1,894 Results Found

The authors derived the analytical solution to diffusion equations. The solution requires linearization of diffusion equations, as well as developing the obtained expression into a series. In particular, the result of the first procedure is highly de...

Accurate precipitation nowcasting is essential for short-term forecasting, but it remains challenging due to the dynamic nature of rainfall mechanisms. This study implements and evaluates two schemes for improving precipitation nowcasting: (1) an adv...

The method of linear determining equations is constructed to study conditional Lie–Bäcklund symmetry and the differential constraint of a two-component second-order evolution system, which generalize the determining equations used in the search for c...

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 article, we study the semi-linear two-dimensional reaction–diffusion equation with Dirichlet boundaries. A reliable numerical scheme is designed, coupling the nonstandard finite difference method in the time together with the Galerkin i...

In this work, the linearity axiom of irreversible thermodynamics for diffusion and heat transfer has been re-examined. It is shown that this axiom is compatible with the entropy production invariance principle with respect to a reference quantity for...

Due to the ability of microgels to rapidly contract and expand in response to external stimuli, assemblies of interconnected microgels are promising for actuation applications, e.g., as contracting fibers for artificial muscles. Among the properties...

Approximate models are a fast and most often precise tool for determining the effectiveness factor for heterogeneous catalysis processes that are realized in the real world. They are also frequently applied as robust transient models describing the w...

In buildings, the HVAC systems are responsible for a major part of the energy consumption. Incorrect design or selection of the system and improper installation, operation, and maintenance of the systems’ elements may result in increased energy consu...

The primary concern of synthetic aperture radar (SAR) images is speckle noise, an inherent property. The creation of speckle noise is in a granular form and its nature is multiplicative. To reduce such noise from the radar images, the researchers&rsq...

Coarse Mesh Finite Difference (CMFD) is a widely-used iterative acceleration method for neutron transport problems in which nonlinear terms are introduced in the derivation of the low-order CMFD diffusion equation. These terms, including the homogeni...

In this paper, we propose a modified fractional diffusive SEAIR epidemic model with a nonlinear incidence rate. A constructed model of fractional partial differential equations (PDEs) is more general than the corresponding model of fractional ordinar...

In this paper, we investigate parameter estimation for a class of linear self-attracting diffusion processes. Specifically, we consider processes with a drift coefficient given by $-\theta \left({\int }_0^t(X_t-X_u)du\right)$. Employing both maximum likelihoo...

In this short perspective, we analyze the different linear response functions relevant to surface diffusion as studied by helium atom scattering, organizing them around a single object: the intermediate scattering function (ISF), which is also a char...

This paper is devoted to the study of the chemotaxis model for drug delivery purposes. The pattern formation for a volume-filling with nonlinear diffusive terms is investigated. The proposed mathematical model is governed by a reaction–diffusion syst...

Using magnetohydrodynamics (MHD), the thermal energy and mass transport boundary layer flow parameters of Reiner–Philippoff fluid (non-Newtonian) are numerically investigated. In terms of energy and mass transfer, non-linear radiation, Cattaneo...

Adsorbed gas may account for a significant part of the gas resources in shale gas and coalbed methane plays. Understanding gas sorption behaviors and integrating gas desorption into analytical reservoir modeling and an associated transient performanc...

We consider the estimation of parameter-dependent statistics of functional outputs of steady-state convection–diffusion–reaction equations with parametrized random and deterministic inputs in the framework of linear elliptic partial differential equa...

We consider the existence and uniqueness of the saturated classical solutions and the positive classical solutions to initial boundary value problems of semi-linear sub-diffusion with gradient terms. Applying this to the fractional power of the secto...

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...

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...

The numerical solutions to a non-linear Fractional Fokker–Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The aim is to model anomalous diffusion using an FFP description with fractional velocity derivatives...

Double diffusive convection in a binary viscoelastic fluid saturated porous layer in the presence of a cross diffusion effect and an internal heat source is studied analytically using linear and nonlinear stability analysis. The linear stability theo...

In this paper, we study the indefinite linear-quadratic (LQ) stochastic optimal control problem for stochastic differential equations (SDEs) with jump diffusions and random coefficients driven by both the Brownian motion and the (compensated) Poisson...

Guided diffusion planners for robot manipulators often fail in bottleneck scenes. The reason is that local collision corrections must be coordinated through a limited latent parameterization. This study examines the issue at the level of trajectory r...

The conditional Lie–Bäcklund symmetry method is applied to investigate the functionally generalized separation of variables for quasi-linear diffusion equations with a source. The equations and the admitted conditional Lie–Bäckl...

This paper presents a novel methodology for estimating space- and time-dependent source terms in heat and mass diffusion problems. The approach combines classical integral transform techniques (CITTs) with the least squares optimization method, enabl...

