Irreversibility by competition on a Glauber-Ising model by means of the entropy production.

An out of equilibrium Ising model subjected to an irreversible dynamics is analyzed by means of a stochastic dynamics, on a effort that aims to understand the observed critical behavior as consequence of the intrinsic microscopic characteristics. The study focus on the kinetic phase transitions that take place by assuming a lattice model with inversion symmetry and under the influence of two competing Glauber dynamics, intended to describe the stationary states using the entropy production, which characterize the system behavior and clarifies its reversibility conditions. Thus, it is considered a square lattice formed by two sublattices interconnected, each one of which is in contact with a heat bath at different temperature from the other. Analytical and numerical treatments are faced, using mean-field approximations and Monte Carlo simulations. For the one dimensional model exact results for the entropy production were obtained, though in this case the phase transition that takes place in the two dimensional counterpart is not observed, fact which is in accordance with the behavior shared by lattice models presenting inversion symmetry. Results found for the stationary state show a critical behavior of the same class as the equilibrium Ising model with a phase transition of the second order, which is evidenced by a divergence with an exponent µ ¼ 0:003 of the entropy production derivative.

Numerical and analytical approaches to strongly correlated electron systems

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.

Mass Transport Perspective on an Accelerated Exclusion Process: Analysis of Augmented Current and Unit-Velocity Phases

In an accelerated exclusion process (AEP), each particle can "hop" to its adjacent site if empty as well as "kick" the frontmost particle when joining a cluster of size ℓ⩽ℓ_{max}. With various choices of the interaction range, ℓ_{max}, we find that the steady state of AEP can be found in a homogeneous phase with augmented currents (AC) or a segregated phase with holes moving at unit velocity (UV). Here we present a detailed study on the emergence of the novel phases, from two perspectives: the AEP and a mass transport process (MTP). In the latter picture, the system in the UV phase is composed of a condensate in coexistence with a fluid, while the transition from AC to UV can be regarded as condensation. Using Monte Carlo simulations, exact results for special cases, and analytic methods in a mean field approach (within the MTP), we focus on steady state currents and cluster sizes. Excellent agreement between data and theory is found, providing an insightful picture for understanding this model system.

SNA--a toolbox for the stoichiometric analysis of metabolic networks

BACKGROUND: Despite recent algorithmic and conceptual progress, the stoichiometric network analysis of large metabolic models remains a computationally challenging problem. RESULTS: SNA is a interactive, high performance toolbox for analysing the possible steady state behaviour of metabolic networks by computing the generating and elementary vectors of their flux and conversions cones. It also supports analysing the steady states by linear programming. The toolbox is implemented mainly in Mathematica and returns numerically exact results. It is available under an open source license from: http://bioinformatics.org/project/?group_id=546. CONCLUSION: Thanks to its performance and modular design, SNA is demonstrably useful in analysing genome scale metabolic networks. Further, the integration into Mathematica provides a very flexible environment for the subsequent analysis and interpretation of the results.

Oceanographical and meterological observations in the Westafrican area of upwelling during the 'Deutsche Nordatlantische Expedition' 1937

