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We investigate the structure of rank-to-rank elementary embeddings at successor rank, working in ZF set theory without the Axiom of Choice. Recall that the set-theoretic universe is naturally stratified by the cumulative hierarchy, whose levels V α are defined via iterated application of the power set operation, starting from V 0 =∅, setting V α+1 =P(V α), and taking unions at limit stages. Assuming that j:V α+1 →V α+1 is a (non-trivial) elementary embedding, we show that V α is fundamentally different from V α+1: we show that j is definable from parameters over V α+1 iff α+1 is an odd ordinal. The definability is uniform in odd α+1 and j. We also give a characterization of elementary j:Vα+2 → Vα+2 in terms of ultrapower maps via certain ultrafilters. For limit ordinals λ, we prove that if j:Vλ→Vλ is Σ1-elementary, then j is not definable over Vλ from parameters, and if β < λ and j:Vβ → Vλ is fully elementary and ∈-cofinal, then j is likewise not definable. If there is a Reinhardt cardinal, then for all sufficiently large ordinals α, there is indeed an elementary j: Vα → Vα, and therefore the cumulative hierarchy is eventually periodic (with period 2). [ABSTRACT FROM AUTHOR]

In this two-paper series, we prove the invariance of the Gibbs measure for a threedimensional wave equation with a Hartree nonlinearity. The novelty lies in the singularity of the Gibbs measure with respect to the Gaussian free field. In this paper, we focus on the dynamical aspects of our main result. The local theory is based on a paracontrolled approach, which combines ingredients from dispersive equations, harmonic analysis, and random matrix theory. The main contribution, however, lies in the global theory. We develop a new globalization argument, which addresses the singularity of the Gibbs measure and its consequences. [ABSTRACT FROM AUTHOR]

A generalized scaled-particle theory for the uniform hard-disk mixture is derived in the spirit of the White Bear II free energy of the hard-sphere fluid [H. Hansen-Goos and R. Roth, J. Phys. C: Condens. Matter 18, 8413 (2006)]. The theory provides a very simple result for the interfacial free energy γ of the hard-disk fluid at a planar hard wall (which in d = 2 is a line) in terms of the equation of state. To complement and assess the theory, we perform Monte Carlo simulations from which we obtain γ using Gibbs-Cahn integration. While we find excellent overall agreement between theory and simulation, it also becomes apparent that the set of scaled-particle variables available in d = 2 is too limited, prohibiting a quasi-exact result for γ. Furthermore, this is reflected in the mixture equation of state resulting from our theory, which, similar to a previous attempt by Santos et al. [Mol. Phys. 96, 1 (1999)], displays a small but systematic deviation from simulations. [ABSTRACT FROM AUTHOR]

A fast and accurate sampling method is in high demand, in order to bridge the large gaps between molecular dynamic simulations and experimental observations. Recently, an integrated tempering enhanced sampling (ITS) method has been proposed and successfully applied to various biophysical examples, significantly accelerating conformational sampling. The mathematical validation for its effectiveness has not been elucidated yet. Here we show that the integrated tempering enhanced sampling method can be viewed as a reformulation of the infinite switching limit of the simulated tempering method over a mixed potential. Moreover, we demonstrate that the efficiency of simulated tempering molecular dynamics improves as the frequency of switching between the temperatures is increased, based on the large deviation principle of empirical distributions. Our theory provides the theoretical justification of the advantage of ITS. Finally, we illustrate the utility of the infinite switching simulated tempering method through several numerical examples. [ABSTRACT FROM AUTHOR]

The 76th issue of the journal "Foundations of Chemistry" features contributions from various countries including Australia, Belgium, Denmark, India, Italy, Spain, UK, and USA. The articles cover a range of topics such as alchemy, the periodic table, chemical affinity, collaboration in chemistry, Slater's work, spectroscopy teaching, the relationship between mathematics and chemistry, bond order, and Gibbs' equation for the change in Free Energy. The issue also includes information about the upcoming 27th meeting of the International Society for the Philosophy of Chemistry in Varazdin, Croatia. The publisher remains neutral in terms of jurisdictional claims and institutional affiliations. [Extracted from the article]

