Keijo Ruotsalainen - Academia.edu (original) (raw)
Papers by Keijo Ruotsalainen
Comptes Rendus Mécanique, 2015
ABSTRACT For the honeycomb lattice of quantum waveguides, the limit passage is performed when the... more ABSTRACT For the honeycomb lattice of quantum waveguides, the limit passage is performed when the relative thickness h of ligaments tends to zero and the asymptotic structure of the spectrum of the Dirichlet Laplacian is described.
Different clustering algorithms are widely used for image segmentation. In recent years, spectral... more Different clustering algorithms are widely used for image segmentation. In recent years, spectral clustering has risen among the most popular methods in the field of clustering and has also been included in many image segmentation algorithms. However, the classical spectral clustering algorithms have their own weaknesses, which affect directly to the accuracy of the data partitioning. In this paper, a novel clustering method, that overcomes some of these problems, is proposed. The method is based on tracking the time evolution of the connections between data points inside each cluster separately. This enables the algorithm proposed to perform well also in the case when the clusters have different inner geometries. In addition to that, this method suits especially well for image segmentation using the color and texture information extracted from small regions called patches around each pixel. The nature of the algorithm allows to join the segmentation results reliably from different ...
Journal of Mathematical Physics
We study waveguides with two right-angled bends. These waveguides are in shape of letter Z or alt... more We study waveguides with two right-angled bends. These waveguides are in shape of letter Z or alternatively C. For both cases, we assume the semi-infinite arms of waveguides to be of unit width. These arms are connected to each other by a rectangle with side lengths H and L. We consider the Dirichlet boundary value problem for Laplacian and study the spectrum of the corresponding operator. It is shown that the total multiplicity of the discrete spectrum depends on the parameters H and L. In particular, for the width H = 1, we compare the relation between the eigenvalues of both waveguides and moreover, we observe that the monotonicity in height L of the first eigenvalue of the Z-shaped waveguide is not achieved while the question of the monotonicity of the second eigenvalue remains open. The eigenvalues in the C-shaped waveguide are monotone. We construct and justify the asymptotics of the eigenvalues for the cases H = 1, L -> infinity, H = 1, L -> 1 + 0, and H, L -> infini...
Communications in Computer and Information Science, 2014
ABSTRACT An image segmentation process can be considered as a process of solving a pixel clusteri... more ABSTRACT An image segmentation process can be considered as a process of solving a pixel clustering problem. This paper represents and combines a new clustering algorithm that we call as a Diffusion Tracking (DT) algorithm and a new clustering based image segmentation algorithm. The DT algorithm is related to classical spectral clustering techniques but overcomes some of their problems which guarantees a better starting point for the image segmentation process. The image segmentation process introduced in this paper joins seamlessly to the DT algorithm but can also be used together with other clustering methods like k-means. The segmentation algorithm is based on oversampling pixels from classified patches and using simple statistical methods for joining the information collected. The experimental results at the end of this paper show clearly that the algorithms proposed suit well also for very demanding segmentation tasks.
Journal of Mathematical Analysis and Applications
The starting point of our study is the knowledge that certain surface piercing bodies support a t... more The starting point of our study is the knowledge that certain surface piercing bodies support a trapped mode, i.e. an embedded eigenvalue in the continuous spectrum. In the framework of the two-dimensional theory of linear water waves, we investigate the question whether a trapped mode still exists after the small perturbation of the body contours. The perturbation of the obstacle is performed by a linear combination of appropriate profile functions. The coefficients of the profile functions and a perturbation parameter of the eigenvalue form a parameter space which controls the embedded eigenvalue as well as the geometry of the water domain. Based on the concept of enforced stability of embedded eigenvalues in the continuous spectrum, we will show that the trapped mode is preserved in the small perturbation, if the profile functions fulfil problem dependent orthogonalization and normalization conditions. The argumentation relies on a sufficient condition for the existence of a trap...
Thermosense XXI, 1999
ABSTRACT
Integral Methods in Science and Engineering, Volume 2, 2009
ABSTRACT Condition monitoring is becoming more and more important in various areas of industry, d... more ABSTRACT Condition monitoring is becoming more and more important in various areas of industry, due to the demands of efficiency and prolonged continuous running time of machinery. For example, in the Finnish pulp industry there have been demands for continuous running times of up to 18 months. To be cost efficient, maintenance operations should be carried out during scheduled downtime; hence, early and reliable fault detection is very important. Vibration measurements have been the central tool in condition monitoring. Signals from displacement, velocity, and acceleration sensors have been used to estimate the condition of the machinery. For example, increased rootmean- square (RMS) values or changes in the frequency spectrum may indicate different types of faults, such as unbalance, misalignment, and bearing defects. In rolling element bearings, a local fault on the raceways or on the rolling elements causes wideband bursts in the vibration signal measured from the bearing house. When the fault is on the inner race, the time interval between the bursts corresponds to the shaft frequency. If the shaft is rotating slowly, as in pulp washers, these bursts occur at long intervals and may be hard to detect from the frequency spectrum or the RMS value of the signal.
