Correlation Radius Research Articles

Force distribution in a granular medium under dynamic loading.

Force distribution in a granular medium subjected to an impulse loading is investigated in experiment and computer simulations. An experimental technique is developed to measure forces acting on individual grains at the bottom of the granular sample consisting of steel balls. Discrete element method simulation also is performed under conditions mimicking those in experiment. Both theory and experiment display exponentially decaying maximum force distributions at the bottom of the sample in the range of large forces. In addition, the simulations also reveal exponential force distribution throughout the sample and uncover correlation properties of the interparticle forces during dynamic loading of the granular samples. Simulated time dependence of coordination number, orientational order parameter, correlation radius, and force distribution clearly demonstrates the nonequilibrium character of the deformation process in a granular medium under impulse loading.

Phase transitions and critical properties in the antiferromagnetic Heisenberg model on a layered cubic lattice

Phase transitions and critical properties in the antiferromagnetic Heisenberg model on a layered cubic lattice with allowance for intralayer next nearest neighbor interactions have been studied using the replica Monte Carlo algorithm. The character of phase transitions has been analyzed using the histogram method and the Binder cumulant method. It has been found that a transition from the collinear to paramagnetic phase in the model under study occurs as a second order phase transition. The statistical critical exponents of the specific heat α, susceptibility γ, order parameter β, and correlation radius ν, as well as the Fisher index η, have been calculated using the finite-size scaling theory. It has been shown that the three-dimensional Heisenberg model on the layered cubic lattice with allowance for the next nearest neighbor interaction belongs to the same universality class of the critical behavior as the antiferromagnetic Heisenberg model on a layered triangular lattice.

On reflection of terahertz radiation from a rough surface

We computationally analyze the influence of random inhomogeneities of the interface surface between two media that are diagnosed by the pulsed THz spectroscopy method. The statistics of inhomogeneities is characterized by the rms dispersion and correlation radius. The medium to be diagnosed is modeled by a Lorentz contour, the position and the width of which can serve as recognizable indicators. For monochromatic radiation and for a radiation pulse with a wide spectrum (close to the video pulse), a signal at a “point” detector is calculated in the absence and in the presence of inhomogeneities. The results yield conditions under which inhomogeneities significantly affect the recognition of different substances.

Electronic structure and magnetic phase transition in MnSi

Temperature variations of the amplitude of zero-point and thermal spin fluctuations in a helicoidal ferromagnetic (MnSi) are characterized using the electronic structure model that follows from ab initio LDA + U + SO calculations. It is found that a drastic reduction in the amplitude of zero-point spin fluctuations at temperature T S (in the vicinity of the magnetic phase transition) leads to ferromagnetic solution instability (a change in the sign of the intermode interaction parameter). The observed magnetovolume effect and a sharp change in the radius of spin correlations have the same underlying cause. The results of calculation of the volumetric coefficient of thermal expansion agree well with the observed anomaly in the region of the magnetic phase transition.

Development of the self-consistent approximation and its application to the problem of magnetoelastic resonance in an inhomogeneous medium