In 1937 the "Meteor" performed the cruises of the first part of the "Deutsche Nordatlantische Expedition". This publication treats seven stations of three-day-anchoring occupied during that time, five of which are located on the shelf, one on the continental slope and one on a ridge between the Capverde islands. The Bohnecke current meter, an instrument developed for the expedition, is described briefly and it's accuracy studied by comparing the measurements of two instruments which operated simultaneously at the same depth. It is shown that it is very sensitive for movements of the anchored ship because of the very short measuring intervall (2 minutes). The influence of the ship's movements could not be eliminated completely, the mode of using the instrument at different depths being unsuitable for this. Considering the stratification the accuracy of it's representation by the mean temperature and salinity distributionis studied. It is shown that under certain conditions a distribution estimated from observed values gives more exact results. This especially applies to the TS-diagram. Station Meteor336, located on the shelf near Cape Juby, shows temperatures 4 °C less than the open ocean and so belongs to the area of upwelling. During the observation period, however, internal tides are prominent. The diurnal component is of considerable influence, the distinction from inertial oscillations (25.5 hours) not being possible, however. Station Meteor341, on the shelf off Spanish-Sahara, gives an excellent example of the movements in the centre of the area of upwelling. Changing it's direction by 45° at the beginning of the measurements, the wind causes a change of current direction at all depths which, after some inertial oscillations (period 28.3 hours), settles down to a final value. At the beginning and the end of the observations the current at the upper depths is directed off-shore, the angle between current and wind being 22°, while at the lower depths it is orientated towards the shore. The depth of the upper homogenous layer gives the origin of the water transported upwards When during the inertial oscillations the current goes offshore at all depths temporarily, a sudden disturbance occurs in the temperature measurements. Station Meteor311 is located similar to station Meteor341 but was occupied one month earlier. At that time the wind situation was unnormal, the usual wind direction of 45° occuring at the end of the station. Therefore an unnormally high vertical shear of current speed and direction has been observed, the current vector being directed off-shore at the surface and near the bottom, towards the coast inbetween. The TS-diagram shows that the bottom water is replaced first so that upwelling does not occur during observation time. The state reached at the end of the station does not seem to be stable. Station Meteor369, on the continental slope, is governed by internal waves. Besides the internal tide of 12.4 hours a wave of 6.5 hour period is observed, being possibly amplified by the large bottom slope. In 40 - 60 m depth, where the thermocline is located, a wave with 3.3 hour period is observed which is argued to be an internal boundary wave. Station Meteor334 is located on the shelf NW of the mouth of the Senegal river. A marked temperature stratification, associated with large disturbances, and nearly constant salinity have been found there. The current was going slowly towards S or SW in the upper 20 - 30 m, towards N underneath. At the boundary of the current systems intense turbulence developed,including as it seems a water type of less salinity which is transported from the Senegal river by the lower current. Station Meteor327, located at 100 m depth between two of the Capverde islands, shows oceanic characteristics. The semidiurnal tide is found mainly, the diurnal component having considerable influence. Furtheron an internal wave of 6 hour period is seen the maximum amplitude of which is moving slowly downwards. Two possibilities of explaining it are discussed. Station Meteor366 is found in the area of ceasing winds off the coast of upper Guinea. The temperature there depends strongly on the depth, the salinity being nearly constant. The currents are divided into an upper and a lower system with large variations in both of them. A change of wind direction of nearly 90° is supposed to be the reason. The variations in salinity accordingly are interpreted as the influence of fresh water outflow from land which is felt in a different way at different wind directions. In the last section the daily changes in air and water temperature are studied. The upwelling having large influence on these, a centre of the area of upwelling can be located at about 100 miles north of Cape Blanc (Station Meteor311). The semidiurnal tidal component is compared with previous results for the Atlantic Ocean yielding considerable differences for the direction and time of occurence of the current maximum which might be due to the topographical influences around the shelf.

Self-consistent, nonlocal electron heat flux at arbitrary ion charge number

A single, nonlocal expression for the electron heat flux, which closely reproduces known results at high and low ion charge number 2, and “exact” results for the local limit at all 2, is derived by solving the kinetic equation in a narrow, tail-energy range. The solution involves asymptotic expansions of Bessel functions of large argument, and (Z-dependent)order above or below it, corresponding to the possible parabolic or hyperbolic character of the kinetic equation; velocity space diffusion in self-scattering is treated similarly to isotropic thermalization of tail energies in large Z analyses. The scale length H characterizing nonlocal effects varies with Z, suggesting an equal dependence of any ad hoc flux limiter. The model is valid for all H above the mean-free path for thermal electrons.

Tethered Monte Carlo: computing the effective potential without critical slowing down

We present Tethered Monte Carlo, a simple, general purpose method of computing the effective potential of the order parameter (Helmholtz free energy). This formalism is based on a new statistical ensemble, closely related to the micromagnetic one, but with an extended configuration space (through Creutz-like demons). Canonical averages for arbitrary values of the external magnetic field are computed without additional simulations. The method is put to work in the two-dimensional Ising model, where the existence of exact results enables us to perform high precision checks. A rather peculiar feature of our implementation, which employs a local Metropolis algorithm, is the total absence, within errors, of critical slowing down for magnetic observables. Indeed, high accuracy results are presented for lattices as large as L = 1024.

Tethered Monte Carlo: computing the effective potential without critical slowing down

We present Tethered Monte Carlo, a simple, general purpose method of computing the effective potential of the order parameter (Helmholtz free energy). This formalism is based on a new statistical ensemble, closely related to the micromagnetic one, but with an extended configuration space (through Creutz-like demons). Canonical averages for arbitrary values of the external magnetic field are computed without additional simulations. The method is put to work in the two-dimensional Ising model, where the existence of exact results enables us to perform high precision checks. A rather peculiar feature of our implementation, which employs a local Metropolis algorithm, is the total absence, within errors, of critical slowing down for magnetic observables. Indeed, high accuracy results are presented for lattices as large as L = 1024.

