Long-range Behavior Research Articles

Modeling online user behaviors with competitive interactions

Online user behaviors are increasingly modulated by social media. Extant literature mainly focuses on investigating how network structures affect user behaviors. However, recent empirical results demonstrate that user behaviors and network structures usually coevolve dynamically, and topological patterns turn out to be inadequate for characterizing real-world user behaviors. In this paper, we present a dynamic model to deal with this challenge. This proposed model is mainly governed by two competing principles: homophily and homeostasis. Empirical evaluations of three online real-world datasets suggest that the proposed dynamic model can well predict long-range online user behaviors.

A continuous transition from chaotic bursting to chaotic spiking in a glow discharge plasma and its associated long range correlation to anti correlation behaviour

An experimental investigation on the self-excited spiky oscillations in a glow discharge plasma device is presented. The system showed a continuous transition from chaotic bursting to chaotic spiking states with the increase in the applied discharge voltage at a particular pressure. Below a threshold discharge voltage, the system exhibits a fixed point dynamical behaviour and with the increase in the discharge voltage bursting type oscillations appear which are identified as “fold/fold circle” type. The occurrence of the relaxation type spiky oscillations is attributed to the formation and disruption of anode double layer. The burst phases occurred intermittently and the frequency of their occurrence increased with increase in the discharge voltage and finally the oscillation turned into spiking behaviour. The intermittent oscillations manifested the scaling law of the average laminar phase with respect to the change in the discharge voltage. The scaling law of the intermittent oscillations was similar to type III intermittency. During the transition, the system changes its behaviour from long range correlation to long range anti correlation. Detrended fluctuation analysis technique has been used to identify the nature of long range correlations. We found that bursting oscillations show scale invariant, long-range correlation behaviour whereas spiking oscillations show scale invariant, long range anti correlation behaviour.

Influences of vacancy and doping on electronic and magnetic properties of monolayer SnS

Based on the first-principles calculations, we investigate the structural, electronic, and magnetic properties of defects in monolayer SnS. We study the formation and migration of vacancies at both Sn- and S-sites. In comparison to the S-site vacancy, our calculations show that creating a vacancy at the Sn-site requires lesser energy, indicating that the vacancy at the Sn-site is more likely to be formed in experiments with energetic particle irradiation. For the Sn-rich (S-rich) environment, the vacancy at the S-site (Sn-site) is more likely to be found than the vacancy at the Sn-site (S-site). Reducing the formation of vacancy clusters, the S vacancy remains at the position where it is created because of the high vacancy migration barrier. Both types of vacancies remain nonmagnetic. To induce magnetism in monolayer SnS, we also study the transition metal (TM = Mn, Fe, and Co) doping at the Sn-site and find a significant influence on the electronic and magnetic properties of monolayer SnS. The doping of TM changes non-magnetic monolayer SnS to magnetic one and keeps it semiconducting. Additionally, long-range ferromagnetic behavior is observed for all the doped system. Hence, doping TM atoms in monolayer SnS could be promising to realize a two-dimensional diluted magnetic semiconductor. More interestingly, all the doped TM configurations show a high spin state, which can be used in nanoscale spintronic applications such as spin-filtering devices.

Spectroscopic studies of dye-doped porous alumina membranes

We have studied the spectroscopic properties of nanoporous alumina membranes impregnated with rhodamine 6G (R6G) dye molecules. At small dye concentrations, the reflectance spectra feature one minimum, corresponding to the absorption band of R6G. With increase of the dye concentration, the reflectance dip splits in two and the energy difference between the two minima increases. A similar behavior is shared by the emission spectral band. We explain these observations in terms of strong coupling of closely situated dye molecules inside the channels. At the same time, the experimentally observed angular dependence of the reflectance spectrum is consistent with a long-range collective behavior of dye molecules across an array of dye-impregnated channels.

