Gap Distribution Function Research Articles

Learn2Extend: Extending Sequences by Retaining their Statistical Properties with Mixture Models

This paper addresses the challenge of extending general finite sequences of real numbers within a subinterval of the real line, maintaining their inherent statistical properties by employing machine learning. Our focus lies on preserving the gap distribution and pair correlation function of these point sets. Leveraging advancements in deep learning applied to point processes, this paper explores the use of an auto-regressive Sequence Extension Mixture Model (SEMM) for extending finite sequences, by estimating directly the conditional density, instead of the intensity function. We perform comparative experiments on multiple types of point processes, including Poisson, locally attractive, and locally repelling sequences, and we perform a case study on the prediction of Riemann ζ function zeroes. The results indicate that the proposed mixture model outperforms traditional neural network architectures in sequence extension with the retention of statistical properties. Given this motivation, we showcase the capabilities of a mixture model to extend sequences, maintaining specific statistical properties, i.e. the gap distribution, and pair correlation indicators.

Synthesis of natural glucomannan derivative as a highly-efficient green inhibitor for mild steel in the simulated seawater

Herein, we report a rational design and synthesis of a highly-efficient and eco-friendly glucomannan derivative (GA-2) by the introduction of the thiazole and Schiff base groups into glucomannan (GA). After confirmation of GA-2 by the spectroscopic methods, it was introduced as corrosion inhibitor with excellent anti-corrosion action for mild steel (MS) in the simulated seawater. As-obtained results reveal that GA-2 has a significantly enhanced anticorrosion performance, and its inhibitive efficiency reaches 98.8% at the 0.5 mmol L−1 inhibitor concentration, much higher than that of GA (69.8%) and the intermediate derivative GA-1 (81.2%). The significantly enhanced protection performance could be attributed to the rich S heteroatoms, aromatic rings, and Schiff base groups in the GA-2, which strongly promotes the chemisorption as well as physisorption between GAD and MS. X-ray photoelectron spectroscopy (XPS) results, show that the appearance of N-Fe and S-Fe bonds confirms the strongly anchoring interaction between GA and MS. Furthermore, according to the quantum chemical calculations, the results from the lowe energy gap and radical distribution function (RDF) analyses further confirm the strong chemisorption of GA-2 at the surface of steel, which illustrates the excellent inhibition performance at the molecule and atom level.

Temperature-dependent [formula omitted]-electron evolution in CeCoIn[formula omitted] via a comparative infrared study with LaCoIn[formula omitted

We investigated CeCoIn5 and LaCoIn5 single crystals, which have the same HoCoGa5-type tetragonal crystal structure, using infrared spectroscopy. However, while CeCoIn5 has 4f electrons, LaCoIn5 does not. By comparing these two material systems, we extracted the temperature-dependent electronic evolution of the f electrons of CeCoIn5. We observed that the differences caused by the f electrons are more obvious in low-energy optical spectra at low temperatures. We introduced a complex optical resistivity and obtained a magnetic optical resistivity from the difference in the optical resistivity spectra of the two material systems. From the temperature-dependent average magnetic resistivity, we found that the onset temperature of the Kondo effect is much higher than the known onset temperature of Kondo scattering (≃200 K) of CeCoIn5. Based on momentum-dependent hybridization, the periodic Anderson model, and a maximum entropy approach, we obtained the hybridization gap distribution function of CeCoIn5 and found that the resulting gap distribution function of CeCoIn5 was mainly composed of two (small and large) components (or gaps). We assigned the small and large gaps to the in-plane and out-of-plane hybridization gaps, respectively. We expect that our results will provide useful information for understanding the temperature-dependent electronic evolution of f-electron systems near Fermi level.

Analysis on the Income Tax Compliance Behavior of Muzaki at Lazismu Sragen

Introduction to The Problem: Zakat as a deduction of taxable income has become an issue that has attracted the attention of the public economy. The most obvious thing is that the low realization of zakat collection and tax ratios affect the welfare gap (distribution function) and public services received by the citizens (allocation function). On an extreme scale, non-compliance with zakat and tax may threaten social cohesion and legal authority. Purpose/Objective Study: This study aims to find out how zakat regulation as a deduction of taxable income affects muzaki's behavior to comply or not comply with tax obligations. Design/Methodology/Approach: The research design is empirical legal research with qualitative analysis. The primary source builds on focus group discussions (FGDs). Otherwise, secondary sources are collected through a literature study of primary, secondary, and tertiary legal materials. Findings: Zakat as a deduction of taxable income affects muzaki's behavior to comply with tax obligations. The zakat scheme as a deduction of taxable income greatly influences muzaki's behavior within the level of tax compliance, specifically the level of resistance to tax because the system is considered oppressive, to move up to the level of tax compliance trying to comply but having difficulty understanding tax. This significant change occurs because the Zakat scheme as a deduction of taxable income is able to eliminate the characteristic of “tax is conflicting with zakat” in the level of tax compliance resistance because the system is considered oppressive. Paper Type: Research Article.

