Divergence-free vector-field and reduction

By the Lie symmetry group, the reduction for divergence-free vector-fields (DFVs) is studied, and the following results are found. A n-dimensional DFV can be locally reduced to a (n − 1)-dimensional DFV if it admits a one-parameter symmetry group that is spatial and divergenceless. More generally, a n-dimensional DFV admitting a r-parameter, spatial, divergenceless Abelian (commutable) symmetry group can be locally reduced to a (n − r)-dimensional DFV.     

Growing networks with preferential deletion and addition of edges

A preferential attachment model for a growing network incorporating the deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step t=1,2,…, with probability π₁>0 a new vertex with one edge attached to it is added to the network and the edge is connected to an existing vertex chosen proportionally to its degree, with probability π₂ a vertex is chosen proportionally to its degree and an edge is added between this vertex and a randomly chosen other vertex, and with probability π₃=1−π₁−π₂<1/2 a vertex is chosen proportionally to its degree and a random edge of this vertex is deleted. The model is intended to capture a situation where high-degree vertices are more dynamic than low-degree vertices in the sense that their connections tend to be changing. A recursion formula is derived for the expected asymptotic fraction p_k of vertices with degree k, and solving this recursion reveals that, for π₃<1/3, we have p_k∼k^{−(3−7π₃)/(1−3π₃)}, while, for π₃>1/3, the fraction p_k decays exponentially at rate (π₁+π₂)/2π₃. There is hence a non-trivial upper bound for how much deletion the network can incorporate without losing the power-law behavior of the degree distribution. The analytical results are supported by simulations.     

Resonances in a circular dielectric cavity

We study resonance distributions in a circular dielectric cavity. It is shown that the decay-rate distribution has a peak structure and the details of the peak are consistent with the classical survival probability time distribution. We also investigate the behavior of the complex resonance positions at the small opening limit (n→∞, n is the refractive index of the cavity). At the large n limit, the real part of complex resonance positions approaches the solutions with different m of Dirichlet problem with a scale n⁻² and the imaginary part goes zero as n−2m for TM and n−2(m+1) for TE polarization, where m is the order of the resonance.     

Linear scaling of the interlayer relaxations of the vicinal Cu(p,p,p − 2) surfaces with the number of atom-rows in the terraces

We investigate the multilayer relaxation trends in the vicinal Cu(p,p,p − 2) surfaces employing the all-electron full-potential linearized augmented plane-wave method. Calculations are performed for the (3 3 1), (2 2 1), (5 5 3), (3 3 2), (7 7 5), and (4 4 3) surfaces, which have 3, 4, 5, 6, 7, and 8 atom-rows in the terrace, respectively. The following trends are identified: (i) The interlayer relaxations perpendicular to the surface scale almost linearly with the number of atom-rows in the terraces. (ii) The nearest-neighbor distances do not depend on the surface termination, but only on the local coordination. (iii) For Cu(p,p,p − 2) in which the topmost n surface layers have nearest-neighbor coordination smaller than the bulk Cu (calculated for the unrelaxed surfaces), the topmost (n − 1) interlayer spacings (d₁₂, … , d_n−1,n) contract compared with the unrelaxed spacing, while the nth interlayer spacing (d_n,n+1) expands. The next (n − 2) interlayer spacings (d_n+1,n+2, … , d_{2n−2,2n−1}) contract, while the interlayer spacing indicated by d_2n−1,2n expands. A similar rule was found for the relaxations parallel to the surfaces. These trends provide a better understanding of the atomic structure of vicinal Cu surfaces.     

First-principles investigation of the surface structures of Cu(n, n−1, 0) (n=2, 3 and 4) stepped surfaces

Multilayer relaxation at high-index Cu(n, n−1, 0) (n=2, 3 and 4) stepped surfaces was determined by the first-principles pseudopotential plane wave (PPPW) method. For those surfaces that have n and n−1 atom-rows in terrace and subterrace, respectively, the topmost 2n−2 interlayer spacings contract, while the 2n−1st interlayer spacing expands. There is no similar rule found for the relaxations parallel to the surfaces. Compared with the bulk terminated structure, a thin compact layer, which consisted of the topmost 2n−1 atom layers and separated slightly from the underneath atom layers, makes the surface more flat after relaxation. The bond-lengths between the step edge (first layer) atom and its nearest-neighbors do not depend on the surface termination, but only on the local coordination.     

