Search results for: inverse/backward equation

Authors: Solaine Hachem, Frédéric Bourquin, Dominique Siegert

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The brutal collapse of bridges is mainly due to scour. Indeed, the soil erosion in the riverbed around a pier modifies the embedding conditions of the structure, reduces its overall stiffness and threatens its stability. Hence, finding an efficient technique that allows early scour detection becomes mandatory. Vibration analysis is an indirect method for scour detection that relies on real-time monitoring of the bridge. It tends to indicate the presence of a scour based on its consequences on the stability of the structure and its dynamic response. Most of the research in this field has focused on the dynamic behavior of a single pile and has examined the depth of the scour. In this paper, a bridge is fully modeled with all piles and spans and the scour is represented by a reduction in the foundation's stiffnesses. This work aims to identify the vibration modes sensitive to the rigidity’s loss in the foundations so that their variations can be considered as a scour indicator: the decrease in soil-structure interaction rigidity leads to a decrease in the natural frequencies’ values. By using the first-order perturbation method, the expression of sensitivity, which depends only on the selected vibration modes, is established to determine the deficiency of foundations stiffnesses. The solutions are obtained by using the singular value decomposition method for the regularization of the inverse problem. The propagation of uncertainties is also calculated to verify the efficiency of the inverse problem method. Numerical simulations describing different scenarios of scour are investigated on a simplified model of a real composite steel-concrete bridge located in France. The results of the modal analysis show that the modes corresponding to in-plane and out-of-plane piers vibrations are sensitive to the loss of foundation stiffness. While the deck bending modes are not affected by this damage.

Keywords: bridge’s piers, inverse problems, modal sensitivity, scour detection, vibration analysis

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Authors: Abolfazl Zaraki, Yoshikatsu Hayashi, Harry Thorpe, Vincent Strong, Gisle-Andre Larsen, William Holderbaum

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Thanks to the high maneuverability of the cable-driven hyper-redundant manipulators (HRMs), this class of robots has shown a superior capability in highly confined and unstructured space applications. Although the large number of degrees of freedom (DOF) of HRMs enhances the motion flexibility and the robot’s reachability range, it highly increases the complexity of the kinematic configuration which makes the kinematic control problem very challenging or even impossible to solve. This paper presents our current progress achieved on the development of a kinematic-based leader-follower control system which is designed to control not only the robot’s body posture but also to control the trajectory of the robot’s movement in a semi-autonomous manner (the human operator is retained in the robot’s control loop). To obtain the forward kinematic model, the coordinate frames are established by the classical Denavit–Hartenburg (D-H) convention for a hyper-redundant serial manipulator which has a controlled cables-driven mechanism. To solve the inverse kinematics of the robot, unlike the conventional methods, a leader-follower mechanism, based on the sequential inverse kinematic, is followed. Using this mechanism, the inverse kinematic problem is solved for all sequential joints starting from the head joint to the base joint of the robot. To verify the kinematic design and simulate the robot motion, the MATLAB robotic toolbox is used. The simulation result demonstrated the promising capability of the proposed leader-follower control system in controlling the robot motion and trajectory in our confined space application.

Keywords: hyper-redundant robots, kinematic analysis, semi-autonomous control, serial manipulators

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Authors: Adriano Valdes-Gomez, Francisco Javier Sevilla

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We devise a numerical algorithm to simulate the diffusion of a Brownian particle restricted to the surface of a three-dimensional sphere when the particle is under the effects of an external potential that is coupled linearly. It is obtained using elementary geometry, yet, it converges, in the weak sense, to the solutions to the Smoluchowski equation. Rotations on the sphere, which are the analogs of linear displacements in euclidean spaces, are calculated using algebraic operations and then by a proper scaling, which makes the algorithm efficient and quite simple, especially to what may be the short-time propagator approach. Our findings prove that the global effects of curvature are taken into account in both dynamic and stationary processes, and it is not restricted to work in configuration space, neither restricted to the overdamped limit. We have generalized it successfully to simulate the Kramers or the Ornstein-Uhlenbeck process, where it is necessary to work directly in phase space, and it may be adapted to other two dimensional surfaces with non-constant curvature.

