Dissertations / Theses on the topic 'Problem of the many'
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Nagy, Gabor. "Heuristic methods for the many-to-many location-routing problem." Thesis, University of Birmingham, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.268969.
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Woods, Evan T. "The Problems of the Many." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1563318642660876.
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Guertler, Siegfried. "Large scale computer-simulations of many-body Bose and Fermi systems at low temperature." Thesis, Click to view the E-thesis via HKUTO, 2008. http://sunzi.lib.hku.hk/hkuto/record/B40887741.
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Dale, Edward Robert. "Visualizing the inner structure of n-body data using splatting and skeletonization /." Link to online version, 2006. https://ritdml.rit.edu/dspace/handle/1850/2071.
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Fritsch, Stefan. "Chiral dynamics and the nuclear many-body problem." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=973410205.
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Gifford, Christopher S. "All bar one : the problem of the many." Thesis, University of Bristol, 2014. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.659104.
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The subject of this thesis is the problem of the many - a problem which presents the challenge of there being many objects in situations in which we putatively take there to be one. The problem demands attention since it is paradoxical, ubiquitous in its extent, prompts a revision of the concepts it invokes (identity, distinctness, vagueness, and indeterminacy) , and promises a revelation of the relation between it and other philosophical problems. Chapters 2-3 establish what the problem of the many is and establishes its relationship to other problems and paradoxes. Chapters 3-9 consider the most standard responses to the problem and chapter 10 presents a new response called role theory. There are three main original contributions: 1. The introduction of a new delegic and aoristic modality which models theoretical commitment and indeterminacy (respect.). It is claimed that the modality is more appropriate to model indeterminacy than current methods of modeling indeterminacy which are based on alethic modality, such as those supplied by the supervaluationist and the ontic indeterminist. 2. The introduction of a new theory called role theory which is an axiomatic ontology that quantifies over roles and the objects that fill them. The theory is defended against presented responses to the problem of the many. 3. The demonstration of a significant difference between the sorites paradox and the problem of the many. This is achieved by contrasting the necessary conditions for the problems and by diagnosing the former as an instance of underdeterminacy and the latter as an instance of overdeterminacy. The difference gives us cause to revise the putative suitability of theories of vagueness as responses to the problem of the many especially due to a demonstrated inability of the theories to cope with situations in which there are instances of both problems.
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Dyhdalo, Alexander. "Aspects of the Many-Body Problem in Nuclear Physics." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1524186564591926.
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Meng, Tan Chee. "Infinitely Many Radial Solutions to a Superlinear Dirichlet Problem." Scholarship @ Claremont, 2007. https://scholarship.claremont.edu/hmc_theses/202.
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My thesis work started in the summer of 2005 as a three way joint project by Professor Castro and Mr. John Kwon and myself. A paper from this joint project was written and the content now forms my thesis.
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Peres, Nuno Miguel Machado Reis. "The Many-Electron Problem In Novel Low-Dimensional Materials." Doctoral thesis, Universidade de Évora, 1998. http://hdl.handle.net/10174/11018.
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"Sem resumo feito pelo autor"; - This Thesis deals with the one-dimensional (1D) Hubbard model [1, 2, 3], which describes single-band interacting (correlated) electrons in a (1D) lattice. According to Lieb [4]:
" The Hubbard model is to the problem of electron correlations as the Ising model is to the problem of spin-spin interactions; it is the simplest possible model displaying many "real world" features."
The model depends on the parameter t, the hopping integral, characterizing the kinetic energy of the electrons when they hop between two adjacent lattice sites, and on the parameter U, the on-site Coulomb integral, characterizing the Coulomb interaction energy when two electrons occupy the same lattice site (Chapter 2).
Strictly one-dimensional systems are not found in real solid-state materials, how-ever there are quasi-one-dimensional materials in nature. Theoretically, a quasi-one-dimensional. solid – the definition of which is quite broad [5]– may be represented by a three-dimensional array of one-dimensional chains, such that the hopping in-tegrais between the chains are much smaller than the hopping integral along them [6]. The correspondente with real materials – for which t and U can be estimated froco infrared spectroscopy data [7, 8, 9]– is then made by means of quantum chem-istry calculations [10], where the hopping integrais and the Coulomb on-site energy are computed by means of the atomic (molecular) wave functions of the atoms (molecules) of the solid under consideration.
Obviously, approximating real materials by a simple one-dimensional model is not enough in general to make a quantitativa description of the solid properties. In spite of this, a description based on the parameters t and U contains many "real
world" features [7, 8]. On the other hand, effects like electron-phonon coupling
and more general Coulomb interactions, for example, are needed to account for a
more quantitativa description of the physical properties of real quasi-one-dimensional
materiais [11, 12, 13, 14, 15, 16, 17].
The systems described by the 1D Hubbard model (and its generalizations) have
narrow energy bands, and, therefore, the tight-binding approximation for independent
electrons can be applied [18].
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Hampton, Marshall. "Concave central configurations in the four-body problem /." Thesis, Connect to this title online; UW restricted, 2002. http://hdl.handle.net/1773/5728.
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Steiger, Don. "Numerical n-body methods in computational chemistry /." free to MU campus, to others for purchase, 1998. http://wwwlib.umi.com/cr/mo/fullcit?p9924930.
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Stadel, Joachim Gerhard. "Cosmological N-body simulations and their analysis /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/5449.
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D'Amico, Irene. "Some aspects of the dynamics of many-body systems /." free to MU campus, to others for purchase, 2000. http://wwwlib.umi.com/cr/mo/fullcit?p9988653.
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James, Alan John. "Solving the many electron problem with quantum Monte-Carlo methods." Thesis, Imperial College London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.309224.
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Khan, Imran. "QUANTUM THEORY OF MANY BOSE ATOM SYSTEMS." Connect to Online Resource-OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=Toledo1195507917.
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Harvey, Michael. "Diophantine problems in many variables." Thesis, University of Bristol, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.529849.
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Moghrabi, Kassem. "Beyond-mean-field corrections and effective interactions in the nuclear many-body problem." Phd thesis, Paris 11, 2013. http://tel.archives-ouvertes.fr/tel-00908607.
