Scaling,stability and distribution of the high-frequency returns of the Ibex35 index

In this paper we perform a statistical analysis of the high-frequency returns of the Ibex35 Madrid stock exchange index. We find that its probability distribution seems to be stable over different time scales, a stylized fact observed in many different financial time series. However, an in-depth analysis of the data using maximum likelihood estimation and different goodness-of-fit tests rejects the Lévy-stable law as a plausible underlying probabilistic model. The analysis shows that the Normal Inverse Gaussian distribution provides an overall fit for the data better than any of the other subclasses of the family of Generalized Hyperbolic distributions and certainly much better than the Lévy-stable laws. Furthermore, the right (resp. left) tail of the distribution seems to follow a power-law with exponent α≈4.60$\alpha \approx 4.60$ (resp. α≈4.28$\alpha \approx 4.28$). Finally, we present evidence that the observed stability is due to temporal correlations or non-stationarities of the data.     

Visibility graph network analysis of gold price time series

Mapping time series into a visibility graph network, the characteristics of the gold price time series and return temporal series, and the mechanism underlying the gold price fluctuation have been explored from the perspective of complex network theory. The network degree distribution characters, which change from power law to exponent law when the series was shuffled from original sequence, and the average path length characters, which change from L∼lnN$L\sim lnN$ into lnL∼lnN$lnL\sim lnN$ as the sequence was shuffled, demonstrate that price series and return series are both long-rang dependent fractal series. The relations of Hurst exponent to the power-law exponent of degree distribution demonstrate that the logarithmic price series is a fractal Brownian series and the logarithmic return series is a fractal Gaussian series. Power-law exponents of degree distribution in a time window changing with window moving demonstrates that a logarithmic gold price series is a multifractal series. The Power-law average clustering coefficient demonstrates that the gold price visibility graph is a hierarchy network. The hierarchy character, in light of the correspondence of graph to price fluctuation, means that gold price fluctuation is a hierarchy structure, which appears to be in agreement with Elliot’s experiential Wave Theory on stock price fluctuation, and the local-rule growth theory of a hierarchy network means that the hierarchy structure of gold price fluctuation originates from persistent, short term factors, such as short term speculation.     

Low-Frequency Seismic Noise Properties in the Japanese Islands

The records of seismic noise in Japan for the period of 1997–2020, which includes the Tohoku seismic catastrophe on 11 March 2011, are considered. The following properties of noise are analyzed: The wavelet-based Donoho–Johnston index, the singularity spectrum support width, and the entropy of the wavelet coefficients. The question of whether precursors of strong earthquakes can be formulated on their basis is investigated. Attention is paid to the time interval after the Tohoku mega-earthquake to the trends in the mean properties of low-frequency seismic noise, which reflect the constant simplification of the statistical structure of seismic vibrations. Estimates of two-dimensional probability densities of extreme values are presented, which highlight the places in which extreme values of seismic noise properties are most often realized. The estimates of the probability densities of extreme values coincide with each other and have a maximum in the region: 30° N ≤ Lat ≤ 34° N, 136° E ≤ Lon≤ 140° E. The main conclusions of the conducted studies are that the preparation of a strong earthquake is accompanied by a simplification of the structure of seismic noise. It is shown that bursts of coherence between the time series of the day length and the noise properties within annual time window precede bursts of released seismic energy. The value of the lag in the release of seismic energy relative to bursts of coherence is about 1.5 years, which can be used to declare a time interval of high seismic hazard after reaching the peak of coherence.     

On the scaling ranges of detrended fluctuation analysis for long-term memory correlated short series of data

We examine the scaling regime for the detrended fluctuation analysis (DFA)—the most popular method used to detect the presence of long-term memory in data and the fractal structure of time series. First, the scaling range for DFA is studied for uncorrelated data as a function of time series length L$L$ and the correlation coefficient of the linear regression R²$R^2$ at various confidence levels. Next, a similar analysis for artificial short series of data with long-term memory is performed. In both cases the scaling range λ$\lambda$ is found to change linearly—both with L$L$ and R²$R^2$. We show how this dependence can be generalized to a simple unified model describing the relation λ=λ(L,R²,H)$\lambda =\lambda (L,R^2,H)$ where H$H$ (1/2≤H≤1$1/2\le H\le 1$) stands for the Hurst exponent of the long range autocorrelated signal. Our findings should be useful in all applications of DFA technique, particularly for instantaneous (local) DFA where a huge number of short time series has to be analyzed at the same time, without possibility of checking the scaling range in each of them separately.     

