Search results for: newton raphson

Authors: Surendra Mund

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At the beginning, the physical entity force was defined mathematically by Sir Isaac Newton in his Principia Mathematica as F ⃗=(dp ⃗)/dt in form of his second law of motion. Newton also defines his Universal law of Gravitational force exist in same outstanding book, but at the end of 20th century and beginning of 21st century, we have tried a lot to specify and unify four or five Fundamental forces or Interaction exist in universe, but we failed every time. Usually, Gravity creates problems in this unification every single time, but in my previous papers and presentations, I defined and derived Field and force equations for Gravitational like Interactions for each and every kind of central systems. This force is named as Variational Force by me, and this force is generated by variation in the scalar field density around the body. In this particular paper, at first, I am specifying which type of Interactions are Fundamental in Universal sense (or in all type of central systems or bodies predicted by my N-time Inflationary Model of Universe) and then unify them in Universal framework (defined and derived by me as Universal Mechanics in a separate paper) as well. This will also be valid in Universal dynamical sense which includes inflations and deflations of universe, central system relativity, Universal relativity, ϕ-ψ transformation and transformation of spin, physical perception principle, Generalized Fundamental Dynamical Law and many other important Generalized Principles of Generalized Quantum Mechanics (GQM) and Central System Theory (CST). So, In this article, at first, I am Generalizing some Fundamental Principles, and then Unifying Variational Forces (General form of Gravitation like Interactions) and Flow Generated Force (General form of EM like Interactions), and then Unify all Fundamental Forces by specifying Weak and Strong Interactions in form of more basic terms - Variational, Flow Generated and Transformational Interactions.

Keywords: Central System Force, Disturbance Force, Flow Generated Forces, Generalized Nuclear Force, Generalized Weak Interactions, Generalized EM-Like Interactions, Imbalance Force, Spin Generated Forces, Transformation Generated Force, Unified Force, Universal Mechanics, Uniform And Non-Uniform Variational Interactions, Variational Interactions

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Authors: Mohamed Belhorma, Aboubakar S. Bouchikhi, Belkacem Bounab

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This paper addresses modeling a Double A-Arm suspension, a three-dimensional nonlinear model has been developed using the multibody systems formalism. Dynamical study of the different components responses was done, particularly for the wheel assembly. To validate those results, the system was constructed and simulated by RecurDyn, a professional multibody dynamics simulation software. The model has been used as the Objectif function in an optimization algorithm for ride quality improvement.

Keywords: double A-Arm suspension, multibody systems, ride quality optimization, dynamic simulation

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Authors: Wang Xingbo

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Computation of determinant in the form |I-X| is primary and fundamental because it can help to compute many other determinants. This article puts forward a time-reducible approach to compute determinant |I-X|. The approach is derived from the Newton’s identity and its time complexity is no more than that to compute the eigenvalues of the square matrix X. Mathematical deductions and numerical example are presented in detail for the approach. By comparison with classical approaches the new approach is proved to be superior to the classical ones and it can naturally reduce the computational time with the improvement of efficiency to compute eigenvalues of the square matrix.

Keywords: algorithm, determinant, computation, eigenvalue, time complexity

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Authors: Sean Kinney

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In 1666, Newton created the Law of Universal Gravitation. And in 1915, Einstein improved it to incorporate factors such as time dilation and gravitational lensing. But currently, there is a problem with this “universal” law. The math doesn’t work outside the confines of our solar system. And something is missing; any evidence of what gravity actually is and how it manifest. This paper explores the notion that gravity must obey the law of conservation of energy as all other forces in this universe have been shown to do. Explaining exactly what gravity is and how it manifests itself. And looking at many different implications that would be created are explained. And finally, using the math of Dynamic Gravity to calculate Dark Energy and Dark Matter effects to explain all observations without the need of exotic measures.

Keywords: gravity, dynamic gravity, dark matter, dark energy

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Authors: Sean Michael Kinney

Abstract:

In 1666, Newton created the Law of Universal Gravitation. And in 1915, Einstein improved it to incorporate factors such as time dilation and gravitational lensing. But currently, there is a problem with this “universal” law. The math doesn’t work outside the confines of our solar system. And something is missing; any evidence of what gravity actually is and how it manifests. This paper explores the notion that gravity must obey the law of conservation of energy as all other forces in this universe have been shown to do. Explaining exactly what gravity is and how it manifests itself. And looking at many different implications that would be created are explained. And finally, use the math of Dynamic gravity to calculate Dark Energy and Dark Matter effects to explain all observations without the need for exotic measures.

