Rumor Propagation Model: An Equilibrium Study

Compartmental epidemiological models have been developed since the 1920s and successfully applied to study the propagation of infectious diseases. Besides, due to their structure, in the 1960s an interesting version of these models was developed to clarify some aspects of rumor propagation, considering that spreading an infectious disease or disseminating information is analogous phenomena. Here, in an analogy with the SIR (Susceptible-Infected-Removed) epidemiological model, the ISS (Ignorant-Spreader-Stifler) rumor spreading model is studied. By using concepts from the Dynamical Systems Theory, stability of equilibrium points is established, according to propagation parameters and initial conditions. Some numerical experiments are conducted in order to validate the model.

Coherent Stranski-Krastanov growth in 1+1 dimensions with anharmonic interactions: An equilibrium study

The formation of coherently strained three-dimensional (3D) islands on top of the wetting layer in the Stranski-Krastanov mode of growth is considered in a model in 1 + 1 dimensions accounting for the anharmonicity and nonconvexity of the real interatomic forces. It is shown that coherent 3D islands can be expected to form in compressed rather than expanded overlayers beyond a critical lattice misfit. In expanded overlayers the classical Stranski-Krastanov growth is expected to occur because the misfit dislocations can become energetically favored at smaller island sizes. The thermodynamic reason for coherent 3D islanding is incomplete wetting owing to the weaker adhesion of the edge atoms. Monolayer height islands with a critical size appear as necessary precursors of the 3D islands. This explains the experimentally observed narrow size distribution of the 3D islands. The 2D-3D transformation takes place by consecutive rearrangements of mono- to bilayer, bi- to trilayer islands, etc., after the corresponding critical sizes have been exceeded. The rearrangements are initiated by nucleation events, each one needing to overcome a lower energetic barrier than the one before. The model is in good qualitative agreement with available experimental observations.

Coherent Stranski-Krastanov growth in 1+1 dimensions with anharmonic interactions: An equilibrium study

The formation of coherently strained three-dimensional (3D) islands on top of the wetting layer in the Stranski-Krastanov mode of growth is considered in a model in 1 + 1 dimensions accounting for the anharmonicity and nonconvexity of the real interatomic forces. It is shown that coherent 3D islands can be expected to form in compressed rather than expanded overlayers beyond a critical lattice misfit. In expanded overlayers the classical Stranski-Krastanov growth is expected to occur because the misfit dislocations can become energetically favored at smaller island sizes. The thermodynamic reason for coherent 3D islanding is incomplete wetting owing to the weaker adhesion of the edge atoms. Monolayer height islands with a critical size appear as necessary precursors of the 3D islands. This explains the experimentally observed narrow size distribution of the 3D islands. The 2D-3D transformation takes place by consecutive rearrangements of mono- to bilayer, bi- to trilayer islands, etc., after the corresponding critical sizes have been exceeded. The rearrangements are initiated by nucleation events, each one needing to overcome a lower energetic barrier than the one before. The model is in good qualitative agreement with available experimental observations.

Studies of solute self-association by sedimentation equilibrium: allowance for effects of thermodynamic non-ideality beyond the consequences of nearest-neighbor interactions

A sedimentation equilibrium study of a-chymotrypsin self-association in acetate-chloride buffer, pH 4.1 I 0.05, has been used to illustrate determination of a dimerization constant under conditions where thermodynamic non-ideality is manifested beyond the consequences of nearest-neighbor interactions. Because the expressions for the experimentally determinable interaction parameters comprise a mixture of equilibrium constant and excluded volume terms, the assignment of reasonable magnitudes to the relevant virial coefficients describing non-associative cluster formation is essential for the evaluation of a reliable estimate of the dimerization constant. Determination of these excluded volume parameters by numerical integration over the potential-of-mean-force is shown to be preferable to their calculation by approximate analytical solutions of the integral for this relatively small enzyme monomer with high net charge (+ 10) under conditions of low ionic strength (0.05 M). (C) 2001 Elsevier Science B.V. All rights reserved.

