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  • 151.
    Ibragimov, Nail
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Ibragimov, R.N.
    Bifurcation of Nonlinear Conservation Laws from the Classical Energy Conservation Law for Internal Gravity Waves in Cylindrical Wave Field2013In: Mathematical Modelling of Natural Phenomena, ISSN 0973-5348, E-ISSN 1760-6101, Vol. 8, no 5, p. 119-130Article in journal (Refereed)
    Abstract [en]

    New conservation laws bifurcating from the classical form of conservation laws are constructed to the nonlinear Boussinesq model describing internal Kelvin waves propagating in a cylindrical wave field of an uniformly stratified water affected by the earth's rotation. The obtained conservation laws are different from the well known energy conservation law for internal waves and they are associated with symmetries of the Boussinesq model. Particularly, it is shown that application of Lie group analysis provide three infinite sets of nontrivial integral conservation laws depending on two arbitrary functions, namely a(t, theta),b(t, r) and an arbitrary function c(t, theta, r) which is given implicitly as a nontrivial solution of a partial differential equation involving a(t, theta) and b(t,r).

  • 152. Ibragimov, Nail
    et al.
    Sophocleous, C.Damianou, P.A.
    Proceedings of the 10th International conference on “Modern group Analysis”. Larnaca, Cyprus, 20042004Other (Other academic)
    Abstract [en]

    This book contains 33 papers presented at the 10th International conference "Modern Group Analysis" held in Larnaca, Cyprus, during 24-31 October 2004. All papers have been reviewed by two independent referees.

  • 153. Ibragimov, Ranis
    et al.
    Ibragimov, Nail H.
    Effects of rotation on self-resonant internal gravity waves in the ocean2010In: Ocean Modelling, ISSN 1463-5003, E-ISSN 1463-5011, Vol. 31, no 3-4Article in journal (Refereed)
    Abstract [en]

    The Resonant Triad Model (RTM) developed in (Ibragimov, 2007), is used to study the Thorpe’s problem (Thorpe, 1997) on the existence of self-resonant internal waves, i.e., the waves for which a resonant interaction occurs at second order between the incident and reflected internal waves off slopes. The RTM represents the extension of the McComas and Bretherton’s three wave hydrostatic model (McComas and Bretherton, 1977) which ignores the effects of the earth’s rotation to the case of the non-hydrostatic analytical model involving arbitrarily large number of rotating internal waves with frequencies spanning the range of possible frequencies, i.e., between the maximum of the buoyancy frequency (vertical motion) and a minimum of the inertial frequency (horizontal motion). The present analysis is based on classification of resonant interactions into the sum, middle and difference interaction classes. It is shown in this paper that there exists a certain value of latitude, which is classified as the singular latitude, at which the coalescence of the middle and difference interaction classes occurs. Such coalescence, which apparently had passed unnoticed before, can be used to study the Thorpe’s problem on the existence of selfresonant waves. In particular, it is shown that the value of the bottom slope at which the second-order frequency and wave number components of the incident and reflected waves satisfy the internal wave dispersion relation can be approximated by two latitude-dependent parameters in the limiting case when latitude approaches its singular value. Since the existence of a such singular latitude is generic for resonant triad interactions, a question on application of the RTM to the modeling of enhanced mixing in the vicinity of ridges in the ocean arises.

  • 154. Ilie, Dragos
    Gnutella Network Traffic: Measurements and Characteristics2006Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    Wide availability of computing resources at the edge of the network has lead to the appearance of new services based on peer-to-peer architectures. In a peer-to-peer network nodes have the capability to act both as client and server. They self-organize and cooperate with each other to perform more efficiently operations related to peer discovery, content search and content distribution. The main goal of this thesis is to obtain a better understanding of the network traffic generated by Gnutella peers. Gnutella is a well-known, heavily decentralized file-sharing peer-to-peer network. It is based on open protocol specifications for peer signaling, which enable detailed measurements and analysis down to individual messages. File transfers are performed using HTTP. An 11-days long Gnutella link-layer packet trace collected at BTH is systematically decoded and analyzed. Analysis results include various traffic characteristics and statistical models. The emphasis for the characteristics has been on accuracy and detail, while for the traffic models the emphasis has been on analytical tractability and ease of simulation. To the author's best knowledge this is the first work on Gnutella that presents statistics down to message level. The results show that incoming requests to open a session follow a Poisson distribution. Incoming messages of mixed types can be described by a compound Poisson distribution. Mixture distribution models for message transfer rates include a heavy-tailed component.

  • 155. Ilie, Dragos
    et al.
    Erman, David
    Popescu, Adrian
    Transfer Rate Models for Gnutella Signaling Traffic2006Conference paper (Refereed)
    Abstract [en]

    This paper reports on transfer rate models for the Gnutella signaling protocol. New results on message-level and IP-level rates are presented. The models are based on traffic captured at the Blekinge Institute of Technology (BTH) campus in Sweden and offer several levels of granularity: message type, application layer and network layer. The aim is to obtain parsimonous models suitable for analysis and simulation of P2P workload.

  • 156. Kaltenborn, B.
    et al.
    Emmelin, Lars
    Bruken av Femundsmarka nasjonalpark – en studie 1985 – 19982004Report (Other academic)
  • 157.
    Kazhura, Yury
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Worosz, Heather
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Souza, Paulo Bento Maffei de
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Kommunal hållbar utveckling i Baltik havets region2005Independent thesis Advanced level (degree of Master (One Year))Student thesis
    Abstract [en]

    This study examines Sustainable Community Development (SCD) in the context of the Baltic Sea Region. The research focuses on understanding a model for SCD piloted in Robertsfors, Sweden. The model is said to be transferable to any community around the world. This study seeks to understand the concepts and tools used in the Robertsfors Model. It also examines whether the model is strategic with regards to sustainability and whether it is successful in engaging the local community around these issues. Considerations for transferability are also addressed, focusing specifically on the Eastern Baltic Sea Region. Opportunities for improving the model are also studied. A combination of secondary research, in the form of literature review and primary research (structured interviews and questionnaires) was used to explore these questions. Propositions about SCD and questions for further research emerged from this study.

