films. The sag velocity was measured through the thickness of the film for these systems at a 5° incline using the Variable Angle Inspection Microscope (VAIM). Measurements showed an increase in sag velocity for thinner and less viscous films, which was somewhat surprising both because a thinner film will experience lower gravitational stress and quicker drying times as compared to a thicker film. From these data we conclude that formulating a coating with higher molecular weight resin, although likely to increase drying time, will tend to deter sag because of the large impact of viscosity on these phenomena.

Superconvergence analysis of spectral volume methods for one-dimensional diffusion and third-order wave equations

Superconvergence analysis of spectral volume methods for one-dimensional diffusion and third-order wave equations

Effects of aging processes on the microstructure, texture, properties and precipitation kinetics of the Cu–Cr–Zr–Nb alloy

The Cu–Cr–Zr–Nb alloy bars were prepared by vacuum melting, hot forging, solution treatment, and drawing. The effects of aging processes on the microstructure, texture, mechanical properties and electrical conductivity of the alloy were studied, and the precipitation kinetics was analyzed. Besides, the effect of adding Nb to the Cu–Cr–Zr alloy was simulated by the first-principles calculation. The results showed that when the aging temperature increased from 400 °C to 460 °C, Cube texture and Brass texture were transformed into Copper texture. The Cu–Cr–Zr–Nb alloy exhibited superior comprehensive properties such as a hardness of 84.3 HRB, a tensile strength of 520 MPa, an elongation of 19.0 %, and an electrical conductivity of 83.5 International Annealed Copper Standard (%IACS) after being aged at 460 °C for 4 h. The precipitation kinetics and electrical conductivity equations under different aging temperatures were established, and the precipitation activation energy of 24 kJ/mol was obtained. Moreover, the precipitation process of the alloy was also described by the Avrami empirical equation. It was found that the reaction mechanism of the alloy changed from nucleation and growth to one-dimensional diffusion as the aging temperature increased from 400 °C to 520 °C. It was also confirmed that Nb and Cr formed the Cr2Nb compound according to the first-principles calculation.

Recovery of iron from copper slag using jatropha oil as a green reductant: Investigation of pyrolysis analysis, reaction kinetic and artificial neural network model prediction

Jatropha oil (JO) is a non-edible vegetable oil and a potential renewable energy source. In this paper, JO was proposed as a reductant to recover iron from copper slag (CS), and the effects of JO dosage, reduction temperature and reduction time on the recovery of iron by deep reduction of CS were investigated. Based on Coats-Redfern method, a thermogravimetric analyzer was used to explore the reactivity, mass loss behavior, and kinetic mechanism of CS reduction by JO, and to compare the reduction characteristics of anthracite and JO char when used as a reductant. Additionally, artificial neural network (ANN) modeling was used to predict the effects of reductant type, temperature, and heating rate on mass loss during CS reduction. The results showed that the optimum condition for CS reduction when JO was used as the reductant was 3 wt% JO at 1250 °C for 45 min, which resulted in 84.97 % Fe recovery and 94.58 % Fe grade in CS; the reduction mechanism of CS followed a one-dimensional diffusion model (D1); and ANN5 (15*1) was the optimum ANN model to predict the reduction of CS. This research introduces innovative strategies for the environmentally friendly and efficient recovery of iron from iron-containing furnace slag.