Simulation of the Large Hadrons Collisions Using Monte Carlo Tools
In many cases, theoretical treatments are available for models for which there is no perfect physical realization. In this situation, the only possible test for an approximate theoretical solution is to compare with data generated from a computer simulation. In this paper, Monte Carlo tools are used to study and compare the elementary particles models. All the experiments are implemented using 10000 events, and the simulated energy is 13 TeV. The mean and the curves of several variables are calculated for each model using MadAnalysis 5. Anomalies in the results can be seen in the muons masses of the minimal supersymmetric standard model and the two Higgs doublet model.
Mathematical Modeling of Human Cardiovascular System: A Lumped Parameter Approach and Simulation
The purpose of this work is to develop a mathematical
model of Human Cardiovascular System using lumped parameter
method. The model is divided in three parts: Systemic Circulation,
Pulmonary Circulation and the Heart. The established mathematical
model has been simulated by MATLAB software. The innovation of
this study is in describing the system based on the vessel diameters
and simulating mathematical equations with active electrical
elements. Terminology of human physical body and required
physical data like vessel’s radius, thickness etc., which are required
to calculate circuit parameters like resistance, inductance and
capacitance, are proceeds from well-known medical books. The
developed model is useful to understand the anatomic of human
cardiovascular system and related syndromes. The model is deal with
vessel’s pressure and blood flow at certain time.
Transport of Analytes under Mixed Electroosmotic and Pressure Driven Flow of Power Law Fluid
In this study, we have analyzed the transport of analytes
under a two dimensional steady incompressible flow of power-law
fluids through rectangular nanochannel. A mathematical model
based on the Cauchy momentum-Nernst-Planck-Poisson equations is
considered to study the combined effect of mixed electroosmotic
(EO) and pressure driven (PD) flow. The coupled governing
equations are solved numerically by finite volume method. We
have studied extensively the effect of key parameters, e.g., flow
behavior index, concentration of the electrolyte, surface potential,
imposed pressure gradient and imposed electric field strength on
the net average flow across the channel. In addition to study
the effect of mixed EOF and PD on the analyte distribution
across the channel, we consider a nonlinear model based on
general convective-diffusion-electromigration equation. We have also
presented the retention factor for various values of electrolyte
concentration and flow behavior index.
Jointly Learning Python Programming and Analytic Geometry
The paper presents an original Python-based application that outlines the advantages of combining some elementary notions of mathematics with the study of a programming language. The application support refers to some of the first lessons of analytic geometry, meaning conics and quadrics and their reduction to a standard form, as well as some related notions. The chosen programming language is Python, not only for its closer to an everyday language syntax – and therefore, enhanced readability – but also for its highly reusable code, which is of utmost importance for a mathematician that is accustomed to exploit already known and used problems to solve new ones. The purpose of this paper is, on one hand, to support the idea that one of the most appropriate means to initiate one into programming is throughout mathematics, and reciprocal, one of the most facile and handy ways to assimilate some basic knowledge in the study of mathematics is to apply them in a personal project. On the other hand, besides being a mean of learning both programming and analytic geometry, the application subject to this paper is itself a useful tool for it can be seen as an independent original Python package for analytic geometry.
Effects of Thermal Radiation on Mixed Convection in a MHD Nanofluid Flow over a Stretching Sheet Using a Spectral Relaxation Method
The effects of thermal radiation, Soret and Dufour
parameters on mixed convection and nanofluid flow over a stretching
sheet in the presence of a magnetic field are investigated. The flow is
subject to temperature dependent viscosity and a chemical reaction
parameter. It is assumed that the nanoparticle volume fraction at the
wall may be actively controlled. The physical problem is modelled
using systems of nonlinear differential equations which have been
solved numerically using a spectral relaxation method. In addition
to the discussion on heat and mass transfer processes, the velocity,
nanoparticles volume fraction profiles as well as the skin friction
coefficient are determined for different important physical parameters.
A comparison of current findings with previously published results
for some special cases of the problem shows an excellent agreement.
