Applied Mathematics Commons^™

Dynamics Of Discontinuities In Elastic Solids, Arkadi Berezovski, Mihhail Berezovski

Publications

The paper is devoted to evolving discontinuities in elastic solids. A discontinuity is represented as a singular set of material points. Evolution of a discontinuity is driven by the configurational force acting at such a set. The main attention is paid to the determination of the velocity of a propagating discontinuity. Martensitic phase transition fronts and brittle cracks are considered as representative examples.

An A Posteriori Error Analysis Of Stationary Incompressible Magnetohydrodynamics, Ari E. Rappaport

Mathematics & Statistics ETDs

Adjoint based a posteriori error analysis is a technique to produce exact error repre- sentations for quantities of interests that are functions of the solution of systems of partial differential equations (PDE). The tools used in the analysis consist of duality arguments and compatible residuals. In this thesis we apply a posteriori error anal- ysis to the magnetohydrodynamics (MHD) equations . MHD provides a continuum level description of conducting fluids in the presence of electromagnetic fields. The MHD system is therefore a multi-physics system, capturing both fluid and electro- magnetic effects. Mathematically, The equations of MHD are highly nonlinear and …

Numerical Solution Of Ordinary Differential Equations Using Continuous Runge-Kutta Methods (Feldberg Of Order Four And Five), Madeha Yousif

Emirates Journal for Engineering Research

In this paper the continuous Runge-Kutta method (Runge-Kutta Feldberg method of order four and five) have been used to find the numerical solution of ordinary differential equation not only at the mesh points but also the all points between them. the results are computed using matlab program..

Multigrid Methods For Elliptic Optimal Control Problems, Sijing Liu

LSU Doctoral Dissertations

In this dissertation we study multigrid methods for linear-quadratic elliptic distributed optimal control problems.

For optimal control problems constrained by general second order elliptic partial differential equations, we design and analyze a $P_1$ finite element method based on a saddle point formulation. We construct a $W$-cycle algorithm for the discrete problem and show that it is uniformly convergent in the energy norm for convex domains. Moreover, the contraction number decays at the optimal rate of $m^{-1}$, where $m$ is the number of smoothing steps. We also prove that the convergence is robust with respect to a regularization parameter. The robust …

2n-Dimensional Canonical Systems And Applications, Andrei Ludu, Keshav Baj Acharya

Publications

We study the 2N-dimensional canonical systems and discuss some properties of its fundamental solution. We then discuss the Floquet theory of periodic canonical systems and observe the asymptotic behavior of its solution. Some important physical applications of the systems are also discussed: linear stability of periodic Hamiltonian systems, position-dependent effective mass, pseudo-periodic nonlinear water waves, and Dirac systems.

How To Detect Future Einsteins: Towards Systems Approach, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Talents are rare. It is therefore important to detect and nurture future talents as early as possible. In many disciplines, this is already being done -- via gifted and talented programs, Olympiads, and other ways to select kids with unusually high achievements. However, the current approach is not perfect: some of the kids are selected simply because they are early bloomers, they do not grow into unusually successful researchers; on the other hand, many of those who later become very successful are not selected since they are late bloomers. To avoid these problems, we propose to use systems approach: to …

Which Classes Of Bi-Intervals Are Closed Under Addition?, Olga Kosheleva, Vladik Kreinovich, Jonatan Contreras

Departmental Technical Reports (CS)

In many practical situations, uncertainty with which we know each quantity is described by an interval. In processing such data, it is useful to know that the sum of two intervals is always an interval. In some cases, however, the set of all possible value of a quantity is described by a bi-interval -- i.e., by a union of two intervals. It is known that the sum of two bi-intervals is not always a bi-interval. In this paper, we describe all the class of bi-intervals which are closed under addition -- i.e., for which the sum of bi-intervals is a …

Preference For Boys Does Not Necessarily Lead To A Gender Disbalance: A Realistic Example, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Intuitively, it seems that cultural preference for boys should lead to a gender disbalance -- more boys than girls. This disbalance is indeed what is often observed, and this disbalance is what many models predict. However, in this paper, we show, on a realistic example, that preference for boys does not necessarily lead to a gender disbalance: in our simplified example, boys are clearly preferred, but still there are exactly as many girls as there are boys.

