Convergence of solutions for the fractional Cahn–Hilliard system

This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but $C^1$) nonlinearities.     

Study of spatial inhomogeneity in inverted all‐polymer solar cells: Effect of solvent and annealing

The efficiency optimization of bulk heterojunction solar cells requires the control of the local active materials arrangement in order to obtain the best compromise between efficient charge generation and charge collection. Here, we investigate the large scale (10–100 μm) inhomogeneity of the photoluminescence (PL) and the external quantum efficiency (EQE) in inverted all‐polymer solar cells (APSC) with regioregular poly(3‐hexylthiophene) (P3HT):poly(9,9‐dioctylfluorene‐co‐benzothiadiazole) (F8BT) active blends. The morphology and the local active polymer mixing are changed by depositing the active layer from four different solvents and by thermal annealing. The simultaneous PL and EQE mapping allowed us to inspect the effects of local irregularities of active layer thickness, polymer mixing, polymer aggregation on the charge generation and collection efficiencies. In particular, we show that the increase of the solvent boiling point affects the EQE non‐uniformity due to thickness fluctuations, the density non‐uniformity of rrP3HT aggregate phase, and the blend components clustering. The thermal annealing leads to a general improvement of EQE and to an F8BT clustering in all the samples with locally decrease of the EQE. We estimate that the film uniformity optimization can lead to a total EQE improvement between 2.7 and 6.3 times. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 804–813     

Photochemical Bromination of 2,5-Dimethylbenzoic Acid as Key Step of an Improved Alkyne-Functionalized Blue Box Synthesis**

Cyclobis(paraquat-p-phenylene), also known as “blue box”, is a highly electron-deficient macrocycle, widely used as a molecular receptor for small electron-rich molecules. Inserting a reactive functional group onto the molecular structure of this cyclophane is paramount for its inclusion into complex architectures. To this aim, including an alkyne moiety would be ideal, because it can participate in click reactions. However, the synthesis of such alkyne-functionalized cyclophane suffers from several drawbacks: the use of toxic and expensive CCl₄, the need for high-pressure reactors, and overall low yield. We have revised the existing synthesis of this cyclophane derivative bearing an alkyne moiety, to overcome all these limitations. In particular, photochemical radical bromination is adopted to obtain a sensitive intermediate. We demonstrated that the synthesized host molecule can be functionalized via click reactions and take part in radical-radical interactions. Our work makes a key functionalized paraquat macrocycle more accessible, facilitating the development of novel redox-responsive systems.     

Generalised continuation by means of right limits

Several theories have been proposed to generalise the concept of analytic continuation to holomorphic functions of the disc for which the circle is a natural boundary. Elaborating on Breuer-Simon’s work on right limits of power series, Baladi-Marmi-Sauzin recently introduced the notion of renascent right limit and rrl-continuation. We discuss a few examples and consider particularly the classical example of Poincaré simple pole series in this light. These functions are represented in the disc as series of infinitely many simple poles located on the circle; they appear, for instance, in small divisor problems in dynamics. We prove that any such function admits a unique rrl-continuation, which coincides with the function obtained outside the disc by summing the simple pole expansion. We also discuss the relation with monogenic regularity in the sense of Borel.     

Combining Different Docking Engines and Consensus Strategies to Design and Validate Optimized Virtual Screening Protocols for the SARS-CoV-2 3CL Protease

The 3CL-Protease appears to be a very promising medicinal target to develop anti-SARS-CoV-2 agents. The availability of resolved structures allows structure-based computational approaches to be carried out even though the lack of known inhibitors prevents a proper validation of the performed simulations. The innovative idea of the study is to exploit known inhibitors of SARS-CoV 3CL-Pro as a training set to perform and validate multiple virtual screening campaigns. Docking simulations using four different programs (Fred, Glide, LiGen, and PLANTS) were performed investigating the role of both multiple binding modes (by binding space) and multiple isomers/states (by developing the corresponding isomeric space). The computed docking scores were used to develop consensus models, which allow an in-depth comparison of the resulting performances. On average, the reached performances revealed the different sensitivity to isomeric differences and multiple binding modes between the four docking engines. In detail, Glide and LiGen are the tools that best benefit from isomeric and binding space, respectively, while Fred is the most insensitive program. The obtained results emphasize the fruitful role of combining various docking tools to optimize the predictive performances. Taken together, the performed simulations allowed the rational development of highly performing virtual screening workflows, which could be further optimized by considering different 3CL-Pro structures and, more importantly, by including true SARS-CoV-2 3CL-Pro inhibitors (as learning set) when available.     