Equilibrium studies on mixed ligand complex formation of Co(II), Ni(II), Cu(II) and Zn(II) with N-(2-hydroxybenzyl)-L-histidine (H(2)hb-L-his) and typical N,N donor ligands: Crystal structure of [Ni(hb-L-his)(bipyridine)]center dot H2O complex

Equilibrium study on complex formation of Co(II), Ni(II), Cu(II) and Zn(II), hereafter M(II), with the quadridentate (O-, N, O-, N) donor ligand, N-(2-hydroxybenzyl)-L-histidine (H(2)hb-L-his, hereafter H2L), in the absence and in the presence of typical (N, N) donor bidentate ligands, 1,10 phenanthroline(phen), 2, 2'-bipyridine(bipy), ethylenediamine(en), hereafter B, in aqueous solution at 25 +/- 1 degrees C was done at a fixed ionic strength, I = 0.1 mol dm(-3) (NaNO3) by combined pH-metric, UV-Vis and EPR measurements provide evidence for the formation of mononuclear and dinuclear binary and mixed ligand complexes of the types: M(L), M(L)(2)(2-), M-2(L)(2+), M-2(H-1L)(+), M(L)(B), (B)M(H-1L)M(B)(+). The imidazole moiety of the ligand is found to act as a bridging bidentate ligand in the dinuclear M-2(L)(2+), M-2(H-1L)(+) and (B)M(H-1L)M(B)(+) complexes, using its N-3 atom and N1-H deprotonated moiety. Stability constants of the complexes provide evidence of discrimination of Cu(II) from the other M(II) ions by this ligand. Solid complexes: [Ni(L)(H2O)(2)] (1), [Cu(L)(H2O)] (2), and [Ni(L)(bipy)] (.) H2O (3) have been isolated and characterized by various physicochemical studies. Single crystal X-ray diffraction of the ternary complex, 3, shows an octahedral [(O-,N,N,O-)(N,N)] geometry with extensive pi-pi stacking of the aromatic rings and H-bonding with imidazole (N1-H), secondary amino N-atom, the lattice H2O molecule, and the carboxylate and phenolate O-atoms. (c) 2006 Elsevier B.V. All rights reserved.

Biotransformation/separation routes to obtain pure enantiomers

The objective of the work presented in this thesis was the development of an innovative approach for the separation of enantiomers of secondary alcohols, combining the use of an ionic liquid (IL) - both as solvent for conducting enzymatic kinetic resolution and as acylating agent - with the use of carbon dioxide (CO2) as solvent for extraction. Menthol was selected for testing this reaction/separation approach due to the increasing demand for this substance, which is widely used in the pharmaceutical, cosmetics and food industries. With a view to using an ionic ester as acylating agent, whose conversion led to the release of ethanol, and due to the need to remove this alcohol so as to drive reaction equilibrium forward, a phase equilibrium study was conducted for the ehtanol/(±)-menthol/CO2 system, at pressures between 8 and 10 MPa and temperatures between 40 and 50 oC. It was found that CO2 is more selective towards ethanol, especially at the lowest pressure and highest temperature tested, leading to separation factors in the range 1.6-7.6. The pressure-temperature-composition data obtained were correlated with the Peng-Robinson equation of state and the Mathias-Klotz-Prausnitz mixing rule. The model fit the experimental results well, with an average absolute deviation (AAD) of 3.7 %. The resolution of racemic menthol was studied using two lipases, namely lipase from Candida rugosa (CRL) and immobilized lipase B from Candida antarctica (CALB), and two ionic acylating esters. No reaction was detected in either case. (R,S)-1-phenylethanol was used next, and it was found that with CRL low, nonselective, conversion of the alcohol took place, whereas CALB led to an enantiomeric excess (ee) of the substrate of 95%, at 30% conversion. Other acylating agents were tested for the resolution of (±)-menthol, namely vinyl esters and acid anhydrides, using several lipases and varying other parameters that affect conversion and enantioselectivity, such as substrate concentration, solvent and temperature. One such acylating agent was propionic anhydride. It was thus performed a phase equilibrium study on the propionic anhydride/CO2 system, at temperatures between 35 and 50 oC. This study revealed that, at 35 oC and pressures from 7 MPa, the system is monophasic for all compositions. The enzymatic catalysis studies carried out with propionic anhydride revealed that the extent of noncatalyzed reaction was high, with a negative effect on enantioselectivity. These studies showed also that it was possible to reduce considerably the impact of the noncatalyzed reaction relative to the reaction catalyzed by CRL by lowering temperature to 4 oC. Vinyl decanoate was shown to lead to the best results at conditions amenable to a process combining the use of supercritical CO2 as agent for post-reaction separation. The use of vinyl decanoate in a number of IL solvents, namely [bmim][PF6], [bmim][BF4], [hmim][PF6], [omim][PF6], and [bmim][Tf2N], led to an enantiomeric excess of product (eep) values of over 96%, at about 50% conversion, using CRL. In n-hexane and supercritical CO2, reaction progressed more slowly.(...)

