929 resultados para non-uniform scale perturbation finite difference scheme


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We consider modifications of the nonlinear Schrodinger model (NLS) to look at the recently introduced concept of quasi-integrability. We show that such models possess an in finite number of quasi-conserved charges which present intriguing properties in relation to very specific space-time parity transformations. For the case of two-soliton solutions where the fields are eigenstates of this parity, those charges are asymptotically conserved in the scattering process of the solitons. Even though the charges vary in time their values in the far past and the far future are the same. Such results are obtained through analytical and numerical methods, and employ adaptations of algebraic techniques used in integrable field theories. Our findings may have important consequences on the applications of these models in several areas of non-linear science. We make a detailed numerical study of the modified NLS potential of the form V similar to (vertical bar psi vertical bar(2))(2+epsilon), with epsilon being a perturbation parameter. We perform numerical simulations of the scattering of solitons for this model and find a good agreement with the results predicted by the analytical considerations. Our paper shows that the quasi-integrability concepts recently proposed in the context of modifications of the sine-Gordon model remain valid for perturbations of the NLS model.

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The elephant walk model originally proposed by Schutz and Trimper to investigate non-Markovian processes led to the investigation of a series of other random-walk models. Of these, the best known is the Alzheimer walk model, because it was the first model shown to have amnestically induced persistence-i.e. superdiffusion caused by loss of memory. Here we study the robustness of the Alzheimer walk by adding a memoryless stochastic perturbation. Surprisingly, the solution of the perturbed model can be formally reduced to the solutions of the unperturbed model. Specifically, we give an exact solution of the perturbed model by finding a surjective mapping to the unperturbed model. Copyright (C) EPLA, 2012

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Abstract Background How are morphological evolution and developmental changes related? This rather old and intriguing question had a substantial boost after the 70s within the framework of heterochrony (changes in rates or timing of development) and nowadays has the potential to make another major leap forward through the combination of approaches: molecular biology, developmental experimentation, comparative systematic studies, geometric morphometrics and quantitative genetics. Here I take an integrated approach combining life-history comparative analyses, classical and geometric morphometrics applied to ontogenetic series to understand changes in size and shape which happen during the evolution of two New World Monkeys (NWM) sister genera. Results Cebus and Saimiri share the same basic allometric patterns in skull traits, a result robust to sexual and ontogenetic variation. If adults of both genera are compared in the same scale (discounting size differences) most differences are small and not statistically significant. These results are consistent using both approaches, classical and geometric Morphometrics. Cebus is a genus characterized by a number of peramorphic traits (adult-like) while Saimiri is a genus with paedomorphic (child like) traits. Yet, the whole clade Cebinae is characterized by a unique combination of very high pre-natal growth rates and relatively slow post-natal growth rates when compared to the rest of the NWM. Morphologically Cebinae can be considered paedomorphic in relation to the other NWM. Geometric morphometrics allows the precise separation of absolute size, shape variation associated with size (allometry), and shape variation non-associated with size. Interestingly, and despite the fact that they were extracted as independent factors (principal components), evolutionary allometry (those differences in allometric shape associated with intergeneric differences) and ontogenetic allometry (differences in allometric shape associated with ontogenetic variation within genus) are correlated within these two genera. Furthermore, morphological differences produced along these two axes are quite similar. Cebus and Saimiri are aligned along the same evolutionary allometry and have parallel ontogenetic allometry trajectories. Conclusion The evolution of these two Platyrrhini monkeys is basically due to a size differentiation (and consequently to shape changes associated with size). Many life-history changes are correlated or may be the causal agents in such evolution, such as delayed on-set of reproduction in Cebus and larger neonates in Saimiri.

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[EN]In this paper we propose a finite element method approach for modelling the air quality in a local scale over complex terrain. The area of interest is up to tens of kilometres and it includes pollutant sources. The proposed methodology involves the generation of an adaptive tetrahedral mesh, the computation of an ambient wind field, the inclusion of the plume rise effect in the wind field, and the simulation of transport and reaction of pollutants. We apply our methodology to simulate a fictitious pollution episode in La Palma island (Canary Island, Spain)...

