Invariant Measures for a Stochastic Kuramoto–Sivashinsky Equation

Abstract

For the one-dimensional Kuramoto–Sivashinsky equation with random forcing term, existence and uniqueness of solutions is proved. Then, the Markovian semigroup is well defined; its properties are analyzed in order to provide sufficient conditions for existence and uniqueness of invariant measures for this stochastic equation. Finally, regularity results are presented.     

Invariant Measures of Gaussian Type for 2D Turbulence

Gaussian measures ?? ^??,?? are associated to some stochastic 2D models of turbulence. They are Gibbs measures constructed by means of an invariant quantity of the system depending on some parameter ?? (related to the 2D nature of the fluid) and the viscosity???. We prove the existence and the uniqueness of the global flow for the stochastic viscous system; moreover the measure ?? ^??,?? is invariant for this flow and is the unique invariant measure. Finally, we prove that the deterministic inviscid equation has a ?? ^??,?? -stationary solution (for any ??>0).     

High-order-harmonic generation and superradiance in a seeded free-electron laser

Higher order harmonic generation in a free-electron laser amplifier operating in the superradiant regime [R. H. Dicke, Phys. Rev. 93, 99 (1954).] has been observed. Superradiance has been induced by seeding a single-pass amplifier with the second harmonic of a Ti:sapphire laser, generated in a β-Barium borate crystal, at seed intensities comparable to the free-electron laser saturation intensity. Pulse energy and spectral distributions of the harmonics up to the 11th order have been measured and compared with simulations.     

Improved T2* assessment in liver iron overload by magnetic resonance imaging

In the clinical MRI practice, it is common to assess liver iron overload by T2* multi-echo gradient-echo images. However, there is no full consensus about the best image analysis approach for the T2* measurements. The currently used methods involve manual drawing of a region of interest (ROI) within MR images of the liver. Evaluation of a representative liver T2* value is done by fitting an appropriate model to the signal decay within the ROIs vs. the echo time. The resulting T2* value may depend on both ROI placement and choice of the signal decay model. The aim of this study was to understand how the choice of the analysis methodology may affect the accuracy of T2* measurements. A software model of the iron overloaded liver was inferred from MR images acquired from 40 thalassemia major patients. Different image analysis methods were compared exploiting the developed software model. Moreover, a method for global semiautomatic T2* measurement involving the whole liver was developed. The global method included automatic segmentation of parenchyma by an adaptive fuzzy-clustering algorithm able to compensate for signal inhomogeneities. Global liver T2* value was evaluated using a pixel-wise technique and an optimized signal decay model. The global approach was compared with the ROI-based approach used in the clinical practice. For the ROI-based approach, the intra-observer and inter-observer coefficients of variation (CoVs) were 3.7% and 5.6%, respectively. For the global analysis, the CoVs for intra-observers and inter-observers reproducibility were 0.85% and 2.87%, respectively. The variability shown by the ROI-based approach was acceptable for use in the clinical practice; however, the developed global method increased the accuracy in T2* assessment and significantly reduced the operator dependence and sampling errors. This global approach could be useful in the clinical arena for patients with borderline liver iron overload and/or requiring follow-up studies.     

Nonclassical Pschorr and Sandmeyer Reactions in Pyrazole Series

The diazonium salt derived from 4‐amino‐N,1,3‐trimethyl‐N‐(3‐methyl‐1‐phenyl‐1H‐pyrazol‐5‐yl)‐1H‐pyrazole‐5‐carboxamide ( 14 ) was reacted with a mixture of CuSO₄ and NaCl, with ascorbic acid as an initiator to afford the planar derivative 4,6‐dihydro‐1,4,6,8‐tetramethyl‐3‐phenyldipyrazolo[3,4‐b:4′,3′‐d]pyridin‐5(3H)‐one ( 16 ) and its unexpected isomer 4,6‐dihydro‐3,4,6,8‐tetramethyl‐1‐phenyldipyrazolo[4,3‐b:4′,3′‐d]pyridin‐5(1H)‐one ( 17 ), as well as the epimers (3S,4S)‐ (or (3S,4R)‐) and (3S,4R)‐ (or (3S,4S)‐) 4‐chloro‐2,4‐dihydro‐1′,3′,5,5′‐tetramethyl‐2‐phenylspiro[pyrazole‐3,4′(1′H)‐pyrrolo[3,4‐c]pyrazol]‐6′(5′H)‐one ( 18a and b , respectively). Epimers 18a and b were converted under basic conditions to 4′‐chloro‐N,1,3,3′‐tetramethyl‐1′‐phenyl‐[4,5′‐bi‐1H‐pyrazole]‐5‐carboxamide ( 19 ). The structures of isomers 16 and 17 determined by single‐crystal X‐ray analysis are also reported. Linear dichroism (LD) measurements for the above isomers suggest that 17 intercalates into DNA, and 17 exhibited antiproliferation activity against human NCI‐H460 pulmonary carcinoma cells.     

