### Organizers

The occasion of the annual Board meeting of the International Council for Industrial and Applied Mathematics (ICIAM) provides a confluence of distinguished applied mathematicians from around the world. This workshop provides a forum to exchange ideas, to review recent developments in applied mathematics, and to allow the local community of mathematical scientists to share this international perspective.

The theme of the meeting will be broad, reflecting the range of expertise of these scientists.

The workshop is hosted by the Mathematical Biosciences Institute at OSU, with additional funding provided by the Mathematics Research Institute of OSU and by the Institute for Mathematics and its Applications (University of Minnesota).

The grant from the IMA allows us to support speakers and participants from neighboring institutions in Ohio and throughout the Midwest. In particular, we would like to invite graduate students to attend.

Partial support is available for students and junior participants. We solicit contributions for a poster session.

### Accepted Speakers

Thursday, May 15, 2014 | |
---|---|

Time | Session |

07:45 AM | Shuttle to MBI |

08:00 AM 09:00 AM | Breakfast |

09:00 AM 09:30 AM | Workshop opening: Remarks by Dean David Manderscheid; welcome to MBI by Marty Golubitsky; introduction to workshop by Barbara Keyfitz |

09:30 AM 10:00 AM | Marty Golubitsky - Binocular Rivalry and Symmetry-Breaking In binocular rivalry a subject is presented with two different images --- one to each eye. Usually, the subject perceives alternation between these two images. However, in a number of binocular rivalry experiments, subjects report perceiving surprising combinations of the two presented images. Wilson has proposed a class of neuronal networks that admit multiple competing patterns. We show that symmetry-breaking in appropriately constructed Wilson-type networks predicts the surprising perceived images in the rivalry experiments. This is joint work with Casey Diekman and Yunjiao Wang. |

10:00 AM 10:30 AM | Akitoshi Takayasu - An approach for verified computations of semilinear parabolic equations using the semigroup theory For an initial-boundary value problem of semilinear parabolic equations, a computational method is proposed to rigorously prove that the exact solution is enclosed in a ball. Central to our method is to use the semigroup theory with fully discretized approximations organized by Galerkin method and the backward Euler method, which is the most elementary scheme for parabolic equations. Using the scheme as it is, a step-by-step approach has been investigated. Our method is capable of verifying the weak solutions by using the Galerkin method. It implies that the domain is allowed to be a polygonal or polyhedral domain with arbitrary shape. This work is joint with Mr. Makoto Mizuguchi, Dr. Takayuki Kubo, and Prof. Shin'ichi Oishi |

10:30 AM 11:00 AM | Poster and Coffee Break |

11:00 AM 11:30 AM | Facundo Memoli - A spectral notion of distance between shapes A spectral notion of distance between shapes |

11:30 AM 12:00 PM | Daniel Thompson - Coding Sequence Density Estimation via Topological Pressure I will describe an approach to coding sequence (CDS) density estimation in genomic analysis introduced recently by myself and David Koslicki. Our approach is based on the topological pressure, which is a measure of ‘weighted information content’ adapted from ergodic theory. We use the topological pressure (with suitable training data) to give ab initio predictions of CDS density on the genomes of Mus Musculus, Rhesus Macaque and Drososphilia Melanogaster. While our method is not sufficiently precise to predict, for example, the exact locations of genes, we demonstrate that our method gives reasonable estimates for the ‘coarse scale’ problem of predicting CDS density. This is joint work with David Koslicki (Oregon State). |

12:00 PM 01:30 PM | Lunch Break |

01:30 PM 02:00 PM | Noore Zahra - Vanishing point algorithm using curvelet for denoising MR images In this paper a new algorithm is developed to denoise the MR image using the edge detection and vanishing point detection with curvelet transform . Different Shrinkage functions such as Soft and Hard wavelet Shrinkage rules, curvelet and this new algorithm are used to remove noise and the performance of these results are compared. The algorithm is applied on brain MRIs with different noisy conditions by varying standard deviation of noise. Gaussian noise is taken as the additive noise. The results of proposed methods are compared with the results of wavelet and curvelet using peak signal to noise ratio, mean square error and edge keeping index . |

02:00 PM 02:30 PM | Pierangelo Marcati - Problems on Quantum Hydrodynamics The QHD system is used to describe models in superfluidity, in superconductivity, in Bose Einstein condensates and also to model carrier transport for semiconductor devices at nanoscale. Several mathematical questions need to be addressed to fully understand the various hydrodynamic quantities and their relationships with the Schroedinger and the Wigner pictures. The mathematics need to agree with the requirement from the physics on various issues. In particular the meaning of the velocity in presence of vacuum, the presence of quantum vortices, the presence of the collision terms in semiconductors modeling. Our approach is devised from an the analysis of the dispersive behavior of the solutions, on the factorization of the wave functions (polar decomposition) and stability of null forms. There will be sketched recent advances on Magneto Quantum Hydridynamics and on other dispersive models like Euler Korteweg systems. Weak Strong uniqueness via relative entropy methods will also be mentioned. Finally we discuss perspectives related to the study of quantum turbulence. |