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Mean-field approaches successfully reproduce nuclear bulk properties like masses and radii within the Energy Density Functional (EDF) framework. However, complex correlations are missing in mean-field models and several observables related to single-particle and collective nuclear properties cannot be predicted accurately. The necessity to provide a precise description of the available data as well as reliable predictions in the exotic regions of the nuclear chart motivates the use of more sophisticated beyond-mean-field models. Correlations and higher-order corrections (beyond the leading mean-field order) are introduced. A crucial aspect in these calculations is the choice of the effective interaction to be used when one goes beyond the leading order (available effective interactions are commonly adjusted at the mean-field level). In the first part, we deal with the equation of state of nuclear matter evaluated up to the second order with the phenomenological Skyrme force. We analyze the ultraviolet divergence that is related to the zero range of the interaction and we introduce Skyrme-type regularized interactions that can be used at second order for matter. Cutoff regularization and dimen- sional regularization techniques are explored and applied. In the latter case, connections are naturally established between the EDF framework and some techniques employed in Effective Field Theories. In the second part, we check whether the regularized interactions introduced for nuclear matter can be employed also for finite nuclei. As an illustration, this analysis is performed within the particle- vibration model that represents an example of beyond mean-field models where an ultraviolet divergence appears if zero-range forces are used. These first applications suggest several directions to be explored to finally provide regularized interactions that are specially tailored for beyond- mean-field calculations for finite nuclei. Conclusions and perspectives are finally illustrated.
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Albertsson, Martin. "Analysis of the Many-Body Problem in One Dimension with Repulsive Delta-Function Interaction." Thesis, Uppsala universitet, Teoretisk fysik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-226119.
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The repulsive delta-function interaction model in one dimension is reviewed for spinless particles and for spin-1/2 fermions. The problem of solving the differential equation related to the Schrödinger equation is reduced by the Bethe ansatz to a system of algebraic equations. The delta-function interaction is shown to have no effect on spinless fermions which therefore behave like free fermions, in agreement with Pauli's exclusion principle. The ground-state problem of spinless bosons is reduced to an inhomogeneous Fredholm equation of the second kind. In the limit of impenetrable interactions, the spinless bosons are shown to have the energy spectrum of free fermions. The model for spin-1/2 fermions is reduced by the Bethe ansatz to an eigenvalue problem of matrices of the same sizes as the irreducible representations R of the permutation group of N elements. For some R's this eigenvalue problem itself is solved by a generalized Bethe ansatz. The ground-state problem of spin-1/2 fermions is reduced to a generalized Fredholm equation.
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Yang, C. J., M. Grasso, K. Moghrabi, and Kolck U. van. "Renormalizability of the nuclear many-body problem with the Skyrme interaction beyond mean field." AMER PHYSICAL SOC, 2017. http://hdl.handle.net/10150/624477.
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Phenomenological effective interactions like Skyrme forces are currently used in mean-field calculations in nuclear physics. Mean-field models have strong analogies with the first order of the perturbative many-body problem and the currently used effective interactions are adjusted at the mean-field level. In this work, we analyze the renormalizability of the nuclear many-body problem in the case where the effective Skyrme interaction is employed in its standard form and the perturbative problem is solved up to second order. We focus on symmetric nuclear matter and its equation of state, which can be calculated analytically at this order. It is shown that only by applying specific density dependence and constraints to the interaction parameters can renormalizability be guaranteed in principle. This indicates that the standard Skyrme interaction does not in general lead to a renormalizable theory. To achieve renormalizability, other terms should be added to the interaction and employed perturbatively only at first order.
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Dereziński, Jan. "Existence and analyticity of many body scattering amplitudes at low energies." Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/53870.
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We study elastic and inelastic (2 cluster) - (2 cluster) scattering amplitudes for N-body quantum systems. For potentials falling off like r⁻-1-E we prove that below the lowest 3-cluster threshold these amplitudes exist, are continuous and that asymptotic completeness holds. Moreover, if potentials fall off exponentially we prove that these amplitudes can be meromorphically continued in the energy, with square root branch points at the 2 cluster thresholds.Ph. D.
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Bröcker, Peter [Verfasser], Simon [Gutachter] Trebst, and David [Gutachter] Gross. "Disentangling and machine learning the many-fermion problem / Peter Bröcker ; Gutachter: Simon Trebst, David Gross." Köln : Universitäts- und Stadtbibliothek Köln, 2018. http://d-nb.info/1163728357/34.
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Marsden, David Charles. "An investigation of the Tucson-Melbourne three-nucleon force in the nuclear many-body problem." Diss., The University of Arizona, 2002. http://hdl.handle.net/10150/289793.
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The no-core shell-model approach has proven to be extremely useful for the theoretical determination of the properties of light (A ≤ 12) nuclei. However, at present this method does not accommodate a three-nucleon interaction into the potential that it employs. The problem is introduced with a largely historical development of both the effective interaction formalism and three-nucleon interactions, placing the motivation in context. This work makes a first attempt to incorporate such a three-nucleon interaction into the no-core shell-model ansatz. To this end, a variant of the two-pion-exchange Tucson-Melbourne three-nucleon interaction has been chosen. A three-body translationally-invariant harmonic-oscillator basis is constructed, and matrix elements of the three-nucleon interaction in this basis are calculated. The majority of this is accomplished through standard angular-momentum algebraic techniques, with the most expensive component being the spatial one, as it requires a transformation of the basis set with computationally intensive transformation brackets. Given the ability to determine the matrix elements for the chosen Tucson-Melbourne force, the practicality of employing these in calculations is demonstrated, with calculations on the three-body nuclei ³H and ³He. These are simple calculations, where the Tucson-Melbourne matrix elements are added to those of the two-body effective potential (a slight inconsistency which future studies will aim to fix). The dependence of binding energies on the harmonic-oscillator parameter, hΩ, and the Tucson-Melbourne cutoff parameter, Λ are examined. The former is found to be small in the range of hΩ considered, while the latter is shown to be consistent with previous works that have explored this dependence using other methods. The convergence of the binding energy with increasing model space size is slow, but this is perhaps attributable to the unrenormalized nature of the three-body matrix elements. The ultimate aim of this research is to find a viable method for constructing a three-body effective interaction from a given "realistic" three nucleon interaction, for use in no-core shell-model calculations. The current work demonstrates that such a scheme is feasible, and should yield results more consistent with experiment. Such a three-body effective interaction should also achieve quicker convergence with model space size than shown here, as the three-nucleon matrix elements will be renormalized to account for the geometry of the model space. Thus, one will have constructed an ab initio method for calculations on light nuclei, that includes a three-nucleon interaction, and converges quickly in the determination of nuclear properties.