Our previously proposed approximation involving both the first and second terms of the expansion of the vertex function is generalized to the system of two interacting wavefields of different physical nature. A system of self-consistent equations for the matrix Green’s function and matrix vertex function is derived. On the basis of this matrix generalization of the new self-consistent approximation, a theory of magnetoelastic resonance is developed for a ferromagnetic model, where the magnetoelastic coupling parameter e(x) is inhomogeneous. Equations for magnetoelastic resonance are analyzed for one-dimensional inhomogeneities of the coupling parameter. The diagonal and off-diagonal elements of the matrix Green’s function of the system of coupled spin and elastic waves are calculated with the change in the ratio between the average value e and rms fluctuation Δe of the coupling parameter between waves from the homogeneous case (e ≠ 0, Δe = 0) to the extremely randomized case (e = 0, Δe ≠ 0) at various correlation wavenumbers of inhomogeneities k c. For the limiting case of infinite correlation radius (k c = 0), in addition to approximate expressions, exact analytical expressions corresponding to the summation of all diagrams of elements of the matrix Green’s function are obtained. The results calculated for an arbitrary k c value in the new self-consistent approximation are compared to the results obtained in the standard self-consistent approximation, where only the first term of the expansion of the vertex function is taken into account. It is shown that the new approximation corrects disadvantages of the Green’s functions calculated in the standard approximation such as the dome shape of resonances and bends on the sides of resonance peaks. The appearance of a fine structure of the spectrum in the form of a narrow resonance on the Green’s function of spin waves and a narrow antiresonance on the Green’s function of elastic waves, which was previously predicted in the standard self-consistent approximation, is confirmed. With an increase in the parameter k c, the Green’s functions calculated in the standard and new approximations approach each other and almost coincide with each other at k c/k ≥ 0.5. At the same time, the results of this work indicate that the new self-consistent approximation has a certain advantage for studying the problems of stochastic radiophysics in media with long-wavelength inhomogeneities (small k c values), because it describes both the shape and width of peaks much better than the standard approximation.

A study of the critical properties of the Ising model on body-centered cubic lattice taking into account the interaction of next behind nearest neighbors

The replica Monte Carlo method has been used to investigate the critical behavior of a threedimensional antiferromagnetic Ising model on a body-centered cubic lattice, taking into account interactions of the adjacent behind neighbors. Investigations are carried out for the ratios of the values of exchange interactions behind the nearest and next nearest neighbors k = J 2/J 1 in the range of k ∈ [0.0, 1.0] with the step Δk = 0.1. In the framework of the theory of finite-dimensional scaling the static critical indices of heat capacity α, susceptibility γ, of the order parameter β, correlation radius ν, and also the Fisher index η are calculated. It is shown that the universality class of the critical behavior of this model is kept in the interval of k ∈ [0.0, 0.6]. It is established that a nonuniversal critical behavior is observed in the range k ∈ [0.8, 1.0].

Improved Scaling of the Magnetic Heat Capacity in La0.85Ag0.15MnO3 Manganite

The heat capacity in a La0.85Ag0.15MnO3 manganite was measured near Curie temperature TC under the applied magnetic fields up to 26 kOe to study scaling critical behavior and obtain universality class. The conventional scaling fails in application to the manganites with a hysteresis and the strong sensitivity of TC to a magnetic field. But the application of the improved scaling procedure designed by us allows of yielding the good scaling the magnetic heat capacity in La0.85Ag0.15MnO3, which may belong to a new universality class for systems with the strong spin-orbital coupling of t2g-electrons–Double 3D-Heisenberg with the critical exponent of the heat capacity α = −0.23 and the critical exponent of the correlation radius ν = 0.7433. This new universality class is consistent with the crystal, magnetic and orbital symmetries for the La0.85Ag0.15MnO3. Scaling failure in the vicinity of TC in the range of t/H1/2ν ≈ [−0.033; 0.024] is understood by finite-size and other disordering effects when T → TC. It is remarkable that finite-size effect is consistent with grain size, L ≈ 50 μm, in the La0.85Ag0.15MnO3. The correlation radius, Ltν ≈ 30.28 A, estimated from the finite-size effect is of the same order of magnitude with the sizes of the ferromagnetic fluctuations and drops in manganites.

