Positivity-Preserving, Energy Stable Numerical Schemes For The Cahn-Hilliard Equation With Logarithmic Potential,
2019
Missouri University of Science and Technology
Positivity-Preserving, Energy Stable Numerical Schemes For The Cahn-Hilliard Equation With Logarithmic Potential, Wenbin Chen, Cheng Wang, Xiaoming Wang, Steven M. Wise
Mathematics and Statistics Faculty Research & Creative Works
In this paper we present and analyze finite difference numerical schemes for the Cahn-Hilliard equation with a logarithmic Flory Huggins energy potential. Both first and second order accurate temporal algorithms are considered. in the first order scheme, we treat the nonlinear logarithmic terms and the surface diffusion term implicitly and update the linear expansive term and the mobility explicitly. We provide a theoretical justification that this numerical algorithm has a unique solution, such that the positivity is always preserved for the logarithmic arguments, i.e., the phase variable is always between −1 and 1, at a point-wise level. in particular, our …
Closing Banquet Eulogies,
2019
Westmont College
Closing Banquet Eulogies, Russell Howell, C. Ray Rosentrater
ACMS Conference Proceedings 2019
A tribute to David Lay; A tribute to John Roe
On The Bures–Wasserstein Distance Between Positive Definite Matrices,
2019
Ashoka University
On The Bures–Wasserstein Distance Between Positive Definite Matrices, Rajendra Bhatia, T. Jain, Yongdo Lim
Journal Articles
The metric d(A,B)=trA+trB−2tr(A1∕2BA1∕2)1∕21∕2 on the manifold of n×n positive definite matrices arises in various optimisation problems, in quantum information and in the theory of optimal transport. It is also related to Riemannian geometry. In the first part of this paper we study this metric from the perspective of matrix analysis, simplifying and unifying various proofs. Then we develop a theory of a mean of two, and a barycentre of several, positive definite matrices with respect to this metric. We explain some recent work on a fixed point iteration for computing this Wasserstein barycentre. Our emphasis is on ideas natural to …
Convergent Solutions Of Stokes Oldroyd-B Boundary Value Problems Using The Immersed Boundary Smooth Extension (Ibse) Method,
2019
Simons Foundation
Convergent Solutions Of Stokes Oldroyd-B Boundary Value Problems Using The Immersed Boundary Smooth Extension (Ibse) Method, David B. Stein, Robert D. Guy, Becca Thomases
Mathematics Sciences: Faculty Publications
The Immersed Boundary (IB) method has been widely used to solve fluid-structure interaction problems, including those where the structure interacts with polymeric fluids. In this paper, we examine the convergence of one such scheme for a well known two-dimensional benchmark flow for the Oldroyd-B constitutive model, and we show that the traditional IB-based scheme fails to adequately capture the polymeric stress near to embedded boundaries. We analyze the reason for such failure, and we argue that this feature is not specific to the case study chosen, but a general feature of such methods due to lack of convergence in velocity …
Increasing C-Additive Processes,
2019
Department of Mathematical Sciences, University of Indianapolis, Indianapolis, IN 46627, USA
Increasing C-Additive Processes, Nadjib Bouzar
Communications on Stochastic Analysis
No abstract provided.
A Limiting Process To Invert The Gauss-Radon Transform,
2019
Department of Mathematics and Statistics, Stephen F. Austin State University, Nacogdoches, Texas 75962-3040, USA
A Limiting Process To Invert The Gauss-Radon Transform, Jeremy J. Becnel
Communications on Stochastic Analysis
No abstract provided.
Spectral Theorem Approach To The Characteristic Function Of Quantum Observables,
2019
Universitá di Roma Tor Vergata, Via di Torvergata, Roma, Italy
Spectral Theorem Approach To The Characteristic Function Of Quantum Observables, Andreas Boukas, Philip J. Feinsilver
Communications on Stochastic Analysis
No abstract provided.
Smoothing Parameters For Recursive Kernel Density Estimators Under Censoring,
2019
Univ. Poitiers, Lab. Math. et Appl., Futuroscope Chasseneuil, France
Smoothing Parameters For Recursive Kernel Density Estimators Under Censoring, Yousri Slaoui
Communications on Stochastic Analysis
No abstract provided.
Strong Convergence Rate In Averaging Principle For The Heat Equation Driven By A General Stochastic Measure,
2019
Department of Mathematical Analysis, Taras Shevchenko National University of Kyiv, Kyiv 01601, Ukraine
Strong Convergence Rate In Averaging Principle For The Heat Equation Driven By A General Stochastic Measure, Vadym Radchenko
Communications on Stochastic Analysis
No abstract provided.
Unified Ball Convergence Of Inexact Methods For Finding Zeros With Multiplicity,
2019
Cameron University
Unified Ball Convergence Of Inexact Methods For Finding Zeros With Multiplicity, Ioannis K. Argyros, Santhosh George
Applications and Applied Mathematics: An International Journal (AAM)
We present an extended ball convergence of inexact methods for approximating a zero of a nonlinear equation with multiplicity m; where m is a natural number. Many popular methods are special cases of the inexact method.
On The Lucas Difference Sequence Spaces Defined By Modulus Function,
2019
Bitlis Eren University
On The Lucas Difference Sequence Spaces Defined By Modulus Function, Murat Karakaş, Tayfur Akbaş, Ayşe M. Karakaş
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, firstly, we define the Lucas difference sequence spaces by the help of Lucas sequence and a sequence of modulus function. Besides, we give some inclusion relations and examine geometrical properties such as Banach-Saks type p, weak fixed point property.
