Phase field modeling of hysteresis in sessile drops

We propose a novel approach to describe wetting of plane solid surfaces by liquid drops. A two-dimensional nonconserved phase field variable is employed to distinguish between wetted and nonwetted regions on the surface. The imbalance in the Young's force provides for the exchange of relative stability of the two phases. The three-phase contact line tension arises from the gradient energy and contact angle hysteresis from the kinetic coefficient. Using this theory, we discuss contact angle hysteresis on chemically heterogeneous surfaces. We show significant departure from the classical Cassie theory, which is attributed to defect pinning of the continuous triple line.     

On a class of nonlinear integral equations

In this paper we consider abstract equations of the typeK _ν ν +ν =w ₀, in a closed convex subset of a separable Hilbert spaceH. For eachv in the closed convex subset,K _v :H →H is a bounded linear map. As an application of our abstract result we obtain an existence result for nonlinear integral equations of the typeν(s)+ν(s)∫ ₀ ¹ k(s,t)ν(t)dt =W ₀(s) in the spaceL ² [0,1].     

Methanol diffusion rates through the anode diffusion layer in direct methanol fuel cells from limiting current measurements

Metal foams may be used in direct methanol fuel cells to feed reactants to the catalyst layer and to collect current from the resulting electrochemical reaction. Although the mass transfer from the metal foam to the underlying gas diffusion layer (GDL) is diffusion-dominated, it is found that at a fixed methanol concentration, the limiting current density increases with increasing methanol flow rates. This unexpected result is attributed to the more efficient removal of product CO₂ from the GDL. A methodology is developed to estimate the effective diffusion coefficient of methanol in the anode diffusion layer from limiting current density measurements, and to extract the fraction of GDL volume occupied by CO₂.     

Bifurcation and symmetry breaking for a class of semilinear elliptic equations in an annulus

In this paper we consider the problem $$\left\{ \begin{array}{ll} -\Delta u=u^p+\lambda u & \quad\hbox{ in }A,\\ u > 0&\quad \hbox{ in }A,\\ u=0 &\quad \hbox{ on }\partial A, \end{array}\right. $$ where A is an annulus of ${\mathbb{R}^N,N\ge2}$ and p?>?1. We prove bifurcation of nonradial solutions from the radial solution in correspondence of a sequence of exponents {p _k } and for expanding annuli.     

Functional GPCR microarrays

This paper describes G-protein-coupled receptor (GPCR) microarrays on porous glass substrates and functional assays based on the binding of a europium-labeled GTP analogue. The porous glass slides were made by casting a glass frit on impermeable glass slides and then coating with gamma-aminopropyl silane (GAPS). The emitted fluorescence was captured on an imager with a time-gated intensified CCD detector. Microarrays of the neurotensin receptor 1, the cholinergic receptor muscarinic 2, the opioid receptor mu, and the cannabinoid receptor 1 were fabricated by pin printing. The selective agonism of each of the receptors was observed. The screening of potential antagonists was demonstrated using a cocktail of agonists. The amount of activation observed was sufficient to permit determinations of EC50 and IC50. Such microarrays could potentially streamline drug discovery by helping integrate primary screening with selectivity and safety screening without compromising the essential functional information obtainable from cellular assays.     

Entanglement dynamics in two-qubit open system interacting with a squeezed thermal bath via quantum nondemolition interaction

We analyze the dynamics of entanglement in a two-qubit systeminteracting with an initially squeezed thermal environment via aquantum nondemolition system-reservoir interaction, with the systemand reservoir assumed to be initially separable. We compare andcontrast the decoherence of the two-qubit system in the case wherethe qubits are mutually close-by (`collective regime’) or distant(`localized regime’) with respect to the spatial variation of theenvironment. Sudden death of entanglement (as quantified byconcurrence) is shown to occur in the localized case rather than inthe collective case, where entanglement tends to `ring down’.A consequence of the QND character of the interaction is that thetime-evolved fidelity of a Bell state never falls below \(1/\sqrt{2}\),a fact that is useful for quantum communication applicationslike a quantum repeater. Usinga novel quantification of mixed state entanglement, we show thatthere are noise regimes where even though entanglementvanishes, the state is still available forapplications like NMR quantum computation, because of the presenceof a pseudo-pure component.     

Symmetries in the representation of grain boundary-plane distributions

Symmetries play a crucial role in the theoretical analysis and visualization of the five macroscopic grain boundary parameters, including the misorientation (three parameters) and the orientation of the boundary-plane (two parameters). The symmetry aspects of the misorientation spaces are very well documented and in this article all possible boundary-plane symmetries are enumerated for the 32 crystallographic point groups. It is observed that the boundary-plane spaces exhibit a wide variety of point group symmetries, which depend both on the crystallographic point group and on the corresponding misorientation (i.e. location in the fundamental zone). The list of symmetries presented here should serve as a guide for graphical representations of not only the distributions of boundary-plane orientations but also for the representation of boundary-plane related properties such as energy, mobility etc.     

RCM/PCC oxidation strategy for synthesis of functionalized cyclic α,β-unsaturated lactones: synthesis of (+)-triacetoxygoniotriol and its diastereomers

A novel methodology leading to the synthesis of (+)-triacetoxygoniotriol 2 from d-glucose is described. Construction of the core six-membered α,β-unsaturated lactone moiety involved ring closing metathesis (RCM) followed by a PCC oxidation. Later exploiting the pseudo-symmetry of d-glucose three other diastereomers of triacetoxygoniotriol were synthesized using the developed methodology.     

Statistical Mechanics and the Climatology of the Arctic Sea Ice Thickness Distribution

We study the seasonal changes in the thickness distribution of Arctic sea ice, g(h), under climate forcing. Our analytical and numerical approach is based on a Fokker–Planck equation for g(h) (Toppaladoddi and Wettlaufer in Phys Rev Lett 115(14):148501, 2015), in which the thermodynamic growth rates are determined using observed climatology. In particular, the Fokker–Planck equation is coupled to the observationally consistent thermodynamic model of Eisenman and Wettlaufer (Proc Natl Acad Sci USA 106:28–32, 2009). We find that due to the combined effects of thermodynamics and mechanics, g(h) spreads during winter and contracts during summer. This behavior is in agreement with recent satellite observations from CryoSat-2 (Kwok and Cunningham in Philos Trans R Soc A 373(2045):20140157, 2015). Because g(h) is a probability density function, we quantify all of the key moments (e.g., mean thickness, fraction of thin/thick ice, mean albedo, relaxation time scales) as greenhouse-gas radiative forcing, \(\Delta F_0\), increases. The mean ice thickness decays exponentially with \(\Delta F_0\), but much slower than do solely thermodynamic models. This exhibits the crucial role that ice mechanics plays in maintaining the ice cover, by redistributing thin ice to thick ice-far more rapidly than can thermal growth alone.     

Homological invariants of modules over contracting endomorphisms

It is proved that when R is a local ring of positive characteristic, \({\phi\colon R{\to} R}\) is its Frobenius endomorphism, and some non-zero finite R-module has finite flat dimension or finite injective dimension for the R-module structure induced through \({\phi}\) , then R is regular. This broad generalization of Kunz’s characterization of regularity in positive characteristic is deduced from a theorem concerning a local ring R with residue field of k of arbitrary characteristic: If \({\phi}\) is a contracting endomorphism of R, then the Betti numbers and the Bass numbers over \({\phi}\) of any non-zero finitely generated R-module grow at the same rate, on an exponential scale, as the Betti numbers of k over R.