Figures of equilibrium for tidally deformed non-homogeneous celestial bodies

Abstract (2,250 Maximum Characters): Several theories of tidal evolution, since the theory developed by Darwin in the XIX century, are based on the figure of equilibrium of the tidally deformed body. Frequently the adopted figure is a Jeans prolate spheroid. In some case, however, the rotation is important and Roche ellipsoids are used. The main limitations of these models are (a) they refer to homogeneous bodies; (b) the rotation axis is perpendicular to the plane of the orbit. This communication aims at presenting several results in which these hypotheses are not done. In what concerns the non-homogeneity, the presented results concerns initially bodies formed by N homogeneous layers and we study the non sphericity of each layer and relate them to the density distribution. The result is similar to the Clairaut figure of equilibrium, often used in planetary sciences, but taking into full account the tidal deformation. The case of the rotation axis non perpendicular to the orbital plane is much more complex and the study has been restricted for the moment to the case of homogeneous bodies.

Irreversibility by competition on a Glauber-Ising model by means of the entropy production.

An out of equilibrium Ising model subjected to an irreversible dynamics is analyzed by means of a stochastic dynamics, on a effort that aims to understand the observed critical behavior as consequence of the intrinsic microscopic characteristics. The study focus on the kinetic phase transitions that take place by assuming a lattice model with inversion symmetry and under the influence of two competing Glauber dynamics, intended to describe the stationary states using the entropy production, which characterize the system behavior and clarifies its reversibility conditions. Thus, it is considered a square lattice formed by two sublattices interconnected, each one of which is in contact with a heat bath at different temperature from the other. Analytical and numerical treatments are faced, using mean-field approximations and Monte Carlo simulations. For the one dimensional model exact results for the entropy production were obtained, though in this case the phase transition that takes place in the two dimensional counterpart is not observed, fact which is in accordance with the behavior shared by lattice models presenting inversion symmetry. Results found for the stationary state show a critical behavior of the same class as the equilibrium Ising model with a phase transition of the second order, which is evidenced by a divergence with an exponent µ ¼ 0:003 of the entropy production derivative.

Intrinsic organization of the suprachiasmatic nucleus in the capuchin monkey

The suprachiasmatic nucleus (SCN), which is the main circadian biological clock in mammals, is composed of multiple cells that function individually as independent oscillators to express the self-sustained mRNA and protein rhythms of the so-called clock genes. Knowledge regarding the presence and localization of the proteins and neuroactive substances of the SCN are essential for understanding this nucleus and for its successful manipulation. Although there have been advances in the investigation of the intrinsic organization of the SCN in rodents, little information is available in diurnal species, especially in primates. This study, which explores the pattern of expression and localization of PER2 protein in the SCN of capuchin monkey, evaluates aspects of the circadian system that are common to both primates and rodents. Here, we showed that PER2 protein immunoreactivity is higher during the light phase. Additionally, the complex organization of cells that express vasopressin, vasoactive intestinal polypeptide, neuron-specific nuclear protein, calbindin and calretinin in the SCN, as demonstrated by their immunoreactivity, reveals an intricate network that may be related to the similarities and differences reported between rodents and primates in the literature.

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.

Solid-phase Microextraction and Detection of Organophosphate Triesters in Indoor air

