Multilayer metal/metal-oxide diffractive structure for photonic temperature sensing

We designed and fabricated multilayer metal/metal-oxide surface relief diffractive grating structures by growing alternating Pt and SnO(x) layers. Optical interrogation at 633 nm reveals the temperature dependence of their reflection and transmission diffractive effects. This function is explored here in the context of a remote, spatially localized, photonic temperature sensing operation, achieving sensitivity of 10% per °C for the zeroth-order in the transmission mode. The experimental demonstration is found to be in good agreement with the results of rigorous coupled wave analysis of the composite metal/metal-oxide element.     

The D-optimal saturated designs of order 22

This paper attempts to prove the D-optimality of the saturated designs X${}^1$ and X${}^{11}$ of order 22, already existing in the current literature. The corresponding non-equivalent information matrices M${}^1$=(X${}^1$)${}^T$X${}^1$ and M${}^{11}$=(X${}^{11}$)${}^T$X${}^{11}$ have the maximum determinant. Within the application of a specific procedure, all symmetric and positive definite matrices M of order 22 with determinant the square of an integer and $\ge$det(M${}^1$) are constructed. This procedure has indicated that there are 26 such non-equivalent matrices M, for 24 of which the non-existence of designs X such that X${}^T$X =M is proved. The remaining two matrices M are the information matrices M${}^1$ and M${}^{11}$.     

Multiple recurrence and convergence for hardy sequences of polynomial growth

We study the limiting behavior of multiple ergodic averages involving sequences of integers that satisfy some regularity conditions and have polynomial growth. We show that for “typical” choices of Hardy field functions a(t) with polynomial growth, the averages

${1 \over N}\sum\nolimits_{n = 1}^N {{f_1}({T^{[a(n)]}}x) \cdots {f_\ell }({T^{\ell [a(n)]}}x)} $

converge in mean and we determine their limit. For example, this is the case if a(t) = t ^3/2, t log t, or t ² + (log t)². Furthermore, if {a ₁(t), …, a _? (t)} is a “typical” family of logarithmico-exponential functions of polynomial growth, then for every ergodic system, the averages

${1 \over N}\sum\nolimits_{n = 1}^N {{f_1}({T^{[{a_1}(n)]}}x) \cdots {f_\ell }({T^{[{a_\ell }(n)]}}x)} $

converge in mean to the product of the integrals of the corresponding functions. For example, this is the case if the functions a _i (t) are given by different positive fractional powers of t. We deduce several results in combinatorics. We show that if a(t) is a non-polynomial Hardy field function with polynomial growth, then every set of integers with positive upper density contains arithmetic progressions of the form {m,m + [a(n)], …, m + ?[a(n)]}. Under suitable assumptions, we get a related result concerning patterns of the form {m,m + [a ₁(n)], …,m + [a _? (n)]}.

     

Crystallization and Physical Ageing of Poly (2-vinyl pyridine)-b-poly(ethylene oxide) Diblock Copolymers

Summary: A set of melt miscible Poly(2-vinyl pyridine)-b-Poly(ethylene oxide) (P2VP-b-PEO) block copolymers of different compositions were studied. Transmission electron microscopy shows phase separation in the materials during the crystallization process of the PEO block as crystalline lamellae are observed for all compositions evaluated. The isothermal crystallization kinetics of PEO is progressively retarded as the P2VP content in the copolymer increases, since P2VP hinders molecular mobility in the miscible amorphous phase. Polarized light optical microscopy demonstrated that the glassy P2VP block has a negative effect on the secondary nucleation of the PEO. Finally, physical ageing experiments performed in the glassy state of the amorphous mixed phase, at different ageing times, demonstrated that a nucleating effect can be induced in the glassy state as a consequence of the reorganization of the amorphous regions. This nucleating effect significantly alters the cold crystallization rate upon subsequent heating above the glass transition temperature.     

The polynomial multidimensional Szemerédi Theorem along shifted primes

If $\vec q_1 ,...,\vec q_m $ : ? → ? ^? are polynomials with zero constant terms and E ? ? ^? has positive upper Banach density, then we show that the set E ∩ (E ? $\vec q_1 $ (p ? 1)) ∩ … ∩ (E ? $\vec q_m $ (p ? 1)) is nonempty for some prime p. We also prove mean convergence for the associated averages along the prime numbers, conditional to analogous convergence results along the full integers. This generalizes earlier results of the authors, of Wooley and Ziegler, and of Bergelson, Leibman and Ziegler.     