A relativistic Hamiltonian–Lagrangian formalism for a composite system submitted to conservative and non-conservative forces is developed. A block descending an incline with a frictional force, mechanical energy dissipation process, is described, obtaining an Euler–Lagrange equation including a Rayleigh's dissipation function. A cannonball rising on an incline, process evolving with mechanical energy production, is described by an Euler–Lagrange equation including a Gibbs' production function, with a chemical origin force. A matrix four-vector mechanical equation, considering processes' mechanical and phenomenological aspects, is postulated. This relativistic Hamiltonian–Lagrangian four-vector formalism complements the Einstein–Minkowski–Lorentz four-vector fundamental equation formalism. By considering a process' mechanical and thermodynamic description, temporal evolution equations, relating process' Hamiltonian (mechanical energy) evolution and the involved thermodynamic potentials (entropy of the universe, Helmholtz free energy, Gibbs free enthalpy) variations, are obtained. [ABSTRACT FROM AUTHOR]

Heterogeneous nucleation in solutions on planar solid surfaces is modeled taking into account changes of the state parameters of the critical clusters in dependence on supersaturation. The account of the variation of the state parameters of the cluster phase on nucleation is performed in the framework of the generalized Gibbs' approach. A regular solution is chosen as a model for the analysis of the basic qualitative characteristics of the process. It is shown that, employing the generalized Gibbs approach, contact angle and catalytic activity factor for heterogeneous nucleation become dependent on the degree of metastability (supersaturation) of the solution. For the case of formation of a cluster in supersaturated solutions on a surface of low wettability (the macroscopic equilibrium contact angles being larger than 90?), the solid surface has only a minor influence on nucleation. In the alternative case of high wettability (for macroscopic equilibrium contact angles being less than 90?), nucleation is significantly enhanced by the solid surface. Effectively, the existence of the solid surface results in a significant shift of the spinodal to lower supersaturations as compared with homogeneous nucleation. Qualitatively, the same behavior is observed now near the new (solid surface induced) limits of instability of the solution as compared with the behavior near to the spinodal curve in the case of homogeneous nucleation. [ABSTRACT FROM AUTHOR]

Variational models are considered as successful methods for image processing and analysis, especially in the case of the super-resolution algorithms. In this paper, we present some comparisons between the Total Variation (TV) and other high-order variational models and provide detailed discretization of these models and numerical implementation for solving these models. We demonstrate the advantages and disadvantages between these models in the context of super-resolution through many experiments. The methods and techniques can also be used for other applications, such as image segmentation, dehazing and illumination reduction. [ABSTRACT FROM AUTHOR]

We study the thermodynamic and structural properties of a simple, one-patch fluid model using the reference hypernetted-chain (RHNC) integral equation and specialized Monte Carlo simulations. In this model, the interacting particles are hard spheres, each of which carries a single identical, arbitrarily oriented and attractive circular patch on its surface; two spheres attract via a simple square-well potential only if the two patches on the spheres face each other within a specific angular range dictated by the size of the patch. For a ratio of attractive to repulsive surface of 0.8, we construct the RHNC fluid-fluid separation curve and compare with that obtained by Gibbs ensemble and grand canonical Monte Carlo simulations. We find that RHNC provides a quick and highly reliable estimate for the position of the fluid-fluid critical line. In addition, it gives a detailed (though approximate) description of all structural properties and their dependence on patch size. [ABSTRACT FROM AUTHOR]

A derivation of chemical equilibrium equations for a spherical thin film of solution around a soluble solid nanoparticle is presented. The equations obtained generalize the Gibbs–Kelvin–Köhler and Ostwald–Freundlich equations for a soluble particle immersed in the bulk phase. The generalized equations describe the dependence of the chemical potentials of a condensate and dissolved nanoparticle matter in the thin solution film, the condensate saturated pressure, and the solubility of the nanoparticle matter on the film thickness, and the nanoparticle size with account of the disjoining pressure of the liquid film. [ABSTRACT FROM AUTHOR]

The Gibbs ensemble Monte Carlo method has been combined with the connectivity altering osmotic Gibbs ensemble to study water solubility and clustering in decane and polyethylene. We show that the presence of oppositely charged ion pairs that have fixed positions in the hydrocarbon matrices leads to an order of magnitude increase in the water solubility. This is important to a wide range of technical applications, since the uptake of the water leads to an increase in volume—or expansion—of the hydrocarbon phase which, in the case of polyethylene, may change the polymer properties and lead to water treeing. The increase in solubility is largest when the ions are sufficiently close so that rod-shaped clusters of water molecules form between the ions. [ABSTRACT FROM AUTHOR]