Keywords: diffusion on the sphere, Fokker-Planck equation on the sphere, non equilibrium processes on the sphere, numerical methods for diffusion on the sphere

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Authors: Shangerganesh Lingeshwaran

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In this presentation, we have performed numerical simulations for a reaction-diffusion equation with various nonlinear density-dependent diffusion operators and proliferation functions. The mathematical model represented by parabolic partial differential equation is considered to study the invasion of gliomas (the most common type of brain tumors) and to describe the growth of cancer cells and response to their treatment. The unknown quantity of the given reaction-diffusion equation is the density of cancer cells and the mathematical model based on the proliferation and migration of glioma cells. A standard Galerkin finite element method is used to perform the numerical simulations of the given model. Finally, important observations on the each of nonlinear diffusion functions and proliferation functions are presented with the help of computational results.

Keywords: glioma invasion, nonlinear diffusion, reaction-diffusion, finite eleament method

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Authors: Gautam Kumar Saharia, Sagardeep Talukdar, Riki Dutta, Sudipta Nandy

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The physics-informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on a strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary conditions to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of the Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful in studying various optical phenomena.

Keywords: deep learning, optical soliton, physics informed neural network, partial differential equation

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Authors: S. O. Oyamakin, A. U. Chukwu

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Richard's growth equation being a generalized logistic growth equation was improved upon by introducing an allometric parameter using the hyperbolic sine function. The integral solution to this was called hyperbolic Richard's growth model having transformed the solution from deterministic to a stochastic growth model. Its ability in model prediction was compared with the classical Richard's growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using the coefficient of determination (R2), Mean Absolute Error (MAE) and Mean Square Error (MSE) results. The Kolmogorov-Smirnov test and Shapiro-Wilk test was also used to test the behavior of the error term for possible violations. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic Richard's nonlinear growth models better than the classical Richard's growth model.

Keywords: height, Dbh, forest, Pinus caribaea, hyperbolic, Richard's, stochastic

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Authors: Soran Aminiaghdam, Christian Rode, Reinhard Blickhan, Astrid Zech

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Despite considerable studies on the impact of imposed trunk posture on human walking, less is known about such locomotion while negotiating changes in ground level. The aim of this study was to investigate the behavior of the VBCOM in response to a two-fold expected perturbation, namely alterations in body posture and in ground level. To this end, the kinematic data and ground reaction forces of twelve able participants were collected. We analyzed the vertical position of the body center of mass (VBCOM) from the ground determined by the body segmental analysis method relative to the laboratory coordinate system at touchdown and toe-off instants during walking across uneven ground — characterized by perturbation contact (a 10-cm visible drop) and pre- and post-perturbation contacts — in comparison to unperturbed level contact while maintaining three postures (regular erect, ~30° and ~50° of trunk flexion from the vertical). The VBCOM was normalized to the distance between the greater trochanter marker and the lateral malleoli marker at the instant of TD. Moreover, we calculated the backward rotation during step-down as the difference of the maximum of the trunk angle in the pre-perturbation contact and the minimal trunk angle in the perturbation contact. Two-way repeated measures ANOVAs revealed contact-specific effects of posture on the VBCOM at touchdown (F = 5.96, p = 0.00). As indicated by the analysis of simple main effects, during unperturbed level and pre-perturbation contacts, no between-posture differences for the VBCOM at touchdown were found. In the perturbation contact, trunk-flexed gaits showed a significant increase of VBCOM as compared to the pre-perturbation contact. In the post-perturbation contact, the VBCOM demonstrated a significant decrease in all gait postures relative to the preceding corresponding contacts with no between-posture differences. Main effects of posture revealed that the VBCOM at toe-off significantly decreased in trunk-flexed gaits relative to the regular erect gait. For the main effect of contact, the VBCOM at toe-off demonstrated changes across perturbation and post-perturbation contacts as compared to the unperturbed level contact. Furthermore, participants exhibited a backward trunk rotation during step-down possibly to control the angular momentum of their whole body. A more pronounced backward trunk rotation (2- to 3-fold compared with level contacts) in trunk-flexed walking contributed to the observed elevated VBCOM during the step-down which may have facilitated drop negotiation. These results may shed light on the interaction between posture and locomotion in able gait, and specifically on the behavior of the body center of mass during perturbed locomotion.

Keywords: center of mass, perturbation, posture, uneven ground, walking

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Authors: Changqiao Wu, Guoqing Ding, Xin Chen

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In this paper, ways of modeling dynamic measurement systems are discussed. Specially, for linear system with single-input single-output, it could be modeled with shallow neural network. Then, gradient based optimization algorithms are used for searching the proper coefficients. Besides, method with normal equation and second order gradient descent are proposed to accelerate the modeling process, and ways of better gradient estimation are discussed. It shows that the mathematical essence of the learning objective is maximum likelihood with noises under Gaussian distribution. For conventional gradient descent, the mini-batch learning and gradient with momentum contribute to faster convergence and enhance model ability. Lastly, experimental results proved the effectiveness of second order gradient descent algorithm, and indicated that optimization with normal equation was the most suitable for linear dynamic models.

