Diffusion Process Research Articles

Contrast estimation of the Vasicek integrated diffusion process for high-frequency data

The purpose of this paper is to study the parameter estimation of the Vasicek integrated diffusion process. Based on the contrast function, the parameter contrast estimators of the Vasicek integrated diffusion process are given, and the mean-square errors of drift parameter estimators are derived, so as to obtain the optimal sampling intervals for the parameter estimators. Then we prove the strong consistency of the contrast estimators by the tail probability exponential inequality of α-mixing long-span high-frequency data. In numerical simulation, we investigate the fitting effect of the estimates under different sampling intervals and different sample sizes. The results indicate that using optimal interval sampling can achieve good estimation performance. We use the daily closing price data of CSI 300 index to conduct an empirical analysis and give a logarithmic price prediction model. The analysis results show that the prediction model works well.

Inverse problem solver for epidemiological geographic profiling

AbstractThis work studies machine-learning-based inverse problem solvers for a reaction–diffusion process. The study focus is on the performance of a state-of-the-art convolutional neural network in discovering the source of disease spreading. This problem is called epidemiological geographic profiling. The performance is investigated with synthetic datasets for SIR epidemiological compartments on a square grid geo-space. The convolutional neural network works effectively in discovering a single source and achieves the largest time average of accuracy for growing infection in a heterogeneous geo-space. The hit score remains near the lower bound over time. Discovering multiple sources is feasible potentially as well by learning the dataset for a single source.

Micromagnetic simulations of Nd-Fe-B hot-deformed magnets subjected to eutectic grain boundary diffusion process

The grain boundary diffusion process (GBDP) is one of the most efficient treatments for increasing the coercivity (Hc) of Nd-Fe-B magnets. However, this enhancement typically occurs at the expense of remanence (Mr). In this study, micromagnetic simulations were performed to quantify this tradeoff in hot-deformed Nd-Fe-B magnets subjected to the GBDP using a Nd-based eutectic alloy. The GBDP was imitated in a series of models with a gradually increasing volume fraction of the infiltrated Nd-rich nonmagnetic phase. This infiltration reduced the remanence and grain connectivity via the remaining thin magnetic intergranular phase (IGP), which in turn increased the coercivity. We distinguished between the roles of exchange and magnetostatic interactions in this coercivity enhancement. Furthermore, the simulated Mr vs. Hc curves defined realistic limits for coercivity that depended on the IGP magnetization, which was estimated to be 0.9 ± 0.1 T by reproducing experimental Mr vs. Hc data from the literature.

Isolation and Identification of Oral Bacteria and Characterization for biofilm formation and antibiotics resistance

In this study, 100 bacterial isolates were obtained from tooth surface swabs of male and female patients with different ages who visited specialized centers and dental clinics in Baghdad city after they were clinically diagnosed with oral (dental) infections by specialist doctors for the period from 1/10/2022 to 1/3/2023. The methods employed to identify the bacterial isolates were the Vitek system, as well as highest isolated rate was among Streptococcus mutans species (48%). Isolates of S. mutans and their drug sensitivity was tested against 10 antibiotics using the disc diffusion process, showing that the separators’ Antibiotic resistance was larger than their sensitivity to these antibiotics. The resistance rate of the isolates to erythromycin was (98.21 and 94.64%), to amoxicillin (85.71)% for each of them, to ampicillin (80.35 and 83.92)%, to Nalidixic acid (80.35 and 87.50)%, to cefotaxime (69.64 and 75.00)%, and to chloramphenicol (69.64 and 89%), to amoxicillin–Clavulanic acid (58.92 and 76.78)%), to gentamycin (57.14 and 78.57)%, and to tetracycline the resistance rate was (55.35 and 66.07)% for each of them, respectively, while it showed high sensitivity to the antibiotics amikacin (25.00 and 48.21)% and trimethoprim sulfamethaxyl (7.14 and 19.64)% for each of them respectively.