Gauge Poisson representations for birth/death master equations

Poisson representation techniques provide a powerful method for mapping master equations for birth/death processes -- found in many fields of physics, chemistry and biology -- into more tractable stochastic differential equations. However, the usual expansion is not exact in the presence of boundary terms, which commonly occur when the differential equations are nonlinear. In this paper, a gauge Poisson technique is introduced that eliminates boundary terms, to give an exact representation as a weighted rate equation with stochastic terms. These methods provide novel techniques for calculating and understanding the effects of number correlations in systems that have a master equation description. As examples, correlations induced by strong mutations in genetics, and the astrophysical problem of molecule formation on microscopic grain surfaces are analyzed. Exact analytic results are obtained that can be compared with numerical simulations, demonstrating that stochastic gauge techniques can give exact results where standard Poisson expansions are not able to.

Reliability analysis for hazard and operability studies

Fault tree analysis is used as a tool within hazard and operability (Hazop) studies. The present study proposes a new methodology for obtaining the exact TOP event probability of coherent fault trees. The technique uses a top-down approach similar to that of FATRAM. This new Fault Tree Disjoint Reduction Algorithm resolves all the intermediate events in the tree except OR gates with basic event inputs so that a near minimal cut sets expression is obtained. Then Bennetts' disjoint technique is applied and remaining OR gates are resolved. The technique has been found to be appropriate as an alternative to Monte Carlo simulation methods when rare events are countered and exact results are needed. The algorithm has been developed in FORTRAN 77 on the Perq workstation as an addition to the Aston Hazop package. The Perq graphical environment enabled a friendly user interface to be created. The total package takes as its input cause and symptom equations using Lihou's form of coding and produces both drawings of fault trees and the Boolean sum of products expression into which reliability data can be substituted directly.

Non-Gaussian statistics of an optical soliton in the presence of amplified spontaneous emission

A study was performed on non-Gaussian statistics of an optical soliton in the presence of amplified spontaneous emission. An approach based on the Fokker-Planck equation was applied to study the optical soliton parameters in the presence of additive noise. The rigorous method not only allowed to reproduce and justify the classical Gordon-Haus formula but also led to new exact results.

Coagulation equations with mass loss

We derive and solve models for coagulation with mass loss arising, for example, from industrial processes in which growing inclusions are lost from the melt by colliding with the wall of the vessel. We consider a variety of loss laws and a variety of coagulation kernels, deriving exact results where possible, and more generally reducing the equations to similarity solutions valid in the large-time limit. One notable result is the effect that mass removal has on gelation: for small loss rates, gelation is delayed, whilst above a critical threshold, gelation is completely prevented. Finally, by forming an exact explicit solution for a more general initial cluster size distribution function, we illustrate how numerical results from earlier work can be interpreted in the light of the theory presented herein.

Hacia la conformación de un modelo de distrribución de usos y asignación de características de ocupación a partir de análisis Geo estadístico: caso estudio Av. Paseo de los Cañarís de la ciudad de Cuenca año 2015

La presente tesis tiene por objeto generar estrategias para la distribución de usos y asignación de características de ocupación de suelo, este proceso se apoya en análisis geo estadísticos para obtener resultados más ajustados a la realidad y de esta manera comprender la dinámica de los espacios urbanos, las formas de ocupación del espacio por parte de la población, así también las dinámicas que generan ciertos elementos y el impacto en su contexto inmediato. Este estudio inicia con el desarrollo del marco teórico que aborda definiciones e investigaciones referentes a las dinámicas que los usos presentan en una ciudad.Posteriormente se analizan los elementos urbanos relevantes del área de estudio, iniciando con la delimitación y sectorización, los equipamientos, la vialidad, el transporte, las características de ocupación y la normativa vigente; mediante estos diagnósticos se llega a identificar como está conformada el área de estudio.Partiendo de estos diagnósticos se procede a realizar el estudio y análisis sistemático de los usos y la ocupación de suelo urbano, mediante la aplicación de herramientas geo estadísticas como el Kriging y MORAN-LISA. Los resultados obtenidos se representan en un corema, con la finalidad de crear un modelo espacial de análisis, apoyado también de un análisis de diversidad.Finalmente estos resultados generan estrategias apoyadas en datos estadísticos.

Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator–to–superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

Sparseness vs estimating conditional probabilities : some asymptotic results

One of the nice properties of kernel classifiers such as SVMs is that they often produce sparse solutions. However, the decision functions of these classifiers cannot always be used to estimate the conditional probability of the class label. We investigate the relationship between these two properties and show that these are intimately related: sparseness does not occur when the conditional probabilities can be unambiguously estimated. We consider a family of convex loss functions and derive sharp asymptotic results for the fraction of data that becomes support vectors. This enables us to characterize the exact trade-off between sparseness and the ability to estimate conditional probabilities for these loss functions.