We present a rigorous description of chemical space within a molecular grand-canonical ensemble multi-component density functional theory framework. A total energy density functional for chemical compounds in contact with an electron and a proton bath is introduced using Lagrange multipliers which correspond to the energetic response to changes of the elementary particle densities. From a generalized Gibbs-Duhem equation analog, reactivity indices such as the nuclear hardness and a molecular Fukui function, which couples the grand-canonical electronic and nuclear degrees of freedom, are obtained. Maxwell relations between composition particles, ionic displacements, and the external potential are discussed. Numerical results for the molecular Fukui function are presented as well as finite temperature estimates for the oxidation of ammonia. [ABSTRACT FROM AUTHOR]

The magnetostrictive strain-applied field curve typical of giant magnetostrictive materials is nonlinear and it is affected notably by prestress and temperature. A constitutive model to describe these properties is suggested in this paper. The model considered here is built on the Gibbs free energy function G(σij,Mk,T). Thermodynamic relations are used to obtain the constitutive expressions. Results based on the model show that the nonlinear property of magnetostrictive strain, the magnetization, and Young’s modulus under different prestress and temperature are in excellent agreement with experimental data. Moreover, the proposed model is convenient to be used in engineering applications since the parameters referred to the model can all be easily determined by experiments. [ABSTRACT FROM AUTHOR]

We introduce a new class of systems based on the Nosé-Hoover equations. We show that we can add time-dependent terms without destroying the measure and energy conservation properties of the initial system. These “shakers” are typically pseudoperiodic in time, i.e., depend on a collection of harmonic oscillators. We show by numerical examples that it strengthens the sampling properties of the initial system with respect to the Gibbs measure and helps the computation of averages in the canonical ensemble. [ABSTRACT FROM AUTHOR]

The binary classical nucleation theory (BCNT) is based on the Gibbsian thermodynamics and applies the macroscopic concept of surface tension to nanosize clusters. This leads to severe inconsistencies and large discrepancies between theoretical predictions and experimental results regarding the nucleation rate. We present an alternative approach to the kinetics of binary nucleation which avoids the use of classical thermodynamics for clusters. The new approach is an extension to binary mixtures of the kinetic theory previously developed by Narsimhan and Ruckenstein and Ruckenstein and Nowakowski [J. Colloid Interface Sci. 128, 549 (1989); 137, 583 (1990)] for unary nucleation which is based on molecular interactions and in which the rate of emission of molecules from a cluster is determined via a mean first passage time analysis. This time is calculated by solving the single-molecule master equation for the probability distribution of a “surface” molecule moving in a potential field created by the cluster. The starting master equation is a Fokker-Planck equation for the probability distribution of a surface molecule with respect to its phase coordinates. Owing to the hierarchy of characteristic time scales in the evolution of the molecule, this equation can be reduced to the Smoluchowski equation for the distribution function involving only the spatial coordinates. The new theory is combined with density functional theory methods to determine the density profiles. This is essential for nucleation in binary systems particularly when one of the components is surface active. Knowing these profiles, one can determine the potential fields created by the cluster, its rate of emission of molecules, and the nucleation rate more accurately than by using the uniform density approximation. The new theory is illustrated by numerical calculations for a model binary mixture of Lennard-Jones monomers and rigidly bonded dimers of Lennard-Jones atoms. The amphiphilic character of the dimer component (i.e., its surface activity) is induced by the asymmetry in the interaction between a monomer and the two different sites of a dimer. The inconsistencies of the BCNT are avoided in the new theory. [ABSTRACT FROM AUTHOR]

