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Edvardsson, Sverker
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Edvardsson, S., Karlsson, K. & Olin, H. (2016). corr3p_tr: A particle approach for the general three-body problem. Computer Physics Communications, 200, 259-273
Open this publication in new window or tab >>corr3p_tr: A particle approach for the general three-body problem
2016 (English)In: Computer Physics Communications, ISSN 0010-4655, E-ISSN 1879-2944, Vol. 200, p. 259-273Article in journal (Refereed) Published
Abstract [en]

This work presents a convenient way to solve the non-relativistic Schrodinger equation numerically for a general three-particle system including full correlation and mass polarization. Both Coulombic and non-Coulombic interactions can be studied. The eigensolver is based on a second order dynamical system treatment (particle method). The Hamiltonian matrix never needs to be realized. The wavefunction evolves towards the steady state solution for which the Schrodinger equation is fulfilled. Subsequent Richardson extrapolations for several meshes are then made symbolically in matlab to obtain the continuum solution. The computer C code is tested under Linux 64 bit and both double and extended precision versions are provided. Test runs are exemplified and, when possible, compared with corresponding values in the literature. The computer code is small and self contained making it unusually simple to compile and run on any system. Both serial and parallel computer runs are straight forward. Program summary Program title: corr3p_tr Catalogue identifier: AEYR_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEYR_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.ukilicence/licence.html No. of lines in distributed program, including test data, etc.: 15025 No. of bytes in distributed program, including test data, etc.: 156430 Distribution format: tar.gz Programming language: ANSI C. Computer: Linux 64bit PC. Operating system: Linux 64bit. RAM: 300 M bytes Classification: 2.7, 2.8, 2.9. Nature of problem: The Schrodinger equation for an arbitrary three -particle system is solved using finite differences and a fast particle method for the eigenvalue problem [20, 21, 23]. Solution method: A fast eigensolver is applied (see Appendix). This solver works for both symmetrical and nonsymmetrical matrices (which opens up for more accurate nonsymmetrical finite difference expressions to be applied at the boundaries). The three-particle Schrodinger equation is transformed in two major steps. First step is to introduce the function Q(r(1), (r)2, mu) = r(1)r(2)(1 - mu(2))phi(r(1), r(2), mu), where mu = cos (0(12)). The cusps (r(1) = r(2), mu = 1) are then transformed into boundary conditions. The derivatives of Qare then continuous in the whole computational space and thus the finite difference expressions are well defined. Three-particle coalescence (r(1) = r(2) = 0, mu) is treated in the same way. The second step is to replace Q(r(1), r(2), mu) with (2,root x(1)x(2))(-1)Q(x(1) x(2), mu). The space (x(1), x(2), mu) is much more appropriate for a finite difference approach since the square roots x(1) = root r(1), x(2) = root r(2) allow the boundaries to be much further out. The non-linearity of the x-grid also leads to a finer description near the nucleus and a coarser one further out thus resulting in a saving of grid points. Also, in contrast to the usual variable r(12), we have instead used mu which is an independent variable. This simplifies the mathematics and numerical treatments. Several different grids can naturally run completely independent of each other thus making parallel computations trivial. From several grid results the physical property of interest is extrapolated to continuum space. The extrapolations are made in a matlab m-script where all computations can be made symbolically so the loss of decimal figures are minimized during this process. The computer code, including correlation effects and mass polarization, is highly optimized and deals with either triangular or quadratic domains in (x(1), x(2)). Restrictions: The amount of CPU time may become unreasonable for states needing boundary conditions very far beyond the origin. Also if the condition number of the corresponding Hamiltonian matrix is very high, the number of iterations will grow. The use of double precision computations also puts a limit on the accuracy of extrapolated results to about 6-7 decimal figures. Unusual features: The numerical solver is based on a particle method presented in [20, 21, 23]. In the Appendix we provide specific details of dealing with eigenvalue problems. The program uses a 64 bit environment (Linux 64bit). Parallel runs can be made conveniently through a simple bash script. Additional comments: The discretized wavefunction is complete on every given grid. New interactions can therefore conveniently be added to the Hamiltonian without the need to seek for an appropriate basis set. Running time: Given a modern CPU such as Intel core i5 and that the outer boundary conditions of r(1) and r(2) is limited to, say 16 atomic units, the total CPU time of totally 10 grids of a serial run is typically limited to a few minutes. One can then expect about 6-7 correct figures in the extrapolated eigenvalue. A single grid of say h(1) = h(2) = h(3) = 1/16 converges in less than 1 s (with an error in the eigenvalue of about 1 percent). Parallel runs are possible and can further minimize CPU times for more demanding tasks. References: [20] S. Edvardsson, M. Gulliksson, and J. Persson.). Appl. Mech. ASME, 79 (2012) 021012. [21] S. Edvardsson, M. Neuman, P Edstrom, and H. Olin. Comp. Phys. Commun. 197 (2015) 169. [23] M. Neuman, S. Edvardsson, P. Edstrom, Opt. Lett. 40 (2015) 4325.