Keywords: dynamic system modeling, neural network, normal equation, second order gradient descent

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Authors: Kamel Al-Khaled

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A comparative study of the Sinc-Galerkin and Sinc-Collocation methods for solving the Kuramoto-Sivashinsky equation is given. Both approaches depend on using Sinc basis functions. Firstly, a numerical scheme using Sinc-Galerkin method is developed to approximate the solution of Kuramoto-Sivashinsky equation. Sinc approximations to both derivatives and indefinite integrals reduces the solution to an explicit system of algebraic equations. The error in the solution is shown to converge to the exact solution at an exponential. The convergence proof of the solution for the discrete system is given using fixed-point iteration. Secondly, a combination of a Crank-Nicolson formula in the time direction, with the Sinc-collocation in the space direction is presented, where the derivatives in the space variable are replaced by the necessary matrices to produce a system of algebraic equations. The methods are tested on two examples. The demonstrated results show that both of the presented methods more or less have the same accuracy.

Keywords: Sinc-Collocation, nonlinear PDEs, numerical methods, fixed-point

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Authors: Priyanka Ghosh, Priti Kumar Roy

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Every year a considerable number of people die due to methyl alcohol poisoning, in which most of them die even before proper treatment. This work gives a simple and cheap first aid to those affected individuals by the administration of activated charcoal. In this article, we emphasise on the adsorption capability of activated charcoal for the treatment of poisoning and use an impulsive differential equation to study the effect of activated charcoal during adsorption. We also investigate the effects of various parameters on the adsorption which are incorporated in the model system.

Keywords: activated charcoal, adsorption, impulsive differential equation, methanol poisoning

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Authors: Jiradeach Kalayaruan, Tosawat Seetawan

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This paper studied the energy of the nature systems by looking at the overall image throughout the universe. The energy of the nature systems was developed from the Einstein’s energy equation. The researcher used the new ideas called even 2n and odd 3n light dimension energy states systems, which were developed from Einstein’s relativity energy theory equation. In this study, the major methodology the researchers used was the basic principle ideas or beliefs of some religions such as Buddhism, Christianity, Hinduism, Islam, or Tao in order to get new discoveries. The basic beliefs of each religion - Nivara, God, Ether, Atman, and Tao respectively, were great influential ideas on the researchers to use them greatly in the study to form new ideas from philosophy. Since the philosophy of each religion was alive with deep insight of the physical nature relative energy, it connected the basic beliefs to light dimension energy states systems. Unfortunately, Einstein’s original relative energy equation showed only even 2n light dimension energy states systems (if n = 1,…,∞). But in advance ideas, the researchers multiplied light dimension energy by Einstein’s original relative energy equation and get new idea of theoritical physics in odd 3n light dimension energy states systems (if n = 1,…,∞). Because from basic principle ideas or beliefs of some religions philosophy of each religion, you had to add the media light dimension energy into Einstein’s original relative energy equation. Consequently, the simple meaning picture in deep insight showed that you could touch light dimension energy of Nivara, God, Ether, Atman, and Tao by light dimension energy. Since light dimension energy was transferred by Nivara, God, Ether, Atman and Tao, the researchers got the new equation of odd 3n light dimension energy states systems. Moreover, the researchers expected to be able to solve overview problems of all light dimension energy in all nature relative energy, which are developed from Eistein’s relative energy equation.The finding of the study was called 'super nature relative energy' ( in odd 3n light dimension energy states systems (if n = 1,…,∞)). From the new ideas above you could do the summation of even 2n and odd 3n light dimension energy states systems in all of nature light dimension energy states systems. In the future time, the researchers will expect the new idea to be used in insight theoretical physics, which is very useful to the development of quantum mechanics, all engineering, medical profession, transportation, communication, scientific inventions, and technology, etc.