Structural-Phase Features of Low-Stability Pre-Transitional States of BCC-Alloys with Complexes of Planar Defects (Antiphase Boundaries)

Using the Monte Carlo method, the influence of the complexes of antiphase boundaries (APBs) (a pair of shear APBs and a pair of thermal APBs) on the low-stability, pre-transitional states of BCC-alloys is considered by the example of a conventional copper alloy CuZn and an intermetallic compound NiAl. It is shown that in the region of low-stability structural-phase states the energy of formation of a complex of thermal APBs is higher than that of shear APBs. The contribution of APBs into disordering is appreciable up to the structural-phase transition temperature. The most significant factor in terms of the long-range order is the formation of the defect itself; the differences in the APB type or the plane of their occurrence do not so much affect the longrange order behavior with the temperature variation. The type of APBs however appreciably affects the structural-energy characteristics of the system at the temperatures below the phase transformation temperature. Logically, a system with structural defects is less ordered than a defect-free system. The presence of a defect favors the onset of disordering at lower temperatures: it starts at lower temperatures in the case of thermal APBs (TAPBs) compared to shear APBs (TAPBs). In a BCC-system with a complex of TAPBs the first signs of disordering invariably appear near the phase boundary in the neighborhood of large atoms (Zn–Zn in the CuZn alloy or Al–Al in the NiAl intermetallide). In the alloy with a complex of shear APBs the distortion of ordering at low temperatures is observed in the regions where the boundaries cross. The presence of antiphase boundaries affects the alloy stability under heating. It is shown that disordering is accompanied by smearing of the boundaries and their faceting. It follows from a comparative analysis of the peculiarities of disordering in the BCC-system under study (classical alloy CuZn and intermetallide NiAl) under conditions of higher temperatures in the region of low-stability, pre-transitional states that the order – disorder phase transition in the CuZn alloy takes place as a result of disordering of the system, while in the intermetallide NiAl the change of long-range order results from the structural-phase transition.

What Does Second-Harmonic Scattering Measure in Diluted Electrolytes?

We derive a theoretical expression of the second harmonic scattering signal in diluted electrolytes compared with bulk water. We show that the enhancement of the signal with respect to pure water observed recently for electrolytes at very low dilution in the micromolar range is a mere manifestation of the Debye screening that makes the infinite-range dipole-dipole solvent correlations in 1/ r3 disappear as soon as the ionic concentration becomes finite. In q space, this translates into a correlation function having a well known singular behavior around q = 0, which drives the observed ionic effects. We find that the signal is independent of the ion-induced long-range behavior of the function ⟨cos ϕ( r)⟩ that has been recently discussed. We find also that the enhancement depends on the experimental geometry and occurs only for in-plane polarization detection, as observed experimentally. On the contrary, the measured isotope effect between light and heavy water cannot be fully explained.

Semi-empirical ground-state potential of carbon monoxide with physical behavior in the limits of small and large inter-atomic separations

Recently, several empirical models of the potential energy function (PEF) of the ground electronic state of CO have been developed by Coxon and Hajigeorgiou using the direct-potential-fit (DPF) analysis. These models reproduce more than twenty thousand of observed ro-vibrational line positions within their experimental accuracies and follow the theoretically predicted long-range asymptotic behavior of the potential beyond Le Roy's radius. However, the applicability of these models to calculations of the intensities of weak transitions is not obvious due to limitations discussed in this work. Here, we make the next step by imposing an additional requirement that the model has to display physical behavior outside the region to which the available spectroscopic data pertain. We perform ab initio calculations of the potential in the short-range region r = 0.3–0.8 Å where the potential increases well above the dissociation limit and include these data along with the estimated uncertainties in the DPF analysis. At smaller r, our PEF tends to the well-known united-atom limit. In the long-range region, it follows the ab initio data with their estimated accuracies available in the literature. On top of the above, the model is analytical, i.e. it has continuous derivatives of all orders. The model constructed is a linear function of twenty three adjustable parameters, and a non-linear function of additional five parameters. The properties of the new PEF are investigated in comparison with the previous empirical model due to Coxon and Hajigeorgiou (2004). Our PEF provides reproduction of all observed lines at the same level of accuracy. The new potential changes the intensities of high overtone transitions dramatically. In addition, we find that the anomalies in the purely rotational and ro-vibrational spectra change their intensities between the two PEFs even for the low-v bands.

