Logarithmic Dispersion Research Articles

Multiphase Gas in Elliptical Galaxies: The Role of Type Ia Supernovae

Massive elliptical galaxies harbor large amounts of hot gas (T ≳ 106 K) in their interstellar medium (ISM) but are typically quiescent in star formation. The jets of active galactic nuclei (AGNs) and Type Ia supernovae (SNe Ia) inject energy into the ISM, which offsets its radiative losses and keeps it hot. SNe Ia deposit their energy locally within the galaxy compared to the larger few ×10 kiloparsec-scale AGN jets. In this study, we perform high-resolution (5123) hydrodynamic simulations of a local (1 kpc3) density-stratified patch of the ISM of massive galaxies. We include radiative cooling and shell-averaged volume heating, as well as randomly exploding SN Ia. We study the effect of different fractions of supernova (SN) heating (with respect to the net cooling rate), different initial ISM density/entropy (which controls the growth time t ti of the thermal instability), and different degrees of stratification (which affect the freefall time t ff). We find that SNe Ia drive predominantly compressive turbulence in the ISM with a velocity dispersion of σ v up to 40 km s−1 and logarithmic density dispersion of σ s ∼ 0.2–0.4. These fluctuations trigger multiphase condensation in regions of the ISM, where min(tti)/tff≲0.6exp(6σs) , in agreement with theoretical expectations that large density fluctuations efficiently trigger multiphase gas formation. Since the SN Ia rate is not self-adjusting, when the net cooling drops below the net heating rate, SNe Ia drive a hot wind which sweeps out most of the mass in our local model. Global simulations are required to assess the ultimate fate of this gas.

Myths and realities of endurance time analysis: Discussion/Comments Regarding “Seismic assessment of deep water bridges in reservoir considering hydrodynamic effects using endurance time analysis” by Yutao Pang, Li Cai, Wei He, and Li Wu; Ocean Engineering, 2020, 198:106846

This discussion is based on the paper by Pang et al. (2020) (hereafter identified as “the original authors” and “the original paper” or “the reference paper”). The original authors employed the endurance time analysis (ETA) and incremental dynamic analysis (IDA) techniques to investigate the probabilistic response of a deep water bridge in a reservoir. They derived multiple fragility curves using both techniques. Derivation of ETA-based fragility functions in the original paper is not fully consistent with the nature of seismic fragility curves. The underpinning concept of fragility curves is tied with ground motion record-to-record (RTR) variability, while the conventional ETA does not offer such an ability. We discussed several underlying assumptions in the ETA method, as well as different sources of ground motion RTR variability (from IDA technique) which may affect the logarithmic dispersion in a fragility curve (and it is unseen in conventional ETA method).

Simplified damage models for circular section reinforced concrete bridge columns

Damage models are fundamental elements within probabilistic frameworks, such as Performance-Based Earthquake Engineering (PBEE), for the seismic assessment of RC structures. For bridges, in specific, there are not many available experimental results for the characterization of damage in the RC columns hence the numerical counterpart acquires particular relevance. In this paper, via Monte Carlo simulation and comparison with complementary experimental results, a damage model consisting of a library of median and logarithmic dispersion values for curvature ductility, displacement ductility and drift, describing the probability of reaching a particular damage limit state are generated as a function of key parameters of circular RC bridge columns. Four damage limit states are considered: slight, moderate, extensive and complete. Simplified relationships based on the full datasets are proposed for easier implementation. The proposed damage models can be used for threshold identification and economic loss assessment in performance-based earthquake engineering of RC bridges.

