A one-dimensional coagulation–fragmentation process with a dynamical phase transition

We introduce a reversible Markovian coagulation–fragmentation process on the set of partitions of {1,…,L}$\{1,\dots ,L\}$ into disjoint intervals. Each interval can either split or merge with one of its two neighbors. The invariant measure can be seen as the Gibbs measure for a homogeneous pinning model (Giacomin (2007) [10]). Depending on a parameter λ$\lambda$, the typical configuration can be either dominated by a single big interval (delocalized phase), or composed of many intervals of order 1$1$ (localized phase), or the interval length can have a power law distribution (critical regime). In the three cases, the time required to approach equilibrium (in total variation) scales very differently with L$L$. In the localized phase, when the initial condition is a single interval of size L$L$, the equilibration mechanism is due to the propagation of two “fragmentation fronts” which start from the two boundaries and proceed by power-law jumps.     

Hamiltonian structural analysis of curved beams with or without generalized two-parameter foundation

The solution of curved Timoshenko beams with or without generalized two-parameter elastic foundation is presented. Beam can be subjected to any kind of loads and imposed external actions, distributed or concentrated along the beam. It can have external and internal restraints and any kind of internal kinematical or mechanical discontinuity. Moreover, the beam may have any spatial curved geometry, by dividing the entire structure into segments of constant curvature and constant elastic properties, each segment resting or not on elastic foundation. The foundation has six parameters like a generalized Winkler soil with the addition of other two parameters involving the link between settlements in transverse direction, as occurs for Pasternak soil model. The solution is obtained by the Hamiltonian structural analysis method, based on an energetic approach, solving a mixed canonical Hamiltonian system of twelve differential equations, leading to the fundamental matrix. The solution, numerically expressed or in closed form, is fast and simple to be implemented on a software, being the solving matrix always of order 12 for any kind of geometry and loads, without increasing in computational complexity. Numerical examples are given, comparing the results of the proposed procedure with the literature data, for rectilinear and curved beams with different soil properties.     

Complex Dynamics in Pendulum-Type Equations with Variable Length

We prove the existence of complex dynamics for a generalized pendulum type equation with variable length. The solutions we find switch from an oscillatory behavior around the stable vertical position to a rotational type behavior crossing the unstable position with positive or negative velocity following any prescribed two-sided sequence of symbols. Moreover, to any periodic sequence of symbols corresponds a periodic solution of the equation. The proof is based on a topological approach and the results are robust with respect to small perturbations. In particular a small friction term can be added to the equation.     

The dynamical behavior of homogeneous scalar-field spacetimes with general self-interaction potentials

The dynamics of homogeneous Robertson–Walker cosmological models with a self-interacting scalar field source is examined here in full generality, requiring only the scalar field potential to be bounded from below and divergent when the field diverges. In this way we are able to give a unified treatment of all the already studied cases—such as positive potentials which exhibit asymptotically polynomial or exponential behaviors—together with its extension to a much wider set of physically sensible potentials. Since the set includes potentials with negative inferior bound, we are able to give, in particular, the analysis of the asymptotically anti De Sitter states for such cosmologies.     

(−)-epi-Presilphiperfolan-1-ol, a new triquinane sesquiterpene from the essential oil of Anemia tomentosa var. anthriscifolia (Pteridophyta)

(−)-epi-Presilphiperfolan-1-ol, (1), a new triquinane sesquiterpene, was isolated from the essential oil of Anemia tomentosa var. anthriscifolia by column chromatography. Its structure elucidation was accomplished by extensive 1D- and 2D-NMR analyses, as well as by GC-MS, chiral bidimensional GC, dehydration reactions, and a comparative (GIAO/DFT) theoretical study of the ¹³C NMR chemical shifts of 1 and its known isomers (presilphiperfolan-1-ol (1a), presilphiperfolan-8-ol (3), and presilphiperfolan-9-ol (4)).     