Keywords: 2n light dimension energy states systems effect, Ether, even 2n light dimension energy states systems, nature relativity, Nivara, odd 3n light dimension energy states systems, perturbation points energy, relax point energy states systems, stress perturbation energy states systems effect, super relative energy

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Authors: Alireza Abdikian

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By assuming a quantum relativistic degenerate electron-positron (e-p) plasma media, the nonlinear acoustic solitary propagation in the presence of the stationary ions for neutralizing the plasma background of bounded cylindrical geometry was investigated. By using the standard reductive perturbation technique with cooperation the quantum hydrodynamics model for the e-p fluid, the spherical Kadomtsev-Petviashvili equation was derived for small but finite amplitude waves and was given the solitary wave solution for the parameters relevant for dense astrophysical objects such as white dwarf stars. By using a suitable coordinate transformation and using improved F-expansion technique, the SKP equation can be solved analytically. The numerical results reveal that the relativistic effects lead to propagate the electrostatic bell shape structures and by increasing the relativistic effects, the amplitude and the width of the e-p acoustic solitary wave will decrease.

Keywords: Electron-positron plasma, Acoustic solitary wave, Relativistic plasmas, the spherical Kadomtsev-Petviashvili equation

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Authors: Arash Jafari, Mehdi Taghaddosi, Azin Parvin

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In the paper, our purpose is to enhance the ability to solve a nonlinear differential equation which is about the motion of an incompressible fluid flow going down of an inclined plane without thermal effect with a simple and innovative approach which we have named it new method. Comparisons are made amongst the Numerical, new method, and HPM methods, and the results reveal that this method is very effective and simple and can be applied to other nonlinear problems. It is noteworthy that there are some valuable advantages in this way of solving differential equations, and also most of the sets of differential equations can be answered in this manner which in the other methods they do not have acceptable solutions up to now. A summary of the excellence of this method in comparison to the other manners is as follows: 1) Differential equations are directly solvable by this method. 2) Without any dimensionless procedure, we can solve equation(s). 3) It is not necessary to convert variables into new ones. According to the afore-mentioned assertions which will be proved in this case study, the process of solving nonlinear equation(s) will be very easy and convenient in comparison to the other methods.

Keywords: viscos fluid, incompressible fluid flow, inclined plane, nonlinear phenomena

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Authors: Rajkumar N. Ingle

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In this paper, the existence of a solution of nonlinear functional random differential equations of the first order is proved under caratheodory condition. The study of the functional random differential equation has got importance in the random analysis of the dynamical systems of universal phenomena. Objectives: Nonlinear functional random differential equation is useful to the scientists, engineers, and mathematicians, who are engaged in N.F.R.D.E. analyzing a universal random phenomenon, govern by nonlinear random initial value problems of D.E. Applications of this in the theory of diffusion or heat conduction. Methodology: Using the concepts of probability theory, functional analysis, generally the existence theorems for the nonlinear F.R.D.E. are prove by using some tools such as fixed point theorem. The significance of the study: Our contribution will be the generalization of some well-known results in the theory of Nonlinear F.R.D.E.s. Further, it seems that our study will be useful to scientist, engineers, economists and mathematicians in their endeavors to analyses the nonlinear random problems of the universe in a better way.

Keywords: Random Fixed Point Theorem, functional random differential equation, N.F.R.D.E., universal random phenomenon

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Authors: Nishant Parashar, Sawan S. Sinha, Balaji Srinivasan

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We perform an investigation of the unclosed terms in the evolution equation of the velocity gradient tensor (VGT) in compressible decaying turbulent flow. Velocity gradients in a compressible turbulent flow field influence several important nonlinear turbulent processes like cascading and intermittency. In an attempt to understand the dynamics of the velocity gradients various researchers have tried to model the unclosed terms in the evolution equation of the VGT. The existing models proposed for these unclosed terms have limited applicability. This is mainly attributable to the complex structure of the higher order gradient terms appearing in the evolution equation of VGT. We investigate these higher order gradients using the data from direct numerical simulation (DNS) of compressible decaying isotropic turbulent flow. The gas kinetic method aided with weighted essentially non-oscillatory scheme (WENO) based flow- reconstruction is employed to generate DNS data. By applying neural-network to the DNS data, we map the structure of the unclosed higher order gradient terms in the evolution of the equation of the VGT with VGT itself. We validate our findings by performing alignment based study of the unclosed higher order gradient terms obtained using the neural network with the strain rate eigenvectors.

