Dynamical self-stabilization of the Mott insulator: Time evolution of the density and entanglement entropy of out-of-equilibrium cold fermion gases

The time evolution of the out-of-equilibrium Mott insulator is investigated numerically through calculations of space-time-resolved density and entropy profiles resulting from the release of a gas of ultracold fermionic atoms from an optical trap. For adiabatic, moderate and sudden switching-off of the trapping potential, the out-of-equilibrium dynamics of the Mott insulator is found to differ profoundly from that of the band insulator and the metallic phase, displaying a self-induced stability that is robust within a wide range of densities, system sizes and interaction strengths. The connection between the entanglement entropy and changes of phase, known for equilibrium situations, is found to extend to the out-of-equilibrium regime. Finally, the relation between the system`s long time behavior and the thermalization limit is analyzed. Copyright (C) EPLA, 2011

Instability of equilibrium points of some Lagrangian systems

In this work we show that, if L is a natural Lagrangian system such that the k-jet of the potential energy ensures it does not have a minimum at the equilibrium and such that its Hessian has rank at least n - 2, then there is an asymptotic trajectory to the associated equilibrium point and so the equilibrium is unstable. This applies, in particular, to analytic potentials with a saddle point and a Hessian with at most 2 null eigenvalues. The result is proven for Lagrangians in a specific form, and we show that the class of Lagrangians we are interested can be taken into this specific form by a subtle change of spatial coordinates. We also consider the extension of this results to systems subjected to gyroscopic forces. (C) 2008 Elsevier Inc. All rights reserved.

Structure and Calcium-Binding Activity of LipL32, the Major Surface Antigen of Pathogenic Leptospira sp.

Leptospixosis, a spirochaetal zoonotic disease caused by Leptospira, has been recognized as an important emerging infectious disease. LipL32 is the major exposed outer membrane protein found exclusively in pathogenic leptospires, where it accounts for up to 75% of the total outer membrane proteins. It is highly immunogenic, and recent studies have implicated LipL32 as an extracellular matrix binding protein, interacting with collagens, fibronectin, and laminin. In order to better understand the biological role and the structural requirements for the function of this important lipoprotein, we have determined the 2.25-angstrom-resolution structure of recombinant LipL32 protein corresponding to residues 21-272 of the wild-type protein (LipL32(21-272)). The LipL32(21-272) monomer is made of a jelly-roll fold core from which several peripheral secondary structures protrude. LipL32(21-272) is structurally similar to several other jelly-roll proteins, some of which bind calcium ions and extracellular matrix proteins. Indeed, spectroscopic data (circular dichroism, intrinsic tryptophan fluorescence, and extrinsic 1-amino-2-naphthol-4-sulfonic acid fluorescence) confirmed the calcium-binding properties of LipL32(21-272). Ca(2+) binding resulted in a significant increase in the thermal stability of the protein, and binding was specific for Ca(2+) as no structural or stability perturbations were observed for Mg(2+), Zn(2+), or Cu(2+). Careful examination of the crystal lographic structure suggests the locations of putative regions that could mediate Ca(2+) binding as well as binding to other interacting host proteins, such as collagens, fibronectin, and lamixidn. (C) 2009 Elsevier Ltd. All rights reserved.

Structural parameters of polyacrylamide hydrogels obtained by the Equilibrium Swelling Theory

In this paper, the synthesis and structural characterization of a series of polyacrylamide hydrogels with different degrees of reticulation are reported. Although the Equilibrium Swelling Theory was recognized as a simple and reliable tool for the determination of structural hydrogels network parameters like equilibrium degree of swelling, cross-link ratio and mesh size, this is the first application of this methodology for polyacrylamide hydrogels. By changing the total monomer content in the synthesis solution (%T) from 5 to 30%, at a fixed value of cross-linker content in the total monomer amount (%C) of 5%, the final parameter obtained, the mesh size, can be tuned from 2 to 0.3 nm. It was also possible to change the mesh size (0.19-0.35) by varying %C from 5 to 12% (at %T = 20%). Scanning Electron Microscopy images for the most different formulations are shown and corroborate data obtained from the theory. (c) 2008 Elsevier Ltd. All rights reserved.

