Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat

A microcanonical finite-size ansatz in terms of quantities measurable in a finite lattice allows extending phenomenological renormalization the so-called quotients method to the microcanonical ensemble. The ansatz is tested numerically in two models where the canonical specific heat diverges at criticality, thus implying Fisher renormalization of the critical exponents: the three-dimensional ferromagnetic Ising model and the two-dimensional four-state Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows simulating systems as large as L = 1024 Potts or L= 128 (Ising). The quotients method provides accurate determinations of the anomalous dimension, η, and of the (Fisher-renormalized) thermal ν exponent. While in the Ising model the numerical agreement with our theoretical expectations is very good, in the Potts case, we need to carefully incorporate logarithmic corrections to the microcanonical ansatz in order to rationalize our data.

Phase transition in the three dimensional Heisenberg spin glass: Finite-size scaling analysis

We have investigated the phase transition in the Heisenberg spin glass using massive numerical simulations to study very large sizes, 483. A finite-size scaling analysis indicates that the data are compatible with the most economical scenario: a common transition temperature for spins and chiralities.

Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model

We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation including additive white noise and Gilbert damping. Using a collective variable theory with no adjustable parameters we derive an equation of motion for the vortices with stochastic forces which are shown to represent white noise with an effective diffusion constant linearly dependent on temperature. We solve these stochastic equations of motion by means of a Green's function formalism and obtain the mean vortex trajectory and its variance. We find a non-standard time dependence for the variance of the components perpendicular to the driving force. We compare the analytical results with Langevin dynamics simulations and find a good agreement up to temperatures of the order of 25% of the Kosterlitz-Thouless transition temperature. Finally, we discuss the reasons why our approach is not appropriate for higher temperatures as well as the discreteness effects observed in the numerical simulations.

Finite size effects in the specific heat of glass-formers

We report clear finite size effects in the specific heat and in the relaxation times of a model glass former at temperatures considerably smaller than the Mode Coupling transition. A crucial ingredient to reach this result is a new Monte Carlo algorithm which allows us to reduce the relaxation time by two order of magnitudes. These effects signal the existence of a large correlation length in static quantities.

The Finite Embeddability Property for some noncommutative knotted varieties of RL and DRL.

Residuated lattices, although originally considered in the realm of algebra providing a general setting for studying ideals in ring theory, were later shown to form algebraic models for substructural logics. The latter are non-classical logics that include intuitionistic, relevance, many-valued, and linear logic, among others. Most of the important examples of substructural logics are obtained by adding structural rules to the basic logical calculus

Finite Element Analysis of Thermal Buckling in Auotmotive Clutch and Brake Discs

Thermal buckling behavior of automotive clutch and brake discs is studied by making the use of finite element method. It is found that the temperature distribution along the radius and the thickness affects the critical buckling load considerably. The results indicate that a monotonic temperature profile leads to a coning mode with the highest temperature located at the inner radius. Whereas a temperature profile with the maximum temperature located in the middle leads to a dominant non-axisymmetric buckling mode, which results in a much higher buckling temperature. A periodic variation of temperature cannot lead to buckling. The temperature along the thickness can be simplified by the mean temperature method in the single material model. The thermal buckling analysis of friction discs with friction material layer, cone angle geometry and fixed teeth boundary conditions are also studied in detail. The angular geometry and the fixed teeth can improve the buckling temperature significantly. Young’s Modulus has no effect when single material is applied in the free or restricted conditions. Several equations are derived to validate the result. Young’s modulus ratio is a useful factor when the clutch has several material layers. The research findings from this paper are useful for automotive clutch and brake discs design against structural instability induced by thermal buckling.

A finite element model of perforated panel absorbers including viscothermal effects

Most of the analytical models devoted to determine the acoustic properties of a rigid perforated panel consider the acoustic impedance of a single hole and then use the porosity to determine the impedance for the whole panel. However, in the case of not homogeneous hole distribution or more complex configurations this approach is no longer valid. This work explores some of these limitations and proposes a finite element methodology that implements the linearized Navier Stokes equations in the frequency domain to analyse the acoustic performance under normal incidence of perforated panel absorbers. Some preliminary results for a homogenous perforated panel show that the sound absorption coefficient derived from the Maa analytical model does not match those from the simulations. These differences are mainly attributed to the finite geometry effect and to the spatial distribution of the perforations for the numerical case. In order to confirm these statements, the acoustic field in the vicinities of the perforations is analysed for a more complex configuration of perforated panel. Additionally, experimental studies are carried out in an impedance tube for the same configuration and then compared to previous methods. The proposed methodology is shown to be in better agreement with the laboratorial measurements than the analytical approach.