Synthesis of non-uniformly spaced linear antenna arrays using a data-driven probabilistic model

The problem of beam-forming from non-uniformly spaced antenna elements on linear and planar arrays is investigated. The objective is to design a probabilistic model for identifying the locations of a minimal set of elements that collaboratively generate a beam that matches specified beam width and side lobe level. A data-driven approach is undertaken with several thousand viable element positions obtained computationally using the firefly metaheuristic optimization algorithm, where each firefly models an antenna array of fixed number of elements. Analysis of inter-element spacings of the viable positions shows that whereas all spacings exhibit some degree of dependence with neighboring spacings, the region at the end of the array exhibits a higher correlation radius. Accurate modeling of this section is important for minimizing variability in generated random beam forms. A sequential regression model is proposed to predict successive inter-element spacings beginning with the boundary of the aperture. Application of the aggregate of previously predicted spacings as the predictor allows one to transform the non-linear structure to a linear predictive model. Arrays synthesized by this model yield a good performance, with nearly 90% of generated array beam patterns satisfying required beam width and side lobe level.

A correlation radius estimate between in-panel faults and high-stress areas using Monte Carlo simulation and point process statistics

Since quantitative correlation association between in-panel faults and high-stress areas have not been well understood, we propose a workflow to quantitatively estimate this spatial association through Monte Carlo simulations and point process statistics using measured fault traces and tomographic seismic velocities as inputs. According to different distribution scenarios of fault traces and high-stress areas based on in situ characteristics, we build three different spatial statistical models: a no spatial correlation model, an anti-correlation model and a correlation model to analyze and compare with the observed data. By estimating and cross plotting RHA (Ratio of High-stress Areas over total area) and RFL (Ratio of included Fault-trace Length over total fault-trace length) pairs for Monte Carlo realizations of those models, we generate a template to estimate the correlation association between in-panel faults and high-stress areas for the study panel. After comparing the observed cross plots of RHA vs. RFL pairs with the template, we find that the in-panel faults and high-stress areas have positive correlation association and yield an estimate of correlation radius for the study panel. This result is in accordance with previous geological analysis. However, the estimated correlation radius can be affected by velocity artifacts and inaccurate interpreted faults. Considering the influence of velocity artifacts, we achieve a calibrated template to better estimate the correlation radius between in-panel faults and high-stress areas. This estimate could be a practical parameter to optimize mining methods and to minimize stress related rock failures.

Control of cell interaction using quasi-monochromatic light with varying spatiotemporal coherence

By the example of plants, fungi and bacteria, we consider the possibility of controlling the interaction of cells, being in competitive, antagonistic, or parasitic relations. For this aim we used short-time irradiation (a few seconds or minutes) with the red (633 nm) quasi-monochromatic light having different spatiotemporal coherence. It is shown that the functional activity is mostly increased in the cells whose size does not exceed the coherence length and the correlation radius of the light field. Thus, in the case of cells essentially differing in size, it is possible to increase the activity of smaller cells, avoiding the stimulation of larger ones. For example, the radiation having relatively low coherence (Lcoh, rcor ≤ 10 μm) facilitates mainly the damage of large-size plant cells by pathogen fungi, while the exposure to light with less statistical regularity (Lcoh = 4 μm, rcor = 5 μm) inhibits the growth of the Fusarium microcera fungus, infected by the bacterium of the Pseudomonas species. The quasi-monochromatic radiation with sufficiently high spatiotemporal coherence stimulated all interacting species (bacteria, fungi, plants). In the considered biocenosis, the equilibrium was shifted towards the favour of organisms having the highest rate of cell division or the ones better using their adaptation potential.

Statistical parameters of the spatiotemporal variability of the wind direction in the surface layer

Multipoint measurements of wind direction were carried out during the expedition of the Institute of Atmospheric Physics, Russian Academy of Sciences (IPA RAS), in Tsimlyansk in 2012. Spatial correlation functions for the transverse direction and temporal correlation functions for the longitudinal direction are plotted under stable and unstable stratification of the atmosphere. The longitudinal correlation radius is much higher than the transverse one, and radii in daytime realizations are larger than in nighttime. To determine the stratification conditions, an ultrasonic anemometer–thermometer was used. Autospectra of wind direction fluctuations were plotted. They include long segments of power dependence on the frequency. The spectral correlation coefficients of variations in the wind direction versus intersensor distance in the transverse direction are also calculated. A set of fast-response thermometers was used in the experiment. They allowed temperature mapping, i.e., plotting the time variations in the isothermal surface altitude. That analysis was also applied to visualization of the spatiotemporal variability of wind direction. The resulting data were used for planning the helicity measurements in the Tsimlyansk expedition in 2014.

