Power-law and exponential rank distributions: A panoramic Gibbsian perspective

Rank distributions are collections of positive sizes ordered either increasingly or decreasingly. Many decreasing rank distributions, formed by the collective collaboration of human actions, follow an inverse power-law relation between ranks and sizes. This remarkable empirical fact is termed Zipf’s law, and one of its quintessential manifestations is the demography of human settlements — which exhibits a harmonic relation between ranks and sizes. In this paper we present a comprehensive statistical-physics analysis of rank distributions, establish that power-law and exponential rank distributions stand out as optimal in various entropy-based senses, and unveil the special role of the harmonic relation between ranks and sizes. Our results extend the contemporary entropy-maximization view of Zipf’s law to a broader, panoramic, Gibbsian perspective of increasing and decreasing power-law and exponential rank distributions — of which Zipf’s law is one out of four pillars.     

Local elastic properties of nano-confined fluids: A density functional study

The understanding of mechanical properties of confined fluids is essential for modeling and manipulating of nano-scaled systems. Unlike the uniform phase, the confined fluids usually display different features in structure and related properties. Due to the presence of the confining geometry, the density profile and many physical and chemical properties may be position-dependent. The aim of our research is to derive an expression for the local elastic property by using the classical elastic theory. Both the bulk and shear moduli are expressed as functional of density of particle. The theoretical result derived is applied to the Lennard-Jones fluids confined in nano-cavity. Comparison of our numerical result and the simulation result is made and qualitative agreement is observed. Further, influence of bulk density, temperature and external potential on moduli is calculated and the physical mechanism is analyzed. Relationship between contact modulus and the interfacial tension is also calculated. Their opposite trend with temperature is observed.     

Analyzing integrated-optical inhomogeneous planar waveguides by Galerkin's method: A detailed comparison of two different basis functions

Abstract

The trigonometric and Hermite-Gaussian basis functions for determining the modal characteristics of inhomogeneous optical waveguides by means of the Galerkin's method are presented and analyzed. The results obtained with each set of basis functions for mode spectra and field distributions are compared with other exact and approximate methods. The merits and problems arising with each set of basis functions are discussed.     

Evaluation of nonlinear optical parameters of TiN/PVA nanocomposite – A comparison between semi empirical relation and Z-Scan results

We report on the third order non linearity of TiN/PVA nanocomposites. Linear and nonlinear optical properties were studied from theoretical and experimental method. Theoretical method involved Tichy and Ticha relation pooled with generalised Miller's rule. During the study dispersion of refractive index is analysed using the Wemple–Di Domenico single oscillator model. Z-Scan was used as the experimental tool. The results derived from theoretical method deviated greatly from the experimental. We believe that such incongruity is due to the SPR property of the TiN nanoparticle whose SPR peak almost coincides with the irradiated laser wavelength.     

Fitting models to correlated data III: A comparison between residual analysis and other methods

Applications of the χ² test, the F test, the Durbin-Watson d test, and the f (or Sign) test, to examples of correlated data treatment, show important drawbacks with the d test and (apparently) with the f test. An analytical approach based on residual analysis suggests an improvement in their use that leads to better results at lowest order; it also points out a distinction between goodness-of-fit tests, as the f test, and goodness-of-modeling tests, as the χ² and F tests. The residual analysis method is applied to the same examples; it looks faster, simpler, and often more accurate than the classical ones.     

Benford analysis of quantum critical phenomena: First digit provides high finite-size scaling exponent while first two and further are not much better

Benford's law is an empirical edict stating that the lower digits appear more often than higher ones as the first few significant digits in statistics of natural phenomena and mathematical tables. A marked proportion of such analyses is restricted to the first significant digit. We employ violation of Benford's law, up to the first four significant digits, for investigating magnetization and correlation data of paradigmatic quantum many-body systems to detect cooperative phenomena, focusing on the finite-size scaling exponents thereof. We find that for the transverse field quantum XY model, behavior of the very first significant digit of an observable, at an arbitrary point of the parameter space, is enough to capture the quantum phase transition in the model with a relatively high scaling exponent. A higher number of significant digits do not provide an appreciable further advantage, in particular, in terms of an increase in scaling exponents. Since the first significant digit of a physical quantity is relatively simple to obtain in experiments, the results have potential implications for laboratory observations in noisy environments.     

The electronic properties and electron transport of sawtooth penta-graphene nanoribbon under uniaxial strain: ab-initio study

ABSTRACT

The electronic properties and electron transport of a sawtooth penta-graphene nanoribbon (SSPGNR) under uniaxial strains are theoretically studied by density-functional theory (DFT) in combination with the non-equilibrium Green's function formalism. We investigated the electronic structures and the current–voltage (I–V) characteristics of the SSPGNRs under a sequence of uniaxial strains in range from 10% compression to 10% stretch. In this strained range, carbon atoms still keep a pentagon network, but with the changing bond lengths. The C–C bond lengths change almost linearly with the tolerable strain. The value of the band gap of SSPGNRs can be depicted as a parabola under uniaxial strain. Our calculations show that the current is monotonous increase with compressive strain at the same applied bias voltage. In case of tensile strain, the variable rule of the current is different that it increases at first and decrease later. The fundamental physical properties (band structure, I–V characteristic) of SSPGNRs seem to be more sensitive to compressive strain than the stretch strain. The current intensity of the compressive-SSPGNR is by 2 orders of magnitude compared to that of the tensile-SSPGNR at the same strain in range from 6% to 10%. The results obtained from our calculations are beneficial to practical applications of these strained structures in SSPGNRs-based electromechanical devices.     