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Korattiyil, Thomas. "Many poor and many religions toward a theology of liberative dialogue of religions /." Theological Research Exchange Network (TREN), 1997. http://www.tren.com.
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Gardner, Jeffrey P. "Numerical simulations of galaxy formation in a cosmological context /." Thesis, Connect to this title online; UW restricted, 2000. http://hdl.handle.net/1773/5416.
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Alkurtass, B. "A quantum information approach to many-body problems." Thesis, University College London (University of London), 2015. http://discovery.ucl.ac.uk/1469005/.
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This thesis investigates the properties of entanglement in one-dimensional many-body systems. In the first part, the non-equilibrium dynamics following a sudden global quench are exploited for the purpose of generating long-range entanglement. A number of initial states are considered. It is shown that the dynamics following the considered quench can be mapped to the problem of a state transfer. The quench can then be optimised by exploiting the literature about quantum state transfer to generate maximal long-range entanglement and maximal block entropy. In the second part of the thesis, a spin chain emulation of the two-channel, Kondo (2CK) model is proposed. Studying the local magnetisation and susceptibility we show that the spin-only emulation truly represent the two-channel Kondo model and extract the Kondo temperature. A detailed entanglement analysis is presented. Using density matrix renormalisation group (DMRG), which allow for real space analysis, Kondo temperature and Kondo length are evaluated. An entanglement measure, namely the negativity, as well as the Schmidt gap are used as possible order parameters predicting the critical point. An extensive analysis of the block entropy of the system is presented for different limiting values of Kondo coupling. A universal scaling of the impurity contribution to the entropy is found and the 2CK residual entropy is extracted. The last part explores quench dynamics in Kondo systems using time-dependent DMRG. For a quench in the Kondo coupling a travelling and breathing clouds are ob-served. A measurement-induced dynamics lead to an oscillation between an effective singlet and triplet states of the impurity and the Kondo cloud. Kondo temperature can be extracted from the frequency of the oscillation.
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Campbell, Luke. "Inelastic losses in x-ray absorption theory /." Thesis, Connect to this title online; UW restricted, 2002. http://hdl.handle.net/1773/9711.
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Li, Miqing. "Evolutionary many-objective optimisation : pushing the boundaries." Thesis, Brunel University, 2015. http://bura.brunel.ac.uk/handle/2438/11778.
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Many-objective optimisation poses great challenges to evolutionary algorithms. To start with, the ineffectiveness of the Pareto dominance relation, which is the most important criterion in multi-objective optimisation, results in the underperformance of traditional Pareto-based algorithms. Also, the aggravation of the conflict between proximity and diversity, along with increasing time or space requirement as well as parameter sensitivity, has become key barriers to the design of effective many-objective optimisation algorithms. Furthermore, the infeasibility of solutions' direct observation can lead to serious difficulties in algorithms' performance investigation and comparison. In this thesis, we address these challenges, aiming to make evolutionary algorithms as effective in many-objective optimisation as in two- or three-objective optimisation. First, we significantly enhance Pareto-based algorithms to make them suitable for many-objective optimisation by placing individuals with poor proximity into crowded regions so that these individuals can have a better chance to be eliminated. Second, we propose a grid-based evolutionary algorithm which explores the potential of the grid to deal with many-objective optimisation problems. Third, we present a bi-goal evolution framework that converts many objectives of a given problem into two objectives regarding proximity and diversity, thus creating an optimisation problem in which the objectives are the goals of the search process itself. Fourth, we propose a comprehensive performance indicator to compare evolutionary algorithms in optimisation problems with various Pareto front shapes and any objective dimensionality. Finally, we construct a test problem to aid the visual investigation of evolutionary search, with its Pareto optimal solutions in a two-dimensional decision space having similar distribution to their images in a higher-dimensional objective space. The work reported in this thesis is the outcome of innovative attempts at addressing some of the most challenging problems in evolutionary many-objective optimisation. This research has not only made some of the existing approaches, such as Pareto-based or grid-based algorithms that were traditionally regarded as unsuitable, now effective for many-objective optimisation, but also pushed other important boundaries with novel ideas including bi-goal evolution, a comprehensive performance indicator and a test problem for visual investigation. All the proposed algorithms have been systematically evaluated against existing state of the arts, and some of these algorithms have already been taken up by researchers and practitioners in the field.
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Dinh, Thi Hanh Physics Faculty of Science UNSW. "Application of many-body theory methods to atomic problems." Publisher:University of New South Wales. Physics, 2009. http://handle.unsw.edu.au/1959.4/43734.
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There is strong interest in atomic and nuclear physics to the study of superheavy elements by the search for the island of stability in the region Z=104 to Z=126. There are many experimental efforts and theoretical works devoted to these study in measuring the spectra and chemical properties. In this thesis, calculations of the spectra and the hyperfine structure of some superheavy elements have been performed in an attempt to enrich our knowledge about the elements and even may help in their detection. We perform the high-precision relativistic calculations to determine the spectra of the superheavy element Z=119 (eka-Fr) and the singly-ionized superheavy element Z=120+ (eka-Ra+). Dominating correlation corrections beyond relativistic Hartree-Fock are included to all orders in the residual electron interaction using the Feynman diagram technique and the correlation potential method. The Breit interaction and quantum electrodynamics radiative corrections are considered. Also, the volume isotope shift is determined. We present the relativistic calculations for the energy levels of the superheavy element Z=120. The relativistic Hartree-Fock and configuration interaction techniques are employed. The correlations between core and valence electrons are treated by means of the correlation potential method and many-body perturbation theory. We also try to address the absence of experimental data on the electron structure and energy spectrum of the Uub element (Z=112) by calculating its energy levels. The relativistic Hartree-Fock and configuration interaction methods are combined with the many-body perturbation theory to construct the many-electron wave function for valence electrons and to include core-valence correlations. The hyperfine structure constants of the lowest s and p1/2 states of superheavy elements Z=119 and Z= 120+ are calculated. Core polarization, dominating correlation, Breit and quantum electrodynamic effects are considered. The dependence of the hyperfine structure constants on nuclear radius is discussed. Measurements of the hyperfine structure combined with our calculations will allow one to study nuclear properties and distribution of magnetic moment inside nucleus. Finally, we discuss the possibility of measuring nuclear anapole moments in atomic Zeeman transitions and perform the necessary calculations. Advantages of using Zeeman transitions include variable transition frequencies and the possibility of enhancement of parity nonconservation effects.
