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In this work, we examine the surface thermodynamics of a hard-disk fluid at curved hard walls using Monte Carlo (MC) simulation and a generalized scaled particle theory (gSPT). The curved walls are modeled as hard disks of varying radii

To explore the curvature dependence of solid–fluid interfacial thermodynamics, we calculate, using Grand Canonical Monte Carlo simulation, the surface free energy for a 2 d hard-disk fluid confined in a circular hard container of radius R as a function of the bulk packing fraction η and wall curvature [Formula: see text]. (The curvature is negative because the surface is concave.) Combining this with our previous data [Martin et al., J. Phys. Chem. B 124, 7938–7947 (2020)] for the positive curvature case (a hard-disk fluid at a circular wall, [Formula: see text]), we obtain a complete picture of surface thermodynamics in this system over the full range of positive and negative wall curvatures. Our results show that γ is linear in [Formula: see text] with a slope that is the same for both positive and negative wall curvatures, with deviations seen only at high negative curvatures (strong confinement) and high density. This observation indicates that the surface thermodynamics of this system is consistent with the predictions of so-called morphometric thermodynamics at both positive and negative curvatures. In addition, we show that classical density functional theory and a generalized scaled particle theory can be constructed that give excellent agreement with the simulation data over most of the range of curvatures and densities. For extremely high curvatures, where only one or two disks can occupy the container at maximum packing, it is possible to calculate γ exactly. In this limit, the simulations and density functional theory calculations are in remarkable agreement with the exact results.

For a standard model of patchy colloidal fluids with patch number M = 2, where chain formation (polymerization) occurs, we show that Wertheim theory predicts critical behavior at vanishing density and temperature. The analysis is based on determining lines in the phase diagram of maximal correlation length and compressibility. Simulation studies identify the latter line and confirm our prediction of Fisher-Widom crossover, i.e., the asymptotic decay of the pair correlation function changes from monotonic to damped oscillatory as the density is increased. For M > 2, it is known that phase separation occurs with a true critical point. Our results support the notion that a "disappearing" critical point occurs in the limit M = 2 and we uncover its remnants.

Background: Adalimumab is the only approved compound for the treatment of adult patients with moderate-to-severe hidradenitis suppurativa (HS) who did not respond to a systemic classical treatment. Despite its significant short- and long-term efficacy, a percentage of patients do not respond sufficiently. Moreover, some primary responders experience a response loss with time. Objective: To analyse the effectiveness of adalimumab dose intensification in HS patients. Methods: A case series of adalimumab 80 mg/week subcutaneously (s.c.) compassionate use in patients with HS, who did not respond sufficiently or in primary responders with progressive response loss to the registered adalimumab dose of 40 mg/week s.c. Patients were collected and evaluated retrospectively. Patients’ data were extracted from medical records. Results: The 14 patients collected were Caucasian with HS of Hurley stage II–III and moderate or severe International HS Severity Score System (IHS4) stage. Adalimumab dose intensification significantly improved IHS4 score, Pain Index, HS-Physician Global Assessment, pain, and Cardiff Dermatology Life Quality Index. Two young female patients with HS and Crohn’s disease developed psoriatic lesions during the treatment with adalimumab 80 mg/week s.c. Conclusion: An enhanced level of effectiveness was assessed in the majority of the HS patients treated with adalimumab dose intensification (80 mg/week s.c.). Larger studies are required to evaluate this observation.

Typically the quality of an approximate density functional is evaluated by a direct comparison of its predictions in a given test case to exact data obtained by computer simulations. An important e...

Within scaled-particle theory, we construct an equation of state (EOS) for hard-disk mixtures by making use of an additional scaled-particle variable which weighs the densities of the different components by its radii to the power χ. This allows us to simultaneously respect exact results pertaining to the cases of a large particle or a point particle being added to the mixture. In the limit χ → 2, the mixture EOS of Santos et al. [Mol. Phys. 96, 1 (1999)] is recovered, while the limit χ → 0 yields the accurate expression for the interfacial free energy of Martin et al. [J. Chem. Phys. 149, 084701 (2018)]. From the low-density limit of the EOS, the value χ ≈ 0.8 is extracted, which is shown to yield a mixture EOS that is significantly more accurate than the expressions due to Santos et al. and Martin et al. In particular, the systematic deviation inherent to these prior results is remedied.