  • 158.
    Khamitova, Raisa
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Self-Adjointness and Quasi-Self-Adjointness of the Magma Equation2008Conference paper (Refereed)
    Abstract [en]

    A recent theorem on nonlocal conservation laws is applied to a magma equation modelling a melt migration through the Earth´s mantle. It is shown that the equation in question is quasi-self-adjoint. The self-adjoint equations are singled out. Nonlocal and local conservation densities are obtained using the symmetries of the magma equation.

  • 159.
    Khamitova, Raisa
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Symmetries and conservation laws2009Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Conservation laws play an important role in science. The aim of this thesis is to provide an overview and develop new methods for constructing conservation laws using Lie group theory. The derivation of conservation laws for invariant variational problems is based on Noether’s theorem. It is shown that the use of Lie-Bäcklund transformation groups allows one to reduce the number of basic conserved quantities for differential equations obtained by Noether’s theorem and construct a basis of conservation laws. Several examples on constructing a basis for some well-known equations are provided. Moreover, this approach allows one to obtain new conservation laws even for equations without Lagrangians. A formal Lagrangian can be introduced and used for computing nonlocal conservation laws. For self-adjoint or quasi-self-adjoint equations nonlocal conservation laws can be transformed into local conservation laws. One of the fields of applications of this approach is electromagnetic theory, namely, nonlocal conservation laws are obtained for the generalized Maxwell-Dirac equations. The theory is also applied to the nonlinear magma equation and its nonlocal conservation laws are computed.

  • 160. Khamitova, Raisa
    Symmetries and Nonlocal Conservation Laws of the General Magma Equation2009In: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, E-ISSN 1878-7274, Vol. 14, no 11, p. 3754-3769Article in journal (Refereed)
    Abstract [en]

    In this paper the general magma equation modelling a melt flow in the Earth's mantle is discussed. Applying the new theorem on nonlocal conservation laws [Ibragimov NH. A new conservation theorem. J Math Anal Appl 2007;333(1):311-28] and using the symmetries of the model equation nonlocal conservation laws are computed. In accordance with Ibragimov [Ibragimov NH. Quasi-self-adjoint differential equations. Preprint in Archives of ALGA, vol. 4, BTH, Karlskrona, Sweden: Alga Publications; 2007. p. 55-60, ISSN: 1652-4934] it is shown that the general magma equation is quasi-self-adjoint for arbitrary m and n and self-adjoint for n = -m. These important properties are used for deriving local conservation laws. © 2008 Elsevier B.V. All rights reserved.

  • 161.
    Klonowska, Kamilla
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Systems and Software Engineering.
    Lennerstad, Håkan
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Lundberg, Lars
    Blekinge Institute of Technology, School of Engineering, Department of Systems and Software Engineering.
    Svahnberg, Charlie
    Blekinge Institute of Technology, School of Engineering, Department of Systems and Software Engineering.
    Optimal recovery schemes in fault tolerant distributed computing2005In: Acta Informatica, ISSN 0001-5903, E-ISSN 1432-0525, Vol. 41, no 6, p. 341-365Article in journal (Refereed)
    Abstract [en]

    Clusters and distributed systems offer fault tolerance and high performance through load sharing. When all n computers are up and running, we would like the load to be evenly distributed among the computers. When one or more computers break down, the load on these computers must be redistributed to other computers in the system. The redistribution is determined by the recovery scheme. The recovery scheme is governed by a sequence of integers modulo n. Each sequence guarantees minimal load on the computer that has maximal load even when the most unfavorable combinations of computers go down. We calculate the best possible such recovery schemes for any number of crashed computers by an exhaustive search, where brute force testing is avoided by a mathematical reformulation of the problem and a branch-and-bound algorithm. The search nevertheless has a high complexity. Optimal sequences, and thus a corresponding optimal bound, are presented for a maximum of twenty one computers in the distributed system or cluster.

  • 162. Klonowska, Kamilla
    et al.
    Lundberg, Lars
    Lennerstad, Håkan
    The maximum gain of increasing the number of preemptions in multiprocessor scheduling2009In: ACTA INFORMATICA, ISSN 0001-5903 , Vol. 46, no 4, p. 285-295Article in journal (Refereed)
    Abstract [en]

    We consider the optimal makespan C(P, m, i) of an arbitrary set P of independent jobs scheduled with i preemptions on a multiprocessor with m identical processors. We compare the ratio for such makespans for i and j preemptions, respectively, where i < j. This ratio depends on P, but we are interested in the P that maximizes this ratio, i. e. we calculate a formula for the worst case ratio G(m, i, j) defined as G(m, i, j) = max C(P, m, i)/C(P, m, j), where the maximum is taken over all sets P of independent jobs.

  • 163. Klonowska, Kamilla
    et al.
    Lundberg, Lars
    Lennerstad, Håkan
    Svahnberg, Charlie
    Extended Golomb Rulers as the New Recovery Schemes in Distributed Dependable Computing2005Conference paper (Refereed)
    Abstract [en]

    Clusters and distributed systems offer fault tolerance and high performance through load sharing. When all computers are up and running, we would like the load to be evenly distributed among the computers. When one or more computers break down the load on these computers must be redistributed to other computers in the cluster. The redistribution is determined by the recovery scheme. The recovery scheme should keep the load as evenly distributed as possible even when the most unfavorable combinations of computers break down, i.e. we want to optimize the worst-case behavior. We have previously defined recovery schemes that are optimal for some limited cases. In this paper we find a new recovery schemes that are based on so called Golomb rulers. They are optimal for a much larger number of cases than the previous results.

  • 164. Kovalev, Guest editors: N.H. Ibragimov and V.F.
    Special issue: Group analysis of nonlinear wave problems2004Other (Other academic)
    Abstract [en]

    "Communications in Nonlinear Science and Numerical Simulation'' is given entirely to appreciation of applications of Lie groups to nonlinear problems in acoustics, engineering, biomedicine, etc. The selection of papers covers the following topics: a) group classification of differential equations and optimal systems of invariant and partially invariant solutions including classification of differential equations according to their symmetries; b) equivalence groups and invariants of families of differential equations; c) symmetries of delay equations; d) symmetries of stochastic differential equations; e) application to nonlinear physics and biomathematics. We hope that this special issue highlights the recent major developments in this fascinating field of mathematics and mathematical modelling.

