Differential forms on Carnot groups

The main goal of this thesis is to understand and link together some of the early works by Michel Rumin and Pierre Julg. The work is centered around the so-called Rumin complex, which is a construction in subRiemannian geometry. A Carnot manifold is a manifold endowed with a horizontal distribution. If further a metric is given, one gets a subRiemannian manifold. Such data arise in different contexts, such as: - formulation of the second principle of thermodynamics; - optimal control; - propagation of singularities for sums of squares of vector fields; - real hypersurfaces in complex manifolds; - ideal boundaries of rank one symmetric spaces; - asymptotic geometry of nilpotent groups; - modelization of human vision. Differential forms on a Carnot manifold have weights, which produces a filtered complex. In view of applications to nilpotent groups, Rumin has defined a substitute for the de Rham complex, adapted to this filtration. The presence of a filtered complex also suggests the use of the formal machinery of spectral sequences in the study of cohomology. The goal was indeed to understand the link between Rumin's operator and the differentials which appear in the various spectral sequences we have worked with: - the weight spectral sequence; - a special spectral sequence introduced by Julg and called by him Forman's spectral sequence; - Forman's spectral sequence (which turns out to be unrelated to the previous one). We will see that in general Rumin's operator depends on choices. However, in some special cases, it does not because it has an alternative interpretation as a differential in a natural spectral sequence. After defining Carnot groups and analysing their main properties, we will introduce the concept of weights of forms which will produce a splitting on the exterior differential operator d. We shall see how the Rumin complex arises from this splitting and proceed to carry out the complete computations in some key examples. From the third chapter onwards we will focus on Julg's paper, describing his new filtration and its relationship with the weight spectral sequence. We will study the connection between the spectral sequences and Rumin's complex in the n-dimensional Heisenberg group and the 7-dimensional quaternionic Heisenberg group and then generalize the result to Carnot groups using the weight filtration. Finally, we shall explain why Julg required the independence of choices in some special Rumin operators, introducing the Szego map and describing its main properties.

Análise de um queimador infravermelho funcionando com combustível híbrido : GLP/Bio-óleo

Biomass is considered the largest renewable energy source that can be used in an environmentally sustainable. From the pyrolysis of biomass is possible to obtain products with higher energy density and better use properties. The liquid resultant of this process is traditionally called bio-oil. The use of infrared burners in industrial applications has many advantages in terms of technical-operational, for example, uniformity in the heat supply in the form of radiation and convection, with a greater control of emissions due to the passage of exhaust gases through a macroporous ceramic bed. This paper presents a commercial infrared burner adapted with an ejector proposed able to burn a hybrid configuration of liquefied petroleum gas (LPG) and bio-oil diluted. The dilution of bio-oil with absolute ethanol aimed to decrease the viscosity of the fluid, and improving the stability and atomization. It was introduced a temperature controller with thermocouple modulating two stages (low heat / high heat), and solenoid valves for fuels supply. The infrared burner has been tested, being the diluted bio-oil atomized, and evaluated its performance by conducting energy balance. The method of thermodynamic analysis to estimate the load was used an aluminum plate located at the exit of combustion gases and the distribution of temperatures measured by thermocouples. The dilution reduced the viscosity of the bio-oil in 75.4% and increased by 11% the lower heating value (LHV) of the same, providing a stable combustion to the burner through the atomizing with compressed air and burns combined with LPG. Injecting the hybrid fuel there was increase in the heat transfer from the plate to the environment in 21.6% and gain useful benefit of 26.7%, due to the improved in the efficiency of the 1st Law of Thermodynamics of infrared burner

Temperature dependence of the distribution of the first passage time: Results from discontinuous molecular dynamics simulations of an all-atom model of the second beta-hairpin fragment of protein G

More than 22 000 folding kinetic simulations were performed to study the temperature dependence of the distribution of first passage time (FPT) for the folding of an all-atom Go-like model of the second beta-hairpin fragment of protein G. We find that the mean FPT (MFPT) for folding has a U (or V)-shaped dependence on the temperature with a minimum at a characteristic optimal folding temperature T-opt*. The optimal folding temperature T-opt* is located between the thermodynamic folding transition temperature and the solidification temperature based on the Lindemann criterion for the solid. Both the T-opt* and the MFPT decrease when the energy bias gap against nonnative contacts increases. The high-order moments are nearly constant when the temperature is higher than T-opt* and start to diverge when the temperature is lower than T-opt*. The distribution of FPT is close to a log-normal-like distribution at T* greater than or equal to T-opt*. At even lower temperatures, the distribution starts to develop long power-law-like tails, indicating the non-self-averaging intermittent behavior of the folding dynamics. It is demonstrated that the distribution of FPT can also be calculated reliably from the derivative of the fraction not folded (or fraction folded), a measurable quantity by routine ensemble-averaged experimental techniques at dilute protein concentrations.