Is the present-day water-land ratio a necessary outcome of the evolution of plate tectonic planets with a similar age, volume, mass, and total water inventory as the Earth? This would be the case – largely independent of initial conditions – if Earth’s present-day continental volume were at a stable unique equilibrium with strong self-regulating mechanisms of continental growth steering the evolution to this state. In this paper, we question this conjecture. Instead we suggest that positive feedbacks in the plate tectonics model of continental production and erosion may dominate and show that such a model can explain the history of continental growth. We investigate the main mechanisms that contribute to the growth of the volume of the continental crust. In particular, we analyze the effect of the oceanic plate speed, depending on the area and thickness of thermally insulating continents, on production and erosion mechanisms. Effects that cause larger continental production rates for larger values of continental volume are positive feedbacks. In contrast, negative feedbacks act to stabilize the continental volume. They are provided by the increase of the rate of surface erosion, subduction erosion, and crustal delamination with the continental volume. We systematically analyze the strengths of positive and negative feedback contributions to the growth of the continental crust. Although the strengths of some feedbacks depend on poorly known parameters, we conclude that a net predominance of positive feedbacks is plausible. We explore the effect of the combined feedback strength on the feasibility of modeling the observed small positive net continental growth rate over the past 2–3 billion years. We show that a model with dominating positive feedbacks can readily explain this observation in spite of the cooling of the Earth’s mantle acting to reduce the continental production rate. In contrast, explaining this observation using a model with dominating negative feedbacks would require the continental erosion and production rates to both have the same or a sufficiently similar functional dependence on the thermal state of the mantle, which appears unreasonable considering erosion to be largely dominated by the surface relief and weathering. The suggested scenario of dominating positive feedbacks implies that the present volume of the continental crust and its evolution are strongly determined by initial conditions. Therefore, exoplanets with Earth-like masses and total water inventories may substantially differ from the Earth with respect to their relative land/surface ratios and their habitability.

Suspended colloids are often considered as models for molecules, which are sufficiently big so that they can be observed directly in (light) microscopes and for which the effective interaction among each other can be tailored. The Asakura-Oosawa model of ideal colloid-polymer mixtures captures the idea of tuning the interaction between the colloids via a potential, which possesses a range set by the size of the polymers and an attractive strength characterized by the (reservoir) number density of the polymers, which plays the role of an inverse temperature. The celebrated Asakura-Oosawa depletion potential allows one to recreate the bulk phase diagram of a simple fluid by employing a colloid-polymer mixture. This has been verified in theory, by computer simulations, and via experiments. Here, we study the phase behavior of a confined colloid-polymer mixture with two polymer species. The sizes and densities are chosen such that the resulting bulk phase diagram exhibits a second stable critical point within the framework of the classical density functional theory. Our results suggest that a suitably tuned colloid-polymer mixture can be an interesting model system to study fluids with two critical points.

Protein adsorption at the solid-liquid interface is an important phenomenon that often can be observed as a first step in biological processes. Despite its inherent importance, still relatively little is known about the underlying microscopic mechanisms. Here, using multivalent ions, we demonstrate the control of the interactions and the corresponding adsorption of net-negatively charged proteins (bovine serum albumin) at a solid-liquid interface. This is demonstrated by ellipsometry and corroborated by neutron reflectivity and quartz-crystal microbalance experiments. We show that the reentrant condensation observed within the rich bulk phase behavior of the system featuring a nonmonotonic dependence of the second virial cofficient on salt concentration c_s is reflected in an intriguing way in the protein adsorption d(c_s) at the interface. Our findings are successfully described and understood by a model of ion-activated patchy interactions within the framework of classical density functional theory. In addition to the general challenge of connecting bulk and interface behavior, our work has implications for, inter alia, nucleation at interfaces., Comment: 5 pages, 3 Figures, accepted by Phys. Rev. Lett

Growth of hard--rod monolayers via deposition is studied in a lattice model using rods with discrete orientations and in a continuum model with hard spherocylinders. The lattice model is treated with kinetic Monte Carlo simulations and dynamic density functional theory while the continuum model is studied by dynamic Monte Carlo simulations equivalent to diffusive dynamics. The evolution of nematic order (excess of upright particles, "standing--up" transition) is an entropic effect and is mainly governed by the equilibrium solution, {rendering a continuous transition} (paper I, J. Chem. Phys. 145, 074902 (2016)). Strong non--equilibrium effects (e.g. a noticeable dependence on the ratio of rates for translational and rotational moves) are found for attractive substrate potentials favoring lying rods. Results from the lattice and the continuum models agree qualitatively if the relevant characteristic times for diffusion, relaxation of nematic order and deposition are matched properly. Applicability of these monolayer results to multilayer growth is discussed for a continuum--model realization in three dimensions where spherocylinders are deposited continuously onto a substrate via diffusion., Comment: 22 pages, 14 figures