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Congresos y conferencias

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[EN]This paper shows a finite element method for pollutant transport with several pollutant sources. An Eulerian convection–diffusion–reaction model to simulate the pollutant dispersion is used. The discretization of the different sources allows to impose the emissions as boundary conditions. The Eulerian description can deal with the coupling of several plumes. An adaptive stabilized finite element formulation, specifically Least-Squares, with a Crank-Nicolson temporal integration is proposed to solve the problem. An splitting scheme has been used to treat separately the transport and the reaction. A mass-consistent model has been used to compute the wind field of the problem…

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The present thesis is concerned with the study of a quantum physical system composed of a small particle system (such as a spin chain) and several quantized massless boson fields (as photon gasses or phonon fields) at positive temperature. The setup serves as a simplified model for matter in interaction with thermal "radiation" from different sources. Hereby, questions concerning the dynamical and thermodynamic properties of particle-boson configurations far from thermal equilibrium are in the center of interest. We study a specific situation where the particle system is brought in contact with the boson systems (occasionally referred to as heat reservoirs) where the reservoirs are prepared close to thermal equilibrium states, each at a different temperature. We analyze the interacting time evolution of such an initial configuration and we show thermal relaxation of the system into a stationary state, i.e., we prove the existence of a time invariant state which is the unique limit state of the considered initial configurations evolving in time. As long as the reservoirs have been prepared at different temperatures, this stationary state features thermodynamic characteristics as stationary energy fluxes and a positive entropy production rate which distinguishes it from being a thermal equilibrium at any temperature. Therefore, we refer to it as non-equilibrium stationary state or simply NESS. The physical setup is phrased mathematically in the language of C*-algebras. The thesis gives an extended review of the application of operator algebraic theories to quantum statistical mechanics and introduces in detail the mathematical objects to describe matter in interaction with radiation. The C*-theory is adapted to the concrete setup. The algebraic description of the system is lifted into a Hilbert space framework. The appropriate Hilbert space representation is given by a bosonic Fock space over a suitable L2-space. The first part of the present work is concluded by the derivation of a spectral theory which connects the dynamical and thermodynamic features with spectral properties of a suitable generator, say K, of the time evolution in this Hilbert space setting. That way, the question about thermal relaxation becomes a spectral problem. The operator K is of Pauli-Fierz type. The spectral analysis of the generator K follows. This task is the core part of the work and it employs various kinds of functional analytic techniques. The operator K results from a perturbation of an operator L0 which describes the non-interacting particle-boson system. All spectral considerations are done in a perturbative regime, i.e., we assume that the strength of the coupling is sufficiently small. The extraction of dynamical features of the system from properties of K requires, in particular, the knowledge about the spectrum of K in the nearest vicinity of eigenvalues of the unperturbed operator L0. Since convergent Neumann series expansions only qualify to study the perturbed spectrum in the neighborhood of the unperturbed one on a scale of order of the coupling strength we need to apply a more refined tool, the Feshbach map. This technique allows the analysis of the spectrum on a smaller scale by transferring the analysis to a spectral subspace. The need of spectral information on arbitrary scales requires an iteration of the Feshbach map. This procedure leads to an operator-theoretic renormalization group. The reader is introduced to the Feshbach technique and the renormalization procedure based on it is discussed in full detail. Further, it is explained how the spectral information is extracted from the renormalization group flow. The present dissertation is an extension of two kinds of a recent research contribution by Jakšić and Pillet to a similar physical setup. Firstly, we consider the more delicate situation of bosonic heat reservoirs instead of fermionic ones, and secondly, the system can be studied uniformly for small reservoir temperatures. The adaption of the Feshbach map-based renormalization procedure by Bach, Chen, Fröhlich, and Sigal to concrete spectral problems in quantum statistical mechanics is a further novelty of this work.