In the work underlying this thesis solid-phase microextraction (SPME) was evaluated as a passive sampling technique for organophosphate triesters in indoor air. These compounds are used on a large scale as flame-retarding and plastizicing additives in a variety of materials and products, and have proven to be common pollutants in indoor air. The main objective of this work was to develop an accurate method for measuring the volatile fraction. Such a method can be used in combination with active sampling to obtain information regarding the vapour/particulate distribution in different indoor environments. SPME was investigated under both equilibrium and non-equilibrium conditions and parameters associated with these different conditions were estimated. In Paper I, time-weighted average (TWA) SPME under dynamic conditions was investigated in order to obtain a fast air sampling method for organophosphate triesters. Among the investigated SPME coatings, the absorptive PDMS polymer had the highest affinity for the organophosphate triesters and was consequently used in all further work. Since the sampling rate is dependent on the agitation conditions, the linear airflow rates had to be carefully considered. Sampling periods as short as 1 hour were shown to be sufficient for measurements in the ng-μg m-3 range when using a PDMS 100-μm fibre and a linear flow rate above 7 cm s-1 over the fibre. SPME under equilibrium conditions is rather time-consuming, even under dynamic conditions, for slowly partitioning compounds such as organophosphate triesters. Nevertheless, this method has some significant advantages. For instance, the limit of detection is much lower compared to 1 h TWA sampling. Furthermore, the sampling time can be ignored as long as equilibrium has been attained. In Paper II, SPME under equilibrium conditions was investigated and evaluated for organophosphate triester vapours. Since temperature and humidity are closely associated with the distribution constant a simple study of the effect of these parameters was performed. The obtained distribution constants were used to determine the air levels in a common indoor environment. SPME and parallel active sampling on filters yielded similar results, indicating that the detected compounds were almost entirely associated with the vapour phase To apply dynamic SPME method in the field a sampler device, which enables controlled linear airflow rates to be applied, was constructed and evaluated (Paper III). This device was developed for application of SPME and active sampling in parallel. A GC/PICI-MS/MS method was developed and used in combination with active sampling of organophosphate triesters in indoor air (Paper IV). The combination of MS/MS and the soft ionization achieved with methanol as reagent gas yielded high selectivity and detection limits comparable to those provided by GC with nitrogen-phosphorus detection (NPD). The method limit of detection, when sampling 1.5 m3 of air, was in the range 0.1-1.4 ng m-3. In Paper V, the developed MS method was used in combination with SPME for indoor air measurements. The levels detected in the investigated indoor environments range from a few ng to μg m-3. Tris(2-chloropropyl) phosphate was detected at a concentration as high as 7 μg m-3 in a newly rebuilt lecture room.

On some Banach space constants arising in nonlinear fixed point and eigenvalue theory

[EN] As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero maps without positive eigenvalues and normalized eigenvectors. In this paper, we give upper and lower estimates, or even explicit formulas, for the minimal Lipschitz constant and measure of noncompactness of such maps.

A pocket beach that reaches equilibrium after becoming disconnected from a large system of beaches. Playa Barca (Fuerteventura)

[EN] Playa Barca is a 370 m long beach located within the system of the Leeward beaches on the Jandía peninsula, Fuerteventura. This system of beaches represents one of the major sources of economic income to the island, both because of its natural landscape that attract a specific type of tourism, and because of its particular climate conditions that make these beaches ideal for practicing wind-water sports. Nevertheless, in the past decades, this area has suffered from a significant and worrying coastline retreat. In order to look for an explanation to this retreat, five topographic surveys were carried out in October 1999, February 2001, February 2002, February 2003 and February 2013 to track the beach behavior in the last 15 years. A total station Topcon GTS-303D was used for this purpose. Surveys were carried out during low spring tides, so that the outer limit was the furthest possible depending on wave conditions. The inner limit covered part of the dunes in the backshore. From these topographic data both coastline changes and the sedimentary balance have been obtained.

Multiproperty correlation of experimental data of the binaries propyl ethanoate+alkanes (pentane to decane). New experimental information for vapor-liquid equilibrium and mixing properties

[EN]A thermodynamic study is carried out on binary systems composed of propyl ethanoate with six alkanes, from pentane to decane. Vapor pressures of the ester and the isobaric vapor−liquid equilibria of these six mixtures were measured at 101.32 kPa in a small-capacity ebulliometer and also the mixing properties yE = vE,hE over a range of temperatures and at atmospheric pressure. Adequate correlations are drawn for the surfaces yE = yE(x,T) with an interpretation on the behavior of the mixtures and also using cp E data from literature.