Keywords: compressible turbulence, neural network, velocity gradient tensor, direct numerical simulation

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Authors: Shidvash Vakilipour, Masoud Mohammadi, Rouzbeh Riazi, Scott Ormiston, Kimia Amiri, Sahar Barati

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An essential component of a finite volume method (FVM) is the advection scheme that estimates values on the cell faces based on the calculated values on the nodes or cell centers. The most widely used advection schemes are upwind schemes. These schemes have been developed in FVM on different kinds of structured and unstructured grids. In this research, the physical influence scheme (PIS) is developed for a cell-centered FVM that uses an implicit coupled solver. Results are compared with the exponential differencing scheme (EDS) and the skew upwind differencing scheme (SUDS). Accuracy of these schemes is evaluated for a lid-driven cavity flow at Re = 1000, 3200, and 5000 and a backward-facing step flow at Re = 800. Simulations show considerable differences between the results of EDS scheme with benchmarks, especially for the lid-driven cavity flow at high Reynolds numbers. These differences occur due to false diffusion. Comparing SUDS and PIS schemes shows relatively close results for the backward-facing step flow and different results in lid-driven cavity flow. The poor results of SUDS in the lid-driven cavity flow can be related to its lack of sensitivity to the pressure difference between cell face and upwind points, which is critical for the prediction of such vortex dominant flows.

Keywords: cell-centered finite volume method, coupled solver, exponential differencing scheme (EDS), physical influence scheme (PIS), pressure weighted interpolation method (PWIM), skew upwind differencing scheme (SUDS)

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Authors: Shashank Patidar, Sumit Kumar, Atul Srivastava, Suneet Singh

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Present work is concerned with the numerical investigation of thermal response of biological tissues during laser-based photo-thermal therapy for destroying cancerous/abnormal cells with minimal damage to the surrounding normal cells. Light propagation through the biological sample is mathematically modelled by transient radiative transfer equation. In the present work, application of the Lattice Boltzmann Method is extended to analyze transport of short-pulse radiation in a participating medium.In order to determine the two-dimensional temperature distribution inside the tissue medium, the RTE has been coupled with Penne’s bio-heat transfer equation based on Fourier’s law by several researchers in last few years.

Keywords: lattice Boltzmann method, transient radiation transfer equation, dual phase lag model

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Authors: M. O. Olayiwola

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Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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Authors: Sheryl Avendaño, Miguel Ospina, Hebert Montegranario

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Full Wave Inversion (FWI) is a variant of seismic tomography for obtaining velocity profiles by an optimization process that combine forward modelling (or solution of wave equation) with the misfit between synthetic and observed data. In this research we are modelling wave propagation in a visco-acoustic medium in the frequency domain. We apply finite differences for the numerical solution of the wave equation with a mix between usual and rotated grids, where density depends on velocity and there exists a damping function associated to a linear dissipative medium. The velocity profiles are obtained from an initial one and the data have been modeled for a frequency range 0-120 Hz. By an iterative procedure we obtain an estimated velocity profile in which are detailed the remarkable features of the velocity profile from which synthetic data were generated showing promising results for our method.

Keywords: seismic inversion, full wave inversion, visco acoustic wave equation, finite diffrence methods

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Authors: Jeremie Coullon, Robert J. Webber

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We introduce a Markov chain Monte Carlo (MCMC) sam-pler for infinite-dimensional inverse problems. Our sam-pler is based on the affine invariant ensemble sampler, which uses interacting walkers to adapt to the covariance structure of the target distribution. We extend this ensem-ble sampler for the first time to infinite-dimensional func-tion spaces, yielding a highly efficient gradient-free MCMC algorithm. Because our ensemble sampler does not require gradients or posterior covariance estimates, it is simple to implement and broadly applicable. In many Bayes-ian inverse problems, Markov chain Monte Carlo (MCMC) meth-ods are needed to approximate distributions on infinite-dimensional function spaces, for example, in groundwater flow, medical imaging, and traffic flow. Yet designing efficient MCMC methods for function spaces has proved challenging. Recent gradi-ent-based MCMC methods preconditioned MCMC methods, and SMC methods have improved the computational efficiency of functional random walk. However, these samplers require gradi-ents or posterior covariance estimates that may be challenging to obtain. Calculating gradients is difficult or impossible in many high-dimensional inverse problems involving a numerical integra-tor with a black-box code base. Additionally, accurately estimating posterior covariances can require a lengthy pilot run or adaptation period. These concerns raise the question: is there a functional sampler that outperforms functional random walk without requir-ing gradients or posterior covariance estimates? To address this question, we consider a gradient-free sampler that avoids explicit covariance estimation yet adapts naturally to the covariance struc-ture of the sampled distribution. This sampler works by consider-ing an ensemble of walkers and interpolating and extrapolating between walkers to make a proposal. This is called the affine in-variant ensemble sampler (AIES), which is easy to tune, easy to parallelize, and efficient at sampling spaces of moderate dimen-sionality (less than 20). The main contribution of this work is to propose a functional ensemble sampler (FES) that combines func-tional random walk and AIES. To apply this sampler, we first cal-culate the Karhunen–Loeve (KL) expansion for the Bayesian prior distribution, assumed to be Gaussian and trace-class. Then, we use AIES to sample the posterior distribution on the low-wavenumber KL components and use the functional random walk to sample the posterior distribution on the high-wavenumber KL components. Alternating between AIES and functional random walk updates, we obtain our functional ensemble sampler that is efficient and easy to use without requiring detailed knowledge of the target dis-tribution. In past work, several authors have proposed splitting the Bayesian posterior into low-wavenumber and high-wavenumber components and then applying enhanced sampling to the low-wavenumber components. Yet compared to these other samplers, FES is unique in its simplicity and broad applicability. FES does not require any derivatives, and the need for derivative-free sam-plers has previously been emphasized. FES also eliminates the requirement for posterior covariance estimates. Lastly, FES is more efficient than other gradient-free samplers in our tests. In two nu-merical examples, we apply FES to challenging inverse problems that involve estimating a functional parameter and one or more scalar parameters. We compare the performance of functional random walk, FES, and an alternative derivative-free sampler that explicitly estimates the posterior covariance matrix. We conclude that FES is the fastest available gradient-free sampler for these challenging and multimodal test problems.