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Al-Saedi, Ahmed Eid. "The orbits of periodic solutions of many body problems." Thesis, Swansea University, 2001. https://cronfa.swan.ac.uk/Record/cronfa42792.
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This thesis is concerned with the equal mass many-body problem and the stability of periodic solutions, with Keplerian (Coulombic) potential and other potentials. The classical n-body problem is a system of ordinary differential equations that describes the motion of n particles moving under Newton/Coulomb laws of motion, where the forces acting are the mutual gravitational attractions, Coulonibic interaction with the presence of a constant magnetic field. The main contributions of the present work are: 1. The e-equation which characterises the linear stability of the f-equation of the DTW-solutions and provides information about the stability of the non-planar periodic solutions of the many-body problems. To note that the method can be applied to any conservative Hamiltonian system with three degrees of freedom which can be reduced to two degrees of freedom using the Cylindrical polar coordinates (Chapter 3). 2. A numerical approach to solving the e-equation for our standard examples providing a set of illustrative systems that show that the general solution to the e-equation is well behaved. The comparison of numerical and approximate analytical solutions of the e-solution for the four body gravitational problem appears to be good. (Chapter 4). 3. New periodic solutions, weaving styles and chasing styles, with axial symetry and non-collison of the bodies, we describe the algebra and symmetry that allows us to reduce a full system of equations to just those for essentially one particle. Some of these styles provided the figure eight periodic solutions (Chapter 5). 4. We try to give approximate solutions for the new families of the weaving periodic solutions (Chapter 5). 5. DTW-periodic solutions with a Logarithmic potential energy. One interesting feature of these solutions is the appearance of double points in the initial data space corresponding to specified nodal structures. We also have the appearance of periodic orbits with the same nodal structure but different winding numbers. In the work of DTW these were denoted by use of a notation like "11/7", ie. 11 nodes with 7 revolutions required to complete the orbit (Chapter 5). 6. The extention of the use of the f-equation, the -equation and the numerical approach to other potentials (Chapter 5). 7. New style of periodic solution, the weaving style with the Logarithmic potential energy, this gave the figure eight periodic solution (Chapter 5). 8. Suggestion for further research areas in which one could continue this investigation (Chapter 5).
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Svensson, Carl Edward. "Collectivity in A ~ 60 nuclei : superdeformed and smoothly terminating rotational bands /." *McMaster only, 1998.
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Furuhashi, Takeshi, Tomohiro Yoshikawa, and Shun Otake. "A Study on Aggregation of Objective Functions in MaOPs Based on Evaluation Criteria." 日本知能情報ファジィ学会, 2010. http://hdl.handle.net/2237/20688.
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Session ID: TH-E1-4SCIS & ISIS 2010, Joint 5th International Conference on Soft Computing and Intelligent Systems and 11th International Symposium on Advanced Intelligent Systems. December 8-12, 2010, Okayama Convention Center, Okayama, Japan
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Scarlatella, Orazio. "Driven-Dissipative Quantum Many-Body Systems." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS281/document.
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Ma thèse de doctorat était consacrée à l'étude des systèmes quantiques à plusieurs corps dissipatifs et pilotés. Ces systèmes représentent des plateformes naturelles pour explorer des questions fondamentales sur la matière dans des conditions de non-équilibre, tout en ayant un impact potentiel sur les technologies quantiques émergentes. Dans cette thèse, nous discutons d'une décomposition spectrale de fonctions de Green de systèmes ouverts markoviens, que nous appliquons à un modèle d'oscillateur quantique de van der Pol. Nous soulignons qu’une propriété de signe des fonctions spectrales des systèmes d’équilibre ne s’imposait pas dans le cas de systèmes ouverts, ce qui produisait une surprenante "densité d’états négative", avec des conséquences physiques directes. Nous étudions ensuite la transition de phase entre une phase normale et une phase superfluide dans un système prototype de bosons dissipatifs forcés sur un réseau. Cette transition est caractérisée par une criticité à fréquence finie correspondant à la rupture spontanée de l'invariance par translation dans le temps, qui n’a pas d’analogue dans des systèmes à l’équilibre. Nous discutons le diagramme de phase en champ moyen d'une phase isolante de Mott stabilisée par dissipation, potentiellement pertinente pour des expériences en cours. Nos résultats suggèrent qu'il existe un compromis entre la fidélité de la phase stationnaire à un isolant de Mott et la robustesse d'une telle phase à taux de saut fini. Enfin, nous présentons des développements concernant la théorie du champ moyen dynamique (DMFT) pour l’étude des systèmes à plusieurs corps dissipatifs et forcés. Nous introduisons DMFT dans le contexte des modèles dissipatifs et forcés et nous développons une méthode pour résoudre le problème auxiliaire d'une impureté couplée simultanément à un environnement markovien et à un environnement non-markovien. À titre de test, nous appliquons cette nouvelle méthode à un modèle simple d’impureté fermioniqueMy PhD was devoted to the study of driven-dissipative quantum many-body systems. These systems represent natural platforms to explore fundamental questions about matter under non-equilibrium conditions, having at the same time a potential impact on emerging quantum technologies. In this thesis, we discuss a spectral decomposition of single-particle Green functions of Markovian open systems, that we applied to a model of a quantum van der Pol oscillator. We point out that a sign property of spectral functions of equilibrium systems doesn't hold in the case of open systems, resulting in a surprising ``negative density of states", with direct physical consequences. We study the phase transition between a normal and a superfluid phase in a prototype system of driven-dissipative bosons on a lattice. This transition is characterized by a finite-frequency criticality corresponding to the spontaneous break of time-translational invariance, which has no analog in equilibrium systems. Later, we discuss the mean-field phase diagram of a Mott insulating phase stabilized by dissipation, which is potentially relevant for ongoing experiments. Our results suggest that there is a trade off between the fidelity of the stationary phase to a Mott insulator and robustness of such a phase at finite hopping. Finally, we present some developments towards using dynamical mean field theory (DMFT) for studying driven-dissipative lattice systems. We introduce DMFT in the context of driven-dissipative models and developed a method to solve the auxiliary problem of a single impurity, coupled simultaneously to a Markovian and a non-Markovian environment. As a test, we applied this novel method to a simple model of a fermionic, single-mode impurity
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Seewald, Nadiane Cristina Cassol [UNESP]. "Método do hamiltoniano termodinamicamente equivalente para sistemas de muitos corpos." Universidade Estadual Paulista (UNESP), 2012. http://hdl.handle.net/11449/102540.
