Search Results (1,856)

Properties of recycled aggregate concrete (RAC) are influenced by the composition and particle size distribution of recycled coarse aggregate (RCA). The study herein designed seven distinct groups of RACs with varying aggregate fractal dimensions (D) and one group of natural concrete (NAC). The impact of D on the workability, compressive strength, resistance to chloride ion penetration, and carbonation resistance of RAC was measured. It was found that an increase in the D value led to a decrease in the slump and slump flow, with the compressive strength and chloride ion penetration increasing and then decreasing, and carbonation gradually declined. The optimal fractal dimension was thereby determined to be 2.547 by a strength model accommodating two parameters of D and the curing age. Additionally, the mass percentage of each particle size for the corresponding gradation was presented. The compressive strength and chloride permeation resistance of RAC (D = 1.0) relative to RAC (D = 2.5) was increased by 16.7% and 13.3%, respectively. Furthermore, the carbonation depth of RAC (D = 2.5) was comparable to that of NAC. Additionally, the carbonation resistance of RAC was influenced by both the size distribution and the degree of natural carbonation of RCA, resulting in four distinct features relative to NAC. It is thereby feasible to enhance RAC performance through the manipulation of RCA’s fractal dimensions. Full article

Lagrangian dispersion of fluid particle pairs refers to the study of how individual fluid particles disperse and move in a fluid flow, providing insights to understand transport phenomena in various environments, from laminar to turbulent conditions. Here, we explore this phenomenon in synthetic velocity and magnetic fields generated through a reduced-order model of the magnetohydrodynamic equations, which is able to mimic both a laminar and a turbulent environment. In the case of laminar conditions, we find that the average square distance between particle pairs increases linearly with time, implying a dispersion pattern similar to Brownian motion at all time steps. On the other hand, under turbulent conditions, surprisingly enough we observe a Richardson scaling, indicating a super-ballistic dispersion pattern, which aligns with the expected scaling properties for a turbulent environment. Additionally, our study reveals that the magnetic field plays an organizing role. Lastly, we explore a purely hydrodynamic case without magnetic field effects, showing that, even in a turbulent environment, the behavior remains Brownian-like, highlighting the crucial role of the magnetic field in generating the Richardson scaling observed in our model. Full article

This research shows an image processing method to determine the liver tissue’s mechanical behavior under physiological damage caused by fibrosis pathology. The proposed method consists of using a liver tissue CAD/CAE model obtained from a tomography of the human abdomen, where the diaphragmatic surface of this tissue is compressed by a moving flat surface. For this work, two tools were created—the first to analyze the deformations and the second to analyze the displacements of the liver tissue. Gibbon and MATLAB^® were used for numerical analysis with the FEBio computer program. Although deformation in the scenario can be treated as an orthogonal coordinate system, the relationship between the total change in height (measured) and the deformation was obtained. The outcomes show liver tissue behavior as a hyperelastic model; the Mooney–Rivlin mathematical characterization model was proposed in this case. Another method to determine the level of physiological damage caused by fibrosis is fractal analysis. This work used the Hausdorff fractal dimension (HFD) method to calculate and analyze the 2D topological surface. Full article

In this work, we study the possibility of using a new non-homogeneous stochastic diffusion process based on the Rayleigh density function to model the evolution of the active cases of COVID-19 in Morocco. First, the main probabilistic characteristics and analytic expression of the proposed process are obtained. Next, the parameters of the model are estimated by the maximum likelihood methodology. This estimation and the subsequent statistical inference are based on the discrete observation of the variable $x\left(t\right)$ “number of active cases of COVID-19 in Morocco” by using the data for the period of 28 January to 4 March 2022. Then, we analyze the mean functions by using simulated data for fit and forecast purposes. Finally, we explore the illustration of using this new process to fit and forecast the active cases of COVID-19 data. Full article

Self-similarities at different time scales embedded within a self-organizing neural manifold are well recognized. In this study, we hypothesize that the Hurst fractal dimension (HFD) of the scalp electroencephalographic (EEG) signal reveals statistical differences between chronic pain and opioid use. We test this hypothesis by using EEG resting state signals acquired from a total of 23 human subjects: 14 with chronic pain, 9 with chronic pain taking opioid medications, 5 with chronic pain and not taking opioid medications, and 9 healthy controls. Using the multifractal analysis algorithm, the HFD for full spectrum EEG and EEG frequency band time series was computed for all groups. Our results indicate the HFD varies spatially and temporally across all groups and is of lower magnitude in patients not taking opioids as compared to those taking opioids and healthy controls. A global decrease in HFD was observed with changes in gamma and beta power in the chronic pain group compared to controls and when paired to subject handedness and sex. Our results show the loss of complexity representative of brain wide dysfunction and reduced neural processing can be used as an EEG biomarker for chronic pain and subsequent opioid use. Full article