Estudo do comportamento ácido-base da 4,4'-ditiodipiridina

Despite the importance of the 4,4'-dithiodipyridine as an electrode modifier on the protein electrochemical studies and as a remarkable bridged-ligand on conducting electronic density in binuclear mixed valence complexes, there is no data available in the literature concerning acid-base behavior of this compound. Aiming to afford such information we undertook the ionization equilibrium study of this ligand. Although two acid species, DTDPH+ and DTDPH2+ have been detected in solution, only the diacid-form was possible to be isolated as a perclorate salt DTDPH2(ClO4)2. The ionization constants for the two step equilibrium processes (pKa1=2.70 and pKa2=4.80) were determined by using the spectrophotometric technique and aqueous solutions of CF3COONa, mu=0,1 mol.L-1 .

Fe (ii) adsorption on Ucides Cordatus crab shells

In this study Ucides cordatus crab shells were utilized as Fe (II) sorbent as material of low cost and simple preparation. Values of pH of standard solution, biosorbent mass, particles size, contact time (t c) and initial concentration of the standard solution were optimized. The best conditions were pH = 2.00, t c = 840 min and Mc = 0.25 g. The kinetic pseudo first-order model displayed the best description of the adsorption process and the equilibrium study showed that the Langmuir model better describes the adsorption of the Fe (II). There is great affinity between the Fe (II) and the biosorbent.

Complexes cationiques POCOP de nickel : synthèse, caractérisation, réactivité et étude catalytique

Ce mémoire traite de la chimie des complexes pinceurs de nickel (II) cationiques ayant un ligand de type POCOP. Elle se divise en deux parties. La première traite de la synthèse, de la caractérisation et de la réactivité des complexes cationiques pinceurs de Ni(II) de type POCOP (POCOP = 1,3-bis(phosphinitobenzene), où C fait partie d’un cycle benzénique et est lié au métal, et P est un ligand phosphoré aussi lié au métal). Ces complexes ont un ligand acétonitrile coordonné au centre métallique et sont du type [(R-POCOPR’)Ni(NCMe)][OSO2CF3], où R est un substituant du cycle benzénique et R’ est un substituant sur le ligand phosphoré (R’ = iPr: R = H (1), p-Me(2), p-OMe(3), p-CO2Me(4), p-Br(5), m,m-tBu2(6), m-OMe(7), m-CO2Me(8); R’ = t-Bu : R = H (9), p-CO2Me(10)). Les complexes cationiques sont préparés en faisant réagir le dérivé Ni(II) neutre correspondant R-(POCOPR’)Ni-Br avec Ag(OSO2CF3¬) dans l’acétonitrile à température ambiante. L’impact des groupements R et R’ du ligand POCOP sur la structure et sur les propriétées électroniques du complexe a été étudié par spectroscopies RMN, UV-VIS et IR, analyse électrochimique, et diffraction des rayons X. Les valeurs de fréquence du lien C≡N (ν(C≡N)) augmentent avec le caractère électroattracteur du complexe, dans l’ordre 7 < 3 ~ 2 ~ 6 < 1 < 5 ~ 8 < 4 et 9 < 10. Ces résultats sont en accord avec le fait qu’une augmentation du caractère électrophile du centre métallique devrait résulter en une augmentation de la donation σ MeCN→Ni. De plus, les complexes cationiques montrent tous un potentiel d’oxydation Ni(II)/Ni(III) plus élevé que leurs analogues neutres Ni-Br. Ensuite, une étude d’équilibre entre un complexe neutre (R-POCOPR’)NiBr et un complexe cationique [(R-POCOPR’)Ni(NCMe)][OSO2CF3] démontre l’échange facile des ligands MeCN et Br. La deuxième partie de ce mémoire consiste en deux chapitres. Le premier (Chapitre 3) est une étude structurelle permettant une meilleure compréhension du mécanisme d’hydroamination des oléfines activées promue par les complexes présentés au chapitre 1, suivi de tentatives de synthèse de nouveaux composés POCOP cationiques comportant un ligand amine et nitrile, et de déplacement du groupement amine par un groupement nitrile. Le deuxième chapitre (4) décrit la réactivité et la cinétique de la réaction d’hydroamination et d’hydroalkoxylation d’oléfines activées, qui permet ainsi de mieux comprendre l’impact des différentes variables du système (groupements R et R’, température, substrats, solvent, etc.) sur la réactivité catalytique.