Keywords
Second order dynamical system, Schrodinger equation, Three-particle systems, Correlation, Mass polarization, S-states
National Category
Physical Sciences
Identifiers
urn:nbn:se:miun:diva-27245 (URN)10.1016/j.cpc.2015.10.022 (DOI)000369451900023 ()2-s2.0-84957647417 (Scopus ID)
Available from: 2016-03-21 Created: 2016-03-17 Last updated: 2017-11-30Bibliographically approved
Edvardsson, S., Neuman, M., Edström, P. & Olin, H. (2015). Solving equations through particle dynamics. Computer Physics Communications, 197, 169-181
Open this publication in new window or tab >>Solving equations through particle dynamics
2015 (English)In: Computer Physics Communications, ISSN 0010-4655, E-ISSN 1879-2944, Vol. 197, p. 169-181Article in journal (Refereed) Published
Abstract [en]

The present work evaluates a recently developed particle method (DFPM). The basic idea behind this method is to utilize a Newtonian system of interacting particles that through dissipation solves mathematical problems. We find that this second order dynamical system results in an algorithm that is among the best methods known. The present work studies large systems of linear equations. Of special interest is the wide eigenvalue spectrum. This case is common as the discretization of the continuous problem becomes dense. The convergence rate of DFPM is shown to be in parity with that of the conjugate gradient method, both analytically and through numerical examples. However, an advantage with DFPM is that it is cheaper per iteration. Another advantage is that it is not restricted to symmetric matrices only, as is the case for the conjugate gradient method. The convergence properties of DFPM are shown to be superior to the closely related approach utilizing only a first order dynamical system, and also to several other iterative methods in numerical linear algebra. The performance properties are understood and optimized by taking advantage of critically damped oscillators in classical mechanics. Just as in the case of the conjugate gradient method, a limitation is that all eigenvalues (spring constants) are required to be of the same sign. DFPM has no other limitation such as matrix structure or a spectral radius as is common among iterative methods. Examples are provided to test the particle algorithm’s merits and also various performance comparisons with existent numerical algorithms are provided.

Place, publisher, year, edition, pages
Elsevier, 2015
Keywords
Particle methods, Computational mechanics, Many-particle dynamics, System of linear equations, Dynamical functional particle method
National Category
Computational Mathematics
Identifiers
urn:nbn:se:miun:diva-26030 (URN)10.1016/j.cpc.2015.08.028 (DOI)000362919500018 ()2-s2.0-84942990585 (Scopus ID)
Available from: 2015-10-05 Created: 2015-10-05 Last updated: 2017-12-01Bibliographically approved
Neuman, M., Edvardsson, S. & Edström, P. (2015). Solving the radiative transfer equation with a mathematical particle method. Optics Letters, 40(18), 4325-4328
Open this publication in new window or tab >>Solving the radiative transfer equation with a mathematical particle method
2015 (English)In: Optics Letters, ISSN 0146-9592, E-ISSN 1539-4794, Vol. 40, no 18, p. 4325-4328Article in journal (Refereed) Published
Abstract [en]

We solve the radiative transfer equation (RTE) using a recently proposed mathematical particle method, originally developed for solving general functional equations. We show that, in the case of the RTE, it gives several advantages, such as handling arbitrary boundary conditions and phase functions and avoiding numerical instability in strongly forward-scattering media. We also solve the RTE, including fluorescence, and an example is shown with a fluorescence cascade where light is absorbed and emitted in several steps. We show that the evaluated particle method is straightforward to implement, which is in contrast with many traditional RTE solvers, but a potential drawback is the tuning of the method parameters.