Influence of massive projectile size and energy on secondary ion yields from organic surfaces

We investigated the influence of the projectile size and energy using Au_n^q+ clusters (5 < n < 400, 1 < q < 4) impacting on a glycine target with a 19q-34q keV energy range. We show that both CN⁻ fragment and Gly⁻ molecular ion yields are equivalent for projectiles with n > 9 and increase with the energy per projectile atoms. A maximum yield of 0.5 (50%) for both CN⁻ and Gly⁻ was obtained with the Au₄₀₀⁴⁺ projectile at 136 keV total energy. For Gly⁻, the yield enhancement is linear for Au_n when n > 5. Trends for the CN⁻ fragment are different. A nonlinear yield enhancement proportional to n³ is observed for Au_n when n < 9.     

Phase separation transition in a driven diffusive system with anti-ferromagnetic interaction

One-dimensional non-equilibrium systems with short-range interaction can undergo phase transitions from homogeneous states to phase separated states as interaction (?) among particles is increased. One of the model systems where such a transition has been observed is the extended Katz-Lebowitz-Spohn (KLS) model with ferromagnetically interacting particles at ?=4/5. Here, the system remains homogeneous for small interaction strength (?<4/5), and for anti-ferromagnetic interactions (?<0). We show that the phase separation transitions can also occur in anti-ferromagnetic systems if interaction among particles depends explicitly on the size of the block (n) they belong to. We study this transition in detail for a specific case ?=δ/n, where phase separation occurs for δ<−1.     

Galvanomagnetic properties of air-stable and highly conductive potassium-intercalated graphite sheet

Magnetoresistance and Hall coefficient of air-stable potassium-intercalated graphite sheets (hereafter abbreviated as K-PGS) were determined at room temperature. The magnitude of the magnetoresistance and the absolute value of Hall coefficient of K-PGS decreased with increasing potassium content of K-PGS, n_K/n_C. Two-carrier model was used for calculating carrier density and mobility. The electron density increased with increasing n_K/n_C: 3.07×10²⁰ cm⁻³ (n_K/n_C=0.005), 5.67×10²⁰ cm⁻³ (n_K/n_C=0.008) and 6.40×10²⁰ cm⁻³ (n_K/n_C=0.011). The value of the electron density of K-PGS with n_K/n_C=0.011 (nominal composition KC₉₁) was about 80% of the reported value, 7.8×10²⁰ cm⁻³, for KC₄₈ (n_K/n_C=0.021) prepared from HOPG (highly oriented pyrolytic graphite). The mobility decreased with increasing n_K/n_C: 2.11×10³ cm² V⁻¹ s⁻¹ (n_K/n_C=0.005), 1.42×10³ cm² V⁻¹ s⁻¹ (n_K/n_C=0.008) and 1.34×10³ cm² V⁻¹ s⁻¹ (n_K/n_C=0.011). The value of the mobility of K-PGS with n_K/n_C=0.011 was about 60% of the reported value (2300 cm² V⁻¹ s⁻¹) for KC₄₈ prepared from HOPG.     

Reversible authentication and cross-recovery of images using (t, n)-threshold and modified-RCM watermarking

This paper presents an image authentication scheme for digital images. The proposed scheme protects a group of n images mutually. It designs a block matching procedure to generate the recovery data for each image, and applies a (t, n − 1), 2 ≤ t < n, threshold mechanism to encode each recovery data in n − 1 shares. The recovery shares are cross-embedded in the n images using a modified reversible contrast mapping watermarking scheme. A signature-based authentication code is finally generated and stamped to provide evidence for integrity of each image. The scheme not only can detect the tampering activities, but also can locate and recover the invalid regions of the tampered image if t or more watermarked images in the same group were intact. A nice characteristic of the proposed scheme is that the original images can be reconstructed lossless if no watermarked image was tampered, making the technique feasible in the application of protecting very sensitive images such as military or medical images. Experimental results show that the proposed scheme successfully detects various kinds of image alterations such as filtering, cropping, and replacement, and the corrupted images are properly recovered using the cross-recovery scheme.     