The frequency–magnitude statistics of 6527 earthquakes with 1.0 ≤ ml ≤ 5.7 and focal depths between 0 and 49 km in the Red Sea region between 1980 and 2021 show that the threshold magnitude, above which most of the Red Sea earthquakes are precisely located, is 1.5. The b-value, which identifies regional stress situations and associated energy release modalities, has a value of 0.75, less than in historical data, and averages between 0.4 and 0.85 as it varies over time, indicating modest stress accumulation. We utilised these instrumental data to examine dynamic stress patterns in the Red Sea region, shedding light on the region’s geodynamics and providing a foundation for estimating the region’s seismic hazard. The computed fractal dimension ($Dc$) has a relatively high value of 2.3, which is significant for the Red Sea’s geological complexity and structural diversity. This result indicates the regular distribution of Red Sea earthquakes, which occur in clusters or along fault lines. The low b-value and comparatively high $Dc$ were most likely due to major earthquakes in the past and the greater stress they caused. The focal mechanisms of the big earthquakes, predominantly normal solutions, are consistent with the movement and extensional regime. The pressure and tension (P-T) axes show a compression axis trending NW-SE and a tension axis trending NE-SW. According to the stress inversion results, the maximum principal stress (σ1) is oriented vertically, the minimum stress axis (σ3) is subhorizontal and strikes in the NE-SW direction, and the intermediate principal stress (σ2) is trending in the NE-SW direction. The variance in the region that characterises the homogeneity of stress directions within the range is 0.19. The stress ratio (R), which identifies the faulting type, is 0.76, suggesting a normal faulting pattern for the region. The hazard parameters are expressed by the probability of exceedance for 1-, 10-, 50-, and 100-year return periods. The highest probability that an earthquake will occur within a 50-year period is thought to be around 6.0. The largest observed catalogue and instrumental magnitudes in the area, 5.7 and 6.7, respectively, show average recurrence intervals of 36 and 142 years. Full article

We consider the numerical solution of a one-dimensional time-fractional diffusion problem, where the order of the Caputo time derivative belongs to (0, 1). Using the technique of the method of lines, we first develop from the original problem a system of fractional ordinary differential equations. Using an integral equation reformulation of this system, we study the regularity properties of the exact solution of the system of fractional differential equations and construct a piecewise polynomial collocation method to solve it numerically. We also investigate the convergence and the convergence order of the proposed method. To conclude, we present the results of some numerical experiments. Full article

In this work, the existence and uniqueness solution of the fractional nonlinear mixed integro-differential equation (FrNMIoDE) is guaranteed with a general discontinuous kernel based on position and time-space $L_2\left[\mathsf{\Omega }\right]\times C\left[0,T\right], T<1$. The FrNMIoDE conformed to the Volterra-Hammerstein integral equation (V-HIE) of the second kind, after applying the characteristics of a fractional integral, with a general discontinuous kernel in position for the Hammerstein integral term and a continuous kernel in time to the Volterra integral (VI) term. Then, using a separation technique methodology, we developed HIE, whose physical coefficients were time-variable. By examining the system’s convergence, the product Nystrom technique (PNT) and associated schemes were employed to create a nonlinear algebraic system (NAS). Full article

In this paper, global dynamics of fractional-order discrete maps is analyzed by an extended generalized cell mapping (EGCM) method. Considering the lack of valid global analysis methods, the EGCM method is used to explore the global dynamics for fractional-order discrete maps. Firstly, considering the slowly convergence speed of solution of fractional-order discrete maps, the one-step mapping time of the EGCM method should be sufficient long to guarantee the precision of the results. Secondly, global dynamics of three typical fractional-order discrete maps is analyzed by the EGCM method. The stable and the unstable invariant sets can be obtained by the method. The results confirm their previous results, and furthermore obtain the global dynamics in the interesting region which includes attractors, saddles, basin boundaries and domains of attraction. These indicate that the EGCM method is also valid and efficient for fractional-order discrete maps. Full article