Complexes cationiques POCOP de nickel : synthèse, caractérisation, réactivité et étude catalytique

Ce mémoire traite de la chimie des complexes pinceurs de nickel (II) cationiques ayant un ligand de type POCOP. Elle se divise en deux parties. La première traite de la synthèse, de la caractérisation et de la réactivité des complexes cationiques pinceurs de Ni(II) de type POCOP (POCOP = 1,3-bis(phosphinitobenzene), où C fait partie d’un cycle benzénique et est lié au métal, et P est un ligand phosphoré aussi lié au métal). Ces complexes ont un ligand acétonitrile coordonné au centre métallique et sont du type [(R-POCOPR’)Ni(NCMe)][OSO2CF3], où R est un substituant du cycle benzénique et R’ est un substituant sur le ligand phosphoré (R’ = iPr: R = H (1), p-Me(2), p-OMe(3), p-CO2Me(4), p-Br(5), m,m-tBu2(6), m-OMe(7), m-CO2Me(8); R’ = t-Bu : R = H (9), p-CO2Me(10)). Les complexes cationiques sont préparés en faisant réagir le dérivé Ni(II) neutre correspondant R-(POCOPR’)Ni-Br avec Ag(OSO2CF3¬) dans l’acétonitrile à température ambiante. L’impact des groupements R et R’ du ligand POCOP sur la structure et sur les propriétées électroniques du complexe a été étudié par spectroscopies RMN, UV-VIS et IR, analyse électrochimique, et diffraction des rayons X. Les valeurs de fréquence du lien C≡N (ν(C≡N)) augmentent avec le caractère électroattracteur du complexe, dans l’ordre 7 < 3 ~ 2 ~ 6 < 1 < 5 ~ 8 < 4 et 9 < 10. Ces résultats sont en accord avec le fait qu’une augmentation du caractère électrophile du centre métallique devrait résulter en une augmentation de la donation σ MeCN→Ni. De plus, les complexes cationiques montrent tous un potentiel d’oxydation Ni(II)/Ni(III) plus élevé que leurs analogues neutres Ni-Br. Ensuite, une étude d’équilibre entre un complexe neutre (R-POCOPR’)NiBr et un complexe cationique [(R-POCOPR’)Ni(NCMe)][OSO2CF3] démontre l’échange facile des ligands MeCN et Br. La deuxième partie de ce mémoire consiste en deux chapitres. Le premier (Chapitre 3) est une étude structurelle permettant une meilleure compréhension du mécanisme d’hydroamination des oléfines activées promue par les complexes présentés au chapitre 1, suivi de tentatives de synthèse de nouveaux composés POCOP cationiques comportant un ligand amine et nitrile, et de déplacement du groupement amine par un groupement nitrile. Le deuxième chapitre (4) décrit la réactivité et la cinétique de la réaction d’hydroamination et d’hydroalkoxylation d’oléfines activées, qui permet ainsi de mieux comprendre l’impact des différentes variables du système (groupements R et R’, température, substrats, solvent, etc.) sur la réactivité catalytique.