Multi-step laser excitation of the highly excited states of zinc

We report experimental data on the highly excited states of zinc in the energy range 74,625-75,740 cm⁻¹ using two-step laser excitation scheme in conjunction with a thermionic diode ion detector. The 4s4p ³P₁ inter-combination level at 32501.399 cm⁻¹ was populated using a frequency doubled dye laser. The 4s5s ³S₁ level at 53672.28 cm⁻¹ gets populated from the ASE (amplified spontaneous emission) of the second step dye laser. The Rydberg series 4snp ³P₂ (12 ? n ? 60), 4snp ¹P₁ (16 ? n ? 30) and parity forbidden transitions 4sns ³S₁ (19 ? n ? 44) have been observed. A two parameter fit to excitation energies of the observed series yields the binding energy of the 4s5s ³S₁ level as 22097.03 ± 0.03 cm⁻¹ and consequently, the first ionization potential of zinc is determined as 75769.31 ± 0.05 cm⁻¹, that is in excellent agreement with the earlier work.     

An effective scaling frequency factor method for scaling of harmonic vibrational frequencies: The use of redundant primitive coordinates

A modified effective scaling frequency factor (ESFF) method that takes advantage of the potential energy distribution (PED) coefficients calculated in the basis of redundant primitive internal coordinates is presented. This approach is simpler and more flexible than that based on the natural internal coordinates. The sets of optimal scaling factors for routine 9- and 11-parameter ESFF calculations based on B3LYP/6-311G∗∗ force fields are derived from Baker’s training set of 30 molecules (660 frequencies). The calculated root-mean-square (RMS) deviations for all frequencies are 11.42 and 11.44 cm⁻¹ for 9- and 11-parameter scaling, respectively. They are somewhat lower than in the case of ordinary ESFF calculations. The new sets of factors seem to be particularly well suited for scaling of frequencies in the middle region of the vibrational spectra (1000-2500 cm⁻¹) - the RMS values in this range are 8.37 for 9-, and 9.56 cm⁻¹ for 11-parameter scaling. These values are to be compared with 9.20 and 10.29 cm⁻¹, respectively, calculated within the natural coordinates based ESFF formalism.     

Sputtering of clusters from nickel-aluminium

A NiAl(1 1 1) single crystal was bombarded with 15 keV Ar⁺, and the resulting secondary neutrals were analysed by laser postionisation secondary neutral mass spectrometry. By measuring the individual cluster photoion intensity as a function of laser power, the sputter yields of 33 individual clusters were determined. The yield of Al_n clusters sputtered from NiAl falls with increasing cluster nuclearity as n^−8.7 while Ni_n and Al_m−nNi_n yields are proportional to n^−5.9 and n^−5.2, respectively. The distribution of thee yields of mixed Al_m−nNi_n clusters with n and m is found to diverge significantly from the expected distribution based on a random combinatorial approach, indicating that the energetics due to the chemical bonding in the clusters plays a significant role during cluster formation in the sputtering process.     

Propagation of Hermite-cosh-Gaussian laser beams in n-InSb

The propagation of Hermite-cosh-Gaussian (HChG) laser beams in n-InSb are investigated for 0, 1 and 2 mode indices. The field distribution in the medium is expressed in terms of beam-width parameter f and decentred parameter b. The differential equations for f-parameter are established by parabolic wave equation approach under paraxial approximation. Analytical solutions are obtained under the condition R_n < R_d, where, R_n is the self-focusing length and R_d is the diffraction length. The behaviour of f-parameter with the dimensionless distance of propagation η for various b values is examined by numerical estimates. The results are presented graphically.     

Landau quantization of a two-dimensional electron with the nonparabolic dispersion law, pseudospin components and chirality terms

The Landau quantization of a two-dimensional electron in a perpendicular magnetic field on the basis of a Hamiltonian with two pseudospin components is considered. The diagonal elements of the Hamiltonian have non-parabolic but circular symmetric dispersion laws, whereas the off diagonal elements contain the chirality terms of different degrees. The solution of the matrix form Schrödinger equation was found following the method proposed by Rashba in his theory of spin-orbit coupling, taking into account different degrees of chirality and deviations on the parabolic dispersion law. The Landau quantization Hamiltonians were obtained by substituting the canonical momentum operators by the kinetic momentum operators. Two concrete examples were discussed. One of them concerns the Mexican hatlike dispersion law in the biased bilayer graphene with second order chirality, when the Landau quantization levels except two are characterized by two quantum numbers (n−2) and n for n≥2, corresponding to different pseudospin projections. They differ by 2 as the degree of chirality is. There are two energy levels E^±(n−2,n) with the same numbers (n−2) and n. The lower energy levels E⁻(n−2,n) have a linear decreasing behavior with dependence on the magnetic field strength H with different slopes and minima for different values of n≥2. At the intersection point H_th, two energy levels E⁻(1,3) and E⁻(0,2) have the same energy forming two degenerate LLLs. Touching the minima at different values of H, the energy branches gradually transform in the increasing quadratic dependences proportional to (2n+1)²H². The similar results were obtained in the case of cosine-type dispersion law in the frame of one-band model.     

