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Gulliksson, Mårtenorcid.org/0000-0003-0332-2315

Open this publication in new window or tab >>A coupled complex boundary expanding compacts method for inverse source problems### Zhang, Ye

### Gong, Rongfang

### Gulliksson, Mårten

### Cheng, Xiaoliang

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 27, no 1, p. 67-86Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Walter de Gruyter, 2019
##### Keywords

Inverse source problem, expanding compacts method, finite element method, error estimation
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:oru:diva-68829 (URN)10.1515/jiip-2017-0002 (DOI)000457195600006 ()2-s2.0-85053166222 (Scopus ID)
#####

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##### Funder

Knowledge Foundation, 20170059
##### Note

Örebro University, School of Science and Technology. Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany .

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, P. R. China .

Örebro University, School of Science and Technology.

Department of Mathematics, Zhejiang University, Hangzhou, P. R. China.

In this paper, we consider an inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary conditions. The unknown source term is to be determined by additional boundary data. This problem is ill-posed since the dimensionality of the boundary is lower than the dimensionality of the inner domain. To overcome the ill-posed nature, using the a priori information (sourcewise representation), and based on the coupled complex boundary method, we propose a coupled complex boundary expanding compacts method (CCBECM). A finite element method is used for the discretization of CCBECM. The regularization properties of CCBECM for both the continuous and discrete versions are proved. Moreover, an a posteriori error estimate of the obtained finite element approximate solution is given and calculated by a projected gradient algorithm. Finally, numerical results show that the proposed method is stable and effective.

Funding Agencies:

Alexander von Humboldt foundation

Natural Science Foundation of China 11571311 11401304

Fundamental Research Funds for the Central Universities NS2018047

Available from: 2018-09-11 Created: 2018-09-11 Last updated: 2019-02-13Bibliographically approvedOpen this publication in new window or tab >>An Iterative Approach to Ill-Conditioned Optimal Portfolio Selection### Gulliksson, Mårten

### Mazur, Stepan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Computational Economics, ISSN 0927-7099, , p. 21Article in journal (Refereed) Epub ahead of print
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer, 2019. p. 21
##### Keywords

Mean-variance portfolio, singular covariance matrix, linear ill-posed problems, second order damped dynamical systems
##### National Category

Probability Theory and Statistics Economics Other Mathematics
##### Research subject

Statistics; Economics; Mathematics
##### Identifiers

urn:nbn:se:oru:diva-74364 (URN)10.1007/s10614-019-09943-6 (DOI)
#####

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Available from: 2019-05-22 Created: 2019-05-22 Last updated: 2019-11-18Bibliographically approved

Örebro University, School of Science and Technology.

Örebro University, Örebro University School of Business.

Covariance matrix of the asset returns plays an important role in the portfolioselection. A number of papers is focused on the case when the covariance matrixis positive definite. In this paper, we consider portfolio selection with a singu-lar covariance matrix. We describe an iterative method based on a second orderdamped dynamical systems that solves the linear rank-deficient problem approxi-mately. Since the solution is not unique, we suggest one numerical solution that canbe chosen from the iterates that balances the size of portfolio and the risk. The nu-merical study confirms that the method has good convergence properties and givesa solution as good as or better than the constrained least norm Moore-Penrose solu-tion. Finally, we complement our result with an empirical study where we analyzea portfolio with actual returns listed in S&P 500 index.

Open this publication in new window or tab >>Damped Dynamical Systems for Solving Equations and Optimization Problems### Gulliksson, Mårten

### Ögren, Magnus

### Oleynik, Anna

### Zhang, Ye

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Handbook of the Mathematics of the Arts and Sciences / [ed] Bharath Sriraman, Springer , 2019Chapter in book (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer, 2019
##### Keywords

Optimization, damped dynamical systems, convex problems, eigenvalue problems, image analysis, inverse problems, quantum physics, Schrödinger equation
##### National Category

Computational Mathematics
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:oru:diva-71881 (URN)10.1007/978-3-319-70658-0 (DOI)978-3-319-70658-0 (ISBN)
#####

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Available from: 2019-01-29 Created: 2019-01-29 Last updated: 2019-04-01Bibliographically approved

Örebro University, School of Science and Technology.

Örebro University, School of Science and Technology.

Department of Mathematics, University of Bergen, Norway.

Faculty of Mathematics, Chemnitz University of Technology, Germany.