We propose Lennard-Jones potential parameters for interatomic interactions of linear and branched alkanes based on matching the results of Gibbs ensemble simulations of vapor-liquid equilibria to experimental data. The alkane model is similar as in the OPLS-AA [W. L. Jorgensen, D. S. Maxwell, and J. Tirado-Rives, J. Am. Chem. Soc. 118, 11225 (1996)], but multiple atom types for carbon based on the number of covalently bonded hydrogen atoms are necessary to accurately reproduce liquid densities and enthalpies of vaporization with the errors of 2.1% and 3.3%, respectively, for hydrocarbons of various chain lengths and structures. We find that the attraction energies of the carbon atoms are almost proportional to the number of covalent hydrogen atoms with each increasing the carbon energy parameter by ≈0.033 kcal/mol. Though the present force field outperforms the OPLS-AA force field for alkanes we studied, systematic deviations for vapor pressures are still observed with errors of 15%–30%, and critical temperatures are slightly underestimated. We think that these shortcomings are probably due to the inadequacy of the two-parameter Lennard-Jones potential, and especially its behavior at short distances. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In the present paper, some further results of application of the generalized Gibbs’ approach [J. W. P. Schmelzer et al., J. Chem. Phys. 112, 3820 (2000); 114, 5180 (2001); 119, 6166 (2003)] to describing new-phase formation processes are outlined. The path of cluster evolution in size and composition space is determined taking into account both thermodynamic and kinetic factors. The basic features of these paths of evolution are discussed in detail for a simple model of a binary mixture. According to this analysis, size and composition of the clusters of the newly evolving phase change in an unexpected way which is qualitatively different as compared to the classical picture of nucleation-growth processes. As shown, nucleation (i.e., the first stage of cluster formation starting from metastable initial states) exhibits properties resembling spinodal decomposition (the size remains nearly constant while the composition changes) although the presence of an activation barrier distinguishes the nucleation process from true spinodal decomposition. In addition, it is shown that phase formation both in metastable and unstable initial states near the classical spinodal may proceed via a passage of a ridge of the thermodynamic potential with a finite work of the activation barrier even though (for unstable initial states) the value of the work of critical cluster formation (corresponding to the saddle point of the thermodynamic potential) is zero. This way, it turns out that nucleation concepts—in a modified form as compared with the classical picture—may govern also phase formation processes starting from unstable initial states. In contrast to the classical Gibbs’ approach, the generalized Gibbs’ method provides a description of phase changes both in binodal and spinodal regions of the phase diagram and confirms the point of view assuming a continuity of the basic features of the phase transformation kinetics in the vicinity of the classical spinodal curve. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The temperature dependence of the α-relaxation time out of equilibrium has been investigated by means of dielectric relaxation in a series of fragile glass formers including several polymers. The influence of physical aging on this behavior has also been studied. The experimental results have been quantitatively compared with the predictions of the Adam–Gibbs equation. It has been found that, whereas for small molecule glass formers the experimental values of the apparent activation energy agree quite well with the prediction of the Adam–Gibbs equation, for polymers the experimental activation energy values are systematically higher. Moreover, whereas for small molecule glass formers the experimental values of the apparent activation energy remains essentially unaffected by physical aging, for polymers a pronounced reduction of the experimental apparent activation energy is observed. These results are found to be consistent with the Adam–Gibbs equation if a significant temperature variation of the configurational entropy in the investigated temperature range would occur for nonannealed polymers, being the possible variation hardly noticeable for the small molecules. With this assumption, all the obtained results would support the validity of the Adam–Gibbs equation for describing the temperature dependence of the time scale of the α-relaxation also out of equilibrium, at least for fragile glass formers. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A thermodynamically consistent formalism is applied to calculate the reversible work needed to form a small layer of a new phase (embryo) around a charged insoluble conducting sphere within a uniform macroscopic mother phase. To treat the embryos of arbitrary size which are not the critical nuclei (i.e., which are not fragments that are in unstable equilibrium with the mother phase), a constraint in the form of an external field is introduced. When a critical nucleus is of primary interest, the specification of this constraint is not required. The results that are obtained for a critical cluster do not depend on which path approaches a critical state. However, the properties of noncritical clusters depend on the external constraining field and this effect is discussed in detail. The obtained new expression for the work of embryo formation differs from the one commonly used in the nucleation literature. The conditions of its extrema yield the correct conditions of equilibrium between the critical nucleus and the mother phase. Expressions are derived that are suitable for practical calculations of the size and composition of a critical nucleus. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A Gibbs ensemble algorithm implemented previously for mixtures of homopolymers and copolymers in a cubic lattice with coordination number z=26 is now used to characterize the complete phase separation diagram of the ternary mixtures formed by AA and BB homopolymers and their common symmetric diblock copolymer AB, all chains of the same length. We consider two alternative types of systems with repulsions between neighboring A and B units or with attractions between A and A or B and B neighboring units. A certain proportion of voids is included in both cases. The 3-phase region of the diagram is obtained by using a 3-box algorithm that has not been previously employed for polymer mixtures. The 3-phase region is composed of two homopolymer-rich asymmetric phases, each one mainly composed of a different homopolymer component together with a small proportion of copolymer. These two phases are in equilibrium with a third phase rich in copolymer. The 3-phase region connects smoothly with the 2-phase region covered by our 2-box simulations reported earlier for low copolymer composition. Similarly, it also connects with two asymmetric 2-phase regions characterized now through 2-box simulations performed with a low initial proportion of one of the homopolymer components. The data obtained for the systems with repulsions are in agreement with earlier single box Monte Carlo estimations for ternary mixtures with a symmetric homopolymer composition. They show a non-clearly structured copolymer-rich phase with a substantial amount of homopolymer, while the presence of copolymer in the AA or BB enriched phases is small. The systems with attractions, however, exhibit important differences with respect to this picture, due to a more specific role of the voids. Some differences with respect to the mean-field theory predictions are also discussed. [ABSTRACT FROM AUTHOR]