Keywords: Bayesian inverse problems, Markov chain Monte Carlo, infinite-dimensional inverse problems, dimensionality reduction

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Authors: Sangbaek Park, Seungju Lee, Soo-Won Chae

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Unstable shoes are known to strengthen lower extremity muscles and improve gait ability and to change the user’s gait pattern. The change in gait pattern affects human body enormously because the walking is repetitive and steady locomotion in daily life. It is possible to estimate the joint motion including joint moment, force and inertia effect using kinematic and kinetic analysis. However, the change of internal stress at the articular cartilage has not been possible to estimate. The purpose of this research is to evaluate the internal stress of human body during gait with unstable shoes. In this study, FE analysis was combined with motion capture experiment to obtain the boundary condition and loading condition during walking. Motion capture experiments were performed with a participant during walking with normal shoes and with unstable shoes. Inverse kinematics and inverse kinetic analysis was performed with OpenSim. The joint angle and muscle forces were estimated as results of inverse kinematics and kinetics analysis. A detailed finite element (FE) lower extremity model was constructed. The joint coordinate system was added to the FE model and the joint coordinate system was coincided with OpenSim model’s coordinate system. Finally, the joint angles at each phase of gait were used to transform the FE model’s posture according to actual posture from motion capture. The FE model was transformed into the postures of three major phases (1st peak of ground reaction force, mid stance and 2nd peak of ground reaction force). The direction and magnitude of muscle force were estimated by OpenSim and were applied to the FE model’s attachment point of each muscle. Then FE analysis was performed to compare the stress at knee cartilage during gait with normal shoes and unstable shoes.

Keywords: finite element analysis, gait analysis, human model, motion capture

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Authors: Maria Amelia V. C. Araujo, Billy J. Araujo, Brian Greenwood

