Let M be a short extender mouse. We prove that if $E\in M$ and $M\models $“E is a countably complete short extender whose support is a cardinal $\theta $ and $\mathcal {H}_\theta \subseteq \mathrm {Ult}(V,E)$”, then E is in the extender sequence $\mathbb {E}^M$ of M. We also prove other related facts, and use them to establish that if $\kappa $ is an uncountable cardinal of M and $\kappa ^{+M}$ exists in M then $(\mathcal {H}_{\kappa ^+})^M$ satisfies the Axiom of Global Choice. We prove that if M satisfies the Power Set Axiom then $\mathbb {E}^M$ is definable over the universe of M from the parameter $X=\mathbb {E}^M\!\upharpoonright \!\aleph _1^M$, and M satisfies “Every set is $\mathrm {OD}_{\{X\}}$”. We also prove various local versions of this fact in which M has a largest cardinal, and a version for generic extensions of M. As a consequence, for example, the minimal proper class mouse with a Woodin limit of Woodin cardinals models “$V=\mathrm {HOD}$”. This adapts to many other similar examples. We also describe a simplified approach to Mitchell–Steel fine structure, which does away with the parameters $u_n$.

The adsorption-condensation of olefins was studied on 7 adsorbents: 2 commercial clays, a natural clay and its protonated form, γ-alumina and porous and nonporous silicas. These adsorbents were characterized by X-ray diffraction (XRD), chemical analysis, thermogravimetric analysis (TGA), differential thermal analysis (DTA) and determination of specific surface area measurement by the BET method. The experiments were carried out gravimetrically, in gas- or vapor-solid systems, at 25 °C and on adsorbents dried at 120 °C. Adsorption-condensation of olefins are fast processes, diffusion controlled. Alumina and silicas adsorb olefins and paraffins only reversibly, but are unable to condense olefins. The water polarized by the countercations is the source of Brønsted acid sites. When the gas phase is evacuated or swept with inert gas, the condensation terminates. On clays, paraffins are reversibly adsorbed but no condensation was observed.

The polyphenol theory of humic-substance formation has been studied extensively; however, an alternative theory, that humic substances are formed through the condensation of amino acids and reducing sugars (Maillard reaction), has not been explored to the same extent. The general objectives of this study were to determine whether smectites and goethites catalyze the abiotic polymerization of arginine and glucose to form humic-like compounds. The effects of smectite type, saturating cation, and the degree of Al substitution in goethites on the polymerization reaction were also studied. Four cation-saturated smectites and four Al-substituted goethites were incubated abiotically with solutions containing a mixture of arginine + glucose for 21 days at 37°C. After the incubations, total C recovered ranged from 80.6 to 123.8% and from 100.5 to 105.1% for the smectite and goethite systems, respectively. At the end of the incubations, 21.4–50.3% of the added C and 16.5–90% of the added N were sorbed on the various smectites, and 6.2–9.0% of the added C and 2.3–4.6% of added N was sorbed on the goethites in a form that could not be desorbed by washing with 100 mM CaCl2. X-ray diffraction analysis indicated that some of the sorbed C was intercalated in the smectites and FTIR analysis provided evidence of new absorption bands at 1650 and 1668 cm−1, which are consistent with Maillard reaction products. Thus, it is concluded that smectites catalyze the condensation of arginine and glucose to form humic-like products. Goethites, however, have little or no ability to catalyze this reaction.

We study the large-volume asymptotics of the sum of power-weighted edge lengths $\sum_{e \in E}|e|^\alpha$ in Poisson-based spatial random networks. In the regime $\alpha > d$, we provide a set of sufficient conditions under which the upper-large-deviation asymptotics are characterized by a condensation phenomenon, meaning that the excess is caused by a negligible portion of Poisson points. Moreover, the rate function can be expressed through a concrete optimization problem. This framework encompasses in particular directed, bidirected, and undirected variants of the k-nearest-neighbor graph, as well as suitable $\beta$-skeletons.