Solvatochromism in Binary Mixtures: First Report on a Solvation Free Energy Relationship between Solvent Exchange Equilibrium Constants and the Properties of the Medium

We have employed UV-vis spectroscopy in order to investigate details of the solvation of six solvatochromic indicators, hereafter designated as ""probes"", namely, 2,6-diphenyl-4-(2,4,6-triphenylpyridinium-1-yl) phenolate (RB); 4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePM; 1-methylquinolinium-8-olate, QB; 2-bromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr, 2,6-dichloro-4-(2,4,6-triphenylpyridinium-1-yl) phenolate (WB); and 2,6-dibromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr,, respectively. These can be divided into three pairs, each includes two probes of similar pK(a) in water and different lipophilicity. Solvation has been studied in binary mixtures, BMs, of water, W, with 12 protic organic solvents, S, including mono- and bifunctional alcohols (2-alkoxyethanoles, unsaturated and chlorinated alcohols). Each medium was treated as a mixture of S, W, and a complex solvent, S-W, formed by hydrogen bonding. Values of lambda(max) (of the probe intramolecular charge transfer) were converted into empirical polarity scales, E(T)(probe) in kcal/mol, whose values were correlated with the effective mole fraction of water in the medium, chi w(effective). This correlation furnished three equilibrium constants for the exchange of solvents in the probe solvation shell; phi(W/S) (W substitutes S): phi(S-W/W) (S-W substitutes W), and phi(S-W/S) (S-W substitutes S), respectively. The values of these constants depend on the physicochemical properties of the probe and the medium. We tested, for the first time, the applicability of a new solvation free energy relationship: phi = constant + a alpha(BM) + b beta(BM) + s(pi*(BM) + d delta) + p log P(BM), where a, b, s, and p are regression coefficients alpha(BM), beta(BM), and pi*(BM) are solvatochromic parameters of the BM, delta is a correction term for pi*, and log P is an empirical scale of lipophilicity. Correlations were carried out with two-, three-, and four-medium descriptors. In all cases, three descriptors gave satisfactory correlations; use of four parameters gave only a marginal increase of the goodness of fit. For phi(W/S), the most important descriptor was found to be the lipophilicity of the medium; for phi(S-W/W) and phi(S-W/S), solvent basicity is either statistically relevant or is the most important descriptor. These responses are different from those of E(T)(probe) of many solvatochromic indicators in pure solvents, where the importance of solvent basicity is usually marginal, and can be neglected.

The effect of calcium salts on the viscosity and adsorption behavior of xanthan

The effect of CaCl(2), Ca(NO(3))(2), CaSO(4), CaCO(3) and Ca(3)(PO(4))(2) on the flow behavior of xanthan gum solutions was investigated. Regardless the concentration and type of calcium salt used, xanthan solutions presented pseudoplastic behavior. The soluble salts (CaCl(2) and Ca(NO(3))(2)) induced the disordered state in the xanthan chains at concentration of 1.0 g/L or 10 g/L, decreasing the flow consistency index (K) values. At 100 g/L soluble salts K values were similar to those found for pure xanthan solutions, whereas at the same concentration of insoluble particles the K values increased 20%. The adsorption of xanthan gum onto Si/SiO(2) surfaces in the presence of calcium salts was investigated by ellipsometry and atomic force microscopy (AFM). The adsorbed layer of xanthan onto Si/SiO(2) consisted of two regions: (i) a thin acid resistant sublayer, where xanthan chains were like highly entangled fibers and (ii) a thick upperlayer, whose morphology was calcium salt dependent. (C) 2010 Elsevier Ltd. All rights reserved.

Effect of Calcium Pre-rinse and Fluoride Dentifrice on Enamel and on Dental Plaque Formed In Situ

Purpose: The aim of this in situ double-blind randomised crossover study was to investigate the effect of calcium (Ca) pre-rinse on the composition of plaque and on enamel prior to the use of fluoride (F) dentifrice. Materials and Methods: During four phases (14 days each) of this study, 10 volunteers had agreed to wear dental appliances containing two healthy bovine enamel blocks. A fresh solution containing 20% weight/volume (w/v) sucrose was dripped on the enamel blocks ex vivo for 5 min three times a day. Subsequently, the appliances were replaced in the mouth, and the volunteers rinsed their mouth with 10 mL of a Ca (150 mmol/L) or a placebo rinse (1 min). In sequence, a slurry (1:3 w/v) of F (1030 ppm) or placebo dentifrice was dripped onto the blocks ex vivo for 1 min. During this time, the volunteers brushed their teeth with the respective dentifrice. The appliances were replaced in the mouth, and the volunteers rinsed their mouth with water. The plaque formed on the blocks was analysed for F and Ca. The enamel demineralisation as well as the incorporation of F on enamel was evaluated by cross-sectional microhardness and alkali-soluble F analysis, respectively. Data were tested using analysis of variance (P < 0.05). Results: The Ca pre-rinse prior to the use of the F dentifrice led to a three- and sixfold increase in the plaque F and Ca concentrations, respectively. It also did not have any additive effect on the F content on the enamel and the demineralisation of the enamel, in comparison with the use of F dentifrice alone. Conclusions: A Ca lactate rinse used prior to the F dentifrice was able to change the mineral content in the plaque, but it was unable to prevent enamel demineralisation.