Discusses the theoretical foundation for the temperature-entropy diagram for irreversible absorption chillers that employ either a volatile or nonvolatile working pair. Applications of the Gibbs' equation for single stream; Application of the Gibbs' equation for multistream nonisothermal heat-and-mass transfer processes.

Studies the phase behavior of model colloidal systems composed of infinitely thin hard platelets, with polydispersity in the size of the particles. Use of the semi-grand Gibbs ensemble simulations to study the coexisting nematic and isotropic phases; Relationship between the size of a particle and its orientation in the nematic phase.

David E. Laughlin When magnetic phases are included on phase diagrams some unfamiliar features appear. Most magnetic transformations are not first-order phase transformations and therefore their depictions on phase diagrams do not have to follow the well-known construction requirements such as those based on the Gibbs Equilibrium Phase Rule. In particular, the transformation from a paramagnetic to ferromagnetic phase should be designated differently than those of the more widely known first-order transformations. The transformation curve (Curie curve) does not display a two-phase equilibrium: rather it shows the limit of stability of the disordered (paramagnetic) phase. In this paper, various examples of phase diagrams which include such transformations will be presented and discussed. The role of externally applied magnetic fields will be presented based on fundamental thermodynamic principles and the role that applied magnetic fields play in changing the degrees of freedom of systems (alloys) will be discussed. [ABSTRACT FROM AUTHOR]

Understanding and predicting extreme events and their anomalous statistics in complex nonlinear systems are a grand challenge in climate, material, and neuroscience as well as for engineering design. Recent laboratory experiments in weakly turbulent shallow water reveal a remarkable transition from Gaussian to anomalous behavior as surface waves cross an abrupt depth change (ADC). Downstream of the ADC, probability density functions of surface displacement exhibit strong positive skewness accompanied by an elevated level of extreme events. Here, we develop a statistical dynamical model to explain and quantitatively predict the above anomalous statistical behavior as experimental control parameters are varied. The first step is to use incoming and outgoing truncated Korteweg-de Vries (TKdV) equations matched in time at the ADC. The TKdV equation is a Hamiltonian system, which induces incoming and outgoing statistical Gibbs invariant measures. The statistical matching of the known nearly Gaussian incoming Gibbs state at the ADC completely determines the predicted anomalous outgoing Gibbs state, which can be calculated by a simple sampling algorithm verified by direct numerical simulations, and successfully captures key features of the experiment. There is even an analytic formula for the anomalous outgoing skewness. The strategy here should be useful for predicting extreme anomalous statistical behavior in other dispersive media. [ABSTRACT FROM AUTHOR]

Using the fermionic basis, we obtain the expectation values of all sl2-invariant and C-invariant local operators on 10 sites for the anisotropic six-vertex model on a cylinder with generic Matsubara data. This is equivalent to the generalised Gibbs ensemble for the XXX spin chain. In the case when the sl2 and C symmetries are not broken this computation is equivalent to finding the entire density matrix up to 10 sites. As application, we compute the entanglement entropy without and with temperature, and compare the results with CFT predictions. [ABSTRACT FROM AUTHOR]