Keywords: dynamic gravity, gravity, dark matter, dark energy

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Authors: Parshanth Maroju, Ramandeep Behl, Sandile S. Motsa

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In this study, we proposed a simple and interesting family of fourth-order multi-point methods without memory for obtaining simple roots. This family requires only three functional evaluations (viz. two of functions f(xn), f(yn) and third one of its first-order derivative f'(xn)) per iteration. Moreover, the accuracy and validity of new schemes is tested by a number of numerical examples are also proposed to illustrate their accuracy by comparing them with the new existing optimal fourth-order methods available in the literature. It is found that they are very useful in high precision computations. Further, the dynamic study of these methods also supports the theoretical aspect.

Keywords: basins of attraction, nonlinear equations, simple roots, Newton's method

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Authors: Sonia Sonia

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This paper presents a family of iterative scheme for solving nonlinear systems of equations which have wide application in sciences and engineering. The proposed iterative family is based upon some parameters which generates many different iterative schemes. This family is completely derivative free and uses first of divided difference operator. Moreover some numerical experiments are performed and compared with existing methods. Analysis of convergence shows that the presented family has fourth-order of convergence. The dynamical behaviour of proposed family and local convergence have also been discussed. The numerical performance and convergence region comparison demonstrates that proposed family is efficient.

Keywords: convergence, divided difference operator, nonlinear system, Newton's method

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Authors: Danni Cong, Meiping Wu, Hua Mu, Xiaofeng He, Junxiang Lian, Juliang Cao, Shaokun Cai, Hao Qin

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Gravity field is of great significance in geoscience, national economy and national security, and gravitational gradient measurement has been extensively studied due to its higher accuracy than gravity measurement. Gravity gradient sensor, being one of core devices of the gravity gradient instrument, plays a key role in measuring accuracy. Therefore, this paper starts from analyzing the working principle of the gravity gradient sensor by Newton’s law, and then considers the relative motion between inertial and non-inertial systems to build a relatively adequate mathematical model, laying a foundation for the measurement error calibration, measurement accuracy improvement.

Keywords: gravity gradient, gravity gradient sensor, accelerometer, single-axis rotation modulation

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Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieha

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In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: polynomial constitutive equation, solitary, stress solitary waves, nonlinear constitutive law

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Authors: Nevena Jakovčević Stor, Ivan Slapničar

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Any polynomial can be expressed as a characteristic polynomial of a complex symmetric arrowhead matrix. This expression is not unique. If the polynomial is real with only real distinct roots, the matrix can be chosen as real. By using accurate forward stable algorithm for computing eigen values of real symmetric arrowhead matrices we derive a forward stable algorithm for computation of roots of such polynomials in O(n^2 ) operations. The algorithm computes each root to almost full accuracy. In some cases, the algorithm invokes extended precision routines, but only in the non-iterative part. Our examples include numerically difficult problems, like the well-known Wilkinson’s polynomials. Our algorithm compares favorably to other method for polynomial root-finding, like MPSolve or Newton’s method.

Keywords: roots of polynomials, eigenvalue decomposition, arrowhead matrix, high relative accuracy

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Authors: Satyendra Pratap Singh, S. P. Singh

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This paper presents a methodology using Gravitational Search Algorithm for optimal placement of Phasor Measurement Units (PMUs) in order to achieve complete observability of the power system. The objective of proposed algorithm is to minimize the total number of PMUs at the power system buses, which in turn minimize installation cost of the PMUs. In this algorithm, the searcher agents are collection of masses which interact with each other using Newton’s laws of gravity and motion. This new Gravitational Search Algorithm based method has been applied to the IEEE 14-bus, IEEE 30-bus and IEEE 118-bus test systems. Case studies reveal optimal number of PMUs with better observability by proposed method.