We present an approach for solving optimization problems with or without constrains which we call Dynamical Functional Particle Method (DFMP). The method consists of formulating the optimization problem as a second order damped dynamical system and then applying symplectic method to solve it numerically. In the first part of the chapter, we give an overview of the method and provide necessary mathematical background. We show that DFPM is a stable, efficient, and given the optimal choice of parameters, competitive method. Optimal parameters are derived for linear systems of equations, linear least squares, and linear eigenvalue problems. A framework for solving nonlinear problems is developed and numerically tested. In the second part, we adopt the method to several important applications such as image analysis, inverse problems for partial differential equations, and quantum physics. At the end, we present open problems and share some ideas of future work on generalized (nonlinear) eigenvalue problems, handling constraints with reflection, global optimization, and nonlinear ill-posed problems.

Open this publication in new window or tab >>Damped second order flow applied to image denoising### Baravdish, G.

### Svensson, O.

### Gulliksson, Mårten

### Zhang, Ye

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: IMA Journal of Applied Mathematics, ISSN 0272-4960, E-ISSN 1464-3634, Vol. 84, no 6, p. 1082-1111Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Oxford University Press, 2019
##### Keywords

Nonlinear flow, image denoising, p-parabolic, p-Laplace, inverse problems, regularization, damped Hamiltonian system, symplectic method, Störmer–Verlet.
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:oru:diva-79218 (URN)10.1093/imamat/hxz027 (DOI)000509388900002 ()
#####

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#####

##### Note

Department of Science and Technology, Linköping University, Linköping, Sweden .

Department of Science and Technology, Linköping University, Linköping, Sweden .

Örebro University, School of Science and Technology.

Shenzhen MSU-BIT University, 518172 Shenzhen, China; School of Mathematics and Statistics, Beijing Institude of Technology, China.

In this paper, we introduce a new image denoising model: the damped flow (DF), which is a second order nonlinear evolution equation associated with a class of energy functionals of an image. The existence, uniqueness and regularization property of DF are proven. For the numerical implementation, based on the Störmer–Verlet method, a discrete DF, SV-DDF, is developed. The convergence of SV-DDF is studied as well. Several numerical experiments, as well as a comparison with other methods, are provided to demonstrate the efficiency of SV-DDF.

Funding Agency:

Alexander von Humboldt Foundation

Available from: 2020-01-16 Created: 2020-01-16 Last updated: 2020-02-06Bibliographically approved

Open this publication in new window or tab >>Numerical simulations of NMR relaxation in chalk using local Robin boundary conditions### Ögren, Magnus

### Jha, Diwaker

### Dobberschütz, Sören

### Müter, Dirk

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); ### Carlsson, Marcus

### Gulliksson, Mårten

### Stipp, Susan

### Sørensen, Henning

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_4_j_idt188_j_idt202",{id:"formSmash:j_idt184:4:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2019 (English)In: Journal of magnetic resonance, ISSN 1090-7807, E-ISSN 1096-0856, Vol. 308, article id 106597Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2019
##### Keywords

NMR-relaxation, random walk, boundary conditions, CT-scanning, T-inversion
##### National Category

Geophysics Computational Mathematics
##### Research subject

Physics; Mathematics
##### Identifiers

urn:nbn:se:oru:diva-76669 (URN)10.1016/j.jmr.2019.106597 (DOI)000495003900019 ()2-s2.0-85072525625 (Scopus ID)
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##### Note

Örebro University, School of Science and Technology. Nano-Science Center, Department of Chemistry, University of Copenhagen, Denmark.

Nano-Science Center, Department of Chemistry, University of Copenhagen, Denmark..

Nano-Science Center, Department of Chemistry, University of Copenhagen, Denmark..

Nano-Science Center, Department of Chemistry, University of Copenhagen, Denmark..

Center for Mathematical Sciences, Lund University, Lund, Sweden.

Örebro University, School of Science and Technology.

Nano-Science Center, Department of Chemistry, University of Copenhagen, Denmark..

Nano-Science Center, Department of Chemistry, University of Copenhagen, Denmark..

The interpretation of nuclear magnetic resonance (NMR) data is of interest in a number of fields. In Ögren [Eur. Phys. J. B (2014) 87: 255] local boundary conditions for random walk simulations of NMR relaxation in digital domains were presented. Here, we have applied those boundary conditions to large, three-dimensional (3D) porous media samples. We compared the random walk results with known solutions and then applied them to highly structured 3D domains, from images derived using synchrotron radiation CT scanning of North Sea chalk samples. As expected, there were systematic errors caused by digitalization of the pore surfaces so we quantified those errors, and by using linear local boundary conditions, we were able to significantly improve the output. We also present a technique for treating numerical data prior to input into the ESPRIT algorithm for retrieving Laplace components of time series from NMR data (commonly called T-inversion).

