Search Results (1,661)

Partial Differential Equation (PDE)-based hydrologic models demand extensive preprocessing, creating a bottleneck and slowing down the model setup process. Mesh generation typically lacks integration with hydrological features like river networks. We present GHOST Mesh (GMesh), an automated, watershed-oriented mesh generator built within the Watershed Modeling Framework (WMF), to address this. While primarily designed for the GHOST hydrological model, GMesh’s functionalities can be adapted for other models. GMesh enables rapid mesh generation in Python by incorporating Digital Elevation Models (DEMs), flow direction maps, network topology, and online services. The software creates Voronoi polygons that maintain connectivity between river segments and surrounding hillslopes, ensuring accurate surface–subsurface interaction representation. Key features include customizable mesh generation and variable refinement to target specific watershed areas. We applied GMesh to Iowa’s Bear Creek watershed, generating meshes from 10,000 to 30,000 elements and analyzing their effects on simulated stream flows. Results show that higher mesh resolutions enhance peak flow predictions and reduce response time discrepancies, while local refinements improve model performance with minimal additional computation. GMesh’s open-source nature streamlines mesh generation, offering researchers an efficient solution for hydrological analysis and model configuration testing. Full article

In this study, we explore the soliton solutions of the truncated M-fractional fifth-order Korteweg–de Vries (KdV) equation by applying the improved modified extended tanh function method (IMETM). Novel analytical solutions are obtained for the proposed system, such as brigh soliton, dark soliton, hyperbolic, exponential, Weierstrass, singular periodic, and Jacobi elliptic periodic solutions. To validate these results, we present detailed graphical representations of selected solutions, demonstrating both their mathematical structure and physical behavior. Furthermore, we conduct a comprehensive linear stability analysis to investigate the stability of these solutions. Our findings reveal that the fractional derivative significantly affects the amplitude, width, and velocity of the solitons, offering new insights into the control and manipulation of soliton dynamics in fractional systems. The novelty of this work lies in extending the IMETM approach to the truncated M-fractional fifth-order KdV equation for the first time, yielding a wide spectrum of exact analytical soliton solutions together with a rigorous stability analysis. This research contributes to the broader understanding of fractional differential equations and their applications in various scientific fields. Full article

(1) Chronic heart failure (CHF) is a typical component of the polymorbid profile of an elderly patient. The aim of this systematic review was to search for data from pharmacokinetic (PK) studies of any drugs in patients with CHF to systematize information on changes in PK parameters depending on the physicochemical properties (PCPs) of the drug and route of its administration. (2) A systematic review of PK studies in patients with CHF was performed using Elibrary.ru, United States National Library of Medicine (PubMed), China National Knowledge Infrastructure (CNKI), and Directory of Open Access Journals (DOAJ). The final number of included articles was 106. A descriptive and correlation analysis of PK data and PCPs of drugs included in the study was carried out. Inclusion criteria: PK study, available PK parameters, demographic data, and diagnosed CHF. Risk of bias was assessed using ROBINS-I. (3) Evaluation of correlations between PCPs of drugs and their PK revealed a link between (i) plasma protein binding (PPB) and volume of distribution for lipophilic drugs; (ii) PCPs, half-life, and clearance for drugs with high PPB; and (iii) PPB and clearance for hydrophilic and amphiphilic drugs. (4) Hypoalbuminemia associated with CHF may lead to an increased volume of distribution of lipophilic drugs; lipophilic drugs used in CHF patients may be associated with prolongation of the half-life period and reduction in clearance; highly protein-bound drugs may manifest with reduced clearance. PK characteristics identified in this review should guide modifications to dosing regimens in CHF patients receiving medications from different groups. Full article

Erectile dysfunction (ED) and cognitive decline share overlapping vascular, metabolic, and neurodegenerative mechanisms, particularly in aging populations. Phosphodiesterase type 5 inhibitors (PDE5-Is), such as sildenafil and vardenafil, are widely used to treat ED by elevating cyclic guanosine monophosphate (cGMP) levels and enhancing vascular function. Emerging evidence suggests that PDE5-Is may also benefit cognitive function by promoting neurovascular coupling, synaptic plasticity, and neuroprotection. This review synthesizes clinical, preclinical, and mechanistic studies on PDE5-Is in the context of learning, memory, and Alzheimer’s disease, highlighting their potential as therapeutic agents for cognitive impairment. Full article