Benchmark study of ionization potentials and electron affinities of armchair single-walled carbon nanotubes using density functional theory

The intrinsic parameters of carbon nanotubes (CNTs) such as ionization potential (IP) and electron affinity (EA) are closely related to their unique properties and associated applications. In this work, we demonstrated the success of optimal tuning method based on range-separated (RS) density functionals for both accurate and efficient prediction of vertical IPs and electron affinities (EAs) of a series of armchair single-walled carbon nanotubes C20nH20 (n = 2–6) compared to the high-level IP/EA equation-of-motion coupled-cluster method with single and double substitutions (IP/EA-EOM-CCSD). Notably, the resulting frontier orbital energies (–εHOMO and –εLUMO) from the tuning method exhibit an excellent approximation to the corresponding IPs and EAs, that significantly outperform other conventional density functionals. In addition, it is suggested that the RS density functionals that possess both a fixed amount of exact exchange in the short-range and a correct long-range asymptotic behavior are suitable for calculating electronic structures of finite-sized CNTs. Next the performance of density functionals for description of various molecular properties such as chemical potential, hardness and electrophilicity are assessed as a function of tube length. Thanks to the efficiency and accuracy of this tuning method, the related behaviors of much longer armchair single-walled CNTs until C200H20 were studied. Lastly, the present work is proved to provide an efficient theoretical tool for future materials design and reliable characterization of other interesting properties of CNT-based systems.

Interaction potentials and transport properties of Ba, Ba+, and Ba2+ in rare gases from He to Xe.

A highly accurate, consistent set of ab initio interaction potentials is obtained for the title systems at the coupled cluster with singles, doubles, and non-iterative triples level of theory with extrapolation to the complete basis set limit. These potentials are shown to be more reliable than the previous potentials based on their long-range behavior, equilibrium properties, collision cross sections, and transport properties.

Random walks with long-range steps generated by functions of Laplacian matrices

In this paper, we explore different Markovian random walk strategies on networks with transition probabilities between nodes defined in terms of functions of the Laplacian matrix. We generalize random walk strategies with local information in the Laplacian matrix, that describes the connections of a network, to a dynamic determined by functions of this matrix. The resulting processes are non-local allowing transitions of the random walker from one node to nodes beyond its nearest neighbors. We find that only two types of Laplacian functions are admissible with distinct behaviors for long-range steps in the infinite network limit: type (i) functions generate Brownian motions, type (ii) functions Lévy flights. For this asymptotic long-range step behavior only the lowest non-vanishing order of the Laplacian function is relevant, namely first order for type (i), and fractional order for type (ii) functions.In the first part, we discuss spectral properties of the Laplacian matrix and a series of relations that are maintained by a particular type of functions that allow to define random walks on any type of undirected connected networks. Once described general properties, we explore characteristics of random walk strategies that emerge from particular cases with functions defined in terms of exponentials, logarithms and powers of the Laplacian as well as relations of these dynamics with non-local strategies like Lévy flights and fractional transport. Finally, we analyze the global capacity of these random walk strategies to explore networks like lattices and trees and different types of random and complex networks.

Unbiased detrended fluctuation analysis: Long-range correlations in very short time series

Detrended fluctuation analysis (DFA) is a standard method to evaluate long-range correlations embedded in non-stationary time series. To obtain a reliable estimation of scaling behavior, it requires the length of a time series is long enough (at least ∼10,000), which is not always the case in reality. How to evaluate long-range correlation behavior in a very short time series is still an open problem. In the present paper, we propose an improvement of DFA by correcting the bias in estimation of variance, called Unbiased Detrended Fluctuation Analysis (UDFA). Extensive calculations show its high-performance. For instance, from a fractional Brownian motion (fBm) series with length 500 the estimated long-range correlation exponent has negligible bias and acceptable confidence region (standard deviation less than 0.05). As a typical example, the proposed method is used to monitor evolution of fractal gait rhythm of a volunteer. Rich patterns are found in the evolutionary process.