We study a general model of recursive trees where vertices are equipped with independent weights and at each time-step a vertex is sampled with probability proportional to its fitness function, which is a function of its weight and degree, and connects to $\ell$ new-coming vertices. Under a certain technical assumption, applying the theory of Crump–Mode–Jagers branching processes, we derive formulas for the limiting distributions of the proportion of vertices with a given degree and weight, and proportion of edges with endpoint having a certain weight. As an application of this theorem, we rigorously prove observations of Bianconi related to the evolving Cayley tree (Phys. Rev. E 66, paper no. 036116, 2002). We also study the process in depth when the technical condition can fail in the particular case when the fitness function is affine, a model we call ‘generalised preferential attachment with fitness’. We show that this model can exhibit condensation, where a positive proportion of edges accumulates around vertices with maximal weight, or, more drastically, can have a degenerate limiting degree distribution, where the entire proportion of edges accumulates around these vertices. Finally, we prove stochastic convergence for the degree distribution under a different assumption of a strong law of large numbers for the partition function associated with the process.

A synthetic protonic magadiite was used as a silica source to prepare zeolitic material (PLS-1) in the presence of tetramethylammonium hydroxide and water. The conversion of the protonic magadiite to the PLS-1 phase was achieved at 150°C after 5 days, or at 170°C after 3 days for SiO2: TMAOH:H2O molar ratios of 2.54:1:4.4. The synthesis of the pure PLS-1 phase depended also on the amounts of tetramethylammonium hydroxide and water used. Analysis by 29Si magic angle spinning nuclear magnetic resonance spectroscopy confirmed the layered character of the PLS-1 phase with a resonance at −93 ppm, and its dehydroxylation-condensation process. The chemical formula of (TMA)2Si18O33(OH)6 for PLS-1 was refined with the Rietveld method and the tetrahedron-splitting model. The later model has been proposed to describe the presence of silanol defects in the layered structure of PLS-1. Upon calcinations of the PLS-1 phase at temperatures >400°C, the removal of TMA cations and dehydroxlyation of PLS-1 layers resulted in a three-dimensional structure phase identified as the CDS-1 phase, with a chemical formula of Si18O36. The CDS-1 phase exhibited a large specific surface area of 288 m2/g and microporous character, as indicated by the nitrogen adsorption isotherms. The temperature-programmed desorption profile of ammonia indicated that CDS-1 exhibited one weak type of acid sites, confirmed, by pyridine desorption studies, as weak Lewis acid sites.

Aerosol modeling is very important to study the behavior of aerosol dynamics in atmospheric environment. In this paper we consider numerical methods for the nonlinear aerosol dynamic equations on time and particle size. The finite volume element methods based on the linear interpolation and Hermite interpolation are provided to approximate the aerosol dynamic equation where the condensation and removal processes are considered. Numerical examples are provided to show the efficiency of these numerical methods.

We present a forcing to obtain a localized version of Local Club Condensation, a generalized Condensation principle introduced by Sy Friedman and the first author in [3] and [5]. This forcing will have properties nicer than the forcings to obtain this localized version that could be derived from the forcings presented in either [3] or [5]. We also strongly simplify the related proofs provided in [3] and [5]. Moreover our forcing will be capable of introducing this localized principle at κ while simultaneously performing collapses to make κ become the successor of any given smaller regular cardinal. This will be particularly useful when κ has large cardinal properties in the ground model. We will apply this to measure how much L-likeness is implied by Local Club Condensation and related principles. We show that Local Club Condensation at κ+ is consistent with ¬☐κ whenever κ is regular and uncountable, generalizing and improving a result of the third author in [14], and that if κ ≥ ω2 is regular, CC(κ+) - Chang’s Conjecture at κ+ - is consistent with Local Club Condensation at κ+, both under suitable large cardinal consistency assumptions.