Analysis of the geometrical properties and electronic structure of arsenide doped boron clusters: Ab-initio approach

Abstract Density functional theory (DFT) and coupled-cluster (CCSD(T)) theory have been applied to investigate the geometric, growth pattern, bonding, stability, dissociation, adsorption and electronic properties of arsenide doped boron clusters BnAs (n = 1–9). Vertical ionization potential (VIP), vertical electron affinity (VEA), HOMO-LUMO energy gap (Eg), binding energy (Eb), chemical hardness (η), and radial distribution functions (RDFs) of B-As and B-B interactions have also been investigated and discussed for the most stable isomers. The results show that the As-dopant atom prefers to locate in peripheral regions for the studied sizes. Arsenic atom can obviously enhance the stability of BnAs clusters.

Systematic analysis of Persson’s contact mechanics theory of randomly rough elastic surfaces

We systematically check explicit and implicit assumptions of Persson’s contact mechanics theory. It casts the evolution of the pressure distribution Pr(p) with increasing resolution of surface roughness as a diffusive process, in which resolution plays the role of time. The tested key assumptions of the theory are: (a) the diffusion coefficient is independent of pressure p, (b) the diffusion process is drift-free at any value of p, (c) the point p = 0 acts as an absorbing barrier, i.e., once a point falls out of contact, it never re-enters again, (d) the Fourier component of the elastic energy is only populated if the appropriate wave vector is resolved, and (e) it no longer changes when even smaller wavelengths are resolved. Using high-resolution numerical simulations, we quantify deviations from these approximations and find quite significant discrepancies in some cases. For example, the drift becomes substantial for small values of p, which typically represent points in real space close to a contact line. On the other hand, there is a significant flux of points re-entering contact. These and other identified deviations cancel each other to a large degree, resulting in an overall excellent description for contact area, contact geometry, and gap distribution functions. Similar fortuitous error cancellations cannot be guaranteed under different circumstances, for instance when investigating rubber friction. The results of the simulations may provide guidelines for a systematic improvement of the theory.

Energy-gap analysis of quantum spin-glass transitions at zero temperature

We study for random quantum spin systems the energy gap between the ground and first excited states to clarify a relation to the spin-glass-paramagnetic phase transition. We find that for the transverse Sherrington-Kirkpatrick model the vanishing of the averaged gap does not identify the transition. A power-law form of the gap distribution function leads to power-law distributions of the linear, spin-glass, and nonlinear susceptibilities. They diverge at different points, which we attribute to a quantum "Griffiths" mechanism. On the other hand, the classical treatment is justified for the transverse random energy model and the phase transition can be found by a sudden change of the ground state.

Deterministic reaction models with power-law forces

We study a one-dimensional particles system, in the overdamped limit, where nearest particles attract with a force inversely proportional to a power α of their distance and coalesce upon encounter. The detailed shape of the distribution function for the gap between neighbouring particles serves to discriminate between different laws of attraction. We develop an exact Fokker–Planck approach for the infinite hierarchy of distribution functions for multiple adjacent gaps and solve it exactly, at the mean-field level, where correlations are ignored. The crucial role of correlations and their effect on the gap distribution function is explored both numerically and analytically. Finally, we analyse a random input of particles, which results in a stationary state where the effect of correlations is largely diminished.

Interactions and microstructures in electric field mediated colloidal assembly

We report video microscopy measurements and computer simulations of quasi-two-dimensional configurations of micron sized colloids in 1 MHz ac electric fields between coplanar thin film electrodes. Interactions of induced dipoles (IDs) with each other and inhomogeneous electric fields (IFs) as a function of concentration and field amplitude produced microstructures including confined hard disk fluids, oriented dipolar chains, and oriented hexagonal close packed crystals. Equilibrium measurements and analyses of single colloids within electric fields were used to directly measure ID-IF interactions in the absence of many body effects. Measurements of concentrated systems were characterized in terms of density profiles across the electrode gap and angular pair distribution functions. In concentrated measurements, an inverse Monte Carlo analysis was used to extract the ID-ID interaction. A single adjustable parameter consistently modified the ID-IF potential and the ID-ID potential to account for weakening of ID as the result of the local particle concentration and configuration.

