Integration of chaos theory and mathematical models in building simulation: Part I: Literature review

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasingly complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I) reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develops conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to building simulation scientists, initiates a dialogue and builds bridges between scientists and engineers, and stimulates future research about a wide range of issues on building environmental systems.

Integration of chaos theory and mathematical models in building simulation: Part II: Conceptual frameworks

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasing complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I), published in the previous issue, reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develop conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to (1) building simulation scientists and designers (2) initiating a dialogue between scientists and engineers, and (3) stimulating future research on a wide range of issues involved in designing and managing building environmental systems.

A joint state and parameter estimation scheme for nonlinear dynamical systems

We present a novel algorithm for concurrent model state and parameter estimation in nonlinear dynamical systems. The new scheme uses ideas from three dimensional variational data assimilation (3D-Var) and the extended Kalman filter (EKF) together with the technique of state augmentation to estimate uncertain model parameters alongside the model state variables in a sequential filtering system. The method is relatively simple to implement and computationally inexpensive to run for large systems with relatively few parameters. We demonstrate the efficacy of the method via a series of identical twin experiments with three simple dynamical system models. The scheme is able to recover the parameter values to a good level of accuracy, even when observational data are noisy. We expect this new technique to be easily transferable to much larger models.

Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

Tree-structured smooth transition models

The goal of this paper is to introduce a class of tree-structured models that combines aspects of regression trees and smooth transition regression models. The model is called the Smooth Transition Regression Tree (STR-Tree). The main idea relies on specifying a multiple-regime parametric model through a tree-growing procedure with smooth transitions among different regimes. Decisions about splits are entirely based on a sequence of Lagrange Multiplier (LM) tests of hypotheses.

Cleavage of the dimeric cyclopalladated [Pd(N,C-dmba)(mu-X)](2), (dmba = N,N-dimethylbenzylamine; X = SCN and NCO) by diphosphines. Palladium(II) compounds with distinct structures in the solid-state and in solution

The reactions of the pseudohalide-bridged dimer [Pd(N,C-dmba)(mu -SCN)](2) (1) (dmba = N,N-dimethylbenzylamine) with cis-Ph2PCH=CHPPh2 (cis-dppet) (1:1 molar ratio) and of [Pd(N,C-dmba)(mu -NCO)](2) (2) with Ph2PCH2CH2PPh2 (dppe) (1:2 molar ratio) gave mononuclear [Pd(C-dmba)(SCN)(cis-dppet)].H2O (1a) and [Pd(C-dmba)(NCO)(dppe)] (2a), respectively, with the diphosphines acting as chelating ligands. Reaction of (2) with Fe(C5H4PPh2)(2) (dppf) (1:1 molar ratio) yielded [{Pd(N,C-dmba)(NCO)}(2)(mu -dppf)] (2b), a bimetallic species containing two palladium atoms bridged by the diphosphine, whereas reaction in a 1:2 molar ratio gave the mononuclear [Pd(N,C-dmba)(dppf)][NCO]. CH2Cl2 (2c), with the diphosphine acting as a chelating ligand. The compounds have been characterized by elemental analysis, i.r., P-31{H-1}, C-13- and H-1-n.m.r. spectroscopies. Conductivity measurements together with spectroscopic data showed that (1a) and (2a) do not have the same structure in the solid state and in MeCl solution, whereas for compounds (2b) and (2c) no structural changes were observed when the solids were dissolved in MeCl.

Test systems and mathematical models for transmission network expansion planning

The data of four networks that can be used in carrying out comparative studies with methods for transmission network expansion planning are given. These networks are of various types and different levels of complexity. The main mathematical formulations used in transmission expansion studies-transportation models, hybrid models, DC power flow models, and disjunctive models are also summarised and compared. The main algorithm families are reviewed-both analytical, combinatorial and heuristic approaches. Optimal solutions are not yet known for some of the four networks when more accurate models (e.g. The DC model) are used to represent the power flow equations-the state of the art with regard to this is also summarised. This should serve as a challenge to authors searching for new, more efficient methods.

