Mathematical Sciences Faculty PublicationsCopyright (c) 2020 University of Nevada, Las Vegas All rights reserved.
https://digitalscholarship.unlv.edu/math_fac_articles
Recent documents in Mathematical Sciences Faculty Publicationsen-usWed, 18 Mar 2020 08:07:46 PDT3600Optimal Control for Electromagnetic Cloaking Metamaterial Parameters Design
https://digitalscholarship.unlv.edu/math_fac_articles/161
https://digitalscholarship.unlv.edu/math_fac_articles/161Wed, 18 Mar 2020 08:07:40 PDT
In this paper, we develop an optimal control problem to optimize the permittivity and permeability of the metamaterial which can have the invisible cloaking effect. The inverse problem is calibrated as an optimization problem constrained by the time-harmonic Maxwell’s equations. Proper objective functional is introduced with coefficients of the Maxwell’s equations as control variables. We adopt the discontinuous Galerkin method to solve the state equation. Several two-dimensional cloaking benchmark problems are used to test our optimal control method. Numerical results demonstrate that the optimized permittivity and permeability of the metamaterial can achieve the cloaking effectively.
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Zhiwei Fang et al.Computation of Fermat’s Pseudoprimes (Dedicated to the Memory of Professor Leetsch C. Hsu)
https://digitalscholarship.unlv.edu/math_fac_articles/160
https://digitalscholarship.unlv.edu/math_fac_articles/160Wed, 18 Mar 2020 08:07:35 PDT
This note discussed the computation of Fermat’s pseudoprimes (Fermat’s Psp).
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Tian-Xiao He et al.Towards a Novel Generalized Chinese Remainder Algorithm for Extended Rabin Cryptosystem
https://digitalscholarship.unlv.edu/math_fac_articles/159
https://digitalscholarship.unlv.edu/math_fac_articles/159Wed, 18 Mar 2020 08:07:31 PDT
This paper proposes a number of theorems and algorithms for the Chinese Remainder Theorem, which is used to solve a system of linear congruences, and the extended Rabin cryptosystem, which accepts a key composed of an arbitrary finite number of distinct primes. This paper further proposes methods to relax the condition on the primes with trade-offs in the time complexity. The proposed algorithms can be used to provide ciphertext indistinguishability. Finally, this paper conducts extensive experimental analysis on six large data sets. The experimental results show that the proposed algorithms are asymptotically tight to the existing decryption algorithm in the Rabin cryptosystem with the key composed of two distinct primes while maintaining increased generality.
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Justin Zhan et al.A Monolithic Arbitrary Lagrangian–Eulerian Finite Element Analysis for a Stokes/Parabolic Moving Interface Problem
https://digitalscholarship.unlv.edu/math_fac_articles/158
https://digitalscholarship.unlv.edu/math_fac_articles/158Wed, 18 Mar 2020 08:07:27 PDT
In this paper, an arbitrary Lagrangian–Eulerian (ALE)—finite element method (FEM) is developed within the monolithic approach for a moving-interface model problem of a transient Stokes/parabolic coupling with jump coefficients—a linearized fluid-structure interaction (FSI) problem. A new H^1-projection is defined for this problem for the first time to account for the mesh motion due to the moving interface. The well-posedness and optimal convergence properties in both the energy norm and L^2 norm are analyzed for this mixed-type H^1-projection, with which the stability and optimal error estimate in the energy norm are derived for both semi- and fully discrete mixed finite element approximations to the Stokes/parabolic interface problem. Numerical experiments are carried out to validate all theoretical results. The developed analytical approach can be extended to a general FSI problem.
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Rihui Lan et al.A Discontinuous Galerkin Method for the Stolz–Adams Approximate Deconvolution Model for Turbulent Flows
https://digitalscholarship.unlv.edu/math_fac_articles/157
https://digitalscholarship.unlv.edu/math_fac_articles/157Thu, 27 Feb 2020 13:32:08 PST
We consider the zeroth order model of the family of approximate deconvolution models of Stolz and Adams. We propose and analyze fully discrete schemes using discontinuous finite elements. Optimal error estimates are derived. The dependence of these estimates with respect to the Reynolds number Re is O(ReeRe), which is an improvement with respect to the classical continuous finite element method where the dependence is O(ReeRe3), Layton [1].
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Monika Neda et al.Efficiently Constructing Tangent Circles
https://digitalscholarship.unlv.edu/math_fac_articles/156
https://digitalscholarship.unlv.edu/math_fac_articles/156Thu, 27 Feb 2020 13:32:05 PST
In this short note we present, by what we surmise is the most efficient method, a straight-edge and compass construction of four mutually tangent circles in a plane.