02:30 PM 03:00 PM | Ian Frigaard - Encapsulation and forming using yield stress fluids Yield stress fluids have the property that they do not deform unless a given yield stress is exceeded. While in some flows this leads to unwanted features, this property can also be exploited in order to produce novel flow features. One example of such flows are visco-plastically lubricated (VPL) flows, in which a yield stress fluid is used to stabilize the interface in a multi-layer flow, far beyond what might be expected for a typical viscous-viscous interface. Here we extend this idea in 2 directions. Firstly, we consider the encapsulation of droplets within a visco-plastic fluid, for the purpose of transportation, e.g. in pipelines. The main advantage of this method, compared to others that involve capillary forces is that significantly larger droplets may be stably encapsulated, governed by the length scale of the flow and yield stress of the encapsulating fluid. We explore this setup both analytically and computationally. We show that sufficiently small droplets are held in the unyielded plug of the Poiseuille flow. As the length or radius of the droplets increase the carrier fluid eventually yields, potentially breaking the encapsulation. We study this process of breaking and give estimates for the limiting size of droplets that can be encapsulated. Secondly, we study multi-layer VPL flows in which we experiment with oscillating the flow rates of the individual phases. According to the flow rate variations we succeed in freezing in a range of different interfacial patterns. Experiments performed with carbopol as lubricating fluid, and with xanthan and PEO as core fluid, serve to illustrate the potential of the method. For the PEO, repeated oscillation leads to strings of elegant diamond shapes, for which we can control the frequency and amplitude. Numerical simulations extend the range of shapes achievable and give us interesting insights into the forming process. Joint work with G. Dunbrack, S. Hormozi, A. Maleki-Zamenjani, A. Roustaie |

03:00 PM 03:30 PM | Poster and Coffee Break |

03:30 PM 04:00 PM | Sean Bohun - The Mathematics Underlying the Carbonate System Modelling and simulation of real-life problems involve the very real dilemma of having to incorporate crucial mathematical structure that is locked within other disciples. An example of a particularly pervasive process is the carbonate chemical system, being responsible for ocean acidification due to green house gases, limestone cave formation, degradation of monuments and even arterial blood gas makeup. A problem from the oil and gas industry concerning the reproducibility of the characterization of carbonate rock formations forms the backdrop for an application of this chemical system. The analysis of the resulting reaction-diffusion-advection system of equations that describe the experimental process benefits in two distinct ways: 1) it provides the form of the reaction terms and 2) it infers a natural rescaling of the chemical species. This second point results in an asymptotic analysis that is uniformly applicable across the complete chemical reactivity of the process. An explanation is offered for the variability in the observed experiments and other future problems are posed that capitalize on these new insights. |

04:00 PM 04:30 PM | Jean-Paul Berrut - The linear barycentric rational quadrature method for Volterra integral equations We shall first introduce linear barycentric rational interpolation to the unaware audience : it can be viewed as a small modification of the classical interpolating polynomial. Then we present two direct quadrature methods based on linear rational interpolation for solving general Volterra integral equations of the second kind. The first, deduced by a direct application of linear barycentric rational quadrature given in former work, is shown to converge at the same rate, but is costly on long integration intervals. The second, based on a composite version of the rational quadrature rule, looses one order of convergence, but is much cheaper. Both require only a sample of the involved functions at equispaced nodes and yield a stable, infinitely smooth solution of most classical examples with machine precision. |

04:30 PM 05:00 PM | LÃª HÃ¹ng Sơn - Applications of the Initial value Problems in weather and nature catastrophe forecasts Many problems of weather and nature catastrophe forecasts are reduced to the Initial Value Problem (IVP) of the type: $$egin{equation}partial _t u=Lleft({t,x,u,partial_{x_j}u} ight)end{equation}$$ $$egin{equation}u(0, x)={u_0}(x)end{equation}$$ where $x = (x_{1}, ldots., x_{n}) in Omega subset mathbb{R}^n$, $t geq 0$ is time variable, $u = u(t, x) in C^1 $ is the unknown vector function and $L$ in $( ef{eq:1})$ is a differential operator of the first order. The abstracts Cauchy-Kovalevskaya theorem states that the IVP $( ef{eq:1})$ and $( ef{eq:2})$ is uniquely solved if the initial data ${u_0}(x)$ satisfies the supplement condition $ell u = 0$, where $ell$ is an elliptic differential operator and associated to the operator $L$ In this paper $ell$ is defined by $$egin{equation}ell u:=sumlimits_{j=1}^{3}A_jfrac{partial u}{partial x_j},end{equation}$$ where $$A_1=egin{pmatrix} 1 & 0 & 0 \ 0 & -1 & 0 \ 0 & 0 & -1 \ 0 & 0 & 0end{pmatrix}, A_2=egin{pmatrix} 0 & 1 & 0 \ 1 & 0 & 0 \ 0 & 0 & 0 \ 0 & 0 & -1end{pmatrix}, A_3=egin{pmatrix} 0 & 0 & 1 \ 0 & 0 & 0 \ 1 & 0 & 0 \ 0 & 1 & 0end{pmatrix},dfrac{partial u}{partial x_j}=egin{pmatrix}dfrac{partial u_1}{partial x_j}\ dfrac{partial u_2}{partial x_j}\ dfrac{partial u_3}{partial x_j}end{pmatrix},$$ $u = (u_1, u_2, u_3)$ is the unknown vector function. $L$ are the operators of following type $$egin{equation}Lu:=sum_{k=1}^{3}B_kfrac{partial u}{partial x_k}+Cu+Dend{equation}$$ where $B_k=[b_{ij}^k]_{3 imes 3}$, $C = [c_{ij}]_{3 imes 3}$, $D=[d_1, d_2, d_3]^T$. The matrix elements are the continuously differentiable functions up to second order of the space-variables $x_1, x_2, x_3$ and continuously differentiable up to first order of the time variable $t$. $ell$ and $L$ are called an associated operator if $ell u = 0$Rightarrow $ell(Lu) = 0$.The general theorem for problem $( ef{eq:1})$ and $( ef{eq:2})$ states that if $L$ is associated with $ell$ then the problem $( ef{eq:1})$ and $( ef{eq:2})$ is uniquely solvable with ${u_0}$ belongs to root space of $ell u = 0$. In his Ph.D. dissertation (2013) Le Cuong given the necessary and sufficient conditions so that the $L$ is associated to the operator $ell$ Based on the results of Le Cuong we will use the scientific computing software Mathematica to build a program to find all $L$ operators of type $( ef{eq:4})$ associated with $ell$ of type $( ef{eq:3})$ Therefore we can describe all differential operators $L$ so that the IVP $( ef{eq:1})$ and $( ef{eq:2})$ is uniquely solved. Keywords: Initial Value Problem; Associated space; Interior estimate; Mathematica; 2000 MR Subject Classifications; 35B45; 35F10; 47H10 |

