Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay

Liquid-liquid phase transition for soft-core attractive potential

Using event-driven molecular dynamics simulations, we study a three-dimensional one-component system of spherical particles interacting via a discontinuous potential combining a repulsive square soft core and an attractive square well. In the case of a narrow attractive well, it has been shown that this potential has two metastable gas-liquid critical points. Here we systematically investigate how the changes of the parameters of this potential affect the phase diagram of the system. We find a broad range of potential parameters for which the system has both a gas-liquid critical point C1 and a liquid-liquid critical point C2. For the liquid-gas critical point we find that the derivatives of the critical temperature and pressure, with respect to the parameters of the potential, have the same signs: they are positive for increasing width of the attractive well and negative for increasing width and repulsive energy of the soft core. This result resembles the behavior of the liquid-gas critical point for standard liquids. In contrast, for the liquid-liquid critical point the critical pressure decreases as the critical temperature increases. As a consequence, the liquid-liquid critical point exists at positive pressures only in a finite range of parameters. We present a modified van der Waals equation which qualitatively reproduces the behavior of both critical points within some range of parameters, and gives us insight on the mechanisms ruling the dependence of the two critical points on the potential¿s parameters. The soft-core potential studied here resembles model potentials used for colloids, proteins, and potentials that have been related to liquid metals, raising an interesting possibility that a liquid-liquid phase transition may be present in some systems where it has not yet been observed.

Classical predictive electrodynamics of two charges with radiation: General framework. I.

Outgoing radiation is introduced in the framework of the classical predictive electrodynamics using LorentzDiracs equation as a subsidiary condition. In a perturbative scheme in the charges the first radiative self-terms of the accelerations, momentum and angular momentum of a two charge system without external field are calculated.

Estudi dinàmic i manipulació de fluxos en monocapes de Langmuir de molècules fotosensibles

Durant el període de gaudiment de la beca, des del dia 9 de març del 2007 fins el dia 8 de març del 2010, s’han dut a terme diferents tipus d’experiments amb sistemes bidimensionals com són les monocapes de Langmuir. Inicialment es va començar per l’estudi i la caracterització d’aquests sistemes experimentals, tant en repòs com en dinàmic, com és l’estudi de la reposta col•lectiva molecular de dominis d’un azoderivat fotosensible al rotar el pla de polarització mentre es mante sota il•luminació constant i els estudis de sistemes bidimensionals al collapse que es poden relacionar a les propietats viscoplàstiques dels sòlids. Una altra via d’estudi és la reologia d’aquests sistemes bidimensionals quan flueixen a través de canals. Arrel del sistema experimental més simple, una monocapa fluint per un canal, s’ha observat i estudiat l’efecte coll d’ampolla. Un cop assolit i estudiat el sistema més senzill, s’han aplicat tècniques més complexes de fabricació per fotolitografia per fer fluir monocapes de Langmuir per circuits on hi ha un gran contrast de mullat. Un cop aquests circuits es van implementar satisfactòriament en un sistema pel control de fluxos bidimensionals, es posen de manifest les possibles aplicacions futures d’aquests sistemes per l’estudi i el desenvolupament de la microfluídica bidimensional.

Political Competition in Hard Times

This paper analyzes a spatial model of political competition between two policy- motivated parties in hard times of crisis. Hard times are modeled in terms of policy- making costs carried by a newly elected party. The results predict policy divergence in equilibrium. If the ideological preferences of parties are quite diverse and extreme, there is a unique equilibrium in which the parties announce symmetric platforms and each party wins with probability one half. If one party is extreme while the other is more moderate, there is a unique equilibrium in which the parties announce asymmetric platforms. If the preferred policies of the parties are not very distinct, there are two equilibria with asymmetric platforms. An important property of equilibrium with asymmetric platforms is that a winning party necessarily announces its most preferred policy as a platform. JEL classification: D72. Keywords: Spatial model; Political competition; Two-party system; Policy-motivated parties; Hard times; Crisis.

Policy Making in Divided Government. A Pivotal Actors Model with Party Discipline.

This article presents a formal model of policy decision-making in an institutional framework of separation of powers in which the main actors are pivotal political parties with voting discipline. The basic model previously developed from pivotal politics theory for the analysis of the United States lawmaking is here modified to account for policy outcomes and institutional performances in other presidential regimes, especially in Latin America. Legislators' party indiscipline at voting and multi-partism appear as favorable conditions to reduce the size of the equilibrium set containing collectively inefficient outcomes, while a two-party system with strong party discipline is most prone to produce 'gridlock', that is, stability of socially inefficient policies. The article provides a framework for analysis which can induce significant revisions of empirical data, especially regarding the effects of situations of (newly defined) unified and divided government, different decision rules, the number of parties and their discipline. These implications should be testable and may inspire future analytical and empirical work.