Regional subsidence modelling in Murcia city (SE Spain) using 1-D vertical finite element analysis and 2-D interpolation of ground surface displacements

Subsidence is a hazard that may have natural or anthropogenic origin causing important economic losses. The area of Murcia city (SE Spain) has been affected by subsidence due to groundwater overexploitation since the year 1992. The main observed historical piezometric level declines occurred in the periods 1982–1984, 1992–1995 and 2004–2008 and showed a close correlation with the temporal evolution of ground displacements. Since 2008, the pressure recovery in the aquifer has led to an uplift of the ground surface that has been detected by the extensometers. In the present work an elastic hydro-mechanical finite element code has been used to compute the subsidence time series for 24 geotechnical boreholes, prescribing the measured groundwater table evolution. The achieved results have been compared with the displacements estimated through an advanced DInSAR technique and measured by the extensometers. These spatio-temporal comparisons have showed that, in spite of the limited geomechanical data available, the model has turned out to satisfactorily reproduce the subsidence phenomenon affecting Murcia City. The model will allow the prediction of future induced deformations and the consequences of any piezometric level variation in the study area.

On the forbidden gap of finite graphene nanoribbons

The electronic structure of isolated finite graphene nanoribbons is investigated by solving, at the Hartree-Fock (HF) level, the Pariser, Parr and Pople (PPP) many-body Hamiltonian. The study is mainly focused on 7-AGNR and 13-AGNR (Armchair Graphene Nano-Ribbons), whose electronic structures have been recently experimentally investigated. Only paramagnetic solutions are considered. The characteristics of the forbidden gap are studied as a function of the ribbon length. For a 7-AGNR, the gap monotonically decreases from a maximum value of ~6.5 eV for short nanoribbons to a very small value of ~0.12 eV for the longer calculated systems. Gap edges are defined by molecular orbitals that are spatially localized near the nanoribbon extremes, that is, near both zig-zag edges. On the other hand, two delocalized orbitals define a much larger gap of about 5 eV. Conductance measurements report a somewhat smaller gap of ~3 eV. The small real gap lies in the middle of the one given by extended states and has been observed by STM and reproduced by DFT calculations. On the other hand, the length dependence of the gap is not monotonous for a 13-AGNR. It decreases initially but sharply increases for lengths beyond 30 Å remaining almost constant thereafter at a value of ~2.1 eV. Two additional states localized at the nanoribbon extremes show up at energies 0.31 eV below the HOMO (Highest Occupied Molecular Orbital) and above the LUMO (Lowest Unoccupied Molecular Orbital). These numbers compare favorably with those recently obtained by means of STS for a 13-AGNR sustained by a gold surface, namely 1.4 eV for the energy gap and 0.4 eV for the position of localized band edges. We show that the important differences between 7- and 13-AGNR should be ascribed to the charge rearrangement near the zig-zag edges obtained in our calculations for ribbons longer than 30 Å, a feature that does not show up for a 7-AGNR no matter its length.

Quantum theory of spin waves in finite chiral spin chains

We calculate the effect of spin waves on the properties of finite-size spin chains with a chiral spin ground state observed on biatomic Fe chains deposited on iridium(001). The system is described with a Heisenberg model supplemented with a Dzyaloshinskii-Moriya coupling and a uniaxial single ion anisotropy that presents a chiral spin ground state. Spin waves are studied using the Holstein-Primakoff boson representation of spin operators. Both the renormalized ground state and the elementary excitations are found by means of Bogoliubov transformation, as a function of the two variables that can be controlled experimentally, the applied magnetic field and the chain length. Three main results are found. First, because of the noncollinear nature of the classical ground state, there is a significant zero-point reduction of the ground-state magnetization of the spin spiral. Second, there is a critical external field from which the ground state changes from chiral spin ground state to collinear ferromagnetic order. The character of the two lowest-energy spin waves changes from edge modes to confined bulk modes over this critical field. Third, in the spin-spiral state, the spin-wave spectrum exhibits oscillatory behavior as function of the chain length with the same period of the spin helix.

A Finite Element Numerical Algorithm for Modelling and Data Fitting in Complex Systems

Numerical modelling methodologies are important by their application to engineering and scientific problems, because there are processes where analytical mathematical expressions cannot be obtained to model them. When the only available information is a set of experimental values for the variables that determine the state of the system, the modelling problem is equivalent to determining the hyper-surface that best fits the data. This paper presents a methodology based on the Galerkin formulation of the finite elements method to obtain representations of relationships that are defined a priori, between a set of variables: y = z(x1, x2,...., xd). These representations are generated from the values of the variables in the experimental data. The approximation, piecewise, is an element of a Sobolev space and has derivatives defined in a general sense into this space. The using of this approach results in the need of inverting a linear system with a structure that allows a fast solver algorithm. The algorithm can be used in a variety of fields, being a multidisciplinary tool. The validity of the methodology is studied considering two real applications: a problem in hydrodynamics and a problem of engineering related to fluids, heat and transport in an energy generation plant. Also a test of the predictive capacity of the methodology is performed using a cross-validation method.