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O objetivo da Tese é investigar a aplicabilidade e propor extensões do método do hamiltoniano termodinamicamente equivalente (MHTE) para sistemas de muitos corpos descritos por uma teoria de campos. Historicamente, o MHTE tem sua origem na teoria quântica de muitos corpos para descrever o fenômeno da supercondutividade. O método consiste na observação de que o hamiltoniano de um sistema pode ser diagonalizado exatamente através de uma transformação unitária quando um número finito de momentos transferidos que contribuem para a interação é levado em conta no limite termodinâmico. Essa transformação unitária depende explicitamente de funções de gap que podem ser determinadas através do método variacional de Gibbs. Na presente Tese, extensões do método são feitas visando aplicações em sistemas de muitos corpos em diferentes situações, tais como: transições de fase estáaticas, evolução temporal de parâmetros de ordem descrita por equações dinâmicas estocásticas do tipo Ginzburg-Landau-Langevin (GLL), teorias quânticas de campos escalares relativísticos e teorias de muitos corpos para sistemas fermiônicos não relativísticos. Mostra-se, em particular, que o MHTE é um esquema de aproximação sistemático e controlável que permite incorporar acoplamentos de componentes de Fourier de parâmetros de ordem além do modo zero, da mesma forma que em teorias quânticas relativísticas ou não relativísticas ele incorpora correlações não perturbativas entre as partículas além daquelas levadas em conta pelas tradicionais aproximações de campo médio. Métodos são desenvolvidos para obtermos soluções numéricas explícitas com o objetivo de avaliar a aplicabilidade do MHTE em alguns casos específicos. Particular atenção é dedicada ao controle de divergências de Rayleigh-Jeans nas simulações numéricas de equações de GLL
The general objective of the Thesis is to apply the Method of the Thermodynamically Equivalent Hamiltonian (MTEH) to many-body systems described by a field theory. Historically, the MTEH has its origins in the quantum theory of manybody systems to describe the phenomenon of superconductivity. The method is based on the observation that the Hamiltonian of the system can be diagonalized exactly with a unitary transformation when a finite number of transfer momenta of the interaction are taken into account in the thermodynamic limit. This unitary transformation depends explicitly on gap functions that can be determined with the use of the Gibbs variational principle. In the present Thesis, extensions of the method are made envisaging applications in many-body systems in different situations, like: static phase transitions, time evolution of order parameters described by dynamic stochastic Ginzburg-Landau-Langevin equations, relativistic quantum scalar field theories, and many-body theories for nonrelativistic fermionic systems. It is shown that the MTEH is a systematic and controllable approximation scheme that in the theory of phase transitions allows to incorporate Fourier modes of the order parameter beyond the zero mode, in the same way that in the relativistic and nonrelativistic theories it incorporates particle nonperturbative correlations beyond those taken into account by the traditional mean field approximation. Methods are developed to obtain explicit numerical solutions with the aim to assess the applicability of the MTEH in specific situations. Particular attention is devoted to the control of Rayleigh-Jeans ultraviolet divergences in the numerical simulations of Ginzburg-Landau-Langevin equations
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Seewald, Nadiane Cristina Cassol. "Método do hamiltoniano termodinamicamente equivalente para sistemas de muitos corpos /." São Paulo, 2012. http://hdl.handle.net/11449/102540.
