979 resultados para Numerical renormalization-group


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In this thesis we consider three different models for strongly correlated electrons, namely a multi-band Hubbard model as well as the spinless Falicov-Kimball model, both with a semi-elliptical density of states in the limit of infinite dimensions d, and the attractive Hubbard model on a square lattice in d=2. In the first part, we study a two-band Hubbard model with unequal bandwidths and anisotropic Hund's rule coupling (J_z-model) in the limit of infinite dimensions within the dynamical mean-field theory (DMFT). Here, the DMFT impurity problem is solved with the use of quantum Monte Carlo (QMC) simulations. Our main result is that the J_z-model describes the occurrence of an orbital-selective Mott transition (OSMT), in contrast to earlier findings. We investigate the model with a high-precision DMFT algorithm, which was developed as part of this thesis and which supplements QMC with a high-frequency expansion of the self-energy. The main advantage of this scheme is the extraordinary accuracy of the numerical solutions, which can be obtained already with moderate computational effort, so that studies of multi-orbital systems within the DMFT+QMC are strongly improved. We also found that a suitably defined Falicov-Kimball (FK) model exhibits an OSMT, revealing the close connection of the Falicov-Kimball physics to the J_z-model in the OSM phase. In the second part of this thesis we study the attractive Hubbard model in two spatial dimensions within second-order self-consistent perturbation theory. This model is considered on a square lattice at finite doping and at low temperatures. Our main result is that the predictions of first-order perturbation theory (Hartree-Fock approximation) are renormalized by a factor of the order of unity even at arbitrarily weak interaction (U->0). The renormalization factor q can be evaluated as a function of the filling n for 00, the q-factor vanishes, signaling the divergence of self-consistent perturbation theory in this limit. Thus we present the first asymptotically exact results at weak-coupling for the negative-U Hubbard model in d=2 at finite doping.

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The optical quality of the human eye mainly depends on the refractive performance of the cornea. The shape of the cornea is a mechanical balance between intraocular pressure and tissue intrinsic stiffness. Several surgical procedures in ophthalmology alter the biomechanics of the cornea to provoke local or global curvature changes for vision correction. Legitimated by the large number of surgical interventions performed every day, the demand for a deeper understanding of corneal biomechanics is rising to improve the safety of procedures and medical devices. The aim of our work is to propose a numerical model of corneal biomechanics, based on the stromal microstructure. Our novel anisotropic constitutive material law features a probabilistic weighting approach to model collagen fiber distribution as observed on human cornea by Xray scattering analysis (Aghamohammadzadeh et. al., Structure, February 2004). Furthermore, collagen cross-linking was explicitly included in the strain energy function. Results showed that the proposed model is able to successfully reproduce both inflation and extensiometry experimental data (Elsheikh et. al., Curr Eye Res, 2007; Elsheikh et. al., Exp Eye Res, May 2008). In addition, the mechanical properties calculated for patients of different age groups (Group A: 65-79 years; Group B: 80-95 years) demonstrate an increased collagen cross-linking, and a decrease in collagen fiber elasticity from younger to older specimen. These findings correspond to what is known about maturing fibrous biological tissue. Since the presented model can handle different loading situations and includes the anisotropic distribution of collagen fibers, it has the potential to simulate clinical procedures involving nonsymmetrical tissue interventions. In the future, such mechanical model can be used to improve surgical planning and the design of next generation ophthalmic devices.

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OBJECTIVE: In a prospective study we investigated whether numerical and functional changes of CD4+CD25(high) regulatory T cells (Treg) were associated with changes of disease activity observed during pregnancy and post partum in patients with rheumatoid arthritis (RA). METHODS: The frequency of CD4+CD25(high) T cells was determined by flow cytometry in 12 patients with RA and 14 healthy women during and after pregnancy. Fluorescence-activated cell sorting (FACS) was used to sort CD4+CD25(high) T cells and CD4+CD25- T cells were stimulated with anti-CD3 and anti-CD28 monoclonal antibodies alone or in co-culture to investigate proliferation and cytokine secretion. RESULTS: Frequencies of CD4+CD25(high) Treg were significantly higher in the third trimester compared to 8 weeks post partum in patients and controls. Numbers of CD4+CD25(high) Treg inversely correlated with disease activity in the third trimester and post partum. In co-culture experiments significantly higher amounts of IL10 and lowered levels of tumour necrosis factor (TNF)alpha and interferon (IFN)gamma were found in supernatants of the third trimester compared to postpartum samples. These findings were independent from health or disease in pregnancy, however postpartum TNFalpha and IFN gamma levels were higher in patients with disease flares. CONCLUSION: The amelioration of disease activity in the third trimester corresponded to the increased number of Treg that induced a pronounced anti-inflammatory cytokine milieu. The pregnancy related quantitative and qualitative changes of Treg suggest a beneficial effect of Treg on disease activity.