Advanced characterization technique for mechanochemically synthesized materials: neutron total scattering analysis

Materials that adopt the pyrochlore (A2B2O7) structure show promise for use in a variety of energy-related applications such as immobilization of actinide-rich nuclear waste and oxide fuel cells. Mechanochemical synthesis, a combination of milling and high-temperature treatment, has been successfully applied to fabricate many different pyrochlore compositions. High-resolution neutron total scattering experiments were used to gain fundamental insight into the structural details of milled Er2Ti2O7 pyrochlore and the subsequent evolution under high-temperature treatment. The milling process creates a highly disordered structure in which local atomic ordering is present that is significantly different than the observed long-range behavior. Thermal annealing leads to a complex defect recovery scheme with a gradual local rearrangement from a weberite-type atomic ordering to a pyrochlore phase independent of the sharp long-range crystallization process. Annealing of the milled sample up to 1200 °C does not reproduce the local structure of the same pyrochlore sample prepared by solid-state synthesis. This indicates that despite both samples possessing identical long-range structures, local defects induced by the milling process persist to very high temperatures. These findings provide a direct insight into the mechanochemical synthesis of pyrochlore oxides and help to better elucidate the structural properties of highly disordered complex oxides under extreme conditions from the local atomic arrangement to the macroscale.

A new empirical potential energy function for Ar2

ABSTRACTA critical re-analysis of all available spectroscopic and virial coefficient data for Ar2 has been used to determine an improved empirical analytic potential energy function that has been ‘tuned’ to optimise its agreement with viscosity, diffusion and thermal diffusion data, and whose short-range behaviour is in reasonably good agreement with the most recent ab initio calculations for this system. The recommended Morse/long-range potential function is smooth and differentiable at all distances, and incorporates both the correct theoretically predicted long-range behaviour and the correct limiting short-range functional behaviour. The resulting value of the well depth is cm−1 and the associated equilibrium distance is re = 3.766 (±0.002) Å, while the 40Ar s-wave scattering length is −714 Å.

Particle–hole symmetry in many-body theories of electron correlation

ABSTRACTSecond-quantised creation and annihilation operators for fermionic particles anticommute, but the same is true for the creation and annihilation operators for holes. This introduces a symmetry into the quantum theory of fermions that is absent for bosons. In ab initio electronic structure theory, it is common to classify methods by the number of electrons for which the method returns exact results: for example Hartree–Fock theory is exact for one-electron systems, whereas coupled-cluster theory with single and double excitations is exact for two-electron systems. Here, we discuss the generalisation: methods based on approximate wavefunctions that are exact for n-particle systems are also exact for n-hole systems. Novel electron correlation methods that attempt to improve on the coupled-cluster framework sometimes retain this property, and sometimes lose it. Here, we argue for retaining particle–hole symmetry as a desirable design criterion of approximate electron correlation methods. Dispensing with it might lead to loss of n-representability of density matrices, and this in turn can lead to spurious long-range behaviour in the correlation energy.

Applicability of Kerker preconditioning scheme to the self-consistent density functional theory calculations of inhomogeneous systems.

The Kerker preconditioner, based on the dielectric function of homogeneous electron gas, is designed to accelerate the self-consistent field (SCF) iteration in the density functional theory calculations. However, a question still remains regarding its applicability to the inhomogeneous systems. We develop a modified Kerker preconditioning scheme which captures the long-range screening behavior of inhomogeneous systems and thus improves the SCF convergence. The effectiveness and efficiency is shown by the tests on long-z slabs of metals, insulators, and metal-insulator contacts. For situations without a priori knowledge of the system, we design the a posteriori indicator to monitor if the preconditioner has suppressed charge sloshing during the iterations. Based on the a posteriori indicator, we demonstrate two schemes of the self-adaptive configuration for the SCF iteration.