Seismic Risk Assessment of a 2-storey Steel-sheathed CFS Building Considering Different Sources of Uncertainty

In this paper, four types of uncertainties are considered for seismic risk assessment of steel-sheathed CFS structures. The record-to-record uncertainty is examined by using 40 ground motions selected from SAC project. The structural uncertainties are modeled by 6 random variables by using Latin hypercube sampling method (LHS). The uncertainty in defining performance limits is introduced and determined by statistical analyses of test results. Besides, epistemic uncertainty is considered in three levels: small, moderate and high levels. The seismic risks of a 2-story typical steel-sheathed CFS building are investigated by considering different sources of these uncertainties, and their effects on the building are discussed. The results shown that the uncertainty in defining performance limits has significant impact on the risk of the building which cannot be neglected. It is found that the increment on the probability in 50 years of the building with considering the structural uncertainty is <8.8%. It is suggested that the structural uncertainty could be taken into account in the uncertainty in defining performance limits because these uncertainties are generated from the structural system, and the integrated logarithmic standard deviation dispersion (LSD) is proposed as 0.41 for the steel-sheathed CFS building. The collapse probability in 50 years of the building with considering these four types of uncertainties is 1.84 to 4.56 times of the value with solely considering the record-to-record uncertainty.

Yes, Multi-periodic Dwarfs in Upper Scorpius Are Binaries

Abstract We found that multi-periodic low-mass stars discovered by Kepler K2 in the Upper Scorpius association are close binaries with typical separations of the order of 10 au and large mass ratios. These stars were surveyed by speckle interferometry at the SOAR telescope with spatial resolution of 0.″04. Out of 129 observed targets, we resolved 70 pairs (including 16 previously known ones and three new triple systems). The distribution of projected separations of binaries with primary stars less massive than the Sun corresponds to a log-normal with median of 11.6 au and logarithmic dispersion of 0.60 dex, similar to M dwarfs in the field. Future orbits of newly discovered binaries will provide accurate measurements of masses to calibrate pre-main-sequence evolutionary tracks; a tentative orbit of one previously known binary is determined here.

An Enhanced Method for Least Significant Bit Image Steganography using Discrete Logarithmic Dispersion Strategy

this paper a novel method for information security using image steganography technique is proposed. This project simply hides a text message in an image file. For hiding secret information in images, there exist a large variety of steganographic techniques some are more complex than others and all of them have respective strong and weak points. Different applications have different requirements of the steganography technique used. For example, some applications may require absolute invisibility of the secret information, while others require a larger secret message to be hidden. This work intends to give an overview of image steganography, its uses and techniques. The proposed method uses the LSB (Least Significant Bit) technique to hide information in the cover image. The system enhanced the LSB technique by randomly dispersing the bits of the message in the image and thus making it harder for unauthorized people to extract the original image. Discrete logarithm calculation technique is used for determining the location of the bit into pixel to embed the message. The proposed algorithm provides a stego-key that will be used during the embedding and extracting of the message.

Quantum spectral dimension in quantum field theory

We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory (QFT), when the system is probed at a given resolution. This picture has four main advantages: (a) it dispenses with the usual interpretation (unsatisfactory in covariant approaches) where, instead of a transition amplitude, one has a probability density solving a nonrelativistic diffusion equation in an abstract diffusion time; (b) it solves the problem of negative probabilities known for higher-order and nonlocal dispersion relations in classical and quantum gravity; (c) it clarifies the concept of quantum spectral dimension as opposed to the classical one. We then consider a class of logarithmic dispersion relations associated with quantum particles and show that the spectral dimension [Formula: see text] of spacetime as felt by these quantum probes can deviate from its classical value, equal to the topological dimension [Formula: see text]. In particular, in the presence of higher momentum powers it changes with the scale, dropping from [Formula: see text] in the infrared (IR) to a value [Formula: see text] in the ultraviolet (UV). We apply this general result to Stelle theory of renormalizable gravity, which attains the universal value [Formula: see text] for any dimension [Formula: see text].

The phase problem for X-ray specular reflectivity from thin films: A new approach

A new approach to solving the phase problem for X-ray specular reflectivity is proposed. An iterative algorithm is used to solve the nonlinear Fredholm integral equation describing the intensity of the X-rays reflection from the sample surface and to determine the concentration depth-profile of element. Effectiveness of the proposed method was tested by numerical experiments for the thin film. We compare the results obtained for the Cr film experimental data using the Parratt model, phaseless inverse scattering method (logarithmic dispersion relations), and the proposed method.