Place, publisher, year, edition, pages
Optical Society of America, 2015
National Category
Computational Mathematics
Identifiers
urn:nbn:se:miun:diva-26029 (URN)10.1364/OL.40.004325 (DOI)000361556700035 ()26371927 (PubMedID)2-s2.0-84957710820 (Scopus ID)
Available from: 2015-10-05 Created: 2015-10-05 Last updated: 2017-12-01Bibliographically approved
Hellström, L. M., Biller, S.-O., Edvardsson, S. & Gradin, P. A. (2014). A theoretical and experimental study of the circular sawing process. Holzforschung, 68(3), 307-312
Open this publication in new window or tab >>A theoretical and experimental study of the circular sawing process
2014 (English)In: Holzforschung, ISSN 0018-3830, E-ISSN 1437-434X, Vol. 68, no 3, p. 307-312Article in journal (Refereed) Published
Abstract [en]

To gain further insight into the energy dissipation during the wood sawing process, a theoretical model has been developed. The model is based on the assumption that there are two basic causes for energy dissipation during sawing: the creation of a new surface and the compression of material below a saw tooth. It is assumed that both contributions can be dependent on the cutting angle (the angle between the fiber direction and the tangent to the path followed by a saw tooth) because a saw tooth changes its angle of attack during its way through a log. To determine this dependence of the dissipation on the cutting angle, a series of experiments with pine plank sawing were performed by means of different feeding rates and cutting angles while the electrical power supplied to the saw was measured. The parameters in the theoretical model were derived from the experimental findings. Finally, two tests were carried out under different conditions with respect to thickness and cutting angles and the validity of the model was confirmed concerning the prediction of the electrical power consumption.

Keywords
chipper canter, energy consumption, modeling, sawing, sawmill, surface energy
National Category
Chemical Engineering
Identifiers
urn:nbn:se:miun:diva-22593 (URN)10.1515/hf-2013-0066 (DOI)000333798400007 ()2-s2.0-84903118796 (Scopus ID)
Available from: 2014-08-19 Created: 2014-08-19 Last updated: 2017-12-05Bibliographically approved
Zhang, R., Andersson, H., Olsen, M., Hummelgård, M., Edvardsson, S., Nilsson, H.-E. & Olin, H. (2014). Piezoelectric gated ZnO nanowire diode studied by in situ TEM probing. Nano Energy, 3, 10-15
Open this publication in new window or tab >>Piezoelectric gated ZnO nanowire diode studied by in situ TEM probing
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2014 (English)In: Nano Energy, ISSN 2211-2855, Vol. 3, p. 10-15Article in journal (Refereed) Published
Abstract [en]

The piezoelectricity of ZnO nanowires has shown rising interests during the last few years and fields such as piezotronics and piezophotonics are emerging with a number of applications and devices. One such device is the piezoelectric gated ZnO nanowire diode, where the p–n junction is replaced by a dynamically created potential barrier created simply by bending the otherwise homogeneously doped nanowire. To further study this type of diode we used in situ transmission electron microscope (TEM) probing, where one electrode was fixed at the end of a ZnO nanowire and another moveable electrode was used both for bending and contacting the wire. Thereby we were able to further characterise this diode and found that the diode characteristics depended on whether the contact was made to the stretched (p-type) surface or to the compressed (n-type) surface of the wire. When the neutral line of the wire contacted, between the stretched and the compressed side, the I–V characteristics were independent on the current direction. The performance of the diodes upon different bending intensity showed a rectifying ratio up to the high value of 60:1. The diode ideality factor was found to be about 5. Moreover, the reverse breakdown voltages of the diode were measured and a local but permanent damage to the diode action was found when the voltage went over the reverse breakdown voltage. 