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The flow over a backward-facing step is characterized by the presence of flow separation, recirculation and reattachment, for a simple geometry. This type of fluid behaviour takes place in many practical engineering applications, hence the reason for being investigated. Historically, fluid flows over a backward-facing step have been examined in many experiments using a variety of measuring techniques such as laser Doppler velocimetry (LDV), hot-wire anemometry, particle image velocimetry or hot-film sensors. However, some of these techniques cannot conveniently be used in separated flows or are too complicated and expensive. In this work, the applicability of the acoustic Doppler velocimetry (ADV) technique is investigated to such type of flows, at various Reynolds numbers corresponding to different flow regimes. The use of this measuring technique in separated flows is very difficult to find in literature. Besides, most of the situations where the Reynolds number effect is evaluated in separated flows are in numerical modelling. The ADV technique has the advantage in providing nearly non-invasive measurements, which is important in resolving turbulence. The ADV Nortek Vectrino+ was used to characterize the flow, in a recirculating laboratory flume, at various Reynolds Numbers (Reh = 3738, 5452, 7908 and 17388) based on the step height (h), in order to capture different flow regimes, and the results compared to those obtained using other measuring techniques. To compare results with other researchers, the step height, expansion ratio and the positions upstream and downstream the step were reproduced. The post-processing of the AVD records was performed using a customized numerical code, which implements several filtering techniques. Subsequently, the Vectrino noise level was evaluated by computing the power spectral density for the stream-wise horizontal velocity component. The normalized mean stream-wise velocity profiles, skin-friction coefficients and reattachment lengths were obtained for each Reh. Turbulent kinetic energy, Reynolds shear stresses and normal Reynolds stresses were determined for Reh = 7908. An uncertainty analysis was carried out, for the measured variables, using the moving block bootstrap technique. Low noise levels were obtained after implementing the post-processing techniques, showing their effectiveness. Besides, the errors obtained in the uncertainty analysis were relatively low, in general. For Reh = 7908, the normalized mean stream-wise velocity and turbulence profiles were compared directly with those acquired by other researchers using the LDV technique and a good agreement was found. The ADV technique proved to be able to characterize the flow properly over a backward-facing step, although additional caution should be taken for measurements very close to the bottom. The ADV measurements showed reliable results regarding: a) the stream-wise velocity profiles; b) the turbulent shear stress; c) the reattachment length; d) the identification of the transition from transitional to turbulent flows. Despite being a relatively inexpensive technique, acoustic Doppler velocimetry can be used with confidence in separated flows and thus very useful for numerical model validation. However, it is very important to perform adequate post-processing of the acquired data, to obtain low noise levels, thus decreasing the uncertainty.

Keywords: ADV, experimental data, multiple Reynolds number, post-processing

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Authors: Kunpeng Wang, Hongchun, Wu, Liangzhi Cao, Chuanqi Zhao

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The distributions of homogeneous neutron flux within a node were expanded into a set of analytic basis functions which satisfy the diffusion equation at any point in a triangular-z node for each energy group, and nodes were coupled with each other with both the zero- and first-order partial neutron current moments across all the interfaces of the triangular prism at the same time. Based this method, a code TABFEN has been developed and applied to solve the neutron diffusion equation in a complicated geometry. In addition, after a series of numerical derivation, one can get the neutron adjoint diffusion equations in matrix form which is the same with the neutron diffusion equation; therefore, it can be solved by TABFEN, and the low-high scan strategy is adopted to improve the efficiency. Four benchmark problems are tested by this method to verify its feasibility, the results show good agreement with the references which demonstrates the efficiency and feasibility of this method.

Keywords: analytic basis function expansion method, arbitrary triangular-z node, adjoint neutron flux, complicated geometry

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Authors: M. Qorbani

Abstract:

Neuromuscular control of posture as understood through studies of responses to mechanical sudden acceleration automatically has been previously demonstrated in individuals with chronic ankle instability (CAI), but the presence of acute condition has not been previously explored specially in a sudden acceleration. The aim of this study was to determine neuromuscular control pattern in those with and without unilateral acute ankle sprains. Design: Case - control. Setting: University research laboratory. The sinker–card protocol with surface translation was be used as a sudden acceleration protocol with study of EMG upon 4 posture stabilizer muscles in two sides of the body in response to sudden acceleration in forward and backward directions. 20 young adult women in two groups (10 LAS; 23.9 ± 2.03 yrs and 10 normal; 26.4 ± 3.2 yrs). The data of EMG were assessed by using multivariate test and one-way repeated measures 2×2×4 ANOVA (P< 0.05). The results showed a significant muscle by direction interaction. Higher TA activity of left and right side in LAS group than normal group in forward direction significantly be showed. Higher MGR activity in normal group than LAS group in backward direction significantly showed. These findings suggest that compared two sides of the body in two directions for 4 muscles EMG activities between and within group for neuromuscular control of posture in avoiding fall. EMG activations of two sides of the body in lateral ankle sprain (LAS) patients were symmetric significantly. Acute ankle instability following once ankle sprains caused to coordinated temporal spatial patterns and strategy selection.

Keywords: neuromuscular response, sEMG, lateral ankle sprain, posture.

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Authors: Youssef Abdelli, Rachid Nasri

Abstract:

The large amplitude free vibration analysis of three-layered symmetric sandwich beams is carried out using two different approaches. The governing nonlinear partial differential equations of motion in free natural vibration are derived using Hamilton's principle. The formulation leads to two nonlinear partial differential equations that are coupled both in axial and binding deformations. In the first approach, the method of multiple scales is applied directly to the governing equation that is a nonlinear partial differential equation. In the second approach, we discretize the governing equation by using Galerkin's procedure and then apply the shooting method to the obtained ordinary differential equations. In order to check the validity of the solutions obtained by the two approaches, they are compared with the solutions obtained by two approaches; they are compared with the solutions obtained numerically by the finite difference method.