Revisit to diffraction anomalous fine structure.

The diffraction anomalous fine structure (DAFS) method that is a spectroscopic analysis combined with resonant X-ray diffraction enables the determination of the valence state and local structure of a selected element at a specific crystalline site and/or phase. This method has been improved by using a polycrystalline sample, channel-cut monochromator optics with an undulator synchrotron radiation source, an area detector and direct determination of resonant terms with a logarithmic dispersion relation. This study makes the DAFS method more convenient and saves a large amount of measurement time in comparison with the conventional DAFS method with a single crystal. The improved DAFS method has been applied to some model samples, Ni foil and Fe3O4 powder, to demonstrate the validity of the measurement and the analysis of the present DAFS method.

A novel two-stage spectral compression structure employing a logarithmic DIF interconnected with an HNLF-NOLM

A novel two-stage spectral compression structure which employs a logarithmic dispersion increasing fiber (DIF) interconnected with a highly nonlinear linear fiber-nonlinear optical loop mirror (HNLF-NOLM) is proposed and demonstrated by numerical simulation. The numerical simulation is implemented by solving the generalized nonlinear Schrodinger equation using split-step Fourier method, where the soliton number is in the range of 0.5≤N≤1.4. The results show that the spectra are well-compressed and low-pedestal, and the maximum spectral compression ratio (SCR) can reach 10.93 when N=1.4.

FROM BINARIES TO MULTIPLES. II. HIERARCHICAL MULTIPLICITY OF F AND G DWARFS

Statistics of hierarchical multiplicity among solar-type dwarfs are studied using the distance-limited sample of 4847 targets presented in the accompanying Paper I. Known facts about binaries (multiplicity fraction 0.46, log-normal period distribution with median period 100yr and logarithmic dispersion 2.4, and nearly uniform mass-ratio distribution independent of the period) are confirmed with a high statistical significance. The fraction of hierarchies with three or more components is 0.13+-0.01, the fractions of targets with n=1,2,3,... components are 54:33:8:4:1. Sub-systems in the secondary components are almost as frequent as in the primary components, but in half of such cases both inner pairs are present. The high frequency of those 2+2 hierarchies (4%) suggests that both inner pairs were formed by a common process. The statistics of hierarchies can be reproduced by simulations, assuming that the field is a mixture coming from binary-rich and binary-poor environments. Periods of the outer and inner binaries are selected recursively from the same log-normal distribution, subject to the stability constraint and accounting for the correlation between inner sub-systems. The simulator can be used to evaluate the frequency of multiple systems with specified parameters. However, it does not reproduce the observed excess of inner periods shorter than 10d, caused by tidal evolution.

Spectral catalogue of bright gamma-ray bursts detected with theBeppoSAX/GRBM

The emission process responsible for the so-called "prompt" emission of gamma-ray bursts is still unknown. A number of empirical models fitting the typical spectrum still lack a satisfactory interpretation. A few GRB spectral catalogues derived from past and present experiments are known in the literature and allow to tackle the issue of spectral properties of gamma-ray bursts on a statistical ground. We extracted and studied the time-integrated photon spectra of the 200 brightest GRBs observed with the Gamma-Ray Burst Monitor which flew aboard the BeppoSAX mission (1996-2002) to provide an independent statistical characterisation of GRB spectra. The spectra were fit with three models: a simple power-law, a cut-off power law or a Band function. The typical photon spectrum of a bright GRB consists of a low-energy index around 1.0 and a peak energy of the nuFnu spectrum E_p~240 keV in agreement with previous results on a sample of bright CGRO/BATSE bursts. Spectra of ~35% of GRBs can be fit with a power-law with a photon index around 2, indicative of peak energies either close to or outside the GRBM energy boundaries. We confirm the correlation between E_p and fluence, with a logarithmic dispersion of 0.13 around the power-law with index 0.21+-0.06. The low-energy and peak energy distributions are not yet explained in the current literature. The capability of measuring time-resolved spectra over a broadband energy range, ensuring precise measurements of parameters such as E_p, will be crucial for future experiments (abridged).