In our search for new bioactive compounds that interfere with the sugar recognition process, we have designed and synthesized C3- and Cs-symmetrical tripodal receptor-type molecules. Among the synthesized C3-symmetrical 2,4,6-trisubstituted 1,3,5-triazine (TAZ) derivatives, compounds A [2,4,6-tris(2-propoxy)-TAZ] and B [2,4,6-tris(3,4-dimethoxyphenyl)-TAZ] showed high levels of anti-HSV-1 activity. We carried out isothermal titration calorimetry on compound B·HCl in aqueous 25% 2-PrOH solution with some sugar derivatives including methyl α/β-D-galactopyranoside (MeO-α/β-Gal), methyl α/β-D-mannopyranoside (MeO-α/β-Man) and methyl α/β-D-glucopyranoside (MeO-α/β-Glc). The reactions of compound B·HCl with MeO-β-Gal and MeO-α-Man were exothermic, and the obtained thermodynamic profiles indicated that both reactions are spontaneous and that there is a considerably large enthalpic contribution (ΔH) in total Gibbs free energy change (ΔG), indicating favorable hydrogen bonding interactions. The reaction of compound B·HCl showed a thermodynamic signature different from that of the entropically driven reaction of compound A. [ABSTRACT FROM AUTHOR]

We verify a key component of the replica symmetry breaking hypothesis put forward in the physics literature (Mézard and Montanari in Information, physics and computation. Oxford University Press, Oxford, 2009) on random factor graph models. For a broad class of these models we verify that the Gibbs measure can be decomposed into a moderate number of Bethe states, subsets of the state space in which both short and long range correlations of the measure take a simple form. Moreover, we show that the marginals of these Bethe states can be obtained from fixed points of the Belief Propagation operator. We derive these results from a new result on the approximation of general probability measures on discrete cubes by convex combinations of product measures. [ABSTRACT FROM AUTHOR]

Highlights • A new method for the estimation of NRTL binary interaction parameters from liquid-liquid equilibrium data. • The method improves the phase stability of the solutions found. • The problem formulated can be solved in conventional mathematical computing software. Abstract Fitting liquid-liquid equilibrium (LLE) data to common thermodynamic models (NRTL, UNIQUAC...) has been proved in the past to be a non trivial task. Many times it leads to inconsistent solutions where the Gibbs stability criteria is not satisfied. In this work, a simplified parameter estimation problem is formulated where the Gibbs stability criteria and the minimization of experimental and calculated phase composition distances, are simultaneously applied. This formulation is intended to be implemented in general mathematical computing software. Five isothermal ternary systems are studied and the obtained NRTL binary interaction parameters are compared with both existing published parameters and those obtained from commercial data regression tools. Results show that the combination of the proposed problem formulation with commercial non-linear programming solvers improves the quality of the ternary fittings obtained. [ABSTRACT FROM AUTHOR]

Abstract In the present investigation, we report the surface activity, micellar, thermodynamic properties and bioactivity studies of synthesized counterion coupled (COCO) gemini surfactant, 1,6-bis(N , N -hexadecyldimethylammonium) adipate (16-6-16). In aqueous solution, the CMC (critical micelle concentration) of 16-6-16 was measured by electrical conductivity, surface tension, dye solubilization and fluorescence measurements techniques. The surface activities and surface properties of the COCO gemini surfactant, 16-6-16 were evaluated. The CMC as well as A min (the minimum area per surfactant molecule at the air/water interface) decrease and the Γ max (the maximum surface excess concentration at the air/water interface) increases with increasing the temperature. We also report the thermodynamics of 16-6-16 and evaluated Gibbs energies. The aggregation number (N agg) of 16-6-16 is reported. The bioactivity studies of 16-6-16 showed to be nontoxic, biocompatible and having good antibacterial activity. Graphical abstract Fluorescence micrographs using EtBr/AO staining of HaCat cells Control (A), Coco Gemini surfactant 1 μM (B), 2.5 μM (C), 5 μM (D), 7.5 μM (E) and 10 μM (F). Unlabelled Image Highlights • Surface, micellar, thermodynamics & bioactivity studies of COCO gemini, 16-6-16 • Surface properties (viz., C 20 Π CMC Γ max A min , etc.) of the COCO gemini 16-6-16 were evaluated. • The CMC as well as A min decrease and the Γ max increases with increasing the temperature. • The Gibbs energies (viz., G min (s), Δ G m 0, Δ G ads 0, Δ G ex m ) of 16-6-16 were evaluated. • Bioactivity studies of 16-6-16: nontoxic, biocompatible & antibacterial activity [ABSTRACT FROM AUTHOR]

