External dichotomous noise: The problem of the mean-first-passage time

A retarded backward equation for a non-Markovian process induced by dichotomous noise (the random telegraphic signal) is deduced. The mean-first-passage time of this process is exactly obtained. The Gaussian white noise and the white shot noise limits are studied. Explicit physical results in first approximation are evaluated.

Higher-order colored-noise effects in multivariable systems

We extend the partial resummation technique of Fokker-Planck terms for multivariable stochastic differential equations with colored noise. As an example, a model system of a Brownian particle with colored noise is studied. We prove that the asymmetric behavior found in analog simulations is due to higher-order terms which are left out in that technique. On the contrary, the systematic ¿-expansion approach can explain the analog results.

Escape over a potential barrier driven by colored noise: Large but finite correlation times

The recent theory of Tsironis and Grigolini for the mean first-passage time from one metastable state to another of a bistable potential for long correlation times of the noise is extended to large but finite correlation times.

Passage times for the decay of an unstable state triggered by colored noise

We study the decay of an unstable state in the presence of colored noise by calculating the moment generating function of the passage-time distribution. The problems of the independence of the initial condition in this non-Markovian process and that of nonlinear effects are addressed. Our results are compared with recent analog simulations.

Transient and preparation colored-noise effects: The nonlinear relaxation-time approach

We develop a singular perturbation approach to the problem of the calculation of a characteristic time (the nonlinear relaxation time) for non-Markovian processes driven by Gaussian colored noise with small correlation time. Transient and initial preparation effects are discussed and explicit results for prototype situations are obtained. New effects on the relaxation of unstable states are predicted. The approach is compared with previous techniques.

First-passage time in a bistable potential with colored noise

A precise digital simulation of a bistable system under the effect of colored noise is carried out. A set of data for the mean first-passage time is obtained. The results are interpreted and compared with presently available theories, which are revisited following a new insight. Discrepancies that have been discussed in the literature are understood within our framework.

Decay of unstable states in the presence of colored noise and random initial conditions. I. Theory of nonlinear relaxation times

The general theory of nonlinear relaxation times is developed for the case of Gaussian colored noise. General expressions are obtained and applied to the study of the characteristic decay time of unstable states in different situations, including white and colored noise, with emphasis on the distributed initial conditions. Universal effects of the coupling between colored noise and random initial conditions are predicted.

Decay of unstable states in the presence of colored noise and random initial conditions. II. Analog experiments and digital simulations

The decay of an unstable state under the influence of external colored noise has been studied by means of analog experiments and digital simulations. For both fixed and random initial conditions, the time evolution of the second moment ¿x2(t)¿ of the system variable was determined and then used to evaluate the nonlinear relaxation time. The results obtained are found to be in excellent agreement with the theoretical predictions of the immediately preceding paper [Casademunt, Jiménez-Aquino, and Sancho, Phys. Rev. A 40, 5905 (1989)].