  • 165. Kyhlbäck, Hans
    et al.
    Svensson, Marcus Sanchez
    Stille, Björn
    Nilsson, Monica E
    Sutter, Berthel
    Lärande genom deltagande i praktikgemenskaper2006Conference paper (Refereed)
    Abstract [sv]

    Sammanfattning— Vår erfarenhet är att teknisk grundutbildning blir bra om sammanhang skapas där studenterna kan lära av varandra och där utbildningen kan ske i nära samverkan med FoU och annan yrkesmässig och professionell verksamhet. I denna artikel driver vi tesen att studenternas lärande i teknisk grundutbildning borde ske mer genom interaktion och deltagande i ”praktik- gemenskaper”. Det betyder att lärande är en aspekt av deltagande i en kollektiv och produktiv verksamhet. Med olika exempel visar vi på sammanhang och arrangemang som kan skapa förutsättning för att experimentera med och utveckla lärande genom deltagande i sådana praktik-gemenskaper. Slutligen diskuterar vi styrkor och svagheter med att genomföra utbildning i enlighet med våra intentioner.

  • 166. Laksman, Efraim
    Bounds on the Performance of PSK Block Codes2010Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    In wireless communication, the minimum Euclidean distance between codewords is a major factor for the ability to correct errors in messages, and it is of interest to maximize the minimum Euclidean distance. The thesis improves previously established general upper bounds on minimum Euclidean distance of phase shift keying block codes. There are no requirements on structure of codes, as the bound depends only on alphabet size, word length and code size. Prior to this thesis, bounds found by use of a method of Elias, had been improved by generalization of Elias' method. The method used here is an attempt to optimize that generalization.

  • 167.
    Laksman, Efraim
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Combinatorial Optimization: Three Applications2012Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Combinatorial optimization is a diverse area of mathematics. It concerns optimization on feasible regions defined by discrete sets, graphs, hypergraphs, matroids, etc. . . which all have a large number of applications. They occur in virtually all domains of human activity since humans always want to do things easier, faster, consume less resources, etc. . . This thesis concerns three applied problems within combinatorial optimization. The first paper generalizes previous optimal upper bounds on the minimum Euclidean distance for phase-shift keying (PSK) block codes, that are explicit in the parameters alphabet size, block length and code size. There is a strong connection between high minimum Euclidean distance and good error-correcting capabilities. The bounds are generalized in several respects, such as from codes on symmetric PSK to codes on asymmetric PSK. They are also generalized to other types of noise than Gaussian, allowing more efficient block codes when noise is non-Gaussian. We provide examples of codes on asymmetric PSK that have higher minimum Euclidean distance than any comparable codes on symmetric PSK.Several classes of codes are shown to be optimal among codes on symmetric PSK since their Euclidean distance coincides with the bound. The second paper considers a parallel computer system with m identical computers,where we study optimal performance precaution for one possible computer crash. We anticipate that some computer may crash, and restrict the cost in such a situation. How costly is such a precaution when no crash occurs? We set a restriction that the completion time of a parallel program after a crash is at most a factor r + 1 larger than if we use an optimal allocation with m - 1 computers. This is an r-dependent restriction of the set of allocations of a program. Then the worst-case ratio of the optimal r-dependent completion time in the case of no crash and the unrestricted optimal completion time defines a function f(r,m). In the paper we establish upper and lower bounds of the worst-case cost function f(r,m) and characterize worst-case programs. The third paper considers the problem of Map Matching (MM), i.e. matching time and location measurements of a vehicle to a route in a road network. The paper presents a probabilistic algorithm for MM based on a second order hidden Markov model (HMM), as opposed to first order HMMs which are usually used. This allows a more detailed analysis of the data while preserving algorithmic complexity O(n). Both measurement densities and transition probabilities are determined with respect to Kolmogorov's third axiom, which in this context implies that the probabilities are additive over a partition of a road segment.

  • 168.
    Laksman, Efraim
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Lennerstad, Håkan
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Lundberg, Lars
    Blekinge Institute of Technology, School of Computing.
    Optimal computer crash performance precaution2012In: Discrete Mathematics and Theoretical Computer Science, ISSN 1462-7264, Vol. 14, no 1, p. 55-68Article in journal (Refereed)
    Abstract [en]

    For a parallel computer system withmidentical computers, we study optimal performance precaution for one possible computer crash. We want to calculate the cost of crash precaution in the case of no crash. We thus define a tolerance level r meaning that we only tolerate that the completion time of a parallel program after a crash is at most a factor r + 1 larger than if we use optimal allocation on m - 1 computers. This is an r-dependent restriction of the set of allocations of a program. Then, what is the worst-case ratio of the optimal r-dependent completion time in the case of no crash and the unrestricted optimal completion time of the same parallel program? We denote the maximal ratio of completion times f(r, m) - i.e., the ratio for worst-case programs. In the paper we establish upper and lower bounds of the worst-case cost function f(r, m) and characterize worst-case programs.

  • 169. Laksman, Efraim
    et al.
    Lennerstad, Håkan
    Nilsson, Magnus
    Bounding the minimal Euclidean distance for any PSK block codes of alphabet size 82009Conference paper (Refereed)
    Abstract [en]

    We consider a bound for the minimal Euclidean distance of any PSK block code with eight symbols. The main result was established in [6] - here we prove that the bound is in fact stronger than was proven there. The bound is deduced by generalizing Elias' method of a critical sphere. It is not asympthotic, as previous Elias' sphere bounds, but valid for any specific word length and code size. Many known codes fulfil the bound with equality, proving the sharpness of the bound for these parameter values as well as the optimality of these codes.