Multivariate stochastic Vasicek diffusion process: computational estimation and application to the analysis of $$CO_2$$ and $$N_2O$$ concentrations

Multivariate stochastic Vasicek diffusion process: computational estimation and application to the analysis of $$CO_2$$ and $$N_2O$$ concentrations

Synthesis and electrochemical studies of 1,1’-binaphthyl-2,2’-diol for aqueous rechargeable lithium-ion battery applications

The constant increase in the utilization of lithium-ion batteries (LIBs) in various field applications, including electrical vehicles and electronic devices, has led researchers to focus on their multiple path developments to obtain new electrode materials. The practical development of these electrode materials, based on organic and inorganic moieties, is challenging for various groups of LIB scientists. The concept of organic electrode materials is highly competitive with inorganic electrode materials because of the accessibility of more active sites with structural diversity, high energy and power density, environmental friendliness potential sustainability, and low cost. Herein, 1,1’-binaphthyl-2,2’-diol (BINOL) is investigated as an organic electrode material that contains two hydroxyl groups that act as active centers. The oxidative coupling process is employed to synthesize BINOL and so obtained product was characterized by using FT-IR, 1H-NMR and MASS techniques. The electrochemical investigations were carried out using sat. Li2SO4 electrolytic medium at three-electrode cell system. The Cyclic voltammetry (CV) has provided information on the anodic behavior of the material and its stability studied at different scan rates. The battery performance of the cell BINOL | Sat. Li2SO4 | LiMn2O4 by galvanostatic charge-discharge potential limit (GCPL) shows 197/171mAhg−1 specific capacity and 90% columbic efficiency. The electrochemical kinetic obtained by potentiostatic electrochemical impedance spectroscopy (PEIS) shows a semi-infinite diffusion process.

Small organic molecules for aqueous zinc-ion batteries with stable structure and ultrafast H-ion and Zn-ion diffusion kinetics via coating

Aqueous Zn-ion batteries (AZIBs) with excellent electrochemical performance are achieved by using small organic molecules VO(acac)2 (IV) as cathode. The surface area and electrical conductivity of IV are increased by coating wrinkled rGO, thereby improving the electrochemical sluggishness of IV cathode. The VO(acac)2@rGO (IV@rGO) aqueous battery can display a high capacity of 327.2 mAh g−1 at 100 mA g−1. The Zn2+ and H+ con-insertion/extraction reactions within IV@rGO are a joint control of pseudocapacitance and diffusion process. The in-situ XRD combinded with ex-situ Raman and XPS reveal that the multivalent transition of vanadium and coordination reaction of organic functional groups (VO), and no significant volume change of IV structure implying near-zero expansion characteristic during charging/discharging process.

An image encryption scheme based on the four-dimensional chaotic system and the mealy finite state machine

This paper proposes a four-dimensional hyperchaotic system to overcome the defect of weak encryption effect due to the simple complexity of low-dimensional chaotic systems in chaos-based image encryption schemes, which is verified to have better chaotic properties by dynamics analysis, sensitivity analysis, and randomness test. In addition, this paper proposes an image encryption scheme by combining the proposed chaotic system with the Mealy finite state machine (MFSM) to overcome the problem that some schemes are not resistant to statistical analysis. Firstly, the chaotic sequence is applied in the Knuth-Durstenfeld shuffling method to scramble the original image efficiently; secondly, according to the different information contained in the bit-plane, the pixel is decomposed and cyclically shifted at the bit level to achieve bit-level scrambling and diffusion; thirdly, the chaotic sequence is applied to select the rules for DNA encoding, and the diffusion process is achieved by Mealy finite state machine transformation; lastly, decoding the diffused image by selecting DNA rules randomly to get cipher image. This paper gives the experimental results, demonstrating that the scheme is highly secure. It can improve the encryption scheme’s sensitivity to plaintext and resist attacks such as differential attacks and select attacks.

