| 1. |
- Holmberg, Andreas, 1982-
(författare)
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Aeroacoustic Characterization using Multiport Methods
- 2012
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Noise is a major environmental pollutant, which can inict physical and psychologicalinjury. An important noise contribution stems from aeroacousticsources, which are found in e.g., ventilation ducts, engine exhaust systems andairplane engines.In this thesis, research methods for low Mach number aeroacoustic sourcesin ducts are developed. The basis of the methods is the ability to describe theintrinsic linear properties of the source as an N-port (multiport), where theoutput sound eld is related to the input sound eld and the generated soundeld, all consisting of plane waves. The methods presented are both numericaland experimental. The numerical method treats the passive properties, i.e.,scattering, attenuation and amplication of incident sound, while the experimentalmethod treats the active part (intrinsic sound generation) as well. Themethods are applied in the study of noise generation by a vortex mixer plate,placed in an airow of Mach 0.2, and in the study of acoustic-hydrodynamicinteraction in a T-junction of rectangular ducts.It is found that the accuracy of the experimental methods is signicantly increasedwhen the equations are over-determined, which is achieved by addingadditional microphones to the test rig. In the frequency range studied, themixer plate is found to generate less sound when made exible, without disturbingthe mixing quality.For the numerical method { based on the linearized Navier-Stokes equations,a model of the oscillation of the Reynolds stress (\turbulent damping")due to the acoustic eld is introduced. By comparing with experimental results,it is found that not using this model results in an over-prediction of theamplication at higher frequencies with several factors in magnitude, whileimplementing the model results in a much better agreement.
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| 2. |
- Altafi, Nasrin
(författare)
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Lefschetz properties and Jordan types of Artinian algebras
- 2020
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis contains six papers concerned with studying the Lefschetz properties and Jordan types of linear forms for graded Artinian algebras. Lefschetz properties and Jordan types carry information about the ranks of multiplication maps by linear forms on graded Artinian algebras. A graded Artinian algebra is said to have the weak Lefschetz property (WLP) if multiplication map by some linear form on has maximal rank in all degrees. If it holds for all powers of the algebra is said to have the strong Lefschetz property (SLP). Jordan type is a partition determining the Jordan block decomposition for the multiplication map by on . It is a finer invariant than the WLP and SLP, which determines the ranks of multiplication maps by all powers of on .Papers A and B concern the study of the Lefschetz properties of Artinian algebras quotient of a polynomial ring in variables over a field of characteristic zero by a monomial ideal generated in a single degree . Paper A studies the connection between the Lefschetz properties of such algebras and their minimal free resolutions, namely the number of linear steps in their resolutions. Paper B consists of two parts. The first part provides sharp lower bounds for the Hilbert function in degree of such algebras failing the WLP. The second part of Paper B deals algebras quotients of polynomial rings by ideals generated by forms of the same degree and invariant under action of a cyclic group. The main result of this part classifies such algebras satisfying the WLP in terms of the representation of the action. Papers C and D both deal with determining the Jordan type partitions of linear forms for graded Artinian algebras with codimension two. Paper C concerns the problem for complete intersection Artinian algebras over an algebraically closed field of characteristic zero or large enough. The results of Paper C classify partitions of an integer that occur as Jordan type partitions for Artinian complete intersection algebras and some linear forms. Such classifications are provided in terms of the numerical conditions of the partitions. Also for a given Hilbert function of such algebras, the Jordan type partitions are completely determined by which higher Hessians vanish at the point corresponding to the linear form. Some combinatorial invariants of such partitions, namely branch label or hook code, have been studied in this paper as well. Paper D concerns the generalization of the results of Paper C. The family of graded Artinian quotients of , having arbitrary Hilbert function has been studied. The cell corresponding to a partition having diagonal lengths is comprised of all ideals in whose initial ideal is the monomial ideal determined by . These cells give a decomposition of the variety into affine spaces. The main result of Paper D determines the generic number of generators for the ideals in each cell ; generalizing a result of Paper C. In particular, partitions having the generic number of generators for an ideal defining an algebra in are determined.Paper E concerns the SLP of Artinian Gorenstein algebras via studying the higher Hessians of dual generators. The main result of this paper characterizes the Hilbert functions of Artinian Gorenstein algebras having arbitrary codimension satisfying the SLP. It proves that a sequence of non-negative integers is the Hilbert function of some Artinian Gorenstein algebra with the SLP if and only if is an SI-sequence. This is done by studying the higher Hessians of the dual generator of an Artinian Gorenstein quotient of the coordinate ring of a set of points in the projective space. Using this approach, we provide families of Artinian Gorenstein algebras obtained by points in the projective plane satisfying the SLP. Paper F concerns the study of Jordan types of linear forms for graded Artinian Gorenstein algebras having arbitrary codimension. This paper introduces rank matrices of linear forms for such algebras. There is a 1-1 correspondence between rank matrices and Jordan degree types. The main result of this paper classifies all matrices that occur as the rank matrix for some Artinian Gorenstein algebra of codimension three and a linear form such that . As a consequence, we prove that Jordan types with parts of length at most four are uniquely determined by at most three parameters.
