Discrete angle rotations of Bi nanoparticles embedded in a Ga matrix

Spontaneous instabilities of nanoparticles are known to be influenced by the temperature, and strongly depend on the particle size. However, it is not clear what is the role of the surrounding material that is in contact with the particle. Here we report on the difference between spontaneous rotations of Bi nanoparticles embedded in amorphous SiO and those embedded in liquid Ga. The phenomenon was studied quantitatively by time resolved transmission electron microscopy using Fourier Transform analysis of highresolution electron microscopy images. While rotations of Bi nanoparticles embedded in amorphous SiO occur by all angles, the rotations of Bi nanoparticles embedded in liquid Ga occur by discrete angles. Our results point quantitatively, for the first time, to the role and importance of the contacting surrounding surface during the rotation of nanoparticles.     

Invariant generalized functions supported on an orbit

We study the space of invariant generalized functions supported on an orbit of the action of a real algebraic group on a real algebraic manifold. This space is equipped with the Bruhat filtration. We study the generating function of the dimensions of the filtras, and give some methods to compute it. To illustrate our methods we compute those generating functions for the adjoint action of GL₃(C). Our main tool is the notion of generalized functions on a real algebraic stack, introduced recently in [Sak16].     

Poly(N‐isopropylacrylamide) Phase Diagrams: Fifty Years of Research

In 1968, Heskins and Guillet published the first systematic study of the phase diagram of poly(N‐isopropylacrylamide) (PNIPAM), at the time a “young polymer” first synthesized in 1956. Since then, PNIPAM became the leading member of the growing families of thermoresponsive polymers and of stimuli‐responsive, “smart” polymers in general. Its thermal response is unanimously attributed to its phase behavior. Yet, in spite of 50 years of research, a coherent quantitative picture remains elusive. In this Review we survey the reported phase diagrams, discuss the differences and comment on theoretical ideas regarding their possible origins. We aim to alert the PNIPAM community to open questions in this reputably mature domain.     

Ion-Interaction Approach: Pressure Effect on the Solubility of Some Minerals in Submarine Brines and Seawater

The pressure dependence of salt solubility in multiple electrolyte solutions was estimated to 1000 atm. The activity coefficients, thermodynamic solubility products, degrees of saturation, and mineral solubility were calculated with high precision only up to 300 atm because of the absence of compressibility data for mixed electrolyte solutions. The ion-interaction approach developed during the last 2 decades allows the prediction of various thermodynamic properties, including volumetric ones for multiple-solute natural solutions. This approach was applied to the estimation of the depth dependence of solubility for certain evaporite minerals in natural brines. The influence of pressure on solubility products, mean activity coefficients, and degrees of saturation of minerals, such as, halite (NaCl), anhydrite (CaSO₄), gypsum (CaSO₄·2 H₂O), celestite (SrSO₄), and barite (BaSO₄) were calculated for in situ depths in the Orca Basin (Gulf of Mexico), the Tyro and Bannock II depressions (the Mediterranean Sea), and for average seawater.     

Causality and strict causality for symmetric bilinear systems

It is shown that if W is a symmetric bilinear operator on a Hilbert resolution space, then the causality and strict causality of W is equivalent to the causality and strict causality of the bipower map $\text{W}\text{?}$ induced by W.     

Martin’s axiom does not imply that every two ℕ1-dense sets of reals are isomorphic

Assuming the consistency of ZFC we prove the claim in the title by showing the consistency with ZFC of: There exists a set of realsA such that every function fromA toA is order preserving on an uncountable set. We prove related results among which is the consistency with ZFC of: Every function from the reals into the reals is monotonic on an uncountable set. I would like to thank the United States-Israel Binational Science Foundation for supporting this research by a grant.     

The chemistry of THPC–urea polymers and relationship to flame retardance on wool and wool–polyester blends. II. Relative flame-retardant efficiency on wool,polyester, and wool-polyester blends

Optimum flame retardance in THPC-urea-type formulations was achieved by approximately 1—0.9 THPC-urea mole ratio and slow urea addition. A phosphonium salt structure is more efficient in flame retarding 100% wool and wool-polyester blends than a phosphine oxide structure. Both structures are equivalent in flame retarding 100% polyester. It is considered probable that a vapor-phase mechanism is predominant in the phosphorus-based flame retardancy of wool, whereas a mixed solid-vapor phase mechanism operates for 100% polyester.