Policy making in divided government. A pivotal actors model with party discipline

This article presents a formal model of policy decision-making in an institutional framework of separation of powers in which the main actors are pivotal political parties with voting discipline. The basic model previously developed from pivotal politics theory for the analysis of the United States lawmaking is here modified to account for policy outcomes and institutional performances in other presidential regimes, especially in Latin America. Legislators' party indiscipline at voting and multi-partism appear as favorable conditions to reduce the size of the equilibrium set containing collectively inefficient outcomes, while a two-party system with strong party discipline is most prone to produce 'gridlock', that is, stability of socially inefficient policies. The article provides a framework for analysis which can induce significant revisions of empirical data, especially regarding the effects of situations of (newly defined) unified and divided government, different decision rules, the number of parties and their discipline. These implications should be testable and may inspire future analytical and empirical work.

Random mixtures with orientational order, and the anisotropic resistivity tensor of high Tc superconductors

By generalizing effective-medium theory to the case of orientationally ordered but positionally disordered two component mixtures, it is shown that the anisotropic dielectric tensor of oxide superconductors can be extracted from microwave measurements on oriented crystallites of YBa2Cu3O7¿x embedded in epoxy. Surprisingly, this technique appears to be the only one which can access the resistivity perpendicular to the copper¿oxide planes in crystallites that are too small for depositing electrodes. This possibility arises in part because the real part of the dielectric constant of oxide superconductors has a large magnitude. The validity of the effective-medium approach for orientationally ordered mixtures is corroborated by simulations on two¿dimensional anisotropic random resistor networks. Analysis of the experimental data suggests that the zero-temperature limit of the finite frequency resistivity does not vanish along the c axis, a result which would simply the existence of states at the Fermi surface, even in the superconducting state

Finite-size scaling investigation of the liquid-liquid critical point in ST2 water and its stability with respect to crystallization.

The liquid-liquid critical point scenario of water hypothesizes the existence of two metastable liq- uid phases low-density liquid (LDL) and high-density liquid (HDL) deep within the supercooled region. The hypothesis originates from computer simulations of the ST2 water model, but the stabil- ity of the LDL phase with respect to the crystal is still being debated. We simulate supercooled ST2 water at constant pressure, constant temperature, and constant number of molecules N for N ≤ 729 and times up to 1 μs. We observe clear differences between the two liquids, both structural and dynamical. Using several methods, including finite-size scaling, we confirm the presence of a liquid-liquid phase transition ending in a critical point. We find that the LDL is stable with respect to the crystal in 98% of our runs (we perform 372 runs for LDL or LDL-like states), and in 100% of our runs for the two largest system sizes (N = 512 and 729, for which we perform 136 runs for LDL or LDL-like states). In all these runs, tiny crystallites grow and then melt within 1 μs. Only for N ≤ 343 we observe six events (over 236 runs for LDL or LDL-like states) of spontaneous crystal- lization after crystallites reach an estimated critical size of about 70 ± 10 molecules.

Nonequilibrium patterns and shape fluctuations in reactive membranes

A simple kinetic model of a two-component deformable and reactive bilayer is presented. The two differently shaped components are interconverted by a nonequilibrium reaction, and a phenomenological coupling between local composition and curvature is proposed. When the two components are not miscible, linear stability analysis predicts, and numerical simulations show, the formation of stationary nonequilibrium composition/curvature patterns whose typical size is determined by the reactive process. For miscible components, a linearization of the dynamic equations is performed in order to evaluate the correlation function for shape fluctuations from which the behavior of these systems in micropipet aspiration experiments can be predicted.

Experimental evidence of localized oscillations in the photosensitive chlorine dioxide-iodine-malonic acid reaction

The interaction between Hopf and Turing modes has been the subject of active research in recent years. We present here experimental evidence of the existence of mixed Turing-Hopf modes in a two-dimensional system. Using the photosensitive chlorine dioxide-iodine-malonic acid reaction (CDIMA) and external constant background illumination as a control parameter, standing spots oscillating in amplitude and with hexagonal ordering were observed. Numerical simulations in the Lengyel-Epstein model for the CDIMA reaction confirmed the results.