  • 170. Laksman, Efraim
    et al.
    Lennerstad, Håkan
    Nilsson, Magnus
    Improving bounds on the minimum Euclidean distance for block codes by inner distance measure optimization2010In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 310, no 22 Special issue SI, p. 3267-3275Article in journal (Refereed)
    Abstract [en]

    The minimum Euclidean distance is a fundamental quantity for block coded phase shift keying (PSK). In this paper we improve the bounds for this quantity that are explicit functions of the alphabet size q, block length n and code size | C |. For q = 8, we improve previous results by introducing a general inner distance measure allowing different shapes of a neighborhood for a codeword. By optimizing the parameters of this inner distance measure, we find sharper bounds for the outer distance measure, which is Euclidean. The proof is built upon the Elias critical sphere argument, which localizes the optimization problem to one neighborhood. We remark that any code with q = 8 that fulfills the bound with equality is best possible in terms of the minimum Euclidean distance, for given parameters n and | C |. This is true for many multilevel codes.

  • 171. Laksman, Efraim
    et al.
    Lennerstad, Håkan
    Nilsson, Magnus
    Inner Distance Measure Bounds on the Minimal Euclidean Distance for Symmetric PSK Block Codes2009Conference paper (Refereed)
    Abstract [en]

    The minimum Euclidean distance is a fundamental quantity for block-coded PSK. In this paper improvements are made of bounds for this quantity that are explicit functions of the alphabet size q, block length n and code size |C|. Earlier work, where the restriction q=8 was used, is continued by a generalisation allowing any q. The bound generalizes Elias critical sphere argument, which localizes the optimization problem to one neighbourhood, by use of so called inner distance measure for defining the shape of a sphere. Remark that codes which fulfill the bound with equality exist, and are best possible in terms of minimum Euclidean distance, for given parameters q, n and |C|.

  • 172. Lennerstad, Håkan
    An evolutionary textbook evolving by student activity2007In: Journal of Online Mathematics and its Applications, ISSN 1935-6439 , Vol. 7, no JuneArticle in journal (Refereed)
    Abstract [en]

    Successful education requires that the teacher has two knowledge competencies. The teacher not only needs to be familiar with the subject knowledge, it is also essential that the teacher have a realistic, detailed and practical knowledge of the students' understanding of the subject. This second kind of knowledge concerns the students' typical understanding and misunderstanding of the subject, and ways to handle them. It also includes ways to communicate meaning and interest in the subject--not to idealized students, but to real students. This paper describes a Swedish project that opens a channel allowing a teacher to systematically develop this knowledge while helping students. Teacher-student dialogues are conducted through a web page. As a result of the underlying goal, the project also extends the students' role in their education to a more responsible one. The textbook author uses the students' opinions and work at the web page to improve the book for the benefit of future students. Thus, the textbook evolves to be better adapted to the environment for which it is intended: studies by students. We present empiric results for an undergraduate distance course in calculus with 20 students.

  • 173. Lennerstad, Håkan
    Commensurable and rational triangles2007Report (Other academic)
    Abstract [en]

    One may ask which property the equilateral, the right isosceles, the half equilateral, and the two golden triangles, with angles (π/5),((2π)/5),((2π)/5) and (π/5),(π/5),((3π)/5), have in common. One answer is that their angles are commensurable with each other -- such triangles are commensurable. We investigate properties of this class of triangles, which is a countable subset of the entire class of triangles -- we do not distinguish between similar triangles. It can naturally be endowed with a family structure by integer triples. The equilateral is the only member of the first generation, and the other triangles mentioned above populate the first generations. A formula for the number of non-similar triangles that can be formed by triples of corners in a regular n-polygon is calculated, which gives the number of commensurable triangles at each generation. Three "metatriangles" are described -- so called because each possible triangle is represented as a point in each of them. The set of right triangles form a height in one of the metatriangles. The eye is the point of a metatriangle in the same metatriangle. In the second part of this report, triangles are studied by side length. A rational triangle is a triangle where all sides and all heights are rational numbers. We show that the right rational triangles are the Pythagorean triangles, and each non-right rational triangle consists of two Pythagorean triangles. Almost all triangles are irrational. It turns out that no Pythagorean triangle is commensurable. We prove that the only triangle with commensurable angles and also commensurable sides is the equilateral triangle.

  • 174. Lennerstad, Håkan
    Envariabelanalys, idéer och kalkyler2005Book (Other academic)
  • 175.
    Lennerstad, Håkan
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Matematikens dubbelnatur –undflyende innehåll,självtillräckligt språk2005In: Utbildning och Demokrati, ISSN 1102-6472, E-ISSN 2001-7316, Vol. 14, no 2, p. 27-55Article in journal (Refereed)
    Abstract [en]

    This article discusses the role in mathematics of its formal language, here called Mathematish. This language became significant when symbolic mathematics gradually replaced rhetoric mathematics. Mathematics gained in efficiency and calculation became dominant. It is claimed that this happened on the expense of mathematical interpretation, except for those who intuitively understand Mathematish. It is also claimed by linguistic arguments that the structure of a language isnaturally non-articulated for intuitive learners, often teachers, while teaching requires articulation. Languages are often excluding. Therelationship between content and language in mathematics is described from several viewpoints. Three distinct types of mathematical knowl-edge are suggested: 1. How to successfully use Mathematish rules, 2. Mathematish rules (computer programmable grammar), 3. Ideas and meanings of mathematics, e.g. applications and metaphors. Non-formal ways of hinting mathematical ideas and meanings, shedding light on both Mathematish and content, are suggested.

  • 176.
    Lennerstad, Håkan
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    The n-dimensional Stern-Brocot tree2012Report (Other academic)
    Abstract [en]

    The n-dimensional Stern-Brocot tree consists of all sequences (p₁, ...,p_{n}) of positive integers with no common multiple. The relatively prime sequences can be generated branchwise from each other by simple vector summation, starting with an ON-base, and controlled by a generalized Euclidean algorithm.The tree induces a multiresolution partition of the first quadrant of the (n-1)-dimensional unit sphere, providing a direction approximation property of a sequence by its ancestors. Two matrix representations are introduced, where in both a matrix contains the parents of a sequence. From one of them the isomorphism of a subtree to the entire tree of dimension equal to the number of parents of the top sequence follows. A form of Fibonacci sequences turn out to be the sequences of fastest growing sums. The construction can be regarded an n-dimensional continued fraction, and it may invite further n-dimesional number theory.

