Mesoscale simulations of organized convection: importance of convective equilibrium

The validity of convective parametrization breaks down at the resolution of mesoscale models, and the success of parametrized versus explicit treatments of convection is likely to depend on the large-scale environment. In this paper we examine the hypothesis that a key feature determining the sensitivity to the environment is whether the forcing of convection is sufficiently homogeneous and slowly varying that the convection can be considered to be in equilibrium. Two case studies of mesoscale convective systems over the UK, one where equilibrium conditions are expected and one where equilibrium is unlikely, are simulated using a mesoscale forecasting model. The time evolution of area-average convective available potential energy and the time evolution and magnitude of the timescale of convective adjustment are consistent with the hypothesis of equilibrium for case 1 and non-equilibrium for case 2. For each case, three experiments are performed with different partitionings between parametrized and explicit convection: fully parametrized convection, fully explicit convection and a simulation with significant amounts of both. In the equilibrium case, bulk properties of the convection such as area-integrated rain rates are insensitive to the treatment of convection. However, the detailed structure of the precipitation field changes; the simulation with parametrized convection behaves well and produces a smooth field that follows the forcing region, and the simulation with explicit convection has a small number of localized intense regions of precipitation that track with the mid-levelflow. For the non-equilibrium case, bulk properties of the convection such as area-integrated rain rates are sensitive to the treatment of convection. The simulation with explicit convection behaves similarly to the equilibrium case with a few localized precipitation regions. In contrast, the cumulus parametrization fails dramatically and develops intense propagating bows of precipitation that were not observed. The simulations with both parametrized and explicit convection follow the pattern seen in the other experiments, with a transition over the duration of the run from parametrized to explicit precipitation. The impact of convection on the large-scaleflow, as measured by upper-level wind and potential-vorticity perturbations, is very sensitive to the partitioning of convection for both cases. © Royal Meteorological Society, 2006. Contributions by P. A. Clark and M. E. B. Gray are Crown Copyright.

A mathematical approach to chemical equilibrium theory for gaseous systems—I: theory

Equilibrium theory occupies an important position in chemistry and it is traditionally based on thermodynamics. A novel mathematical approach to chemical equilibrium theory for gaseous systems at constant temperature and pressure is developed. Six theorems are presented logically which illustrate the power of mathematics to explain chemical observations and these are combined logically to create a coherent system. This mathematical treatment provides more insight into chemical equilibrium and creates more tools that can be used to investigate complex situations. Although some of the issues covered have previously been given in the literature, new mathematical representations are provided. Compared to traditional treatments, the new approach relies on straightforward mathematics and less on thermodynamics, thus, giving a new and complementary perspective on equilibrium theory. It provides a new theoretical basis for a thorough and deep presentation of traditional chemical equilibrium. This work demonstrates that new research in a traditional field such as equilibrium theory, generally thought to have been completed many years ago, can still offer new insights and that more efficient ways to present the contents can be established. The work presented here can be considered appropriate as part of a mathematical chemistry course at University level.

The sensitivity of convective aggregation to diabatic processes in idealized radiative-convective equilibrium simulations

Idealized explicit convection simulations of the Met Office Unified Model exhibit spontaneous self-aggregation in radiative-convective equilibrium, as seen in other models in previous studies. This self-aggregation is linked to feedbacks between radiation, surface fluxes, and convection, and the organization is intimately related to the evolution of the column water vapor field. Analysis of the budget of the spatial variance of column-integrated frozen moist static energy (MSE), following Wing and Emanuel [2014], reveals that the direct radiative feedback (including significant cloud longwave effects) is dominant in both the initial development of self-aggregation and the maintenance of an aggregated state. A low-level circulation at intermediate stages of aggregation does appear to transport MSE from drier to moister regions, but this circulation is mostly balanced by other advective effects of opposite sign and is forced by horizontal anomalies of convective heating (not radiation). Sensitivity studies with either fixed prescribed radiative cooling, fixed prescribed surface fluxes, or both do not show full self-aggregation from homogeneous initial conditions, though fixed surface fluxes do not disaggregate an initialized aggregated state. A sensitivity study in which rain evaporation is turned off shows more rapid self-aggregation, while a run with this change plus fixed radiative cooling still shows strong self-aggregation, supporting a “moisture memory” effect found in Muller and Bony [2015]. Interestingly, self-aggregation occurs even in simulations with sea surface temperatures (SSTs) of 295 K and 290 K, with direct radiative feedbacks dominating the budget of MSE variance, in contrast to results in some previous studies.

