Initial-Boundary Value Problems for Linear and Soliton PDEs

Evolution PDEs for dispersive waves are considered in both linear and nonlinear integrable cases, and initial-boundary value problems associated with them are formulated in spectral space. A method of solution is presented, which is based on the elimination of the unknown boundary values by proper restrictions of the functional space and of the spectral variable complex domain. Illustrative examples include the linear Schroedinger equation on compact and semicompact n-dimensional domains and the nonlinear Schroedinger equation on the semiline.Comment: 18 pages, LATEX, submitted to the proccedings of NEEDS 2001 - Special Issue, to be published in the Journal of Theoretical and Mathematical Physic

Many-body models for molecular nanomagnets

We present a flexible and effective ab-initio scheme to build many-body models for molecular nanomagnets, and to calculate magnetic exchange couplings and zero-field splittings. It is based on using localized Foster-Boys orbitals as one-electron basis. We apply this scheme to three paradigmatic systems, the antiferromagnetic rings Cr8 and Cr7Ni and the single molecule magnet Fe4. In all cases we identify the essential magnetic interactions and find excellent agreement with experiments.Comment: 5 pages, 3 figure

Normal-fault stress and displacement through finite-element analysis

We compute displacement and stress due to a normal fault by means of two-dimensional plane-strain finite-element analysis. To do so, we apply a system of forces to the fault nodes and develop an iterative algorithm serving to determine the force magnitudes for any slip distribution. As a sample case, we compute the force magnitudes assuming uniform slip on a 10-km two-dimensional normal fault. The numerical model generates displacement and stress fields that compare well with the analytical solution. In fact, we found little difference in displacements (<5%), displacement orientation (<15°), and stress components (<35%, half of which due to slip tolerance). We analyze such misfit, and discuss how the error propagates from displacement to stress. Our scheme provides a convenient way to use the finite-elements direct method in a trial-and-error procedure to reproduce any smooth slip distribution

S-mixing and quantum tunneling of the magnetization in molecular nanomagnets

The role of $S$-mixing in the quantum tunneling of the magnetization in nanomagnets has been investigated. We show that the effect on the tunneling frequency is huge and that the discrepancy (more than 3 orders of magnitude in the tunneling frequency) between spectroscopic and relaxation measurements in Fe$_8$ can be resolved if $S$-mixing is taken into account.Comment: REVTEX, 10 pages, 3 jpg figures, to appear in PR

The evolution of the AGN content in groups up to z~1

Determining the AGN content in structures of different mass/velocity dispersion and comparing them to higher mass/lower redshift analogs is important to understand how the AGN formation process is related to environmental properties. We use our well-tested cluster finding algorithm to identify structures in the GOODS North and South fields, exploiting the available spectroscopic redshifts and accurate photometric redshifts. We identify 9 structures in GOODS-south (presented in a previous paper) and 8 new structures in GOODS-north. We only consider structures where at least 2/3 of the members brighter than M_R=-20 have a spectroscopic redshift. For those group members that coincide with X-ray sources in the 4 and 2 Msec Chandra source catalogs respectively, we determine if the X-ray emission originates from AGN activity or it is related to the galaxies' star-formation activity. We find that the fraction of AGN with Log L_H > 42 erg/s in galaxies with M_R < -20 is on average 6.3+-1.3%, much higher than in lower redshift groups of similar mass and more than double the fraction found in massive clusters at a similarly high redshift. We then explore the spatial distribution of AGN in the structures and find that they preferentially populate the outer regions. The colors of AGN host galaxies in structures tend to be confined to the green valley, thus avoiding the blue cloud and, partially, also the red-sequence, contrary to what happens in the field. We finally compare our results to the predictions of two sets of semi analytic models to investigate the evolution of AGN and evaluate potential triggering and fueling mechanisms. The outcome of this comparison attests the importance of galaxy encounters, not necessarily leading to mergers, as an efficient AGN triggering mechanism. (abridged)Comment: 11 pages, 8 figures, Accepted accepted for publication in A&

The beneficial role of green bonds as a new strategic asset class: Dynamic dependencies, allocation and diversification before and during the pandemic era

The paper proposes a full comprehensive analysis of green bond diversification benefits, their co-movement with multiple market indices, and the corresponding implications for portfolio allocation. Based on a time frame of seven years, divided into four sub-periods, the co-movements of green-bond indices, i.e. Solactive Green Bond Index and Bloomberg Barclays MSCI Green Bond Index, and the stock/bond market have been described, shedding light on the connections with sectors most affected by the Covid-19 pandemic. The Solactive Green Bond Index is found to provide the greater diversification benefit of the two green-bond indices, on average during the seven years and also during the pandemic. Allocation strategies and risk performances have also been analyzed to assess the impact of green-bond indices on otherwise traditional portfolios; their diversification power is discussed by use of traditional measures and an additional behavioral approach, drawing attention to its evolution in time and its consistency in terms of diminished risks and increased returns. Portfolios constructed with the inclusion of green bonds prove preferable in terms of risk, in all periods and for all strategies, while the superiority of returns depends on the allocation strategy

A Bell-Evans-Polanyi principle for molecular dynamics trajectories and its implications for global optimization

The Bell-Evans-Polanyi principle that is valid for a chemical reaction that proceeds along the reaction coordinate over the transition state is extended to molecular dynamics trajectories that in general do not cross the dividing surface between the initial and the final local minima at the exact transition state. Our molecular dynamics Bell-Evans-Polanyi principle states that low energy molecular dynamics trajectories are more likely to lead into the basin of attraction of a low energy local minimum than high energy trajectories. In the context of global optimization schemes based on molecular dynamics our molecular dynamics Bell-Evans-Polanyi principle implies that using low energy trajectories one needs to visit a smaller number of distinguishable local minima before finding the global minimum than when using high energy trajectories

Bott--Kitaev periodic table and index theory

We consider topological insulators and superconductors with discrete symmetries and clarify the relevant index theory behind the periodic table proposed by Kitaev. An effective Hamiltonian determines the analytical index, which can be computed by a topological index. We focus on the spatial dimensions one, two and three, and only consider the bulk theory. In two dimensions, the $\mathbb{Z}$-valued invariants are given by the first Chern number. Meanwhile, $\mathbb{Z}_2$-valued invariants can be computed by the odd topological index and its variations. The Bott-Kitaev periodic table is well-known in the physics literature, we organize the topological invariants in the framework of KR-theory.Comment: 37 page