We investigate the effect of mass transfer on the evolution of a thin, two-dimensional, partially wetting drop. While the effects of viscous dissipation, capillarity, slip and uniform mass transfer are taken into account, other effects, such as gravity, surface tension gradients, vapour transport and heat transport, are neglected in favour of mathematical tractability. Our focus is on a matched-asymptotic analysis in the small-slip limit, which reveals that the leading-order outer formulation and contact-line law depend delicately on both the sign and the size of the mass transfer flux. This leads, in particular, to novel generalisations of Tanner's law. We analyse the resulting evolution of the drop on the timescale of mass transfer and validate the leading-order predictions by comparison with preliminary numerical simulations. Finally, we outline the generalisation of the leading-order formulations to prescribed non-uniform rates of mass transfer and to three dimensions.

Two related aspects of nano-droplet condensation and droplets coalescence are studied for droplets on self-supported thin water films. The experiments are conducted in the environmental scanning electron microscope using wet scanning transmission electron microscopy. Favorable condensation sites are examined and in-situ position-controlled condensation experiments are conducted. The interaction among condensed multi-droplets as well as between a single droplet and the underneath nano-thick water film are dynamically examined with 10nm lateral resolution. The droplet round shape is reshaped to flat-like facets in-between droplets of 30-230 nm separation. Dynamic imaging of a few minutes duration shows a delayed coalescence effect, being explained by increased droplet-droplet electrostatic interaction relative to van der Waals interaction.

In his book on ℙmax [7], Woodin presents a collection of partial orders whose extensions satisfy strong club guessing principles on ω1. In this paper we employ one of the techniques from this book to produce ℙmax variations which separate various club guessing principles. The principle (+) and its variants are weak guessing principles which were first considered by the second author [4] while studying games of length ω1. It was shown in [1] that the Continuum Hypothesis does not imply (+) and that (+) does not imply the existence of a club guessing sequence ω1. In this paper we give an alternate proof of the second of these results, using Woodin's ℙmax technology, showing that a strengthening of (+) does not imply a weakening of club guessing known as the Interval Hitting Principle. The main technique in this paper, in addition to the standard ℙmax machinery, is the use of condensation principles to build suitable iterations.

This paper presents a thermodynamic model for a heat engine based on evaporative cooling of unsaturated air at reduced pressure. Also analysed is a related heat pump based on condensation of water vapour in moist air at reduced pressure. These devices operate as two-stroke reciprocating engines, which are their simplest possible embodiments. The mathematical models for the two devices are based on conservation of mass for both air and water vapour, ideal gas laws, constant specific heats, and, as appropriate, either constant entropy processes or cooling/heating by evaporation/condensation. Both models take the form of coupled algebraic systems in six variables, which require numerical solution for certain stages of the cycle. The specific work output of the heat engine increases as the inlet air becomes hotter and as the expansion ratio of the engine increases. The engine provides evaporative cooling of air from inlet to outlet. The heat pump has a good coefficient of performance, which decreases as the expansion ratio increases. The heat pump also has the effect of drying the air from inlet to outlet, producing distilled water as a by-product.

L'étude en convection forcée de la condensation en film laminaire d'une vapeur pure et saturée sur une plaque poreuse inclinée par rapport à la verticale, est présentée. Le modèle de Darcy-Brinkman est utilisé pour décrire l'écoulement dans le milieu poreux, tandis que les équations classiques de la couche limite ont été exploitées dans le liquide pur en tenant compte des termes d'inertie et de convection d'enthalpie. Le problème posé a été résolu par voies analytique et numérique. Les résultats sont essentiellement présentés sous forme de l'épaisseur adimensionnelle du film liquide, des profils de vitesse et de température et des coefficients d'échanges thermiques représentés par le nombre de Nusselt. Les résultats obtenus ont été comparés à ceux expérimentaux de Renken et al. [1]. Les effets de différents paramètres influents tels que : l'inclinaison (ϕ), la viscosité effective (nombre de Reynolds ReK), l'épaisseur adimensionnelle du substrat poreux H* et la conductivité thermique adimensionnelle k*, sur l'écoulement et les transferts thermiques sont illustrés.