05:00 PM | Shuttle pick-up to Crowne Plaza Hotel from MBI |

06:30 PM 08:00 PM | Reception/dinner at Marty and Barbara's home. Directions will be provided. |

Friday, May 16, 2014 | |
---|---|

Time | Session |

07:45 AM | Shuttle to MBI |

08:00 AM 09:00 AM | Breakfast |

09:00 AM 09:30 AM | Robert Kass - Statistical Assessment of Network Connectivity: The Case of Neural Synchrony Statistical Assessment of Network Connectivity: The Case of Neural Synchrony |

09:30 AM 10:00 AM | Iain S. Duff - Preconditioning of Least-Squares Problems by Identifying Basic Variables We study the preconditioning of the augmented system formulation of the least squares problem $min_x || b - A x ||^2_2$, viz. $$ left[egin{array}{cc}I_m&A\A^T&0end{array}
ight];left[egin{array}{c}r\xend{array}
ight]=left[egin{array}{c}b\0end{array}
ight], $$ where A is a sparse matrix of order $m imes n$ with full column rank and $r$ is the residual vector equal to $b - Ax$. We split the matrix $A$ into basic and non-basic parts so that $P A = left[ egin{array}{c} B\N end{array}
ight],$ where $P$ is a permutation matrix, and we use the preconditioner $$M = left[ egin{array}{cc} I & 0\ 0 & B^{-T} end{array}
ight] $$ to symmetrically precondition the system to obtain, after a simple block Gaussian elimination, the reduced symmetric quasi-definite (SQD) system $$ egin{eqnarray*} left[ egin{array}{cc} I_{m-n} & N B^{-1}\ B^{-T}N^T & -I_n end{array}
ight] ; left[ egin{array}{c} r_N\ B x end{array}
ight] = left[ egin{array}{c} b_N\-b_B end{array}
ight] . end{eqnarray*} $$ We discuss the conditioning of the SQD system with some minor extensions to standard eigenanalysis, show the difficulties associated with choosing the basis matrix $B$, and discuss how sparse direct techniques can be used to choose it. We also comment on the common case where A is an incidence matrix and the basis can be chosen graphically. |

10:00 AM 10:30 AM | Pingwen Zhang - Defects of Liquid Crystals Defects in liquid crystals (LCs) are of great practical and theoretical importance. Recently there is a growing interest in LCs materials under topological constrain and/or external force, but the defects pattern and dynamics are still poorly understood. We investigate three-dimensional spherical droplet within the Landau-de Gennes model under different boundary conditions. When the Q-tensor is uniaxial, the model degenerates to vector model (Oseen-Frank), but Q-tensor model is superior to vector model as the former allows biaxial in the order parameter. Using numerical simulation, a rich variety of defects pattern are found, and the results suggest that, line disclinations always involve biaxial, or equivalently, uniaxial only admits point defects. Then we believe that Q-tensor model is essential to include the disclinations line which is a common phenomena in LCs. The mathematical implication of this observation will be discussed in this talk. |

10:30 AM 11:00 AM | Poster and Coffee Break |

11:00 AM 11:30 AM | Chang-Ock Lee - Accurate surface reconstruction in 3D using two-dimensional parallel cross sections In medical imaging or computational biology, it is required to reconstruct a surface from contours in cross sections for visualization and further processing. We propose a method to generate a surface which is smooth enough and exactly passes through contours in each cross section. For smoothness, we define an energy of the surface as the gradient of the normal vector. Also, we express the surface using a level set function, and assign values of level set function on each cross section to make the surface exactly passing through contours. Finally, we get an energy minimization problem with constraints and it can be solved using the augmented Lagrangian method. The solution of the minimization problem is the surface which we look for. Implementation of the algorithm and numerical experiments are presented. |

11:30 AM 12:00 PM | GrÃ©goire Allaire - Geometrical Constraints in the Level Set Method for Shape and Topology Optimization In the context of structural optimization via a level-set method we propose a framework to handle geometric constraints related to a notion of local thickness. The local thickness is calculated using the signed distance function to the shape. We formulate global constraints using integral functionals and compute their shape derivatives. We discuss different strategies and possible approximations to handle the geometric constraints. We implement our approach in two and three space dimensions for a model of linearized elasticity. This is a joint work with F. Jouve and G. Michailidis. |

12:00 PM 01:30 PM | Lunch Break |

01:30 PM 02:00 PM | Hiroshi Kokubu - Detecting Morse Decompositions of the Global Attractor of Regulatory Networks by Time Series Data Complex network structure frequently appear in biological systems such as gene regulatory networks, circadian rhythm models, signal transduction circuits, etc. As a mathematical formulation of such biological complex network systems, Fiedler, Mochizuki and their collaborators (JDDE 2013) recently defined a class of ODEs associated with a finite directed graph called a regulatory network, and proved that its dynamics on the global attractor can in principle be faithfully monitored by information from a (potentially much) fewer number of vertices of the graph called the feedback vertex set. In this talk, I will use their theory to give a method for detecting a more detailed information on the dynamics of regulatory networks, namely the Morse decomposition of its global attractor. The main idea is to take time series data from the feedback vertex set of a regulatory network, and construct a combinatorial multi-valued map, to which we apply the so-called Conley-Morse Database method. As a test example, we study Mirskyâ€™s mathematical model for mammalian circadian rhythm which can be represented as a regulatory network with 21 vertices. This is a joint work with B. Fielder, A. Mochizuki, G. Kurosawa, and H. Oka. |