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Is numerical mimicry a third way of establishing truth? Kevin Heng received his M.S. and Ph.D. in astrophysics from the Joint Institute for Laboratory Astrophysics (JILA) and the University of Colorado at Boulder. He joined the Institute for Advanced Study in Princeton from 2007 to 2010, first as a Member and later as the Frank & Peggy Taplin Member. From 2010 to 2012 he was a Zwicky Prize Fellow at ETH Z¨urich (the Swiss Federal Institute of Technology). In 2013, he joined the Center for Space and Habitability (CSH) at the University of Bern, Switzerland, as a tenure-track assistant professor, where he leads the Exoplanets and Exoclimes Group. He has worked on, and maintains, a broad range of interests in astrophysics: shocks, extrasolar asteroid belts, planet formation, fluid dynamics, brown dwarfs and exoplanets. He coordinates the Exoclimes Simulation Platform (ESP), an open-source set of theoretical tools designed for studying the basic physics and chemistry of exoplanetary atmospheres and climates (www.exoclime.org). He is involved in the CHEOPS (Characterizing Exoplanet Satellite) space telescope, a mission approved by the European Space Agency (ESA) and led by Switzerland. He spends a fair amount of time humbly learning the lessons gleaned from studying the Earth and Solar System planets, as related to him by atmospheric, climate and planetary scientists. He received a Sigma Xi Grant-in-Aid of Research in 2006

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This study combined data on fin whale Balaenoptera physalus, humpback whale Megaptera novaeangliae, minke whale B. acutorostrata, and sei whale B. borealis sightings from large-scale visual aerial and ship-based surveys (248 and 157 sightings, respectively) with synoptic acoustic sampling of krill Meganyctiphanes norvegica and Thysanoessa sp. abundance in September 2005 in West Greenland to examine the relationships between whales and their prey. Krill densities were obtained by converting relationships of volume backscattering strengths at multiple frequencies to a numerical density using an estimate of krill target strength. Krill data were vertically integrated in 25 m depth bins between 0 and 300 m to obtain water column biomass (g/m**2) and translated to density surfaces using ordinary kriging. Standard regression models (Generalized Additive Modeling, GAM, and Generalized Linear Modeling, GLM) were developed to identify important explanatory variables relating the presence, absence, and density of large whales to the physical and biological environment and different survey platforms. Large baleen whales were concentrated in 3 focal areas: (1) the northern edge of Lille Hellefiske bank between 65 and 67°N, (2) north of Paamiut at 63°N, and (3) in South Greenland between 60 and 61° N. There was a bimodal pattern of mean krill density between depths, with one peak between 50 and 75 m (mean 0.75 g/m**2, SD 2.74) and another between 225 and 275 m (mean 1.2 to 1.3 g/m**2, SD 23 to 19). Water column krill biomass was 3 times higher in South Greenland than at any other site along the coast. Total depth-integrated krill biomass was 1.3 x 10**9 (CV 0.11). Models indicated the most important parameter in predicting large baleen whale presence was integrated krill abundance, although this relationship was only significant for sightings obtained on the ship survey. This suggests that a high degree of spatio-temporal synchrony in observations is necessary for quantifying predator-prey relationships. Krill biomass was most predictive of whale presence at depths >150 m, suggesting a threshold depth below which it is energetically optimal for baleen whales to forage on krill in West Greenland.

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Sloshing describes the movement of liquids inside partially filled tanks, generating dynamic loads on the tank structure. The resulting impact pressures are of great importance in assessing structural strength, and their correct evaluation still represents a challenge for the designer due to the high level of nonlinearities involved, with complex free surface deformations, violent impact phenomena and influence of air trapping. In the present paper, a set of two-dimensional cases, for which experimental results are available, is considered to assess the merits and shortcomings of different numerical methods for sloshing evaluation, namely two commercial RANS solvers (FLOW-3D and LS-DYNA), and two academic software (Smoothed Particle Hydrodynamics and RANS). Impact pressures at various critical locations and global moment induced by water motion in a partially filled rectangular tank, subject to a simple harmonic rolling motion, are evaluated and predictions are compared with experimental measurements. 2012 Copyright Taylor and Francis Group, LLC.

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García et al. present a class of column generation (CG) algorithms for nonlinear programs. Its main motivation from a theoretical viewpoint is that under some circumstances, finite convergence can be achieved, in much the same way as for the classic simplicial decomposition method; the main practical motivation is that within the class there are certain nonlinear column generation problems that can accelerate the convergence of a solution approach which generates a sequence of feasible points. This algorithm can, for example, accelerate simplicial decomposition schemes by making the subproblems nonlinear. This paper complements the theoretical study on the asymptotic and finite convergence of these methods given in [1] with an experimental study focused on their computational efficiency. Three types of numerical experiments are conducted. The first group of test problems has been designed to study the parameters involved in these methods. The second group has been designed to investigate the role and the computation of the prolongation of the generated columns to the relative boundary. The last one has been designed to carry out a more complete investigation of the difference in computational efficiency between linear and nonlinear column generation approaches. In order to carry out this investigation, we consider two types of test problems: the first one is the nonlinear, capacitated single-commodity network flow problem of which several large-scale instances with varied degrees of nonlinearity and total capacity are constructed and investigated, and the second one is a combined traffic assignment model