Funding Agencies:

Innovation Fund Denmark through the project P3 - Predicting Petrophysical Parameters

Maersk Oil through the project P3 - Predicting Petrophysical Parameters

Available from: 2019-09-23 Created: 2019-09-23 Last updated: 2020-01-16Bibliographically approvedOpen this publication in new window or tab >>A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations### Zhang, Ye

### Gong, Rongfang

### Cheng, Xiaoliang

### Gulliksson, Mårten

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 34, no 6, article id 065001Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Institute of Physics (IOP), 2018
##### Keywords

inverse source problems, dynamical system, regularization, convergence, symplectic method
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:oru:diva-66813 (URN)10.1088/1361-6420/aaba85 (DOI)000431055900001 ()
#####

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##### Funder

Knowledge Foundation, 20170059
##### Note

Örebro University, School of Science and Technology. Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany.

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, People's Republic of China.

Department of Mathematics, Zhejiang University, Hangzhou, People's Republic of China.

Örebro University, School of Science and Technology.

This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

Funding Agencies:

Alexander von Humboldt foundation

Natural Science Foundation of China 11401304 11571311

Available from: 2018-04-27 Created: 2018-04-27 Last updated: 2018-05-14Bibliographically approvedOpen this publication in new window or tab >>A modified coupled complex boundary method for an inverse chromatography problem### Cheng, Xiaoliang

### Lin, Guangliang

### Zhang, Ye

### Gong, Rongfang

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); ### Gulliksson, Mårten

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_6_j_idt188_j_idt202",{id:"formSmash:j_idt184:6:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2018 (English)In: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 26, no 1, p. 33-49Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Walter de Gruyter, 2018
##### Keywords

Chromatography; adsorption isotherm; inverse problem; coupled complex boundary method; Tikhonov regularization
##### National Category

Computational Mathematics
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:oru:diva-58691 (URN)10.1515/jiip-2016-0057 (DOI)000423813300003 ()
#####

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##### Funder

Swedish Research Council, 2015-04627
##### Note

Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, China.

Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, China.

Örebro University, School of Science and Technology. Department of Mathematics.

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China.

Örebro University, School of Science and Technology. Department of Mathematics.

Adsorption isotherms are the most important parameters in rigorous models of chromatographic processes. In this paper, in order to recover adsorption isotherms, we consider a coupled complex boundary method (CCBM), which was previously proposed for solving an inverse source problem [2]. With CCBM, the original boundary fitting problem is transferred to a domain fitting problem. Thus, this method has advantages regarding robustness and computation in reconstruction. In contrast to the traditional CCBM, for the sake of the reduction of computational complexity and computational cost, the recovered adsorption isotherm only corresponds to the real part of the solution of a forward complex initial boundary value problem. Furthermore, we take into account the position of the profiles and apply the momentum criterion to improve the optimization progress. Using Tikhonov regularization, the well-posedness, convergence properties and regularization parameter selection methods are studied. Based on an adjoint technique, we derive the exact Jacobian of the objective function and give an algorithm to reconstruct the adsorption isotherm. Finally, numerical simulations are given to show the feasibility and efficiency of the proposed regularization method.

Funding Agencies:

NSFC 11571311 11401304

STINT IB2015-5989

KK HOG 20150233

AForsk 15/497

Available from: 2017-07-17 Created: 2017-07-17 Last updated: 2018-02-12Bibliographically approvedOpen this publication in new window or tab >>A regularizing Kohn–Vogelius formulation for the model-free adsorption isotherm estimation problem in chromatography### Lin, G.

### Zhang, Ye

### Cheng, X.

### Gulliksson, Mårten

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); ### Forssén, P.

### Fornstedt, T.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_7_j_idt188_j_idt202",{id:"formSmash:j_idt184:7:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2018 (English)In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 97, no 1, p. 13-40Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Taylor & Francis Group, 2018
##### Keywords

Chromatography; adsorption isotherm; inverse problem; Kohn–Vogelius method; convergence rate
##### National Category

Computational Mathematics
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:oru:diva-55172 (URN)10.1080/00036811.2017.1284311 (DOI)000417831700003 ()2-s2.0-85011298596 (Scopus ID)
#####

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##### Funder

Knowledge Foundation, 20150233Swedish Research Council, 2015-04627
##### Note

Department of Mathematics, Zhejiang University, Hangzhou, China.

Örebro University, School of Science and Technology. Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.

Department of Mathematics, Zhejiang University, Hangzhou, China.

Örebro University, School of Science and Technology.

Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.

Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.