Analysis, modelling and visualisation of spatiotemporal data for urban studies

The proportion of population living in or around cites is more important than ever. Urban sprawl and car dependence have taken over the pedestrian-friendly compact city. Environmental problems like air pollution, land waste or noise, and health problems are the result of this still continuing process. The urban planners have to find solutions to these complex problems, and at the same time insure the economic performance of the city and its surroundings. At the same time, an increasing quantity of socio-economic and environmental data is acquired. In order to get a better understanding of the processes and phenomena taking place in the complex urban environment, these data should be analysed. Numerous methods for modelling and simulating such a system exist and are still under development and can be exploited by the urban geographers for improving our understanding of the urban metabolism. Modern and innovative visualisation techniques help in communicating the results of such models and simulations. This thesis covers several methods for analysis, modelling, simulation and visualisation of problems related to urban geography. The analysis of high dimensional socio-economic data using artificial neural network techniques, especially self-organising maps, is showed using two examples at different scales. The problem of spatiotemporal modelling and data representation is treated and some possible solutions are shown. The simulation of urban dynamics and more specifically the traffic due to commuting to work is illustrated using multi-agent micro-simulation techniques. A section on visualisation methods presents cartograms for transforming the geographic space into a feature space, and the distance circle map, a centre-based map representation particularly useful for urban agglomerations. Some issues on the importance of scale in urban analysis and clustering of urban phenomena are exposed. A new approach on how to define urban areas at different scales is developed, and the link with percolation theory established. Fractal statistics, especially the lacunarity measure, and scale laws are used for characterising urban clusters. In a last section, the population evolution is modelled using a model close to the well-established gravity model. The work covers quite a wide range of methods useful in urban geography. Methods should still be developed further and at the same time find their way into the daily work and decision process of urban planners. La part de personnes vivant dans une région urbaine est plus élevé que jamais et continue à croître. L'étalement urbain et la dépendance automobile ont supplanté la ville compacte adaptée aux piétons. La pollution de l'air, le gaspillage du sol, le bruit, et des problèmes de santé pour les habitants en sont la conséquence. Les urbanistes doivent trouver, ensemble avec toute la société, des solutions à ces problèmes complexes. En même temps, il faut assurer la performance économique de la ville et de sa région. Actuellement, une quantité grandissante de données socio-économiques et environnementales est récoltée. Pour mieux comprendre les processus et phénomènes du système complexe "ville", ces données doivent être traitées et analysées. Des nombreuses méthodes pour modéliser et simuler un tel système existent et sont continuellement en développement. Elles peuvent être exploitées par le géographe urbain pour améliorer sa connaissance du métabolisme urbain. Des techniques modernes et innovatrices de visualisation aident dans la communication des résultats de tels modèles et simulations. Cette thèse décrit plusieurs méthodes permettant d'analyser, de modéliser, de simuler et de visualiser des phénomènes urbains. L'analyse de données socio-économiques à très haute dimension à l'aide de réseaux de neurones artificiels, notamment des cartes auto-organisatrices, est montré à travers deux exemples aux échelles différentes. Le problème de modélisation spatio-temporelle et de représentation des données est discuté et quelques ébauches de solutions esquissées. La simulation de la dynamique urbaine, et plus spécifiquement du trafic automobile engendré par les pendulaires est illustrée à l'aide d'une simulation multi-agents. Une section sur les méthodes de visualisation montre des cartes en anamorphoses permettant de transformer l'espace géographique en espace fonctionnel. Un autre type de carte, les cartes circulaires, est présenté. Ce type de carte est particulièrement utile pour les agglomérations urbaines. Quelques questions liées à l'importance de l'échelle dans l'analyse urbaine sont également discutées. Une nouvelle approche pour définir des clusters urbains à des échelles différentes est développée, et le lien avec la théorie de la percolation est établi. Des statistiques fractales, notamment la lacunarité, sont utilisées pour caractériser ces clusters urbains. L'évolution de la population est modélisée à l'aide d'un modèle proche du modèle gravitaire bien connu. Le travail couvre une large panoplie de méthodes utiles en géographie urbaine. Toutefois, il est toujours nécessaire de développer plus loin ces méthodes et en même temps, elles doivent trouver leur chemin dans la vie quotidienne des urbanistes et planificateurs.