Keywords: gravitational search algorithm (GSA), law of motion, law of gravity, observability, phasor measurement unit

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Authors: Makhlouf Mourad, Medkour Mihoub, Bouchher Omar, Messabih Sidi Mohamed, Benrachedi Khaled

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This work is the modeling and simulation of fluid flow (liquid) through porous media. This type of flow occurs in many situations of interest in applied sciences and engineering, fluid (oil) consists of several individual substances in pure, single-phase flow is incompressible and isothermal. The porous medium is isotropic, homogeneous optionally, with the rectangular format and the flow is two-dimensional. Modeling of hydrodynamic phenomena incorporates Darcy's law and the equation of mass conservation. Correlations are used to model the density and viscosity of the fluid. A finite volume code is used in the discretization of differential equations. The nonlinearity is treated by Newton's method with relaxation coefficient. The results of the simulation of the pressure and the mobility of liquid flowing through porous media are presented, analyzed, and illustrated.

Keywords: Darcy equation, middle porous, continuity equation, Peng Robinson equation, mobility

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Authors: Jing-Gang Xie

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The research, in this case, considers the integration of the Quantum Field Theory and the General Relativity Theory. As two successful models in explaining behaviors of particles, they are incompatible since they work at different masses and scales of energy, with the evidence that regards the description of black holes and universe formation. It is so considering previous efforts in merging the two theories, including the likes of the String Theory, Quantum Gravity models, and others. In a bid to prove an actionable experiment, the paper’s approach starts with the derivations of the existing theories at present. It goes on to test the derivations by applying the same initial assumptions, coupled with several deviations. The resulting equations get similar results to those of classical Newton model, quantum mechanics, and general relativity as long as conditions are normal. However, outcomes are different when conditions are extreme, specifically with no breakdowns even for less than Schwarzschild radius, or at Planck length cases. Even so, it proves the possibilities of integrating the two theories.

Keywords: general relativity theory, particles, photons, Quantum Gravity Model, gravitational frequency shift

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Authors: Eric Asare, Jamie Evans, Mark Newton, Emiliano Bilotti

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Two types of filler shapes (sphere and flakes) and three different sizes are employed to study the size effect on PTC. The composite is prepared using a mini-extruder with high-density polyethylene (HDPE) as the matrix. A computer modelling is used to fit the experimental results. The percolation threshold decreases with decreasing filler size and this was observed for both the spherical particles as well as the flakes. This was caused by the decrease in interparticle distance with decreasing filler size. The 100 µm particles showed a larger PTC intensity compared to the 5 µm particles for the metal coated glass sphere and flake. The small particles have a large surface area and agglomeration and this makes it difficult for the conductive network to e disturbed. Increasing the filler content decreased the PTC intensity and this is due to an increase in the conductive network within the polymer matrix hence more energy is needed to disrupt the network.

Keywords: positive temperature coefficient (PTC) effect, conductive polymer composite (CPC), electrical conductivity

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Authors: Yollande Sènan Djivoh, Dominique de Jaeger

