Towards in Silico Liquid Crystals. Realistic Transition Temperatures and Physical Properties for n‐Cyanobiphenyls via Molecular Dynamics Simulations

We study the important n‐cyanobiphenyl (with n= 4–8) series of mesogens, using modelling and molecular dynamics simulations. We are able to obtain spontaneously ordered nematics upon cooling isotropic samples of 250 molecules. By using the united‐atom force field developed herein, we show that the experimental isotropic–nematic transition temperatures are reproduced within 4 K, allowing a molecular‐level interpretation of the odd–even effect along the series. Other properties, like densities, orientational order parameters and NMR residual dipolar couplings are also reproduced well, demonstrating the feasibility of predictive in silico modelling of nematics from the molecular structure.     

Remarks on the stability of mass minimizing currents in the Monge-Kantorovich problem

The Monge-Kantorovich problem is equivalent to the problem of finding 1-currents with fixed boundary and minimal mass. We address the question of the stability for the mass minimizing currents. In particular, we state a Γ-convergence result. We provide proofs relying just on basic properties of currents and on the notion of flat norm.     

Non-trapping magnetic fields and Morrey-Campanato estimates for Schrödinger operators

We prove some uniform in ? a priori estimates for solutions of the equation

     

Electrocrystallization of Phase I, CuTCNQ (TCNQ = 7,7,8,8-Tetracyanoquinodimethane), on indium tin oxide and boron-doped diamond electrodes

The electrochemical reduction of TCNQ to TCNQ*- in acetonitrile in the presence of [Cu(MeCN)4]+ has been undertaken at boron-doped diamond (BDD) and indium tin oxide (ITO) electrodes. The nucleation and growth process at BDD is similar to that reported previously at metal electrodes. At an ITO electrode, the electrocrystallization of more strongly adhered, larger, branched, needle-shaped phase I CuTCNQ crystals is detected under potential step conditions and also when the potential is cycled over the potential range of 0.7 to -0.1 V versus Ag/AgCl (3 M KCl). Video imaging can be used at optically transparent ITO electrodes to monitor the growth stage of the very large branched crystals formed during the course of electrochemical experiments. Both in situ video imaging and ex situ X-ray diffraction and scanning electron microscopy (SEM) data are consistent with the nucleation of CuTCNQ taking place at a discrete number of preferred sites on the ITO surface. At BDD electrodes, ex situ optical images show that the preferential growth of CuTCNQ occurs at the more highly conducting boron-rich areas of the electrode, within which there are preferred sites for CuTCNQ formation.     

Spectral measurement of the caesium D(2) line with a tunable heterodyne interferometer

The optical properties of a caesium atomic beam driven on a resonant hyperfine transition in the D(2) line were studied as a function of the probe laser frequency. Using a third off-resonant laser system, a heterodyne interferometer allowed simultaneous absorption and phase shift measurements of either the probe or the coupling laser. The signal features of the probe and coupling laser transmitted intensities showed strong differences in the vicinity of the hyperfine transitions excited by the probe laser. Regular absorption signals and electromagnetically induced transparency were found in either transmitted intensities. Furthermore, light induced birefringence of the probe laser was measured.     

Counteranion dependent protonation and aggregation of tetrakis(4-sulfonatophenyl)porphyrin in organic solvents

The tetrabutylammonium salt of 5,10,15,20-tetrakis(4-sulfonatophenyl)porphyrin (TPPS) is soluble in dichloromethane, and the general properties of this compound have been investigated as function of various added acids HX (X = Cl, Br, I, CF(3)COO, CF(3)SO(3), TFPB) through UV-vis absorption spectroscopy, steady state fluorescence emission, and resonance light-scattering (RLS) techniques. Upon addition of HX, the initial monomeric free base TPPS is readily converted in an aggregated species, whose spectroscopic features are independent of the nature of the counteranion X. All the spectroscopic evidence suggest a J-type arrangement of chromophores in this aggregate, involving strong hydrogen bonds, electrostatic, and dispersive interactions. In the specific case of chloride and bromide, in the presence of a TBAX excess, the addition of the corresponding acid leads to a monomeric ion-pair between the TBA cations and the diacid TPPS, whose central core is strongly interacting with the halide. On further increasing the acid concentration in these latter solutions, fully protonated species are formed that eventually start to aggregate.     

Elliptic operators with unbounded diffusion coefficients in L 2 spaces with respect to invariant measures

We study the self-adjoint and dissipative realization A of a second order elliptic differential operator with unbounded regular coefficients in , where μ(dx) = ρ (x)dx is the associated invariant measure. We prove a maximal regularity result under suitable assumptions, that generalize the well known conditions in the case of constant diffusion part. Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday     

On squares in polynomial products

Let ${f(X) \in \mathbb {Z}[X]}$ be an irreducible polynomial of degree D ≥ 2 and let N be a sufficiently large positive integer. We estimate the number of positive integers n ≤ N such that the product $$F(n) = \prod\limits_{k =1}^n f(k)$$ is a perfect square. We also consider more general questions and give a lower bound on the number of distinct quadratic fields of the form ${\mathbb {Q}(\sqrt{F(n)})}$ , n  = M + 1, ... , M + N.     

Ergodicity and Kolmogorov Equations for Dissipative SPDEs with Singular Drift: a Variational Approach

Potential Analysis - We prove existence of invariant measures for the Markovian semigroup generated by the solution to a parabolic semilinear stochastic PDE whose nonlinear drift term satisfies...