The origin and evolution of life has undoubtedly had a major impact on the evolution of Earth's oceans and atmosphere. Recent studies have suggested that bioactivity may have had an even deeper impact and may have caused a change in the redox-state of the mantle and provided a path for the formation of continents. We here present a numerical model that assumes that bioactivity increases the continental weathering rate and that relates the sedimentation rate to the growth of continents and to the hydration of the mantle using elements of plate tectonics and mantle convection. The link between these factors is provided by assuming that an increase of the thickness of the sedimentary layer of low permeability on top of a subducting oceanic slab will reduce its dewatering upon subduction. This in turn leads to a greater availability of water in the source region of andesitic partial melt, resulting in an enhanced rate of continental crust production, and to an increased regassing rate of the mantle. The mantle in turn responds by reducing the mantle viscosity while increasing the convective circulation rate, degassing rate and plate speed. We use parameters that are observed for the present Earth and gauge uncertain parameters such that the present day continental surface area and mantle water concentration can be obtained. Our steady state results show two stable fixed points in a phase plane defined by the fractional continental surface area and the water concentration in the mantle, one of them pertaining to a wet mantle and the continental surface area of the present day Earth, and the other to a dry mantle and a small continental surface area. When the sedimentation rate is reduced, both fixed points move and the area of attraction of the latter fixed point increases systematically. We conclude that if the presence of life has increased the continental weathering rate, as is widely believed, and led to the observables of a wet mantle and a continental surface coverage of roughly 40%, an abiotic Earth would likely have evolved toward a dry mantle with a small continental surface area instead.

The physical and biological mechanisms that extend the equilibrium domain of liquid water into the ice region of the bulk phase diagram are examined in view of their importance for the enhancement of planetary habitability. The physical phenomena studied are the premelting of ice, which allows for films of liquid water at temperatures well below freezing, and the wetting of hygroscopic salts with the persistence of briny films even for thermodynamic conditions remote from those of bulk liquid water. Organisms are known to produce a variety of frost-suppressing substances, one of which, the anti-freeze protein, is described here. In this article, we provide a synthesis of theoretical and experimental studies whilst extending ideas into new territory as we address the question of habitability.

We re-visit the competition between attractive and repulsive interparticle forces in simple fluids and how this governs and connects the macroscopic phase behavior and structural properties as manifest in pair correlation functions. We focus on the asymptotic decay of the total correlation function $h(r)$ which is, in turn, controlled by the form of the pair direct correlation function $c(r)$. The decay of $r h(r)$ to zero can be either exponential (monotonic) if attraction dominates repulsion and exponentially damped oscillatory otherwise. The Fisher-Widom (FW) line separates the phase diagram into two regions characterized by the two different types of asymptotic decay. We show that there is a new and physically intuitive thermodynamic criterion which approximates well the actual FW line. This new criterion defines a line where the isothermal compressibility takes its ideal gas value $\chi_T=\chi_T^\text{id}$. We test our hypothesis by considering four commonly used models for simple fluids. In all cases the new criterion yields a line in the phase diagram that is close to the actual FW line for the thermodynamic state points that are most relevant. We also investigate (Widom) lines of maximal correlation length, emphasizing the importance of distinguishing between the true and Ornstein-Zernike correlation lengths

Within the Asakura-Oosawa model, we study structural relaxation in mixtures of colloids and polymers subject to Brownian motion in the overdamped limit. We obtain the time evolution of the self and distinct parts of the van Hove distribution function G(r,t) by means of dynamical density functional theory (DDFT) using an accurate free-energy functional based on Rosenfeld's fundamental measure theory. In order to remove unphysical interactions within the self part, we extend the recently proposed quenched functional framework (Stopper et al 2015 J. Chem. Phys. 143 181105) toward mixtures. In addition, we obtain results for the long-time self diffusion coefficients of colloids and polymers from dynamic Monte Carlo simulations, which we incorporate into the DDFT. From the resulting DDFT equations we calculate G(r, t), which we find to agree very well with our simulations. In particular, we examine the influence of polymers which are slow relative to the colloids-a scenario for which both DDFT and simulation show a significant peak forming at r = 0 in the colloid-colloid distribution function, akin to experimental findings involving gelation of colloidal suspensions. Moreover, we observe that, in the presence of slow polymers, the long-time self diffusivity of the colloids displays a maximum at an intermediate colloid packing fraction. This behavior is captured by a simple semi-empirical formula, which provides an excellent description of the data.

