The physical and chemical interactions between organic amines and mineral surfaces are of considerable importance in many industrial applications. For example, the preparation of organophilic minerals often involves the adsorption of organic amines, or the ion exchange of the minerals with quaternary ammonium salts (Jordon, 1951; Miller and Faust, 1972). Chemical interactions occurring in these systems have been studied because of their relevance to an understanding of the chemical nature of the clay surface. A number of these studies have reported on the decomposition of adsorbed amines and alkylammonium-mineral complexes at elevated temperatures, usually in excess of 100°C (Chaussidon and Calvet, 1965; Weiss and Roloff, 1963; Durand, Pellet and Fripiat, 1972; Chou and McAtee, 1969). It is now well established that under these conditions the mineral may have potential strong-acidity, and these reactions have been explained in terms of acid-induced decomposition or rearrangement of the adsorbed amines or their derivatives. However, there have been few studies of the reactions of organo-mineral complexes at temperatures below 100°C, under conditions where retention of adsorbed water could be expected to moderate the mineral surface acidity.

Surface acidity of almost homoionic montmorillonites was measured by titrating selected Hammett indicators adsorbed on the clay with n-butylamine.

As expected, the acidity is strongly affected by the exchangeable cations and the degree of hydration of the clay. Greater polarizing ability of the interlayer cations increases both the strength and number of acid sites per H0 value. The acidity of ‘activated’ or heated H-montmorillonite does not exceed that of untreated H-montmorillonite. The origin of the negative charge in the montmorillonite appears to affect the acidity of the clay.

It is concluded that the very high acidities reported in the literature (H0 < −5·6) are apparent only and are due to physisorption of the indicator.

Clays may catalyze chemical reactions by acting as Brönsted acids, Lewis acids, and/or Lewis bases. The changes occurring when limonene (p-menthadiene) is heated in the presence of montmorillonite illustrate how Brönsted and Lewis acidity may operate competitively, the nature of the interlayer cations determining which reaction dominates. The rate at which the starting material disappears increases with the acidity of the clay, which depends upon the interlayer cations (Na < Mg < Al < H). The concentration of disproportionation and isomerization products reaches a maximum after reaction times which decrease with increasing surface acidity of the clay, p-cymene is produced by oxidation in concentrations inversely related to the surface acidity of the clay. The course of the chemical reaction can thus be steered in the preferred direction by an appropriate choice of interlayer cations.

The effect of anions on clay dispersion and the hydraulic conductivity (HC) of clay-sand mixtures has received little attention. This study investigates the effect that adding small amounts of anions has on the dispersivity and HC of reference clays. Mixtures of 3 and 6 g 100 g−1 kaolinite, smectite, and illite with quartz sand were packed in columns. The columns were saturated with Ca and then leached with 1 molc m−3 of one of the following organic and inorganic Na salts: chloride, hydroxide, EDTA, silicate, citrate, formate, oxalate, hexametaphosphate, orthophosphate, tartrate, or humate. Changes in HC and clay concentration in the effluent were measured and clay dispersion was evaluated as a function of the various anions added. In the kaolinite clay-sand mixtures, a significant amount of clay was observed in the effluent for all anions tested, and the HC increased above its original value. The HC of smectite clay-sand mixtures decreased following the addition of the various anions. Dispersed clay appeared in the effluent only upon addition of citrate or hexametaphosphate. In the latter two cases, the HC started to increase once maximum clay concentration appeared in the effluent. Clay concentration in the effluent of smectite was one order of magnitude lower than that of kaolinite. Illite clay-sand mixtures showed dispersion behavior intermediate between smectite and kaolinite but behaved in the same way as kaolinite with respect to HC changes.