Healthy Lifestyle Decreases The Risk Of Alzheimer Disease: A Possible Partial Explanation Of An Empirical Dependence, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

A recent paper showed that for people who follow all five healthy lifestyle recommendations, the risk of Alzheimer disease is only 40% of the risk for those who do not follow any of these recommendations, and that for people two or three of these recommendations, the risk is 63% of the not-followers risk. In this paper, we show that a relation between the two numbers -- namely, that 0.40 is the square of 0.63 -- can be naturally explained by a simple model.

When Can We Be Sure That Measurement Results Are Consistent: 1-D Interval Case And Beyond, Hani Dbouk, Steffen Schön, Ingo Neumann, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, measurements are characterized by interval uncertainty -- namely, based on each measurement result, the only information that we have about the actual value of the measured quantity is that this value belongs to some interval. If several such intervals -- corresponding to measuring the same quantity -- have an empty intersection, this means that at least one of the corresponding measurement results is an outlier, caused by a malfunction of the measuring instrument. From the purely mathematical viewpoint, if the intersection is non-empty, there is no reason to be suspicious, but from the practical viewpoint, if …

What If Not All Interval-Valued Fuzzy Degrees Are Possible?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the applications of intervals is in describing experts' degrees of certainty in their statements. In this application, not all intervals are realistically possible. To describe all realistically possible degrees, we end up with a mathematical question of describing all topologically closed classes of intervals which are closed under the appropriate minimum and maximum operations. In this paper, we provide a full description of all such classes.

Common-Sense-Based Theoretical Explanation For An Empirical Formula Estimating Road Quality, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich

Departmental Technical Reports (CS)

The quality of a road is usually gauged by a group of trained raters; the resulting numerical value is known as the Present Serviceability Index (PSI). There are, however, two problems with this approach. First, while it is practical to use trained raters to gauge the quality of major highways, there are also numerous not-so-major roads, and there is not enough trained raters to gauge the quality of all of them. Second, even for skilled raters, their estimates are somewhat subjective: different groups of raters may estimate the quality of the same road segment somewhat differently. Because of these two …

A Study Of The Design Of Adaptive Camber Winglets, Justin J. Rosescu

Master's Theses

A numerical study was conducted to determine the effect of changing the camber of a winglet on the efficiency of a wing in two distinct flight conditions. Camber was altered via a simple plain flap deflection in the winglet, which produced a constant camber change over the winglet span. Hinge points were located at 20%, 50% and 80% of the chord and the trailing edge was deflected between -5° and +5°. Analysis was performed using a combination of three-dimensional vortex lattice method and two-dimensional panel method to obtain aerodynamic forces for the entire wing, based on different winglet camber configurations. …

Stability Of Regular Thin Shell Wormholes Supported By Vdw Quintessence, A. Eid

Applications and Applied Mathematics: An International Journal (AAM)

The dynamical equations of motion for a thin shell wormhole from regular black holes that are supported by Van der Waals (VDW) quintessence equation of state (EoS) are constructed, through cut and -paste technique. The linearized stability of regular wormhole is derived. The presences of unstable and stable static solutions with different value of some parameters are analyzed.

Spherically Symmetric Charged Anisotropic Solution In Higher Dimensional Bimetric General Relativity, D. N. Pandya, A. H. Hasmani

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we have obtained a solution of field equations of Rosen’s bimetric general relativity (BGR) for the static spherically symmetric space-time with charged anisotropic fluid distribution in (n+2)-dimensions. An exact solution is obtained and a special case is considered. This work is an extension of our previous work where four-dimensional case was discussed.