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Coupled-cluster theory provides one of the most successful concepts in electronic-structure theory. This work covers the parallelization of coupled-cluster energies, gradients, and second derivatives and its application to selected large-scale chemical problems, beside the more practical aspects such as the publication and support of the quantum-chemistry package ACES II MAB and the design and development of a computational environment optimized for coupled-cluster calculations. The main objective of this thesis was to extend the range of applicability of coupled-cluster models to larger molecular systems and their properties and therefore to bring large-scale coupled-cluster calculations into day-to-day routine of computational chemistry. A straightforward strategy for the parallelization of CCSD and CCSD(T) energies, gradients, and second derivatives has been outlined and implemented for closed-shell and open-shell references. Starting from the highly efficient serial implementation of the ACES II MAB computer code an adaptation for affordable workstation clusters has been obtained by parallelizing the most time-consuming steps of the algorithms. Benchmark calculations for systems with up to 1300 basis functions and the presented applications show that the resulting algorithm for energies, gradients and second derivatives at the CCSD and CCSD(T) level of theory exhibits good scaling with the number of processors and substantially extends the range of applicability. Within the framework of the ’High accuracy Extrapolated Ab initio Thermochemistry’ (HEAT) protocols effects of increased basis-set size and higher excitations in the coupled- cluster expansion were investigated. The HEAT scheme was generalized for molecules containing second-row atoms in the case of vinyl chloride. This allowed the different experimental reported values to be discriminated. In the case of the benzene molecule it was shown that even for molecules of this size chemical accuracy can be achieved. Near-quantitative agreement with experiment (about 2 ppm deviation) for the prediction of fluorine-19 nuclear magnetic shielding constants can be achieved by employing the CCSD(T) model together with large basis sets at accurate equilibrium geometries if vibrational averaging and temperature corrections via second-order vibrational perturbation theory are considered. Applying a very similar level of theory for the calculation of the carbon-13 NMR chemical shifts of benzene resulted in quantitative agreement with experimental gas-phase data. The NMR chemical shift study for the bridgehead 1-adamantyl cation at the CCSD(T) level resolved earlier discrepancies of lower-level theoretical treatment. The equilibrium structure of diacetylene has been determined based on the combination of experimental rotational constants of thirteen isotopic species and zero-point vibrational corrections calculated at various quantum-chemical levels. These empirical equilibrium structures agree to within 0.1 pm irrespective of the theoretical level employed. High-level quantum-chemical calculations on the hyperfine structure parameters of the cyanopolyynes were found to be in excellent agreement with experiment. Finally, the theoretically most accurate determination of the molecular equilibrium structure of ferrocene to date is presented.

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In this thesis we develop further the functional renormalization group (RG) approach to quantum field theory (QFT) based on the effective average action (EAA) and on the exact flow equation that it satisfies. The EAA is a generalization of the standard effective action that interpolates smoothly between the bare action for krightarrowinfty and the standard effective action rnfor krightarrow0. In this way, the problem of performing the functional integral is converted into the problem of integrating the exact flow of the EAA from the UV to the IR. The EAA formalism deals naturally with several different aspects of a QFT. One aspect is related to the discovery of non-Gaussian fixed points of the RG flow that can be used to construct continuum limits. In particular, the EAA framework is a useful setting to search for Asymptotically Safe theories, i.e. theories valid up to arbitrarily high energies. A second aspect in which the EAA reveals its usefulness are non-perturbative calculations. In fact, the exact flow that it satisfies is a valuable starting point for devising new approximation schemes. In the first part of this thesis we review and extend the formalism, in particular we derive the exact RG flow equation for the EAA and the related hierarchy of coupled flow equations for the proper-vertices. We show how standard perturbation theory emerges as a particular way to iteratively solve the flow equation, if the starting point is the bare action. Next, we explore both technical and conceptual issues by means of three different applications of the formalism, to QED, to general non-linear sigma models (NLsigmaM) and to matter fields on curved spacetimes. In the main part of this thesis we construct the EAA for non-abelian gauge theories and for quantum Einstein gravity (QEG), using the background field method to implement the coarse-graining procedure in a gauge invariant way. We propose a new truncation scheme where the EAA is expanded in powers of the curvature or field strength. Crucial to the practical use of this expansion is the development of new techniques to manage functional traces such as the algorithm proposed in this thesis. This allows to project the flow of all terms in the EAA which are analytic in the fields. As an application we show how the low energy effective action for quantum gravity emerges as the result of integrating the RG flow. In any treatment of theories with local symmetries that introduces a reference scale, the question of preserving gauge invariance along the flow emerges as predominant. In the EAA framework this problem is dealt with the use of the background field formalism. This comes at the cost of enlarging the theory space where the EAA lives to the space of functionals of both fluctuation and background fields. In this thesis, we study how the identities dictated by the symmetries are modified by the introduction of the cutoff and we study so called bimetric truncations of the EAA that contain both fluctuation and background couplings. In particular, we confirm the existence of a non-Gaussian fixed point for QEG, that is at the heart of the Asymptotic Safety scenario in quantum gravity; in the enlarged bimetric theory space where the running of the cosmological constant and of Newton's constant is influenced by fluctuation couplings.