Quadratic programming and theory of elastic-perfectly plastic structures

Summary For elastic perfectly plastic discretized structures acted upon by given loads and dislocations, it is shown, under holonomic constitutive laws or no local unloading hypothesis, that the formulation of the analysis problem in terms of finite (not incremental) stresses, is amenable to the Kuhn-Tucker conditions of a quadratic program. Then it is readily derived a generalized form of the principle of Haar and Kármán, together with an extremum theorem for displacements and plastic strains, which is the dual of the preceding one. As special cases of this theorems known variational principles follow, which thus turn out to be related in pairs by the duality notion as understood in programming theory. Also the statical and kinematical theorems of limit analysis are proved by means of the unitary conceptual framework supplied by quadratic programming.

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Sommario Con riferimento a strutture discretizzate idealmente elastoplastiche, soggette a dati carichi e distorsioni, si mostra che nell'ipotesi di olonomia dei legami costitutivi o di assenza di ritorni elastici, la formulazione del problema strutturale negli sforzi finiti (non incrementali) è riducibile alle condizioni di Kuhn e Tucker di un programma quadratico. Se ne deducono direttamente una forma generalizzata del principio di Haar e Kármán ed un teorema di estremo negli spostamenti e nelle deformazioni plastiche, duale al precedente. Dai due teoremi discendono come casi speciali noti principi variazionali, che cosi risultano collegati in coppie dalla nozione di dualitá propria della teoria delle ottimizzazioni.Si mostra come anche i teoremi statico e cinematico del calcolo a rottura trovano una nuova dimostrazione nell'inquadramento teorico unitario fondato sulla programmazione quadratica.

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The results presented here form part of a series of studies supported by the C.N.R. (National Research Council).     

Elastic-plastic dynamic behavior of a beam-column model

Summary An elastoplastic beam-column model with one degree of freedom subjected statically to an on-center or off-center axial compressive force is considered. Its dynamic behavior in the elastoplastic range, resulting from a transverse periodic acting force in resonance with the structure in the elastic range, is examined. The principal features are highlighted by a phase plane study.

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Sommario Si considera il modello a un grado di libertà di un'asta elastoplastica sollecitata staticamente da una forza assiale di compressione centrata o eccentrica. Si esamina il suo comportamento dinamico in campo elastoplastico per effetto di una forza trasversale periodica e in risonanza con la struttura in campo elastico, evidenziandone le principali caratteristiche attraverso lo studio nel piano delle fasi.

     

Dynamic pressure and response factors for progressive gravity waves to third order approximation

Summary This paper proposes expressions of the dynamic pressure and of the transfer functions (response factors) between the dynamic pressure amplitude and the wave amplitude and between the dynamic pressure and the vertical displacement of the wave profile, for irrotational progressive gravity waves to third order approximation (non-linear theory).Some characteristic behaviours of the dynamic pressure and of the response factors are examined and compared with those of waves to first order approximation (linear theory).

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Sommario Si ricavano le espressioni della pressione dinamica per onde irrotazionali progressive di gravità al terzo ordine di approssimazione (modello non lineare).Si individuano le funzioni di trasferimento (fattori di risposta) sia tra l'ampiezza della pressione dinamica e l'ampiezza d'onda, sia tra la pressione dinamica e lo spostamento verticale della superficie di ondulazione.Si esaminano comportamenti caratteristici della pressione dinamica e dei fattori di risposta e si confrontano tali comportamenti con quelli relativi alle onde al primo ordine di approssimazione (modello lineare).

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Heat and moisture transfer in sol–gel treated cotton fabrics

Cotton fabrics have been treated by sol–gel processes in order to produce an inorganic coating on fibres, able to modify their thermal conductivity under an irradiating flow. To this aim, fabric specimens with different silica content have been tested following the ISO 6942 standard in order to establish the effect of the coating on coupled heat and moisture transfer through the cotton fibres. The collected results have been compared with those obtained by an optimized method using a cone calorimeter as the heating source. By this latter approach, it has been demonstrated that sol–gel cotton treated fabrics with high moisture uptake possess a significantly lower thermal conductivity with respect to cotton alone.     

Quantum curves and q-deformed Painlevé equations

Letters in Mathematical Physics - We propose that the grand canonical topological string partition functions satisfy finite-difference equations in the closed string moduli. In the case of genus...