The Viscous-Grain-Shearing (VGS) theory of wave propagation in marine sediments

The grain-shearing (GS) theory of wave propagation in a marine sediment is based upon the idea that, as grains slide against one another, the dissipation becomes progressively stronger, a phenomenon known as strain hardening. The GS theory predicts a sound speed showing weak, logarithmic dispersion and an attenuation that scales linearly with frequency. At frequencies above about 10 kHz, such behavior matches the sound speed and attenuation data obtained during the SAX99 experiment in the Gulf of Mexico. But at lower frequencies, the measured dispersion curves show a lower sound speed and higher attenuation than predicted by the GS theory. A generalized version of the GS theory, designated the VGS theory, takes account of the effective viscosity of the molecularly thin layer of pore fluid between contiguous grains, which limits the degree of strain hardening that can occur during sliding. The VGS dispersion expressions are the same as those of the GS theory, except for the appearance of a simple algebraic function that has an effect only at low frequencies, below 10 kHz. The resultant VGS curves match the sound speed and attenuation measurements from SAX99 over the measurement frequency band from 1 to 400 kHz. (Research supported by ONR.)

Sound waves and shear waves in saturated unconsolidated sediments

A recent, continuum‐mechanics theory of compressional and shear wave propagation in saturated unconsolidated sediments relies on grain‐to‐grain interactions as the sole source of internal stress in the porous medium. On the basis of a statistical argument, nonlinear microscopic processes occurring at grain boundaries are incorporated into the intrinsically linear grain‐shearing theory. The result is two sets of algebraic dispersion relationships, one of which represents a compressional wave and the other a shear wave. The shear wave is predicted to exist even in the absence of an elastic ‘‘frame.’’ For both types of wave, the theory predicts logarithmic dispersion and a near‐linear dependence of attenuation on frequency. The grain‐shearing dispersion relations, which are functions not only of frequency but also of the geophysical parameters of the sediment (porosity, bulk density, grain size, and overburden pressure), show excellent agreement with multiple data sets that have appeared in the literature ov...

The Ep,i-Eiso correlation in gamma-ray bursts: updated observational status, re-analysis and main implications

The correlation between the cosmological rest-frame vF v spectrum peak energy, E p,i , and the isotropic-equivalent radiated energy, E iso , discovered by Amati et al. in 2002 and confirmed/extended by subsequent osbervations, is one of the most intriguing and debated observational evidences in gamma-ray burst (GRB) astrophysics. In this paper, I provide an update and a re-analysis of the E p,i -E iso correlation basing on an updated sample consisting of 41 long GRBs/X-ray flashes (XRFs) with firm estimates of z and observed peak energy, E p,obs , 12 GRB s with uncertain values of z and/or E p,obs , two short GRBs with firm estimates of z and E p,obs and the peculiar subenergetic events GRB 980425/SN1998bw and GRB 031203/SN20031w. In addition to standard correlation analysis and power-law fitting, the data analysis here reported includes modelling that accounts for sample variance. All 53 classical long GRBs and XRFs, including 11 Swift events with published spectral parameters and fluences, have E p,i and E iso values, or upper/lower limits, consistent with the correlation, which shows a chance probability as low as ∼7 x 10 -15 , a slope of ∼0.57 (∼0.5 when fitting by accounting for sample variance) and an extra-Poissonian logarithmic dispersion of ∼0.15, it extends over ∼5 orders of magnitude in E iso and ∼3 orders of magnitude in E p,i and holds from the closer to the higher z GRBs. Subenergetic GRBs (980425 and possibly 031203) and short GRBs are found to be inconsistent with the E p,i -E iso correlation, showing that it can be a powerful tool for discriminating different classes of GRBs and understanding their nature and differences. I also discuss the main implications of the updated E p,i -E iso correlation for the models of the physics and geometry of GRB emission, its use as a pseudo-redshift estimator and the tests of possible selection effects with GRBs of unknown redshift.