  • 177. Lennerstad, Håkan
    et al.
    Bergsten, Christer
    Matematiska språk2008Collection (editor) (Other academic)
    Abstract [sv]

    Sju författare från olika områden ger sin syn på frågan om matematikens språk. Det är matematikerna Christer Kiselman och Håkan Lennerstad, didaktikerna Christer Bergsten och Madeleine Löwing, lingvisten Östen Dahl, och Bo Göranzon och Lars Mouwitz som är forskare inom forskningsområdet yrkeskunnande och teknologi.

  • 178. Lennerstad, Håkan
    et al.
    Jogréus, Claes
    Serier och transformer2002Book (Other academic)
  • 179. Lennerstad, Håkan
    et al.
    Lundberg, Lars
    En annan addition och Stern-Brocots träd2006In: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, no 3, p. 45-48Article in journal (Refereed)
    Abstract [sv]

    När två bråk adderas så adderar man bråkens täljare för sig och nämnare för sig. Så får man väl inte göra? Jodå, det får man, men inte med vanlig addition. Här får vi en glimt av vad följderna blir av denna annorlunda addition.

  • 180.
    Lennerstad, Håkan
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Lundberg, Lars
    Blekinge Institute of Technology, School of Engineering, Department of Systems and Software Engineering.
    Generalizations of the floor and ceiling functions using the Stern-Brocot tree2006Report (Refereed)
    Abstract [en]

    We consider a fundamental number theoretic problem where practial applications abound. We decompose any rational number a/b in c ratios as evenly as possible while maintaining the sum of numerators and the sum of denominators. The minimum and maximum of the ratios give rational estimates of a/b from below and from above. The case c=b gives the usual floor and ceiling functions. We furthermore define the max-min-difference, which is zero iff c≤GCD(a,b), quantifying the distance to relative primality. A main tool for investigating the properties of these quantities is the Stern-Brocot tree, where all positive rational numbers occur in lowest terms and in size order. We prove basic properties such that there is a unique decomposition that gives both the minimum and the maximum. It turns out that this decomposition contains at most three distinct ratios. The problem has arisen in a generalization of the 4/3-conjecture in computer science.

  • 181. Lennerstad, Håkan
    et al.
    Lundberg, Lars
    Guaranteeing Response Times for Aperiodic Tasks in Global Multiprocessor Scheduling2007In: Real-time systems, ISSN 0922-6443, E-ISSN 1573-1383, Vol. 35, no 2, p. 135-151Article in journal (Refereed)
    Abstract [en]

    We provide a constant time schedulability test for an on-line multiprocessor server handling aperiodic tasks. Dhall's effect is avoided by dividing the tasks in two priority classes based on task utilization: heavy and light. We prove that if the load on the multiprocessor server stays below U threshold = 3 - root 7 approximately equals 35.425%, the server can accept an incoming aperiodic task and guarantee that the deadlines of all accepted tasks will be met. The same number 35.425% is also a threshold for a task to be characterized as heavy. The bound U threshold = 3 - root 7 approximately equals 35.425% is easy-to-use, but not sharp if we know the number of processors in the multiprocessor system. Assuming the server to be equipped with m processors, we calculate a formula for the sharp bound U threshold (m), which converges to U threshold from above as m -> infinity . The results are based on a utilization function u(x) = 2(1 - x)/(2 + root 2+2x). By using this function, the performance of the multiprocessor server can in some cases be improved beyond U threshold(m) by paying the extra overhead of monitoring the individual utilization of the current tasks.

  • 182.
    Lennerstad, Håkan
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Olteanu, Constanta
    Åtta IKT-projekt för matematiken i skolan: empiri och analys2012Report (Other (popular science, discussion, etc.))
    Abstract [en]

    Denna rapport presenterar empiri och analys av en granskning av åtta projekt som mottagit medel från Skolverket för att tillämpa IKT i skolans matematikundervisning. Empirin är organiserad enligt aktivitetsteorin, vilken sätter relationerna mellan människa, miljö, aktiviteter och mål i förgrunden. Empirin som presenteras är till stor del sammanställda repliker från lärare och elever vid intervjuerna, organi¬sera¬de för att belysa verksamhetens olika relationer. Det betyder att presentationen är till stor del på de verksammas villkor, och på deras språk. Ett stort antal konkreta slutsatser framkommer ur detta material. En av dem är att klass¬upp-sätt¬ningar av datorer är sällan framgångsrika, på grund av att teknisk support ofta var otillräcklig, och att lärarna inte kan veta hur mycket eleverna använder datorerna till icke-skol-verk¬sam¬het. Dessa problem finns inte för interaktiva skrivtavlor. De framstår däremot som ett socialt verktyg, som gör utbyte och dialog om ämnet lättare att få till stånd. I flera fall framkom indirekt, men ändå tydligt, att utbildningen på tekniken hade varit otillräcklig, trots att lärarna inte uttryckte ett tydligt missnöje med den. Skrivtavlan ökade lärarnas motivation för samarbete. En framåtriktad slutsats är att en lärargrupp som har ett fungerande samarbete och goda didaktiska, ämnesmässiga, ledar- och relationella kompe¬tenser med en interaktiv skrivtavla har en möjlighet att komma längre med elevernas måluppfyllelse.

