Long Time Behavior of the Cahn-Hilliard Equation with Irregular Potentials and Dynamic Boundary Conditions

The Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions is considered.The existence of the global attractor is proved and the long time behavior of the trajectories,namely,the convergence to steady states,is studied.     

Existence of Indecomposable Rank Two Vector Bundles on Higher Dimensional Toric Varieties

In the mid 1970s, Hartshorne conjectured that, for all n > 7, any rank 2 vector bundles on ? ⁿ is a direct sum of line bundles. This conjecture remains still open. In this paper, we construct indecomposable rank two vector bundles on a large class of Fano toric varieties. Unfortunately, this class does not contain ? ⁿ .     

Synthesis and characterization of graphene-based nanocomposites with potential use for biomedical applications

In this paper, GaN nanoparticles were synthesized from the complex Ga(H₂NCONH₂)₆Cl₃ in the flow of NH₃ at a mild temperature (350 °C). Further purification was performed by the ethanol-thermal method. The ethanol-thermal method also prompted the GaN nanoparticles to grow into an anisotropic morphology. XRD patterns reveal that GaN nanoparticles have crystallized in a hexagonal wurtzite structure. TEM observation shows that the average size of the as-prepared nanoparticles is about 5–10 nm. The photoluminescence spectrum exhibits a broad green emission band with a peak at 510 nm. It can be known from the first-principle theoretic simulation by the TDDFT method that this fluorescence emission band is attributed to the hydride defects of V _N-H on the surface of GaN nanoparticles.     

Individual‐Molecule Perspective Analysis of Chemical Reaction Networks: The Case of a Light‐Driven Supramolecular Pump

The first study in which stochastic simulations of a two‐component molecular machine are performed in the mass‐action regime is presented. This system is an autonomous molecular pump consisting of a photoactive axle that creates a directed flow of rings through it by exploiting light energy away from equilibrium. The investigation demonstrates that the pump can operate in two regimes, both experimentally accessible, in which light‐driven steps can be rate‐determining or not. The number of photons exploited by an individual molecular pump, as well as the precision of cycling and the overall efficiency, critically rely on the operating regime of the machine. This approach provides useful information not only to guide the chemical design of a self‐assembling molecular device with desired features, but also to elucidate the effect of the environment on its performance, thus facilitating its experimental investigation.     

A New Class of Cellular Automata with a Discontinuous Glass Transition

We introduce a new class of two-dimensional cellular automata with a bootstrap percolation-like dynamics. Each site can be either empty or occupied by a single particle and the dynamics follows a deterministic updating rule at discrete times which allows only emptying sites. We prove that the threshold density ρ _c for convergence to a completely empty configuration is non trivial, 0<ρ _c <1, contrary to standard bootstrap percolation. Furthermore we prove that in the subcritical regime, ρ<ρ _c , emptying always occurs exponentially fast and that ρ _c coincides with the critical density for two-dimensional oriented site percolation on ℤ². This is known to occur also for some cellular automata with oriented rules for which the transition is continuous in the value of the asymptotic density and the crossover length determining finite size effects diverges as a power law when the critical density is approached from below. Instead for our model we prove that the transition is discontinuous and at the same time the crossover length diverges faster than any power law. The proofs of the discontinuity and the lower bound on the crossover length use a conjecture on the critical behaviour for oriented percolation. The latter is supported by several numerical simulations and by analytical (though non rigorous) works through renormalization techniques. Finally, we will discuss why, due to the peculiar mixed critical/first order character of this transition, the model is particularly relevant to study glassy and jamming transitions. Indeed, we will show that it leads to a dynamical glass transition for a Kinetically Constrained Spin Model. Most of the results that we present are the rigorous proofs of physical arguments developed in a joint work with D.S. Fisher.     

Memory effects in quantum channel discrimination

We consider quantum-memory assisted protocols for discriminating quantum channels. We show that for optimal discrimination of memory channels, memory assisted protocols are needed. This leads to a new notion of distance for channels with memory, based on the general theory of quantum testers. For discrimination and estimation of sets of independent unitary channels, we prove optimality of parallel protocols among all possible architectures.     

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     

Computing Integrated Information (Φ) in Discrete Dynamical Systems with Multi-Valued Elements

Integrated information theory (IIT) provides a mathematical framework to characterize the cause-effect structure of a physical system and its amount of integrated information (Φ). An accompanying Python software package (“PyPhi”) was recently introduced to implement this framework for the causal analysis of discrete dynamical systems of binary elements. Here, we present an update to PyPhi that extends its applicability to systems constituted of discrete, but multi-valued elements. This allows us to analyze and compare general causal properties of random networks made up of binary, ternary, quaternary, and mixed nodes. Moreover, we apply the developed tools for causal analysis to a simple non-binary regulatory network model (p53-Mdm2) and discuss commonly used binarization methods in light of their capacity to preserve the causal structure of the original system with multi-valued elements.