02:00 PM 02:30 PM | Irene Fonseca - Variational Methods for Crystal Surface Instability Using the calculus of variations it is shown that important qualitative features of the equilibrium shape of a material void in a linearly elastic solid may be deduced from smoothness and convexity properties of the interfacial energy. In addition, short time existence, uniqueness, and regularity for an anisotropic surface diffusion evolution equation with curvature regularization are proved in the context of epitaxially strained two-dimensional films. This is achieved by using the $H^{-1}$-gradient flow structure of the evolution law, via De Giorgi's minimizing movements. This seems to be the first short time existence result for a surface diffusion type geometric evolution equation in the presence of elasticity. |

02:30 PM 03:00 PM | Michael GÃ¼nther - Multiphysics problems in chip-design: from modelling to efficient numerical simulation Modeling of complex multiphysical problems usually leads to coupled systems of differential-algebraic and partial differential equations (PDAEs). Whereas differential-algebraic equations describe dynamical constrained processes in a network purely described by its topology, partial differential equations are used to model spatial or temporal-spatial phenomena in different subcomponents. The talk will discuss the PDAE-modeling, analysis and numerical simulation of multiphysical problems by inspecting the coupling of electronic networks with electromagnetic fields and semiconductor devices. The efficient numerical simulation of the arising coupled DAE systems is based on combining dynamic iteration schemes (co-simulation), model order reduction and multirate schemes. This work is part of two German projects (SIMOROM, KOSMOS) and one European funded project (NANOCOPS). |

03:00 PM 03:30 PM | Poster and Coffee Break |

03:30 PM 04:00 PM | Helena J. Nussenzveig Lopes - Boundary correctors and energy estimates for the boundary layer problem In a short note in 1984 T. Kato established a criterion for the vanishing viscosity limit to hold in the presence of boundaries, namely that the energy dissipation must vanish in a small region near the boundary, as viscosity tends to zero. The proof is based on the use of a boundary corrector and energy estimates. In this talk, we will discuss Kato's result and its relation to the physical phenomenon of the boundary layer. We then describe the application of these boundary correctors to several different scenarios involving boundary layers, including small obstacles, large domains, and Euler-alpha. |

04:00 PM 04:30 PM | Peter Benner - Parametric Model Order Reduction using Bilinear Systems Model order reduction (MOR) nowadays is an important tool in simulation and control for dynamical systems arising in various engineering disciplines. Often, models of physical processes contain parameters, either describing material properties and geometry variations or arising from changing boundary conditions. For purposes of design, optimization and uncertainty quantification, it is often desirable to preserve these parameters as symbolic quantities in the reduced-order model (ROM). This allows the re-use of the ROM after changing the parameter so that the repeated computation of reduced-order models can be avoided. Significant savings in simulation times for full parameter sweeps, Monte Carlo simulations, or within optimization algorithms can be achieved this way. In this talk, we study a particular approach for computing ROMs for linear parametric systems based on interpreting the reduced-order model as a bilinear system. This open the door to employ methods designed for MOR of bilinear systems in the context of parametric MOR. We will discuss the merits and pitfalls of using this approach as well as the MOR methods that become available via this re-formulation of the MOR problem. Numerical results illustrate the performance of all the methods under consideration. |

04:30 PM 05:00 PM | Yuan Lou - ESS in Spatial Models for Evolution of Dispersal From habitat degradation and climate change to spatial spread of invasive species, dispersal plays a central role in determining how organisms cope with a changing environment. How should organisms disperse â€œoptimallyâ€? in heterogeneous environments? I will discuss some recent development on the evolution of dispersal, focusing on finding evolutionarily stable strategies (ESS) for dispersal. |

05:00 PM | Shuttle pick-up to Crowne Plaza Hotel from MBI |

06:00 PM 07:00 PM | Cash bar at Crowne Plaza (Fusion Room) |

07:00 PM 09:00 PM | Banquet dinner at Crowne Plaza (Fusion Room) |

Name | Affiliation | |
---|---|---|

Allaire, Gregoire | Applied Mathematics, Ecole Polytechnique | |

Benner, Peter | benner@mpi-magdeburg.mpg.de | Computational Methods in Systems and Control, Max Planck Institute for Dynamics of Complex Technical Systems |

Berrut, Jean-Paul | jean-paul.berrut@unifr.ch | Departement de Mathematiques, Universite de Fribourg |

Bohun, Sean | sean.bohun@uoit.ca | Science, University of Ontario Institute of Technology |

Brezzi, Franco | brezzi@imati.cnr.it | Science and Technology, IUSS |

Chen, Zhiming | zmchen@lsec.cc.ac.cn | CSCM, Acadamy of Mathematics and Systems Science |

Conti, Sergio | sergio.conti@uni-bonn.de | Institute for Applied Mathematics, University of Bonn |

Cuminato, Jose | jacumina@icmc.usp.br | Applied Mathematics and Statistics, University of Sao Paulo |

Damlamian, Alain | damla@univ-paris12.fr | Dept. of Mathematics, Universite Paris Est Creteil Val de Marne |

Dawes, Adriana | dawes.33@osu.edu | Department of Mathematics / Department of Molecular Genetics, The Ohio State University |

Duff, Iain S. | iain.duff@stfc.ac.uk | SCD, Rutherford Appleton Laboratory |

Esteban, Maria J. | esteban@ceremade.dauphine.fr | CEREMADE, CNRS & University Paris-Dauphine |