Place, publisher, year, edition, pages
Elsevier, 2014
Keywords
Breakdown bias, Diode, In situ TEM probing, Piezoelectric, ZnO
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:miun:diva-20156 (URN)10.1016/j.nanoen.2013.10.002 (DOI)000330915300002 ()2-s2.0-84886737106 (Scopus ID)STC (Local ID)STC (Archive number)STC (OAI)
Projects
KKS foundationthe European regional development fundLänstyrelsen Västernorrland
Available from: 2013-11-06 Created: 2013-11-06 Last updated: 2017-03-06Bibliographically approved
Neuman, M., Edvardsson, S. & Edström, P. (2013). A particle approach to the radiative transfer equation with fluorescence.
Open this publication in new window or tab >>A particle approach to the radiative transfer equation with fluorescence
2013 (English)Article in journal (Refereed) Submitted
National Category
Other Physics Topics
Identifiers
urn:nbn:se:miun:diva-18693 (URN)
Available from: 2013-04-04 Created: 2013-04-04 Last updated: 2016-12-09Bibliographically approved
Zhang, R., Andersson, H., Andersson, M., Andres, B., Edström, P., Edvardsson, S., . . . Olin, H. (2013). High-speed deposition of multilayer nanofilms using soap-film coating. In: : . Paper presented at 19th International Vacuum Congress (IVC-19), Paris, France, September 9-13 2013.
Open this publication in new window or tab >>High-speed deposition of multilayer nanofilms using soap-film coating
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2013 (English)Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

High-speed deposition of multilayer nanofilms using soap-film coating

Renyun Zhang, Henrik A. Andersson, Mattias Andersson, Britta Andres, Per Edström, Sverker Edvardsson, Sven Forsberg, Magnus Hummelgård, Niklas Johansson, Kristoffer Karlsson, Hans-Erik Nilsson, Martin Olsen, Tetsu Uesaka, Thomas Öhlund & Håkan Olin

Department of Applied Science and Design, Mid Sweden University, SE-85170 Sundsvall, Sweden

Email: renyun.zhang@miun.se or hakan.olin@miun.se

Coating1 of thin films is of importance for making functionalized surfaces with applications in many fields from electronics to consumer packaging. To decrease the cost, large scale roll-to-roll2 coating techniques are usually done at high speed, for example, ordinary printing paper is coated at a speed of tens of meters per second by depositing micrometer thick layers of clay. However, nanometer thin films are harder to coat at high speed by wet-chemical methods, requiring special roll-to-roll vacuum techniques3 with the cost of higher complexity.

Here, we report a simple wet chemical method for high-speed coating of films down to molecular thicknesses, called soap-film coating (SFC)4. The technique is based on forcing a substrate through a soap film that contains nanomaterials. In the simplest laboratory version, the films can be deposited by a hand-coating procedure set up in a couple of minutes. The method is quite general molecules or nanomaterials or sub-micrometer materials (Figure 1) with thicknesses ranging from less than a monolayer to several layers at speeds up to meters per second. The applications of soap-film coating is quite wide an we will show solar cells, electrochromic devices, optical nanoparticle crystals, and nano-film devices. We believe that the soap-film coating method is potentially important for industrial-scale nanotechnology.

Fig. 1. Soap film coating of nanoparticles, layered materials, nanowires, and molecules. a sub-monolayer 240 nm silica nanoparticle (scale bar 2 µm) b monolayer c double layer. d monolayer gold nanoparticles. e single layer TiO2 nanoparticles. f sub-monolayer polystyrene (scale 2 µm), g monolayer of polystyrene. h triple-layer of polystyrene. i monolayer of Ferritin.  j AFM image of <1.5 layer GO film (3 µm x 2 µm). k clay on glass (scale 2 µm). l SFC coated nanocellulose. m Absorbance spectra Rhodamine B on a glass slide. AFM of SDS layers n (2 µm x 1.5 µm) and o (20 µm x 15 µm).

References

  1. Tracton, A. A. Coating Technology Handbook (CRC Press, Boca Raton, 2006).

  2. Ohring, M. Materials science of thin films. (Academic press., 2001).

  3. Charles, B. Vacuum deposition onto webs, films and foils. (William Andrew, 2011).

Zhang, R. Y., Andersson, H. A., Andersson, M., Andres, B., Edström, P., Edvardsson, S., Forsberg, S., Hummelgård, M., Johansson, N., Karlsson, K., Nilsson, H.-E., Olsen, M., Uesaka, T., Öhlund, T., Olin H. Soap film coating: High-speed deposition of multilayer nanofilms. Submitted.