This study aimed to examine the caregiver burden among offspring of Holocaust survivors (OHS) caring for their parents during the COVID-19 pandemic, hypothesizing that caregivers whose parents suffer from posttraumatic stress disorder (PTSD) would report an increased burden. The sample consisted of 109 caregivers with older adult care recipient parents (average caregivers’ age = 57.67, SD = 8.49). Caregivers were divided into three groups: 20 OHS who reported that at least one care recipient had PTSD, 60 OHS who reported that their care recipients did not have PTSD, and 29 comparison caregivers (whose care recipients did not undergo the Holocaust). Caregivers completed questionnaires about SARS-CoV-2 exposure, COVID-19 concerns, helping their care recipients, their experiences of caregiver burden, and perceived changes to their caregiver burden during the pandemic. The caregivers also reported PTSD symptoms—in themselves as well as in their care recipients. Relative to comparisons, OHS with parental PTSD reported higher caregiver burden in four aspects: time-dependent burden, developmental burden, physical burden, and social burden. Furthermore, OHS reported a greater perceived increase in caregiver burden during the pandemic than the comparisons. The study findings illuminate the difficulties OHS caregivers, especially those whose care recipients have PTSD, face during the COVID-19 pandemic. This group of caregivers is at risk of experiencing more distress and may need help and support. Further research is needed to determine whether people taking care of their posttraumatic parents following other massive traumatic events also feel a heavier caregiver burden—both in general and specifically during the current pandemic.

We prove duality isomorphisms of certain representations of ${\mathcal{W}}$-algebras which play an essential role in the quantum geometric Langlands program and some related results.

Regrasping is a manipulation to alternate between grasp configurations of an object to perform different tasks. We address a regrasping problem termed longitude regrasping to reposition a gripper along an elongated object. We propose an algorithm using the dynamics of the arm and a non-dexterous gripper to perform the manipulation. Energy control is used to toss the object up and catch it under the goal position. Clipped Linear Quadratic Regulator control approach is then applied to the gripper jaws to control the friction force on the object and to let it slide to the final goal position. The object sliding within the gripper is modeled as a semi-active linear joint where only dissipative forces can be applied to it. A set of experiments validated the feasibility of the method.

The joint effects of an insoluble surfactant and gravity on the linear stability of a two-layer Couette flow in a horizontal channel are investigated. The inertialess instability regimes are studied for arbitrary wavelengths and with no simplifying requirements on the system parameters: the ratio of thicknesses of the two fluid layers; the viscosity ratio; the base shear rate; the Marangoni number $Ma$; and the Bond number $Bo$. As was established in the first part of this investigation (Frenkel, Halpern & Schweiger, J. Fluid Mech., vol. 863, 2019, pp. 150–184), a quadratic dispersion equation for the complex growth rate yields two, largely continuous, branches of the normal modes, which are responsible for the flow stability properties. This is consistent with the surfactant instability case of zero gravity studied in Halpern & Frenkel (J. Fluid Mech., vol. 485, 2003, pp. 191–220). The present paper focuses on the mid-wave regimes of instability, defined as those having a finite interval of unstable wavenumbers bounded away from zero. In particular, the location of the mid-wave instability regions in the ($Ma$, $Bo$)-plane, bounded by their critical curves, depending on the other system parameters, is considered. The changes of the extremal points of these critical curves with the variation of external parameters are investigated, including the bifurcation points at which new extrema emerge. Also, it is found that for the less unstable branch of normal modes, a mid-wave interval of unstable wavenumbers may sometimes coexist with a long-wave one, defined as an interval having a zero-wavenumber endpoint.