Moment Estimators of the Parameters of Zero-One Inflated Negative Binomial Distribution
In this paper, zero-one inflated negative binomial distribution is considered, along with some of its structural properties, then its parameters were estimated using the method of moments. It is found that the method of moments to estimate the parameters of the zero-one inflated negative binomial models is not a proper method and may give incorrect conclusions.
Warning about the Risk of Blood Flow Stagnation after Transcatheter Aortic Valve Implantation
In this work, the hemodynamics in the sinuses of
Valsalva after Transcatheter Aortic Valve Implantation is numerically
examined. We focus on the physical results in the two-dimensional
case. We use a finite element methodology based on a Lagrange
multiplier technique that enables to couple the dynamics of blood
flow and the leaflets’ movement. A massively parallel implementation
of a monolithic and fully implicit solver allows more accuracy and
significant computational savings. The elastic properties of the aortic
valve are disregarded, and the numerical computations are performed
under physiologically correct pressure loads. Computational results
depict that blood flow may be subject to stagnation in the lower
domain of the sinuses of Valsalva after Transcatheter Aortic Valve
Topological Sensitivity Analysis for Reconstruction of the Inverse Source Problem from Boundary Measurement
In this paper, we consider a geometric inverse source
problem for the heat equation with Dirichlet and Neumann boundary
data. We will reconstruct the exact form of the unknown source
term from additional boundary conditions. Our motivation is to
detect the location, the size and the shape of source support.
We present a one-shot algorithm based on the Kohn-Vogelius
formulation and the topological gradient method. The geometric
inverse source problem is formulated as a topology optimization
one. A topological sensitivity analysis is derived from a source
function. Then, we present a non-iterative numerical method for the
geometric reconstruction of the source term with unknown support
using a level curve of the topological gradient. Finally, we give
several examples to show the viability of our presented method.
A Hyperexponential Approximation to Finite-Time and Infinite-Time Ruin Probabilities of Compound Poisson Processes
This article considers the problem of evaluating
infinite-time (or finite-time) ruin probability under a given compound
Poisson surplus process by approximating the claim size distribution
by a finite mixture exponential, say Hyperexponential, distribution. It
restates the infinite-time (or finite-time) ruin probability as a solvable
ordinary differential equation (or a partial differential equation).
Application of our findings has been given through a simulation study.
Analytical Solutions for Corotational Maxwell Model Fluid Arising in Wire Coating inside a Canonical Die
The present paper applies the optimal homotopy perturbation method (OHPM) and the optimal homotopy asymptotic method (OHAM) introduced recently to obtain analytic approximations of the non-linear equations modeling the flow of polymer in case of wire coating of a corotational Maxwell fluid. Expression for the velocity field is obtained in non-dimensional form. Comparison of the results obtained by the two methods at different values of non-dimensional parameter l10, reveal that the OHPM is more effective and easy to use. The OHPM solution can be improved even working in the same order of approximation depends on the choices of the auxiliary functions.
Analysis of Multilayer Neural Network Modeling and Long Short-Term Memory
This paper analyzes fundamental ideas and concepts related to neural networks, which provide the reader a theoretical explanation of Long Short-Term Memory (LSTM) networks operation classified as Deep Learning Systems, and to explicitly present the mathematical development of Backward Pass equations of the LSTM network model. This mathematical modeling associated with software development will provide the necessary tools to develop an intelligent system capable of predicting the behavior of licensed users in wireless cognitive radio networks.
Algorithms for Computing of Optimization Problems with a Common Minimum-Norm Fixed Point with Applications
This research is aimed to study a two-step iteration
process defined over a finite family of σ-asymptotically
quasi-nonexpansive nonself-mappings. The strong convergence
is guaranteed under the framework of Banach spaces with some
additional structural properties including strict and uniform
convexity, reflexivity, and smoothness assumptions. With similar
projection technique for nonself-mapping in Hilbert spaces, we
hereby use the generalized projection to construct a point within
the corresponding domain. Moreover, we have to introduce the use
of duality mapping and its inverse to overcome the unavailability
of duality representation that is exploit by Hilbert space theorists.