Experimental study of phase equilibria in the "FeO"-ZnO-(CaO+SiO2) system with CaO/SiO2 weight ratios of 0.33, 0.93, and 1.2 in equilibrium with metallic iron

The pseudoternary sections FeO-ZnO-(CaO + SiO2) with CaO/SiO2 weight ratios of 0.33, 0.93, and 1.2 in equilibrium with metallic iron have been experimentally investigated in the temperature range from 1000 degreesC to 1300 degreesC (1273 to 1573 K). The liquidus surfaces in these pseudoternary sections have been experimentally determined in the composition range from 0 to 33 wt pct ZnO and 30 to 70 wt pct (CaO + SiO2). The sections contain primary-phase fields of wustite (FexZn1-xO1+y), zincite (ZnzFe1-zO), fayalite (Fu(w)Zn(2-w)SiO(4)), melilite (Ca2ZnuFe1-uSi2O7), willemite (ZnvFe2-vSiO4), dicalcium silicate (Ca2SiO4), pseudowollastonite and wollastonite (CaSiO3), and tridymite (SiO2). The phase equilibria involving the liquid phase and the solid solutions-have also been measured.

Non-equilibrium energy and momentum accommodation coefficients of Ar atoms scattered from Ni(001) in the thermal regime: A molecular dynamics study

Molecular dynamics simulations are used to study energy and momentum transfer of low-energy Ar atoms scattered from the Ni(001) surface. The investigation concentrates on the dependence of these processes on incident energy, angles of incidence and surface temperature. Energy transfer exhibits a strong dependence on the surface temperature, at incident energies below 500 meV, and incident angles close to specular incidence. Above 500 meV, the surface temperature dependence vanishes, and a limiting value in the amount of energy transferred to the surface is attained. Momentum exchange is investigated in terms of tangential and normal components. Both components exhibit a weak surface temperature dependence, but they have opposite behaviours at all incidence angles. In each component, momentum can be lost or gained following the interaction with the surface. (C) 1997 Elsevier Science B.V.

H-1 NMR study of the states of water in equilibrium Poly(HEMA-co-THFMA) hydrogels

The spin-spin relaxation times, T-2, of hydrated samples of poly(hydroxymethyl methacrylate), PHEMA, poly(tetrahydrofurfuryl methacrylate),PTHFMA, and the,corresponding HEMA-THFMA copolymers have been examined to probe the states of,the imbibed water in these polymers. The decay in the transverse magnetization of water. in fully hydrated samples of PHEMA, PTHFMA, and copolymers of HEMA and THFMA was described by a multiexponential function. The short component of T-2 was interpreted as water molecules that were strongly interacting with the polymer chains. The intermediate component of T-2 was assigned to water residing in the porous structure of the samples. The long component of T-2 was believed to arise from water residing in the remnants of cracks formed in the polymer network during water sorption.

The effect of candidate quality on electoral equilibrium: an experimental study

When two candidates of different quality compete in a one dimensional policy space, the equilibrium outcomes are asymmetric and do not correspond to the median. There are three main effects. First, the better candidate adopts more centrist policies than the worse candidate. Second, the equilibrium is statistical, in the sense that it predicts a probability distribution of outcomes rather than a single degenerate outcome. Third, the equilibrium varies systematically with the level of uncertainty about the location of the median voter. We test these three predictions using laboratory experiments, and find strong support for all three. We also observe some biases and show that they canbe explained by quantal response equilibrium.

Non-hyperbolic boundary equilibrium bifurcations in planar Filippov systems: a case study approach

Boundary equilibrium bifurcations in piecewise smooth discontinuous systems are characterized by the collision of an equilibrium point with the discontinuity surface. Generically, these bifurcations are of codimension one, but there are scenarios where the phenomenon can be of higher codimension. Here, the possible collision of a non-hyperbolic equilibrium with the boundary in a two-parameter framework and the nonlinear phenomena associated with such collision are considered. By dealing with planar discontinuous (Filippov) systems, some of such phenomena are pointed out through specific representative cases. A methodology for obtaining the corresponding bi-parametric bifurcation sets is developed.