Measurement of long-range multiparticle azimuthal correlations with the subevent cumulant method in pp and p +Pb collisions with the ATLAS detector at the CERN Large Hadron Collider

A detailed study of multi-particle azimuthal correlations is presented using $pp$ data at $\sqrt{s}=5.02$ and 13 TeV, and $p$+Pb data at $\sqrt{s_{\rm{NN}}}=5.02$ TeV, recorded with the ATLAS detector at the LHC. The azimuthal correlations are probed using four-particle cumulants $c_{n}\{4\}$ and flow coefficients $v_n\{4\}=(-c_{n}\{4\})^{1/4}$ for $n=2$ and 3, with the goal of extracting long-range multi-particle azimuthal correlation signals and suppressing the short-range correlations. The values of $c_{n}\{4\}$ are obtained as a function of the average number of charged particles per event, $\left\langle N_{\rm{ch}} \right\rangle$, using the recently proposed two-subevent and three-subevent cumulant methods, and compared with results obtained with the standard cumulant method. The three-subevent method is found to be least sensitive to short-range correlations, which originate mostly from jets with a positive contribution to $c_{n}\{4\}$. The three-subevent method gives a negative $c_{2}\{4\}$, and therefore a well-defined $v_2\{4\}$, nearly independent of $\left\langle N_{\rm{ch}} \right\rangle$, which provides direct evidence that the long-range multi-particle azimuthal correlations persist to events with low multiplicity. Furthermore, $v_2\{4\}$ is found to be smaller than the $v_2\{2\}$ measured using the two-particle correlation method, as expected for long-range collective behavior. Finally, the measured values of $v_2\{4\}$ and $v_2\{2\}$ are used to estimate the number of sources relevant for the initial eccentricity in the collision geometry.

Structural-Phase Low-Stability States of BCC-Intermetallic Compounds with APB Complexes

Using a mono-nickel aluminide (NiAl) as an example, the influence of APB complexes (a pair of shear APBs along the direction and a pair of APBs along the direction) on the low-stability pre-transitional states of BCC-intermetallic compounds is investigated by the Monte Carlo method. It is shown that in the region of the low-stability states of this compound the formation energy of a complex of thermal APBs is higher than that of a complex of shear APBs. The contribution of APBs into disordering is essential up to the structural-phase transformation temperature. The most significant factor for the long-range ordering in the system is the appearance of a defect in the form of an APB itself, while the differences in the APB types and planes of their occurrence do not so essentially affect the long-range order behavior with the temperature variations. A system with structural defects is obviously less ordered compared to a defect-free system. The presence of a defect in the form of an APB promotes disordering of the system at lower temperatures: the degree of ordering starts to decrease in the case of thermal APBs at a lower temperature compared to the case of shear APBs. In the NiAl alloy with a complex of APBs, the first distortions of the structural order invariably appear near the Al–Al boundary. In the alloy with a complex of shear APBs, the distortions of the structural order are observed only in the regions where the boundaries cross. The presence of antiphase boundaries affects the alloy stability during heating. It is shown that the process of disordering is accompanied by smearing of the boundaries and their faceting.

Structural-Phase Low-Stability States of BCC-Alloys with APB-Complexes in the Course of an Order-Disorder Phase Transition

Using the Monte Carlo method, the influence of the APB-complexes (a pair of shear-induced APBs along the direction and a pair of thermal APBs along the direction) on the low-stability states of β-brass is investigated during an order – disorder phase transition in the CuZn alloy as an example. It is shown that the formation energy of a complex of thermal APBs is higher than that of a complex of shear APBs. The contribution of APBs into disordering is essential up to the temperature of the order – disorder phase transition. The most significant fact for the long-range order in this system is the appearance of a defect in the form of an APB; the difference in the types of APBs and the plane of their occurrence do not exert a significant influence on the long-range order behavior with the temperature variations. The types of antiphase boundaries do affect the structural-energy characteristics of the system at the temperatures below that of the phase transition. It is obvious that a system with structure defects is less ordered than a defect-free system. The presence of a defect in the form of an APB favors the onset of disordering at lower temperatures: reduction of ordering in the alloy begins in the case of thermal APBs at lower temperatures compared to the case of shear APBs. In the CuZn alloy with a complex of thermal APBs along the direction the first distortions of the structural order invariably appear near the Zn–Zn boundary. In the alloy with a complex of shear-induced APBs along the direction the distortions of the structural order are only observed in the regions where the boundaries intersect. The presence of antiphase boundaries influences the alloy stability during heating. The CuZn alloy without distortions of structural defects is more stable than that with APBs. It is shown that the process of disordering is accompanied by the smearing and faceting of the boundaries.

