An equivalent dipole analysis of PZT ceramics and lead-free piezoelectric single crystals

The recently proposed Equivalent Dipole Model for describing the electromechanical properties of ionic solids in terms of 3 ions and 2 bonds has been applied to PZT ceramics and lead-free single crystal piezoelectric materials, providing analysis in terms of an effective ionic charge and the asymmetry of the interatomic force constants. For PZT it is shown that, as a function of composition across the morphotropic phase boundary, the dominant bond compliance peaks at 52% ZrO2. The stiffer of the two bonds shows little composition dependence with no anomaly at the phase boundary. The effective charge has a maximum value at 50% ZrO2, decreasing across the phase boundary region, but becoming constant in the rhombohedral phase. The single crystals confirm that both the asymmetry in the force constants and the magnitude of effective charge are equally important in determining the values of the piezoelectric charge coefficient and the electromechanical coupling coefficient. Both are apparently temperature dependent, increasing markedly on approaching the Curie temperature

Structure Formation in Dark Matter Particle Production Cosmology

We investigate a cosmological scenario in which the dark matter particles can be created during the evolution of the Universe. By regarding the Universe as an open thermodynamic system and using non-equilibrium thermodynamics, we examine the mechanism of gravitational particle production. In this setup, we study the large-scale structure (LSS) formation of the Universe in the Newtonian regime of perturbations and derive the equations governing the evolution of the dark matter overdensities. Then, we implement the cosmological data from Planck 2018 CMB measurements, SNe Ia and BAO observations, as well as the Riess et al. (2019) local measurement for $H_0$ to provide some cosmological constraints for the parameters of our model. We see that the best case of our scenario ($\chi_{{\rm tot}}^{2}=3834.40$) fits the observational data better than the baseline $\Lambda$CDM model ($\chi_{{\rm tot}}^{2} = 3838.00$) at the background level. We moreover estimate the growth factor of linear perturbations and show that the best case of our model ($\chi_{f\sigma_{8}}^{2}=39.85$) fits the LSS data significantly better than the $\Lambda$CDM model ($\chi_{f\sigma_{8}}^{2}=45.29$). Consequently, our model also makes a better performance at the level of the linear perturbations compared to the standard cosmological model.Comment: 30 pages, 8 figure

Van-der-Waals potentials of paramagnetic atoms

We study single- and two-atom van der Waals interactions of ground-state atoms which are both polarizable and paramagnetizable in the presence of magneto-electric bodies within the framework of macroscopic quantum electrodynamics. Starting from an interaction Hamiltonian that includes particle spins, we use leading-order perturbation theory for the van der Waals potentials expressed in terms of the polarizability and magnetizability of the atom(s). To allow for atoms embedded in media, we also include local-field corrections via the real-cavity model. The general theory is applied to the potential of a single atom near a half space and that of two atoms embedded in a bulk medium or placed near a sphere, respectively.Comment: 18 pages, 3 figures, 1 tabl

Are there any good digraph width measures?

Several different measures for digraph width have appeared in the last few years. However, none of them shares all the "nice" properties of treewidth: First, being \emph{algorithmically useful} i.e. admitting polynomial-time algorithms for all \MS1-definable problems on digraphs of bounded width. And, second, having nice \emph{structural properties} i.e. being monotone under taking subdigraphs and some form of arc contractions. As for the former, (undirected) \MS1 seems to be the least common denominator of all reasonably expressive logical languages on digraphs that can speak about the edge/arc relation on the vertex set.The latter property is a necessary condition for a width measure to be characterizable by some version of the cops-and-robber game characterizing the ordinary treewidth. Our main result is that \emph{any reasonable} algorithmically useful and structurally nice digraph measure cannot be substantially different from the treewidth of the underlying undirected graph. Moreover, we introduce \emph{directed topological minors} and argue that they are the weakest useful notion of minors for digraphs

Analytical evaluation of atomic form factors: application to Rayleigh scattering

Atomic form factors are widely used for the characterization of targets and specimens, from crystallography to biology. By using recent mathematical results, here we derive an analytical expression for the atomic form factor within the independent particle model constructed from nonrelativistic screened hydrogenic wavefunctions. The range of validity of this analytical expression is checked by comparing the analytically obtained form factors with the ones obtained within the Hartee-Fock method. As an example, we apply our analytical expression for the atomic form factor to evaluate the differential cross section for Rayleigh scattering off neutral atoms.Comment: 7 pages, 1 figur

Undirected Graphs of Entanglement Two

Entanglement is a complexity measure of directed graphs that origins in fixed point theory. This measure has shown its use in designing efficient algorithms to verify logical properties of transition systems. We are interested in the problem of deciding whether a graph has entanglement at most k. As this measure is defined by means of games, game theoretic ideas naturally lead to design polynomial algorithms that, for fixed k, decide the problem. Known characterizations of directed graphs of entanglement at most 1 lead, for k = 1, to design even faster algorithms. In this paper we present an explicit characterization of undirected graphs of entanglement at most 2. With such a characterization at hand, we devise a linear time algorithm to decide whether an undirected graph has this property

Geohazards analysis of Pisa tunnel in a fractured incompetent rocks in Zagros Mountains, Iran.

The Pisa 2 tunnel with 740 m in length and 20° N trend is located along the Kazerun fault zone in Simply Folded Belt of Zagros, Iran. This tunnel has been excavated in the fractured incompetent marl layers with high expansive pressure of up to 2 kg/cm2. In this study, the geological hazards along the tunnel have been recognized and categorized. This study revealed that, in the long-term usage of the tunnel, the lining did not endure against the loading and the secondary leakages. It is mainly attributed due to the non-efficiencies of drainage and isolation systems in the tunnel site. Therefore, it caused asphalt damage, drainage damage, and wall distortion. FLAC3D software has been used in this research. We conducted various analyses for pre-excavation stress states, syn-excavation, and post-excavation strain states. The results showed no indication of instability and critical deformations during the excavation time. It also revealed that due to the non-efficiencies of drainage and isolation systems against secondary leakages and consequently marl expansion, the volumetric and shear strains (i.e., expansions and displacements) have exceeded from the critical states of strain along the tunnel. For various remedy purpose, this paper attempted several measures that can be taken in order to modify the drainage and isolation systems along the tunnel area. The reconstruction of drainage systems with suitable reinforced concrete and adequate slope has been proposed. The width of channel and isolation of backside of lining and implementation of multi-order outlets (i.e., backside of lining) for draining of groundwater into where the main drainage systems are located in the tunnel gallery were suggested

Thermal aspects of a low cost power electronic converter for high capacity, smart residential distribution networks

A key challenge facing the UK Distribution Network Operators (DNOs) today is the increasing demand for power being placed on residential networks. Also, the increase in distributed generation (DG) is now resulting in unacceptable local voltage rises and power quality issues. A cost effective solution to these problems can be achieved on the existing infrastructure by increasing the local network phase voltage to 400 V and stepping back down to 230 V at each house, using a DNO-owned, voltage regulated power electronic converter (PEC). The thermal and protection issues associated with the design of such a PEC, which is to be installed in the meterbox of each property, are discussed in this paper