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Der erste Teil der vorliegenden Dissertation befasst sich mit der Untersuchung der perturbativen Unitarität im Komplexe-Masse-Renormierungsschema (CMS). Zu diesem Zweck wird eine Methode zur Berechnung der Imaginärteile von Einschleifenintegralen mit komplexen Massenparametern vorgestellt, die im Grenzfall stabiler Teilchen auf die herkömmlichen Cutkosky-Formeln führt. Anhand einer Modell-Lagrangedichte für die Wechselwirkung eines schweren Vektorbosons mit einem leichten Fermion wird demonstriert, dass durch Anwendung des CMS die Unitarität der zugrunde liegenden S-Matrix im störungstheoretischen Sinne erfüllt bleibt, sofern die renormierte Kopplungskonstante reell gewählt wird. Der zweite Teil der Arbeit beschäftigt sich mit verschiedenen Anwendungen des CMS in chiraler effektiver Feldtheorie (EFT). Im Einzelnen werden Masse und Breite der Deltaresonanz, die elastischen elektromagnetischen Formfaktoren der Roperresonanz, die elektromagnetischen Formfaktoren des Übergangs vom Nukleon zur Roperresonanz sowie Pion-Nukleon-Streuung und Photo- und Elektropionproduktion für Schwerpunktsenergien im Bereich der Roperresonanz berechnet. Die Wahl passender Renormierungsbedingungen ermöglicht das Aufstellen eines konsistenten chiralen Zählschemas für EFT in Anwesenheit verschiedener resonanter Freiheitsgrade, so dass die aufgeführten Prozesse in Form einer systematischen Entwicklung nach kleinen Parametern untersucht werden können. Die hier erzielten Resultate können für Extrapolationen von entsprechenden Gitter-QCD-Simulationen zum physikalischen Wert der Pionmasse genutzt werden. Deshalb wird neben der Abhängigkeit der Formfaktoren vom quadrierten Impulsübertrag auch die Pionmassenabhängigkeit des magnetischen Moments und der elektromagnetischen Radien der Roperresonanz untersucht. Im Rahmen der Pion-Nukleon-Streuung und der Photo- und Elektropionproduktion werden eine Partialwellenanalyse und eine Multipolzerlegung durchgeführt, wobei die P11-Partialwelle sowie die Multipole M1- und S1- mittels nichtlinearer Regression an empirische Daten angepasst werden.