Abstract Flotation tests at laboratory scale describe the metallurgical behavior of the minerals that will be processed in the operational plant. This material is generally composed of ore and gangue minerals. These tests are usually scarce, expensive and sampled in large supports. This research proposes a methodology for the geostatistical modelling of metallurgical recovery, covering the change of support problems through additive auxiliary variables. The methodology consists of simulating these auxiliary variables using a Gibbs Sampler in order to infer the behavior of samples with smaller supports. This allows downscaling a large sample measurement into smaller ones, reproducing the variability at different scales considering the physical restrictions of additivity balance of the metallurgical recovery process. As a consequence, it is possible to apply conventional multivariate geostatistical tools to data at different supports, such as multivariable exploratory analysis, calculation of cross-variograms, multivariate estimations, among others. The methodology was tested using a drillhole database from an ore deposit, modelling recovery at a smaller support than that of the metallurgical tests. The support allowed for the use of the geochemical database, to consistently model the metal content in the feed and in the concentrate, in order to obtain a valid recovery model. Results show that downscaling the composite size reduces smoothing in the final model. Highlights • A downscaling approach to integrate metallurgical and geochemical data is presented. • Metallurgical recovery is simulated using auxiliary additive variables. • A Gibbs Sampler is used to impose constraint on total mass of metal among composites. • A synthetic and a real case study demonstrate the proposed methodology. [ABSTRACT FROM AUTHOR]

Homogeneous nucleation rates of n-butanol in argon were measured in an expansion chamber maintaining pressure, temperature, and vapor supersaturation practically constant during nucleation periods of about 1 ms. Tables of the homogeneous nucleation rates J in the range 105

We determine the liquid–vapor coexistence curve of the restricted primitive model of electrolytes by means of Monte Carlo simulations in the Gibbs ensemble. Our results confirm earlier findings of Panagiotopoulos [Fluid Phase Equilibria 76, 97 (1992)]. A study of the electrical properties of the two coexisting phases reveals that the second Stillinger–Lovett condition is verified in the liquid but not in the vapor. This means that the latter could be dielectric. [ABSTRACT FROM AUTHOR]

In this paper we develop a general mean-field lattice model, in the spirit of the Scheutjens and Fleer theory of polymer solutions [J. M. H. M. Scheutjens and G. J. Fleer, J. Phys. Chem. 83, 1619 (1979); Macromolecules 18, 1882 (1985)], of an N-component polymer blend in the vicinity of an impenetrable surface. We consider the special case of N=3, model one component as noninteracting holes and obtain the bulk density of this system by using the Sanchez–Lacombe equation of state. The free surface of a polymer blend is then modeled by considering the interphase which forms when this ternary mixture is phase separated. One sample case corresponding to the free surface of a symmetric isotopic polystyrenelike blend is probed and we find that the deuterated component is partitioned to the air surface in agreement with experiment. The application of the concept of the Gibbs dividing surface relative to the polymer density profile at the free surface is then examined, and we show that all comparisons to experiment must be conducted relative to this hypothetical plane. Finally, comparisons of the concentration profiles predicted by this theory to existing square gradient theories of binary polymer blends, as well as Monte Carlo simulations, are performed to highlight the usefulness of these calculations to realistic systems. [ABSTRACT FROM AUTHOR]

The maximum entropy formalism maximizes an entropy functional of a phase density ρ(x) subject to conditions that the internal energy and other state variables, such as heat flux Ji and viscous pressure pij, have specified values. By differentiating the entropy thus calculated, one obtains a Gibbs equation. It is shown in the case of a dilute gas that the same Gibbs equation is consistent with the H theorem without additional conditions on the thermodynamic forces. In general, the thermodynamic pressure is not the trace of the momentum flux while the entropy flux, Js, has a nonclassical form. Depending on conditions imposed in maximizing the entropy, these nonclassical features can be eliminated. We find a nonuniqueness which, in fluids not highly dilute, does not appear to affect prediction of observable effects. There is a statistical basis for apparently differing forms of extended thermodynamics. [ABSTRACT FROM AUTHOR]

The equilibrium distribution of isomer groups within a homologous series at a specified partial pressure of molecular hydrogen is given by a geometric distribution when the standard Gibbs energies of formation of the successive isomer groups in the homologous series are given by A+Bn, where n is the carbon number of the isomer group and A and B are functions of temperature only. This distribution depends only on A, the specified partial pressure of molecular hydrogen, and the pressure on the homologous series. This applies to the usual homologous series, where the increment between successive isomer groups is CH2, and to the benzenoid polycyclic aromatic hydrocarbons, where the increment is C4H2. In some homologous series (e.g., alkenes and the coronene series of polycyclic aromatic hydrocarbons), where the successive isomer groups have the same H/C ratio, the equilibrium distribution within the homologous series is, of course, independent of the specified pressure of molecular hydrogen, but the distribution can be calculated in the same way. [ABSTRACT FROM AUTHOR]