Reciprocal action of natural bianisotropy and artificial chirality on electromagnetic propagation in medium

Background. The present article investigates the reciprocal action of specific medium effects on electromagnetic waves propagation. The object of study is a moving dielectric, which at rest already demonstrate bianisotropic properties, i. e., it is a synthetic material, e. g., chiral media with Ω-particles. Bianisotropic material equations are the most general for describing the effects of electromagnetic waves interaction with complex medium. Studying and analyzing them is proving to be a notable scientific problem. Natural bianisotropy is a property of simple media under special conditions (state of motion, internal currents and diffusion processes), whereas artificial bianisotropy is an inherent property of the synthetic material itself (composite material, material with different metaparticles).
 Aim. The main goal of the work is to generalize the already available data. On it basis, then, obtain analytical expressions, which can be effectively used for the experiments designing, creating new computational techniques for solving direct and inverse electromagnetic diffraction problems.
 Methods. In this paper, analytical methods are applied to obtain the resulting close-form expressions.
 Results. Three classes of effects have been identified that have a significant reciprocal effect on each other: gyrotropy, spatial dispersion, and temporal dispersion. In this article it was shown that the gyrotropy of the medium has not only a simple additive effect, but under some, specific conditions, can be related to the system emergence.
 Conclusion. The reciprocal action of the spatial dispersion of the moving chiral medium, generally has different scales in range. Temporal dispersion was investigated, which does not have a simple additive property, because even an isotropic medium acquires fundamentally new material properties of bianisotropy when it moves.

Circulation and Stratification Changes in a Hypersaline Estuary Due to Mean Sea Level Rise

Hypersaline Hamelin Pool, with mean salinity >65, is located in Shark Bay, Western Australia. The high salinity has reduced its biodiversity, but it is home to a diverse assemblage of modern marine stromatolites. The limited exchange of water between Hamelin Pool and the rest of Shark Bay, due to the presence of the shallow Faure Sill together with high evaporation and low rainfall-runoff have resulted in a hypersaline environment. With climate-change-induced mean sea level rise (MSLR), hydrodynamic processes that maintain the hypersaline environment may be affected and are the focus of this paper. Oceanographic observations, together with hydrodynamic model results, were used to examine the hydrodynamic processes under present and future MSLR scenarios. A large attenuation in the tidal range, changes in the tidal characteristics, and current speeds together with a strong salinity gradient were observed across the Faure Sill under present-day conditions. Under an MSLR scenario of 1 m, the tidal amplitude decreased by up to 10% to the north, whilst to the south, the tidal range increased by up to 15%. Regions of strong vertical stratification were present on both sides of the Faure Sill. The simulations indicated that, under MSLR scenarios, these regions expanded in area and exhibited higher levels of vertical stratification. The salt flux across the Faure Sill was maintained as a diffusive process under MSLR scenarios.

Regulating potassium storage kinetics in mesoporous carbon spheres via delicate inner structural design

Carbon materials have been considered to be potential anodes for potassium-ion batteries (PIBs). Different strategies, including designing micro-/nano-structure and porous morphology, introducing heteroatom doping, and creating carbon-based hybrids, have been employed to improve the potassium ion transport kinetics. Nevertheless, it is still a challenge to achieve satisfactory potassium storage performance due to the uncontrolled reaction kinetics of the large-sized potassium ions. Herein, we successfully synthesized mesoporous carbon spheres (MCSs) with tunable internal morphology and structure by using sacrificed template method. The optimized MCSs with novel half inner-shell structures (HIS-MCSs) show excellent electrochemical performance when used as the anode for PIBs. Specifically, a reversible specific capacity of 241.2 mAh/g is achieved at a current density of 0.1 A/g. Even at 5.0 A/g, a reversible specific capacity of 120 mAh/g can still be reached. Long-term stability tests show that the electrode holds a capacity of 166.5 mAh/g after 1000 cycles at 1.0 A/g. The good cycling stability and rate performance of the HIS-MCSs electrode are attributed to the well-defined inner structural design, in which the contribution from ion diffusion and pseudo-capacitance process are compromised.

Epidemic models in well-mixed multiplex networks with distributed time delay

In this paper, we consider an epidemic model in well-mixed multiplex networks with distributed time delay. Specifically, the model consists of two layers of well-mixed networks in the physical and virtual worlds, respectively, where two diffusive processes interact and influence each other within the same individual. We assume that there is a distributed time delay for an individual to become infected, but no delay for an individual to transition from unawareness to awareness. Our main results are as follows: Let R0P and R0V represent the basic reproduction numbers in the physical and virtual worlds, respectively. First, we demonstrate that the disease will die out for any delay time, provided that R0P≤1 or 1<R0P≤R0V. The latter condition emphasizes the significance of effective information spreading in eradicating the disease. Secondly, in the case of R0P>max⁡{1,R0V}, we establish that the model exhibits an endemic and information saturated equilibrium, denoted as E3. Additionally, we show that the model is uniformly persistent, indicating the sustained outbreak of the disease.