2011 Road Use Tax Fund (RUTF) Study A report to the Iowa Legislature, per 2011 Iowa Code Section 307.31

The transportation system is in demand 24/7 and 365 days a year irrespective of neither the weather nor the conditions. Iowa’s transportation system is an integral and essential part of society serving commerce and daily functions of all Iowans across the state. A high quality transportation system serves as the artery for economic activity and, the condition of the infrastructure is a key element for our future growth opportunities. A key component of Iowa’s transportation system is the public roadway system owned and maintained by the state, cities and counties. In order to regularly re-evaluate the conditions of Iowa’s public roadway infrastructure and assess the ability of existing revenues to meet the needs of the system, the Iowa Department of Transportation’s 2006 Road Use Tax Fund (RUTF) report to the legislature included a recommendation that a study be conducted every five years. That recommendation was included in legislation adopted in 2007 and signed into law. The law specifically requires the following (2011 Iowa Code Section 307.31): •“The department shall periodically review the current revenue levels of the road use tax fund and the sufficiency of those revenues for the projected construction and maintenance needs of city, county, and state governments in the future. The department shall submit a written report to the general assembly regarding its findings by December 31 every five years, beginning in 2011. The report may include recommendations concerning funding levels needed to support the future mobility and accessibility for users of Iowa's public road system.” •“The department shall evaluate alternative funding sources for road maintenance and construction and report to the general assembly at least every five years on the advantages and disadvantages and the viability of alternative funding mechanisms.” Consistent with this requirement, the Iowa Department of Transportation (DOT) has prepared this study. Recognizing the importance of actively engaging with the public and transportation stakeholders in any discussion of public roadway conditions and needs, Governor Terry E. Branstad announced on March 8, 2011, the creation of, and appointments to, the Governor’s Transportation 2020 Citizen Advisory Commission (CAC). The CAC was tasked with assisting the Iowa DOT as they assess the condition of Iowa’s roadway system and evaluate current and future funding available to best address system needs. In particular the CAC was directed to gather input from the public and stakeholders regarding the condition of Iowa’s public roadway system, the impact of that system, whether additional funding is needed to maintain/improve the system, and, if so, what funding mechanisms ought to be considered. With this input, the CAC prepared a report and recommendations that were presented to Governor Branstad and the Iowa DOT in November 2011 for use in the development of this study. The CAC’s report is available at www.iowadot.gov/transportation2020/pdfs/CAC%20REPORT%20FINAL%20110211.pdf. The CAC’s report was developed utilizing analysis and information from the Iowa DOT. Therefore, the report forms the basis for this study and the two documents are very similar. Iowa is fortunate to have an extensive public roadway system that provides access to all areas of the state and facilitates the efficient movement of goods and people. However, it is also a tremendous challenge for the state, cities and counties to maintain and improve this system given flattening revenue, lost buying power, changing demands on the system, severe weather, and an aging system. This challenge didn’t appear overnight and for the last decade many studies have been completed to look into the situation and the legislature has taken significant action to begin addressing the situation. In addition, the Iowa DOT and Iowa’s cities and counties have worked jointly and independently to increase efficiency and streamline operations. All of these actions have been successful and resulted in significant changes; however, it is apparent much more needs to be done. A well-maintained, high-quality transportation system reduces transportation costs and provides consistent and reliable service. These are all factors that are critical in the evaluation companies undertake when deciding where to expand or locate new developments. The CAC and Iowa DOT heard from many Iowans that additional investment in Iowa’s roadway system is vital to support existing jobs and continued job creation in the state of Iowa. Beginning June 2011, the CAC met regularly to review material and discuss potential recommendations to address Iowa’s roadway funding challenges. This effort included extensive public outreach with meetings held in seven locations across Iowa and through a Transportation 2020 website hosted by the Iowa DOT (www.iowadot.gov/transportation2020). Over 500 people attended the public meetings held through the months of August and September, with 198 providing verbal or written comment at the meetings or through the website. Comments were received from a wide array of individuals. The public comments demonstrated overwhelming support for increased funding for Iowa’s roads. Through the public input process, several guiding principles were established to guide the development of recommendations. Those guiding principles are: • Additional revenues are restricted for road and bridge improvements only, like 95 percent of the current state road revenue is currently. This includes the fuel tax and registration fees. • State and local governments continue to streamline and become more efficient, both individually and by looking for ways to do things collectively. • User fee concept is preserved, where those who use the roads pay for them, including non¬residents. • Revenue-generating methods equitable across users. • Increase revenue generating mechanisms that are viable now but begin to implement and set the stage for longer-term solutions that bring equity and stability to road funding. • Continue Iowa’s long standing tradition of state roadway financing coming from pay-as-you-go financing. Iowa must not fall into the situation that other states are currently facing where the majority of their new program dollars are utilized to pay the debt service of past bonding. Based on the analysis of Iowa’s public roadway needs and revenue and the extensive work of the Governor’s Transportation 2020 Citizen Advisory Commission, the Iowa DOT has identified specific recommendations. The recommendations follow very closely the recommendations of the CAC (CAC recommendations from their report are repeated in Appendix B). Following is a summary of the recommendations which are fully documented beginning on page 21. 1. Through a combination of efficiency savings and increased revenue, a minimum of $215 million of revenue per year should be generated to meet Iowa’s critical roadway needs. 2. The Code of Iowa should be changed to require the study of the sufficiency of the state’s road funds to meet the road system’s needs every two years instead of every five years to coincide with the biennial legislative budget appropriation schedule. 3.Modify the current registration fee for electric vehicles to be based on weight and value using the same formula that applies to most passenger vehicles. 4.Consistent with existing Code of Iowa requirements, new funding should go to the TIME-21 Fund up to the cap ($225 million) and remaining new funding should be distributed consistent with the Road Use Tax Fund distribution formula. 5.The CAC recommended the Iowa DOT at least annually convene meetings with cities and counties to review the operation, maintenance and improvement of Iowa’s public roadway system to identify ways to jointly increase efficiency. In direct response to this recommendation, Governor Branstad directed the Iowa DOT to begin this effort immediately with a target of identifying $50 million of efficiency savings that can be captured from the over $1 billion of state revenue already provided to the Iowa DOT and Iowa’s cities and counties to administer, maintain and improve Iowa’s public roadway system. This would build upon past joint and individual actions that have reduced administrative costs and resulted in increased funding for improvement of Iowa’s public roadway system. Efficiency actions should be quantified, measured and reported to the public on a regular basis. 6.By June 30, 2012, Iowa DOT should complete a study of vehicles and equipment that use Iowa’s public roadway system but pay no user fees or substantially lower user fees than other vehicles and equipment.