Drawing parameters optimization for birefringence reduction in optical fibers

The impact of the drawing process on the stress-induced birefringence in optical fiber is experimentally analyzed. By means of the photoelastic tomographic technique, residual internal stresses are measured in fiber samples drawn under different conditions of temperature, drawing tension and speed. From measured residual stress distributions, the stress-induced birefringence and beatlength are mathematically derived and compared, proving that an effective birefringence reduction can be obtained by a proper choice of drawing parameters.     

From crystallographic data to the solution structure of photoreceptors: the case of the AppA BLUF domain

Photoreceptor proteins bind a chromophore, which, upon light absorption, modifies its geometry or its interactions with the protein, finally inducing the structural change needed to switch the protein from an inactive to an active or signaling state. In the Blue Light-Using Flavin (BLUF) family of photoreceptors, the chromophore is a flavin and the changes have been connected with a rearrangement of the hydrogen bond network around it on the basis of spectroscopic changes measured for the dark-to-light conversion. However, the exact conformational change triggered by the photoexcitation is still elusive mainly because a clear consensus on the identity not only of the light activated state but also of the dark one has not been achieved. Here, we present an integrated investigation that combines microsecond MD simulations starting from the two conflicting crystal structures available for the AppA BLUF domain with calculations of NMR, IR and UV-Vis spectra using a polarizable QM/MM approach. Thanks to such a combined analysis of the three different spectroscopic responses, a robust characterization of the structure of the dark state in solution is given together with the uncovering of important flaws of the most popular molecular mechanisms present in the literature for the dark-to-light activation.

With an integrated molecular dynamics and QM/MM strategy we characterize the dark-state structure of a BLUF photoreceptor and ration alize the discrepancy between published crystal structures.     

Exploring a new class of singlet fission fluorene derivatives with high-energy triplets

In this study, we report strong experimental evidence for singlet fission (SF) in a new class of fluorene-based molecules, exhibiting two-branched donor–acceptor structures. The time-resolved spectroscopic results disclose ultrafast formation of a double triplet state (occurring in few picoseconds) and efficient triplet exciton separation (up to 145% triplet yield). The solvent polarity effect and the role of intramolecular charge transfer (ICT) on the SF mechanism have been thoroughly investigated with several advanced spectroscopies. We found that a stronger push–pull character favors SF, as long as the ICT does not act as a trap by opening a competitive pathway. Within the context of other widely-known SF chromophores, the unconventional property of generating high-energy triplet excitons (ca. 2 eV) via SF makes these materials outstanding candidates as photosensitizers for photovoltaic devices.

We found that a stronger push–pull character favours SF, as long as the ICT does not act as a trap. The unique property of generating high-energy triplets (ca. 2 eV) via SF makes these materials outstanding candidates for photovoltaic applications.     

Synthesis of Functionalized Six-Membered-Ring Azahelicenes

Functionalization, namely the introduction of side groups onto the molecular scaffold of a helicene, may have either the purpose of modifying the electronic properties of the parent helicene, e.g., by adding electron-withdrawing or electron-donating groups, or the scope of providing the helicene with a “handle”, which can be reacted to bind the molecule to another molecule or to a solid structure, such as a carbon or metal surface, or again to allow for complexation of the helicene with metal ions. The possible approaches are two-fold: the synthesis of the helicene can be performed using starting materials that already contain a side group, or the side group can be introduced after the synthesis of the parent helicene. As azahelicenes are helicenes bearing one or more nitrogen atom(s) in the molecular framework, parent azahelicenes can be functionalized on carbon atoms by exploiting the presence of the electron-withdrawing nitrogen atom. Moreover, they can be transformed into quaternary salts, whose properties are quite different from those of the parent azahelicenes in terms of the solubility and electronic properties. This review aims to provide a survey of the different synthetic methods available to attain this fascinating class of compounds.     

White-light femtosecond Lidar at 100 TW power level

We characterized the white-light supercontinuum emission by a sub-petawatt laser system in the atmosphere via light detection and ranging measurements. As much as 1 J of supercontinuum is generated in the atmosphere, corresponding to a conversion efficiency of 30 %. This generation occurs at altitudes below 100 m. The high initial beam intensity results in the saturation of the number of self-guided filaments. Therefore, the “photon bath” surrounding the filaments strongly contributes to the white-light generation. These finding is well reproduced by numerical simulations based on the experimental parameters.