Intrinsic ordering, combinatorial numbers and reliability engineering

[EN]A new algorithm for evaluating the top event probability of large fault trees (FTs) is presented. This algorithm does not require any previous qualitative analysis of the FT. Indeed, its efficiency is independent of the FT logic, and it only depends on the number n of basic system components and on their failure probabilities. Our method provides exact lower and upper bounds on the top event probability by using new properties of the intrinsic order relation between binary strings. The intrinsic order enables one to select binary n-tuples with large occurrence probabilities without necessity to evaluate them. This drastically reduces the complexity of the problem from exponential (2n binary n-tuples) to linear (n Boolean variables)...

Labeling the nodes in the intrinsic order graph with their weights

[EN] This paper deals with the study of some new properties of the intrinsic order graph. The intrinsic order graph is the natural graphical representation of a complex stochastic Boolean system (CSBS). A CSBS is a system depending on an arbitrarily large number n of mutually independent random Boolean variables. The intrinsic order graph displays its 2n vertices (associated to the CSBS) from top to bottom, in decreasing order of their occurrence probabilities. New relations between the intrinsic ordering and the Hamming weight (i.e., the number of 1-bits in a binary n-tuple) are derived. Further, the distribution of the weights of the 2n nodes in the intrinsic order graph is analyzed…

Complex sochastic boolean systems : new properties of the intrinsic order graph

[EN]A complex stochastic Boolean system (CSBS) is a system depending on an arbitrary number n of stochastic Boolean variables. The analysis of CSBSs is mainly based on the intrinsic order: a partial order relation defined on the set f0; 1gn of binary n-tuples. The usual graphical representation for a CSBS is the intrinsic order graph: the Hasse diagram of the intrinsic order. In this paper, some new properties of the intrinsic order graph are studied. Particularly, the set and the number of its edges, the degree and neighbors of each vertex, as well as typical properties, such as the symmetry and fractal structure of this graph, are analyzed…

Intrinsic Order and Hamming Weight

[EN]The intrinsic order is a partial order relation defined on the set {0, 1} n of all binary n-tuples. This ordering enables one to automatically compare binary n-tuple probabilities without computing them, just looking at the relative positions of their 0s & 1s. In this paper, new relations between the intrinsic ordering and the Hamming weight (i.e., the number of 1-bits in a binary n-tuple) are derived. All theoretical results are rigorously proved and illustrated through the intrinsic order graph…

Intrinsic uncoupling in the ATP synthase of Escherichia coli. Studies on WT and ε-truncated mutants