On the role of atomic motion soft modes in acoustic phonon broadening below the boson peak in glasses

This Letter presents a mechanism of acoustic phonon broadening for frequencies lower than the boson peak frequency in glasses exhibiting a high-frequency sound above the boson peak. The mechanism is based on a resonant interaction of an acoustic phonon with harmonic vibrational excitations of soft modes in such glasses. The related width of the phonon is found to be independent of temperature and characterized by a power-law frequency dependence ν?${\nu }^{?}$, with the exponent ?   varying from ?≈2$?\approx 2$ below the boson peak to ?≈4$?\approx 4$ at lower frequencies. The dependencies do not appear to contradict some recent experimental data, for the glasses under discussion.     

A reduction in the UHE neutrino flux due to neutrino spin precession

Motivated by the stringent flux limits for UHE neutrinos coming from gamma ray bursts or active galactic nuclei, we explore the possibility that the active neutrinos generated in such astrophysical objects could oscillate to sterile right handed states due to a neutrino magnetic moment _μν${\mu }_{\nu }$. We find that a value as small as _μν≈10⁻¹⁵_μB${\mu }_{\nu }\approx {10}^{-15}{\mu }_B$ could produce such a transition thanks to the intense magnetic fields that are expected in these objects.     

Characterization of quenched-in vacancies in Fe–Al alloys

Physical and mechanical properties of Fe–Al alloys are strongly influenced by atomic ordering and point defects. In the present work positron lifetime (LT) measurements combined with slow positron implantation spectroscopy (SPIS) were employed for an investigation of quenched-in vacancies in Fe–Al alloys with the Al content ranging from 18 to 49 at.%. The interpretation of positron annihilation data was performed using ab-initio   theoretical calculations of positron parameters. Quenched-in defects were identified as Fe-vacancies. It was found that the lifetime of positrons trapped at quenched-in defects increases with increasing Al content due to an increasing number of Al atoms surrounding the Fe vacancies. The concentration of quenched-in vacancies strongly increases with increasing Al content from ≈10⁻⁵$\approx {10}^{-5}$ in Fe₈₂Al₁₈${\mathrm{Fe}}_{82}{\mathrm{Al}}_{18}$ (i.e. the alloy with the lowest Al content studied) up to ≈10⁻¹$\approx {10}^{-1}$ in Fe₅₁Al₄₉${\mathrm{Fe}}_{51}{\mathrm{Al}}_{49}$ (i.e. the alloy with the highest Al content studied in this work).     

The neutrino mixing matrix could (almost) be diagonal with entries ±1

It is consistent with the measurement of _θ13∼0.15${\theta }_{13}\sim 0.15$ by Daya Bay to suppose that, in addition to being unitary, the neutrino mixing matrix is also almost Hermitian, and thereby only a small perturbation from diag(+1,−1,−1)$\mathrm{diag}(+1,-1,-1)$ in a suitable basis. We suggest this possibility simply as an easily falsifiable ansatz, as well as to offer a potentially useful means of organizing the experimental data. We explore the phenomenological implications of this ansatz and parametrize one type of deviation from the leading order relation |_Ve3|≈|_Vτ1|$|V_{e3}|\approx |V_{\tau 1}|$. We also emphasize the group-invariant angle between orthogonal matrices as a means of comparing to data. The discussion is purely phenomenological, without any attempt to derive the condition V^†≈V$V^{\mathrm{†}}\approx V$ from a fundamental theory.     

Right unitarity triangles,stable CP-violating phases and approximate quark–lepton complementarity

Current experimental data indicate that two unitarity triangles of the CKM quark mixing matrix V   are almost the right triangles with α≈90°$\alpha \approx 90°$. We highlight a very suggestive parametrization of V and show that its CP-violating phase ? is nearly equal to α   (i.e., ?−α≈1.1°$?-\alpha \approx 1.1°$). Both ? and α   are stable against the renormalizaton-group evolution from the electroweak scale MZ$M_Z$ to a superhigh energy scale MX$M_X$ or vice versa, and thus it is impossible to obtain α=90°$\alpha =90°$ at MZ$M_Z$ from ?=90°$?=90°$ at MX$M_X$. We conjecture that there might also exist a maximal CP-violating phase φ≈90°$\phi \approx 90°$ in the MNS lepton mixing matrix U. The approximate quark–lepton complementarity relations, which hold in the standard parametrizations of V and U, can also hold in our particular parametrizations of V and U   simply due to the smallness of |V_ub|$|V_{ub}|$ and |V_e3|$|V_{e3}|$.     

Nonlocal condensate model for QCD sum rules

We include effects of nonlocal quark condensates into QCD sum rules (QSR) via the Källén–Lehmann representation for a dressed fermion propagator, in which a negative spectral density function manifests their nonperturbative nature. Applying our formalism to the pion form factor as an example, QSR results are in good agreement with data for momentum transfer squared up to Q²≈10 GeV²$Q^2\approx 10{\text{GeV}}^2$. It is observed that the nonlocal quark condensate contribution descends like 1/Q²$1/Q^2$, different from the exponential decrease in Q²$Q^2$ obtained in the literature, and contrary to the linear rise in the local-condensate approximation.     