  • 183. Lindberg, Vanja
    First principles study of CO reactivity on metallic nano particles2007Conference paper (Refereed)
    Abstract [en]

    The activity of a surface is determined by the local electronic structure. When nano particles are adsorbed, the catalytic properties will change. Surfaces with adsorbed nano particles often show a significantly higher chemical reactivity than the clean counterpart. Gold, for instance, shows an extra high activity towards many reactions, such as low-temperature catalytic combustion, partial oxidation of hydrocarbons and CO oxidation when dispersed as ultra-fine particles on metal oxide surfaces. In the case of CO oxidation, the activity has been observed to depend critically on the nano particle size, the nature of the support and the detailed synthetic procedure. Since it has been observed experimentally that the chemical reactivity of a nanoparticulated surface tend to depend on the size of the adatom structures, suggesting a quantum size effect, we find it well motivated to perform a theoretical investigation with focus on the cluster-size dependence. We have chosen to model CO interaction with sodium nano particles with focus on small particles, containing only a few atoms, since we expect the eventual quantum effects to be most pronounced for these. Further, we limit our investigation to unsupported nano particles because our previous investigations [1] have shown that it is predominately states localized to the nano particle region that contribute to the local electronic structure above the particle itself. The calculations have been performed in the context of density functional theory applying the MIKA real-space program package [2], using norm-conserving pseudo-potentials for the molecule. The nano particle has been modeled as a cylindrically symmetric quantum dot. For further details, see [3,4]. Our results show that the charge transfer between the nano particle and the CO molecule depends critically on the nano particle size, and that this dependence is intimately connected to the local electronic structure at the point where the molecule approaches the particle. The key factor for charge transfer turns out to be the presence of states with the symmetry of the chemically active molecular orbital at the Fermi level. [1] T. Torsti, V. Lindberg, M. J. Puska ,and B. Hellsing, Phys. Rev. B 66, 235420 (2002). [2] M. Heiskanen, T. Torsti, M. J. Puska, and R. M. Nieminen, Phys. Rev. B 63, 245106 (2001). [3] V. Lindberg and B. Hellsing, J. Phys. Condens. Matter 17, S1075 (2005). [4] V. Lindberg, T. Petersson, and B. Hellsing, Surf. Sci. 600, 6 (2006).

  • 184.
    Liu, Yang
    et al.
    Blekinge Institute of Technology, School of Computing.
    Bai, Guohua
    Blekinge Institute of Technology, School of Computing.
    Zhou, Qinglei
    Rakus-Andersson, Elisabeth
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Rough Sets Based Inequality Rule Learner for Knowledge Discovery2012Conference paper (Refereed)
    Abstract [en]

    Traditional rule learners employ equality relations between attributes and values to express decision rules. However, inequality relationships, as supplementary relations to equation, can make up a new function for complex knowledge acquisition. We firstly discuss an extended compensatory model of decision table, and examine how it can simultaneously express both equality and inequality relationships of attributes and values. In order to cope with large-scale compensatory decision table, we propose a scalable inequality rule leaner, which initially compresses the input spaces of attribute value pairs. Example and experimental results show that the proposed learner can generate compact rule sets that maintain higher classification accuracies than equality rule learners.

  • 185. Liu, Yang
    et al.
    Zhou, Qinglei
    Rakus-Andersson, Elisabeth
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Bai, Guohua
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    A Fuzzy-Rough Sets Based Compact Rule Induction Method for Classifying Hybrid Data2012Conference paper (Refereed)
    Abstract [en]

    Rule induction plays an important role in knowledge discovery process. Rough set based rule induction algorithms are characterized by excellent accuracy, but they lack the abilities to deal with hybrid attributes such as numeric or fuzzy attributes. In real-world applications, data usually exists with hybrid formats, and thus a unified rule induction algorithm for hybrid data learning is desirable. We firstly model different types of attributes in equivalence relationship, and define the key concepts of block, minimal complex and local covering based on fuzzy rough sets model, then propose a rule induction algorithm for hybrid data learning. Furthermore, in order to estimate performance of the proposed method, we compare it with state-of-the-art methods for hybrid data learning. Comparative studies indicate that rule sets extracted by this method can not only achieve comparable accuracy, but also get more compact rule sets. It is therefore concluded that the proposed method is effective for hybrid data learning.

  • 186. Lundberg, Lars
    et al.
    Lennerstad, Håkan
    Klonowska, Kamilla
    Gustafsson, Göran
    Using Golomb Rulers for Minimizing Collisions in Closed Hashing2004Conference paper (Refereed)
    Abstract [en]

    We give conditions for hash table probing which minimize the expected number of collisions. A probing algorithm is determined by a sequence of numbers denoting jumps for an item during multiple collisions. In linear probing, this sequence consists of only ones – for each collision we jump to the next location. To minimize the collisions, it turns out that one should use the Golomb ruler conditions: consecutive partial sums of the jump sequence should be distinct. The commonly used quadratic probing scheme fulfils the Golomb condition for some cases. We define a new probing scheme – Golomb probing - that fulfills the Golomb conditions for a much larger set of cases. Simulations show that Golomb probing is always better than quadratic and linear and in some cases the collisions can be reduced with 25% compared to quadratic and with more than 50% compared to linear.

  • 187. Lundberg, Lars
    et al.
    Lennerstad, Håkan
    Klonowska, Kamilla
    Gustafsson, Göran
    Using optimal Golomb rulers for minimizing collisions in closed hashing2004Conference paper (Refereed)
    Abstract [en]

    We give conditions for hash table probing which minimize the expected number of collisions. A probing algorithm is determined by a sequence of numbers denoting jumps for an item during multiple collisions. In linear probing, this sequence consists of only ones - for each collision we jump to the next location. To minimize the collisions, it turns out that one should use the Golomb ruler conditions: consecutive partial sums of the jump sequence should be distinct. The commonly used quadratic probing scheme fulfils the Golomb condition for some cases. We define a new probing scheme - Golomb probing that fulfills the Golomb conditions for a much larger set of cases. Simulations show that Golomb probing is always better than quadratic and linear and in some cases the collisions can be reduced with 25% compared to quadratic and with more than 50% compared to linear.

  • 188.
    Magnevall, Martin
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Josefsson, Andreas
    Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering.
    Ahlin, Kjell
    Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering.
    Broman, Göran
    Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering.
    Nonlinear structural identification by the "reverse Path" spectral method2012In: Journal of Sound and Vibration, ISSN 0022-460X, E-ISSN 1095-8568, Vol. 331, no 4, p. 938-946Article in journal (Refereed)
    Abstract [en]

    When dealing with nonlinear dynamical systems, it is important to have efficient, accurate and reliable tools for estimating both the linear and nonlinear system parameters from measured data. An approach for nonlinear system identification widely studied in recent years is "Reverse Path". This method is based on broad-band excitation and treats the nonlinear terms as feedback forces acting on an underlying linear system. Parameter estimation is performed in the frequency domain using conventional multiple-input-multiple- output or multiple-input-single-output techniques. This paper presents a generalized approach to apply the method of "Reverse Path" on continuous mechanical systems with multiple nonlinearities. The method requires few spectral calculations and is therefore suitable for use in iterative processes to locate and estimate structural nonlinearities. The proposed method is demonstrated in both simulations and experiments on continuous nonlinear mechanical structures. The results show that the method is effective on both simulated as well as experimental data.