A linear stability analysis of a two-layer plane Couette flow of two immiscible fluid layers with different densities, viscosities and thicknesses, bounded by two infinite parallel plates moving at a constant relative velocity to each other, with an insoluble surfactant monolayer along the interface and in the presence of gravity is carried out. The normal modes approach is applied to the equations governing flow disturbances in the two layers. These equations, together with boundary conditions at the plates and the interface, yield a linear eigenvalue problem. When inertia is neglected the velocity amplitudes are the linear combinations of certain hyperbolic functions, and a quadratic dispersion equation for the increment, that is the complex growth rate, is obtained, where coefficients depend on the aspect ratio, the viscosity ratio, the basic velocity shear, the Marangoni number $Ma$ that measures the effects of surfactant and the Bond number $Bo$ that measures the influence of gravity. An extensive investigation is carried out that examines the stabilizing or destabilizing influences of these parameters. Since the dispersion equation is quadratic in the growth rate, there are two continuous branches of the normal modes: a robust branch that exists even with no surfactant, and a surfactant branch that, to the contrary, vanishes when $Ma\downarrow 0$. Regimes have been uncovered with crossings of the two dispersion curves, their reconnections at the point of crossing and separations as $Bo$ changes. Due to the availability of the explicit forms for the growth rates, in many instances the numerical results are corroborated with analytical asymptotics.

A horizontal channel flow of two immiscible fluid layers with different densities, viscosities and thicknesses, subject to vertical gravitational forces and with an insoluble surfactant monolayer present at the interface, is investigated. The base Couette flow is driven by the uniform horizontal motion of the channel walls. Linear and nonlinear stages of the (inertialess) surfactant and gravity dependent long-wave instability are studied using the lubrication approximation, which leads to a system of coupled nonlinear evolution equations for the interface and surfactant disturbances. The (inertialess) instability is a combined result of the surfactant action characterized by the Marangoni number $Ma$ and the gravitational effect corresponding to the Bond number $Bo$ that ranges from $-\infty$ to $\infty$ . The other parameters are the top-to-bottom thickness ratio $n$ , which is restricted to $n\geqslant 1$ by a reference frame choice, the top-to-bottom viscosity ratio $m$ and the base shear rate $s$ . The linear stability is determined by an eigenvalue problem for the normal modes, where the complex eigenvalues (determining growth rates and phase velocities) and eigenfunctions (the amplitudes of disturbances of the interface, surfactant, velocities and pressures) are found analytically by using the smallness of the wavenumber. For each wavenumber, there are two active normal modes, called the surfactant and the robust modes. The robust mode is unstable when $Bo/Ma$ falls below a certain value dependent on $m$ and $n$ . The surfactant branch has instability for $m<1$ , and any $Bo$ , although the range of unstable wavenumbers decreases as the stabilizing effect of gravity represented by $Bo$ increases. Thus, for certain parametric ranges, even arbitrarily strong gravity cannot completely stabilize the flow. The correlations of vorticity-thickness phase differences with instability, present when gravitational effects are neglected, are found to break down when gravity is important. The physical mechanisms of instability for the two modes are explained with vorticity playing no role in them. This is in marked contrast to the dynamical role of vorticity in the mechanism of the well-known Yih instability due to effects of inertia, and is contrary to some earlier literature. Unlike the semi-infinite case that we previously studied, a small-amplitude saturation of the surfactant instability is possible in the absence of gravity. For certain $(m,n)$ -ranges, the interface deflection is governed by a decoupled Kuramoto–Sivashinsky equation, which provides a source term for a linear convection–diffusion equation governing the surfactant concentration. When the diffusion term is negligible, this surfactant equation has an analytic solution which is consistent with the full numerics. Just like the interface, the surfactant wave is chaotic, but the ratio of the two waves turns out to be constant.

The historicity of books – their role as a force in history – has been addressed in post-war literary studies from different perspectives and across various disciplines. Nevertheless, the scholarship on the history of the book in medieval Islam is still relatively sparse, even though this society underwent a thorough process of textualization. But even authors who do consider the social and cultural role of books in medieval Islam look only at the production and consumption of Arabic books within the boundaries of Muslim society, relying on Islamic sources which reflect mainly the courtly milieu of scribes and secretariats. None discuss books produced and consumed by the religious minorities that were an indispensable part of this society, and none have made use of the abundant Genizah documents as source material. In the present programmatic article, I call attention to the many book lists found in the Cairo Genizah and to their potential as significant tools for developing a better understanding of the cultural and social history of the medieval Islamicate world.