The equilibrium properties of hard rod monolayers are investigated in a lattice model (where position and orientation of a rod are restricted to discrete values) as well as in an off--lattice model featuring spherocylinders with continuous positional and orientational degrees of freedom. Both models are treated using density functional theory and Monte Carlo simulations. Upon increasing the density of rods in the monolayer, there is a continuous ordering of the rods along the monolayer normal ("standing up" transition). The continuous transition also persists in the case of an external potential which favors flat--lying rods in the monolayer. This behavior is found in both the lattice and the continuum model. For the lattice model, we find very good agreement between the results from the specific DFT used (lattice fundamental measure theory) and simulations. The properties of lattice fundamental measure theory are further illustrated by the phase diagrams of bulk hard rods in two and three dimensions., 15 pages

We derive an analytical equation of state for the hard-sphere fluid that is within 0.01% of computer simulations for the whole range of the stable fluid phase. In contrast, the commonly used Carnahan-Starling equation of state deviates by up to 0.3% from simulations. The derivation uses the functional form of the isothermal compressibility from the Percus-Yevick closure of the Ornstein-Zernike relation as a starting point. Two additional degrees of freedom are introduced, which are constrained by requiring the equation of state to (i) recover the exact fourth virial coefficient B4 and (ii) involve only integer coefficients on the level of the ideal gas, while providing best possible agreement with the numerical result for B5. Virial coefficients B6 to B10 obtained from the equation of state are within 0.5% of numerical computations, and coefficients B11 and B12 are within the error of numerical results. We conjecture that even higher virial coefficients are reliably predicted.

Mortality projections are of special interest in many applications. For example, they are essential in life insurances to determine the annual contributions of their members as well as for population predictions. Due to their importance, there exists a huge variety of mortality forecasting models from which to seek the best approach. In the demographic literature, statements about the quality of the various models are mostly based on empirical ex-post examinations of mortality data for very few populations. On the basis of such a small number of observations, it is impossible to precisely estimate statistical forecasting measures. We use Monte Carlo (MC) methods here to generate time trajectories of mortality tables, which form a more comprehensive basis for estimating the root-mean-square error (RMSE) of different mortality forecasts.

Es wird zunachst ein Uberblick uber die gangigen Methoden der Sterblichkeitsmodellierung gegeben. Von besonderem Interesse sind Vorhersagen. Ein Schwerpunkt der Arbeit liegt in diesem Zusammenhang auf dem Brass-Verhaltnismodell. In einer ex-post Studie an deutschen Daten fuhrt dieser Ansatz zu ebenso guten Prognosen wie die normalerweise verwendeten Vorhersagemodelle. Bei Prognosen fur das Jahr 2050 liegen die Brass-Vorhersagen fur die Lebenserwartung deutlich uber denen des Statistischen Bundesamtes. Es gibt jedoch auch Stimmen, welche die amtlichen Prognosen als zu niedrig einstufen. Uber diesen Aspekt kann daher diskutiert werden.

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.

The political ideas of Islamism as they have been formulated by Hassan al-Banna and Sayyid Qutb share a number of striking similarities with Western political religions like Communism and National Socialism, in particular the radical dualist interpretation of history and the understanding of politics as a struggle against evil. However, the concept of political religions as it has been elaborated by Voegelin and further developed by Gentile implies the deification of a secular entity. Thus, if political religions are defined as being based on secularism, this concept seems to be inappropriate for the analysis of Islamism. This paper investigates whether this interpretation is correct and whether the concept of ‘politicised religions’ should be considered more useful for the analysis of Islamism. It gives an overview of the concepts of political and politicised religions and of the political ideas of Islamism based on the writings of Hassan al-Banna and Sayyid Qutb. The theses are that (1) both ‘fundamentalism’ and ‘politicised religions’ are misleading concepts for a comparison of their political theories with Western political religions; and (2) the concept of political religions is indeed applicable to Islamism, if we arrive at the understanding that not secularism but the radicalisation of the friend–foe-distinction and the understanding of politics as a purge of evil from the world ought to be considered its central themes.

The purpose of this paper is to shed light on the reasons for the strong anti‐western point of view in radical Islamism by comparing its political ideology to the western totalitarian ideologies, Marxism and National Socialism. The comparison is based on a reconstruction of the political theory of three major founders of these ideologies: Sayyid Qutb, Karl Marx and Adolf Hitler. Despite all differences, their arguments follow the same basic structure: the history of mankind is perceived as a life and death struggle between good and evil, in which those who are evil threaten the existence of mankind. Those who personify good have the mission to save humankind by ridding it from evil and by realising the utopia of the classless society, the natural race struggle or the purified society of followers of the true faith. The article concludes that radical Islamism is not a rejection of modernity from a pre‐modern or Islamic standpoint, but is rather an ideology which seduces its followers by criticisin...