Final state and thermodynamics of a dark energy universe

As it follows from the classical analysis, the typical final state of a dark energy universe where a dominant energy condition is violated is a finite-time, sudden future singularity (a big rip). For a number of dark energy universes (including scalar phantom and effective phantom theories as well as specific quintessence models) we demonstrate that quantum effects play the dominant role near a big rip, driving the universe out of a future singularity (or, at least, moderating it). As a consequence, the entropy bounds with quantum corrections become well defined near a big rip. Similarly, black hole mass loss due to phantom accretion is not so dramatic as was expected: masses do not vanish to zero due to the transient character of the phantom evolution stage. Some examples of cosmological evolution for a negative, time-dependent equation of state are also considered with the same conclusions. The application of negative entropy (or negative temperature) occurrence in the phantom thermodynamics is briefly discussed.

Comparative analysis of strut-and-tie models using Smooth Evolutionary Structural Optimization

The strut-and-tie models are widely used in certain types of structural elements in reinforced concrete and in regions with complexity of the stress state, called regions D, where the distribution of deformations in the cross section is not linear. This paper introduces a numerical technique to determine the strut-and-tie models using a variant of the classical Evolutionary Structural Optimization, which is called Smooth Evolutionary Structural Optimization. The basic idea of this technique is to identify the numerical flow of stresses generated in the structure, setting out in more technical and rational members of strut-and-tie, and to quantify their value for future structural design. This paper presents an index performance based on the evolutionary topology optimization method for automatically generating optimal strut-and-tie models in reinforced concrete structures with stress constraints. In the proposed approach, the element with the lowest Von Mises stress is calculated for element removal, while a performance index is used to monitor the evolutionary optimization process. Thus, a comparative analysis of the strut-and-tie models for beams is proposed with the presentation of examples from the literature that demonstrates the efficiency of this formulation. © 2013 Elsevier Ltd.

A comparative evaluation of the CF:CS and CRS models in Pb-210 chronological studies applied to hydrographic basins in Brazil

The Constant Flux: Constant Sedimentation (CF:CS) and Constant Rate of Supply (CRS) of unsupported/excess Pb-210 models have been applied to a Pb-210 data set providing of eighteen sediments profiles sampled at four riverine systems occurring in Brazil, South America: Corumbatai River basin (S1=Site 1, Sao Paulo State), Atibaia River basin (S2=Site 2, Sao Paulo State), Ribeirao dos Bagres basin (S3=Site 3, Sao Paulo State) and Amazon River mouth. (S4=Site 4, Amapa State). These sites were chosen for a comparative evaluation of the performance of the CF:CS and CRS models due to their pronounced differences on the geographical location, geological context, soil composition, biodiversity, climate, rainfall, and water flow regime, among other variable aspects. However, all sediments cores exhibited a common denominator consisting on a database built from the use of the same techniques for acquiring the sediments major chemical composition (SiO2, Al2O3, Na2O, K2O, CaO, MgO, Fe2O3, MnO, P2O5, TiO2 and LOI-Loss on Ignition) and unsupported/excess 210Pb activity data. In terms of sedimentation rates, the performance of the CRS model was better than that of the CF:CS model as it yielded values more compatible with those expected from field evidences. Under the chronological point of view, the CRS model always provided ages within the permitted range of the Pb-210-method in the studied sites, whereas the CF:CS model predicted some values above 150 years. The SiO2 content decreased in accordance with the LOI increase in all cores analyzed and such inverse relationship was also tracked in the SiO2-LOI curves of historical trends. The SiO2-LOI concentration fluctuations in sites S1 and S3 also coincided with some Cu and Cr inputs in the drainage systems. (C) 2014 Elsevier Ltd. All rights reserved.

Capturing Transition Paths and Transition States for Conformational Rearrangements in the Ribosome

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Creep and damage models for the service behaviour of structural members

Deformability is often a crucial to the conception of many civil-engineering structural elements. Also, design is all the more burdensome if both long- and short-term deformability has to be considered. In this thesis, long- and short-term deformability has been studied from the material and the structural modelling point of view. Moreover, two materials have been handled: pultruded composites and concrete. A new finite element model for thin-walled beams has been introduced. As a main assumption, cross-sections rigid are considered rigid in their plane; this hypothesis replaces that of the classical beam theory of plane cross-sections in the deformed state. That also allows reducing the total number of degrees of freedom, and therefore making analysis faster compared with twodimensional finite elements. Longitudinal direction warping is left free, allowing describing phenomena such as the shear lag. The new finite-element model has been first applied to concrete thin-walled beams (such as roof high span girders or bridge girders) subject to instantaneous service loadings. Concrete in his cracked state has been considered through a smeared crack model for beams under bending. At a second stage, the FE-model has been extended to the viscoelastic field and applied to pultruded composite beams under sustained loadings. The generalized Maxwell model has been adopted. As far as materials are concerned, long-term creep tests have been carried out on pultruded specimens. Both tension and shear tests have been executed. Some specimen has been strengthened with carbon fibre plies to reduce short- and long- term deformability. Tests have been done in a climate room and specimens kept 2 years under constant load in time. As for concrete, a model for tertiary creep has been proposed. The basic idea is to couple the UMLV linear creep model with a damage model in order to describe nonlinearity. An effective strain tensor, weighting the total and the elasto-damaged strain tensors, controls damage evolution through the damage loading function. Creep strains are related to the effective stresses (defined by damage models) and so associated to the intact material.