Development of new CdZnTe detectors for room‐temperature high‐flux radiation measurements

Recently, CdZnTe (CZT) detectors have been widely proposed and developed for room‐temperature X‐ray spectroscopy even at high fluxes, and great efforts have been made on both the device and the crystal growth technologies. In this work, the performance of new travelling‐heater‐method (THM)‐grown CZT detectors, recently developed at IMEM‐CNR Parma, Italy, is presented. Thick planar detectors (3 mm thick) with gold electroless contacts were realised, with a planar cathode covering the detector surface (4.1 mm × 4.1 mm) and a central anode (2 mm × 2 mm) surrounded by a guard‐ring electrode. The detectors, characterized by low leakage currents at room temperature (4.7 nA cm^?2 at 1000 V cm^?1), allow good room‐temperature operation even at high bias voltages (>7000 V cm^?1). At low rates (200 counts s^?1), the detectors exhibit an energy resolution around 4% FWHM at 59.5 keV (²⁴¹Am source) up to 2200 V, by using commercial front‐end electronics (A250F/NF charge‐sensitive preamplifier, Amptek, USA; nominal equivalent noise charge of 100 electrons RMS). At high rates (1 Mcounts s^?1), the detectors, coupled to a custom‐designed digital pulse processing electronics developed at DiFC of University of Palermo (Italy), show low spectroscopic degradations: energy resolution values of 8% and 9.7% FWHM at 59.5 keV (²⁴¹Am source) were measured, with throughputs of 0.4% and 60% at 1 Mcounts s^?1, respectively. An energy resolution of 7.7% FWHM at 122.1 keV (⁵⁷Co source) with a throughput of 50% was obtained at 550 kcounts s^?1 (energy resolution of 3.2% at low rate). These activities are in the framework of an Italian research project on the development of energy‐resolved photon‐counting systems for high‐flux energy‐resolved X‐ray imaging.     

A Degenerate Birdcage with Integrated Tx/Rx Switches and Butler Matrix for the Human Limbs at 7 T

The theoretically known degeneracy condition of the band-pass birdcage coil has rarely been exploited in transmit coil designs. We have created an eight-channel degenerate birdcage for the human limbs at 7 T, with dedicated Tx/Rx switches and a Butler matrix. The coil can be split into two half cylinders, as required for its application to patients with limited mobility. The design of the coil, the Butler matrix, and Tx/Rx switches relied on a combination of analytical, circuital, and numerical simulations. The birdcage theory was extended to the degenerate case. The theoretical and practical aspects of the design and construction of the coil are presented. The performance of the coil was demonstrated by simulations, workbench, and scanner measurements. The fully assembled prototype presents good performance in terms of efficiency, B₁ homogeneity, and signal-to-noise ratio, despite the asymmetry introduced by the splittable design. The first in vivo images of the knee are also shown. A novel RF coil design consisting of an eight-channel splittable degenerate birdcage has been developed, and it is now available for 7 T MRI applications of the human lower limbs, including high-resolution imaging of the knee cartilages and of the patellar trabecular structure.     

Experimental and numerical analysis in heat flow sensors calibration

Journal of Thermal Analysis and Calorimetry - The 2010/31/CE directive has highlighted the necessity to improve the energy efficiency in buildings, since they are responsible for 40% of energy...     

A Karplus Equation for the Conformational Analysis of Organic Molecular Crystals

Vicinal scalar couplings (³J) are extensively used for the conformational analysis of organic compounds in the liquid state through empirical Karplus equations. In contrast, there are no examples of such use for the structural investigation of solids. With the support of first principles calculations, we demonstrate here that ¹³C‐¹³C ³J coupling constants (³J_CC) measured on a series of isotopically enriched solid amino acids and sugars can be related to dihedral angles by a simple Karplus‐like relationship, and we provide a parameterized Karplus function for the conformational analysis of organic molecular crystals. Under the experimental conditions discussed, torsional angles can be estimated from the experimental ³J_CC values with an accuracy of 10° using this function. These results open new perspectives towards the use of ³J_CC as a new analytical tool that could considerably simplify structure determination of functional organic solids.