National Category
Natural Sciences
Identifiers
urn:nbn:se:miun:diva-20338 (URN)STC (Local ID)STC (Archive number)STC (OAI)
Conference
19th International Vacuum Congress (IVC-19), Paris, France, September 9-13 2013
Available from: 2013-11-27 Created: 2013-11-27 Last updated: 2016-10-20Bibliographically approved
Zhang, R., Andersson, H., Andersson, M., Andres, B., Edlund, H., Edström, P., . . . Olin, H. (2013). Soap-film coating: High-speed deposition of multilayer nanofilms. Scientific Reports, 3, Art. no. 1477
Open this publication in new window or tab >>Soap-film coating: High-speed deposition of multilayer nanofilms
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2013 (English)In: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 3, p. Art. no. 1477-Article in journal (Refereed) Published
Abstract [en]

The coating of thin films is applied in numerous fields and many methods are employed for the deposition of these films. Some coating techniques may deposit films at high speed; for example, ordinary printing paper is coated with micrometre-thick layers of clay at a speed of tens of meters per second. However, to coat nanometre thin films at high speed, vacuum techniques are typically required, which increases the complexity of the process. Here, we report a simple wet chemical method for the high-speed coating of films with thicknesses at the nanometre level. This soap-film coating technique is based on forcing a substrate through a soap film that contains nanomaterials. Molecules and nanomaterials can be deposited at a thickness ranging from less than a monolayer to several layers at speeds up to meters per second. We believe that the soap-film coating method is potentially important for industrial-scale nanotechnology.

Place, publisher, year, edition, pages
Nature Publishing Group: , 2013
Keywords
Electronic devices; Surfaces, interfaces and thin films; Nanometrology; Design, synthesis and processing
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:miun:diva-18627 (URN)10.1038/srep01477 (DOI)000316249300008 ()23503102 (PubMedID)2-s2.0-84875767174 (Scopus ID)STC (Local ID)STC (Archive number)STC (OAI)
Projects
We acknowledge support from the Sundsvall Community, Länstyrelsen Västernorrland, KK foundation, and EU Regional funds.
Funder
Knowledge FoundationEU, European Research Council
Available from: 2013-03-21 Created: 2013-03-19 Last updated: 2017-12-06Bibliographically approved
Edvardsson, S., Gradin, P., Isaksson, P. & Gulliksson, M. (2012). A Note on Wet Paper Web Adhesion Strength. Journal of Testing and Evaluation, 40(4), 682-686
Open this publication in new window or tab >>A Note on Wet Paper Web Adhesion Strength
2012 (English)In: Journal of Testing and Evaluation, ISSN 0090-3973, E-ISSN 1945-7553, Vol. 40, no 4, p. 682-686Article in journal (Refereed) Published
Abstract [en]

This work is concerned with the determination of the adhesion strength between a paper web and an adhesive surface. Edvardsson et al. [Edvardsson, S., Gradin, P., and Isaksson, P., "On Dissipative Effects of Paper Web Adhesion Strength," Int. J. Solids Struct., Vol. 48(1), 2011, pp. 24-30] suggested recently a model that takes into account the energy dissipation caused by elastic plastic deformation in the bent structure of a paper specimen. This model is further developed and investigated in the present work. A linear relation in plastic dissipation is discovered facilitating a novel analysis of the peeling tension and a more convenient determination of the proper adhesion strength. Industrial relevant examples are made with wet newsprint and kraft stock. A straightforward experimental procedure for determining the consistent adhesion strength is suggested. It is found that the agreement between the model and the experimental observations is good.

Keywords
adhesion strength, paper web, peeling test
National Category
Physical Sciences
Identifiers
urn:nbn:se:miun:diva-17064 (URN)10.1520/JTE103851 (DOI)000307424100020 ()2-s2.0-84864119770 (Scopus ID)
Available from: 2012-10-01 Created: 2012-09-26 Last updated: 2017-12-07Bibliographically approved
Gulliksson, M., Edvardsson, S. & Lind, A. (2012). The dynamical functional method. Arxiv
Open this publication in new window or tab >>The dynamical functional method
2012 (English)Other (Other academic)
Place, publisher, year, pages
Arxiv, 2012
National Category
Computational Mathematics
Identifiers
urn:nbn:se:miun:diva-18691 (URN)
Available from: 2013-04-08 Created: 2013-04-04 Last updated: 2013-04-22Bibliographically approved
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