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Orientador: Gastão Inácio KreinBanca: Marcus Benghi Pinto
Banca: Ney Lemke
Banca: Sandra dos Santos Padula
Banca: Yogiro Hama
Resumo: O objetivo da Tese é investigar a aplicabilidade e propor extensões do método do hamiltoniano termodinamicamente equivalente (MHTE) para sistemas de muitos corpos descritos por uma teoria de campos. Historicamente, o MHTE tem sua origem na teoria quântica de muitos corpos para descrever o fenômeno da supercondutividade. O método consiste na observação de que o hamiltoniano de um sistema pode ser diagonalizado exatamente através de uma transformação unitária quando um número finito de momentos transferidos que contribuem para a interação é levado em conta no limite termodinâmico. Essa transformação unitária depende explicitamente de funções de gap que podem ser determinadas através do método variacional de Gibbs. Na presente Tese, extensões do método são feitas visando aplicações em sistemas de muitos corpos em diferentes situações, tais como: transições de fase estáaticas, evolução temporal de parâmetros de ordem descrita por equações dinâmicas estocásticas do tipo Ginzburg-Landau-Langevin (GLL), teorias quânticas de campos escalares relativísticos e teorias de muitos corpos para sistemas fermiônicos não relativísticos. Mostra-se, em particular, que o MHTE é um esquema de aproximação sistemático e controlável que permite incorporar acoplamentos de componentes de Fourier de parâmetros de ordem além do modo zero, da mesma forma que em teorias quânticas relativísticas ou não relativísticas ele incorpora correlações não perturbativas entre as partículas além daquelas levadas em conta pelas tradicionais aproximações de campo médio. Métodos são desenvolvidos para obtermos soluções numéricas explícitas com o objetivo de avaliar a aplicabilidade do MHTE em alguns casos específicos. Particular atenção é dedicada ao controle de divergências de Rayleigh-Jeans nas simulações numéricas de equações de GLL
Abstract: The general objective of the Thesis is to apply the Method of the Thermodynamically Equivalent Hamiltonian (MTEH) to many-body systems described by a field theory. Historically, the MTEH has its origins in the quantum theory of manybody systems to describe the phenomenon of superconductivity. The method is based on the observation that the Hamiltonian of the system can be diagonalized exactly with a unitary transformation when a finite number of transfer momenta of the interaction are taken into account in the thermodynamic limit. This unitary transformation depends explicitly on gap functions that can be determined with the use of the Gibbs variational principle. In the present Thesis, extensions of the method are made envisaging applications in many-body systems in different situations, like: static phase transitions, time evolution of order parameters described by dynamic stochastic Ginzburg-Landau-Langevin equations, relativistic quantum scalar field theories, and many-body theories for nonrelativistic fermionic systems. It is shown that the MTEH is a systematic and controllable approximation scheme that in the theory of phase transitions allows to incorporate Fourier modes of the order parameter beyond the zero mode, in the same way that in the relativistic and nonrelativistic theories it incorporates particle nonperturbative correlations beyond those taken into account by the traditional mean field approximation. Methods are developed to obtain explicit numerical solutions with the aim to assess the applicability of the MTEH in specific situations. Particular attention is devoted to the control of Rayleigh-Jeans ultraviolet divergences in the numerical simulations of Ginzburg-Landau-Langevin equations
Doutor
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Tran, Nhan Thanh. "Numerical methods for solving wave scattering problems." Diss., Kansas State University, 2016. http://hdl.handle.net/2097/32508.
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Doctor of PhilosophyDepartment of Mathematics
Alexander G. Ramm
In this thesis, the author presents several numerical methods for solving scalar and electromagnetic wave scattering problems. These methods are taken from the papers of Professor Alexander Ramm and the author, see [1] and [2]. In Chapter 1, scalar wave scattering by many small particles of arbitrary shapes with impedance boundary condition is studied. The problem is solved asymptotically and numerically under the assumptions a << d << λ, where k = 2π/λ is the wave number, λ is the wave length, a is the characteristic size of the particles, and d is the smallest distance between neighboring particles. A fast algorithm for solving this wave scattering problem by billions of particles is presented. The algorithm comprises the derivation of the (ORI) linear system and makes use of Conjugate Orthogonal Conjugate Gradient method and Fast Fourier Transform. Numerical solutions of the scalar wave scattering problem with 1, 4, 7, and 10 billions of small impedance particles are achieved for the first time. In these numerical examples, the problem of creating a material with negative refraction coefficient is also described and a recipe for creating materials with a desired refraction coefficient is tested. In Chapter 2, electromagnetic (EM) wave scattering problem by one and many small perfectly conducting bodies is studied. A numerical method for solving this problem is presented. For the case of one body, the problem is solved for a body of arbitrary shape, using the corresponding boundary integral equation. For the case of many bodies, the problem is solved asymptotically under the physical assumptions a << d << λ, where a is the characteristic size of the bodies, d is the minimal distance between neighboring bodies, λ = 2π/k is the wave length and k is the wave number. Numerical results for the cases of one and many small bodies are presented. Error analysis for the numerical method are also provided.
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Fritsche, Gian Mauricio. "Hyper-heuristic based particle swarm optimization for many-objective problems." reponame:Repositório Institucional da UFPR, 2016. http://hdl.handle.net/1884/41790.
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Orientadora : Profª. Ph.D. Aurora PozoDissertação (mestrado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Informática. Defesa: Curitiba, 29/02/2016
Inclui referências : f. 81-87
Resumo: O algoritmo de Otimização por Enxame de Partículas (PSO) e uma meta-heurística inspirada no comportamento de bandos de aves a procura de alimento. Os bons resultados obtidos por esta técnica na otimização de problemas mono-objetivo incentivaram o estudo de variações para problemas multi- objetivo (MOPSO), que também alcançaram bons resultados. Para a adaptação do PSO para problemas multi-objetivo algumas modificações foram necessárias, tais como o uso de um operador para seleção de líder e a aplicação de um operador de arquivamento. Entretanto, a qualidade do algoritmo diminui conforme o aumento do numero de objetivos. Encontrar, dentre os diferentes operadores de selecao de líder e de arquivamento, propostos na literatura, os mais apropriado para determinada instância de um problema permite amenizar esta perda de qualidade. Porem esta tarefa não é uma tarefa trivial. Em trabalhos anteriores o uso de hiper-heurística para a seleção de uma combinação apropriada destes operadores e proposta. Hiper-heurísticas são técnicas para a seleção, ou geração, de heurísticas para problemas de busca. Estas técnicas visam a seleção, ou geração, de uma heurística apropriada para determinada instancia de um problema ou estágio da busca. Neste trabalho foi abordada a hipótese de que, o uso de métodos de seleção mais avançados poderiam melhorar desempenho do MOPSO baseado em Hiper-heurística (H-MOPSO). Para investigar esta hipótese quatro métodos de seleção foram avaliados e comparados a um algoritmo multi-objetivo estado da arte. Nos resultados apresentados o H-MOPSO obteve melhores resultados na maioria dos problemas.
Abstract: Multi-objective Particle Swarm Optimization (MOPSO) is a promising meta-heuristic to solve Many-Objective Problems (MaOPs), however, its performance decreases as the number of objective functions increases. Selecting a good combination of leader and archiving methods helps the algorithm to deal with the challenges caused by this increase in the number of objectives, but finding the most appropriate combination for a given problem is a hard task. To deal with this issue, previous works proposed the use of a simple hyper-heuristic to select dynamically a good combination of leader and archiving methods and achieved promising results. In this work, we hypothesize that by using more advanced heuristic selection methods we could further improve the performance of the algorithm. To investigate this hypothesis we conducted experimental studies comparing four heuristic selection methods. After selecting the best performing variant from this study, we conducted a second empirical study to compare this variant to a state-of-the- art optimizer, where the resulting algorithm outperformed it in most of the problems investigated.