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Arthur Baragar et al.A Finite Volume–Alternating Direction Implicit Method for the Valuation of American Options under the Heston Model
https://digitalscholarship.unlv.edu/math_fac_articles/155
https://digitalscholarship.unlv.edu/math_fac_articles/155Thu, 27 Feb 2020 13:32:01 PST
A finite volume–alternating direction implicit method is proposed for numerical valuation of the American options under the Heston model. It is based on decoupling correlated stock price process and volatility process so that corresponding partial differential operator does not contain the mixed partial derivative term. Hence, the proposed method is numerically simple and fast. Numerical results are presented to examine the accuracy of the proposed method and to compare it with the others.
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Jiacheng Cai et al.Collaboration in a Low-Carbon Supply Chain with Reference Emission and Cost Learning effects: Cost Sharing Versus Revenue Sharing Strategies
https://digitalscholarship.unlv.edu/math_fac_articles/154
https://digitalscholarship.unlv.edu/math_fac_articles/154Wed, 26 Feb 2020 09:17:14 PST
The growing environmental awareness of consumers and the regulation of governments drive supply chain members to collaborate in emission reduction. Considering reference emission and cost learning effects, this study investigates a Stackelberg differential game, where a manufacturer acts as a leader and determines the wholesale price and emission reduction level and a retailer acts as a follower and sets the retail price. Equilibrium emission reduction and pricing strategies in cost- and revenue-sharing contracts are deduced from modelling these two collaboration modes. Results demonstrate that the manufacturer and the entire supply chain prefer the revenue-sharing contract rather than the cost-sharing one, whereas the retailer prefers only the wholesale price contract. High ratios in revenue-sharing contract lead to low emission levels and prices and hence benefit consumers. The environmental awareness of consumers and tax rates considerably affect the emission reduction, but learning effect does not. However, the high learning ability of the manufacturer can improve the performance of supply chain members.
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Baoqin Yu et al.An Enhanced Finite Difference Time Domain Method for Two Dimensional Maxwell's Equations
https://digitalscholarship.unlv.edu/math_fac_articles/153
https://digitalscholarship.unlv.edu/math_fac_articles/153Fri, 21 Feb 2020 14:16:54 PST
An enhanced finite‐difference time‐domain (FDTD) algorithm is built to solve the transverse electric two‐dimensional Maxwell's equations with inhomogeneous dielectric media where the electric fields are discontinuous across the dielectric interface. The new algorithm is derived based upon the integral version of the Maxwell's equations as well as the relationship between the electric fields across the interface. To resolve the instability issue of Yee's scheme (staircasing) caused by discontinuous permittivity across the interface, our algorithm revises the permittivities and makes some corrections to the scheme for the cells around the interface. It is also an improvement over the contour‐path effective permittivity algorithm by including some extra terms in the formulas. The scheme is validated in solving the scattering of a dielectric cylinder with exact solution from Mie theory and is then compared with the above contour‐path method, the usual staircasing and the volume‐average method. The numerical results demonstrate that the new algorithm has achieved significant improvement in accuracy over other methods. Furthermore, the algorithm has a simple structure and can be merged into current FDTD software packages easily. The C++ source code for this paper is provided as supporting information for public access.
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Timothy Meagher et al.Simulating Backward Wave Propagation in Metamaterial with Radial Basis Functions
https://digitalscholarship.unlv.edu/math_fac_articles/152
https://digitalscholarship.unlv.edu/math_fac_articles/152Fri, 21 Feb 2020 14:16:51 PST
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.
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Jichun Li et al.A Note on the Limitations of the CAT Procedure with Application to Mixed-Effects Models
https://digitalscholarship.unlv.edu/math_fac_articles/151
https://digitalscholarship.unlv.edu/math_fac_articles/151Mon, 27 Jan 2020 09:37:09 PST
In the recent past, the CAT procedure introduced by Pal, Lim, and Ling has been successfully applied to obtain improved testing procedures in numerous applications. Having seen such results, practitioners may resort to the CAT procedure in all testing problems, assuming that improvement is assured in all applications. To avoid such myths, in this article, we present an important class of applications, where the CAT test performs poorly, and then discuss the type of applications where CAT procedure could be accepted or avoided. However, this does not mean that it is not possible to develop improved tests by taking the CAT approach, as we show in this article by employing the LRT statistic instead of ML/REML-based CAT tests, as authors of the original CAT article also now advocate. In fact, in terms of the Type I error, LRT-based CAT test performed well among tests we studied, except when k, the number of groups in one-way layout is small, in which case the generalized p-value-based tests can be employed. We believe this note will encourage further research to take full benefits of the CAT approach, in such problems as higher way ANOVA and mixed-effects regression models, for which generalized tests are currently available.