Second law analysis and simulation techniques for the energy optimization of buildings

The research activity described in this thesis is focused mainly on the study of finite-element techniques applied to thermo-fluid dynamic problems of plant components and on the study of dynamic simulation techniques applied to integrated building design in order to enhance the energy performance of the building. The first part of this doctorate thesis is a broad dissertation on second law analysis of thermodynamic processes with the purpose of including the issue of the energy efficiency of buildings within a wider cultural context which is usually not considered by professionals in the energy sector. In particular, the first chapter includes, a rigorous scheme for the deduction of the expressions for molar exergy and molar flow exergy of pure chemical fuels. The study shows that molar exergy and molar flow exergy coincide when the temperature and pressure of the fuel are equal to those of the environment in which the combustion reaction takes place. A simple method to determine the Gibbs free energy for non-standard values of the temperature and pressure of the environment is then clarified. For hydrogen, carbon dioxide, and several hydrocarbons, the dependence of the molar exergy on the temperature and relative humidity of the environment is reported, together with an evaluation of molar exergy and molar flow exergy when the temperature and pressure of the fuel are different from those of the environment. As an application of second law analysis, a comparison of the thermodynamic efficiency of a condensing boiler and of a heat pump is also reported. The second chapter presents a study of borehole heat exchangers, that is, a polyethylene piping network buried in the soil which allows a ground-coupled heat pump to exchange heat with the ground. After a brief overview of low-enthalpy geothermal plants, an apparatus designed and assembled by the author to carry out thermal response tests is presented. Data obtained by means of in situ thermal response tests are reported and evaluated by means of a finite-element simulation method, implemented through the software package COMSOL Multyphysics. The simulation method allows the determination of the precise value of the effective thermal properties of the ground and of the grout, which are essential for the design of borehole heat exchangers. In addition to the study of a single plant component, namely the borehole heat exchanger, in the third chapter is presented a thorough process for the plant design of a zero carbon building complex. The plant is composed of: 1) a ground-coupled heat pump system for space heating and cooling, with electricity supplied by photovoltaic solar collectors; 2) air dehumidifiers; 3) thermal solar collectors to match 70% of domestic hot water energy use, and a wood pellet boiler for the remaining domestic hot water energy use and for exceptional winter peaks. This chapter includes the design methodology adopted: 1) dynamic simulation of the building complex with the software package TRNSYS for evaluating the energy requirements of the building complex; 2) ground-coupled heat pumps modelled by means of TRNSYS; and 3) evaluation of the total length of the borehole heat exchanger by an iterative method developed by the author. An economic feasibility and an exergy analysis of the proposed plant, compared with two other plants, are reported. The exergy analysis was performed by considering the embodied energy of the components of each plant and the exergy loss during the functioning of the plants.

Fugitive slave law [electronic resource] : The religious duty of obedience to law; a sermon preached in the Second Presbyterian Church in Brooklyn, Nov. 24, 1850. /

Electronic text and image data.

Reform of legal immigration [microform] : hearings before the Subcommittee on Immigration, Refugees, and International Law of the Committee on the Judiciary, House of Representatives, One Hundredth Congress, second session, on H.R. 5115 and S. 2104 ... September 7 and 16, 1988.

"Serial no. 101."

Review of the drug law enforcement activities of the Forest Service; and the Omnibus Public Lands Act of 1987 [microform] : hearing before the Subcommittee on Forests, Family Farms, and Energy of the Committee on Agriculture, House of Representatives, One Hundredth Congress, second session, on H.R. 3680, July 12, 1988.

"Serial no. 100-92."

Military implications of the United Nations Convention on the Law of the Sea : hearing before the Committee on Armed Services, United States Senate, One Hundred Eighth Congress, second session, April 8, 2004.

Distributed to some depository libraries in microfiche.

U.S. foreign policy and the law of the sea : hearings before the Committee on Foreign Affairs, House of Representatives, Ninety-seventh Congress, second session, June 17, August 12, and September 16, 1982.

Mode of access: Internet.

A general abridgment of the common law, alphabetically digested under proper titles. With notes and references to the whole. With three tables: the first, of the several titles. The second, of the names of the cases. And the third, of the matter under general heads.

Includes indexes.

Omnibus Maritime Regulatory Reform Revitalization and Reorganization Act of 1980 : hearing before the Subcommittee on Monopolies and Commercial Law of the Committee on the Judiciary, House of Representatives, Ninety-sixth Congress, second session, on H.R. 6899 ... June 5, 1980.

Item 1020.

The first part of the Institutes of the laws of England: or, A commentary upon Littleton, not the name of the author only, but of the law it self ... Hæc ego grandævus posui tibi, candide lector, authore Edwardo Coke, milite. Also three learned tracts of the same author: the first, his Reading upon the 27th of Edward the First, entituled, The statute of levying fines: the second, Of bail and mainprize: and the third, his Compleat copyholder.

French and English text in parallel columns.

The 1980 Geneva session and status of the negotiations on the Law of the Sea : hearing before the Committee on Foreign Affairs, House of Representatives, Ninety-sixth Congress, second session, October 1, 1980.

Mode of access: Internet.