Functional Dimension Of Solution Space Of Differential Operators Of Constant Strength,
2019
Indiana University South Bend
Functional Dimension Of Solution Space Of Differential Operators Of Constant Strength, Morteza Shafii-Mousavi
Applications and Applied Mathematics: An International Journal (AAM)
A differential operator with constant coefficients is hypoelliptic if and only if its solution space is of finite functional dimension. We extend this property to operators with variable coefficient. We prove that an equally strong differential operator with variable coefficients has the same property. In addition, we extend the Zielezny’s result to operators with variable coefficients; prove that an operator with analytic coefficients on ℝn is elliptic if and only if locally the functional dimension of its solution space is the same as the Euclidean dimension n.
Study Of Specially And Temporally Dependent Adsorption Coefficient In Heterogeneous Porous Medium,
2019
Shri Ramswaroop Memorial University
Study Of Specially And Temporally Dependent Adsorption Coefficient In Heterogeneous Porous Medium, Dilip K. Jaiswal, Gulrana _
Applications and Applied Mathematics: An International Journal (AAM)
One-dimensional advection-dispersion equation (ADE) is studied along unsteady longitudinal flow through a semi-infinite heterogeneous medium. Adsorption coefficient is considered temporally and spatially–dependent function i.e., expressed in degenerate form. The dispersion parameter is considered as inversely proportional to adsorption coefficient. The input source is of pulse type. The Laplace Transformation Technique (LTT) is used to obtain the analytical solution by introducing certain new independent variables through separate transformations. The effects of adsorption, heterogeneity and unsteadiness are investigated and discussed with the help of various graphs.
On Nonlinear Contractions In New Extended 𝒃-Metric Spaces,
2019
Université de Sousse
On Nonlinear Contractions In New Extended 𝒃-Metric Spaces, Hassen Aydi, Abdelbasset Felhi, Tayyab Kamran, Erdal Karapınar, Muhammad U. Ali
Applications and Applied Mathematics: An International Journal (AAM)
Very recently, the notion of extended 𝑏-metric spaces was introduced by replacing the modified triangle inequality with a functional triangle inequality and the analog of the renowned Banach fixed point theorem was proved in this new structure. In this paper, continuing in this direction, we further refine the functional inequality and establish some fixed point results for nonlinear contractive mappings in the new setting. A nontrivial example for the new extended 𝑏-metric space is given.
Mirror Symmetry For Non-Abelian Landau-Ginzburg Models,
2019
Brigham Young University
Mirror Symmetry For Non-Abelian Landau-Ginzburg Models, Matthew Michael Williams
Theses and Dissertations
We consider Landau-Ginzburg models stemming from non-abelian groups comprised of non-diagonal symmetries, and we describe a rule for the mirror LG model. In particular, we present the non-abelian dual group G*, which serves as the appropriate choice of group for the mirror LG model. We also describe an explicit mirror map between the A-model and the B-model state spaces for two examples. Further, we prove that this mirror map is an isomorphism between the untwisted broad sectors and the narrow diagonal sectors in general.
Secondary Preservice Mathematics Teachers' Curricular Reasoning,
2019
Brigham Young University
Secondary Preservice Mathematics Teachers' Curricular Reasoning, Kimber Anne Mathis
Theses and Dissertations
Researchers have found that teachers' decisions affect students' opportunity to learn. Prior researchers have investigated teachers' decisions while planning, implementing, or reflecting on lessons, but few researchers have studied teachers' decisions and their reasoning throughout the teaching process. It is important to study teachers' reasoning for why they make the decisions they do throughout the teaching process. Furthermore, because inservice and preservice teachers differ in experience and available resources that they draw on while making decisions, it is helpful to consider the resources PSTs' draw on while reasoning. Curricular reasoning is a framework that describes teachers' thinking processes when making …
Integral Inequalities Of Hermite-Hadamard Type Via Green Function And Applications,
2019
Duzce University
Integral Inequalities Of Hermite-Hadamard Type Via Green Function And Applications, Tuba Tunç, Sümeyye Sönmezoğlu, Mehmet Z. Sarıkaya
Applications and Applied Mathematics: An International Journal (AAM)
In this study, we establish some Hermite- Hadamard type inequalities for functions whose second derivatives absolute value are convex. In accordance with this purpose, we obtain an identity using Green's function. Then using this equality we get our main results.
Generalized Bagley-Torvik Equation And Fractional Oscillators,
2019
Monroe County Community College
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 …
New Approach Of Deterministic Key Pre-Distribution Scheme Using Triangle Free Quasi Symmetric Designs,
2019
C. V. Raman College of Engineering
New Approach Of Deterministic Key Pre-Distribution Scheme Using Triangle Free Quasi Symmetric Designs, Debashis Ghosh, Joydeb Pal
Applications and Applied Mathematics: An International Journal (AAM)
A wireless sensor network (WSN) consists of tiny autonomous sensor nodes with some constraints. There are organizations having moderately necessitates of these kind of networks. So, security become an indispensable concern in WSN, due to potential adversaries. To overcome the security problem, keys are pre-loaded to the nodes before deployment. Among all key distribution schemes, deterministic key pre-distribution scheme (KPS) using combinatorial design is efficient regarding security aspect. In this paper, a deterministic approach, based on combinatorial design, for key assignment before the network deployment has been presented. Here the quasi-symmetric design which is of triangle-free is being used to …
Generalized Differential Transform Method For Solving Some Fractional Integro-Differential Equations,
2019
University of Tabriz
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.
