The approximate solution of charged particle motion equations in oscillating magnetic fields using the local multiquadrics collocation method

The charged particle motion for certain configurations of oscillating magnetic fields can be simulated by a Volterra integro-differential equation of the second order with time-periodic coefficients. This paper investigates a simple and accurate scheme for computationally solving these types of integro-differential equations. To start the method, we first reduce the integro-differential equations to equivalent Volterra integral equations of the second kind. Subsequently, the solution of the mentioned Volterra integral equations is estimated by the collocation method based on the local multiquadrics formulated on scattered points. We also expand the proposed method to solve fractional integro-differential equations including non-integer order derivatives. Since the offered method does not need any mesh generations on the solution domain, it can be recognized as a meshless method. To demonstrate the reliability and efficiency of the new technique, several illustrative examples are given. Moreover, the numerical results confirm that the method developed in the current paper in comparison with the method based on the globally supported multiquadrics has much lesser volume computing.

     

On the numerical solution of Fredholm integral equations utilizing the local radial basis function method

The current investigation describes a computational technique to solve one- and two-dimensional Fredholm integral equations of the second kind. The method estimates the solution using the discrete collocation method by combining locally supported radial basis functions (RBFs) constructed on a small set of nodes instead of all points over the analysed domain. In this work, we employ the Gauss–Legendre integration rule on the influence domains of shape functions to approximate the local integrals appearing in the method. In comparison with the globally supported RBFs for solving integral equations, the proposed method is stable and uses much less computer memory. The scheme does not require any cell structures, so it is meshless. We also obtain the error analysis of the proposed method and demonstrate that the convergence rate of the approach is high. Illustrative examples clearly show the reliability and efficiency of the new method.     

Manual Therapy Facilitates Homeostatic Adaptation to Bone Microstructural Declines Induced by a Rat Model of Repetitive Forceful Task

The effectiveness of manual therapy in reducing the catabolic effects of performing repetitive intensive force tasks on bones has not been reported. We examined if manual therapy could reduce radial bone microstructural declines in adult female Sprague–Dawley rats performing a 12-week high-repetition and high-force task, with or without simultaneous manual therapy to forelimbs. Additional rats were provided 6 weeks of rest after task cessation, with or without manual therapy. The control rats were untreated or received manual therapy for 12 weeks. The untreated TASK rats showed increased catabolic indices in the radius (decreased trabecular bone volume and numbers, increased osteoclasts in these trabeculae, and mid-diaphyseal cortical bone thinning) and increased serum CTX-1, TNF-α, and muscle macrophages. In contrast, the TASK rats receiving manual therapy showed increased radial bone anabolism (increased trabecular bone volume and osteoblast numbers, decreased osteoclast numbers, and increased mid-diaphyseal total area and periosteal perimeter) and increased serum TNF-α and muscle macrophages. Rest, with or without manual therapy, improved the trabecular thickness and mid-diaphyseal cortical bone attributes but not the mineral density. Thus, preventive manual therapy reduced the net radial bone catabolism by increasing osteogenesis, while rest, with or without manual therapy, was less effective.     

On the numerical solution of two-dimensional integral equations using a meshless local discrete Galerkin scheme with error analysis

Engineering with Computers - This investigation presents a simple and effective method for numerically solving two-dimensional Fredholm integral equations of the second kind on non-rectangular...     

The numerical solution of fractional differential equations using the Volterra integral equation method based on thin plate splines

Finding the approximate solution of differential equations, including non-integer order derivatives, is one of the most important problems in numerical fractional calculus. The main idea of the current paper is to obtain a numerical scheme for solving fractional differential equations of the second order. To handle the method, we first convert these types of differential equations to linear fractional Volterra integral equations of the second kind. Afterward, the solutions of the mentioned Volterra integral equations are estimated using the discrete collocation method together with thin plate splines as a type of free-shape parameter radial basis functions. Since the scheme does not need any background meshes, it can be recognized as a meshless method. The proposed approach has a simple and computationally attractive algorithm. Error analysis is also studied for the presented method. Finally, the reliability and efficiency of the new technique are tested over several fractional differential equations and obtained results confirm the theoretical error estimates.