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Lattice Quantum Chromodynamics (LQCD) is the preferred tool for obtaining non-perturbative results from QCD in the low-energy regime. It has by nowrnentered the era in which high precision calculations for a number of phenomenologically relevant observables at the physical point, with dynamical quark degrees of freedom and controlled systematics, become feasible. Despite these successes there are still quantities where control of systematic effects is insufficient. The subject of this thesis is the exploration of the potential of todays state-of-the-art simulation algorithms for non-perturbativelyrn$\mathcal{O}(a)$-improved Wilson fermions to produce reliable results in thernchiral regime and at the physical point both for zero and non-zero temperature. Important in this context is the control over the chiral extrapolation. Thisrnthesis is concerned with two particular topics, namely the computation of hadronic form factors at zero temperature, and the properties of the phaserntransition in the chiral limit of two-flavour QCD.rnrnThe electromagnetic iso-vector form factor of the pion provides a platform to study systematic effects and the chiral extrapolation for observables connected to the structure of mesons (and baryons). Mesonic form factors are computationally simpler than their baryonic counterparts but share most of the systematic effects. This thesis contains a comprehensive study of the form factor in the regime of low momentum transfer $q^2$, where the form factor is connected to the charge radius of the pion. A particular emphasis is on the region very close to $q^2=0$ which has not been explored so far, neither in experiment nor in LQCD. The results for the form factor close the gap between the smallest spacelike $q^2$-value available so far and $q^2=0$, and reach an unprecedented accuracy at full control over the main systematic effects. This enables the model-independent extraction of the pion charge radius. The results for the form factor and the charge radius are used to test chiral perturbation theory ($\chi$PT) and are thereby extrapolated to the physical point and the continuum. The final result in units of the hadronic radius $r_0$ is rn$$ \left\langle r_\pi^2 \right\rangle^{\rm phys}/r_0^2 = 1.87 \: \left(^{+12}_{-10}\right)\left(^{+\:4}_{-15}\right) \quad \textnormal{or} \quad \left\langle r_\pi^2 \right\rangle^{\rm phys} = 0.473 \: \left(^{+30}_{-26}\right)\left(^{+10}_{-38}\right)(10) \: \textnormal{fm} \;, $$rn which agrees well with the results from other measurements in LQCD and experiment. Note, that this is the first continuum extrapolated result for the charge radius from LQCD which has been extracted from measurements of the form factor in the region of small $q^2$.rnrnThe order of the phase transition in the chiral limit of two-flavour QCD and the associated transition temperature are the last unkown features of the phase diagram at zero chemical potential. The two possible scenarios are a second order transition in the $O(4)$-universality class or a first order transition. Since direct simulations in the chiral limit are not possible the transition can only be investigated by simulating at non-zero quark mass with a subsequent chiral extrapolation, guided by the universal scaling in the vicinity of the critical point. The thesis presents the setup and first results from a study on this topic. The study provides the ideal platform to test the potential and limits of todays simulation algorithms at finite temperature. The results from a first scan at a constant zero-temperature pion mass of about 290~MeV are promising, and it appears that simulations down to physical quark masses are feasible. Of particular relevance for the order of the chiral transition is the strength of the anomalous breaking of the $U_A(1)$ symmetry at the transition point. It can be studied by looking at the degeneracies of the correlation functions in scalar and pseudoscalar channels. For the temperature scan reported in this thesis the breaking is still pronounced in the transition region and the symmetry becomes effectively restored only above $1.16\:T_C$. The thesis also provides an extensive outline of research perspectives and includes a generalisation of the standard multi-histogram method to explicitly $\beta$-dependent fermion actions.

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The mass estimation of galaxy clusters is a crucial point for modern cosmology, and can be obtained by several different techniques. In this work we discuss a new method to measure the mass of galaxy clusters connecting the gravitational potential of the cluster with the kinematical properties of its surroundings. We explore the dynamics of the structures located in the region outside virialized cluster, We identify groups of galaxies, as sheets or filaments, in the cluster outer region, and model how the cluster gravitational potential perturbs the motion of these structures from the Hubble fow. This identification is done in the redshift space where we look for overdensities with a filamentary shape. Then we use a radial mean velocity profile that has been found as a quite universal trend in simulations, and we fit the radial infall velocity profile of the overdensities found. The method has been tested on several cluster-size haloes from cosmological N-body simulations giving results in very good agreement with the true values of virial masses of the haloes and orientation of the sheets. We then applied the method to the Coma cluster and even in this case we found a good correspondence with previous. It is possible to notice a mass discrepancy between sheets with different alignments respect to the center of the cluster. This difference can be used to reproduce the shape of the cluster, and to demonstrate that the spherical symmetry is not always a valid assumption. In fact, if the cluster is not spherical, sheets oriented along different axes should feel a slightly different gravitational potential, and so give different masses as result of the analysis described before. Even this estimation has been tested on cosmological simulations and then applied to Coma, showing the actual non-sphericity of this cluster.