Essays on the general equilibrium effects of barriers to trade on economic growth, foreign trade and the location of economic activity in Brazil

This work presents a fully operational interstate CGE model implemented for the Brazilian economy that tries to quantify both the role of barriers to trade on economic growth and foreign trade performance and how the distribution of the economic activity may change as the country opens up to foreign trade. Among the distinctive features embedded in the model, modeling of external scale economies, port efficiency and land-maritime transport costs provides an innovative way of dealing explicitly with theoretical issues related to integrated regional systems. In order to illustrate the role played by the quality of infrastructure and geography on the country‟s foreign and interregional trade performance, a set of simulations is presented where barriers to trade are significantly reduced. The relative importance of trade policy, port efficiency and land-maritime transport costs for the country trade relations and regional growth is then detailed and quantified, considering both short run as well as long run scenarios. A final set of simulations shed some light on the effects of liberal trade policies on regional inequality, where the manufacturing sector in the state of São Paulo, taken as the core of industrial activity in the country, is subjected to different levels of external economies of scale. Short-run core-periphery effects are then traced out suggesting the prevalence of agglomeration forces over diversion forces could rather exacerbate regional inequality as import barriers are removed up to a certain level. Further removals can reverse this balance in favor of diversion forces, implying de-concentration of economic activity. In the long run, factor mobility allows a better characterization of the balance between agglomeration and diversion forces among regions. Regional dispersion effects are then clearly traced-out, suggesting horizontal liberal trade policies to benefit both the poorest regions in the country as well as the state of São Paulo. This long run dispersion pattern, on one hand seems to unravel the fragility of simple theoretical results from recent New Economic Geography models, once they get confronted with more complex spatially heterogeneous (real) systems. On the other hand, it seems to capture the literature‟s main insight: the possible role of horizontal liberal trade policies as diversion forces leading to a more homogeneous pattern of interregional economic growth.

Monetary dynamics in a general equilibrium version of the Baumol-Tobin model

I study the welfare cost of inflation and the effect on prices after a permanent increase in the interest rate. In the steady state, the real money demand is homogeneous of degree one in income and its interest-rate elasticity is approximately equal to −1/2. Consumers are indifferent between an economy with 10% p.a. inflation and one with zero inflation if their income is 1% higher in the first economy. A permanent increase in the interest rate makes the price level to drop initially and inflation to adjust slowly to its steady state level.

Some notes about the determination of current account equilibrium real exchange rate and the relation between real exchange rate and productive specialization

The objective of these notes is to present a simple mathematical model of the determination of current account real exchange rate as defined by Bresser-Pereira (2010); i.e. the real exchange rate that guarantees the inter temporal equilibrium of balance of payments and to show the relation between Real Exchange rate and Productive Specialization at theoretical and empirical level.

STRUCTURE AND DYNAMICS: THE TRANSITION FROM NONEQUILIBRIUM TO EQUILIBRIUM IN INTEGRATE-AND-FIRE DYNAMICS

The transient and equilibrium properties of dynamics unfolding in complex systems can depend critically on specific topological features of the underlying interconnections. In this work, we investigate such a relationship with respect to the integrate-and-fire dynamics emanating from a source node and an extended network model that allows control of the small-world feature as well as the length of the long-range connections. A systematic approach to investigate the local and global correlations between structural and dynamical features of the networks was adopted that involved extensive simulations (one and a half million cases) so as to obtain two-dimensional correlation maps. Smooth, but diverse surfaces of correlation values were obtained in all cases. Regarding the global cases, it has been verified that the onset avalanche time (but not its intensity) can be accurately predicted from the structural features within specific regions of the map (i.e. networks with specific structural properties). The analysis at local level revealed that the dynamical features before the avalanches can also be accurately predicted from structural features. This is not possible for the dynamical features after the avalanches take place. This is so because the overall topology of the network predominates over the local topology around the source at the stationary state.