New relations for coefficients of fractional parentage—The Redmond recursion formula with seniority

We find a relationship between coefficients of fractional parentage (cfp) obtained on the one hand from the principal-parent method and on the other hand from a seniority classification. We apply this to the Redmond recursion formula which relates n → n + 1 cfp’s to n − 1 → n cfp’s where the principal-parent classification is used. We transform this to the seniority scheme. Our formula differs from the Redmond formula inasmuch as we have a sum over the possible seniorities for the n → n + 1 cfp’s, whereas Redmond has only one term. We show that there are useful applications of both the principal-parent and the seniority classification.     

Counting contours on trees

We calculate the exact number of contours of size n containing a fixed vertex in d-ary trees and provide sharp estimates for this number for more general trees. We also obtain a characterization of the locally finite trees with infinitely many contours of the same size containing a fixed vertex.     

Condensation in Nongeneric Trees

We study nongeneric planar trees and prove the existence of a Gibbs measure on infinite trees obtained as a weak limit of the finite volume measures. It is shown that in the infinite volume limit there arises exactly one vertex of infinite degree and the rest of the tree is distributed like a subcritical Galton-Watson tree with mean offspring probability m<1. We calculate the rate of divergence of the degree of the highest order vertex of finite trees in the thermodynamic limit and show it goes like (1−m)N where N is the size of the tree. These trees have infinite spectral dimension with probability one but the spectral dimension calculated from the ensemble average of the generating function for return probabilities is given by 2β−2 if the weight w _n of a vertex of degree n is asymptotic to n ^−β .     

Structures, stabilities and magnetic properties of FeCon−1 (n≤16) clusters

Under GGA, size dependence of the geometrical structures, stabilities and magnetic properties of FeCo_n−1 clusters (n≤16) have been investigated together with the Co_n clusters for comparison using DFT within the PAW method implemented in VASP. The replaced Fe atom is favorable to occupy the surface position except for FeCo₁₃. The peaks appeared at n=6, 9 and 11 for FeCo_n−1 clusters and at n=6, 9 and 12 for Co_n clusters on the size dependence of second difference of total energy imply that these clusters possess relatively higher stability. The magnetic moment is strongly correlated with the effective hybridization, which is closely related to the average bond length 〈d〉 and average coordination number 〈n_c〉. A small change in the total charge of Fe atom in FeCo_n−1 clusters will lead to a relative large reverse change in the total magnetic moment of Fe atom.     

Triple Regge limit in the absorptive multiperipheral model

The x → 1 limit of the inclusive one-particle distribution is studied in the absorptive multiperipheral model: we find a leading behaviour of the type (1−x)⁻¹ 1n⁻³ (1−x), which gives an integrable contribution to the energy conservation sum rule.     

A comparison of intertemporal choices for oneself versus someone else based on Tsallis’ statistics

Impulsivity and inconsistency in intertemporal choice (discounting) have drawn attention in econophysics and neuroeconomics. Although it is well established that most people often show irrational discounting (e.g., hyperbolic discounting), little is known regarding whether the irrationality is mitigated or not, when the choice was performed by someone else instead of subject herself. This point is important for economic policy-making. In order to compare consistency and impulsivity in choices for oneself versus someone else, we experimentally estimated the consistency parameter q in Tsallis’ statistics-based discount function for oneself and someone else, by assessing the points of subjective equality (indifference points) at 7 delays (1 week to 25 years) in humans. We observed that (i) most people are more inconsistent when the outcomes of intertemporal choice are only relevant to someone else (q=−8.89) than when relevant to oneself (q=−2.63), and (ii) impulsivity, distinguished from inconsistency by utilizing the Tsallis statistics-based q-exponential discount function, is also larger in the choice for someone else than for oneself. Our results indicate that (i) leaving decision-making processes with some others may neither reduce impulsivity nor correct inconsistency and (ii) when q-exponential discounting is utilized, the definition range of q-parameter should be extended to q<0, and smaller (q<1) and larger (q>1) values indicate more inconsistent discounting. Together, the usefulness of the q-exponential discounting for analyzing the dynamic consistency of economic policy was demonstrated in the present study.