Basins Of Convergence In The Collinear Restricted Four-Body Problem With A Repulsive Manev Potential, Euaggelos E. Zotos, Md Sanam Suraj, Rajiv Aggarwal, Charanpreet Kaur

Applications and Applied Mathematics: An International Journal (AAM)

The Newton-Raphson basins of convergence, related to the equilibrium points, in the collinear restricted four-body problem with repulsive Manev potential are numerically investigated. We monitor the parametric evolution of the position as well as of the stability of the equilibrium points, as a function of the parameter e. The multivariate Newton-Raphson optimal method is used for revealing the basins of convergence, by classifying dense grids of initial conditions in several types of two-dimensional planes. We perform a systematic and thorough analysis in an attempt to understand how the parameter e affects the geometry as well as the basin entropy …

Dividend Maximization Under A Set Ruin Probability Target In The Presence Of Proportional And Excess-Of-Loss Reinsurance, Christian Kasumo, Juma Kasozi, Dmitry Kuznetsov

Applications and Applied Mathematics: An International Journal (AAM)

We study dividend maximization with set ruin probability targets for an insurance company whose surplus is modelled by a diffusion perturbed classical risk process. The company is permitted to enter into proportional or excess-of-loss reinsurance arrangements. By applying stochastic control theory, we derive Volterra integral equations and solve numerically using block-by-block methods. In each of the models, we have established the optimal barrier to use for paying dividends provided the ruin probability does not exceed a predetermined target. Numerical examples involving the use of both light- and heavy-tailed distributions are given. The results show that ruin probability targets result in …

Dynamic Optimal Control For Multi-Chemotherapy Treatment Of Dual Listeriosis Infection In Human And Animal Population, B. Echeng Bassey

Applications and Applied Mathematics: An International Journal (AAM)

Following the rising cases of high hospitalization versa-vise incessant fatality rates and the close affinity of listeriosis with HIV/AIDS infection, which often emanates from food-borne pathogens associated with listeria monocytogenes infection, this present paper seek and formulated as penultimate model, an 8-Dimensional classical mathematical Equations which directly accounted for the biological interplay of dual listeriosis virions with dual set of population (human and animals). The model was studied under multiple chemotherapies (trimethoprim-sulphamethoxazole with a combination of penicillin or ampicillin and/or gentamicin). Using ODE’s, the positivity and boundedness of system solutions was investigated with model presented as an optimal control problem. …

Complexity Dynamics Of Gumowski-Mira Map, Sada Nand Prasad, K. R. Meena, Abdullah A. Ansari

Applications and Applied Mathematics: An International Journal (AAM)

In the context of nonlinear dynamics, interesting dynamic behavior of Gumowski-Mira Map has been noted under various feasible circumstances. Evolutionary phenomena are discussed through the study of bifurcation analysis leading to period-doubling and chaos. The appearance of chaos in the method is identified by plotting Lyapunov characteristic exponents (LCE) and Topological Entropy within certain parameter range. Dynamic Lyapunov Indicator (DLI) has been procured for further identification of regular and chaotic motions of the Gumowski-Mira Map. The numerical results through the indicator DLI clearly demonstrate the behavior of our map. The correlation dimension has been calculated numerically for the dimension of …

The Traveling Wave Solution Of The Fuzzy Linear Partial Differential Equation, Zahra Shahsavari, Tofigh Allahviranloo, Saeid Abbasbandy, Mohsen Rostamy-Malkhalifeh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we are going to obtain fuzzy traveling wave solutions for fuzzy linear partial differential equations by considering the type of generalized Hukuhara differentiability. In particular, the fuzzy traveling wave solutions for fuzzy Advection equation, fuzzy linear Diffusion equation, fuzzy Convection-Diffusion-Reaction equation, and fuzzy Klein-Gordon equation are obtained.