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Background: Abdominal exercises are commonly practised nowadays. Specific techniques of abdominal muscles strengthening like hypopressive exercises have recently emerged and their practice is encouraged against the practice of Curl-up especially in postpartum. The acute and the training effects of these exercises did not allow to advise one exercise to the detriment of another. However, physiotherapists remain reluctant to perform Curl-up with postpartum women because of its potential harmful effect on the pelvic floor. Design: This study was a randomized control trial registered under the number PACTR202110679363984. Objective: to observe the training effect of two experimental protocols (Curl-up versus Drawing-in+Diaphragmatic aspiration) on the abdominal wall (interrecti distance, rectus and transversus abdominis thickness, abdominal strength) in Beninese postpartum women. Pelvic floor function (tone, endurance, urinary incontinence) will be assessed to evaluate potential side effects of exercises on the pelvic floor. Method: Postpartum women diagnosed with diastasis recti were randomly assigned to one of three groups (Curl-up, Drawingin+Diaphragmatic aspiration and control). Abdominal and pelvic floor parameters were assessed before and at the end of the 6-week protocol. The interrecti distance and the abdominal muscles thickness were assessed by ultrasound and abdominal strength by dynamometer. Pelvic floor tone and strength were assessed with Biofeedback and urinary incontinence was quantified by pad test. To compare the results between the three groups and the two measurements, a two-way Anova test with repeated measures was used (p<0.05). When interaction was significant, a posthoc using Student t test, with Bonferroni correction, was used to compare the three groups regarding the difference (end value minus initial value). To complete these results, a paired Student t test was used to compare in each group the initial and end values. Results: Fifty-eight women participated in this study, divided in three groups with similar characteristics regarding their age (29±5 years), parity (2±1 children), BMI (26±4 kg/m2 ), time since the last birth (10±2 weeks), weight of their baby at birth (330±50 grams). Time effect and interaction were significant (p<0.001) for all abdominal parameters. Experimental groups improved more than control group. Curl-up group improved more (p=0.001) than Drawing-in+Diaphragmatic aspiration group regarding the interrecti distance (9.3±4.2 mm versus 6.6±4.6 mm) and abdominal strength (20.4±16.4 Newton versus 11.4±12.8 Newton). Drawingin+Diaphragmatic aspiration group improved (0.8±0.7 mm) more than Curl-up group (0.5±0.7 mm) regarding the transversus abdominis thickness (p=0.001). Only Curl-up group improved (p<0.001) the rectus abdominis thickness (1.5±1.2 mm). For pelvic floor parameters, both experimental groups improved (p=0.01) except for tone which improved (p=0.03) only in Drawing-in+Diaphragmatic aspiration group from 19.9±4.1 cmH2O to 22.2±4.5 cmH2O. Conclusion: Curl-up was more efficient to improve abdominal function than Drawingin+Diaphragmatic aspiration. However, these exercises are complementary. None of them degraded the pelvic floor, but Drawing-in+Diaphragmatic aspiration improved further the pelvic floor function. Clinical implications: Curl-up, Drawing-in and Diaphragmatic aspiration can be used for the management of abdominal function in postpartum women. Exercises must be chosen considering the specific needs of each woman’s abdominal and pelvic floor function.

Keywords: curl-up, drawing-in, diaphragmatic aspiration, hypopressive exercise, postpartum women

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Authors: Hamid Tavakolipour, Mohsen Mokhtarian, Ahmad Kalbasi Ashtari

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In this study, the effect of various drying methods (sun drying, shade drying and industrial drying) on final moisture content, shell splitting degree, shrinkage and color change were studied. Sun drying resulted higher degree of pistachio nuts shell splitting on pistachio nuts relative other drying methods. The ANOVA results showed that the different drying methods did not significantly effects on color change of dried pistachio nut. The results illustrated that pistachio nut dried by industrial drying had the lowest moisture content. After the end of drying process, initially, the experimental drying data were fitted with five famous drying models namely Newton, Page, Silva et al., Peleg and Henderson and Pabis. The results indicated that Peleg and Page models gave better results compared with other models to monitor the moisture ratio’s pistachio nut in industrial drying and open sun (or shade drying) methods, respectively.

Keywords: industrial drying, pistachio, quality properties, traditional drying

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Authors: V. Tabrizi, A. Vali, R. GHasemi, V. Behnamgol

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In this article, a nonlinear model of an under actuated six degrees of freedom (6 DOF) quadrotor UAV is derived on the basis of the Newton-Euler formula. The derivation comprises determining equations of the motion of the quadrotor in three dimensions and approximating the actuation forces through the modeling of aerodynamic coefficients and electric motor dynamics. The robust nonlinear control strategy includes a smooth second order non-singular terminal sliding mode control which is applied to stabilizing this model. The control method is on the basis of super twisting algorithm for removing the chattering and producing smooth control signal. Also, nonsingular terminal sliding mode idea is used for introducing a nonlinear sliding variable that guarantees the finite time convergence in sliding phase. Simulation results show that the proposed algorithm is robust against uncertainty or disturbance and guarantees a fast and precise control signal.

Keywords: quadrotor UAV, nonsingular terminal sliding mode, second order sliding mode t, electronics, control, signal processing

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Authors: Eric Asare, Jamie Evans, Mark Newton, Emiliano Bilotti

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High-density polyethylene (HDPE) filled with silver coated glass flakes (5µm) was investigated and the effect on PTC by addition of a second filler (100µm silver coated glass flake) or matrix (polypropylene elastomer) to the composite were examined. The addition of the secondary filler promoted the electrical properties of the composite. The bigger flakes acted like a bridge between the small flakes and this helped to enhance the electrical properties. The PTC behaviour of the composite was also improved by the addition of the bigger flakes due to the increase in separation distance between particles caused by the bigger flakes. Addition of small amount of polypropylene elastomer enhanced not only PTC effect but also improved substantially the flexibility of the composite as well as reduces the overall filler content. SEM images showed that the fillers were dispersed in the HDPE phase.