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Malwane A. Ananda et al.Finite Element Analysis of an Arbitrary Lagrangian–Eulerian Method for Stokes/Parabolic Moving Interface Problem With Jump Coefficients
https://digitalscholarship.unlv.edu/math_fac_articles/150
https://digitalscholarship.unlv.edu/math_fac_articles/150Mon, 27 Jan 2020 09:37:06 PST
In this paper, a type of arbitrary Lagrangian–Eulerian (ALE) finite element method in the monolithic frame is developed for a linearized fluid–structure interaction (FSI) problem — an unsteady Stokes/parabolic interface problem with jump coefficients and moving interface, where, the corresponding mixed finite element approximation in both semi- and fully discrete scheme are developed and analyzed based upon one type of ALE formulation and a novel H1- projection technique associated with a moving interface problem, and the stability and optimal convergence properties in the energy norm are obtained for both discretizations to approximate the solution of a transient Stokes/parabolic interface problem that is equipped with a low regularity. Numerical experiments further validate all theoretical results. The developed analytical approaches and numerical implementations can be similarly extended to a realistic FSI problem in the future.
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Rihui Lan et al.Collaboration in a Low-Carbon Supply Chain With Reference Emission and Cost Learning Effects: Cost Sharing Versus Revenue Sharing Strategies
https://digitalscholarship.unlv.edu/math_fac_articles/149
https://digitalscholarship.unlv.edu/math_fac_articles/149Fri, 17 Jan 2020 13:42:13 PST
The growing environmental awareness of consumers and the regulation of governments drive supply chain members to collaborate in emission reduction. Considering reference emission and cost learning effects, this study investigates a Stackelberg differential game, where a manufacturer acts as a leader and determines the wholesale price and emission reduction level and a retailer acts as a follower and sets the retail price. Equilibrium emission reduction and pricing strategies in cost- and revenue-sharing contracts are deduced from modelling these two collaboration modes. Results demonstrate that the manufacturer and the entire supply chain prefer the revenue-sharing contract rather than the cost-sharing one, whereas the retailer prefers only the wholesale price contract. High ratios in revenue-sharing contract lead to low emission levels and prices and hence benefit consumers. The environmental awareness of consumers and tax rates considerably affect the emission reduction, but learning effect does not. However, the high learning ability of the manufacturer can improve the performance of supply chain members.
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Baoqin Yu et al.Distributed Lagrange Multiplier/Fictitious Domain Finite Element Method for Stokes/Parabolic Interface Problems With Jump Coefficients
https://digitalscholarship.unlv.edu/math_fac_articles/148
https://digitalscholarship.unlv.edu/math_fac_articles/148Fri, 17 Jan 2020 13:42:10 PST
In this paper, the distributed Lagrange multiplier/fictitious domain (DLM/FD)–mixed finite element method is developed and analyzed for a type of linearized fluid-structure interaction problem–the transient Stokes/parabolic interface problem with jump coefficients. Stability and optimal convergence properties are obtained for both semi- and fully discrete mixed finite element scheme. Numerical experiments are carried out to validate the theoretical results. Similar DLM/FD method can be developed to tackle FSI problems with different compressibility for the fluid and the structure in the future.
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Pengtao Sun et al.Development and Analysis of Both Finite Element and Fourth-Order in Space Finite Difference Methods for an Equivalent Berenger's PML Model
https://digitalscholarship.unlv.edu/math_fac_articles/147
https://digitalscholarship.unlv.edu/math_fac_articles/147Fri, 17 Jan 2020 13:42:07 PST
This paper deals with an equivalent Berenger's Perfectly Matched Layer (PML) model. We first develop a finite element scheme using edge elements to solve this model. We prove a discrete stability of this method, which inherits the stability obtained in the continuous case. Then we propose a fourth-order in space finite difference scheme for solving this PML model. Numerical stability similar to the continuous stability and the optimal error estimate are established for the difference scheme. Here only second order time discretizations are considered for both schemes. Finally, numerical results are presented to justify our analysis and demonstrate the effectiveness of this PML model for absorbing impinging waves.
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Yunqing Huang et al.Impact of Seasonality and Rainfall on Tea Production in Sri Lanka
https://digitalscholarship.unlv.edu/math_fac_articles/146
https://digitalscholarship.unlv.edu/math_fac_articles/146Mon, 13 Jan 2020 09:06:02 PST
The most popular drink in the world is tea, and ideal conditions for tea cultivation are temperatures between 21 degrees C to 29 degrees C, rainfall of 150-250cm with no stagnation of water, and humus rich soil mixed with lime and iron. In this article, the effect of seasonality and amount of rainfall on tea production in Sri Lanka is investigated via the time series method of autoregressive integrated moving average modeling with predictors (ARMAX); the monthly data for this study is collected from eight tea estates in Sri Lanka, over the years 2009-2017. Our results indicate that, with one exception, rainfall does not significantly affect tea production, possibly due to each tea estate receiving rainfall that is sufficient for tea production. Our results also show that a total of six out of the eight tea estates exhibit increasing trend during the study period.
