On the continuous extension of Adams–Bashforth methods and the event location in discontinuous ODEs

The interpolation polynomial in the $k$-step Adams–Bashforth method may be used to compute the numerical solution at off grid points. We show that such a numerical solution is equivalent to the one obtained by the Nordsieck technique for changing the step size. We also provide an application of this technique to the event location in discontinuous differential systems.     

Efficient Algorithms for Large Scale Global Optimization: Lennard-Jones Clusters

A stochastic global optimization method is applied to the challenging problem of finding the minimum energy conformation of a cluster of identical atoms interacting through the Lennard-Jones potential. The method proposed incorporates within an already existing and quite successful method, monotonic basin hopping, a two-phase local search procedure which is capable of significantly enlarging the basin of attraction of the global optimum. The experiments reported confirm the considerable advantages of this approach, in particular for all those cases which are considered in the literature as the most challenging ones, namely 75, 98, 102 atoms. While being capable of discovering all putative global optima in the range considered, the method proposed improves by more than two orders of magnitude the speed and the percentage of success in finding the global optima of clusters of 75, 98, 102 atoms.     

A modern review of the two-level approximation

The paradigm of the two-level atom is revisited and its perturbative analysis is discussed in view of the principle of duality in perturbation theory. The models we consider are a two-level atom and an ensemble of two-level atoms both interacting with a single radiation mode. The aim is to see how the latter can be actually used as an amplifier of quantum fluctuations to the classical level through the thermodynamic limit of a very large ensemble of two-level atoms [M. Frasca, Phys. Lett. A 283 (2001) 271] and how can remove Schrödinger cat states. The thermodynamic limit can be very effective for producing both classical states and decoherence on a quantum system that evolves without dissipation. Decoherence without dissipation is indeed an effect of a single two-level atom interacting with an ensemble of two-level atoms, a situation that proves to be useful to understand recent experiments on nanoscale devices showing unexpected disappearance of quantum coherence at very low temperatures.     

The MAST-edge centred lumped scheme for the flow simulation in variably saturated heterogeneous porous media

A novel methodology is proposed for the solution of the flow equation in a variably saturated heterogeneous porous medium. The computational domain is descretized using triangular meshes and the governing PDEs are discretized using a lumped in the edge centres numerical technique. The dependent unknown variable of the problem is the piezometric head. A fractional time step methodology is applied for the solution of the original system, solving consecutively a prediction and a correction problem. A scalar potential of the flow field exists and in the prediction step a MArching in Space and Time (MAST) formulation is applied for the sequential solution of the Ordinary Differential Equation of the cells, ordered according to their potential value computed at the beginning of the time step. In the correction step, the solution of a large linear system with order equal to the number of edges is required. A semi-analytical procedure is also proposed for the solution of the prediction step. The computational performance, the order of convergence and the mass balance error have been estimated in several tests and compared with the results of other literature models.     

On the convergence toward nonequilibrium stationary states in thermostatted kinetic models

A differential equation‐based framework is suitable for the modeling of nonequilibrium complex systems if its solution is able to reach, as time goes to infinity, the related nonequilibrium steady states. The thermostatted kinetic theory framework has been recently proposed for the modeling of complex systems subjected to an external force field. The present paper is devoted to the mathematical proof of the convergence of the solutions of the thermostatted kinetic framework towards the related nonequilibrium stationary states. The proof of the main result is gained by employing the Fourier transform and distribution theory arguments.     

On optimal (v, 5, 2, 1) optical orthogonal codes

The size of a (v, 5, 2, 1) optical orthogonal code (OOC) is shown to be at most equal to ${\lceil{\frac{v}{12}}\rceil}$ when v ≡ 11 (mod 132) or v ≡ 154 (mod 924), and at most equal to ${\lfloor{\frac{v}{12}}\rfloor}$ in all the other cases. Thus a (v, 5, 2, 1)-OOC is naturally said to be optimal when its size reaches the above bound. Many direct and recursive constructions for infinite classes of optimal (v, 5, 2, 1)-OOCs are presented giving, in particular, a very strong indication about the existence of an optimal (p, 5, 2, 1)-OOC for every prime p ≡ 1 (mod 12).     

Uniqueness and blow-up for a stochastic viscous dyadic model

We consider the dyadic model with viscosity and additive Gaussian noise as a simplified version of the stochastic Navier–Stokes equations, with the purpose of studying uniqueness and emergence of singularities. We prove pathwise uniqueness and absence of blow-up in the intermediate intensity of the non-linearity, morally corresponding to the 3D case, and blow-up for stronger intensity. Moreover, blow-up happens with probability one for regular initial data.     

Exhaustive computational search of ionic-charge clusters that mediate interactions between mammalian cytochrome P450 (CYP) and P450-oxidoreductase (POR) proteins

In this work, a model for the interaction between CYP2B4 and the FMN domain of rat P450-oxidoreductase is built using as template the structure of a bacterial redox complex. Amino acid residues identified in the literature as cytochrome P450 (CYP)–redox partner interfacial residues map to the interface in our model. Our model supports the view that the bacterial template represents a specific electron transfer complex and moreover provides a structural framework for explaining previous experimental data.We have used our model in an exhaustive search for complementary pairs of mammalian CYP and P450-oxidoreductase (POR) charge clusters. We quantitatively show that among the previously defined basic clusters, the 433K–434R cluster is the most dominant (32.3% of interactions) and among the acidic clusters, the 207D–208D–209D cluster is the most dominant (29%). Our analysis also reveals the previously not described basic cluster 343R–345K (16.1% of interactions) and 373K (3.2%) and the acidic clusters 113D–115E–116E (25.8%), 92E–93E (12.9%), 101D (3.2%) and 179E (3.2%).Cluster pairings among the previously defined charge clusters include the pairing of cluster 421K–422R to cluster 207D–208D–209D. Moreover, 433K–434R and 207D–208D–209D, respectively the dominant positively and negatively charged clusters, are uncorrelated. Instead our analysis suggests that the newly identified cluster 113D–115E–116E is the main partner of the 433K–434R cluster while the newly described cluster 343R–345K is correlated to the cluster 207D–208D–209D.     

Free‐Standing Membranes to Study the Optical Properties of Anodic TiO2 Nanotube Layers

In the present work we investigate various optical properties (such as light absorption and reflectance) of anodic TiO₂ nanotube layers directly transferred as self‐standing membranes onto quartz substrates. This allows investigation in a transmission geometry which provides significantly more reliable data than measurements on the metallic Ti substrate. Light transmission and reflectance measurements were carried out for layers of thickness varying from 1.8 to 50 μm, and the layers were investigated in their amorphous and crystalline forms. A series of wavelength‐dependent light attenuation coefficients are extrapolated and found to match the photocurrent versus irradiation wavelength behavior. A feature specific to anodic nanotubes is that their intrinsic carbon contamination content causes a proportional sub‐bandgap response. Overall, the extracted data provide a valuable basis and understanding for the design of photo‐electrochemical devices based on TiO₂ nanotubes.