  • 189.
    Mama, Mounchili
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Mathematical Modelling of The Global Positioning System Tracking Signals2008Independent thesis Advanced level (degree of Master (One Year))Student thesis
    Abstract [en]

    Recently, there has been increasing interest within the potential user community of Global Positioning System (GPS) for high precision navigation problems such as aircraft non precision approach, river and harbor navigation, real-time or kinematic surveying. In view of more and more GPS applications, the reliability of GPS is at this issue. The Global Positioning System (GPS) is a space-based radio navigation system that provides consistent positioning, navigation, and timing services to civilian users on a continuous worldwide basis. The GPS system receiver provides exact location and time information for an unlimited number of users in all weather, day and night, anywhere in the world. The work in this thesis will mainly focuss on how to model a Mathematical expression for tracking GPS Signal using Phase Locked Loop filter receiver. Mathematical formulation of the filter are of two types: the first order and the second order loops are tested successively in order to find out a compromised on which one best provide a zero steady state error that will likely minimize noise bandwidth to tracks frequency modulated signal and returns the phase comparator characteristic to the null point. Then the Z-transform is used to build a phase-locked loop in software for digitized data. Finally, a Numerical Methods approach is developed using either MATLAB or Mathematica containing the package for Gaussian elimination to provide the exact location or the tracking of a GPS in the space for a given a coarse/acquisition (C/A) code.

  • 190.
    Mbiydzenyuy, Gideon
    et al.
    Blekinge Institute of Technology, School of Computing.
    Dahl, Mattias
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Holmgren, Johan
    Blekinge Institute of Technology, School of Computing.
    Road travel time prediction: A micro-level sampling approach2013Conference paper (Refereed)
    Abstract [en]

    The ability to generate accurate travel time predictions for road freight transport is important when, for example, estimating the arrival times for heavy goods vehicles (HGVs) in order to plan terminal activities. We present a micro-level sampling method for road travel time prediction. The method makes use of historical GPS-data in order to determine the movement of a vehicle from an origin to a destination along a specific route. The method generates a travel time distribution, which can be used to obtain the expected travel time and probabilities for deviations. The method has been illustrated and evaluated in an experiment where the effective travel time was predicted for transport between two terminals. The experiment made use of GPS data that was recorded for two HGVs during a period of two months. An important feature of the method is that it does not need road network information, such as speed limits and number of lanes.

  • 191. Meleshko, Sergey
    et al.
    Ibragimov, Nail H.
    Kovalev, Vladimir
    Symmetries of Integro-Differential Equations2010, XIIIBook (Other academic)
    Abstract [en]

    This book aims to coherently present applications of group analysis to integro-differential equations in an accessible way. The book will be useful to both physicists and mathematicians interested in general methods to investigate nonlinear problems using symmetries. Differential and integro-differential equations, especially nonlinear, present the most effective way for describing complex processes. Therefore, methods to obtain exact solutions of differential equations play an important role in physics, applied mathematics and mechanics. This book provides an easy to follow, but comprehensive, description of the application of group analysis to integro-differential equations. The book is primarily designed to present both fundamental theoretical and algorithmic aspects of these methods. It introduces new applications and extensions of the group analysis method. The authors have designed a flexible text for postgraduate courses spanning a variety of topics.

  • 192. Mfoumou, Etienne
    Remote Acoustic Characterization of Thin Sheets2006Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    There is a need to monitor the existence and effects of damage in structural materials. Aircraft components provide a much publicized example, but the need exists in a variety of other structures, such as layered materials used in food packaging industries. While several techniques and models have been proposed for material characterization and condition monitoring of bulk materials, less attention has been devoted to thin sheets having no flexural rigidity. This study is therefore devoted to the development of a new method for acoustic Non-Destructive Testing (NDT) and material characterization of thin sheets used in food packaging materials or similar structures. A method for assessing the strength in the presence of crack of thin sheets used in food packaging is first presented using a modified Strip Yield Model (SYM). Resonance frequency measurement is then introduced and it is shown, at low frequency range (less than 2kHz), that a change in the physical properties such as a reduction in stiffness resulting from the onset of cracks or loosening of a connection causes detectable changes in the modal properties, specifically the resonance frequency. This observation leads to the implementation of a simple method for damage severity assessment on sheet materials, supported by a new theory illustrating the feasibility of the detection of inhomogeneity in form of added mass, as well as damage severity assessment, using a measurement of the frequency shift. A relationship is then established between the resonance frequency and the material’s elastic property, which yields a new modality for sheet materials remote characterization. The result of this study is the groundwork of a low-frequency vibration-based method with remote acoustic excitation and laser detection, for nondestructive testing and material characterization of sheet materials. The work also enhances the feasibility of the testing and condition monitoring of real structures in their operating environment, rather than laboratory tests of representative structures. The sensitivity of the new experimental approach used is liable to improvement while being high because the frequency measurement is one of the most accurate measurements in physics and metrology.

  • 193. Mfoumou, Etienne
    et al.
    Kao-Walter, Sharon
    Hedberg, Claes
    Remote Acoustic Monitoring of Thin Laminates2007Conference paper (Refereed)
    Abstract [en]

    Understanding the change in material properties in time is necessary for in-service diagnosis of structures and prevention of accidents. Therefore, a new experimental technique for evaluating Young’s (or elastic) modulus of a vibrating thin sheet from a dynamic measurement is presented. The technique utilizes bending resonance from a remote acoustic excitation. Equations relating the natural frequencies to the mechanical properties are obtained, and Young’s modulus is subsequently determined experimentally using the implemented dynamic measurement method. Young’s modulus values from the dynamic test are then compared with those (static) obtained by a standard tensile test and those obtained by the theory of laminated materials. The proposed technique appears relatively simple and is applied in this paper to laminates initially having no (or negligible) bending stiffness, and used in packaging industries. This work emphasizes the feasibility of a remote condition monitoring of components in-service by evaluating changes in the material properties.