Impurity effect on superconducting gap and pseudogap

Co substituted Bi2212 samples of Bi 2.1Sr 1.9Ca(Cu 1−xCo x)O 8+ δ ( x = 0, 0.01, 0.02, 0.04, 0.06, and Tc = 85,71,52,35 K) were prepared, and their electronic density states were characterized by a low temperature STM. The experimental results revealed that superconducting gap-like features were rapidly destroyed, while pseudogap-like features were enhanced with increasing impurities, suggesting that the origin of the pseudogap is different from that of a superconducting gap. We suggested a two phase-like model to explain the behavior of a gap map and a gap distribution function. On the other hand, spatial gap and pseudogap inhomogeneity persisted in all Co concentrations. This indicates that the origin of inhomogeneity is not related to in-plane disorder or impurities.

Violation of the Porod Law in a Freely Cooling Granular Gas in One Dimension

We study a model of freely cooling inelastic granular gas in one dimension, with a restitution coefficient which approaches the elastic limit below a relative velocity scale delta. While at early times (t<<delta;{-1}) the gas behaves as a completely inelastic sticky gas conforming to predictions of earlier studies, at late times (t>>delta;{-1}) it exhibits a new fluctuation-dominated phase ordering state. We find distinct scaling behavior for the (i) density distribution function, (ii) occupied and empty gap distribution functions, (iii) the density structure function, and (iv) the velocity structure function, as compared to the completely inelastic sticky gas. The spatial structure functions (iii) and (iv) violate the Porod law. Within a mean-field approximation, the exponents describing the structure functions are related to those describing the spatial gap distribution functions.

Gap inhomogeneity, phase separation and a pseudogap in Bi2Sr2CaCu2O8+δ

Gap inhomogeneity in Bi2Sr2CaCu2O8 has been studied by low-temperature STM. We found a systematic relation between the local gap energy and local background density of states. A model analysis of the dip–hump structure gave evidence of in-plane charge inhomogeneity. The temperature/doping dependences of the pattern shape of inhomogeneity as well as the gap distribution function were measured. We could identify the signature of phase separation into the superconducting and pseudogapped phases as the appearance of a double-peak structure in the distribution function.

Non-Poissonian Level Spacing Statistics of Classically Integrable Quantum Systems Based on the Berry-Robnik Approach

Along the line of thoughts of Berry and Robnik\cite{[1]}, we investigated the gap distribution function of systems with infinitely many independent components, and discussed the level-spacing distribution of classically integrable quantum systems. The level spacing distribution is classified into three cases: Case 1: Poissonian if $\bar{\mu}(+\infty)=0$, Case 2: Poissonian for large $S$, but possibly not for small $S$ if $0<\bar{\mu}(+\infty)< 1$, and Case 3: sub-Poissonian if $\bar{\mu}(+\infty)=1$. Thus, even when the energy levels of individual components are statistically independent, non-Poisson level spacing distributions are possible.

Hierarchical structure of Azbel-Hofstadter problem: Strings and loose ends of Bethe ansatz

We present numerical evidence that solutions of the Bethe anstaz equations for a Bloch particle in an incommensurate magnetic field (Azbel-Hofstadter or AH model), consist of complexes—“ strings”. String solutions are well known from integrable field theories. They become asymptotically exact in the thermodynamic limit. The string solutions for the AH model are exact in the incommensurate limit, where the flux through the unit cell is an irrational number in units of the elementary flux quantum. We introduce the notion of the integral spectral flow and conjecture a hierarchical tree for the problem. The hierarchical tree describes the topology of the singular continuous spectrum of the problem. We show that the string content of a state is determined uniquely by the rate of the spectral flow (Hall conductance) along the tree. We identify the Hall conductances with the set of Takahashi-Suzuki numbers (the set of dimensions of the irreducible representations of U q ( sl 22) with definite parity). In this paper we consider the approximation of non-interacting strings. It provides the gap distribution function, the mean scaling dimension for the bandwidths and gives a very good approximation for some wave functions which even captures their multifractal properties. However, it misses the multifractal character of the spectrum. © 1998 Elsevier Science B.V