Keywords: positive temperature coefficient, conductive polymer composite, electrical conductivity, high density polyethylene

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Authors: Sheela Tiwari, R. Naresh, R. Jha

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The paper presents an investigation into the effect of neural network predictive control of UPFC on the transient stability performance of a multi-machine power system. The proposed controller consists of a neural network model of the test system. This model is used to predict the future control inputs using the damped Gauss-Newton method which employs ‘backtracking’ as the line search method for step selection. The benchmark 2 area, 4 machine system that mimics the behavior of large power systems is taken as the test system for the study and is subjected to three phase short circuit faults at different locations over a wide range of operating conditions. The simulation results clearly establish the robustness of the proposed controller to the fault location, an increase in the critical clearing time for the circuit breakers and an improved damping of the power oscillations as compared to the conventional PI controller.

Keywords: identification, neural networks, predictive control, transient stability, UPFC

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Authors: Jia-Jang Wu

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This paper presents the scaling laws that provide the criteria of geometry and dynamic similitude between the full-size rotor-shaft system and its scale model, and can be used to predict the torsional vibration characteristics of the full-size rotor-shaft system by manipulating the corresponding data of its scale model. The scaling factors, which play fundamental roles in predicting the geometry and dynamic relationships between the full-size rotor-shaft system and its scale model, for torsional free vibration problems between scale and full-size rotor-shaft systems are firstly obtained from the equation of motion of torsional free vibration. Then, the scaling factor of external force (i.e., torque) required for the torsional forced vibration problems is determined based on the Newton’s second law. Numerical results show that the torsional free and forced vibration characteristics of a full-size rotor-shaft system can be accurately predicted from those of its scale models by using the foregoing scaling factors. For this reason, it is believed that the presented approach will be significant for investigating the relevant phenomenon in the scale model tests.

Keywords: torsional vibration, full-size model, scale model, scaling laws

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Authors: Ritu Rani

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In this paper, we apply minimalistically upheld linear semi-orthogonal B-spline wavelets, exceptionally developed for the limited interim to rough the obscure function present in the integral equations. Semi-orthogonal wavelets utilizing B-spline uniquely developed for the limited interim and these wavelets can be spoken to in a shut frame. This gives a minimized help. Semi-orthogonal wavelets frame the premise in the space L²(R). Utilizing this premise, an arbitrary function in L²(R) can be communicated as the wavelet arrangement. For the limited interim, the wavelet arrangement cannot be totally introduced by utilizing this premise. This is on the grounds that backings of some premise are truncated at the left or right end purposes of the interim. Subsequently, an uncommon premise must be brought into the wavelet development on the limited interim. These functions are alluded to as the limit scaling functions and limit wavelet functions. B-spline wavelet method has been connected to fathom linear and nonlinear integral equations and their systems. The above method diminishes the integral equations to systems of algebraic equations and afterward these systems can be illuminated by any standard numerical methods. Here, we have connected Newton's method with suitable starting speculation for solving these systems.

Keywords: semi-orthogonal, wavelet arrangement, integral equations, wavelet development

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Authors: Darsh N. Patel, Eric Olson

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Fractals can be found everywhere, whether it be the shape of a leaf or a system of blood vessels. Fractals are used to help study and understand different physical and mathematical processes; however, their artistic nature is also beautiful to simply explore. This project explores fractals generated by a cubically convergent extension to Newton's method. With this iteration as a starting point, a complex plane spanning from -2 to 2 is created with a color wheel mapped onto it. Next, the polynomial whose roots the fractal will generate from is established. From the Fundamental Theorem of Algebra, it is known that any polynomial has as many roots (counted by multiplicity) as its degree. When generating the fractals, each root will receive its own color. The complex plane can then be colored to indicate the basins of attraction that converge to each root. From a computational point of view, this project’s code identifies which points converge to which roots and then obtains fractal images. A zoom path into the fractal was implemented to easily visualize the self-similar structure. This path was obtained by selecting keyframes at different magnifications through which a path is then interpolated. Using parallel processing, many images were generated and condensed into a video. This project illustrates how practical techniques used for scientific visualization can also have an artistic side.