具有负泊松比效应的2D碳纳米结构设计及其性能的理论计算研究

本文利用第一性原理PBE密度泛函理论计算的方法设计了一种由炔基链、吡啶环及少量氢原子组成的具有内凹六边形结构单元的新型理想二维碳纳米结构,并对其平面内负泊松比效应等力学性能和光学性能与电子结构进行了预测.计算表明,该2D材料具有较好的结构稳定性和特殊的力学性能.当将该2D结构在面内(bc面)沿c方向压缩时,其在b方向收缩;当沿c方向拉伸时,其在b方向伸长,即该2D结构同样具有期望的负泊松比效应.材料的泊松比为-3.26;将该2D结构沿b方向拉伸时,c方向将随之伸长;沿b方向压缩时,c方向将随之收缩.沿b方向拉伸或压缩时,泊松比约为-1.951.即该2D材料在面内具有非常显著的负泊松比效应.此外,该2D材料表现出半导体材料的电子结构特征和良好的光反射和折射性能.希望本工作能为具有本征负泊松比效应和优良电子与光学功能的理想二维碳纳米材料的开发提供一种理想的结构设计策略.     

Multiple mobility edges in a 1D Aubry chain with Hubbard interaction in presence of electric field: Controlled electron transport

Electronic behavior of a 1D Aubry chain with Hubbard interaction is critically analyzed in presence of electric field. Multiple energy bands are generated as a result of Hubbard correlation and Aubry potential, and, within these bands localized states are developed under the application of electric field. Within a tight-binding framework we compute electronic transmission probability and average density of states using Green's function approach where the interaction parameter is treated under Hartree–Fock mean field scheme. From our analysis we find that selective transmission can be obtained by tuning injecting electron energy, and thus, the present model can be utilized as a controlled switching device.     

Historical note: On the simulation of dispersive wave propagation by elasticity models

Attention is called to E. Schrödinger's elegant analytical solution [Annalen der Physik 44 (1914) p.916] of the initial-value problem for the Born–von Kármán model of an infinite one-dimensional chain of uniformly spaced particles of mass M with nearest-neighbour coupling by harmonic springs. This model has recently served as the starting point for a computer study of the transition to partial differential equations describing dispersive wave propagation in inhomogeneous media [Askes et al., Phil. Mag. 88 (2008) p.3415]. Schrödinger's solution allows the main features of the limit process involved in this transition to be studied in a straightforward way.     

Undergraduate Analytical Chemistry: To Use and Evaluate Organic Chelators for Spectrophotometric Determination of Iron

Abstract

An analytical chemistry laboratory project to use and evaluate pyridyl‐ and triazine‐containing chelators for spectrophotometric determination of iron is described. The “Iron Project” introduces students to UV‐visible spectrophotometry and Beer's law via hands‐on development and use of spectrophotometric methods for iron. Nine chelators are currently available for use. Students perform their proposed work, culminating in formal papers and posters. Student values of molar absorptivities (?_max) and λ_max for ligands 1–9 agree with published values to within ±15% (?_max) and ±3 nm (λ_max) for 75% of results obtained so far. Stoichiometries for Fe(II) chelates of ligands 1–5 are within ±1 mole of ligand of the published ratios. Student work shows a basic understanding of Beer's law as well as a need to improve writing, problem‐solving, and laboratory skills.     

Quantitative assessment of iron deposition in the midbrain using 3D-enhanced T2 star weighted angiography (ESWAN): A preliminary cross-sectional study of 20 Parkinson’s disease patients

Conventional magnetic resonance imaging (MRI) assesses neurodegenerative structural changes in the cerebral anatomy of Parkinson's disease (PD) patients but cannot detect non-structural abnormalities; however, enhanced T2 star weighted angiography (ESWAN) can precisely indicate PD-related substantia nigra (SN) iron deposition. The differences in ESWAN-based parameters between different PD stages were assessed using midbrain iron deposits of 20 PD patients aged 64.3 ± 12.7 (41–85) years grouped by Hoehn and Yahr staging into minimal (stages ≤ 2.5) or moderate to severe (stages ≥ 3.0) motor impairment groups and 14 healthy control subjects. Conventional MRI and ESWAN measurements of mean phase value (MPV) and midbrain dimensions (width and diameter) revealed similar anatomical characteristics; however, ESWAN revealed the presence of smaller MPVs and SN pars compacta (SNc) (P < 0.01) and a negative correlation between reduction extent and motor impairment (P < 0.01). SNc width to midbrain diameter was reduced in moderate to severe impairment patients versus control and minimal impairment patients (both P < 0.01). A positive correlation was found between MPV and width or SNc width to midbrain diameter ratio (P < 0.01 and P < 0.05, respectively). Minimal impairment group mean MPV and substantia nigra pars reticulata (SNr) width evidenced no significant reduction, unlike significant reductions in the moderate to severe impairment group (P < 0.01). No significant changes were observed in MPV or width in the RN region (P > 0.05). ESWAN allows for early and accurate iron deposition determination in PD patients, particularly useful as a supplement to conventional MRI in early-stage PD patients.