Integral Methods in Science and Engineering, Volume 2, 2009
In this chapter, we discuss the numerical solution of the space-time boundary integral equation S... more In this chapter, we discuss the numerical solution of the space-time boundary integral equation SG</font >u G</font > (x, t) = ò</font >t0 ò</font >G</font > uG</font > (y, t</font >)E(x -</font > y, t -</font > t</font >)dsy dt</font > = f(x, t), x Î</font > G</font >, 0 t T,S_{\Gamma u \Gamma} (x, t) = \int^t_0 \int_\Gamma u_\Gamma
Zeitschrift für angewandte Mathematik und Physik, 2013
ABSTRACT Trapped modes in the linearized water wave problem are localized free oscillations in an... more ABSTRACT Trapped modes in the linearized water wave problem are localized free oscillations in an unbounded fluid with a free surface. For sometime, it has been known that certain structures, fixed or freely floating, can support such modes. In this paper, we consider the problem on a channel, which consists of a finite part and two cylindrical outlets into infinity. The finite (bounded) part may contain some submerged and/or surface-piercing bodies. Since the ordinary scattering matrix can by no means contribute any information on trapped modes, we introduce the fictitious scattering operator and present a criterion for the existence of trapped modes. The criterion states that the number of trapped modes is the difference of the multiplicities of the eigenvalue 1 of the fictitious scattering operator and the eigenvalue −i of the scattering matrix.
Sbornik: Mathematics, 2012
The existence of an eigenvalue embedded in the continuous spectrum is proved for the Neumann prob... more The existence of an eigenvalue embedded in the continuous spectrum is proved for the Neumann problem for Helmholtz's equation in a two-dimensional waveguide with two outlets to infinity which are half-strips of width 1 and 1 − ε, where ε > 0 is a small parameter. The width function of the part of the waveguide connecting these outlets is of order √ ε; it is defined as a linear combination of three fairly arbitrary functions, whose coefficients are obtained from a certain nonlinear equation. The result is derived from an asymptotic analysis of an auxiliary object, the augmented scattering matrix.
The Quarterly Journal of Mechanics and Applied Mathematics, 2014
We consider the linear water-wave problem in a periodic channel which consists of infinitely many... more We consider the linear water-wave problem in a periodic channel which consists of infinitely many identical containers connected with apertures of width ǫ. Motivated by applications to surface wave propagation phenomena, we study the band-gap structure of the continuous spectrum. We show that for small apertures there exists a large number of gaps and also find asymptotic formulas for the position of the gaps as ǫ → 0: the endpoints are determined within corrections of order ǫ 3/2 . The width of the first bands is shown to be O(ǫ). Finally, we give a sufficient condition which guarantees that the spectral bands do not degenerate into eigenvalues of infinite multiplicity.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012
ABSTRACT In this paper, the essential spectrum of the linear problem on water waves in a water la... more ABSTRACT In this paper, the essential spectrum of the linear problem on water waves in a water layer and in a channel with a gentl corrugated bottom is studied. We show that, under a certain geometric condition, the essential spectrum has spectral gaps. In other words, there exist intervals in the positive real semi-axis that are free of the spectrum but have their endpoint in it. The position and the length of the gaps are found out by applying an asymptotic analysis to the model problem in th periodicity cell.
Physical Review E, 2004
The Schrödinger equation of hydrogenic atoms and the Hartree-Fock equations of some many-electron... more The Schrödinger equation of hydrogenic atoms and the Hartree-Fock equations of some many-electron atoms are solved using interpolating wavelets as basis functions. The nonstandard operator form is used to compute operators in basis sets including multiple resolution levels. We introduce an algorithm for converting matrices from nonstandard operator form to standard operator form. We also consider the different components of the Hamiltonian and Fock operators separately and derive analytic formulas for their evaluation. Extension to many-electron atoms is done within the Hartree-Fock formalism. Convergence of atomic parameters such as orbital eigenvalues with respect to the number of resolution levels is inspected numerically for hydrogenlike atoms (ions) and some light many-electron atoms (helium, lithium, beryllium, neon, sodium, magnesium, and argon).
physica status solidi (b), 2006
Published online zzz PACS 71.15.Ap, 71.15.Dx A characteristic feature of the state-of-the-art of ... more Published online zzz PACS 71.15.Ap, 71.15.Dx A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the main approaches include finite-difference methods, various types of finite-elements and wavelets. This paper reports on the results of several code development projects that approach problems related to the electronic structure using these three different discretization methods. We review the ideas behind these methods, give examples of their applications, and discuss their similarities and differences.