Non-axisymmetric flexural vibrations of free-edge circular silicon wafers

Non-axisymmetric flexural vibrations of circular silicon (111) wafers are investigated. The modes with azimuthal index 2?k?30$2?k?30$ are electrostatically excited and monitored by a capacitive sensor. The splitting of the mode frequencies associated with imperfection of the wafer is observed. The measured loss factors for the modes with 6?k?26$6?k?26$ are close to those calculated according to the thermoelastic damping theory, while clamping losses likely dominate for k?6$k?6$, and surface losses at the level of inverse Q  -factor Q⁻¹≈4×10⁻⁶$Q^{-1}\approx 4\times {10}^{-6}$ prevail for the modes with large k. The modes demonstrate nonlinear behavior of mainly geometrical origin at large amplitudes.     

The high temperature expansion of the classical XYZ chain

The β$\beta$-expansion of the Helmholtz free energy (HFE) up to order β¹²${\beta }^{12}$ of the classical XYZ model with a single-ion anisotropy term and external magnetic field is calculated and compared to the numerical solution of Joyce's [Phys. Rev. Lett. 19 (1967) 581] for the XXZ   classical model, with neither single-ion anisotropy term nor external magnetic field. This comparison shows that the derived analytical expansion is valid for intermediate temperatures such as kT/_Jx≈0.5$\mathit{kT}/J_x\approx 0.5$. The specific heat and magnetic susceptibility of the S=2$S=2$ antiferromagnetic chain can be approximated by their respective classical results, within an error of 2.5%$2.5\%$, up to kT/J≈0.8$\mathit{kT}/J\approx 0.8$. For a vanishing external magnetic field the ferromagnetic and antiferromagnetic chains are shown to have the same classical HFE; their behaviour in a non-vanishing external magnetic field is also described.     

Flame wrinkles from the Zhdanov–Trubnikov equation

The Zhdanov–Trubnikov equation describing wrinkled premixed flames is studied, using pole decompositions as starting points. Its one-parameter (−1?c?+1$-1?c?+1$) nonlinearity generalises the Michelson–Sivashinsky equation (c=0$c=0$) to a stronger Darrieus–Landau instability. The shapes of steady flame crests (or periodic cells) are deduced from Laguerre (or Jacobi) polynomials when c≈−1$c\approx -1$, which numerical resolutions confirm. Large wrinkles are analysed via   a pole density: adapting results of Dunkl relates their shapes to the generating function of Meixner–Pollaczek polynomials, which numerical results confirm for −1<c?0$-1<c?0$ (reduced stabilisation). Although locally ill-behaved if c>0$c>0$ (over-stabilisation) such analytical solutions can yield accurate flame shapes for 0?c?0.6$0?c?0.6$. Open problems are invoked.     

Vortex configurations on a thin superconducting spherical shell in the presence of a magnetic dipole

In this work we study vortex configurations on a thin superconducting spherical shell of radius R and thickness d  (R?d?ξ)$(R?d?\xi )$ with a magnetic dipole inside it. The point magnetic dipole (with magnetic moment, m_z$m_z$) is oriented along one of the sphere main axis. It is placed a distance z₀$z_0$ from the center of the sphere. Due to the symmetry of the sample, there are vortices and antivortices pancakes on the shell resulting in zero total vorticity. The vortex interactions with the shielding currents produced by the external fields – as well as with other vortices – are calculated within the London limit. The vortex configurations are obtained by solving numerically the Bardeen–Stephen equation of motion for the vortices. For z₀≈0$z_0\approx 0$ the most frequent vortex configurations present equal arrangements of vortices and antivortices on the north and south hemispheres. For z₀≈0.5R$z_0\approx 0.5R$, the diversity of vortex configurations increases, with a higher number of configurations (in comparison to smaller z₀$z_0$) having different vortices and antivortices distributions on each shell hemisphere. We also study the equilibrium states dependence on the magnetic dipole strength and position.     

Direct evidence for the onset of intruder configurations in neutron-rich Ne isotopes

We report on direct experimental evidence of the population of the 3/²⁻$3/2^{-}$ intruder state in ²⁷Ne in the knockout of a single neutron from the ground state of ²⁸Ne. This low-lying negative parity state is consistent with a narrower shell gap for exotic nuclei with Z?N$Z?N$ and N≈20$N\approx 20$. Monte Carlo shell-model calculations with the modern SDPF-M interaction successfully describe neutron-rich nuclei in the vicinity of N=20$N=20$ where normal and intruder configurations coexist at low excitation energy. This observation demonstrates the importance of direct reactions for the study of exotic nuclei and the predictive power of these large-scale shell-model calculations.