On the effect of the shape of a flaw on its detectability against noise background

When switching to automatic output-quality testing systems, the aspiration for improving the detectability of insignificant deviations of the output parameters from the statutory ones necessitates the solution of a number of new problems. One of those is assessing the effect of the image-energy spectral density from an axisymmetric flaw on the reliability of its detection against background noise by both human and computer vision systems. Knowing this information is a necessary condition for developing new enhanced testing and evaluating techniques. Results are presented on the probabilities of false alarm and correct detection of axisymmetric circular or rectangular flaws depending on the signal-to-noise ratio (SNR) and the ratio of the flaw radius to the background-fluctuation correlation radius. It has been established that for small SNR, human vision is more effective than machine vision that implements the correlation detector algorithm and the Neyman–Pearson criterion.

Structural characteristics of a three-dimensional Ising-like system in the critical region

An analytic technique for calculating the correlation function and correlation radius of systems belonging to the universality class of the three-dimensional Ising model is elaborated within the collective variables (CV) method. The calculations of these nonuniversal characteristics are performed for the temperatures [Formula: see text], [Formula: see text] and [Formula: see text] ([Formula: see text] is the phase transition temperature) on the microscopic level in the approximation of the quartic distribution for modes of spin moment density oscillations (the [Formula: see text] model). Proceeding from the expression for the Fourier transform of the correlation function, we have also obtained the susceptibility of the system. The correction to scaling and the potential averaging correction are taken into account in our calculations.

Studying the metal structure of anticorrosive cladding for the nuclear-reactor vessels by neutron diffraction and small-angle neutron scattering

The results of neutron studies of the metal nanostructure of anticorrosive cladding for vessels of WWER -1000 nuclear reactors under different conditions of additional tempering are presented. In the anticorrosive-cladding material, small structural components (inhomogeneities) with a correlation radius of 2–3 nm are observed which form fractal structures with a scale of more than 100 nm. It is shown that at different annealing temperature, these small objects create new structures at crystal boundaries in the form of defect surfaces with the fractal dimension Ds = 2.4–2.6. In samples of anticorrosive cladding, nonmagnetic austenitic γ-phase iron (γ-Fe) and magnetic δ-ferrite (α-Fe) are observed. The alloy is found to be magnetically hard.

Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions

The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scaling theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.

Plasmon-polaritons on a surface with fluctuating impedance: Scattering, localization, stability

Scattering of TM-polarized surface plasmon-polariton waves (PPW) by a finite segment of the metal–vacuum interface with randomly fluctuating surface impedance is examined. Solution of the integral equation relating the scattered field with the field of the incident PPW, valid for arbitrary scattering intensity and arbitrary dissipative characteristics of the conductive medium, is analyzed. As a measure of the PPW scattering, the Hilbert norm of the integral scattering operator is used. The strength of the scattering is shown to be determined not only by the parameters of the fluctuating impedance (dispersion, correlation radius and the length of the inhomogeneity region) but also by the conductivity of the metal. If the scattering operator norm is small, the PPW is mainly scattered into the vacuum, thus losing its energy through the excitation of quasi-isotropic bulk Norton waves above the conducting surface. The scattered field intensity is expressed in terms of the random impedance pair-correlation function. Its dependence on the incident and scattered wavenumbers shows that in the case of random-impedance-induced scattering of PPW it is possible to observe the effect analogous to Wood's anomalies on gratings. Under strong scattering, when the norm of the scattering operator becomes large compared to unity, the radiation into free space is strongly suppressed, and, in the limit, the incoming PPW is almost perfectly back-reflected from the inhomogeneous part of the interface. Therefore, within the model of a dissipation-free conducting medium, the surface polariton is unstable against arbitrary small fluctuations of the medium polarizability. Transition from scattering to back-reflection under strong fluctuations of the impedance is interpreted in terms of the Anderson localization.