Numerical Algorithms, 2011
The boundary element spline collocation method is studied for the time-fractional diffusion equat... more The boundary element spline collocation method is studied for the time-fractional diffusion equation in a bounded two-dimensional domain. We represent the solution as the single layer potential which leads to a Volterra integral equation of the first kind. We discretize the boundary integral equation with the spline collocation method on uniform meshes both in spatial and time variables. In the stability analysis we utilize the Fourier analysis technique developed for anisotropic pseudodifferential equations. We prove that the collocation solution is quasi-optimal under some stability condition for the mesh parameters. We have to assume that the mesh parameter in time satisfies (h t = ch 2 α ), where (h) is the spatial mesh parameter.
Mathematical Methods in the Applied Sciences, 1993
... the Neumann-type initial boundary value problem with B(@) = a,@l,r. In (ll), Q c Rz is a boun... more ... the Neumann-type initial boundary value problem with B(@) = a,@l,r. In (ll), Q c Rz is a boundeddomain with a ... operator retains, in the anisotropic Sobolev spaces, all the essential ellipticity properties of the corresponding single-layer potential operator for the Laplace equation. ...
Математический сборник, 2012
Journal of Integral Equations and Applications, 1992
Recently, Galerkin and collocation methods have been analyzed in connection with the nonlinear bo... more Recently, Galerkin and collocation methods have been analyzed in connection with the nonlinear boundary integral equation which arises in solving the potential problem with a nonlinear boundary condition. Considering this model equation, we propose here a discretized scheme such that the nonlinearity is replaced by its L 2 -orthogonal projection. We are able to show that this approximate collocation scheme preserves the theoretical L 2 -convergence. For piecewise linear continuous splines, our numerical experiments confirm the theoretical quadratic L 2 -convergence.
Comptes Rendus Mécanique, 2015
ABSTRACT For the honeycomb lattice of quantum waveguides, the limit passage is performed when the... more ABSTRACT For the honeycomb lattice of quantum waveguides, the limit passage is performed when the relative thickness h of ligaments tends to zero and the asymptotic structure of the spectrum of the Dirichlet Laplacian is described.
Different clustering algorithms are widely used for image segmentation. In recent years, spectral... more Different clustering algorithms are widely used for image segmentation. In recent years, spectral clustering has risen among the most popular methods in the field of clustering and has also been included in many image segmentation algorithms. However, the classical spectral clustering algorithms have their own weaknesses, which affect directly to the accuracy of the data partitioning. In this paper, a novel clustering method, that overcomes some of these problems, is proposed. The method is based on tracking the time evolution of the connections between data points inside each cluster separately. This enables the algorithm proposed to perform well also in the case when the clusters have different inner geometries. In addition to that, this method suits especially well for image segmentation using the color and texture information extracted from small regions called patches around each pixel. The nature of the algorithm allows to join the segmentation results reliably from different ...
Journal of Mathematical Physics
We study waveguides with two right-angled bends. These waveguides are in shape of letter Z or alt... more We study waveguides with two right-angled bends. These waveguides are in shape of letter Z or alternatively C. For both cases, we assume the semi-infinite arms of waveguides to be of unit width. These arms are connected to each other by a rectangle with side lengths H and L. We consider the Dirichlet boundary value problem for Laplacian and study the spectrum of the corresponding operator. It is shown that the total multiplicity of the discrete spectrum depends on the parameters H and L. In particular, for the width H = 1, we compare the relation between the eigenvalues of both waveguides and moreover, we observe that the monotonicity in height L of the first eigenvalue of the Z-shaped waveguide is not achieved while the question of the monotonicity of the second eigenvalue remains open. The eigenvalues in the C-shaped waveguide are monotone. We construct and justify the asymptotics of the eigenvalues for the cases H = 1, L -> infinity, H = 1, L -> 1 + 0, and H, L -> infini...
