The spectral properties of the correlation function of the heights of interlayer boundaries in a lamellar 1,2‑distearoyl-sn-glycero-3-phosphocholine film deposited on the surface of the hydrosol of ...amorphous silica nanoparticles are investigated within the scope of a model-independent approach based on the data of nonspecular X-ray scattering. The data analysis shows that the spectrum of interlayer roughnesses in a multilayer is qualitatively different from the prediction of the capillary wave theory in the entire considered interval of spatial frequencies.
We consider the so-called simplest formula for local approximation by polynomial splines of order
(Schoenberg splines). The spline itself and all derivatives except that of the highest order, ...approximate a given function and its corresponding derivatives with the second order. We show that the jump of the highest derivative of order
; i. e., the value of discontinuity, divided by the meshsize, approximates the
th derivative of the original function. We found an asymptotic expansion of the jump.
A search for sub-GeV dark matter production mediated by a new vector boson A′, called a dark photon, is performed by the NA64 experiment in missing energy events from 100 GeV electron interactions in ...an active beam dump at the CERN SPS. From the analysis of the data collected in the years 2016, 2017, and 2018 with 2.84×1011 electrons on target no evidence of such a process has been found. The most stringent constraints on the A′ mixing strength with photons and the parameter space for the scalar and fermionic dark matter in the mass range ≲0.2 GeV are derived, thus demonstrating the power of the active beam dump approach for the dark matter search.
A dynamic clustering algorithm for temperature signals is considered. It is used for solving the problem of distinguishing climatic regions characterized by a certain homogeneous climate type within ...the boundaries of the region on the Earth’s surface. A numerical experiment implemented with the aim of estimating its stability is described. The reference signal model used in the numerical experiment is presented as a sum of harmonic components. Additive components of the noise are formed in the frequency region. In the numerical experiment, the noise magnitude and sample size are measured. Estimates of root-mean-square deviations and stability of the dynamic clustering algorithm are presented.
The structure of the planar surface of colloidal solutions of amorphous 27-nm silica sol particles enriched with heavy K
+
, Rb
+
, and Cs
+
alkali ions is studied by the methods of reflectometry and ...diffuse (nonspecular) scattering of synchrotron radiation. For liquid-phase systems, we have used a self-consistent approach that makes it possible to reconstruct from experimental data the electron density profiles perpendicular to the hydrosol surface, as well as the spectra of the height–height correlation function in the plane of the surface without using any a priori information about the near-surface structure. Analysis represented here shows that for high values of pH, alkali cations with a large radius and a surface concentration of (5 ± 1) × 10
18
m
–2
replace Na
+
ions with a smaller radius. This result is in qualitative agreement with the dependence of the Kharkats–Ukstrup single-ion electrostatic free energy on the ion radius and in good quantitative agreement with the results obtained by other authors using the capillary-wave approach. The integrated value of the effective height of interface roughness (3.2 ± 0.5 Å) coincides to within the measuring error with the prediction of the capillary-wave theory; however, the experimental spectra of the height-to-height correlation function basically differ from the theoretical spectra in the range of low spatial frequencies ν < 10
–3
nm
–1
. The approximation of the spectra by the sum of two
K
-correlation distributions indicates a transition from the natural roughness of the compact layer of alkali metal ions to the capillary roughness of the liquid surface in the correlation length range of about 1 μm. In our opinion, the aggregate of available data indicates the dispersion of this layer into 2D clusters (Wigner islands).
We consider the problem on shape-preserving interpolation by classical cubic splines. Namely, we consider conditions guaranteeing that, for a positive function (or a function whose
k
th derivative is ...positive), the cubic spline (respectively, its
k
th derivative) is positive. We present a survey of known results, completely describe the cases in which boundary conditions are formulated in terms of the first derivative, and obtain similar results for the second derivative. We discuss in detail mathematical methods for obtaining sufficient conditions for shape-preserving interpolation. We also develop such methods, which allows us to obtain general conditions for a spline and its derivative to be positive. We prove that, for a strictly positive function (or a function whose derivative is positive), it is possible to find an interpolant of the same sign as the initial function (respectively, its derivative) by thickening the mesh.
Computational modeling of experiments on measurement of axial distributions of fission reaction rates in configurations of the ASTRA critical facility simulating a HTGR with annular core is ...performed. Absorbing elements were installed in the internal reflector of critical assemblies to flatten the neutron flux radial distribution. Measurements of the fission reaction rates were performed both in a configuration with a flattened neutron field and in a configuration with control rods (CR) inserted in an external graphite reflector.
Abstract
We present an approach for solving the inverse kinematic problem of seismic with internal sources, based on the method of multidimensional data approximation on irregular grids. The times of ...arrival of elastic waves to the seismic stations are considered as known. The hodographs from earthquake to the stations are approximated for further determining the velocities of longitudinal and transverse waves using the eikonal equation. The ratio of these velocities determines the Poisson’s ratio, and the other elastic parameters of the medium can be found in units of the density. The results of implementation of the approach, based on the real data, are presented.
We carried out a model-independent search for light scalar (s) and pseudoscalar axionlike (a) particles that couple to two photons by using the high-energy CERN SPS H4 electron beam. The new ...particles, if they exist, could be produced through the Primakoff effect in interactions of hard bremsstrahlung photons generated by 100 GeV electrons in the NA64 active dump with virtual photons provided by the nuclei of the dump. The a (s) would penetrate the downstream HCAL module, serving as a shield, and would be observed either through their a (s) → γγ decay in the rest of the HCAL detector, or as events with a large missing energy if the a (s) decays downstream of the HCAL. This method allows for the probing of the a (s) parameter space, including those from generic axion models, inaccessible to previous experiments. No evidence of such processes has been found from the analysis of the data corresponding to 2.84 × 10 11 electrons on target, allowing us to set new limits on the a(s)γγ -coupling strength for a (s) masses below 55 MeV.
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