Fitt, Alistair | afitt@brookes.ac.uk | Senior Management Team, Oxford Brookes University |

Fonseca, Irene | fonseca@andrew.cmu.edu | Department of Mathematical Sciences, Carnegie Mellon University |

Frigaard, Ian | frigaard@math.ubc.ca | Mechanical Engineering and Mathematics, UBC |

Gao, Xiaoshan | xgao@mmrc.iss.ac.cn | Chinese Academy of Sciences, Academy of Mathematics and Systems Science, CAS |

GÃ¼nther, Michael | guenther@math.uni-wuppertal.de | Applied Mathematics / Numerical Analysis, University of Wuppertal |

Golubitsky, Marty | mg@mbi.osu.edu | Mathematical Biosciences Institute, The Ohio State University |

Guan, Bo | guan@math.osu.edu | Mathematics, Ohio State University |

Hsu, Ting-Hao | hsu@math.ohio-state.edu | Mathematics, Ohio State University |

Iyiola, Olaniyi | samuel@kfupm.edu.sa | Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals |

Jin, Yu | yjin6@unl.edu | Mathematics, University of Nebraska-Lincoln |

Kass, Robert | kass@stat.cmu.edu | Department of Statistics, Carnegie-Mellon University |

Keyfitz, Barbara | bkeyfitz@math.ohio-state.edu | Department of Mathematics, The Ohio State University |

Kim, Jae Kyoung | kim.5052@mbi.osu.edu | Mathematical Biosciences Institute, The Ohio State University |

Kokubu, Hiroshi | kokubu@math.kyoto-u.ac.jp | Department of Mathematics, Kyoto University |

Lee, Chang-Ock | colee@kaist.edu | Mathematical Sciences, KAIST |

Lou, Yuan | lou@math.ohio-state.edu | Department of Mathematics, The Ohio State University |

Marcati, Pierangelo | pierangelo.marcati@univaq.it | Information Engineering,Computer Science and Mathematics, University of LAquila |

Marini, Donatella | donatella.marini@unipv.it | Mathematics, Pavia University |

Memoli, Facundo | memoli@math.osu.edu | Mathematics, The Ohio State University |

Mitsui, Taketomo | Professor Emeritus, Nagoya University | |

Nussenzveig Lopes, Helena J. | Mathematics, Universidade Federal do Rio de Janeiro | |

Park, Chunjae | cjpark@konkuk.ac.kr | Mathematics, Konkuk University |

Phillips, Cynthia | caphill@sandia.gov | Analytics, Sandia National Laboratories |

Pipher, Jill | jpipher@math.brown.edu | math, Brown University |

Quy, Tong Dinh | son.lehung@hust.edu.vn | School of Applied Mathematics and Informatics, Hanoi University of Science and Technology |

Rousseau, Christiane | rousseac@DMS.UMontreal.CA | Mathematics and Statistics, University of Montreal |

Sloan, Ian | i.sloan@unsw.edu.au | Applied Mathematics, The University of New South Wales |

Son, Le Hung | son.lehung@hust.edu.vn | Applied Mathematics and Informatics, Hanoi University of Science and Technology |

Takayasu, Akitoshi | takitoshi@aoni.waseda.jp | Department of Applied Mathematics, Waseda University |

Thompson, Daniel | thompson@math.osu.edu | Mathematics, The Ohio State University |

Xu, Xuejun | xxj@lsec.cc.ac.cn | Institute of Computational Mathematics, Chinese Academy of Sciences |

Xue, Chuan | cxue@mbi.osu.edu | Mathematics, The Ohio State University |

Ying, Hao | ying.32@osu.edu | Mathematics, The Ohio State University |

Zahra, Noore | noor_zahra_india@yahoo.co.in | School of Engineering and Technology, Sharda University |

Zhang, Pingwen | pzhang@pku.edu.cn | School of Mathematical Sciences, Peking University |

In the context of structural optimization via a level-set method we propose a framework to handle geometric constraints related to a notion of local thickness. The local thickness is calculated using the signed distance function to the shape. We formulate global constraints using integral functionals and compute their shape derivatives. We discuss different strategies and possible approximations to handle the geometric constraints. We implement our approach in two and three space dimensions for a model of linearized elasticity.

This is a joint work with F. Jouve and G. Michailidis.

Model order reduction (MOR) nowadays is an important tool in simulation and control for dynamical systems arising in various engineering disciplines. Often, models of physical processes contain parameters, either describing material properties and geometry variations or arising from changing boundary conditions. For purposes of design, optimization and uncertainty quantification, it is often desirable to preserve these parameters as symbolic quantities in the reduced-order model (ROM). This allows the re-use of the ROM after changing the parameter so that the repeated computation of reduced-order models can be avoided. Significant savings in simulation times for full parameter sweeps, Monte Carlo simulations, or within optimization algorithms can be achieved this way.

In this talk, we study a particular approach for computing ROMs for linear parametric systems based on interpreting the reduced-order model as a bilinear system. This open the door to employ methods designed for MOR of bilinear systems in the context of parametric MOR. We will discuss the merits and pitfalls of using this approach as well as the MOR methods that become available via this re-formulation of the MOR problem. Numerical results illustrate the performance of all the methods under consideration.

We shall first introduce linear barycentric rational interpolation to the unaware audience : it can be viewed as a small modification of the classical interpolating polynomial.

Then we present two direct quadrature methods based on linear rational interpolation for solving general Volterra integral equations of the second kind. The first, deduced by a direct application of linear barycentric rational quadrature given in former work, is shown to converge at the same rate, but is costly on long integration intervals. The second, based on a composite version of the rational quadrature rule, looses one order of convergence, but is much cheaper. Both require only a sample of the involved functions at equispaced nodes and yield a stable, infinitely smooth solution of most classical examples with machine precision.