Keywords: fractals, cubic method, Julia programming language, basin of attraction

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Authors: Seyedmajid Mehrnia, Maximilan Kuhr, Peter F. Pelz

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Molecular Dynamics (MD) simulation is a proven method to inspect behaviours of lubricant oils in nano-scale gaps. However, most MD simulations on tribology have been performed with atomically smooth walls to determine wall slip and friction properties. This study will investigate the effect of porosity, specifically nano-porous walls, on wall slip properties of hydrocarbon oils confined between two walls in a Couette flow. Different pore geometries will be modelled to investigate the effect on wall slip and bulk shear. In this paper, the Polyalphaolefin (PAO) molecules are confined to a stationary and a moving wall. A hybrid force field consisting of different potential energy functions was employed in this MD simulation. Newton’s law defines how those forces will influence the atoms' movements. The interactions among surface atoms were simulated with an Embedded Atom Method (EAM) potential function which can represent the characteristics of metallic arrangements very strongly. We implemented NERD forcefield for intramolecular potential energy function. Also, Lennard-Jones potential was employed for nonbonded intermolecular interaction.

Keywords: slip length, molecular dynamics, critical shear rate, Couette flow

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Authors: Newton Rathnasiri Ranaweera Kalu Arachchige

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Academics argue that Greek myths and legends have had an influence on Buddhist stories: Jataka tales, Theri Gata (Psalms of older Buddhist nuns), and even Mahavansa (a Sri Lankan historical chronicle). However, this article asserts that there is evidence in Sophocles King Oedipus to argue that the Buddha’s life story and key Buddhist concepts have influenced pre-Christian Greek philosophy and literature, especially Sophocles’ King Oedipus. When reading the text with the notion that there could be intertextual relationships or new texts are built on the existing texts and discourses, the reader may see that Sophocles’ play contains incidents that remind them of the special occasions of the Buddha’s life, his utterances and the key Buddhist concepts such as the truth of suffering, cessation of suffering, the three poisons (greed, hatred, and delusion), and finding the truth within one’s own self. The present intertextual study explored only the special occasions of the Buddha’s life to make it more focused and found that Sophocles alludes to the Buddha’s life story in his attempt to raise a moral culprit to a moral hero with higher moral values. This article, however, acknowledges that one needs to cross-check the other historical and philosophical references when claiming that Sophocles has had influence from the Buddha’s life story in King Oedipus.

Keywords: Buddhism, the Buddha’s life story, King Oedipus, Greece, tragedy, Sri Lanka

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Authors: Fatemeh Behbahani, Rubiyah Yusof

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To avoid collision between following vehicles and vehicles in front, it is vital to keep appropriate, safe spacing between both vehicles over all speeds. Therefore, the following vehicle needs to have exact information regarding the speed and spacing between vehicles. This project is conducted to simulate the tuning of controller gain for a vehicle-following system through the selected control strategy, spacing control policy and fixed-time headway policy. In addition, the paper simulates and designs an adaptive gain controller for a road-vehicle-following system which uses information on the spacing, velocity and also acceleration of a preceding vehicle in the proposed one-vehicle look-ahead strategy. The mathematical model is implemented using Kirchhoff and Newton’s Laws, and stability simulated. The trial-error method was used to obtain a suitable value of controller gain. However, the adaptive-based controller system was able to optimize the gain value automatically. Model Reference Adaptive Control (MRAC) is designed and utilized and based on firstly the Gradient and secondly the Lyapunov approach. The Lyapunov approach considers stability. The Gradient approach was found to improve the best value of gain in the controller system with fixed-time headway.