     

Analysis of rock quality designation (RQD) and Lugeon values in a karstic formation using the sequential indicator simulation approach,Karun IV Dam site,Iran

Bulletin of Engineering Geology and the Environment - The hydraulic properties of hard rock and karst formations are typically highly heterogeneous. Quantification of the groundwater flow in these...     

Linear stability of natural convection in a multilayer system of fluid and porous layers with internal heat sources

The onset of thermal natural convection in a horizontal multilayer system consisting of a homogeneous porous layer sandwiched between two fluid layers has been simulated by an accurate numerical method. The porous and fluid layers include uniform heat sources. Flow in the porous medium has been governed by Darcy–Brinkman’s law. On the other hand, the Navier–Stokes equations with the Boussinesq approximation have ruled over the clear fluid layers. The lower and upper rigid surfaces are assumed to be fixed at the equal temperatures T _L and T _U. The eigenvalues and eigenfunctions of the linear stability analysis have been solved by utilizing the compound matrix method (CMM). The CMM reaches accurate results in a very efficient manner. Moreover, the method removes the stiffness from the equations of the stability system. The results indicate that the onset of convection and the nature of convection cells depend on the relative depths of layers. It has been observed that the thickness of the lower fluid layer increases the critical Rayleigh number of the upper fluid layer and stabilizes it.     

Experimental study of convective heat transfer coefficient for pulsed fluidized bed using microcapsule phase change material

The convective heat transfer coefficient in a pulsating cylindrical fluidized bed using microcapsule particle-phase change material (MPCM) was examined experimentally. A solenoid on and off valve was used to provide the pulsation and was varied from 1 to 10 Hz. The test section in the bed was loaded with granular microparticle-phase change material (MPCM) with an average diameter of 200 µm. The pulsation effect on the thermal field, thermal storage, and heat transfer coefficient was investigated for 1.5, 2, and 2.5 of minimum fluidization velocity. Results indicated that the amplitude of the oscillation decreases with increasing in pulsation frequency. An increase in heat transfer rate was shown to be related to the superficial velocity. The maximum performance was obtained for the frequency of 7 Hz at the velocity ratio of 2.5. The convective heat transfer increased by 17% for frequency pulsation of 7 Hz. Furthermore, the Duty cycle (η) is defined as the ratio of turn-on duration to the total turn-on and off duration for entering airflow to the solenoid valve. It was shown that the η > 0.4 led to better mixing and higher heat transfer. However, the pulsation effect was shown to disappear for the duty cycle of higher than 0.8. Comparison with the available experimental data of others for continuous flow was in good agreement.     

Effect of the Electrodeposition Frequency,Wave Form,and Thermal Annealing on Magnetic Properties of [Co0.975Cr0.025]0.99Cu0.01 Nanowire Arrays

Highly ordered [Co _0.975Cr _0.025]_0.99Cu _0.01 nanowire arrays were electrodeposited by conducting alternating current (AC) conditions from sulfate-based electrolyte into nanopores of anodic aluminum oxide (AAO) template with 37 nm pore diameter and the interpore distances of almost 50 nm. Fabricated nanowire arrays were characterized using scanning electron microscopy, alternating gradient force magnetometer, and X-ray diffraction. The results illustrated that varying frequency, wave form, and annealing procedure had influence on magnetic properties of as deposited nanowires. The nanowire arrays electrodeposited at different electrodeposition frequencies show remarkably different magnetic behaviors. Due to increasing of the electrodeposition frequency, the rate of ions for reduction was decreased. The nanowires prepared at various wave form illustrated insignificant impact on magnetic properties. X-ray diffraction patterns display that both as-deposited and annealed nanowire arrays expose the same structure. The raised value of coercivity has been determined in annealed nanowire arrays. Magnetization measurements show that the maximum value of coercivity for [Co _0.975]_0.99Cu _0.01 nanowires is observed at high temperature.