We then apply our results for σ-asymptotically quasi-nonexpansive
nonself-mappings to solve for ideal efficiency of vector optimization
problems composed of finitely many objective functions. We also
showed that the obtained solution from our process is the closest to
the origin. Moreover, we also give an illustrative numerical example
to support our results.
An Implicit Methodology for the Numerical Modeling of Locally Inextensible Membranes
We present in this paper a fully implicit finite element
method tailored for the numerical modeling of inextensible fluidic
membranes in a surrounding Newtonian fluid. We consider a highly
simplified version of the Canham-Helfrich model for phospholipid
membranes, in which the bending force and spontaneous curvature
are disregarded. The coupled problem is formulated in a fully
Eulerian framework and the membrane motion is tracked using
the level set method. The resulting nonlinear problem is solved
by a Newton-Raphson strategy, featuring a quadratic convergence
behavior. A monolithic solver is implemented, and we report several
numerical experiments aimed at model validation and illustrating
the accuracy of the proposed method. We show that stability is
maintained for significantly larger time steps with respect to an
explicit decoupling method.
Bi-Lateral Comparison between NIS-Egypt and NMISA-South Africa for the Calibration of an Optical Time Domain Reflectometer
Calibration of Optical Time Domain Reflectometer (OTDR) has a crucial role for the accurate determination of fault locations and the accurate calculation of loss budget of long-haul optical fibre links during installation and repair. A comparison has been made between the Egyptian National Institute for Standards (NIS-Egypt) and the National Metrology institute of South Africa (NMISA-South Africa) for the calibration of an OTDR. The distance and the attenuation scales of a transfer OTDR have been calibrated by both institutes using their standards according to the standard IEC 61746-1 (2009). The results of this comparison have been compiled in this report.
Implicit Eulerian Fluid-Structure Interaction Method for the Modeling of Highly Deformable Elastic Membranes
This paper is concerned with the development of a
fully implicit and purely Eulerian fluid-structure interaction method
tailored for the modeling of the large deformations of elastic
membranes in a surrounding Newtonian fluid. We consider a
simplified model for the mechanical properties of the membrane, in
which the surface strain energy depends on the membrane stretching.
The fully Eulerian description is based on the advection of a modified
surface tension tensor, and the deformations of the membrane are
tracked using a level set strategy. The resulting nonlinear problem
is solved by a Newton-Raphson method, featuring a quadratic
convergence behavior. A monolithic solver is implemented, and we
report several numerical experiments aimed at model validation and
illustrating the accuracy of the presented method. We show that
stability is maintained for significantly larger time steps.
Variational Evolutionary Splines for Solving a Model of Temporomandibular Disorders
The aim of this work is to modelize the occlusion of a
person with temporomandibular disorders as an evolutionary equation
and approach its solution by the construction and characterizing
of discrete variational splines. To formulate the problem, certain
boundary conditions have been considered. After showing the
existence and the uniqueness of the solution of such a problem, a
convergence result of a discrete variational evolutionary spline is
shown. A stress analysis of the occlusion of a human jaw with
temporomandibular disorders by finite elements is carried out in
FreeFem++ in order to prove the validity of the presented method.
Loading Factor Performance of a Centrifugal Compressor Impeller: Specific Features and Way of Modeling
A loading factor performance is necessary for the modeling of centrifugal compressor gas dynamic performance curve. Measured loading factors are linear function of a flow coefficient at an impeller exit. The performance does not depend on the compressibility criterion. To simulate loading factor performances, the authors present two parameters: a loading factor at zero flow rate and an angle between an ordinate and performance line. The calculated loading factor performances of non-viscous are linear too and close to experimental performances. Loading factor performances of several dozens of impellers with different blade exit angles, blade thickness and number, ratio of blade exit/inlet height, and two different type of blade mean line configuration. There are some trends of influence, which are evident – comparatively small blade thickness influence, and influence of geometry parameters is more for impellers with bigger blade exit angles, etc. Approximating equations for both parameters are suggested. The next phase of work will be simulating of experimental performances with the suggested approximation equations as a base.