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The purpose of this Project is, first and foremost, to disclose the topic of nonlinear vibrations and oscillations in mechanical systems and, namely, nonlinear normal modes NNMs to a greater audience of researchers and technicians. To do so, first of all, the dynamical behavior and properties of nonlinear mechanical systems is outlined from the analysis of a pair of exemplary models with the harmonic balanced method. The conclusions drawn are contrasted with the Linear Vibration Theory. Then, it is argued how the nonlinear normal modes could, in spite of their limitations, predict the frequency response of a mechanical system. After discussing those introductory concepts, I present a Matlab package called 'NNMcont' developed by a group of researchers from the University of Liege. This package allows the analysis of nonlinear normal modes of vibration in a range of mechanical systems as extensions of the linear modes. This package relies on numerical methods and a 'continuation algorithm' for the computation of the nonlinear normal modes of a conservative mechanical system. In order to prove its functionality, a two degrees of freedom mechanical system with elastic nonlinearities is analized. This model comprises a mass suspended on a foundation by means of a spring-viscous damper mechanism -analogous to a very simplified model of most suspended structures and machines- that has attached a mass damper as a passive vibration control system. The results of the computation are displayed on frequency energy plots showing the NNMs branches along with modal curves and time-series plots for each normal mode. Finally, a critical analysis of the results obtained is carried out with an eye on devising what they can tell the researcher about the dynamical properties of the system.

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Purpose: In this paper the authors aim to show the advantages of using the decomposition method introduced by Adomian to solve Emden's equation, a classical non‐linear equation that appears in the study of the thermal behaviour of a spherical cloud and of the gravitational potential of a polytropic fluid at hydrostatic equilibrium. Design/methodology/approach: In their work, the authors first review Emden's equation and its possible solutions using the Frobenius and power series methods; then, Adomian polynomials are introduced. Afterwards, Emden's equation is solved using Adomian's decomposition method and, finally, they conclude with a comparison of the solution given by Adomian's method with the solution obtained by the other methods, for certain cases where the exact solution is known. Findings: Solving Emden's equation for n in the interval [0, 5] is very interesting for several scientific applications, such as astronomy. However, the exact solution is known only for n=0, n=1 and n=5. The experiments show that Adomian's method achieves an approximate solution which overlaps with the exact solution when n=0, and that coincides with the Taylor expansion of the exact solutions for n=1 and n=5. As a result, the authors obtained quite satisfactory results from their proposal. Originality/value: The main classical methods for obtaining approximate solutions of Emden's equation have serious computational drawbacks. The authors make a new, efficient numerical implementation for solving this equation, constructing iteratively the Adomian polynomials, which leads to a solution of Emden's equation that extends the range of variation of parameter n compared to the solutions given by both the Frobenius and the power series methods.

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Federal Highway Administration, Office of Safety and Traffic Operations Research and Development, McLean, Va.

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Federal Highway Administration, Office of Safety and Traffic Operations Research and Development, McLean, Va.

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Chronic unremittent low back pain (LBP) is characterised by cognitive barriers to treatment. Combining a motor control training approach with individualised education about pain physiology is effective in this group of patients. This randomized comparative trial (i) evaluates an approach to motor control acquisition and training that considers the complexities of the relationship between pain and motor output, and (ii) compares the efficacy and cost of individualized and group pain physiology education. After an "ongoing usual treatment" period, patients participated in a 4-week motor control and pain physiology education program. Patients received four one-hour individualized education sessions (IE) or one 4-hour group lecture (GE). Both groups reduced pain (numerical rating scale) and disability (Roland Morris Disability Questionnaire). IE showed bigger decreases, which were maintained at 12 months (P < 0.05 for all). The combined motor control and education approach is effective. Although group education imparts a lesser effect, it may be more cost-efficient. [ABSTRACT FROM AUTHOR]

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Group decision making is the study of identifying and selecting alternatives based on the values and preferences of the decision maker. Making a decision implies that there are several alternative choices to be considered. This paper uses the concept of Data Envelopment Analysis to introduce a new mathematical method for selecting the best alternative in a group decision making environment. The introduced model is a multi-objective function which is converted into a multi-objective linear programming model from which the optimal solution is obtained. A numerical example shows how the new model can be applied to rank the alternatives or to choose a subset of the most promising alternatives.

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The results of numerical modelling of nonlinear propagation of an optical signal in multimode fibres with a small differential group delay are presented. It is found that the dependence of the error vector magnitude (EVM) on the differential group delay can be reduced by increasing the number of ADC samples per symbol in the numerical implementation of the differential group delay compensation algorithm in the receiver. The possibility of using multimode fibres with a small differential group delay for data transmission in modern digital communication systems is demonstrated. It is shown that with increasing number of modes the strong coupling regime provides a lower EVM level than the weak coupling one.