Fluctuation properties in random walks on networks and simple integrate and fire models

In questa tesi si è studiato l’insorgere di eventi critici in un semplice modello neurale del tipo Integrate and Fire, basato su processi dinamici stocastici markoviani definiti su una rete. Il segnale neurale elettrico è stato modellato da un flusso di particelle. Si è concentrata l’attenzione sulla fase transiente del sistema, cercando di identificare fenomeni simili alla sincronizzazione neurale, la quale può essere considerata un evento critico. Sono state studiate reti particolarmente semplici, trovando che il modello proposto ha la capacità di produrre effetti "a cascata" nell’attività neurale, dovuti a Self Organized Criticality (auto organizzazione del sistema in stati instabili); questi effetti non vengono invece osservati in Random Walks sulle stesse reti. Si è visto che un piccolo stimolo random è capace di generare nell’attività della rete delle fluttuazioni notevoli, in particolar modo se il sistema si trova in una fase al limite dell’equilibrio. I picchi di attività così rilevati sono stati interpretati come valanghe di segnale neurale, fenomeno riconducibile alla sincronizzazione.

Performance Evaluation of the New Connecticut Leading Employment Index Using Lead Profiles and BVAR Models

Dua and Miller (1996) created leading and coincident employment indexes for the state of Connecticut, following Moore's (1981) work at the national level. The performance of the Dua-Miller indexes following the recession of the early 1990s fell short of expectations. This paper performs two tasks. First, it describes the process of revising the Connecticut Coincident and Leading Employment Indexes. Second, it analyzes the statistical properties and performance of the new indexes by comparing the lead profiles of the new and old indexes as well as their out-of-sample forecasting performance, using the Bayesian Vector Autoregressive (BVAR) method. The new indexes show improved performance in dating employment cycle chronologies. The lead profile test demonstrates that superiority in a rigorous, non-parametric statistic fashion. The mixed evidence on the BVAR forecasting experiments illustrates the truth in the Granger and Newbold (1986) caution that leading indexes properly predict cycle turning points and do not necessarily provide accurate forecasts except at turning points, a view that our results support.

Eurozone Crisis and Social Models: What We Can Learn from Italy and Spain. CES Papers - Open Forum #20, 2013-2014

This paper considers the role of social model features in the economic performance of Italy and Spain during the run-up to the Eurozone crisis, as well as the consequences of that crisis, in turn, for the two countries social models. It takes issue with the prevailing view - what I refer to as the “competitiveness thesis” - which attributes the debtor status of the two countries to a lack of competitive capacity rooted in social model features. This competitiveness thesis has been key in justifying the “liberalization plus austerity” measures that European institutions have demanded in return for financial support for Italy and Spain at critical points during the crisis. The paper challenges this prevailing wisdom. First, it reviews the characteristics of the Italian and Spanish social models and their evolution in the period prior to the crisis, revealing a far more complex, dynamic and differentiated picture than is given in the political economy literature. Second, the paper considers various ways in which social model characteristics are said to have contributed to the Eurozone crisis, finding such explanations wanting. Italy and Spain ́s debtor status was primarily the result of much broader dynamics in the Euro- zone, including capital flows from richer to poorer countries that affected economic demand, with social model features playing, at most, an ancillary role. More aggressive reforms responding to EU demands in Spain may have increased the long term social and economic costs of the crisis, whereas the political stalemate that slowed such reforms in Italy may have paradoxically mitigated these costs. The comparison of the two countries thus suggests that, in the absence of broader macro-institutional reform of the Eurozone, compliance with EU dictates may have had perverse effects.