Background: Erectile dysfunction (ED) is a disease whose occurrence is steadily increasing worldwide. This pathology is multifactorial and often combined with other diseases. ED of organic genesis in 50–80% of men is vasculogenic. Methods: A survey was conducted of 88 men (aged 44 to 62) who complained of erectile dysfunction. It consisted of a questionnaire administered according to the protocols “International Index of Erectile Function” and “Aging Male Screening”, and was followed by a color Doppler ultrasound (Logiq 9 ExpertGE with a 7 MHz linear transducer using B mode) and penile scintigraphy (single-photon emission computed tomography). The procedures were initially performed at rest, then during pharmacologically induced erection, which was achieved through the intake of phosphodiesterase-5 (PDE5) inhibitors. Patients who did not respond to pharmacological stimulation and had IIEF scores below 5–7 were offered surgical treatment—penile prosthesis followed by histological examination of the tissue of the corpus cavernosum. Statistical analysis was carried out using Microsoft Excel and STATISTICA 10.0 software. The Mann–Whitney U test was used to assess differences between quantitative variables, with the significance level set at p ≤ 0.05. Results: Penile scintigraphy shows high sensitivity (85.2%) and specificity (83.3%), outperforming color Doppler ultrasonography in detecting vasculogenic ED. Conclusion: Penile scintigraphy is demonstrated to be a highly informative method, allowing us to analyze the condition of the magistral and organ blood flow, as well as the microcirculatory bed of the cavernous bodies of the penis. This improves the effectiveness of this method in diagnosing various types of vasculogenic erectile dysfunction (ED), which opens opportunities for its use together with ultrasound examination when the latter is less informative. Full article

In recent years, paper-based humidity sensors have emerged as a highly promising technology for humidity detection. In this work, a polymerizable deep eutectic solvent (PDES) was prepared via a one-step blending method, which was applied to modify filter paper. The modification process did not alter the overall structure of the paper cellulose but rather targeted only its internal cellulose channels, thereby minimizing any impact on the paper’s original moisture-independent properties. The filter paper functioned both as the substrate and the humidity-sensing material in the fabricated sensor. The finger-like electrodes were designed using AutoCAD 2018 software and then printed onto the modified paper using screen-printing technology to fabricate the humidity sensor. Different saturated salt solutions were used to simulate corresponding humidity environments and evaluate the humidity performance of sensors. Compared with that of the blank paper-based humidity sensor, the sensitivity of the sensor modified by the PDES was significantly greater, and the recovery time was greatly shorter. Specifically, the sensitivity increased from 1.34 to 10.36 at 54% RH and from 166.24 to 519.2 at 98% RH. Additionally, the sensor response time was reduced from 728 s to 137 s. PDES modification significantly improved the moisture-sensitive characteristics and detection performance of the sensor. Full article

We present a hybrid parallel scheme for efficiently solving Caputo time-fractional partial differential equations (CTFPDEs) with integer-order spatial derivatives on multicore CPU and GPU platforms. The approach combines a second-order spatial discretization with the $L1$ time-stepping scheme and employs MATLAB parfor parallelization to achieve significant reductions in runtime and memory usage. A theoretical third-order convergence rate is established under smooth-solution assumptions, and the analysis also accounts for the loss of accuracy near the initial time $t=t_0$ caused by weak singularities inherent in time-fractional models. Unlike many existing approaches that rely on locally convergent strategies, the proposed method ensures global convergence even for distant or randomly chosen initial guesses. Benchmark problems from fractional biological models—including glucose–insulin regulation, tumor growth under chemotherapy, and drug diffusion in tissue—are used to validate the robustness and reliability of the scheme. Numerical experiments confirm near-linear speedup on up to four CPU cores and show that the method outperforms conventional techniques in terms of convergence rate, residual error, iteration count, and efficiency. These results demonstrate the method’s suitability for large-scale CTFPDE simulations in scientific and engineering applications. Full article