Normalizing Logarithms of Realized Volatility in an ARFIMA Model
Modelling realized volatility with high-frequency returns is popular as it is an unbiased and efficient estimator of return volatility. A computationally simple model is fitting the logarithms of the realized volatilities with a fractionally integrated long-memory Gaussian process. The Gaussianity assumption simplifies the parameter estimation using the Whittle approximation. Nonetheless, this assumption may not be met in the finite samples and there may be a need to normalize the financial series. Based on the empirical indices S&P500 and DAX, this paper examines the performance of the linear volatility model pre-treated with normalization compared to its existing counterpart. The empirical results show that by including normalization as a pre-treatment procedure, the forecast performance outperforms the existing model in terms of statistical and economic evaluations.
Optimization of Loudspeaker Part Design Parameters by Air Viscosity Damping Effect
This study optimized the design parameters of a cone loudspeaker as an example of high flexibility of the product design. We developed an acoustic analysis software program that considers the impact of damping caused by air viscosity. In sound reproduction, it is difficult to optimize each parameter of the loudspeaker design. To overcome the limitation of the design problem in practice, this study presents an acoustic analysis algorithm to optimize the design parameters of the loudspeaker. The material character of cone paper and the loudspeaker edge were the design parameters, and the vibration displacement of the cone paper was the objective function. The results of the analysis showed that the design had high accuracy as compared to the predicted value. These results suggested that although the parameter design is difficult, with experience and intuition, the design can be performed easily using the optimized design found with the acoustic analysis software.
On the Optimality of Blocked Main Effects Plans
In this article, experimental situations are considered
where a main effects plan is to be used to study m two-level factors
using n runs which are partitioned into b blocks, not necessarily
of same size. Assuming the block sizes to be even for all blocks,
for the case n ≡ 2 (mod 4), optimal designs are obtained with
respect to type 1 and type 2 optimality criteria in the class of designs
providing estimation of all main effects orthogonal to the block
effects. In practice, such orthogonal estimation of main effects is
often a desirable condition. In the wider class of all available m two
level even sized blocked main effects plans, where the factors do not
occur at high and low levels equally often in each block, E-optimal
designs are also characterized. Simple construction methods based on
Hadamard matrices and Kronecker product for these optimal designs
Development of Extended Trapezoidal Method for Numerical Solution of Volterra Integro-Differential Equations
Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.
Semilocal Convergence of a Three Step Fifth Order Iterative Method under Höolder Continuity Condition in Banach Spaces
In this paper, we study the semilocal convergence of
a fifth order iterative method using recurrence relation under the
assumption that first order Fréchet derivative satisfies the Hölder
condition. Also, we calculate the R-order of convergence and provide
some a priori error bounds. Based on this, we give existence and
uniqueness region of the solution for a nonlinear Hammerstein
integral equation of the second kind.
Investigating the Efficiency of Stratified Double Median Ranked Set Sample for Estimating the Population Mean
Stratified double median ranked set sampling (SDMRSS) method is suggested for estimating the population mean. The SDMRSS is compared with the simple random sampling (SRS), stratified simple random sampling (SSRS), and stratified ranked set sampling (SRSS). It is shown that SDMRSS estimator is an unbiased of the population mean and more efficient than SRS, SSRS, and SRSS. Also, by SDMRSS, we can increase the efficiency of mean estimator for specific value of the sample size. SDMRSS is applied on real life examples, and the results of the example agreed the theoretical results.
A Numerical Method for Diffusion and Cahn-Hilliard Equations on Evolving Spherical Surfaces
In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.
A Study of Numerical Reaction-Diffusion Systems on Closed Surfaces
The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.