El sistema electoral de les Corts Valencianes: orígens i reforma

[cat] Aquest article vol refutar la hipòtesi que els partits decideixen sistemes electorals majoritaris i que decideixen també mantenir-los invariables, sempre que el sistema de partits s"aproximi al bipartidisme i cap dels dos grans partits pugui perdre la seva posició a favor d"un nou competidor. De manera inversa, els sistemes electorals proporcionals són la conseqüència del multipartidisme, en el qual cap partit té opcions de rebre la majoria dels vots. El cas valencià, però, confirma només parcialment la hipòtesi: els partits van aprovar el 1982 regles proporcionals perquè les eleccions dels parlaments autonòmics eren considerades secundàries, no només pel multipartidisme existent aleshores. En canvi, sí que es confirma que el canvi iniciat el 2006 amb la reforma estatutària manté, de moment, l"status quo per no alterar la formació de majories parlamentàries. Encara queda pendent, però, que es modifiqui la Llei Electoral, de la qual depèn quin mínim de vots per entrar a les Corts s"establirà.

Thermodynamic stability of nanosized multicomponent bubbles/droplets: The square gradient theory and the capillary approach

Formation of nanosized droplets/bubbles from a metastable bulk phase is connected to many unresolved scientific questions. We analyze the properties and stability of multicomponent droplets and bubbles in the canonical ensemble, and compare with single-component systems. The bubbles/droplets are described on the mesoscopic level by square gradient theory. Furthermore, we compare the results to a capillary model which gives a macroscopic description. Remarkably, the solutions of the square gradient model, representing bubbles and droplets, are accurately reproduced by the capillary model except in the vicinity of the spinodals. The solutions of the square gradient model form closed loops, which shows the inherent symmetry and connected nature of bubbles and droplets. A thermodynamic stability analysis is carried out, where the second variation of the square gradient description is compared to the eigenvalues of the Hessian matrix in the capillary description. The analysis shows that it is impossible to stabilize arbitrarily small bubbles or droplets in closed systems and gives insight into metastable regions close to the minimum bubble/droplet radii. Despite the large difference in complexity, the square gradient and the capillary model predict the same finite threshold sizes and very similar stability limits for bubbles and droplets, both for single-component and two-component systems.

Extremal principle of entropy production in the climate system

Paltridge found reasonable values for the most significant climatic variables through maximizing the material transport part of entropy production by using a simple box model. Here, we analyse Paltridge's box model to obtain the energy and the entropy balance equations separately. Derived expressions for global entropy production, which is a function of the radiation field, and even its material transport component, are shown to be different from those used by Paltridge. Plausible climatic states are found at extrema of these parameters. Feasible results are also obtained by minimizing the radiation part of entropy production, in agreement with one of Planck's results, Finally, globally averaged values of the entropy flux of radiation and material entropy production are obtained for two dynamical extreme cases: an earth with uniform temperature, and an earth in radiative equilibrium at each latitudinal point

Two complementary molecular energy decomposition schemes: the Mayer and Ziegler-Rauk methods in comparison

In the present paper we discuss and compare two different energy decomposition schemes: Mayer's Hartree-Fock energy decomposition into diatomic and monoatomic contributions [Chem. Phys. Lett. 382, 265 (2003)], and the Ziegler-Rauk dissociation energy decomposition [Inorg. Chem. 18, 1558 (1979)]. The Ziegler-Rauk scheme is based on a separation of a molecule into fragments, while Mayer's scheme can be used in the cases where a fragmentation of the system in clearly separable parts is not possible. In the Mayer scheme, the density of a free atom is deformed to give the one-atom Mulliken density that subsequently interacts to give rise to the diatomic interaction energy. We give a detailed analysis of the diatomic energy contributions in the Mayer scheme and a close look onto the one-atom Mulliken densities. The Mulliken density ρA has a single large maximum around the nuclear position of the atom A, but exhibits slightly negative values in the vicinity of neighboring atoms. The main connecting point between both analysis schemes is the electrostatic energy. Both decomposition schemes utilize the same electrostatic energy expression, but differ in how fragment densities are defined. In the Mayer scheme, the electrostatic component originates from the interaction of the Mulliken densities, while in the Ziegler-Rauk scheme, the undisturbed fragment densities interact. The values of the electrostatic energy resulting from the two schemes differ significantly but typically have the same order of magnitude. Both methods are useful and complementary since Mayer's decomposition focuses on the energy of the finally formed molecule, whereas the Ziegler-Rauk scheme describes the bond formation starting from undeformed fragment densities