This paper systematically studies the exact analytical solutions of the (2+1)-dimensional generalized Burgers–Fisher (gBF) equation. Using the Lie symmetry analysis method, the infinitesimal generators of the equation are derived. Through symmetry reduction, the original (2+1)-dimensional partial differential equation (PDE) is reduced to a (1+1)-dimensional equation, which is further transformed into an ordinary differential equation (ODE) via the traveling wave transformation. On this basis, a series of exact traveling wave solutions are successfully obtained by applying the generalized Bernoulli equation method, including hyperbolic tangent-type kink solitary wave solutions and hyperbolic cotangent-type singular soliton solutions. The study also conducts a visual analysis of the solution characteristics through three-dimensional graphs and contour plots. In particular, this paper discusses the case where the parameter n takes general values, filling the research gap in the existing literature. Full article

This paper presents a Neural Network-Based Symbolic Computation Algorithm (NNSCA) for solving the (2+1)-dimensional Yu-Toda-Sasa-Fukuyama (YTSF) equation. By combining neural networks with symbolic computation, NNSCA bypasses traditional method limitations, deriving and visualizing exact solutions. It designs neural network architectures, converts the PDE into algebraic constraints via Maple, and forms a closed-loop solution process. NNSCA provides a general paradigm for high-dimensional nonlinear PDEs, showing great application potential. Full article

In this paper, we develop a concise differential–potential framework for the functions of a generalized quaternionic variable in the two-parameter algebra ${\mathbb{H}}_{\alpha ,\beta }$, with $\alpha ,\beta \in \mathbb{R}\setminus \left\{0\right\}$. Starting from left/right difference quotients, we derive complete Cauchy–Riemann (CR) systems and prove that, away from the null cone where the reduced norm N vanishes, these first-order systems are necessary and, under ${\mathcal{C}}^1$ regularity, sufficient for left/right differentiability, thereby linking classical one-dimensional calculus to a genuinely four-dimensional setting. On the potential theoretic side, the Dirac factorization ${\Delta }_{\alpha ,\beta }=\overline{\mathcal{D}}\mathcal{D}=\mathcal{D}\overline{\mathcal{D}}$ shows that each real component of a differentiable mapping is ${\Delta }_{\alpha ,\beta }$-harmonic, yielding a clean second-order theory that separates the elliptic (Hamiltonian) and split (coquaternionic) regimes via the principal symbol. In the classical case $(\alpha ,\beta )=(-1,-1)$, we present a Poisson-type representation solving a model Dirichlet problem on the unit ball $B\subset {\mathbb{R}}^4$, recovering mean-value and maximum principles. For computation and symbolic verification, real $4\times 4$ matrix models for left/right multiplication linearize the CR systems. Examples (polynomials, affine CR families, and split-signature contrasts) illustrate the theory, and the outlook highlights boundary integral formulations, Green kernel constructions, and discretization strategies for quaternionic PDEs. Full article

With the increasing application of smart-material-based actuators for vibration suppression in flexible spacecraft, there is a growing need for advanced control strategies suited to distributed-parameter systems. This paper proposes a distributed cooperative control (DCC) scheme to address phase inconsistencies in actuator outputs within a decentralized control framework. The piezoelectric actuators embedded in flexible appendages are modeled as a multi-agent system that utilizes local information to improve coordination. A consensus-based cooperative controller is designed to synchronize actuator actions, with closed-loop stability rigorously established via Lyapunov’s direct method. The robustness of the controller is evaluated through Monte Carlo simulations under varying initial conditions. Comparative numerical results demonstrate that the proposed DCC achieves superior performance and energy efficiency over conventional decentralized control, along with inherent fault tolerance due to its distributed topology. Furthermore, the practical implementability of the approach is supported by discrete-time controller validation and automatic code generation, confirming its readiness for real-time embedded deployment. The study highlights the potential of DCC for enhancing vibration suppression in next-generation flexible spacecraft. Full article

In this paper, we develop the explicit finite difference method (FDM) to solve an ill-posed Cauchy problem for the 3D acoustic wave equation in a time domain with the data on a part of the boundary given (continuation problem) in a cube. FDM is one of the numerical methods used to compute the solutions of hyperbolic partial differential equations (PDEs) by discretizing the given domain into a finite number of regions and a consequent reduction in given PDEs into a system of linear algebraic equations (SLAE). We present a theory, and through Matlab Version: 9.14.0.2286388 (R2023a), we find an efficient solution of a dense system of equations by implementing the numerical solution of this approach using several iterative techniques. We extend the formulation of the Jacobi, Gauss–Seidel, and successive over-relaxation (SOR) iterative methods in solving the linear system for computational efficiency and for the properties of the convergence of the proposed method. Numerical experiments are conducted, and we compare the analytical solution and numerical solution for different time phenomena. Full article