Effect of the transient mobility in one-dimensional continuum deposition

We study the kinetics and the jamming state in the continuum deposition of molecules which present transient mobility, i.e. hot molecules. The transient mobility is caused by the inability to dissipate the energy gained by the particle after formation of the surface bond instantaneously. Accordingly, the particle flies up to a distance R before being immobile. We analyse the continuum deposition of hot monomers in one dimension. The rate equations for the gap distribution functions are written and solved by means of numerical procedures and the results are compared with Monte Carlo simulations. The kinetics of the process show a crossover between power-law and exponential asymptotic regimes for increasing values of R. The jamming state presents a jamming density , which is strongly dependent on the parameter R.

Exact results for surface deposition with precursor layer diffusion

An accelerated random sequential adsorption process is studied as a model of chemisorption on a line with precursor layer diffusion. In this process if the position first selected for deposition is occupied then the particle diffuses and is absorbed on the first vacant position it visits. For k-mer deposition exact results are obtained for the gap distribution function. Physically measurable quantities such as the average island size and the probabilities of island nucleation, growth and coagulation are calculated as a function of coverage and the saturation coverage is calculated as a function of k. The continuum version of this model is also considered and potential applications of the models are discussed.

Optical Characterization of Free-Standing Porous Silicon Films

We report here the optical characterization of two free-standing porous silicon (PS) films of porosity 70% and 85%, grown on a p- and a n-type Si. We determine the optical band gap in these films from the excitation wavelength dependence of the photoluminescence band. As the excitation wavelength is changed from red (800 nm) to UV (355 nm), a blue shift of the photoluminescence (PL) band is observed. We attribute the observed blue shift of the PL band to the emission due to the distribution of bandgap in PS. Both samples are oxidized in air and we believe that the observed bandgap in these films arises from the inhomogeneous distribution of Si particle sizes. However, we find that intrinsic defects play a dominant role in the process of luminescence. Electron spin resonance measurement indicates the presence of defects leading to the saturation of the optical absorption spectra and a decrease in intensity of the PL band. The lineshape of the PL band is modeled using a weighted asymmetric Gaussian that selects a gap distribution function at each excitation wavelength. From Raman measurements in these two films, the quantum confinement effect in Si nanostructures is clearly observed in both films.

Ground-state properties and dynamics of the bilayer t-J model.

We present an exact diagonalization study of bilayer clusters of t-J model. Our results indicate a crossover between two markedly different regimes which occurs when the ratio J_perp/J between inter-layer and intra-layer exchange constants increases: for small J_perp/J the data suggest the development of 3D antiferromagnetic correlations without appreciable degradation of the intra-layer spin order and the d_(x2-y2) hole pairs within the planes persist. For larger values of J_perp/J local singlets along the inter-layer bonds dominate, leading to an almost complete suppression of the intra-layer spin correlation and the breaking of the intra-layer pairs. The ground state with two holes in this regime has s-like symmetry. The data suggest that the crossover may occur for values of J_perp/J as small as 0.2. We present data for static spin correlations, spin gap, and electron momentum distribution and spectral function of the `inter-layer RVB state' realized for large J_perp/J. The latter deviates from the single layer ground state, making it an implausible candidate for modelling high-temperature superconductors.

An adsorption-desorption process on a line: kinetics of the approach to closest packing

We study an adsorption-desorption process of rods on a line. The desorption rate is infinitely small, so that each desorption event is instantly followed by the insertion of one or two new rods. Due to the latter possibility, the system evolves continuously to a close-packed state. The asymptotic kinetics of the densification process is analysed with the aid of gap distribution functions. If it is assumed that the system relaxes completely to equilibrium after each density increment, we show that 1- rho (t) approximately 1/ln(t), while an improved description yields 1- rho (t) approximately 1/ln(2t(ln2t)2). The range of validity of the asymptotic expressions is established by comparison with the results of a numerical simulation of the process.

Exact solution of a generalized ballistic-deposition model.

We study a monolayer deposition model which generalizes both random sequential adsorption and ballistic deposition: hard disks are dropped vertically and randomly onto a line; they can adsorb on the line either by direct deposition or after rolling over preadsorbed disks. An exact solution is given for the gap distribution function and for the density of adsorbed disks. Properties of the system at or close to the jamming limit are discussed. This generalized ballistic-deposition process leads to formation of connected clusters of all sizes: the time evolution of the cluster distribution is obtained analytically