Insight toward the first-passage time in a bistable potential with highly colored noise

The exponential coefficient in the first-passage-time problem for a bistable potential with highly colored noise is predicted to be (8/27 by all existing theories. On the other hand, we show herein that all existing numerical evidence seems to indicate that the coefficient is actually larger by about (4/3, i.e., that the numerical factor in the exponent is approximately (32/81. Existing data cover values of ¿V0/D up to ~20, where V0 is the barrier height, ¿ the correlation time of the noise, and D the noise intensity. We provide an explanation for the modified coefficinet, the explanation also being based on existing numerical simulations. Whether the value (8/27 predicted by all large-¿ theories is achieved for even larger values of ¿V0/D is unknown but appears questionable (except perhaps for enormously large, experimentally inaccessible values of this factor) in view of currently available results.

On The Spot Damage Detection Methodology for Highway Bridges, July 2010

Vibration-based damage identification (VBDI) techniques have been developed in part to address the problems associated with an aging civil infrastructure. To assess the potential of VBDI as it applies to highway bridges in Iowa, three applications of VBDI techniques were considered in this study: numerical simulation, laboratory structures, and field structures. VBDI techniques were found to be highly capable of locating and quantifying damage in numerical simulations. These same techniques were found to be accurate in locating various types of damage in a laboratory setting with actual structures. Although there is the potential for these techniques to quantify damage in a laboratory setting, the ability of the methods to quantify low-level damage in the laboratory is not robust. When applying these techniques to an actual bridge, it was found that some traditional applications of VBDI methods are capable of describing the global behavior of the structure but are most likely not suited for the identification of typical damage scenarios found in civil infrastructure. Measurement noise, boundary conditions, complications due to substructures and multiple material types, and transducer sensitivity make it very difficult for present VBDI techniques to identify, much less quantify, highly localized damage (such as small cracks and minor changes in thickness). However, while investigating VBDI techniques in the field, it was found that if the frequency-domain response of the structure can be generated from operating traffic load, the structural response can be animated and used to develop a holistic view of the bridge’s response to various automobile loadings. By animating the response of a field bridge, concrete cracking (in the abutment and deck) was correlated with structural motion and problem frequencies (i.e., those that cause significant torsion or tension-compression at beam ends) were identified. Furthermore, a frequency-domain study of operational traffic was used to identify both common and extreme frequencies for a given structure and loading. Common traffic frequencies can be compared to problem frequencies so that cost-effective, preventative solutions (either structural or usage-based) can be developed for a wide range of IDOT bridges. Further work should (1) perfect the process of collecting high-quality operational frequency response data; (2) expand and simplify the process of correlating frequency response animations with damage; and (3) develop efficient, economical, preemptive solutions to common damage types.

Brownian motion of spiral waves driven by spatiotemporal structured noise

Spiral chemical waves subjected to a spatiotemporal random excitability are experimentally and numerically investigated in relation to the light-sensitive Belousov-Zhabotinsky reaction. Brownian motion is identified and characterized by an effective diffusion coefficient which shows a rather complex dependence on the time and length scales of the noise relative to those of the spiral. A kinematically based model is proposed whose results are in good qualitative agreement with experiments and numerics.

Noise-induced scenario for inverted phase diagrams

We introduce a class of exactly solvable models exhibiting an ordering noise-induced phase transition in which order arises as a result of a balance between the relaxing deterministic dynamics and the randomizing character of the fluctuations. A finite-size scaling analysis of the phase transition reveals that it belongs to the universality class of the equilibrium Ising model. All these results are analyzed in the light of the nonequilibrium probability distribution of the system, which can be obtained analytically. Our results could constitute a possible scenario of inverted phase diagrams in the so-called lower critical solution temperature transitions.

Effects of external noise on the Swift-Hohenberg Equation

The Swift-Hohenberg equation is studied in the presence of a multiplicative noise. This stochastic equation could describe a situation in which a noise has been superimposed on the temperature gradient between the two plates of a Rayleigh-Bnard cell. A linear stability analysis and numerical simulations show that, in constrast to the additive-noise case, convective structures appear in a regime in which a deterministic analysis predicts a homogeneous solution.