1,065 Results Found

Drying has been widely studied as a necessary process in biomass utilization. The steam diffusion law plays an important role in drying kinetics. The drying kinetics of a single biomass particle using Fick’s second law of diffusion was studied...

Because of the problem of gangue discharge and surface subsidence during coal mining, the current research on underground filling mainly focuses on the paste filling, solid filling, and grouting filling of the overburden separation layer after scaffo...

The permeation of gases through membranes is a fundamental process with wide-ranging applications, from gas separation and fuel cell technology to respiratory physiology. Governed by Fick’s second law of diffusion, the mathematical modelling of...

Conventional continuum thermodynamics is characterized by a classical form of the energy law and the second law of thermodynamics in the form of the Clausius–Duhem inequality. This thermodynamic framework fails to capture certain features in ma...

To investigate the diffusion law of ultrafine cement slurry (UCS) with different water–cement ratios in tunnel second lining cracks during grouting, the grouting of ultrafine cement slurry with different water–cement ratios was carried ou...

Red mud is a strong alkaline solid waste pollutant produced in the process of aluminum smelting, which causes great pollution to the regional groundwater environment due to its high content of fluorine and aluminum and high concentration of strong al...

In this article, we consider how differing approaches that characterize biological microstructure with diffusion weighted magnetic resonance imaging intersect. Without geometrical boundary assumptions, there are techniques that make use of power law...

Polymer slurry is widely used in underground engineering treatment, but due to the concealed nature of underground projects, the diffusion pattern of slurry in the sand has been little studied. In this study, the basic physical properties of water-ba...

We have studied a class of $(1+1)$-dimensional equations that models phenomena with heterogeneous diffusion, advection, and reaction. We have analyzed these fourth-order partial differential equations within the framework of group methods. In this clas...

We investigated the diffusive dynamics of a Lévy walk subject to stochastic resetting through combined numerical and theoretical approaches. Under exponential resetting, the process mean squared displacement (MSD) undergoes a sharp transition...

Cr/low-carbon steel surface composites were prepared by aqueous solution co-deposition and high-temperature solid-state diffusion technology, and the macro rule of the solid-state diffusion of chromium on the surface of low-carbon steel was analyzed....

This study investigates the Lie point and Q-conditional symmetries of a classical two-component reaction–diffusion system in one spatial dimension. The symmetry classifications for the reaction–diffusion system and corresponding symmetry...

Unconventional oil reservoirs are tight and often host micro-nano pores, and huff and puff is usually adopted for such reservoirs, mainly utilizing the mechanism of spontaneous imbibition. The penetration depth into the matrix during imbibition is on...

We analyze two-dimensional isotropic heterogeneous diffusion with a radially decaying diffusion coefficient $D\left(\rho \right)=D_0/{\rho }^2$, subject to Poissonian stochastic resetting to the origin. Since multiplicative noise makes the process interpretation-depe...

The rheological properties and diffusion law of coal-based solid waste geopolymer grouting material (CGGM) slurry were investigated by rheological property test and diffusion theory model derivation. Based on the power-law fluid constitutive equation...

The post-construction improvement technology of bored pile tips has been widely used in the construction of gravel pebble layers, but the diffusion law of the grouting slurry remains to be revealed. To study the diffusion law of the grouting slurry a...

The Selkov system, which is typically employed to model glycolysis phenomena, unveils some rich dynamics and some other complex formations in biochemical reactions. In the present work, the synchronization problem of the glycolysis reaction-diffusion...

In this work, we show that it is possible to obtain important ubiquitous physical characteristics when an aggregation of many systems is taken into account. We discuss the possibility of obtaining not only an anomalous diffusion process, but also a N...

With the continuous development of the times and the natural gas industry, the number of composite laying between natural gas pipelines and power channels has increased. Once a gas pipeline leaks, it is easy to enter the power channel and cause serio...

This study examined the diffusion of nutrients (NH₄⁺, NO₃⁻, and PO₄³⁻) in the pore water of intertidal sediments in Lake Komuke (located in the northeastern part of Hokkaido on the coast of Okhotsk Sea) across nine stations, at 0 cm to 40...

In the present paper, we propose two methods for tracking molecular species in water layers via two approaches of the diffusion equation with a power-law time-dependent diffusion coefficient. The first approach shows the species densities and the gro...

Gas control and extraction are essential for energy use and sustainable development. In order to study the gas diffusion and transportation law of high-gas tunnels after excavation and blasting and the influence of ventilation on gas concentration, a...

Due to the complexity imposed by all the attributes of the fracture network of many naturally fractured reservoirs, it has been observed that fluid flow does not necessarily represent a normal diffusion, i.e., Darcy’s law. Thus, to capture the...

The soft surrounding rock of deep roadways is in the state of “micro-fracture and low permeability”. In order to solve the problem of grouting reinforcement of micro-fractures surrounding rock in deep roadways, the influence characteristi...

A series of porous clay samples prepared at different pretreatment temperatures have been tested in a diffusion chamber. Diffusivity and permeability were examined in a temperature range from ambient to 900 °C. Gaseous mixtures of O₂, CO₂, and N₂ hav...