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Rohan J. Dalpatadu et al.On Fixed-Width Confidence Limits for the Risk Ratio with Sequential Sampling
https://digitalscholarship.unlv.edu/math_fac_articles/145
https://digitalscholarship.unlv.edu/math_fac_articles/145Thu, 05 Dec 2019 16:07:34 PST
A sequential method is presented for determining confidence intervals of fixed-width and corresponding optimal sample sizes for the risk ratio of probabilities of the two independent binomial variates. In general, since the ratio estimators are biased and asymmetrical, corrections must be made when they are used in practice. We suggest to use a bias-correction term 1/n for modification to the maximum likelihood estimator (MLE) to develop the procedure. In addition, we study the following desirable properties of the estimator: Unbiasedness, efficiency in variance, and normality. First-order asymptotic expansions are obtained to investigate large-sample properties of the proposed procedure. Monte Carlo experiment is carried out for various scenarios of samples for examining the finite sample behavior. Through illustrations, we compare these performance of the proposed methods, Wald-based confidence intervals with the likelihood-based confidence intervals in light of invariance, length and sample sizes.
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Hokwon Cho et al.Numerical Analysis for the Cahn-Hilliard-Hele-Shaw System with Variable Mobility and Logarithmic Flory-Huggins Potential
https://digitalscholarship.unlv.edu/math_fac_articles/144
https://digitalscholarship.unlv.edu/math_fac_articles/144Tue, 05 Nov 2019 15:33:20 PST
In this paper, a fully discrete scheme is proposed for solving the Cahn-Hilliard-Hele-Shaw system with a logarithmic potential and concentration dependent mobility. Using the regularization procedure, the domain for the logarithmic free energy density function F(ϕ) is extended from (−1,1) to (−∞,∞). A convex-splitting method of the energy is adopted in time and the mixed finite element method is used in space. Furthermore, we prove the stability of the proposed numerical method and establish the optimal error estimate in the energy norm. Finally, numerical results are presented to support our theoretical analysis.
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Yayu Guo et al.Mathematical Modeling of Gas Transport in Porous Geological Media with Contrast of Properties and Irregular Distribution of Pores
https://digitalscholarship.unlv.edu/math_fac_articles/143
https://digitalscholarship.unlv.edu/math_fac_articles/143Tue, 05 Nov 2019 15:33:17 PST
In this work, we perform multiscale modeling of gas transport through the geological media having irregular pore structure and contrast of properties on different spatial scales. We assume that the medium consists of inorganic matrix with organic inclusions imbedded into it. There exist a contrast of properties and spatial scales between the matrix and organic inclusions. The pore sizes vary from micro to nanometers, permeability and diffusivity can differ by several orders of magnitude. We consider filtration and molecular diffusion as mechanisms for free gas transport in both inorganic and organic materials, and surface diffusion as the main mechanism for sorbed gas transport through nanoporous organic inclusions. The irregularities of porous structure we characterize by their deviations from the periodic distribution. We implement multiscale homogenization together with an averaging with respect to random deviations of distribution of pores to derive the macroscopic equation for evaluating the free gas amount in‐place. It turns out that macroscale parameters characterizing gas transport depend on diffusivity, permeability, and porosity of the components of the system, the amount of inclusions and their spatial distribution. We determine the distribution of gas concentration through the production time and investigate its sensitivity to irregularities of pores distribution. We are also interested in the effect of bottom‐hole pressure and study how depletion can be affected by the interchange of gas between kerogen inclusions and inorganic material.
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Viktoria Savatorova et al.A Note on Breaking of Symmetry for a Class of Variational Problems
https://digitalscholarship.unlv.edu/math_fac_articles/142
https://digitalscholarship.unlv.edu/math_fac_articles/142Tue, 30 Jul 2019 18:41:39 PDT
In this note we present a symmetry breaking result for a class of 2π− periodic problems of the form: −u′′(t)=g(u(t))+f(t); u(0)−u(2π)=u′(0)−u′(2π)=0 where g:R→R is a given C1 function and f:[0,2π]→R is continuous. Our approach is inspired on Willem’s paper (Willem, 1989) and uses actions of finite groups which are not usually considered in the literature.
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David G. Costa et al.