Applied Mathematics Commons^™

Design Of Metamaterials For Optics, Abiti Adili

LSU Doctoral Dissertations

First part of this dissertation studies the problem of designing metamaterial crystals with double negative effective properties for applications in optics by investigating the conditions necessary for generating novel dispersion properties in a metamaterial crystal with subwavelength microstructure. This provides novel optical properties created through local resonances tied to the geometry of the media in subwavelength regime.

In the second part, this dissertation studies the representation formula used to describe band structures in photonic crystals with plasmonic inclusions. By using layer potential techniques, a magnetic dipole operator describing the tangential component of the electrical field generated by magnetic distribution is …

Navigating Around Convex Sets, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We review some basic results of convex analysis and geometry in Rn in the context of formulating a differential equation to track the distance between an observer flying outside a convex set K and K itself.

Simulating Backward Wave Propagation In Metamaterial With Radial Basis Functions, Jichun Li, Bing Nan

Mathematical Sciences Faculty Research

In this paper we revisit the radial basis function (RBF) meshless method and implement it to solve the time-dependent Maxwell's equations in metamaterials. Numerical simulations of the backward wave propagation phenomena are successfully achieved using this RBF method with properly chosen free parameters in the RBFs.

Maximizing And Modeling Malonyl-Coa Production In Escherichia Coli, Tatiana Thompson Silveira Mello

LSU Master's Theses

In E. coli, fatty acid synthesis is catalyzed by the enzyme acetyl-CoA carboxylase (ACC), which converts acetyl-CoA into malonyl-CoA. Malonyl-CoA is a major building block for numerous of bioproducts. Multiple parameters regulate the homeostatic cellular concentration of malonyl-CoA, keeping it at a very low level. Understanding how these parameters affect the bacterial production of malonyl-CoA is fundamental to maximizing it and its bioproducts. To this end, competing pathways consuming malonyl-CoA can be eliminated, and optimal nutritional and environmental conditions can be provided to the fermentation broth. Most previous studies utilized genetic modifications, expensive consumables, and high-cost quantification methods, making …

Boundary Value Problem For Nonhomogeneous Mixed-Type Equation With Two Degenerate Lines, K.S. Fayazov, Y. K. Khudayberganov

Acta of Turin Polytechnic University in Tashkent

In this work, we study boundary value problem for nonhomogeneous mixed-type equation with two degenerate lines. A priori estimate for the solution of the problem is obtained, theorems of uniqueness and conditional stability in the set of correctness are proved. The approximate solution by the regularization method has been constructed.

Introduction To Synchro-Chimera State, Aziza Yusupova

Acta of Turin Polytechnic University in Tashkent

In this work we find a new chimera state in smallest chimera region, the synchronization and chimera phenomena can be alternatively occurred over time intervals.

In The Absence Of Information, 1/N Investment Makes Perfect Sense, Julio Urenda, Vladik Kreinovich

Departmental Technical Reports (CS)

When people have several possible investment instruments, people often invest equally into these instruments: in the case of n instruments, they invest 1/n of their money into each of these instruments. Of course, if additional information about each instrument is available, this 1/n investment strategy is not optimal. We show, however, that in the absence of reliable information, 1/n investment is indeed the best strategy.

Maximum Entropy Approach To Portfolio Optimization: Economic Justification Of An Intuitive Diversity Idea, Laxman Bokati, Vladik Kreinovich

Departmental Technical Reports (CS)

The traditional Markowitz approach to portfolio optimization assumes that we know the means, variances, and covariances of the return rates of all the financial instruments. In some practical situations, however, we do not have enough information to determine the variances and covariances, we only know the means. To provide a reasonable portfolio allocation for such cases, researchers proposed a heuristic maximum entropy approach. In this paper, we provide an economic justification for this heuristic idea.

Closing Banquet Eulogies, Russell Howell, C. Ray Rosentrater

ACMS Conference Proceedings 2019

A tribute to David Lay; A tribute to John Roe

Nonlinear Mechanical Properties Of Road Pavements: Geometric Symmetries Explain The Empirical Difference Between Roads Built On Clay Vs. Granular Soils, Afshin Gholamy, Vladik Kreinovich

Departmental Technical Reports (CS)

It is empirically known that roads built on clay soils have different nonlinear mechanical properties than roads built on granular soils (such as gravel or sand). In this paper, we show that this difficult-to-explain empirical fact can be naturally explained if we analyze the corresponding geometric symmetries.

Why Top Experts Are Paid So Much: Economics-Based Explanation, Julio C. Urenda, Vladik Kreinovich

Departmental Technical Reports (CS)

At first glance, it seems that people should be paid in proportion to their contribution, so if one person produces a little more than the other one, he/she should be paid a little more. In reality, however, top performers are paid dis-proportionally more than those whose performance is slightly worse. How can we explain this from an economic viewpoint? We show that actually there is no paradox here: a simple economic analysis shows that in many area, it makes perfect economic sense to pay much more to top performers.