Two main topics are addressed in the present paper, first, a rigorous qualitative study of a second-order reaction–diffusion problem with non-linear diffusion and cubic-type reactions, as well as inhomogeneous dynamic boundary conditions. Under...

A mean-field linear quadratic stochastic (MF-SLQ for short) optimal control problem with hybrid disturbances and cross terms in a finite horizon is concerned. The state equation is a systems driven by the Wiener process and the Poisson random marting...

Polymer electrolyte was used as a medium for testing the performance of microband electrodes under conditions of linear diffusion. Cyclic voltammetry (CV) and chronoamperometry (CA) experiments were performed in a highly viscous medium, where diffusi...

Positively charged polyelectrolytes hold significant potential as materials for creating antibacterial coatings. We examined the physicochemical and mechanical properties of the macromolecules in water solutions and in coatings for the series of bran...

The effects of relaxation, convection, and anisotropy on a two-dimensional, two-equation system of nonlinearly coupled, second-order hyperbolic, advection–reaction–diffusion equations are studied numerically by means of a three-time-level...

The relationship between absorption and gas concentration was studied using a diffuse integrating cavity as a gas cell. The light transmission process in an arbitrary diffuse cavity was theoretically derived based on a beam reflection analysis. It wa...

This paper is concerned with intriguing possibilities for non-conventional critical behavior that arise when a nearly critical strongly non-equilibrium system is subjected to chaotic or turbulent motion of the environment. We briefly explain the conn...

We construct a stabilized finite element method for linear and nonlinear unsteady advection–diffusion–reaction equations using the method of lines. We propose a residual minimization strategy that uses an ad-hoc modified discrete system t...

Advection–diffusion–reaction-type interface models have wide-ranging applications in environmental science, chemical engineering, and biological systems, particularly in modeling pollutant transport in groundwater, reactive flows, and dru...

In this work, we consider extended irreversible thermodynamics in assuming that the entropy density is a function of both common thermodynamic variables and their higher-order time derivatives. An expression for entropy production, and the linear phe...

Wearable alcohol monitoring devices demand noninvasive, real-time measurement of blood alcohol content (BAC) reliably and continuously. A few commercial devices are available to determine BAC noninvasively by detecting transcutaneous diffused alcohol...

We consider the indefinite, linear-quadratic, mean-field-type stochastic zero-sum differential game for jump-diffusion models (I-LQ-MF-SZSDG-JD). Specifically, there are two players in the I-LQ-MF-SZSDG-JD, where Player 1 minimizes the objective func...

A new closed-form analytical solution to the radial transport of tracers in porous media under the influence of linear drift is presented. Specifically, the transport of tracers under convection–diffusion-dominated flow is considered. First, th...

Accurate short-term precipitation nowcasting remains challenging in complex terrain regions, where storm displacement, evolution, and orographic enhancement strongly affect precipitation distribution. This study evaluates three precipitation nowcasti...

We study reaction–diffusion systems with rapidly oscillating terms in the coefficients of equations and in the boundary conditions, in media with periodic obstacles. The non-linear terms of the equations only satisfy general dissipation conditi...

When a sample of semiconducting material is illuminated by monochromatic light, in which the photon energy is higher than the energy gap of the semiconductor, part of the absorbed electromagnetic energy is spent on the generation of pairs of quasi-fr...

Efficient and accurate time integration is essential for simulating combustion processes with stiff, multiscale dynamics arising from diffusion, reaction, and advection interactions. Standard implicit–explicit (IMEX) methods employ a two-additi...

Polymetallic nodules, found abundantly in deep-ocean deposits, possess significant economic value and represent a valuable resource due to their high metal enrichment, crucial for the high-tech industry. However, accurately evaluating these valuable...

A first-order linear and numerically non-diffusive Eulerian transport algorithm, minVAR, was recently developed for preservation of correlations between interrelated tracers during advective transport. The present study extends this work by: (1) prov...

An accurate determination of transport coefficients in liquids, such as diffusivity, is crucial for studying fundamental chemical processes, for constructing and verifying model theories of liquid, and for the optimization of technological processes....

This study describes the adaptation of non-linear microscopy for single-particle tracking (SPT), a method commonly used in biology with single-photon fluorescence. Imaging moving objects with non-linear microscopy raises difficulties due to the scann...

For a complementary metal-oxide-semiconductor image sensor with highly linear, low noise and high frame rate, the nonlinear correction and frame rate improvement techniques are becoming very important. The in-pixel source follower transistor and the...

When the chloride ion concentration within concrete reaches a certain threshold, it triggers corrosion of the reinforcing steel bars, severely compromising the durability of reinforced concrete structures. Accurately assessing how the chloride ion co...