Entropy and the Shannon-McMillan-Breiman Theorem for Beta Random Matrix Ensembles

We show that beta ensembles in Random Matrix Theory with generic real analytic potential have the asymptotic equipartition property. In addition, we prove a Central Limit Theorem for the density of the eigenvalues of these ensembles.     

Vibrational control of mechanical systems with piecewise linear damping and high-frequency inputs

Nonlinear Dynamics - This paper discusses averaging and vibrational control of mechanical control-affine systems with piecewise linear damping and high-frequency inputs. The results are used for...     

Random Skew Plane Partitions with a Piecewise Periodic Back Wall

Random skew plane partitions of large size distributed according to an appropriately scaled Schur process develop limit shapes. In the present work, we consider the limit of large random skew plane partitions where the inner boundary approaches a piecewise linear curve with non-lattice slopes, describing the limit shape and the local fluctuations in various regions. This analysis is fairly similar to that in Okounkov and Reshetikhin (Commun Math Phys 269:571–609, 2007), but we do find some new behavior. For instance, the boundary of the limit shape is now a single smooth (not algebraic) curve, whereas the boundary in Okounkov and Reshetikhin (Commun Math Phys 269:571–609, 2007) is singular. We also observe the bead process introduced in Boutillier (Ann Probab 37(1):107–142, 2009) appearing in the asymptotics at the top of the limit shape.     

Dynamic analysis and optimal control of drag-based vibratory systems using averaging

Nonlinear Dynamics - This paper presents dynamic analysis and optimal control of vibratory systems with asymmetric drag and asymmetric added mass, moving in a resisting medium. The paper considers...     

Raman and Photoluminescence Spectroscopic Detection of Surface‐Bound Li+O2− Defect Sites in Li‐Doped ZnO Nanocrystals Derived from Molecular Precursors

We present a detailed study of Raman spectroscopy and photoluminescence measurements on Li‐doped ZnO nanocrystals with varying lithium concentrations. The samples were prepared starting from molecular precursors at low temperature. The Raman spectra revealed several sharp lines in the range of 100–200 cm^?1, which are attributed to acoustical phonons. In the high‐energy range two peaks were observed at 735 cm^?1 and 1090 cm^?1. Excitation‐dependent Raman spectroscopy of the 1090 cm^?1 mode revealed resonance enhancement at excitation energies around 2.2 eV. This energy coincides with an emission band in the photoluminescence spectra. The emission is attributed to the deep lithium acceptor and intrinsic point defects such as oxygen vacancies. Based on the combined Raman and PL results, we introduce a model of surface‐bound LiO₂ defect sites, that is, the presence of Li⁺O₂^? superoxide. Accordingly, the observed Raman peaks at 735 cm^?1 and 1090 cm^?1 are assigned to Li? O and O? O vibrations of LiO₂.     

Dyes and Redox Couples with Matched Energy Levels: Elimination of the Dye‐Regeneration Energy Loss in Dye‐Sensitized Solar Cells

In dye‐sensitized solar cells (DSSCs), a significant dye‐regeneration force (ΔG_reg⁰≥0.5 eV) is usually required for effective dye regeneration, which results in a major energy loss and limits the energy‐conversion efficiency of state‐of‐art DSSCs. We demonstrate that when dye molecules and redox couples that possess similar conjugated ligands are used, efficient dye regeneration occurs with zero or close‐to‐zero driving force. By using Ru(dcbpy)(bpy)₂²⁺ as the dye and Ru(bpy)₂(MeIm)₂^3+//2+ as the redox couple, a short‐circuit current (J_sc) of 4 mA cm^?2 and an open‐circuit voltage (V_oc) of 0.9 V were obtained with a ΔG_reg⁰ of 0.07 eV. The same was observed for the N3 dye and Ru(bpy)₂(SCN)₂^1+/0 (ΔG_reg⁰=0.0 eV), which produced an J_sc of 2.5 mA cm^?2 and V_oc of 0.6 V. Charge recombination occurs at pinholes, limiting the performance of the cells. This proof‐of‐concept study demonstrates that high V_oc values can be attained by significantly curtailing the dye‐regeneration force.     

Scaling Limits of Random Skew Plane Partitions with Arbitrarily Sloped Back Walls

The paper studies scaling limits of random skew plane partitions confined to a box when the inner shapes converge uniformly to a piecewise linear function V of arbitrary slopes in [−1, 1]. It is shown that the correlation kernels in the bulk are given by the incomplete Beta kernel, as expected. As a consequence it is established that the local correlation functions in the scaling limit do not depend on the particular sequence of discrete inner shapes that converge to V. A detailed analysis of the correlation kernels at the top of the limit shape, and of the frozen boundary is given. It is shown that depending on the slope of the linear section of the back wall, the system exhibits behavior observed in either Okounkov and Reshetikhin (Commun Math Phys 269(3):571–609, 2007) or Boutillier et al. ( [math-ph], 2009).     

Plane Partitions with Two-Periodic Weights

We study scaling limits of skew plane partitions with periodic weights under several boundary conditions. We compute the correlation kernel of the limiting point process in the bulk and near turning points on the frozen boundary. The system develops pairs of turning points (points where three different phases meet), which are separated by “semi-frozen” regions. We show that the point process at such a turning point is a pair of non-trivially correlated GUE minor processes. In the limit when all weights become the same, i.e. in the homogeneous case, such a pair of turning points collapses into a single turning point and the local process becomes the GUE minor process. We also study an intermediate regime when the weights are periodic but all converge to 1. In this regime the limit shape and correlations in the bulk are the same as in the case of homogeneous weights, and periodicity is not visible in the bulk. However, the process at turning points is still not the GUE minor process.     

Enhanced Optical and Electrical Properties of Graphene Oxide-Silver Nanoparticles Nanocomposite Film by Thermal Annealing in the Air

Russian Journal of Applied Chemistry - Here, we report the enhanced optical and electrical properties of graphene oxide-silver nanoparticles (GO-AgNPs) nanocomposite due to thermal annealing in air...