Keywords: finite difference method, large amplitude vibration, multiple scales, nonlinear vibration

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Authors: Anyeres N. Atehortua Jimenez, J. David Lambraño, Juan Carlos Muñoz

Abstract:

Navier-Stokes equations (NSE), which describe the dynamics of a fluid, have an important application on modeling waves used for data inversion techniques as full waveform inversion (FWI). In this work a linearized version of NSE and its variables, neglecting deviatoric terms of stress tensor, is presented. In order to get a theoretical modeling of pressure p(x,t) and wave velocity profile c(x,t), a wave equation of visco-acoustic medium (VAE) is written. A change of variables p(x,t)=q(x,t)h(ρ), is made on the equation for the VAE leading to a well known Klein-Gordon equation (KGE) describing waves propagating in variable density medium (ρ) with dispersive term α^2(x). KGE is reduced to a Poisson equation and solved by proposing a specific function for α^2(x) accounting for the energy dissipation and dispersion. Finally, an integral form solution is derived for p(x,t), c(x,t) and kinematics variables like particle velocity v(x,t), displacement u(x,t) and bulk modulus function k_b(x,t). Further, it is compared this visco-acoustic formulation with another form broadly used in the geophysics; it is argued that this formalism is more general and, given its integral form, it may offer several advantages from the modern parallel computing point of view. Applications to minimize the errors in modeling for FWI applied to oils resources in geophysics are discussed.

Keywords: Navier-Stokes equations, modeling, visco-acoustic, inversion FWI

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Authors: M. Azarbarmas, J. M. Cabrera, J. Calvo, M. Aghaie-Khafri

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The modeling of hot deformation behavior for unseen conditions is important in metal-forming. In this study, the hot deformation of IN718 has been characterized in the temperature range 950-1100 and strain rate range 0.001-0.1 s-1 using hot compression tests. All stress-strain curves showed the occurrence of dynamic recrystallization. These curves were implemented quantitatively in mathematics, and then constitutive equation indicating the relationship between the flow stress and hot deformation parameters was obtained successfully.

Keywords: compression test, constitutive equation, dynamic recrystallization, hot working

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Authors: A. H. Choudhury

Abstract:

In this paper, a highly accurate numerical method for the solution of one-dimensional fourth-order wave equation is derived. This hyperbolic problem is solved by using semidiscrete approximations. The space direction is discretized by wavelet-Galerkin method, and the time variable is discretized by using Newmark schemes.

Keywords: hyperbolic problem, semidiscrete approximations, stability, Wavelet-Galerkin Method

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Authors: Muhammad Younis

Abstract:

In this article, the novel (G′/G)-expansion method is successfully applied to construct the abundant travelling wave solutions to the modified Burgers’ equation with the aid of computation. The method is reliable and useful, which gives more general exact travelling wave solutions than the existing methods. These obtained solutions are in the form of hyperbolic, trigonometric and rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and engineering. Some of these solutions are new and some have already been constructed. Additionally, the constraint conditions, for the existence of the solutions are also listed.

Keywords: traveling wave solutions, NLPDE, computation, integrability

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Authors: Vethathirri Ramanujam Srinivasan, S. M. Shiva Nagendra

Abstract:

Air quality management in urban areas is a serious concern in both developed and developing countries. In this regard, more number of air quality monitoring stations are planned to mitigate air pollution in urban areas. In India, Central Pollution Control Board has set up 574 air quality monitoring stations across the country and proposed to set up another 500 stations in the next few years. The number of monitoring stations for each city has been decided based on population data. The setting up of ambient air quality monitoring stations and their operation and maintenance are highly expensive. Therefore, there is a need to optimize monitoring networks for air quality management. The present paper discusses the various methods such as Indian Standards (IS) method, US EPA method and European Union (EU) method to arrive at the minimum number of air quality monitoring stations. In addition, optimization of rain-gauge method and Inverse Distance Weighted (IDW) method using Geographical Information System (GIS) are also explored in the present work for the design of air quality network in Chennai city. In summary, additionally 18 stations are required for Chennai city, and the potential monitoring locations with their corresponding land use patterns are ranked and identified from the 1km x 1km sized grids.

Keywords: air quality monitoring network, inverse distance weighted method, population based method, spatial variation

Procedia PDF Downloads 160