In this paper, we solve the space fractional nonlinear Schrödinger equation (SFNSE) by developing an explicit–implicit spectral element scheme, which is formulated based on the Legendre spectral element approximation in space and the Crank–Nicolson leap frog (CNLF) difference discretization in time. Both mass and energy conservative properties are discussed for the spectral element scheme. Numerical stability and convergence of the scheme are proved. Numerical experiments are performed to confirm the high accuracy and efficiency of the proposed numerical scheme. Full article

In this paper, we suggest the modified Extended Direct Algebraic Method (mEDAM) to examine the existence and dynamics of solitary wave solutions in the context of the fractional coupled Higgs system, with Caputo’s fractional derivatives. The method begins with the formulation of nonlinear differential equations using a fractional complex transformation, followed by the derivation of solitary wave solutions. Two-dimensional, Three-dimensional and contour graphs are used to investigate the behavior of traveling wave solutions. The research reveals many families of solitary wave solutions as well as their deep interrelationships and dynamics. These discoveries add to a better understanding of the dynamics of the fractionally coupled Higgs system and have potential applications in areas that use nonlinear Fractional Partial Differential Equations (FPDEs). Full article

In this study, we present an innovative approach involving a spectral collocation algorithm to effectively obtain numerical solutions of the nonlinear time-fractional generalized Kawahara equation (NTFGKE). We introduce a new set of orthogonal polynomials (OPs) referred to as “Eighth-kind Chebyshev polynomials (CPs)”. These polynomials are special kinds of generalized Gegenbauer polynomials. To achieve the proposed numerical approximations, we first derive some new theoretical results for eighth-kind CPs, and after that, we employ the spectral collocation technique and incorporate the shifted eighth-kind CPs as fundamental functions. This method facilitates the transformation of the equation and its inherent conditions into a set of nonlinear algebraic equations. By harnessing Newton’s method, we obtain the necessary semi-analytical solutions. Rigorous analysis is dedicated to evaluating convergence and errors. The effectiveness and reliability of our approach are validated through a series of numerical experiments accompanied by comparative assessments. By undertaking these steps, we seek to communicate our findings comprehensively while ensuring the method’s applicability and precision are demonstrated. Full article

In this paper, we introduce the matrix Mittag–Leffler function, which is a generalization of the multivariate Mittag–Leffler function, in order to investigate the uniqueness of the solutions to a fractional nonlinear partial integro-differential equation in ${\mathbb{R}}^n$ with a boundary condition based on Banach’s contractive principle and Babenko’s approach. In addition, we present an example demonstrating applications of the key results derived using a Python code that computes the approximate value of our matrix Mittag–Leffler function. Full article

In this paper, the fuzzy Volterra integral equations’ solutions are calculated using a hybrid methodology. The combination of the Elzaki transform and Adomian decomposition method results in the development of a novel regime. The precise fuzzy solutions are determined using Elzaki ADM after the fuzzy linear Volterra integral equations are first translated into two crisp integral equations utilizing the fuzzy number in parametric form. Three instances of the considered equations are solved to show the established scheme’s dependability, efficacy, and application. The results have a substantial impact on the fuzzy analytical dynamic equation theory. The comparison of the data in a graphical and tabular format demonstrates the robustness of the defined regime. The lower and upper bound solutions’ theoretical convergence and error estimates are highlighted in this paper. A tolerable order of absolute error is also obtained for this inquiry, and the consistency of the outcomes that are approximated and accurate is examined. The regime generated effective and reliable results. The current regime effectively lowers the computational cost, and a faster convergence of the series solution to the exact answer is signaled. Full article

Invoking the matrix transfer technique, we propose a novel numerical scheme to solve the time-fractional advection–dispersion equation (ADE) with distributed-order Riesz-space fractional derivatives (FDs). The method adopts the midpoint rule to reformulate the distributed-order Riesz-space FDs by means of a second-order linear combination of Riesz-space FDs. Then, a central difference approximation is used side by side with the matrix transform technique for approximating the Riesz-space FDs. Based on this, the distributed-order time-fractional ADE is transformed into a time-fractional ordinary differential equation in the Caputo sense, which has an equivalent Volterra integral form. The Simpson method is used to discretize the weakly singular kernel of the resulting Volterra integral equation. Stability, convergence, and error analysis are presented. Finally, simulations are performed to substantiate the theoretical findings. Full article