Modelling and simulation of real-life problems involve the very real dilemma of having to incorporate crucial mathematical structure that is locked within other disciples.

An example of a particularly pervasive process is the carbonate chemical system, being responsible for ocean acidification due to green house gases, limestone cave formation, degradation of monuments and even arterial blood gas makeup.

A problem from the oil and gas industry concerning the reproducibility of the characterization of carbonate rock formations forms the backdrop for an application of this chemical system.

The analysis of the resulting reaction-diffusion-advection system of equations that describe the experimental process benefits in two distinct ways: 1) it provides the form of the reaction terms and 2) it infers a natural rescaling of the chemical species. This second point results in an asymptotic analysis that is uniformly applicable across the complete chemical reactivity of the process. An explanation is offered for the variability in the observed experiments and other future problems are posed that capitalize on these new insights.

Numerical simulation of viscoelastic flows with high elasticity is challenging due to the exponential growth in time of the numerical solution of the stress tensor. In this case, all numerical methods diverge for critical values of the Weissenberg (Wi) number, limiting numerical solutions of viscoelastic flows. Another challenge appears when such flows involve free surfaces. Motivated by all these difficulties, we present, in this work, numerical simulations of viscoelastic free surface flows at high numbers of Wi. The methodology uses a finite difference scheme based on the Marker-And-Cell (MAC) method. To improve the stability of the numerical simulation for high values of Wi, the log-conformation tensor formulation is used. The parabolic stability restriction imposed on the time step to simulate flows with low Reynolds numbers is eliminated combining the Crank-Nicolson method to solve the momentum equation with an implicit technique for the treatment of pressure at the free surface. All these combined methods created numerical strategies used to simulate viscoelastic free surface flows with high elasticity. To demonstrate the efficiency of these strategies, a study of the influence of the Wi parameter in viscoelastic free surface flows, is presented.

Using the calculus of variations it is shown that important qualitative features of the equilibrium shape of a material void in a linearly elastic solid may be deduced from smoothness and convexity properties of the interfacial energy.

In addition, short time existence, uniqueness, and regularity for an anisotropic surface diffusion evolution equation with curvature regularization are proved in the context of epitaxially strained two-dimensional films. This is achieved by using the $H^{-1}$-gradient flow structure of the evolution law, via De Giorgi's minimizing movements. This seems to be the first short time existence result for a surface diffusion type geometric evolution equation in the presence of elasticity.

Yield stress fluids have the property that they do not deform unless a given yield stress is exceeded. While in some flows this leads to unwanted features, this property can also be exploited in order to produce novel flow features. One example of such flows are visco-plastically lubricated (VPL) flows, in which a yield stress fluid is used to stabilize the interface in a multi-layer flow, far beyond what might be expected for a typical viscous-viscous interface. Here we extend this idea in 2 directions.

Firstly, we consider the encapsulation of droplets within a visco-plastic fluid, for the purpose of transportation, e.g. in pipelines. The main advantage of this method, compared to others that involve capillary forces is that significantly larger droplets may be stably encapsulated, governed by the length scale of the flow and yield stress of the encapsulating fluid. We explore this setup both analytically and computationally. We show that sufficiently small droplets are held in the unyielded plug of the Poiseuille flow. As the length or radius of the droplets increase the carrier fluid eventually yields, potentially breaking the encapsulation. We study this process of breaking and give estimates for the limiting size of droplets that can be encapsulated.

Secondly, we study multi-layer VPL flows in which we experiment with oscillating the flow rates of the individual phases. According to the flow rate variations we succeed in freezing in a range of different interfacial patterns. Experiments performed with carbopol as lubricating fluid, and with xanthan and PEO as core fluid, serve to illustrate the potential of the method. For the PEO, repeated oscillation leads to strings of elegant diamond shapes, for which we can control the frequency and amplitude. Numerical simulations extend the range of shapes achievable and give us interesting insights into the forming process.

Joint work with G. Dunbrack, S. Hormozi, A. Maleki-Zamenjani, A. Roustaie

Modeling of complex multiphysical problems usually leads to coupled systems of differential-algebraic and partial differential equations (PDAEs). Whereas differential-algebraic equations describe dynamical constrained processes in a network purely described by its topology, partial differential equations are used to model spatial or temporal-spatial phenomena in different subcomponents.

The talk will discuss the PDAE-modeling, analysis and numerical simulation of multiphysical problems by inspecting the coupling of electronic networks with electromagnetic fields and semiconductor devices. The efficient numerical simulation of the arising coupled DAE systems is based on combining dynamic iteration schemes (co-simulation), model order reduction and multirate schemes. This work is part of two German projects (SIMOROM, KOSMOS) and one European funded project (NANOCOPS).

In binocular rivalry a subject is presented with two different images --- one to each eye. Usually, the subject perceives alternation between these two images. However, in a number of binocular rivalry experiments, subjects report perceiving surprising combinations of the two presented images. Wilson has proposed a class of neuronal networks that admit multiple competing patterns. We show that symmetry-breaking in appropriately constructed Wilson-type networks predicts the surprising perceived images in the rivalry experiments. This is joint work with Casey Diekman and Yunjiao Wang.

Statistical Assessment of Network Connectivity: The Case of Neural Synchrony

Complex network structure frequently appear in biological systems such as gene regulatory networks, circadian rhythm models, signal transduction circuits, etc. As a mathematical formulation of such biological complex network systems, Fiedler, Mochizuki and their collaborators (JDDE 2013) recently defined a class of ODEs associated with a finite directed graph called a regulatory network, and proved that its dynamics on the global attractor can in principle be faithfully monitored by information from a (potentially much) fewer number of vertices of the graph called the feedback vertex set.