Intuitive Idea Of Implication Vs. Formal Definition: How To Define The Corresponding Degree, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Formal implication does not capture the intuitive idea of "if A then B", since in formal implication, every two true statements -- even completely unrelated ones -- imply each other. A more adequate description of intuitive implication happens if we consider how much the use of A can shorten a derivation of B. At first glance, it may seem that the number of bits by which we shorten this derivation is a reasonable degree of implication, but we show that this number is not in good accordance with our intuition, and that a natural formalization of this intuition leads to …

Image-Based Modeling Of Blood Flow In Cerebral Aneurysms Treated With Intrasaccular Flow Diverting Devices, Fernando Mut, Bong Jae Chung, Jorge Chudyk, Pedro Lylyk, Ramanathan Kadirvel, David F. Kallmes, Juan R. Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Modeling the flow dynamics in cerebral aneurysms after the implantation of intrasaccular devices is important for understanding the relationship between flow conditions created immediately posttreatment and the subsequent outcomes. This information, ideally available a priori based on computational modeling prior to implantation, is valuable to identify which aneurysms will occlude immediately and which aneurysms will likely remain patent and would benefit from a different procedure or device. In this report, a methodology for modeling the hemodynamics in intracranial aneurysms treated with intrasaccular flow diverting devices is described. This approach combines an image-guided, virtual device deployment within patient-specific vascular models with …

Performance And Economic Evaluation Of Differentiated Multiple Vacation Queueing System With Feedback And Balked Customers, Amina A. Bouchentouf, Latifa Medjahri

Applications and Applied Mathematics: An International Journal (AAM)

The present paper deals with a single server feedback queueing system under two differentiated multiple vacations and balked customers. It is assumed that the service times of the two vacation types are exponentially distributed with different means. The steady-state probabilities of the model are obtained. Some important performance measures of the system are derived. Then, a cost model is developed. Further, a numerical study is presented.

Exact Reliability For Consecutive K-Out-Of-R-From-N: F System With Equal And Unequal Components Probabilities, Yaser Amirian, Ahmad Khodadadi, Omid Chatrabgoun

Applications and Applied Mathematics: An International Journal (AAM)

A consecutive k-out-of-r-from-n: F system consists of n linear ordered components such that the system fails if and only if there exist a set of r consecutive linear component that contains at least k failed components. Consecutive k-out-of-r-from-n: F system has been considered in many fields such as reliability analysis. All recent efforts in this area have been focused on acquiring band or approximation for their reliability such that less attention has been paid to their closed form and exact reliability in the literature. In the present paper, with designing an innovative algorithm the exact reliability for extensive class of …

Transient Analysis Of A Markovian Single Vacation Feedback Queue With An Interrupted Closedown Time And Control Of Admission During Vacation, A. Azhagappan, T. Deepa

Applications and Applied Mathematics: An International Journal (AAM)

This paper analyzes the transient behavior of an M/M/1 queueing model with single vacation, feedback, interrupted closedown time and control of admission during vacation. The time-dependent system size probabilities for the proposed model are obtained using generating function in the closed form. Further, the system performance measures like mean and variance of system size are also obtained for the time-dependent case. Finally, numerical illustrations are presented to understand the effect for various system parameters.

Generalized Bagley-Torvik Equation And Fractional Oscillators, Mark Naber, Lucas Lymburner

Applications and Applied Mathematics: An International Journal (AAM)

In this paper the Bagley-Torvik Equation is considered with the order of the damping term allowed to range between one and two. The solution is found to be representable as a convolution of trigonometric and exponential functions with the driving force. The properties of the effective decay rate and the oscillation frequency with respect to the order of the fractional damping are also studied. It is found that the effective decay rate and oscillation frequency have a complex dependency on the order of the derivative of the damping term and exhibit properties one might expect of a thermodynamic Equation of …

An Initial Value Technique Using Exponentially Fitted Non Standard Finite Difference Method For Singularly Perturbed Differential-Difference Equations, M. Adilaxmi, D. Bhargavi, Y. N. Reddy

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, an exponentially fitted non standard finite difference method is proposed to solve singularly perturbed differential-difference equations with boundary layer on left and right sides of the interval. In this method, the original second order differential difference equation is replaced by an asymptotically equivalent singularly perturbed problem and in turn the problem is replaced by an asymptotically equivalent first order problem. This initial value problem is solve by using exponential fitting with non standard finite differences. To validate the applicability of the method, several model examples have been solved by taking different values for the delay parameter δ …

Modified Gaussian Radial Basis Function Method For The Burgers Systems, Hossein Aminikhah, Mostafa Sadeghi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the systems of variable-coefficient coupled Burgers equation are solved by a free mesh method. The method is based on the collocation points with the modified Gaussian (MGA) radial basis function (RBF). Dependent parameters and independent parameters and their effect on the stability are shown. The accuracy and efficiency of the method has been checked by two examples. The results of numerical experiments are compared with analytical solutions by calculating errors infinity-norm.

Generalized Differential Transform Method For Solving Some Fractional Integro-Differential Equations, S. Shahmorad, A. A. Khajehnasiri

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we use a generalized form of two-dimensional Differential Transform (2D-DT) to solve a new class of fractional integro-differential equations. We express some useful properties of the new transform as a proposition and prove a convergence theorem. Then we illustrate the method with numerical examples.