Discovering Liouville-Type Problems for p-Energy Minimizing Maps in Closed Half-Ellipsoids by Calculus Variation Method
The goal of this project is to investigate constant
properties (called the Liouville-type Problem) for a p-stable map
as a local or global minimum of a p-energy functional where
the domain is a Euclidean space and the target space is a
closed half-ellipsoid. The First and Second Variation Formulas
for a p-energy functional has been applied in the Calculus
Variation Method as computation techniques. Stokes’ Theorem,
Cauchy-Schwarz Inequality, Hardy-Sobolev type Inequalities, and
the Bochner Formula as estimation techniques have been used to
estimate the lower bound and the upper bound of the derived
p-Harmonic Stability Inequality. One challenging point in this project
is to construct a family of variation maps such that the images
of variation maps must be guaranteed in a closed half-ellipsoid.
The other challenging point is to find a contradiction between the
lower bound and the upper bound in an analysis of p-Harmonic
Stability Inequality when a p-energy minimizing map is not constant.
Therefore, the possibility of a non-constant p-energy minimizing
map has been ruled out and the constant property for a p-energy
minimizing map has been obtained. Our research finding is to explore
the constant property for a p-stable map from a Euclidean space into
a closed half-ellipsoid in a certain range of p. The certain range of
p is determined by the dimension values of a Euclidean space (the
domain) and an ellipsoid (the target space). The certain range of p
is also bounded by the curvature values on an ellipsoid (that is, the
ratio of the longest axis to the shortest axis). Regarding Liouville-type
results for a p-stable map, our research finding on an ellipsoid is a
generalization of mathematicians’ results on a sphere. Our result is
also an extension of mathematicians’ Liouville-type results from a
special ellipsoid with only one parameter to any ellipsoid with (n+1)
parameters in the general setting.
Stability Analysis for an Extended Model of the Hypothalamus-Pituitary-Thyroid Axis
We formulate and analyze a mathematical model
describing dynamics of the hypothalamus-pituitary-thyroid
homoeostatic mechanism in endocrine system. We introduce
to this system two types of couplings and delay. In our model,
feedback controls the secretion of thyroid hormones and delay
reflects time lags required for transportation of the hormones. The
influence of delayed feedback on the stability behaviour of the
system is discussed. Analytical results are illustrated by numerical
examples of the model dynamics. This system of equations describes
normal activity of the thyroid and also a couple of types of
malfunctions (e.g. hyperthyroidism).
Fractional Order Controller Design for Vibration Attenuation in an Airplane Wing
The wing is one of the most important parts of an airplane because it ensures stability, sustenance and maneuverability of the airplane. Because of its shape, the airplane wing can be simplified to a smart beam. Active vibration suppression is realized using piezoelectric actuators that are mounted on the surface of the beam. This work presents a tuning procedure of fractional order controllers based on a graphical approach of the frequency domain representation. The efficacy of the method is proven by practically testing the controller on a laboratory scale experimental stand.
Solutions to Probabilistic Constrained Optimal Control Problems Using Concentration Inequalities
Recently, optimal control problems subject to probabilistic
constraints have attracted much attention in many research field. Although
probabilistic constraints are generally intractable in optimization problems,
several methods haven been proposed to deal with probabilistic constraints.
In most methods, probabilistic constraints are transformed to deterministic
constraints that are tractable in optimization problems. This paper examines
a method for transforming probabilistic constraints into deterministic
constraints for a class of probabilistic constrained optimal control problems.
A Lagrangian Hamiltonian Computational Method for Hyper-Elastic Structural Dynamics
Performance of a Hamiltonian based particle method in simulation of nonlinear structural dynamics is subjected to investigation in terms of stability and accuracy. The governing equation of motion is derived based on Hamilton's principle of least action, while the deformation gradient is obtained according to Weighted Least Square method. The hyper-elasticity models of Saint Venant-Kirchhoff and a compressible version similar to Mooney- Rivlin are engaged for the calculation of second Piola-Kirchhoff stress tensor, respectively. Stability along with accuracy of numerical model is verified by reproducing critical stress fields in static and dynamic responses. As the results, although performance of Hamiltonian based model is evaluated as being acceptable in dealing with intense extensional stress fields, however kinds of instabilities reveal in the case of violent collision which can be most likely attributed to zero energy singular modes.