In this talk, I will use their theory to give a method for detecting a more detailed information on the dynamics of regulatory networks, namely the Morse decomposition of its global attractor. The main idea is to take time series data from the feedback vertex set of a regulatory network, and construct a combinatorial multi-valued map, to which we apply the so-called Conley-Morse Database method. As a test example, we study MirskyÃ¢â‚¬â„¢s mathematical model for mammalian circadian rhythm which can be represented as a regulatory network with 21 vertices. This is a joint work with B. Fielder, A. Mochizuki, G. Kurosawa, and H. Oka.

In medical imaging or computational biology, it is required to reconstruct a surface from contours in cross sections for visualization and further processing. We propose a method to generate a surface which is smooth enough and exactly passes through contours in each cross section. For smoothness, we define an energy of the surface as the gradient of the normal vector.

Also, we express the surface using a level set function, and assign values of level set function on each cross section to make the surface exactly passing through contours. Finally, we get an energy minimization problem with constraints and it can be solved using the augmented Lagrangian method.

The solution of the minimization problem is the surface which we look for.

Implementation of the algorithm and numerical experiments are presented.

From habitat degradation and climate change to spatial spread of invasive species, dispersal plays a central role in determining how organisms cope with a changing environment. How should organisms disperse Ã¢â‚¬Å“optimallyÃ¢â‚¬? in heterogeneous environments? I will discuss some recent development on the evolution of dispersal, focusing on finding evolutionarily stable strategies (ESS) for dispersal.

The QHD system is used to describe models in superfluidity, in superconductivity, in Bose Einstein condensates and also to model carrier transport for semiconductor devices at nanoscale. Several mathematical questions need to be addressed to fully understand the various hydrodynamic quantities and their relationships with the Schroedinger and the Wigner pictures.

The mathematics need to agree with the requirement from the physics on various issues. In particular the meaning of the velocity in presence of vacuum, the presence of quantum vortices, the presence of the collision terms in semiconductors modeling.

Our approach is devised from an the analysis of the dispersive behavior of the solutions, on the factorization of the wave functions (polar decomposition) and stability of null forms.

There will be sketched recent advances on Magneto Quantum Hydridynamics and on other dispersive models like Euler Korteweg systems. Weak Strong uniqueness via relative entropy methods will also be mentioned. Finally we discuss perspectives related to the study of quantum turbulence.

A spectral notion of distance between shapes

In a short note in 1984 T. Kato established a criterion for the vanishing viscosity limit to hold in the presence of boundaries, namely that the energy dissipation must vanish in a small region near the boundary, as viscosity tends to zero. The proof is based on the use of a boundary corrector and energy estimates. In this talk, we will discuss Kato's result and its relation to the physical phenomenon of the boundary layer. We then describe the application of these boundary correctors to several different scenarios involving boundary layers, including small obstacles, large domains, and Euler-alpha.

Many problems of weather and nature catastrophe forecasts are reduced to the Initial Value Problem (IVP) of the type: $$egin{equation}partial _t u=Lleft({t,x,u,partial_{x_j}u} ight)end{equation}$$ $$egin{equation}u(0, x)={u_0}(x)end{equation}$$ where $x = (x_{1}, ldots., x_{n}) in Omega subset mathbb{R}^n$, $t geq 0$ is time variable, $u = u(t, x) in C^1 $ is the unknown vector function and $L$ in $( ef{eq:1})$ is a differential operator of the first order.

The abstracts Cauchy-Kovalevskaya theorem states that the IVP $( ef{eq:1})$ and $( ef{eq:2})$ is uniquely solved if the initial data ${u_0}(x)$ satisfies the supplement condition $ell u = 0$, where $ell$ is an elliptic differential operator and associated to the operator $L$

In this paper $ell$ is defined by $$egin{equation}ell u:=sumlimits_{j=1}^{3}A_jfrac{partial u}{partial x_j},end{equation}$$ where $$A_1=egin{pmatrix} 1 & 0 & 0 \ 0 & -1 & 0 \ 0 & 0 & -1 \ 0 & 0 & 0end{pmatrix}, A_2=egin{pmatrix} 0 & 1 & 0 \ 1 & 0 & 0 \ 0 & 0 & 0 \ 0 & 0 & -1end{pmatrix}, A_3=egin{pmatrix} 0 & 0 & 1 \ 0 & 0 & 0 \ 1 & 0 & 0 \ 0 & 1 & 0end{pmatrix},dfrac{partial u}{partial x_j}=egin{pmatrix}dfrac{partial u_1}{partial x_j}\ dfrac{partial u_2}{partial x_j}\ dfrac{partial u_3}{partial x_j}end{pmatrix},$$ $u = (u_1, u_2, u_3)$ is the unknown vector function.

$L$ are the operators of following type $$egin{equation}Lu:=sum_{k=1}^{3}B_kfrac{partial u}{partial x_k}+Cu+Dend{equation}$$ where $B_k=[b_{ij}^k]_{3 imes 3}$, $C = [c_{ij}]_{3 imes 3}$, $D=[d_1, d_2, d_3]^T$. The matrix elements are the continuously differentiable functions up to second order of the space-variables $x_1, x_2, x_3$ and continuously differentiable up to first order of the time variable $t$.

$ell$ and $L$ are called an associated operator if $ell u = 0$Rightarrow $ell(Lu) = 0$.The general theorem for problem $( ef{eq:1})$ and $( ef{eq:2})$ states that if $L$ is associated with $ell$ then the problem $( ef{eq:1})$ and $( ef{eq:2})$ is uniquely solvable with ${u_0}$ belongs to root space of $ell u = 0$.

