Quasi-Newton methods for constrained nonlinear systems: complexity analysis and applications

We address the solution of constrained nonlinear systems by new linesearch quasi-Newton methods. These methods are based on a proper use of the projection map onto the convex constraint set and on a derivative-free and nonmonotone linesearch strategy. The convergence properties of the proposed methods are presented along with a worst-case iteration complexity bound. Several implementations of the proposed scheme are discussed and validated on bound-constrained problems including gas distribution network models. The results reported show that the new methods are very efficient and competitive with an existing affine-scaling procedure.     

A reduced Newton method for constrained linear least-squares problems

We propose an iterative method that solves constrained linear least-squares problems by formulating them as nonlinear systems of equations and applying the Newton scheme. The method reduces the size of the linear system to be solved at each iteration by considering only a subset of the unknown variables. Hence the linear system can be solved more efficiently. We prove that the method is locally quadratic convergent. Applications to image deblurring problems show that our method gives better restored images than those obtained by projecting or scaling the solution into the dynamic range.     

Photochemical reaction of N,N-dimethyl-4-chloroaniline with dienes: new synthetic paths via a phenyl cation

The irradiation of N,N-dimethyl-4-chloroaniline in the presence of open-chain dienes in acetonitrile leads to addition of the aminophenyl and chloro groups across one of the double bonds; transannular cyclization takes place with cyclic dienes, leading to an arylnortricyclene from norbornadiene and to 1-arylbicyclo[3.3.0]octanes from 1,5-cyclooctadiene. The reaction proceeds by photoheterolysis of the chloroaniline to yield the 4-aminophenyl cation and addition to a CdoublebondC . The chemistry of the adduct cation depends on structure and medium, involving ion pairs in MeCN and solvated ions in CF(3)CH(2)OH. In the latter solvent, formation of ethers from open-chain alkenes is accompanied by Wagner-Meerwein hydride shift. In acetonitrile, the cation from cyclooctadiene partitions between deprotonation and Ritter addition, while the one from norbornadiene is reduced; both cations undergo nucleophilic addition in trifluoroethanol. The relevance of these cationic reactions under unusually mild conditions is discussed.     

How solvent controls electronic energy transfer and light harvesting

The way that solvent (or host medium) modifies the rate of electronic energy transfer (EET) has eluded researchers for decades. By applying quantum chemical methods that account for the way solvent (in general any host medium including liquid, solid, or protein, etc.) responds to the interaction between transition densities, we quantify the solvent screening. We find that it attains a striking exponential attenuation at separations less than about 20 A, thus interpolating between the limits of no apparent screening and a significant attenuation of the EET rate. That observation reveals a previously unidentified contribution to the distance dependence of the EET rate.     

Conformations of banana-shaped molecules studied by 2H NMR spectroscopy in liquid crystalline solvents

ClPbis11BB and Pbis11BB, two banana-shaped mesogens differing by a chlorine substituent on the central phenyl ring, show a nematic and a B2 phase, respectively. To obtain information on the structural features responsible for their different mesomorphic behavior, a study of the preferred conformations of these mesogens has been performed by NMR spectroscopy in two nematic media (Phase IV and ZLI1167), which should mimic the environment of the molecules in their own mesophases, avoiding problems of sample alignment by a magnetic field. To this aim, 2H NMR experiments have been performed on selectively deuterated isotopomers of ClPbis11BB and Pbis11BB and of two parent molecules, ClPbisB and PbisB, assumed as models in previous theoretical and experimental conformational studies. We found that only a limited number of conformations is compatible with experimental data, often very different from those inferred from theoretical calculations in vacuo, indicating a strong influence of the liquid crystalline environment on molecular conformation. No significant differences between chlorinated and non-chlorinated molecules were found, this suggesting that chlorine does not change the molecular conformational equilibrium, as previously proposed.     

Ligand-Induced Chirality in ClMBA2SnI4 2D Perovskite**

Chiral perovskites possess a huge applicative potential in several areas of optoelectronics and spintronics. The development of novel lead-free perovskites with tunable properties is a key topic of current research. Herein, we report a novel lead-free chiral perovskite, namely (R/S−)ClMBA₂SnI₄ (ClMBA=1-(4-chlorophenyl)ethanamine) and the corresponding racemic system. ClMBA₂SnI₄ samples exhibit a low band gap (2.12 eV) together with broad emission extending in the red region of the spectrum (∼1.7 eV). Chirality transfer from the organic ligand induces chiroptical activity in the 465–530 nm range. Density functional theory calculations show a Rashba type band splitting for the chiral samples and no band splitting for the racemic isomer. Self-trapped exciton formation is at the origin of the large Stokes shift in the emission. Careful correlation with analogous lead and lead-free 2D chiral perovskites confirms the role of the symmetry-breaking distortions in the inorganic layers associated with the ligands as the source of the observed chiroptical properties providing also preliminary structure-property correlation in 2D chiral perovskites.     

Amphiphilicity-Controlled Localization of Red Emitting Bicationic Fluorophores in Tumor Cells Acting as Bio-Probes and Anticancer Drugs

Small organic molecules arouse lively interest for their plethora of possible biological applications, such as anticancer therapy, for their ability to interact with nucleic acids, or bioimaging, thanks to their fluorescence emission. Here, a panchromatic series of styryl-azinium bicationic dyes, which have already proved to exhibit high water-solubility and significant red fluorescence in water, were investigated through spectrofluorimetric titrations to assess the extent of their association constants with DNA and RNA. Femtosecond-resolved transient absorption spectroscopy was also employed to characterize the changes in the photophysical properties of these fluorophores upon interaction with their biological targets. Finally, in vitro experiments conducted on tumor cell lines revealed that some of the bicationic fluorophores had a peculiar localization within cell nuclei exerting important antiproliferative effects, others were instead found to localize in the cytoplasm without leading to cell death, being useful to mark specific organelles in light of live cell bioimaging. Interestingly, this molecule-dependent behavior matched the different amphiphilicity featured by these bioactive compounds, which are thus expected to be caught in a tug-of-war between lipophilicity, ensured by the presence of aromatic rings and needed to pass cell membranes, and hydrophilicity, granted by charged groups and necessary for stability in aqueous media.     

On a Family of Critical Growth-Fragmentation Semigroups and Refracted Lévy Processes

The growth-fragmentation equation models systems of particles that grow and split as time proceeds. An important question concerns the large time asymptotic of its solutions. Doumic and Escobedo (Kinet. Relat. Models, 9(2):251–297, [12]) observed that when growth is a linear function of the mass and fragmentations are homogeneous, the so-called Malthusian behaviour fails. In this work we further analyse the critical case by considering a piecewise linear growth, namely

$$c(x) = \textstyle\begin{cases} a_{{-}} x \quad x < 1 \\ a_{{+}} x \quad x \geq 1, \end{cases} $$

with \(0 < a_{{+}} < a_{{-}}\). We give necessary and sufficient conditions on the coefficients ensuring the Malthusian behaviour with exponential speed of convergence to an asymptotic profile, and also provide an explicit expression of the latter. Our approach relies crucially on properties of so-called refracted Lévy processes that arise naturally in this setting.