Equilibrium topology for plasmas with reversed current density.

Actually, transition from positive to negative plasma current and quasi-steady-state alternated current (AC) operation have been achieved experimentally without loss of ionization. The large transition times suggest the use of MHD equilibrium to model the intermediate magnetic field configurations for corresponding current density reversals. In the present work we show, by means of Maxwell equations, that the most robust equilibrium for any axisymmetric configuration with reversed current density requires the existence of several nonested families of magnetic surfaces inside the plasma. We also show that the currents inside the nonested families satisfy additive rules restricting the geometry and sizes of the axisymmetric magnetic islands; this is done without restricting the equilibrium through arbitrary functions. Finally, we introduce a local successive approximations method to describe the equilibrium about an arbitrary reversed current density minimum and, consequently, the transition between different nonested topologies is understood in terms of the eccentricity of the toroidal current density level sets.

An equilibrium approach to modelling social interaction

The aim of this work is to put forward a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. After showing the formal equivalence linking econometric multinomial logit models to equilibrium statical mechanics, a multi- population generalization of the Curie-Weiss model for ferromagnets is considered as a starting point in developing a model capable of describing sudden shifts in aggregate human behaviour. Existence of the thermodynamic limit for the model is shown by an asymptotic sub-additivity method and factorization of correlation functions is proved almost everywhere. The exact solution for the model is provided in the thermodynamical limit by nding converging upper and lower bounds for the system's pressure, and the solution is used to prove an analytic result regarding the number of possible equilibrium states of a two-population system. The work stresses the importance of linking regimes predicted by the model to real phenomena, and to this end it proposes two possible procedures to estimate the model's parameters starting from micro-level data. These are applied to three case studies based on census type data: though these studies are found to be ultimately inconclusive on an empirical level, considerations are drawn that encourage further refinements of the chosen modelling approach, to be considered in future work.

An infinite level atom coupled to a heat bath

Wir untersuchen die Mathematik endlicher, an ein Wärmebad gekoppelter Teilchensysteme. Das Standard-Modell der Quantenelektrodynamik für Temperatur Null liefert einen Hamilton-Operator H, der die Energie von Teilchen beschreibt, welche mit Photonen wechselwirken. Im Heisenbergbild ist die Zeitevolution des physikalischen Systems durch die Wirkung einer Ein-Parameter-Gruppe auf eine Menge von Observablen A gegeben: Diese steht im Zusammenhang mit der Lösung der Schrödinger-Gleichung für H. Um Zustände von A, welche das physikalische System in der Nähe des thermischen Gleichgewichts zur Temperatur T darstellen, zu beschreiben, folgen wir dem Ansatz von Jaksic und Pillet, eine Darstellung von A zu konstruieren. Die Vektoren in dieser Darstellung definieren die Zustände, die Zeitentwicklung wird mit Hilfe des Standard Liouville-Operators L beschrieben. In dieser Doktorarbeit werden folgende Resultate bewiesen bzw. hergeleitet: - die Konstuktion einer Darstellung - die Selbstadjungiertheit des Standard Liouville-Operators - die Existenz eines Gleichgewichtszustandes in dieser Darstellung - der Limes des physikalischen Systems für große Zeiten.

Identity dynamics and the emergence of new organizational arrangements: A multi-level study