We study here the Boussinesq-type Korteweg–de Vries (KdV) equation, a nonlinear partial differential equation, for describing the wave propagation of long, nonlinear, and dispersive waves in shallow water and other physical scenarios. In order to obtain novel families of wave solutions, we apply two efficient analytical techniques: the Modified Extended tanh (ME-tanh) method and the Modified Residual Power Series Method (mRPSM). These methods are used for the very first time in this equation to produce both exact and high-order approximate solutions with rich wave behaviors including soliton formation and energy localization. The ME-tanh method produces a rich class of closed-form soliton solutions via systematic simplification of the PDE into simple ordinary differential forms that are readily solved, while the mRPSM produces fast-convergent approximate solutions via a power series representation by iteration. The accuracy and validity of the results are validated using symbolic computation programs such as Maple and Mathematica. The study not only enriches the current solution set of the Boussinesq-type KdV equation but also demonstrates the efficiency of hybrid analytical techniques in uncovering sophisticated wave patterns in multimensional spaces. Our findings find application in coastal hydrodynamics, nonlinear optics, geophysics, and the theory of elasticity, where accurate modeling of wave evolution is significant. Full article

In a 1987 article of the last author dedicated to the memory of a pioneer of classical plasticity Aris Philips of Yale, the last author outlined three examples of self-organization during plastic deformation in metals: persistent slip bands (PSBs), shear bands (SBs) and Portevin Le Chatelier (PLC) bands. All three have been observed and analyzed experimentally for a long time, but there was no theory to capture their spatial characteristics and evolution in the process of deformation. By introducing the Laplacian of dislocation density and strain in the standard constitutive equations used for these phenomena, corresponding mathematical models and nonlinear partial differential equations (PDEs) for the governing variable were generated, the solution of which provided for the first time estimates for the wavelengths of the ladder structure of PSBs in Cu single crystals, the thickness of stationary SBs in metals and the spacing of traveling PLC bands in Al-Mg alloys. The present article builds upon the 1987 results of the aforementioned three examples of self-organization in plasticity within a unifying internal length gradient (ILG) framework and expands them in 2 major ways by: (i) introducing the effect of stochasticity and (ii) capturing statistical characteristics when PDEs are absent for the description of experimental observations. The discussion focuses on metallic systems, but the modeling approaches can be used for interpreting experimental observations in a variety of materials. Full article

This study presents the Fourier–Gegenbauer integral Galerkin (FGIG) method, a new numerical framework that uniquely integrates Fourier series and Gegenbauer polynomials to solve the one-dimensional advection–diffusion (AD) equation with spatially symmetric periodic boundary conditions, achieving exponential convergence and reduced computational cost compared to traditional methods. The FGIG method uniquely combines Fourier series for spatial periodicity and Gegenbauer polynomials for temporal integration within a Galerkin framework, resulting in highly accurate numerical and semi-analytical solutions. Unlike traditional approaches, this method eliminates the need for time-stepping procedures by reformulating the problem as a system of integral equations, reducing error accumulation over long-time simulations and improving computational efficiency. Key contributions include exponential convergence rates for smooth solutions, robustness under oscillatory conditions, and an inherently parallelizable structure, enabling scalable computation for large-scale problems. Additionally, the method introduces a barycentric formulation of the shifted Gegenbauer–Gauss (SGG) quadrature to ensure high accuracy and stability for relatively low Péclet numbers. This approach simplifies calculations of integrals, making the method faster and more reliable for diverse problems. Numerical experiments presented validate the method’s superior performance over traditional techniques, such as finite difference, finite element, and spline-based methods, achieving near-machine precision with significantly fewer mesh points. These results demonstrate its potential for extending to higher-dimensional problems and diverse applications in computational mathematics and engineering. The method’s fusion of spectral precision and integral reformulation marks a significant advancement in numerical PDE solvers, offering a scalable, high-fidelity alternative to conventional time-stepping techniques. Full article