Keywords: one-vehicle look-ahead, model reference adaptive, stability, tuning gain controller, MRAC

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Authors: Oswaldo Otero, Eduardo A. Orozco, Ana M. Herrera

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In this work, we present results from analytical and numerical studies of the electron acceleration by a TE₀₁₁ cylindrical microwave mode in a static homogeneous magnetic field under electron cyclotron resonance (ECR) condition. The stability of the orbits is analyzed using the particle orbit theory. In order to get a better understanding of the interaction wave-particle, we decompose the azimuthally electric field component as the superposition of right and left-hand circular polarization standing waves. The trajectory, energy and phase-shift of the electron are found through a numerical solution of the relativistic Newton-Lorentz equation in a finite difference method by the Boris method. It is shown that an electron longitudinally injected with an energy of 7 keV in a radial position r=Rc/2, being Rc the cavity radius, is accelerated up to energy of 90 keV by an electric field strength of 14 kV/cm and frequency of 2.45 GHz. This energy can be used to produce X-ray for medical imaging. These results can be used as a starting point for study the acceleration of electrons in a magnetic field changing slowly in time (GYRAC), which has some important applications as the electron cyclotron resonance ion proton accelerator (ECR-IPAC) for cancer therapy and to control plasma bunches with relativistic electrons.

Keywords: Boris method, electron cyclotron resonance, finite difference method, particle orbit theory, X-ray

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Authors: Amanda Rithieli Pereira Dos Santos, Rute Quelvia De Faria, Álvaro De Oliveira Cardoso, Anderson Rodrigo Da Silva, Érica Leão Fernandes Araújo

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The study of the kinetics of drying has great importance for the mathematical modeling, allowing to know about the processes of transference of heat and mass between the products and to adjust dryers managing new technologies for these processes. The present work had the objective of studying the kinetics of drying of soybean seeds and adjusting different statistical models to the experimental data varying cultivar and temperature. Soybean seeds were pre-dried in a natural environment in order to reduce and homogenize the water content to the level of 14% (b.s.). Then, drying was carried out in a forced air circulation oven at controlled temperatures of 38, 43, 48, 53 and 58 ± 1 ° C, using two soybean cultivars, BRS 8780 and Sambaíba, until reaching a hygroscopic equilibrium. The experimental design was completely randomized in factorial 5 x 2 (temperature x cultivar) with 3 replicates. To the experimental data were adjusted eleven statistical models used to explain the drying process of agricultural products. Regression analysis was performed using the least squares Gauss-Newton algorithm to estimate the parameters. The degree of adjustment was evaluated from the analysis of the coefficient of determination (R²), the adjusted coefficient of determination (R² Aj.) And the standard error (S.E). The models that best represent the drying kinetics of soybean seeds are those of Midilli and Logarítmico.

Keywords: curve of drying seeds, Glycine max L., moisture ratio, statistical models

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Authors: Prashant Pandey

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In the present article, an effective Laguerre collocation method is used to obtain the approximate solution of a system of coupled fractional-order non-linear reaction-advection-diffusion equation with prescribed initial and boundary conditions. In the proposed scheme, Laguerre polynomials are used together with an operational matrix and collocation method to obtain approximate solutions of the coupled system, so that our proposed model is converted into a system of algebraic equations which can be solved employing the Newton method. The solution profiles of the coupled system are presented graphically for different particular cases. The salient feature of the present article is finding the stability analysis of the proposed method and also the demonstration of the lower variation of solute concentrations with respect to the column length in the fractional-order system compared to the integer-order system. To show the higher efficiency, reliability, and accuracy of the proposed scheme, a comparison between the numerical results of Burger’s coupled system and its existing analytical result is reported. There are high compatibility and consistency between the approximate solution and its exact solution to a higher order of accuracy. The exhibition of error analysis for each case through tables and graphs confirms the super-linearly convergence rate of the proposed method.

Keywords: fractional coupled PDE, stability and convergence analysis, diffusion equation, Laguerre polynomials, spectral method

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Authors: Surbhi Kaura, Sachin Kandhari, Shahiduz Zafar

Abstract:

Chronic stroke, characterized by persistent motor deficits, often necessitates comprehensive rehabilitation interventions to improve functional outcomes and mitigate long-term dependency. Luna neurorobotic devices, integrated with EMG feedback systems, provide an innovative platform for facilitating neuroplasticity and functional improvement in stroke survivors. This retrospective study aims to investigate the impact of EMG-based Luna neurorobotic interventions on the strengthening of the affected side in chronic stroke patients. In rehabilitation, active patient participation significantly activates the sensorimotor network during motor control, unlike passive movement. Stroke is a debilitating condition that, when not effectively treated, can result in significant deficits and lifelong dependency. Common issues like neglecting the use of limbs can lead to weakness in chronic stroke cases. In rehabilitation, active patient participation significantly activates the sensorimotor network during motor control, unlike passive movement. This study aims to assess how electromyographic triggering (EMG-triggered) robotic treatments affect walking, ankle muscle force after an ischemic stroke, and the coactivation of agonist and antagonist muscles, which contributes to neuroplasticity with the assistance of biofeedback using robotics. Methods: The study utilized robotic techniques based on electromyography (EMG) for daily rehabilitation in long-term stroke patients, offering feedback and monitoring progress. Each patient received one session per day for two weeks, with the intervention group undergoing 45 minutes of robot-assisted training and exercise at the hospital, while the control group performed exercises at home. Eight participants with impaired motor function and gait after stroke were involved in the study. EMG-based biofeedback exercises were administered through the LUNA neuro-robotic machine, progressing from trigger and release mode to trigger and hold, and later transitioning to dynamic mode. Assessments were conducted at baseline and after two weeks, including the Timed Up and Go (TUG) test, a 10-meter walk test (10m), Berg Balance Scale (BBG), and gait parameters like cadence, step length, upper limb strength measured by EMG threshold in microvolts, and force in Newton meters. Results: The study utilized a scale to assess motor strength and balance, illustrating the benefits of EMG-biofeedback following LUNA robotic therapy. In the analysis of the left hemiparetic group, an increase in strength post-rehabilitation was observed. The pre-TUG mean value was 72.4, which decreased to 42.4 ± 0.03880133 seconds post-rehabilitation, with a significant difference indicated by a p-value below 0.05, reflecting a reduced task completion time. Similarly, in the force-based task, the pre-knee dynamic force in Newton meters was 18.2NM, which increased to 31.26NM during knee extension post-rehabilitation. The post-student t-test showed a p-value of 0.026, signifying a significant difference. This indicated an increase in the strength of knee extensor muscles after LUNA robotic rehabilitation. Lastly, at baseline, the EMG value for ankle dorsiflexion was 5.11 (µV), which increased to 43.4 ± 0.06 µV post-rehabilitation, signifying an increase in the threshold and the patient's ability to generate more motor units during left ankle dorsiflexion. Conclusion: This study aimed to evaluate the impact of EMG and dynamic force-based rehabilitation devices on walking and strength of the affected side in chronic stroke patients without nominal data comparisons among stroke patients. Additionally, it provides insights into the inclusion of EMG-triggered neurorehabilitation robots in the daily rehabilitation of patients.

Keywords: neurorehabilitation, robotic therapy, stroke, strength, paralysis

Procedia PDF Downloads 35

Authors: Hilal Uslu, Salih Eroglu, Betul Ozkan, Ozcan Bulantekin, Alper Kuscu

Abstract:

In this study, the strawberry (Fragaria L.) fruits, which were pretreated with ultrasound (US), were worked on in the microwave by using 90W power. Then mathematical modelling was applied to dried fruits by using different experimental thin layer models. The sliced fruits were subjected to ultrasound treatment at a frequency of 40 kHz for 10, 20, and 30 minutes, in an ultrasonic water bath, with a ratio of 1:4 to fruit/water. They are then dried in the microwave (90W). The drying process continued until the product moisture was below 10%. By analyzing the moisture change of the products at a certain time, eight different thin-layer drying models, (Newton, page, modified page, Midilli, Henderson and Pabis, logarithmic, two-term, Wang and Singh) were tested for verification of experimental data. MATLAB R2015a statistical program was used for the modelling, and the best suitable model was determined with R²adj (coefficient of determination of compatibility), and root mean square error (RMSE) values. According to analysis, the drying model that best describes the drying behavior for both drying conditions was determined as the Midilli model by high R²adj and low RMSE values. Control, 10, 20, and 30 min US for groups R²adj and RMSE values was established as respectively; 0,9997- 0,005298; 0,9998- 0,004735; 0,9995- 0,007031; 0,9917-0,02773. In addition, effective diffusion coefficients were calculated for each group and were determined as 3,80x 10⁻⁸, 3,71 x 10⁻⁸, 3,26 x10⁻⁸ ve 3,5 x 10⁻⁸ m/s, respectively.

Keywords: mathematical modelling, microwave drying, strawberry, ultrasound

Procedia PDF Downloads 126