Competitive adsorption isotherms must be estimated in order to simulate and optimize modern continuous modes of chromatography in situations where experimental trial-and-error approaches are too complex and expensive. The inverse method is a numeric approach for the fast estimation of adsorption isotherms directly from overloaded elution profiles. However, this identification process is usually ill-posed. Moreover, traditional model-based inverse methods are restricted by the need to choose an appropriate adsorption isotherm model prior to estimate, which might be very hard for complicated adsorption behavior. In this study, we develop a Kohn–Vogelius formulation for the model-free adsorption isotherm estimation problem. The solvability and convergence for the proposed inverse method are studied. In particular, using a problem-adapted adjoint, we obtain a convergence rate under substantially weaker and more realistic conditions than are required by the general theory. Based on the adjoint technique, a numerical algorithm for solving the proposed optimization problem is developed. Numerical tests for both synthetic and real-world problems are given to show the efficiency of the proposed regularization method.

Funding Agencies:

AForsk Foundation 15/497

STINT IB2015-5989

NSFC 11571311

Available from: 2017-02-01 Created: 2017-02-01 Last updated: 2018-01-03Bibliographically approvedOpen this publication in new window or tab >>An adaptive regularization algorithm for recovering the rate constant distribution from biosensor data### Zhang, Ye

### Fornstedt, T.

### Gulliksson, Mårten

### Dai, X.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 26, no 10, p. 1464-1489Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Oxfordshire, United Kingdom: Taylor & Francis, 2018
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:oru:diva-64002 (URN)10.1080/17415977.2017.1411912 (DOI)000438638300005 ()2-s2.0-85037706652 (Scopus ID)
#####

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##### Funder

Swedish Research Council, 2015-04627
##### Note

Örebro University, School of Science and Technology. Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.

Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden.

Örebro University, School of Science and Technology.

School of Computing Science, Zhejiang University City College, Hangzhou, China.

We present here the theoretical results and numerical analysis of a regularization method for the inverse problem of determining the rate constant distribution from biosensor data. The rate constant distribution method is a modern technique to study binding equilibrium and kinetics for chemical reactions. Finding a rate constant distribution from biosensor data can be described as a multidimensional Fredholm integral equation of the first kind, which is a typical ill-posed problem in the sense of J. Hadamard. By combining regularization theory and the goal-oriented adaptive discretization technique,we develop an Adaptive Interaction Distribution Algorithm (AIDA) for the reconstruction of rate constant distributions. The mesh refinement criteria are proposed based on the *a posteriori *error estimation of the finite element approximation. The stability of the obtained approximate solution with respect to data noise is proven. Finally, numerical tests for both synthetic and real data are given to show the robustness of the AIDA.

Funding Agencies:

Swedish Knowledge Foundation (KKS) project HOG

AForsk Foundation

Available from: 2018-01-10 Created: 2018-01-10 Last updated: 2018-08-30Bibliographically approvedOpen this publication in new window or tab >>Excitation spectrum of a mixture of two Bose gases confined in a ring potential with interaction asymmetry### Roussou, Alexandra

### Smyrnakis, Ioannis

### Magiropoulos, Manolis

### Efremidis, Nikolaos

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); ### Kavoulakis, Georgios

### Sandin, Patrik

### Ögren, Magnus

### Gulliksson, Mårten

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_9_j_idt188_j_idt202",{id:"formSmash:j_idt184:9:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2018 (English)In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 20, article id 045006Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Institute of Physics (IOP), 2018
##### Keywords

Bose-Einstein condensation; mixtures; superfluidity; vector solitons
##### National Category

Computational Mathematics Atom and Molecular Physics and Optics Condensed Matter Physics
##### Research subject

Physics; Mathematics
##### Identifiers

urn:nbn:se:oru:diva-65601 (URN)10.1088/1367-2630/aab599 (DOI)000430345700001 ()
#####

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Available from: 2018-03-09 Created: 2018-03-09 Last updated: 2018-05-02Bibliographically approved

Department of Applied Mathematics, University of Crete, Heraklion, Greece.

Technological Education Institute of Crete, Heraklion, Greece.

Technological Education Institute of Crete, Heraklion, Greece.

Department of Applied Mathematics, University of Crete, Heraklion, Greece.

Technological Education Institute of Crete, Heraklion, Greece.

Örebro University, School of Science and Technology.

Örebro University, School of Science and Technology.

Örebro University, School of Science and Technology.

We study the rotational properties of a two-component Bose-Einstein condensed gas of distinguishable atoms which are confined in a ring potential using both the mean-field approximation, as well as the method of diagonalization of the many-body Hamiltonian. We demonstrate that the angular momentum may be given to the system either via single-particle, or "collective" excitation. Furthermore, despite the complexity of this problem, under rather typical conditions the dispersion relation takes a remarkably simple and regular form. Finally, we argue that under certain conditions the dispersion relation is determined via collective excitation. The corresponding many-body state, which, in addition to the interaction energy minimizes also the kinetic energy, is dictated by elementary number theory.