High-resolution X-ray diffraction imaging of non-Bragg diffracting materials using phase retrieval X-ray diffractometry (PRXRD) technique

An X-ray diffraction technique has recently been developed and successfully applied to comprehensively, including both phase and amplitude contrast, map the complex refractive index of non-crystalline materials with submicron spatial resolution. The methodology is based on the measurement of a high angular resolution X-ray Fraunhofer diffraction pattern with further application of the phase-retrieval formalism using a logarithmic dispersion relation. The technique is reviewed from the perspective of its ability to deliver ultra-high, order of several nanometres, spatial resolution and to uniquely determine both the real and imaginary components of the complex refractive index of the material under analysis. Potential niche of practical applications is discussed in terms of the spatial resolution and field of view achievable by the method.

Quantitative tomographic X-ray profiling of non-Bragg diffracting materials using phase retrieval X-ray diffractometry

Phase retrieval X-ray diffraction was used to profile the complex refractive index of a slice through an acetate filament sample with a square cross-section. High angular resolution X-ray Fraunhofer diffraction patterns and a logarithmic dispersion relation phase-retrieval formalism were used to recover the projection profile of the sample for each of several sample orientations. The tomographic reconstruction of the slice from these projections closely reproduced the refractive index, geometrical shape and size of the acetate filament, using only limited a priori knowledge of the sample.

The Slow Processes of Polarization Relaxation in the SBN and Doped SBN Single Crystals with Tungsten Bronze Structure

The investigation of both Sr0.61Ba0.39Nb2O6 and Sr0.61Ba0.39Nb2O6 doped with La = 1 at% single crystals has shown the existing of two anomalies in temperature dependencies of logarithmic effective dispersion depth of low and infralow frequency dielectric permittivity lgΔϵ(T). One of them is a maximum of lgΔϵ(T) at T ≈ Tm and it is supposed to be connected with the evolution of phase states from superparaelectric to relaxor phase in cooling of the sample. Another one is a bend of lgΔϵ(T) at low temperature Tf (Tf < Tm). Also, a doping of SBN-61 system by La = 1at% is found to decrease the Tm on ΔTm = 36 K. By that time, the shifting of Tf by La doping is only about ΔTf ≈ 8 K. The low temperature anomaly of lgΔϵ(T) is likely to be connected with the domain (or interphase) boundaries freezing. The time dependencies ϵ′(t) at T ≤ Tm are found to follow two laws: the logarithmic at T < Tm and Kolraush law at T ≈ Tm. The peculiarities of amplitude dependencies ϵ′(E0) at different values of bias field E= by measuring reversal dependencies ϵ′(E=) were found. Such behavior of ϵ′(E0) and ϵ′(E=) suggests an existing of the internal (microelectrets) fields Ei in structure of SBN.

Application of phase-retrieval x-ray diffractometry to carbon doped SiGe(C)/Si(C) superlattice structures

An experimental-analytical technique for the model-independent nondestructive characterization of single crystal alloys is applied to SiGe(C)/Si(C) superlattice structures with different positions of substitutional carbon. The technique is based on the retrieval of the phase of the diffracted x-ray wave via a logarithmic dispersion relation, with subsequent determination of the complex crystal structure factor utilizing limited a priori knowledge of the superlattice structure. High-resolution, x-ray Bragg diffraction profiles were collected using a rotating anode source. The studies have allowed the reconstruction of the complex crystal structure factor as a function of crystal depth, permitting direct observation of strain relaxation in individual layers of the superlattice structure.

Unambiguous x-ray phase retrieval from Fraunhofer diffraction data

An unambiguous inverse solution from Fraunhofer diffraction data has been achieved for an amorphous sample of low-molecular weight. The complex scattering amplitude has been reconstructed with submicron spatial resolution using the phase retrieval x-ray diffractometry technique. The technique relies on a logarithmic dispersion relation to determine the x-ray wave phase from the scattered intensity profile. Successful experimental localization of the zeros of the complex scattering amplitude was achieved by utilizing two data sets taken at different incident x-ray energies, permitting a unique solution.