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| 3. |
- Färm, Anna, 1984-
(författare)
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Absorption of Sound : On the effects of field interaction on absorber performance
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Environmental noise has for decades been a well known problem, especially in urban areas. As noise requirements for vehicles are sharpened, noise reducing concepts are needed in early design stages requiring accurate simulations to support the design. Specifically for optimization of noise treatments, the absorber performance must be simulated correctly.So called noise encapsulations are placed below the powertrain on heavy vehicles to enclose the engine and reduce noise radiation. The attenuation of the absorbers on these shields must be represented correctly in simulations, even in environments with complex sound field, cooling flow and high temperature variations which may affect the absorber performance. This thesis studies the performance variation due to different absorber representations and due to these factors and how to include this in simulations.It is shown that the material representation significantly affects the attenuation performance in the simulations. Assuming locally reacting absorbers neglects the full interaction between the sound field and the material, which was shown to affect the noise reduction considerably. A measurement method to determine the angular dependent surface impedance was evaluated. It was shown sensitive to small samples and a method to improve accuracy was suggested. Including the angular dependence, either by full resolution or an angular dependent impedance, the field-absorber interaction is included in the simulations and more accurate results are obtained. The influence of flow and temperature fields on the absorber performance was also investigated. A method to include these effects was developed and the attenuation performance shown significant, especially for materials with bulk reaction.In conclusion, thorough knowledge of the material behavior and the field in the applications is required to choose appropriate material representation to enable reliable simulation results.
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| 4. |
- Greco, Ornella
(författare)
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Bounds on Hilbert Functions
- 2013
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis is constituted of two articles, both related to Hilbert functions and h-vectors. In the first paper, we deal with h-vectorsof reduced zero-dimensional schemes in the projective plane, and, in particular, with the problem of finding the possible h-vectors for the union of two sets of points of given h-vectors. In the second paper, we generalize the Green’s Hyperplane Restriction Theorem to the case of modules over the polynomial ring.
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| 5. |
- Greco, Ornella, 1987-
(författare)
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Bounds on Hilbert Functions and Betti Numbers of Veronese Modules
- 2014
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The thesis is a collection of four papers dealing with Hilbert functions and Betti numbers.In the first paper, we study the h-vectors of reduced zero-dimensional schemes in . In particular we deal with the problem of findingthe possible h-vectors for the union of two sets of points of given h-vectors. To answer to this problem, we give two kinds of bounds on theh-vectors and we provide an algorithm that calculates many possibleh-vectors.In the second paper, we prove a generalization of Green’s Hyper-plane Restriction Theorem to the case of finitely generated modulesover the polynomial ring, providing an upper bound for the Hilbertfunction of the general linear restriction of a module M in a degree dby the corresponding Hilbert function of a lexicographic module.In the third paper, we study the minimal free resolution of theVeronese modules, , where by giving a formula for the Betti numbers in terms of the reduced homology of the squarefree divisor complex. We prove that is Cohen-Macaulay if and only if k < d, and that its minimal resolutionis linear when k > d(n − 1) − n. We prove combinatorially that the resolution of is pure. We provide a formula for the Hilbert seriesof the Veronese modules. As an application, we calculate the completeBetti diagrams of the Veronese rings .In the fourth paper, we apply the same combinatorial techniques inthe study of the properties of pinched Veronese rings, in particular weshow when this ring is Cohen-Macaulay. We also study the canonicalmodule of the Veronese modules.
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| 6. |
- Weng, Chenyang
(författare)
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Modeling of sound-turbulence interaction in low-Mach-number duct flows
- 2013
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- When sound waves propagate in a duct in the presence of turbulent flow, tur- bulent mixing can cause extra attenuation of the sound waves in addition to that caused by the viscothermal eects. Experiments show that compared to the vis- cothermal eects, turbulent absorption becomes the dominant contribution to the sound attenuation at suciently low frequencies. The mechanism of this turbulent absorption is attributed to the turbulent stress and the turbulent heat transfer act- ing on the coherent perturbations (including to sound waves) near the duct wall, i.e. sound-turbulence interaction.The purpose of the current investigation is to understand the mechanism of the sound-turbulence interaction in low-Mach-number internal flows by means of theoretical modeling and numerical simulation. The turbulence absorption can be modeled through perturbation turbulent Reynolds stresses and perturbation turbu- lent heat flux in the linearized perturbation equations. In this thesis, the linearized perturbation equations are reviewed, and dierent models for the turbulent absorp- tion of the sound waves are investigated. In addition, a new non-equilibrium model for the perturbation turbulent Reynolds stress is proposed. The proposed model is validated by comparing the computed perturbation fields with experimental data from turbulent pipe flow measurements, and large eddy simulations (LES) of turbu- lent channel flow. Good agreements are observed.Besides the theoretical modeling, LES is also carried out as a numerical investi- gation of the sound-turbulence interaction. Some preliminary results from the LES are presented.