Microstructure evolution and coercivity enhancement in hot-deformed Nd-Fe-B magnet processed by Pr60Tb10Cu30 diffusion

The grain boundary diffusion process with Pr60Tb10Cu30 alloy was used to improve the microstructure and coercivity of the hot-deformed Nd-Fe-B magnet. The crystalline intergranular phases consisting of (Pr,Nd)5Ga3, (Pr,Nd)3Co, PrCu and (Nd,Pr)6Fe13Ga were observed in the Pr60Tb10Cu30 diffused magnet. Apparent (Nd,Tb)2Fe14B shell layer on the surface of Nd2Fe14B grains near the triple junctions of the magnet was observed after grain boundary diffusion. The formation of many non-ferromagnetic intergranular phases and Nd2Fe14B/(Nd,Tb)2Fe14B core-shell structure contributes to the significant increase of coercivity from 1.21 T to 2.7 T and the improvement of temperature coefficient of coercivity from −0.469%/℃ to −0.356%/℃.

Experimental Study on Grout–Soil Interaction Effects in Sandy Soil under Different Water-to-Cement Ratios

Due to the unique characteristics of sandy soil layers, there is often a coupling effect of multiple grout diffusion patterns in the grouting process, and different slurry diffusion modes may lead to different responses of soil structures. In this study, laboratory grouting model tests were conducted with homogeneous sand under different water-to-cement (w/c) ratios to reveal the temporal variations in grouting pressure, soil stress fields, and displacement fields during the grout diffusion process. The results show that, during the grouting process in the fine sand layer, the grout mainly exhibited a compaction–splitting diffusion mode. The farther away from the grouting center, the more pronounced the hysteresis effect of soil pressure caused by grout diffusion. Meanwhile, as the w/c ratio increased, the diffusion mode between the slurry and the soil was in a transitional state. At w/c &gt; 1.2, the primary pattern changed from the fracture–compaction pattern to the permeation–fracture–compaction pattern and fracture–permeation pattern. And the overall trend of the grouting pressure curve was similar under all of the w/c ratio conditions, showing a trend of increasing to the maximum value of the pressure first and then decreasing. With the increase in the water–cement ratio, the overall value of the grouting pressure curve showed a decreasing trend, the pressure value increased more slowly with time before reaching the maximum value, and the more obvious the influence of water–cement ratio was when w/c &gt; 1.2. Additionally, the surface displacement also exhibited an overall decreasing trend, and it had no obvious lifting value under the condition of w/c = 1.6.

Scaling law of diffusion processes on fractal networks

We investigate diffusion processes on fractal networks at different length scales. This is achieved by the application of a box covering procedure. We find that a clearly scaling law emerges on a great variety of fractal networks. Specifically, a number of metrics for quantifying diffusion processes, such as Kemeny’s constant, the expected search time and its variation, follow a power-law with the number of boxes for covering. Furthermore, we identify a power-law relation between energy and the number of boxes. Remarkably, we show that the expected time for hunting a moving target similarly presents a power law behavior on a given fractal network. Our work reveals that scaling law is a common characteristic of fractal networks beyond their structural organization.

Computational Approaches to Predict Protein-Protein Interactions in Crowded Cellular Environments.

Investigating protein-protein interactions is crucial for understanding cellular biological processes because proteins often function within molecular complexes rather than in isolation. While experimental and computational methods have provided valuable insights into these interactions, they often overlook a critical factor: the crowded cellular environment. This environment significantly impacts protein behavior, including structural stability, diffusion, and ultimately the nature of binding. In this review, we discuss theoretical and computational approaches that allow the modeling of biological systems to guide and complement experiments and can thus significantly advance the investigation, and possibly the predictions, of protein-protein interactions in the crowded environment of cell cytoplasm. We explore topics such as statistical mechanics for lattice simulations, hydrodynamic interactions, diffusion processes in high-viscosity environments, and several methods based on molecular dynamics simulations. By synergistically leveraging methods from biophysics and computational biology, we review the state of the art of computational methods to study the impact of molecular crowding on protein-protein interactions and discuss its potential revolutionizing effects on the characterization of the human interactome.