In his Ph.D. dissertation (2013) Le Cuong given the necessary and sufficient conditions so that the $L$ is associated to the operator $ell$ Based on the results of Le Cuong we will use the scientific computing software Mathematica to build a program to find all $L$ operators of type $( ef{eq:4})$ associated with $ell$ of type $( ef{eq:3})$

Therefore we can describe all differential operators $L$ so that the IVP $( ef{eq:1})$ and $( ef{eq:2})$ is uniquely solved.

Keywords: Initial Value Problem; Associated space; Interior estimate; Mathematica; 2000 MR Subject Classifications; 35B45; 35F10; 47H10

For an initial-boundary value problem of semilinear parabolic equations, a computational method is proposed to rigorously prove that the exact solution is enclosed in a ball. Central to our method is to use the semigroup theory with fully discretized approximations organized by Galerkin method and the backward Euler method, which is the most elementary scheme for parabolic equations. Using the scheme as it is, a step-by-step approach has been investigated. Our method is capable of verifying the weak solutions by using the Galerkin method.

It implies that the domain is allowed to be a polygonal or polyhedral domain with arbitrary shape. This work is joint with Mr. Makoto Mizuguchi, Dr. Takayuki Kubo, and Prof. Shin'ichi Oishi

I will describe an approach to coding sequence (CDS) density estimation in genomic analysis introduced recently by myself and David Koslicki. Our approach is based on the topological pressure, which is a measure of â€˜weighted information contentâ€™ adapted from ergodic theory. We use the topological pressure (with suitable training data) to give ab initio predictions of CDS density on the genomes of Mus Musculus, Rhesus Macaque and Drososphilia Melanogaster. While our method is not sufficiently precise to predict, for example, the exact locations of genes, we demonstrate that our method gives reasonable estimates for the â€˜coarse scaleâ€™ problem of predicting CDS density. This is joint work with David Koslicki (Oregon State).

In this paper a new algorithm is developed to denoise the MR image using the edge detection and vanishing point detection with curvelet transform . Different Shrinkage functions such as Soft and Hard wavelet Shrinkage rules, curvelet and this new algorithm are used to remove noise and the performance of these results are compared. The algorithm is applied on brain MRIs with different noisy conditions by varying standard deviation of noise. Gaussian noise is taken as the additive noise. The results of proposed methods are compared with the results of wavelet and curvelet using peak signal to noise ratio, mean square error and edge keeping index .

Defects in liquid crystals (LCs) are of great practical and theoretical importance. Recently there is a growing interest in LCs materials under topological constrain and/or external force, but the defects pattern and dynamics are still poorly understood. We investigate three-dimensional spherical droplet within the Landau-de Gennes model under different boundary conditions. When the Q-tensor is uniaxial, the model degenerates to vector model (Oseen-Frank), but Q-tensor model is superior to vector model as the former allows biaxial in the order parameter. Using numerical simulation, a rich variety of defects pattern are found, and the results suggest that, line disclinations always involve biaxial, or equivalently, uniaxial only admits point defects. Then we believe that Q-tensor model is essential to include the disclinations line which is a common phenomena in LCs. The mathematical implication of this observation will be discussed in this talk.

**ESS in Spatial Models for Evolution of Dispersal**

Yuan Lou

From habitat degradation and climate change to spatial spread of invasive species, dispersal plays a central role in determining how organisms cope with a changing environment. How should organisms disperse â€œoptimally&acir

**Variational Methods for Crystal Surface Instability**

Irene Fonseca

Using the calculus of variations it is shown that important qualitative features of the equilibrium shape of a material void in a linearly elastic solid may be deduced from smoothness and convexity properties of the interfacial energy.

**Detecting Morse Decompositions of the Global Attractor of Regulatory Networks by Time Series Data**

Hiroshi Kokubu

Complex network structure frequently appear in biological systems such as gene regulatory networks, circadian rhythm models, signal transduction circuits, etc. As a mathematical formulation of such biological complex network systems, Fiedler

**Geometrical Constraints in the Level Set Method for Shape and Topology Optimization**

Gregoire Allaire

In the context of structural optimization via a level-set method we propose a framework to handle geometric constraints related to a notion of local thickness. The local thickness is calculated using the signed distance function to the shape

**Preconditioning of Least-Squares Problems by Identifying Basic Variables**

Iain S. Duff We study the preconditioning of the augmented system formulation of the least squares problem $min_x || b - A x ||^2_2$, viz. $$ left[egin{array}{cc}I_m&A\A^T&0end{array}
ight];left[egin{array}{c}r\xend{array}
ight]=left[egin{array}{c}b\0

**Statistical Assessment of Network Connectivity: The Case of Neural Synchrony**

Robert Kass

Statistical Assessment of Network Connectivity: The Case of Neural Synchrony

**The Mathematics Underlying the Carbonate System**

Sean Bohun

Modelling and simulation of real-life problems involve the very real dilemma of having to incorporate crucial mathematical structure that is locked within other disciples.

An example of a particularly pervasive proc

**Problems on Quantum Hydrodynamics**

Pierangelo Marcati

The QHD system is used to describe models in superfluidity, in superconductivity, in Bose Einstein condensates and also to model carrier transport for semiconductor devices at nanoscale. Several mathematical questions need to be addressed to

**An approach for verified computations of semilinear parabolic equations using the semigroup theory**

Akitoshi Takayasu

For an initial-boundary value problem of semilinear parabolic equations, a computational method is proposed to rigorously prove that the exact solution is enclosed in a ball. Central to our method is to use the semigroup theory with fully di

**Binocular Rivalry and Symmetry-Breaking**

Marty Golubitsky

In binocular rivalry a subject is presented with two different images --- one to each eye. Usually, the subject perceives alternation between these two images. However, in a number of binocular rivalry experiments, subjects report perceiving