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Johnson, Cory. "Suggestions for Deontic Logicians." Thesis, Virginia Tech, 2013. http://hdl.handle.net/10919/19221.
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The purpose of this paper is to make a suggestion to deontic logic: Respect Hume\'s Law, the answer to the is-ought problem that says that all ought-talk is completely cut off from is-talk. Most deontic logicians have sought another solution: Namely, the solution that says that we can bridge the is-ought gap. Thus, a century\'s worth of research into these normative systems of logic has lead to many attempts at doing just that. At the same time, the field of deontic logic has come to be plagued with paradox. My argument essentially depends upon there being a substantive relation between this betrayal of Hume and the plethora of paradoxes that have appeared in two-adic (binary normative operator), one-adic (unary normative operator), and zero-adic (constant normative operator) deontic systems, expressed in the traditions of von Wright, Kripke, and Anderson, respectively. My suggestion has two motivations: First, to rid the philosophical literature of its puzzles and second, to give Hume\'s Law a proper formalization. Exploring the issues related to this project also points to the idea that maybe we should re-engineer (e.g., further generalize) our classical calculus, which might involve the adoption of many-valued logics somewhere down the line.Master of Arts
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Mathews, Susann Miller. "The effect of using as many variables as are needed to solve word problems on the problem-solving skills and attitudes of students in Algebra I /." The Ohio State University, 1994. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487853913101401.
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Molari, Marco. "Statistical mechanics of polymer models: rigorous results and applications." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/10429/.
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Monomer-dimer models are amongst the models in statistical mechanics which found application in many areas of science, ranging from biology to social sciences. This model describes a many-body system in which monoatomic and diatomic particles subject to hard-core interactions get deposited on a graph.
In our work we provide an extension of this model to higher-order particles. The aim of our work is threefold: first we study the thermodynamic properties of the newly introduced model. We solve analytically some regular cases and find that, differently from the original, our extension admits phase transitions. Then we tackle the inverse problem, both from an analytical and numerical perspective. Finally we propose an application to aggregation phenomena in virtual messaging services.
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Nakib, Protik H. "The Multiconfiguration Time Dependent Hartree-Fock Method for Cylindrical Systems." Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/26297.
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Many-body quantum dynamics is a challenging problem that has induced the development of many different computational techniques. One powerful technique is the multiconfiguration time-dependent Hartree-Fock (MCTDHF) method. This method allows proper consideration of electronic correlation with much less computational overhead compared to other similar methods. In this work, we present our implementation of the MCTDHF method on a non-uniform cylindrical grid. With the one-body limit of our code, we studied the controversial topic of tunneling delay, and showed that our results agree with one recent experiment while
disagreeing with another. Using the fully correlated version of the code, we demonstrated the ability of MCTDHF to address correlation by calculating the ground state ionization energies of a few strongly correlated systems.
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Luu, Thomas C. "Effective interactions within an oscillator basis /." Thesis, Connect to this title online; UW restricted, 2003. http://hdl.handle.net/1773/9803.
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Gibson, Peter C. "Moment problems for Jacobi matrices and inverse problems for systems of many coupled oscillators." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ49497.pdf.
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Xie, Zhifu. "On the N-body Problem." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1444.pdf.
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Olsson, Emma. "Many-body Problems in the Theory of Stellar Collapse and Neutron Stars." Doctoral thesis, Uppsala University, The Uppsala Astronomical Observatory, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4704.
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When modelling the collapse of massive stars leading to supernova explosions and the cooling of neutron stars, understanding the microphysical processes, such as the interaction of neutrinos within a dense medium are of vital importance. The interaction of neutrinos with nucleons (neutrons and protons) is altered by the presence of the medium, compared to the same process with free nucleons. Neutrino scattering and production processes may be characterized in terms of the excitations that are created or destroyed in the nuclear medium. One way to analyse the effects of the medium is by using Landau's theory of normal Fermi liquids. This theory gives simple relationships between physical quantities such as the spin susceptibility or the response to a weak interaction probe in terms of Landau parameters, that are measures of the interaction between quasiparticles. One problem when using Landau Fermi liquid theory for nucleon matter is that the interaction has a tensor component. The tensor interaction does not conserve the total spin and, as a consequence, there are generally contributions to long-wavelength response functions from states that have more than one quasiparticle-quasihole pair in the intermediate state. Such contributions cannot be calculated in terms of Landau parameters alone, since in the usual formulation of Landau theory, only singlepair excitations are considered. In this thesis three problems are addressed. First, we obtain bounds on the contributions from more than one quasiparticle-quasihole pair by using sum-rule arguments. Second, we derive expressions for static response functions allowing for the tensor components of the interaction. We analyse which the most important effects are on the static response of nucleon matter, and find that the major contributions comes from renormalization of coupling constants and transitions to states with more than one quasiparticle-quasihole pair. Third, we show how contributions to the dynamical response coming from states containing two quasiparticle-quasihole pairs may be evaluated in terms of Landau theory if one allows for the effect of collisions in the Landau kinetic equation. We consider the case of asymmetric nuclear matter, and our work goes beyond earlier works in that they contain the effects of collisions in addition to those of the mean field.
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Gmys, Jan. "Heterogeneous cluster computing for many-task exact optimization : application to permutation problems." Thesis, Lille 1, 2017. http://www.theses.fr/2017LIL10142/document.