The expected sample allele frequencies from populations of changing size via orthogonal polynomials

In this article, discrete and stochastic changes in (effective) population size are incorporated into the spectral representation of a biallelic diffusion process for drift and small mutation rates. A forward algorithm inspired by Hidden-Markov-Model (HMM) literature is used to compute exact sample allele frequency spectra for three demographic scenarios: single changes in (effective) population size, boom-bust dynamics, and stochastic fluctuations in (effective) population size. An approach for fully agnostic demographic inference from these sample allele spectra is explored, and sufficient statistics for stepwise changes in population size are found. Further, convergence behaviours of the polymorphic sample spectra for population size changes on different time scales are examined and discussed within the context of inference of the effective population size. Joint visual assessment of the sample spectra and the temporal coefficients of the spectral decomposition of the forward diffusion process is found to be important in determining departure from equilibrium. Stochastic changes in (effective) population size are shown to shape sample spectra particularly strongly.

GLDM: hit molecule generation with constrained graph latent diffusion model.

Discovering hit molecules with desired biological activity in a directed manner is a promising but profound task in computer-aided drug discovery. Inspired by recent generative AI approaches, particularly Diffusion Models (DM), we propose Graph Latent Diffusion Model (GLDM)-a latent DM that preserves both the effectiveness of autoencoders of compressing complex chemical data and the DM's capabilities of generating novel molecules. Specifically, we first develop an autoencoder to encode the molecular data into low-dimensional latent representations and then train the DM on the latent space to generate molecules inducing targeted biological activity defined by gene expression profiles. Manipulating DM in the latent space rather than the input space avoids complicated operations to map molecule decomposition and reconstruction to diffusion processes, and thus improves training efficiency. Experiments show that GLDM not only achieves outstanding performances on molecular generation benchmarks, but also generates samples with optimal chemical properties and potentials to induce desired biological activity.

Systematic Study of the Effect of Cycle Number and Crystal Structure on Si Anodes

AbstractThis paper shows that the number of cycles and the crystal structure play an important role in the capacity and cycling ability of lithium‐ion batteries. However, the detailed dynamics and continuity of the capacity decay mechanism caused by the number of cycles and crystal structure need to be further understood at the nanoscale. Molecular dynamics simulation was used to examine the microstructure development and deformation behavior of the Si anode in an electric field. The results show that the increase of the number of cycles leads to a large expansion of the volume of the Si electrode, which further leads to the loss of capacity and the decrease of cycle capacity, as well as the decrease of structural stability. The formation of Si crystal structure from diamond structure to amorphous depends on the depth of lithiation and desulfurization. Due to the presence of a large number of nanoscale voids, the Si anode has undergone volume expansion. The transformation associated with nanogap nucleation caused by the involuntary diffusion process is driven by more cycles, resulting in irreversible capacity loss of lithium‐ion batteries. The analysis model shows that the stress caused by diffusion is not only related to the position of the Si anode, but also to the cycle time.

Non-Markovian Diffusion and Adsorption-Desorption Dynamics: Analytical and Numerical Results.

The interplay of diffusion with phenomena like stochastic adsorption-desorption, absorption, and reaction-diffusion is essential for life and manifests in diverse natural contexts. Many factors must be considered, including geometry, dimensionality, and the interplay of diffusion across bulk and surfaces. To address this complexity, we investigate the diffusion process in heterogeneous media, focusing on non-Markovian diffusion. This process is limited by a surface interaction with the bulk, described by a specific boundary condition relevant to systems such as living cells and biomaterials. The surface can adsorb and desorb particles, and the adsorbed particles may undergo lateral diffusion before returning to the bulk. Different behaviors of the system are identified through analytical and numerical approaches.