The ‘‘geometric Gibbs equation’’ derived by the authors in an earlier paper is employed in the derivation of the asymptotic form of the hard sphere equation of state near the close-packing density. It leads to the same asymptotic equation as the ‘‘polytope’’ method. The significance of the geometric Gibbs equation is explored and the importance of vacancies in any rigorous theory at high density is both emphasized and demonstrated. [ABSTRACT FROM AUTHOR]

An improved method for studying liquid–liquid phase equilibria in the Gibbs ensemble is described. The improvement is based on the excluded volume map sampling (EVMS) technique, recently introduced by Deitrick et al., which has been shown to increase the liquid density range over which the Widom particle insertion method can be applied for the calculation of the chemical potential. Application of EVMS in the Gibbs ensemble greatly improves the efficiency of the particle interchange moves in a Gibbs simulation. We first demonstrate the improved method with Gibbs simulations of liquid-liquid phase equilibria in a two-component Lennard-Jones fluid. The map method results in a significant reduction in the computing time required for these simulations when the number of attempted interchanges is large. A detailed simulation study of fluid–fluid phase equilibria in a model nitrogen-helium mixture was performed using the EVMS Gibbs technique. Typically, a Gibbs simulation of liquid–liquid equilibrium in this fluid, using the map method, requires only 40% of the time used by a conventional Gibbs ensemble simulation. The results demonstrate that it is possible to determine the form of complex phase diagrams using computer simulation. In this work we calculate the pressure-composition sections of the phase diagram close to the temperature minimum of gas–gas immiscibility. The potential model we used was a Lennard-Jones plus quadrupole interaction, with parameters the same as in a recent theoretical study of this fluid mixture. Comparison of our simulation results with the theoretical work shows that the perturbation theory consistently overestimates the mole fraction of nitrogen in the coexisting phases. At the temperatures and pressures studied the simple potential model predicts thermodynamic properties in surprisingly good agreement with experimental data, even though the potential parameters were not adjusted in any way. [ABSTRACT FROM AUTHOR]

The hard sphere system is discussed with the focus on geometry. Three types of exact relations are derived: (i) purely definitional; (ii) definitional and geometric; and (iii) definitional, geometric, and thermodynamic. This careful separation allows a critical study of the statistical thermodynamics of hard spheres. In particular, a geometric Gibbs equation is derived containing only the fundamental geometric parameters of the system, and a set of exact ‘‘rules’’ can be derived from this equation restricting the behaviors of the fundamental parameters over the entire density range. The geometric Gibbs equation (and the rules) are useful in the derivation of the thermodynamic equation of state, but such application is reserved for a following paper. [ABSTRACT FROM AUTHOR]

Examines the formulation of pseudonoensembles for the simulation of phase coexistence. Applicability of the approach to different ensembles; Validation of the propositions through vapor-liquid phase equilibrium; Formulation of Gibbs-Duhem integrations through pseudoensemble simulations.

Presents a calculation for the reversible work of embryo formation of a new phase within a uniform macroscopic mother phase. Creation of an expression for the embryo formation; Extension of the Gibbsian formalism to noncritical nuclei; Introduction of a constraint preventing the transfer of matter between embryo and mother phase.

Studies thermodynamic variables in the context of a nonequilibrium statistical ensemble approach. Generalization of Gibbs statistical thermostatics and linear and local-equilibrium classical irreversible thermodynamics; Optical properties of highly photoexcited plasma in semiconductors.

Reports on the formulation of pseudo-ensemble simulations and Gibbs-Duhem integrations within the framework of the expanded grand canonical ensemble. Mechanical equilibration achieved by the method faster than both conventional volume moves and canonical simulation of the chemical potential; Coexistence curves for pure homopolymers and polymer mixtures.

Estimates the curvature effect on ice surface tension using the Gibbs model of surface tension. Morphology of aqueous interface and crystal surface; Surface tension of crystal facet; Curvature effect on ice surface tension; Model for calculation of the Gibbs adsorption; Effect of curvature on equilibrium radius.