Organizational and institutional scholars have advocated the need to examine how processes originating at an individual level can change organizations or even create new organizational arrangements able to affect institutional dynamics (Chreim et al., 2007; Powell & Colyvas, 2008; Smets et al., 2012). Conversely, research on identity work has mainly investigated the different ways individuals can modify the boundaries of their work in actual occupations, thus paying particular attention to ‘internal’ self-crafting (e.g. Wrzesniewski & Dutton, 2001). Drawing from literatures on possible and alternative self and on positive organizational scholarship (e.g., Obodaru, 2012; Roberts & Dutton, 2009), my argument is that individuals’ identity work can go well beyond the boundaries of internal self-crafting to the creation of new organizational arrangements. In this contribution I analyze, through multiple case studies, healthcare professionals who spontaneously participated in the creation of new organizational arrangements, namely health structures called Community Hospitals. The contribution develops this form of identity work by building a grounded model. My findings disclose the process that leads from the search for the enactment of different self-concepts to positive identities, through the creation of a new organizational arrangement. I contend that this is a particularly complex form of collective identity work because it requires, to be successful, concerted actions of several internal, external and institutional actors, and it also requires balanced tensions that – at the same time - enable individuals’ aspirations and organizational equilibrium. I name this process organizational collective crafting. Moreover I inquire the role of context in supporting the triggering power of those unrealized selves. I contribute to the comprehension of the consequences of self-comparisons, organizational identity variance, and positive identity. The study bears important insights on how identity work originating from individuals can influence organizational outcomes and larger social systems.

Strong Down-Valley Low-Level Jets over the Atacama Desert: Observational Characterization

The near-surface wind and temperature regime at three points in the Atacama Desert of northern Chile is described using two-year multi-level measurements from 80-m towers located in an altitude range between 2100 and 2700 m ASL. The data reveal the frequent development of strong nocturnal drainage flows at all sites. Down-valley nose-shaped wind speed profiles are observed with maximum values occurring at heights between 20 m and 60 m AGL. The flow intensity shows considerable inter-daily variability and a seasonal modulation of maximum speeds, which in the cold season can attain hourly average values larger than 20 m s−1. Turbulent mixing appears significant over the full tower layer, affecting the curvature of the nighttime temperature profile and possibly explaining the observed increase of surface temperatures in the down-valley direction. Nocturnal valley winds and temperatures are weakly controlled by upper-air conditions observed at the nearest aerological station. Estimates of terms in the momentum budget for the development and the quasi-stationary phases of the down-valley flows suggest that the pressure gradient force due to the near-surface cooling along the sloping valley axes plays an important role in these drainage flows. A scale for the jet nose height of equilibrium turbulent down-slope jets is proposed, based on surface friction velocity and surface inversion intensity. At one of the sites this scale explains about 70% of the case-to-case observed variance of jet nose heights. Further modeling and observational work is needed, however, in order to better define the dynamics, extent and turbulence structure of this flow system, which has significant wind-energy, climatic and environmental implications.

Advanced Physical Chemistry Problems (VIII), Chemical Equilibrium

This is a set of P. Chem. problems posed at a slightly higher level than the normal textbook level, for students who are continuing in the study of this subject.

Practical case with regard to applying the functional and environmental method to low crest level, detached breakwaters

The research work as presented in this article covers the design of detached breakwaters since they constitute a type of coastal defence work with which to combat many of the erosion problems found on beaches in a stable, sustainable fashion. The main aim of this work is to formulate a functional and environmental (but not structural) design method, enabling the fundamental characteristics of a detached breakwater to be defined as a function of the effect it is wished to induce on the coast, and taking into account variables of a different nature (climate, geomorphology and geometry) influencing the changes the shoreline undergoes after its construction. With this article, it is intended to submit the final result of the investigation undertaken, applying the detached breakwater design method as developed to solving a practical case. Thus it may be shown how the method enables a detached breakwater’s geometric pre-sizing to be tackled at a place on the coast with certain climate, geomorphology and littoral dynamic characteristics, first setting the final state of equilibrium it is wanted to obtain therein after its construction.

Contribution to Theme A of the Benchmark Workshop: Effect of Concrete Swelling on the Equilibrium and Displacements of an Arch Dam

The Kariba dam is undergoing concrete expansion as a result of an alkali-aggregate reaction. The model adopted to simulate the process is explained in the paper; it is based on the model first proposed by Ulm et al, as later modified by Saouma and Perotti. It has been implemented in the commercial finite element code Abaqus and applied to solve the benchmark problem. The parameters of the model were calibrated using the data recorded up to 1995. The calibrated model was then used for predicting the evolution of the dam up to the present date. Apart from this prediction the paper offers a number of conclusions, such as the fact that the stress level appears to have a major influence on the expansion process; and it presents some suggestions to improve the formulation of the benchmark, such as providing temperature data and widening the locations and conditions of the data employed in the calibration