Communications in Computer and Information Science, 2014
ABSTRACT An image segmentation process can be considered as a process of solving a pixel clusteri... more ABSTRACT An image segmentation process can be considered as a process of solving a pixel clustering problem. This paper represents and combines a new clustering algorithm that we call as a Diffusion Tracking (DT) algorithm and a new clustering based image segmentation algorithm. The DT algorithm is related to classical spectral clustering techniques but overcomes some of their problems which guarantees a better starting point for the image segmentation process. The image segmentation process introduced in this paper joins seamlessly to the DT algorithm but can also be used together with other clustering methods like k-means. The segmentation algorithm is based on oversampling pixels from classified patches and using simple statistical methods for joining the information collected. The experimental results at the end of this paper show clearly that the algorithms proposed suit well also for very demanding segmentation tasks.
Journal of Mathematical Analysis and Applications
The starting point of our study is the knowledge that certain surface piercing bodies support a t... more The starting point of our study is the knowledge that certain surface piercing bodies support a trapped mode, i.e. an embedded eigenvalue in the continuous spectrum. In the framework of the two-dimensional theory of linear water waves, we investigate the question whether a trapped mode still exists after the small perturbation of the body contours. The perturbation of the obstacle is performed by a linear combination of appropriate profile functions. The coefficients of the profile functions and a perturbation parameter of the eigenvalue form a parameter space which controls the embedded eigenvalue as well as the geometry of the water domain. Based on the concept of enforced stability of embedded eigenvalues in the continuous spectrum, we will show that the trapped mode is preserved in the small perturbation, if the profile functions fulfil problem dependent orthogonalization and normalization conditions. The argumentation relies on a sufficient condition for the existence of a trap...
Thermosense XXI, 1999
ABSTRACT
Integral Methods in Science and Engineering, Volume 2, 2009
ABSTRACT Condition monitoring is becoming more and more important in various areas of industry, d... more ABSTRACT Condition monitoring is becoming more and more important in various areas of industry, due to the demands of efficiency and prolonged continuous running time of machinery. For example, in the Finnish pulp industry there have been demands for continuous running times of up to 18 months. To be cost efficient, maintenance operations should be carried out during scheduled downtime; hence, early and reliable fault detection is very important. Vibration measurements have been the central tool in condition monitoring. Signals from displacement, velocity, and acceleration sensors have been used to estimate the condition of the machinery. For example, increased rootmean- square (RMS) values or changes in the frequency spectrum may indicate different types of faults, such as unbalance, misalignment, and bearing defects. In rolling element bearings, a local fault on the raceways or on the rolling elements causes wideband bursts in the vibration signal measured from the bearing house. When the fault is on the inner race, the time interval between the bursts corresponds to the shaft frequency. If the shaft is rotating slowly, as in pulp washers, these bursts occur at long intervals and may be hard to detect from the frequency spectrum or the RMS value of the signal.
Integral Methods in Science and Engineering, Volume 2, 2009
In this chapter, we discuss the numerical solution of the space-time boundary integral equation S... more In this chapter, we discuss the numerical solution of the space-time boundary integral equation SG</font >u G</font > (x, t) = ò</font >t0 ò</font >G</font > uG</font > (y, t</font >)E(x -</font > y, t -</font > t</font >)dsy dt</font > = f(x, t), x Î</font > G</font >, 0 t T,S_{\Gamma u \Gamma} (x, t) = \int^t_0 \int_\Gamma u_\Gamma
Zeitschrift für angewandte Mathematik und Physik, 2013
ABSTRACT Trapped modes in the linearized water wave problem are localized free oscillations in an... more ABSTRACT Trapped modes in the linearized water wave problem are localized free oscillations in an unbounded fluid with a free surface. For sometime, it has been known that certain structures, fixed or freely floating, can support such modes. In this paper, we consider the problem on a channel, which consists of a finite part and two cylindrical outlets into infinity. The finite (bounded) part may contain some submerged and/or surface-piercing bodies. Since the ordinary scattering matrix can by no means contribute any information on trapped modes, we introduce the fictitious scattering operator and present a criterion for the existence of trapped modes. The criterion states that the number of trapped modes is the difference of the multiplicities of the eigenvalue 1 of the fictitious scattering operator and the eigenvalue −i of the scattering matrix.
Sbornik: Mathematics, 2012
The existence of an eigenvalue embedded in the continuous spectrum is proved for the Neumann prob... more The existence of an eigenvalue embedded in the continuous spectrum is proved for the Neumann problem for Helmholtz's equation in a two-dimensional waveguide with two outlets to infinity which are half-strips of width 1 and 1 − ε, where ε > 0 is a small parameter. The width function of the part of the waveguide connecting these outlets is of order √ ε; it is defined as a linear combination of three fairly arbitrary functions, whose coefficients are obtained from a certain nonlinear equation. The result is derived from an asymptotic analysis of an auxiliary object, the augmented scattering matrix.