  • 194. Mfoumou, Etienne
    et al.
    Rudenko, Oleg
    Hedberg, Claes
    Kao-Walter, Sharon
    Acoustical measurement accompanying tensile test: new modality for non-destructive testing and characterization of sheet materials2006Conference paper (Refereed)
    Abstract [en]

    A series of uniaxial tensile tests was performed for sheet materials like paperboard, polyethylene and packing layered composites. These sheets can be considered as membranes. In parallel with a tensile test, the natural frequency was measured through an acoustical excitation. Firstly, it was shown both theoretically and experimentally that, at a given load, the frequency is sensitive to the local deviation in the standard thickness or to the presence of cracks inside the material. It means that this acoustic measurement can be used as one of the methods of damage assessment, or nondestructive testing in general. Secondly, the resonance frequency shift was continuously monitored for increasing strain on polyethylene and paperboard, and the curves obtained were compared to the stress-strain curves for material characterization. They were not the same and showed a non-monotonic stiffness variation for the polyethylene. It was shown that the resonance frequency shift measurement can successfully replace the stress-strain curve for material characterization under tensile test. During a long time under load an irreversible plastic deformation of the sample takes place, and the frequency shift can also serve as a new method for evaluating the residual strain of the material.

  • 195. Nilsson, Jan-Evert
    Entreprenörskapets dynamik och regionala förankring: generella drag2002In: Entreprenörskapets dynamik och regionala förankring / [ed] , Peter Aronsson & Bengt Johannisson, Växjö: Växjö University Press , 2002Chapter in book (Refereed)
  • 196. Nilsson, Magnus
    et al.
    Lennerstad, Håkan
    An upper bound on the minimum Euclidean distance for block-coded phase-shift keying2000In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 46, no 2, p. 656-662Article in journal (Refereed)
    Abstract [en]

    We present an upper bound on the minimum Euclidean distance d_{Emin}(C) valid for any linear and non-linear block coded PSK. There are several well known block codes that satisfy this upper bound with equality. With given parameters; the alphabet size q, the blocklength n and the number of codewords |C|, it therefore follows that these codes are best possible in terms of minimum Euclidean distance. We furthermore establish a lower bound valid for Gray coded binary block codes. The minimum Euclidean distance is bounded from below by the minimum Hamming distance of the corresponding binary code. For several Gray coded binary block codes the upper and the lower bounds coincide. It can then be concluded without calculating the minimum Euclidean distance that these codes are best possible.

  • 197. Nilsson, Magnus
    et al.
    Lennerstad, Håkan
    Improved upper bound on the minimum Euclidean distance for block coded phase shift keying2005Conference paper (Other academic)
    Abstract [en]

    In an earlier work we presented and upper bound on the minimum Euclidean distance for block coded phase shift keying. The bound presented is valid for any alphabet size q\geq4, but it applies only to codes with medium or high rates: codes for which |C|>(q/3)^n. Here |C| is the number of codewords and n is the block length. The bound is proven to be tight for many parameter values at high rates. In this paper we present for the case q=8 an improved upper bound. This bound is tighter at medium rates, and is valid for all rates.

  • 198. Nilsson, Magnus
    et al.
    Lennerstad, Håkan
    Laksman, Efraim
    A two-metric approach to improve bounds on the minimum Euclidean distance for block codes2008Conference paper (Refereed)
    Abstract [en]

    We consider block coded PSK, and improve a previously established upper bound on the minimum Euclidean distance d_E(C) that is valid for any block code C. The bound is an explicit function of the alphabet size, block length and the number of code words. The improvement involves choosing an inner metric to give the best possible bound for the outer metric, which is Euclidean. we describe this approach and its problems, and present empiric results.

  • 199. Nomura, Hideyuki
    et al.
    Hedberg, Claes
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Kamakura, Tomoo
    Numerical simulation of length-limited parametric sound beam2011Conference paper (Refereed)
    Abstract [en]

    This study proposes a numerical simulation method that predicts nonlinear propagation of ultrasound beams in order to estimate the sound field of parametric array in the time domain. Basically, the method resorts to solving numerically and compactly the governing equations in a compressible viscous fluid using the Yee algorithm finite-difference time domain method. The simulation indicates a narrow audible sound beam which is a feature of the parametric array. Additionally, a length-limited parametric sound beam, which is proposed by Hedberg et al. [C. M. Hedberg et al., Acoust. Phys. 56, 637-639 (2010)], is numerically simulated as a model application. A pair of parametric sound sources generates the length-limited sound beam by control of the amplitudes and initial phases of the sources. The simulation shows a narrow truncated array length-limited sound beam.

  • 200. Nomura, Hideyuki
    et al.
    Hedberg, Claes
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Kamakura, Tomoo
    Numerical simulation of parametric sound generation and its application to length-limited sound beam2012In: Applied Acoustics, ISSN 0003-682X, E-ISSN 1872-910X, Vol. 73, no 12, p. 1231-1238Article in journal (Refereed)
    Abstract [en]

    In this study we propose a simulation model for predicting the nonlinear sound propagation of ultrasound beams over a distance of a few hundred wavelengths, and we estimate the beam profile of a parametric array. Using the finite-difference time-domain method based on the Yee algorithm with operator splitting, axisymmetric nonlinear propagation was simulated on the basis of equations for a compressible viscous fluid. The simulation of harmonic generation agreed with the solutions of the Khokhlov-Zabolotskaya-Kuznetsov equation around the sound axis except near the sound source. As an application of the model, we estimated the profiles of length-limited parametric sound beams, which are generated by a pair of parametric sound sources with controlled amplitudes and phases. The simulation indicated a sound beam with a narrow truncated array length and a width of about one-quarter to half that of regular a parametric beam. This result confirms that the control of sound source conditions changes the shape of a parametric beam and can be used to form a torch like low-frequency sound beam.

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