Coalitions, Power and Institutional Change in Global Patent Politics. IES WORKING PAPER 2/2013

With the 1995 Agreement on Trade - related Aspects of Intellectual Property Rights (TRIPS), a centralised rule - system for the international governance of patents was put in place under the general framework of the World Trade Organisation (WTO). Since then, the number of patent – related institutions has increased monotonically on the multilateral, plurilateral and bilateral levels. I will explain this case of institutional change by focusing on the norm – setting activities of both industrialised and developing countries, arguing that both groups constitute internally highly cohesive coalitions in global patent politics, while institutional change occurs when both coalitions engage in those negotiating settings in which they enjoy a comparative advantage over the other coalition. Specifically, I make the point that industrialised countries’ norm – setting activities take place on the plurilateral and bilateral level, where economic factors can be effectively translated into political outcomes while simultaneously avoiding unacceptably high legitimacy costs; whereas developing countries, on the other hand, use various multilateral United Nations (UN) forums where their claims possess a high degree of legitimacy, but cannot translate into effective political outcomes. The paper concludes with some remarks on how this case yields new insights into ongoing debates in institutionalist International Relations (IR), as pertaining to present discussions on “regime complexity”.

Something Worth Fighting For: The Evolution of Lobbying Coalitions in the Emissions Trading System. Bruges Political Research Papers 50/2015.

This thesis attempts to understand who fought for influence within the European Union’s policy area of the Emissions Trading System (ETS). The ETS is a key aspect of the European Union’s (EU) climate change policy and is particularly important in light of the conclusions at the 2015 United Nations Climate Change Conference in Paris. It was first established in 2003 with Directive 2003/87/EC and completed its first major revision in 2008 with Directive 2009/29/EC. Between these two key Directives, the interplay between industrial and environmental incentives means that the ETS has created a dynamic venue for divergent interest groups. So as to identify the relevant actors, this paper applies the Advocacy Coalition Framework (ACF) of Sabatier. Using position papers, semi-structured interviews, and unpublished documents from the EU institutions, this paper answers it primary research question in its identification of an economy-first and an environment-first lobbying coalition. These coalitions have expanded over time with the environment-first coalition incorporating Greenpeace and the economy-first coalition expanding even further in both scope and speed. However, the economy-first coalition has been susceptible to industry-specific interests. In its application of the ACF, the research shows that a hypothesised effect between the ACF’s external events and these lobbying coalitions is inconclusive. Other hypotheses stemming from the ACF relating to electricity prices and the 2004 enlargement seem to be of significance for the relative composition of the lobbying coalitions. This paper finds that there are certain limitations within the ACF. The findings of this thesis provide a unique insight into how lobbying coalitions within a key EU policy area can form and develop.

Socio-technical transitions and policy change - Advocacy coalitions in Swiss energy policy

Policies and politics are an integral part of socio-technical transitions but have not received much attention in the transitions literature so far. Drawing on the advocacy coalition framework, our paper addresses this gap with a study on actors and coalitions in Swiss energy policy. Our results show that advocacy coalitions in Switzerland have largely remained stable despite the Fukushima shock. However, heterogeneity of beliefs has increased and in 2013, even a majority of actors expressed their support for the energy transition – an indication that major policy change might be ahead. It seems that in socio-technical transitions, changes in the policy issue and in the actor base also work toward policy change, next to changes in core beliefs. We make suggestions how the advocacy coalition framework can inform analysis and theory building in transition studies. We also present first ideas about the interplay of socio-technical systems and policy systems.

Les coalitions politiques et l'orientation du changement économique et politique aux États-Unis : la Grande Dépression et la Grande Récession comparées.

Ce mémoire s’intéresse au concept de crise, économique et politique, comme source de changement idéologique et politique. Au travers de l’étude de l’austérité économique, il sera possible d’identifier des différences majeures entre deux épisodes de troubles économiques importants, la Grande Dépression et la Grande Récession. Alors que la Grande Dépression est caractérisée par une double crise, économique et politique, la Grande Récession, elle, demeure un choc essentiellement économique. L’absence de contagion dans le système politique explique la ténacité d’une idée comme l’austérité, de retour depuis la révolution néolibérale des années 80. L’austérité économique s’est adaptée et s’aligne maintenant aux intérêts d’une frange importante de la coalition démocrate. La persistance de l’allure des coalitions politiques depuis le dernier grand réalignement témoigne de l’absence de transformation majeure du mode d’action étatique, ce qui constitue une différence importante entre les deux crises.