The Quarterly Journal of Mechanics and Applied Mathematics, 2014
We consider the linear water-wave problem in a periodic channel which consists of infinitely many... more We consider the linear water-wave problem in a periodic channel which consists of infinitely many identical containers connected with apertures of width ǫ. Motivated by applications to surface wave propagation phenomena, we study the band-gap structure of the continuous spectrum. We show that for small apertures there exists a large number of gaps and also find asymptotic formulas for the position of the gaps as ǫ → 0: the endpoints are determined within corrections of order ǫ 3/2 . The width of the first bands is shown to be O(ǫ). Finally, we give a sufficient condition which guarantees that the spectral bands do not degenerate into eigenvalues of infinite multiplicity.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012
ABSTRACT In this paper, the essential spectrum of the linear problem on water waves in a water la... more ABSTRACT In this paper, the essential spectrum of the linear problem on water waves in a water layer and in a channel with a gentl corrugated bottom is studied. We show that, under a certain geometric condition, the essential spectrum has spectral gaps. In other words, there exist intervals in the positive real semi-axis that are free of the spectrum but have their endpoint in it. The position and the length of the gaps are found out by applying an asymptotic analysis to the model problem in th periodicity cell.
Physical Review E, 2004
The Schrödinger equation of hydrogenic atoms and the Hartree-Fock equations of some many-electron... more The Schrödinger equation of hydrogenic atoms and the Hartree-Fock equations of some many-electron atoms are solved using interpolating wavelets as basis functions. The nonstandard operator form is used to compute operators in basis sets including multiple resolution levels. We introduce an algorithm for converting matrices from nonstandard operator form to standard operator form. We also consider the different components of the Hamiltonian and Fock operators separately and derive analytic formulas for their evaluation. Extension to many-electron atoms is done within the Hartree-Fock formalism. Convergence of atomic parameters such as orbital eigenvalues with respect to the number of resolution levels is inspected numerically for hydrogenlike atoms (ions) and some light many-electron atoms (helium, lithium, beryllium, neon, sodium, magnesium, and argon).
physica status solidi (b), 2006
Published online zzz PACS 71.15.Ap, 71.15.Dx A characteristic feature of the state-of-the-art of ... more Published online zzz PACS 71.15.Ap, 71.15.Dx A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the main approaches include finite-difference methods, various types of finite-elements and wavelets. This paper reports on the results of several code development projects that approach problems related to the electronic structure using these three different discretization methods. We review the ideas behind these methods, give examples of their applications, and discuss their similarities and differences.
Numerical Algorithms, 2011
The boundary element spline collocation method is studied for the time-fractional diffusion equat... more The boundary element spline collocation method is studied for the time-fractional diffusion equation in a bounded two-dimensional domain. We represent the solution as the single layer potential which leads to a Volterra integral equation of the first kind. We discretize the boundary integral equation with the spline collocation method on uniform meshes both in spatial and time variables. In the stability analysis we utilize the Fourier analysis technique developed for anisotropic pseudodifferential equations. We prove that the collocation solution is quasi-optimal under some stability condition for the mesh parameters. We have to assume that the mesh parameter in time satisfies (h t = ch 2 α ), where (h) is the spatial mesh parameter.
Mathematical Methods in the Applied Sciences, 1993
... the Neumann-type initial boundary value problem with B(@) = a,@l,r. In (ll), Q c Rz is a boun... more ... the Neumann-type initial boundary value problem with B(@) = a,@l,r. In (ll), Q c Rz is a boundeddomain with a ... operator retains, in the anisotropic Sobolev spaces, all the essential ellipticity properties of the corresponding single-layer potential operator for the Laplace equation. ...
Математический сборник, 2012
Journal of Integral Equations and Applications, 1992
Recently, Galerkin and collocation methods have been analyzed in connection with the nonlinear bo... more Recently, Galerkin and collocation methods have been analyzed in connection with the nonlinear boundary integral equation which arises in solving the potential problem with a nonlinear boundary condition. Considering this model equation, we propose here a discretized scheme such that the nonlinearity is replaced by its L 2 -orthogonal projection. We are able to show that this approximate collocation scheme preserves the theoretical L 2 -convergence. For piecewise linear continuous splines, our numerical experiments confirm the theoretical quadratic L 2 -convergence.