Jamming and crystallization in athermal polymer packings

Dense packings of chains of hard spheres possess characteristic features that do not have a counterpart in corresponding packings of monomeric spheres especially near the maximally random jammed (MRJ) state. From the modelling perspective the additional requirement that spheres keep their connectivity while maximizing the occupied volume fraction imposes severe constraints on generation algorithms of dense chain configurations. The extremely sluggish dynamics imposed by the uncrossability of chains precludes the use of deterministic or stochastic dynamics to generate all but dilute polymer packings. As a viable alternative, especially tailored chain-connectivity-altering Monte Carlo (MC) algorithms have been developed that bypass this kinetic hindrance and have actually been able to produce packings of hard-sphere chains in a volume fraction range spanning from infinite dilution up to the MRJ state. Such very dense athermal polymer packings share a number of structural features with packings of monomeric hard spheres, but also display unique characteristics due to the constraints imposed by connectivity. We give an overview of the most relevant results of our recent modeling work on packings of freely-jointed chains of tangent hard spheres about the MRJ state, local structure, chain dimensions and their scaling with density, topological constraints in the form of entanglements and knots, contact network at jamming, and entropically driven crystallization.     

On the Structure of ∞-Harmonic Maps

Let H ∈ C ²(? ^N×n ), H ≥ 0. The PDE system arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E _∞(u, Ω) = ‖H(Du)‖ _{L ^∞(Ω)} defined on maps u: Ω ? ? ⁿ  → ? ^N . (1) first appeared in the author's recent work. The scalar case though has a long history initiated by Aronsson. Herein we study the solutions of (1) with emphasis on the case of n = 2 ≤ N with H the Euclidean norm on ? ^N×n , which we call the “∞-Laplacian”. By establishing a rigidity theorem for rank-one maps of independent interest, we analyse a phenomenon of separation of the solutions to phases with qualitatively different behaviour. As a corollary, we extend to N ≥ 2 the Aronsson-Evans-Yu theorem regarding non existence of zeros of |Du| and prove a maximum principle. We further characterise all H for which (1) is elliptic and also study the initial value problem for the ODE system arising for n = 1 but with H(·, u, u′) depending on all the arguments.     

On‐Surface Reactive Planarization of Pt(II) Complexes

A series of Pt(II) complexes with tetradentate luminophores has been designed, synthesized, and deposited on coinage metal surfaces with the aim to produce highly planar self‐assembled monolayers. Low‐temperature scanning tunneling microscopy (STM) and density functional theory (DFT) calculations reveal a significant initial nonplanarity for all complexes. A subsequent metal‐catalyzed separation of the nonplanar moiety at the bridging unit via the scission of a C?N bond is observed, leaving behind a largely planar core complex. The activation barrier of this bond scission process is found to depend strongly on the chemical nature of both bridging group and coordination plane, and to increase from Cu(111) through Ag(111) to Au(111).     

Weyl’s Type Estimates on the Eigenvalues of Critical Schrödinger Operators

We consider on a bounded domain \(\Omega \subset {\mathbb{R}}^N\) , the Schrödinger operator ? Δ ? V supplemented with Dirichlet boundary solutions. The potential V is either the critical inverse square potential V(x) = (N ? 2)²/4|x|^?2 or the critical borderline potential V(x) =  (1/4)dist(x, ?Ω)^?2. We present explicit asymptotic estimates on the eigenvalues of the critical Schrödinger operator in each case, based on recent results on improved Hardy–Sobolev type inequalities.     

Iodine-transfer polymerization and CuAAC “click” chemistry: A versatile approach toward poly(vinylidene fluoride)-based amphiphilic triblock terpolymers

This study presents the synthesis and properties of linear PVDF-based amphiphilic triblock terpolymers with PS and PEO, [PVDF-b-PS-b-PEO], by adopting a procedure that involves: (a) iodine-transfer polymerization (ITP) of VDF with 1-iodoperfluorohexane (C₆F₁₃I) serving as chain-transfer agent (CTA) to afford C₆F₁₃-PVDF-I, (b) ITP of styrene with the C₆F₁₃-PVDF-I macromolecular-CTA to obtain C₆F₁₃-PVDF-b-PS-I diblock copolymer, (c) end-group exchange from iodo- to azido-group by nucleophilic substitution reaction with NaN_3, and (d) copper-catalyzed azide-alkyne cycloaddition (CuAAC) with alkyne-terminated PEO to achieve C₆F₁₃-PVDF-b-PS-b-PEO triblock terpolymers. The ¹H and ¹⁹F NMR spectroscopy confirmed the presence of all blocks, while gel permeation chromatography traces showed the living nature of ITP technique. The self-assembly of these terpolymers was investigated in films (atomic force microscopy and DSC), as well as in aqueous and organic solvents (DLS). The analysis of crystalline phases based on the FTIR spectroscopy indicated the conversion of PVDF α-phase into α + β-phases and β + γ-phases upon the incorporation of PS and PEO blocks, respectively. The synthesized amphiphilic copolymers were evaluated (fluorescence spectroscopy) as carriers of small hydrophobic molecules in water. © 2019 Wiley Periodicals, Inc. J. Polym. Sci. 2020 , 58, 163–171