The H+/ATP ratio in the catalysis of ATP synthase has generally been considered a fixed parameter. However, Melandri and coworkers have recently shown that, in the ATP synthase of the photosynthetic bacterium Rb.capsulatus, this ratio can significantly decrease during ATP hydrolysis when the concentration of either ADP or Pi is maintained at a low level (Turina et al., 2004). The present work has dealt with the ATP synthase of E.coli, looking for evidence of this phenomenon of intrinsic uncoupling in this organism as well. First of all, we have shown that the DCCD-sensitive ATP hydrolysis activity of E.coli internal membranes was strongly inhibited by ADP and Pi, with a half-maximal effect in the submicromolar range for ADP and at 140 µM for Pi. In contrast to this monotonic inhibition, however, the proton pumping activity of the enzyme, as estimated under the same conditions by the fluorescence quenching of the ΔpH-sensitive probe ACMA, showed a clearly biphasic progression, both for Pi, increasing from 0 up to approximately 200 µM, and for ADP, increasing from 0 up to a few µM. We have interpreted these results as indicating that the occupancy of ADP and Pi binding sites shifts the enzyme from a partially uncoupled state to a fully coupled state, and we expect that the ADP- and Pi-modulated intrinsic uncoupling is likely to be a general feature of prokaryotic ATP synthases. Moreover, the biphasicity of the proton pumping data suggested that two Pi binding sites are involved. In order to verify whether the same behaviour could be observed in the isolated enzyme, we have purified the ATP synthase of E.coli and reconstituted it into liposomes. Similarly as observed in the internal membrane preparation, in the isolated and reconstituted enzyme it was possible to observe inhibition of the hydrolytic activity by ADP and Pi (with half-maximal effects at few µM for ADP and at 400 µM for Pi) with a concomitant stimulation of proton pumping. Both the inhibition of ATP hydrolysis and the stimulation of proton pumping as a function of Pi were lost upon ADP removal by an ADP trap. These data have made it possible to conclude that the results obtained in E.coli internal membranes are not due to the artefactual interference of enzymatic activities other than the ones of the ATP synthase. In addition, data obtained with liposomes have allowed a calibration of the ACMA signal by ΔpH transitions of known extent, leading to a quantitative evaluation of the proton pumping data. Finally, we have focused our efforts on searching for a possible structural candidate involved in the phenomenon of intrinsic uncoupling. The ε-subunit of the ATP-synthase is known as an endogenous inhibitor of the hydrolysis activity of the complex and appears to undergo drastic conformational changes between a non-inhibitory form (down-state) and an inhibitory form (up-state)(Rodgers & Wilce, 2000; Gibbons et al., 2000). In addition, the results of Cipriano & Dunn (2006) indicated that the C-terminal domain of this subunit played an important role in the coupling mechanism of the pump, and those of Capaldi et al. (2001), Suzuki et al. (2003) were consistent with the down-state showing a higher hydrolysis-to-synthesis ratio than the up-state. Therefore, we decided to search for modulation of pumping efficiency in a C-terminally truncated ε mutant. A low copy number expression vector has been built, carrying an extra copy of uncC, with the aim of generating an ε-overexpressing E.coli strain in which normal levels of assembly of the mutated ATP-synthase complex would be promoted. We have then compared the ATP hydrolysis and the proton pumping activity in membranes prepared from these ε-overexpressing E.coli strains, which carried either the WT ε subunit or the ε88-stop truncated form. Both strains yielded well energized membranes. Noticeably, they showed a marked difference in the inhibition of hydrolysis by Pi, this effect being largely lost in the truncated mutant. However, pre-incubation of the mutated enzyme with ADP at low nanomolar concentrations (apparent Kd = 0.7nM) restored the hydrolysis inhibition, together with the modulation of intrinsic uncoupling by Pi, indicating that, contrary to wild-type, during membrane preparation the truncated mutant had lost the ADP bound at this high-affinity site, evidently due to a lower affinity (and/or higher release) for ADP of the mutant relative to wild type. Therefore, one of the effects of the C-terminal domain of ε appears to be to modulate the affinity of at least one of the binding sites for ADP. The lack of this domain does not appear so much to influence the modulability of coupling efficiency, but instead the extent of this modulation. At higher preincubated ADP concentrations (apparent Kd = 117nM), the only observed effects were inhibition of both hydrolysis and synthesis, providing a direct proof that two ADP-binding sites on the enzyme are involved in the inhibition of hydrolysis, of which only the one at higher affinity also modulates the coupling efficiency.

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.

Stability, viscous dissipation and local thermal non-equilibrium in fluid saturated porous media

In this thesis, the field of study related to the stability analysis of fluid saturated porous media is investigated. In particular the contribution of the viscous heating to the onset of convective instability in the flow through ducts is analysed. In order to evaluate the contribution of the viscous dissipation, different geometries, different models describing the balance equations and different boundary conditions are used. Moreover, the local thermal non-equilibrium model is used to study the evolution of the temperature differences between the fluid and the solid matrix in a thermal boundary layer problem. On studying the onset of instability, different techniques for eigenvalue problems has been used. Analytical solutions, asymptotic analyses and numerical solutions by means of original and commercial codes are carried out.