Conservative numerical methods for the Full von Kármán plate equations

This article is concerned with the numerical solution of the full dynamical von Kármán plate equations for geometrically nonlinear (large‐amplitude) vibration in the simple case of a rectangular plate under periodic boundary conditions. This system is composed of three equations describing the time evolution of the transverse displacement field, as well as the two longitudinal displacements. Particular emphasis is put on developing a family of numerical schemes which, when losses are absent, are exactly energy conserving. The methodology thus extends previous work on the simple von Kármán system, for which longitudinal inertia effects are neglected, resulting in a set of two equations for the transverse displacement and an Airy stress function. Both the semidiscrete (in time) and fully discrete schemes are developed. From the numerical energy conservation property, it is possible to arrive at sufficient conditions for numerical stability, under strongly nonlinear conditions. Simulation results are presented, illustrating various features of plate vibration at high amplitudes, as well as the numerical energy conservation property, using both simple finite difference as well as Fourier spectral discretizations. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1948–1970, 2015     

Molecular Pom Poms from Self‐Assembling α,γ‐Cyclic Peptides

The hierarchical self‐assembly properties of a dimer‐forming cyclic peptide that bears a nicotinic acid moiety to form molecular pom‐pom‐like structures are described. This dimeric assembly self organizes into spherical structures that can encapsulate small organic molecules owing to its porosity and it can also facilitate metal deposition on its surface directed by the pyridine moiety.     

Symmetry-Breaking Charge-Transfer Chromophore Interactions Supported by Carbon Nanodots

Carbon dots (CDs) and their derivatives are useful platforms for studying electron-donor/acceptor interactions and dynamics therein. Herein, we couple amorphous CDs with phthalocyanines (Pcs) that act as electron donors with a large extended π-surface and intense absorption across the visible range of the solar spectrum. Investigations of the intercomponent interactions by means of steady-state and pump-probe transient absorption spectroscopy reveal symmetry-breaking charge transfer/separation and recombination dynamics within pairs of phthalocyanines. The CDs facilitate the electronic interactions between the phthalocyanines. Thus, our findings suggest that CDs could be used to support electronic couplings in multichromophoric systems and further increase their applicability in organic electronics, photonics, and artificial photosynthesis.     

An approximation scheme for the two-stage,two-dimensional knapsack problem

We present an approximation scheme for the two-dimensional version of the knapsack problem which requires packing a maximum-area set of rectangles in a unit square bin, with the further restrictions that packing must be orthogonal without rotations and done in two stages. Achieving a solution which is close to the optimum modulo a small additive constant can be done by taking wide inspiration from an existing asymptotic approximation scheme for two-stage two-dimensional bin packing. On the other hand, getting rid of the additive constant to achieve a canonical approximation scheme appears to be widely nontrivial.     

First-principles study of aqueous hydroxide solutions

Car-Parrinello molecular dynamics simulations have been carried out for aqueous NaOH and KOH solutions under ambient conditions over a wide range of concentrations. From these simulations, we have observed a continuous change of the water structure with added hydroxide, characterized by a significant shift of the second peak of the OO radial distribution functions to shorter distances. At the highest concentration investigated, the normal tetrahedral coordination of pure water is completely missing, a result that is consistent with a recent neutron diffraction experiment. The added hydroxide also gives rise to some unique spectroscopic features, including a "free" O-H stretch, a broadening of the normal water OH stretching band, and a large blue shift of both the librational band and the low-frequency translation. These results are in good agreement with the experimental data. Finally, it was demonstrated that the structural and dynamical behavior is inextricably linked to the formation of compact hydroxide-water complexes.     

Lack of self-averaging in neutral evolution of proteins

We simulate neutral evolution of proteins imposing conservation of the thermodynamic stability of the native state in the framework of an effective model of folding thermodynamics. This procedure generates evolutionary trajectories in sequence space which share two universal features for all of the examined proteins. First, the number of neutral mutations fluctuates broadly from one sequence to another, leading to a non-Poissonian substitution process. Second, the number of neutral mutations displays strong correlations along the trajectory, thus causing the breakdown of self-averaging of the resulting evolutionary substitution process.     

Restrictions and expansions of holomorphic representations

We compute tensor products of representations of the holomorphic discrete series of a Lie group G, or restrictions to some subgroup G′. A detailed study is done for the case of the conformal group O(4, 2).     

Principio di entropia e restrizioni termodinamiche per fluidi con memoria

Riassunto In questo lavoro si affrontano i problemi relativi alle restrizioni termodinamiche, imposte dal principio di entropia nella formulazione di Müller [1], per fluidi con memoria, mediante il metodo dei moltiplicatori di Lagrange.

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Summary In this work Author deals with the problems pertinent to the thermodynamic restrictions, which are due to principle of entropy in the formulation of Müller [1], for fluids with a memory, through the Lagrange multipliers.

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Lavoro eseguito nell'ambito del G.N.F.M. del C.N.R.