Local concavifiability of preferences and determinacy of equilibrium

In this paper we consider strictly convex monotone continuous complete preorderings on R+n that are locally representable by a concave utility function. By Alexandroff 's (1939) theorem, this function is twice dífferentiable almost everywhere. We show that if the bordered hessian determinant of a concave utility representation vanishes on a null set. Then demand is countably rectifiable, that is, except for a null set of bundles, it is a countable union of c1 manifolds. This property of consumer demand is enough to guarantee that the equilibrium prices of apure exchange economy will be locally unique, for almost every endowment. We give an example of an economy satisfying these conditions but not the Katzner (1968) - Debreu (1970, 1972) smoothness conditions.

Competitive equilibrium hyperinflation under rational expectations

This paper shows that a competitive equilibrium model, where a representative agent maximizes welfare, expectations are rational and markets are in equilibrium can account for several hyperinflation stylized facts. The theory is built by combining two hypotheses, namely, a fiscal crisis that requires printing money to finance an increasing public deficit and a predicted change in an unsustainable fiscal regime.

On equilibrium prices in continuous time

We combine general equilibrium theory and théorie générale of stochastic processes to derive structural results about equilibrium state prices.

Bubbles, collateral and monetary equilibrium

Consider an economy where infinite-lived agents trade assets collateralized by durable goods. We obtain results that rule out bubbles when the additional endowments of durable goods are uniformly bounded away from zero, regardless of whether the asset’s net supply is positive or zero. However, bubbles may occur, even for state-price processes that generate finite present value of aggregate wealth. First, under complete markets, if the net supply is being endogenously reduced to zero as a result of collateral repossession. Secondly, under incomplete markets, for a persistent positive net supply, under the general conditions guaranteeing existence of equilibrium. Examples of monetary equilibria are provided.

A general-equilibrium closed-form solution to the welfare costs of inflation (Forthcoming, Revista Brasileira de Economia)

This work presents closed-form solutions to Lucasís (2000) generalequilibrium expression for the welfare costs of ináation, as well as to the di§erence between the general-equlibrium measure and Baileyís (1956) partial-equilibrium measure. In Lucasís original work only numerical solutions are provided.

Nash equilibrium under knightian uncertainty: breaking down backward induction (extensively revised version)

We define Nash equilibrium for two-person normal form games in the presence of uncertainty, in the sense of Knight(1921). We use the fonna1iution of uncertainty due to Schmeidler and Gilboa. We show tbat there exist Nash equilibria for any degree of uncertainty, as measured by the uncertainty aversion (Dow anel Wer1ang(l992a». We show by example tbat prudent behaviour (maxmin) can be obtained as an outcome even when it is not rationaliuble in the usual sense. Next, we break down backward industion in the twice repeated prisoner's dilemma. We link these results with those on cooperation in the finitely repeated prisoner's dilemma obtained by Kreps-Milgrom-Roberts-Wdson(1982), and withthe 1iterature on epistemological conditions underlying Nash equilibrium. The knowledge notion implicit in this mode1 of equilibrium does not display logical omniscience.

Nash equilibrium under knightian uncertainty: breaking-down backward induction

We present two alternative definitions of Nash equilibrium for two person games in the presence af uncertainty, in the sense of Knight. We use the formalization of uncertainty due to Schmeidler and Gilboa. We show that, with one of the definitions, prudent behaviour (maxmin) can be obtained as an outcome even when it is not rationalizable in the usual sense. Most striking is that with the Same definition we break down backward induction in the twice repeated prisoner's dilemma. We also link these results with the Kreps-Milgrom-Roberts-Wilson explanation of cooperation in the finitely repeated prisoner's dilemma.