We study structural relaxation of colloidal hard spheres undergoing Brownian motion using dynamical density functional theory. Contrary to the partial linearization route [Stopper {\em et al.}, Phys. Rev. E {\bf 92}, 022151 (2015)] which amounts to using different free energy functionals for the self and distinct part of the van Hove function $G(r,t)$, we put forward a unified description employing a single functional for both components. To this end, interactions within the self part are removed via the zero-dimensional limit of the functional with a quenched self component. In addition, we make use of a theoretical result for the long-time mobility in hard-sphere suspensions, which we adapt to the inhomogeneous fluid. Our results for $G(r,t)$ are in excellent agreement with numerical simulations even in the dense liquid phase. In particular, our theory accurately yields the crossover from free diffusion at short times to the slower long-time diffusion in a crowded environment.

Based on Santos' general solution for the scaled-particle differential equation [Phys. Rev. E 86, 040102(R) (2012)], we construct a free-energy functional for the hard-sphere system. The functional is obtained by a suitable generalization and extension of the set of scaled-particle variables using the weighted densities from Rosenfeld's fundamental measure theory for the hard-sphere mixture [Phys. Rev. Lett. 63, 980 (1989)]. While our general result applies to the hard-sphere mixture, we specify remaining degrees of freedom by requiring the functional to comply with known properties of the pure hard-sphere system. Both for mixtures and pure systems, the functional can be systematically extended following the lines of our derivation. We test the resulting functionals regarding their behavior upon dimensional reduction of the fluid as well as their ability to accurately describe the hard-sphere crystal and the liquid-solid transition.

We demonstrate that the pair potential V(r) in one-dimensional systems can be obtained analytically from the pair-distribution function in case of short-ranged interactions. We re-examine the exact statistical mechanics solution and propose a simple procedure for extracting the pair potential and the equation of state from experimentally measured pair-distribution functions. The method is applied to charge-stabilised colloids which are confined to a one-dimensional laser trap. published

The electrochemical oxidation of 2,4-dimethyl-3-ethylpyrrole in acetonitrile has been studied using cyclic voltammetry, constant current coulometry, preparative electrolyses and ab initio calculations. The product analysis after the preparative electrolyses was carried out by HPLC combined with UV–vis and electrospray ionization MS detection. The aim of the work was to address some of the unresolved problems in the oxidative oligomerization and polymerization of alkylpyrroles. The title compound was chosen as a model for studies of pyrroles that are more basic than the solvent-supporting electrolyte system and for that reason are forced to serve as the base accepting the protons released during the coupling steps. The voltammograms obtained by cyclic voltammetry at a substrate concentration of 2 mM and voltage scan rates between 0.02 and 2 V s−1 showed a characteristic trace-crossing phenomenon that could be demonstrated by digital simulation to be related to that fact that the deprotonations of the initially formed dimer dication are slow with second order rate constants in the range 103–104 M−1 s−1. The relative stability of the different tautomers of the protonated pyrrole monomer and the corresponding 2,2′-dimer was determined by ab initio calculations at the RHF 6-31G(d) level. The studies also included investigations of the effects resulting from addition of a non-nucleophilic base, 2,6-di-tert-butylpyridine, to the voltammetry solutions. The major product observed after preparative electrolyses was a trimer the structure of which is proposed to include a central 2H-pyrrole unit. Since 2H-pyrroles are stronger bases than the corresponding 1H-pyrroles, the trimer is effectively protected against further oxidation by protonation. Two other trimers were observed as minor or trace products as well as a 1H,2H-dimer and several tetramers, also in trace amounts. In addition to the dimer, the trimers and the tetramers, a number of other minor products could be detected. These could all be traced back to the nucleophilic attack by residual water on the radical cations or dications of the 2,2′-dimer and the trimers. The results obtained by constant current coulometry are in agreement with the formation of a 2H-pyrrole based trimer as the major product.

We demonstrate that the Hadwiger form of the free energy of a fluid in contact with a wall is insufficient to describe the low-density behavior of a hard-sphere fluid. This implies that morphological thermodynamics of the hard-sphere fluid is an approximate theory if only four geometric measures are included. In order to quantify deviations from the Hadwiger form we extend standard fundamental measure theory of the bulk fluid by introducing additional scaled-particle variables which allow for the description of non-Hadwiger coefficients. The theory is in excellent agreement with recent computer simulations. The fact that the leading non-Hadwiger coefficient is one order of magnitude smaller than the smallest Hadwiger coefficient lends confidence to the numerous results that have been previously obtained within standard morphological thermodynamics.