Effect of spatial coherence of light on the photoregulation processes in cells.

The effect of the statistical properties of light on the value of the photoinduced reaction of the biological objects, which differ in the morphological and physiological characteristics, the optical properties, and the size of cells, was studied. The fruit of apple trees, the pollen of cherries, the microcuttings of blackberries in vitro, and the spores and the mycelium of fungi were irradiated by quasimonochromatic light fluxes with identical energy parameters but different values of coherence length and radius of correlation. In all cases, the greatest stimulation effect occurred when the cells completely fit in the volume of the coherence of the field, while both temporal and spatial coherence have a significant and mathematically certain impact on the physiological activity of cells. It was concluded that not only the spectral, but also the statistical (coherent) properties of the acting light play an important role in the photoregulation process.

Estimating the navigation informativity of the Earth’s anomalous gravity field

Application of modern global geopotential models to estimate the navigation informativity of the Earth’s anomalous gravity field (EAGF) is considered from the viewpoint of its use in autonomous (correlation- extreme) navigation. Various algorithms for calculating the characteristics of route and area navigation informativity, for which the authors use the variance and correlation radius of a measured EAGF parameter, are presented. The results of the experimental studies on estimation of the EAGF navigation informativity are discussed by analyzing vertical deflections and second derivatives of the perturbing potential in the Sea of Okhotsk with the use of the model EGM-2008 to degree 2190. It is shown that second derivatives of the geopotential demonstrate higher informativity as applied to navigation purposes.

Investigation of critical phenomena of the hard/soft magnetic bilayer model by the Monte-Carlo method

A model for the description of thermodynamic properties of hard/soft magnetic bilayer is proposed. We perform a thorough research of critical phenomena of this model by the Monte-Carlo method. Critical exponents of the heat capacity α, magnetization β, susceptibility γ, and correlation radius ν are calculated using the finite-size scaling theory. Obtained values of critical exponents agree with the theoretical predictions for the XY-model.

Performance of PASA in ocean waveguides

Passive Synthetic Aperture (PASA) is a technique of increasing the length of a small array artificially through array towing motion and signal processing. This will acquire the advantage of a long array while maintaining the maneuverability of short array. Therefore, it has better performance in multi-targets distinguishing and detection than the conventional physical aperture array. However, the performance of PASA is also strongly influenced by the horizontal correlation radius of the sound field. Theory analysis shows that only when the horizontal correlation radius of the sound field is much larger than the length of physical aperture array, the advantage of PASA can be obvious. In this paper, the performance of PASA is compared with physical aperture array in the ocean waveguide through the experiment data from the South China Sea in 2014. With the modified extended towed array method in beam-domain (BD-ETAM), a virtual array with 160 hydrophones (240 m) is synthesized by a physical array with 32 hydrophones (48 m). The result shows that when the horizontal correlation radius exceeds 240 m, the processing gain of the synthesized virtual array with 160 hydrophones is higher than the physical array with 32 hydrophones by 9.5 dB. When the horizontal correlation radius is less than 30 m, the processing gain of the synthesized virtual array with 160 hydrophones is only higher than the physical array with 32 hydrophones by 6 dB. Furthermore, the detection performance of the synthesized virtual array is almost the same as the physical array in such case. That is to say, because the horizontal correlation radius of the sound field is short in the shadow zone of the ocean waveguide, the performance of PASA is limited to near the conventional physical aperture array. In contrast, the performance of PASA is remarkable better than the conventional physical aperture array in the convergence zone of the ocean waveguide since the horizontal correlation radius is large.