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| 7. |
- Altafi, Nasrin, 1989-
(författare)
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Lefschetz Properties of Monomial Ideals
- 2018
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis concerns the study of the Lefschetz properties of artinian monomial algebras. An artinian algebra is said to satisfy the strong Lefschetz property if multiplication by all powers of a general linear form has maximal rank in every degree. If it holds for the first power it is said to have the weak Lefschetz property (WLP).In the first paper, we study the Lefschetz properties of monomial algebras by studying their minimal free resolutions. In particular, we give an afirmative answer to an specific case of a conjecture by Eisenbud, Huneke and Ulrich for algebras having almost linear resolutions. Since many algebras are expected to have the Lefschetz properties, studying algebras failing the Lefschetz properties is of a great interest. In the second paper, we provide sharp lower bounds for the number of generators of monomial ideals failing the WLP extending a result by Mezzetti and Miró-Roig which provides upper bounds for such ideals. In the second paper, we also study the WLP of ideals generated by forms of a certain degree invariant under an action of a cyclic group. We give a complete classication of such ideals satisfying the WLP in terms of the representation of the group generalizing a result by Mezzetti and Miró-Roig.
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| 8. |
- Söderberg, Jonas, 1973-
(författare)
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Graded Betti Numbers and Hilbert Functions of Graded Cohen-Macaulay Modules
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we study graded Cohen-Macaulay modules and their possible Hilbert functions and graded Betti numbers. In most cases the Cohen-Macaulay modules we study are level modules. In order to use dualization to study Hilbert functions of artinian level algebras we extend the notion of level sequences and cancellable sequences, introduced by Geramita and Lorenzini, to include Hilbert functions of certain level modules. As in the case of level algebras, a level sequence is cancellable, but now by dualization its reverse is also cancellable which gives a new condition on level sequences. We also give a characterization of the cancellable sequences. We prove that a sequence of positive integers (h0, h1, . . . ,hc) is the Hilbert function of an artinian level module of codimension two if and only if hi−1 − 2hi + hi+1<= 0 for all 0 <= i <= c, where we assume that h−1 = hc+1 = 0. This generalizes a result already known for artinian level algebras. Zanello gives a lower bound for Hilbert functions of generic level quotients of artinian level algebras. We give a new and more straightforward proof of Zanello’s result. Conjectures on the possible graded Betti numbers of Cohen-Macaulay modules up to multiplication by a positive rational number are given. The idea is that the Betti diagrams should be non-negative linear combinations of pure diagrams. The conjectures are verified for modules of codimension two, for Gorenstein algebras of codimension three and for complete intersections. The motivation for the conjectures comes from the Multiplicity conjecture of Herzog, Huneke and Srinivasan. The h-vectors and graded Betti numbers of level modules up to multiplication by a rational number are studied. Assuming the conjecture, mentioned above, on the set of possible graded Betti numbers of Cohen-Macaulay modules we get a description of the possible h-vectors of level modules up to multiplication by a rational number. We determine, again up to multiplication by a rational number, the cancellable h-vectors and the h-vectors of level modules with the weak Lefschetz property. Furthermore, we prove that level modules of codimension three satisfy the upper bound of the Multiplicity conjecture and that the lower bound holds if the module, in addition, has the weak Lefschetz property.
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| 9. |
- Weng, Chenyang, 1985-
(författare)
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Theoretical and numerical studies of sound propagation in low-Mach-number duct flows
- 2015
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- When sound waves propagate in a duct in the presence of turbulent flow, turbulent mixing can cause attenuation of the sound waves extra to that caused by the viscothermal effects. Experiments show that compared to the viscothermal effects, this turbulent absorption becomes the dominant contribution to the sound attenuation at sufficiently low frequencies. The mechanism of this turbulent absorption is attributed to the turbulent stress and the turbulent heat transfer acting on the coherent perturbations (including the sound waves) near the duct wall, i.e. sound-turbulence interaction.The purpose of the current investigation is to understand the mechanism of the sound-turbulence interaction in low-Mach-number internal flows by theoretical modeling and numerical simulations. The turbulence absorption can be modeled through perturbation turbulent Reynolds stresses and perturbation turbulent heat flux in the linearized perturbation equations. In this thesis, the linearized perturbation equations are reviewed, and different models for the turbulent absorption of the sound waves are investigated. A new non–equilibrium model for the perturbation turbulent Reynolds stress is also proposed. The proposed model is validated by comparing with experimental data from the literature, and with the data from Direct Numerical Simulations (DNS) of pulsating turbulent channel flow. Good agreement is observed.
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