Long-range behavior of the transition dipole moments of heteronuclear dimers XY (X, Y = Li, Na, K, Rb) based on ab initio calculations.

The ab initio electronic transition dipole moments (ETDMs) of heteronuclear dimers XY (X, Y = Li, Na, K, Rb) were calculated between the ground and excited states converging to the lowest three dissociation limits. The spin-allowed ETDMs were evaluated in a wide range of interatomic distances, R, by means of the quasi-relativistic electronic wave functions obtained by the multi-reference configuration interaction method. The inner-shell electrons (2 electrons for Li and Na atoms, and 10 and 28 for K and Rb, respectively) were described using the non-empirical shape-consistent effective core potentials. The l-independent core polarization potentials of each atom were used to take core-polarization and core-valence correlation effects into account. The long-range behavior of both singlet-singlet X1Σ+-(2,3)1Σ+;(1,2)1Π and triplet-triplet a3Σ+-(2,3)3Σ+;(1,2)3Π transition moments is perfectly fitted at large R-distance by the asymptotic formula of X. Chu and A. Dalgarno, Phys. Rev. A: At., Mol., Opt. Phys., 2002, 66, 024701: , where the coefficient β is equal to 2 and -1 for the Σ-Σ and Σ-Π transitions, respectively. The n2S-n2P transition moments, dA, and dynamic polarizabilites, αB, of the alkali atoms in the n2S state extracted from the present molecular calculations coincide with their empirical and ab initio counterparts to within a few percent.

Influence of eikonal-initial-state on ionization of atom by proton

Apart from its fundamental importance, ionization phenomenon of atoms by impact of energetic charged particles has practical applications in various kinds of plasmas, in radiation physics and in the study of penetration of charged particles through matter. Compared with other processes, this particular reaction helps to reveal many details about the dynamical process and the level population, and, in fact, can provide a new insight into and a promising route to studying the e-p interactions in the presence of Coulomb field. The development of ion sources producing multiply charged ions and of antiproton beams allow us to change the potentials and hence the whole final momentum distribution. A great variety of experimental conditions allowed by changing the projectile charge and velocity constitute a stringent test for theory. The continuum-distorted-wave eikonal-initial-state (CDW-EIS) approximation model has emerged as a reliable method to compute cross sections for different projectile/target combinations from intermediate to high non-relativistic impact energies. This model is of the first order in a distorted-wave series. It takes into account the long-range behaviour of the Coulomb potential and includes the distortion of the target states in both the initial and final channels. In the present work, the single different cross sections (SDCS), double different cross sections (DDCS), and total cross sections for single ionization of 1s, 2s and 2p shell of Ne atom by impact of proton are calculated in the framework of continuum-distorted-wave (CDW) method and the CDW-EIS approximation model, respectively. The influence of the eikonal-initial-state on the cross section, and the mechanism of the proton-atom collision ionization are discussed in detail. Moreover, the structures of the SDCS and DDCS of each shell are studied and the ionization mechanism of soft collision, electron capture to the continuum state, binary encounter collision are demonstrated. Our results show that for the 2p shell of Neon, as the incident proton energy increases, the region of the SDCS becomes larger and the soft ionization turns dominant in the low energy region. The eikonal-initial-state effect on the cross section is obvious in the lower energy region, yet smaller as the incident energy increases. These effects on the DDCS are greater than on the SDCS. The present CDW-EIS and CDW results are compared with the experimental data available in the energy range of 1-5000 keV/u for H+ on Ne in the literature, showing that they are quantitatively in good agreement. In general, the CDW-EIS describes well the multiple ionization above 50 keV/u, showing a clear tendency to coalesce with the CDW at high energies.