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L'algorithme Branch-and-Bound (B&B) est une méthode de recherche arborescente fréquemment utilisé pour la résolution exacte de problèmes d'optimisation combinatoire (POC). Néanmoins, seules des petites instances peuvent être effectivement résolues sur une machine séquentielle, le nombre de sous-problèmes à évaluer étant souvent très grand. Visant la resolution de POC de grande taille, nous réexaminons la conception et l'implémentation d'algorithmes B&B massivement parallèles sur de larges plateformes hétérogènes de calcul, intégrant des processeurs multi-coeurs, many-cores et et processeurs graphiques (GPUs). Pour une représentation compacte en mémoire des sous-problèmes une structure de données originale (IVM), dédiée aux problèmes de permutation est utilisée. En raison de la forte irrégularité de l'arbre de recherche, l'équilibrage de charge dynamique entre processus d'exploration parallèles occupe une place centrale dans cette thèse. Basés sur un encodage compact de l'espace de recherche sous forme d'intervalles, des stratégies de vol de tâches sont proposées pour processeurs multi-core et GPU, ainsi une approche hiérarchique pour l'équilibrage de charge dans les systèmes multi-GPU et multi-CPU à mémoire distribuée. Trois problèmes d'optimisation définis sur l'ensemble des permutations, le problème d'ordonnancement Flow-Shop (FSP), d'affectation quadratique (QAP) et le problème des n-dames sont utilisés comme cas d'étude. La resolution en 9 heures d'une instance du FSP dont le temps de résolution séquentiel est estimé à 22 ans demontre la capacité de passage à l'échelle des algorithmes proposés sur une grappe de calcul composé de 36 GPUsBranch-and-Bound (B&B) is a frequently used tree-search exploratory method for the exact resolution of combinatorial optimization problems (COPs). However, in practice, only small problem instances can be solved on a sequential computer, as B&B generates often generates a huge amount of subproblems to be evaluated. In order to solve large COPs, we revisit the design and implementation of massively parallel B&B on top of large heterogeneous clusters, integrating multi-core CPUs, many-core processors and GPUs. For the efficient storage and management of subproblems an original data structure (IVM) dedicated to permutation problems is used. Because of the highly irregular and unpredictable shape of the B&B tree, dynamic load balancing between parallel exploration processes is one of the main issues addressed in this thesis. Based on a compact encoding of the search space in the form of intervals, work stealing strategies for multi-core and GPU are proposed, as well as hierarchical approaches for load balancing in distributed memory multi-CPU/multi-GPU systems. Three permutation problems, the Flowshop Scheduling Problem (FSP), the Quadratic Assignment Problem (QAP) and the n-Queens puzzle problem are used as test-cases. The resolution, in 9 hours, of a FSP instance with an estimated sequential execution time of 22 years demonstrates the scalability of the proposed algorithms on a cluster composed of 36 GPUs
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Song, Chang Liang. "An improved procedure for calculating effective interactions and operators /." Thesis, Connect to this title online; UW restricted, 1998. http://hdl.handle.net/1773/9643.
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Abreu, Bruno Ricardi de 1990. "Matriz densidade a baixas temperaturas para sistemas com interação de pares." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/276983.
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Orientador: Silvio Antonio Sachetto VitielloDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin
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Resumo: A matriz densidade é um objeto fundamental na mecânica estatística de sistemas de muitos corpos quânticos. Através dela pode ser encontrado o valor esperado de qualquer observável do sistema de interesse. Neste trabalho calculamos a matriz densidade a baixas temperaturas para sistemas de muitos corpos que interagem via um potencial de pares através de convolucões da matriz densidade a altas temperaturas, onde é possível utilizar aproximações semi-clássicas
Abstract: The density matrix is a fundamental object in statistical mechanics of quantum many-body systems. Through it the observed value of any observable of a quantum mechanical system of interest can be found. In this work we calculate the density matrix at low temperatures of manybody systems that interact through pairwise potentials using a convolution procedure of the density matrix at high temperatures, where is possible to apply semi-classical approximations
Mestrado
Física
Mestre em Física
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Stevenson, Paul. "Nuclear structure calculations using many-body perturbation theory with a separable interaction." Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312333.
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Duro, Joao A. "Machine learning based decision support for a class of many-objective optimisation problems." Thesis, Cranfield University, 2013. http://dspace.lib.cranfield.ac.uk/handle/1826/8260.
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There is a growing recognition for the multiple criteria decision making (MCDM) based multi-objective evolutionary algorithms (MOEAs) for tackling many-objective optimisation problems (MaOPs). In that, the aim is to utilise the decision makers’ (DMs’) preferences to guide the search towards a few solutions, as against the whole Pareto-optimal front (POF). This thesis is based on the premise that the practical utility of the MCDM based MOEAs may be impaired due to the lack of–objectivity (a rational basis); repeatability (identical preferences for identical options); consistency (alike preferences across multiple interaction stages); and coherence (alike preferences by multiple DMs) in the DMs’ preferences. To counter these limitations, this thesis aimed at developing offline and online decision support by capturing the preference-structure of the objective functions inherent in the problem model itself. This aim has been realised through the following objectives: • Identification of a criterion for the decision support: in that, preservation of the correlation– structure of the MOEA solutions is found to be a robust criterion in the case of MaOPs. • Development of a machine learning based offline objective reduction framework: it com¬prises of linear and nonlinear objective reduction algorithms, which facilitate the decision support through revelation of: (i) the redundant objectives (if any), (ii) preference-ranking of the essential objectives, (iii) the smallest objective sets corresponding to pre-specified errors, and (iv) the objective sets of pre-specified sizes that correspond to minimum error. • Development of an online objective reduction framework: it addresses a major pitfall associated with the offline framework, that–an essential objective if erroneously eliminated as redundant, has no scope of being reconsidered in the subsequent analysis. This pitfall is countered through a probabilistic retention of all the objectives, and this serves as a self-correcting mechanism that enhances the overall accuracy. • Timing the decision support: it is acknowledged that the revelations by the decision support may vary depending on when the offline or online framework is applied during an MOEA run. This uncertainty on the timing of the decision support is countered through the proposition of an entropy based dissimilarity measure. The efficacy of the proposed frameworks is investigated against a broad range of test problems (scaled up to 50 objectives) and some real-world MaOPs; and, the accuracy of the corresponding decision support is compared against that of an alternative approach based on preserving the dominance relations. The results illustrate that the proposed frameworks and the corresponding decision support bear significant utility for those MaOPs, where not all the objectives are essential, or equally important for describing the true POF. The considered real-world problems also bear evidence of the fact that MaOPs with redundant and disparately important objectives may commonly exist in practice.
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Holtz, Susan Lady. "Liouville resolvent methods applied to highly correlated systems." Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/49795.
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