Gamma dicalcium silicate (γ-2CaO∙SiO₂, abbreviated as γ-C₂S) is considered a potential candidate as a construction material owing to its high carbonation reactivity and consequent CO₂ absorption. This study investigates the diffusio...

Modeling metal matrix composites in finite element software requires incorporating a cohesive zone model (CZM) to represent the interface between the constituent materials. The CZM determines the behavior of traction–separation (T–S) in t...

Over the past several decades, over 100 countries have passed legislation banning commercial organ transplantation. What explains this rapid, global diffusion of laws? Based on qualitative data from in-depth interviews, historical analysis, and secon...

When the concentration of a gas exceeds the equilibrium concentration in a liquid, the gas–liquid system is referred as a supersaturated system. The supersaturation can be achieved by either changing the pressure and/or temperature of the syste...

This work investigates bias-temperature instability (BTI) in 1700 V 4H-SiC MOSFETs under realistic 1 MHz switching conditions with simultaneous gate and drain stress. Threshold-voltage measurements reveal that the degradation does not follow the clas...

For the first time, the power law characteristics of stock price jump intervals have been empirically found generally in stock markets. The classical jump-diffusion model is described as the jump-diffusion model with power law (JDMPL). An artificial...

Here, we analyze the degassing process of a byproduct (methane) formed during the peroxide-induced crosslinking of polyethylene. A diffusion model based on Fick’s law is used to obtain the controlling factors of degassing in a crosslinked polye...

Gelation through the liquid-liquid contact between a polymer solution and a gelator solution has been attempted with various combinations of gelator and polymer solutions. In many combinations, the gel growth dynamics is expressed as $X\sim \sqrt{t}$, where $X$...

The Omori-Utsu law shows the temporal power-law-like decrease of the frequency of earthquake aftershocks and, interestingly, is found in a variety of complex systems/phenomena exhibiting catastrophes. Now, it may be interpreted as a characteristic re...

This article investigates the widespread occurrence of wave-like behavior in biological systems and reflects on the importance of reaction–diffusion frameworks to explain fast information transfer. Focusing on the classical Fisher–Kolmogo...

To investigate the impact of experimental interventions on living biological tissue, ex vivo rodent brain slices are often used as a more controllable alternative to a live animal model. However, for meaningful results, the biological sample must be...

Reliability degradation in semiconductor devices originates from microscopic stochastic processes such as defect motion, diffusion, bond rearrangement, and charge trapping occurring under electrical and thermal stress. Experimental degradation measur...

This study develops a numerical model based on a multi-physics coupled finite element method to predict the carbonation depth of hardened alkali-activated slag under accelerated carbonation curing conditions. Drawing on existing literature data, the...

A unitary model of drug release dynamics is proposed, assuming that the polymer–drug system can be assimilated into a multifractal mathematical object. Then, we made a description of drug release dynamics that implies, via Scale Relativity Theo...

Legal transplants have consolidated as a core issue of contemporary comparative law, although their study remains marked by significant theoretical and methodological tensions. This article presents a PRISMA-informed structured systematic review of 2...

Let $B^H=\{B_t^H,t\ge 0\}$ be a fractional Brownian motion with Hurst index $\frac{1}{2}\le H<1$. In this paper, we consider the linear self-attracting diffusion: $d{X}_t^H=d{B}_t^H+\sigma X_t^{H}dt-\theta \left({\int }_0^t\left(X_s^H-X_u^H\right)ds\right)dt$$+\nu dt$ with $X_0^H=0$, where $\theta >0$ and...

A kinetic model has been derived from the classical (Fick and Henry’s) laws of the gas theory for predicting the oxygen permeability of a closed composite container, initially filled by pure nitrogen under a pressure slightly higher than the atmosphe...

Developmental engineering (DE) involves culturing various cells on modular scaffolds (MSs), yielding modular tissues (MTs) assembled into three-dimensional (3D) tissues, mimicking developmental biology. This study employs an integrated approach, merg...

In this study, the protective effect of a Nanoscale Deep Penetration Sealer (NDPS) in improving the chloride erosion resistance of concrete was evaluated and the influence of water–cement ratio (w/c) and the NDPS spray volume on the protective...

Cotton dyeing is a very complex process with many variables in which different phenomena occur simultaneously. This study aimed to describe the cotton dyeing process by natural dye, using a mathematical model that consists of three mass conservation...

Cyclic Voltammetry is an analysis method for characterizing the behaviors of electrochemically active materials by measuring current through defined potential sweeps. The current–potential relationship depends on key variables such concentratio...

The fundamental attributes of charged hydrogels containing predominantly water and controllable amounts of low molar mass electrolytes are of tremendous significance in biological context and applications in healthcare. However, a rigorous theoretica...

To prevent toxic and harmful gas suffocation accidents in underground metal mine stopes, the Fluent numerical simulation method was employed to investigate the wind field distribution patterns and the diffusion laws of blasting fumes in stopes with a...

The lifetime of singlet excitons in conjugated polymer films is a key factor taken into account during organic solar cell device optimization. It determines the singlet exciton diffusion lengths in polymer films and has a direct impact on the photocu...

We study one-dimensional diffusions reflected at a boundary and analyze their pathwise “episodes” away from the boundary through Itô’s excursion theory. Under a fixed height cap of $a>0$, each excursion is equipped with three...