Scattering of the double sine-Gordon kinks

We study the scattering of kink and antikink of the double sine-Gordon model. There is a critical value of the initial velocity \(v_{{\mathrm {cr}}}\) of the colliding kinks, which separates different regimes of the collision. At \(v_{\mathrm {in}}>v_{\mathrm {cr}}\) we observe kinks reflection, while at \(v_{\mathrm {in}}<v_{\mathrm {cr}}\) their interaction is complicated with capture and escape windows. We obtain the dependence of \(v_{\mathrm {cr}}\) on the parameter of the model. This dependence possesses a series of local maxima, which has not been reported by other authors. At some initial velocities below the critical value we observe a new phenomenon – the escape of two oscillons in the final state. Besides that, at \(v_{\mathrm {in}}<v_{\mathrm {cr}}\) we found the initial kinks’ velocities at which the oscillons do not escape, and the final configuration looks like a bound state of two oscillons.     

Uniform Field Re-entrant Cylindrical TE$$_{01\text {U}}$$ Cavity for Pulse Electron Paramagnetic Resonance Spectroscopy at Q-band

Uniform field (UF) resonators create a region-of-interest, where the sample volume receives a homogeneous microwave magnetic field (\(B_1\)) excitation. However, as the region-of-interest is increased, resonator efficiency is reduced. In this work, a new class of uniform field resonators is introduced: the uniform field re-entrant cylindrical TE\(_{\text {01U}}\) cavity. Here, a UF cylindrical TE\(_{\text {01U}}\) cavity is designed with re-entrant fins to increase the overall resonator efficiency to match the resonator efficiency maximum of a typical cylindrical TE\(_{011}\) cavity. The new UF re-entrant cylindrical TE\(_{\text {01U}}\) cavity is designed for Q-band (34 GHz) and is calculated to have the same electron paramagnetic resonance (EPR) signal intensity as a TE\(_{011}\) cavity, a 60% increase in average resonator efficiency \(\Lambda _\mathrm{ave}\) over the sample, and has a \(B_1\) profile that is 79.8% uniform over the entire sample volume (98% uniform over the region-of-interest). A new H-type T-junction waveguide coupler with inductive obstacles is introduced that increases the dynamic range of a movable short coupler while reducing the frequency shift by 43% during over-coupling. The resonator assembly is fabricated and tested both on the bench and with EPR experiments. This resonator provides a template to improve EPR spectroscopy for pulse experiments at high frequencies.     

Shift and broadening of emission lines in Nd<Superscript>3+</Superscript>:YAG laser crystal influenced by input energy

Spectroscopic properties of the flashlamp-pumped Nd ³⁺:YAG laser as a function of input energy were studied over the range of 18–75 J. The spectral widths and shifts of quasi-three-level and four-level inter-Stark emissions within the respective intermanifold transitions of \(^{\mathrm {4}}\mathrm {F}_{\mathrm {3/2}}\to ^{\mathrm {4}}{\kern -2.7pt}\mathrm {I}_{\mathrm {9/2}}\) and \(^{\mathrm {4}}\mathrm {F}_{\mathrm {3/2}}\to ^{\mathrm {4}}{\kern -2.7pt}\mathrm {I}_{\mathrm {11/2}}\) were investigated. The emission lines of \(^{\mathrm {4}}\mathrm {F}_{\mathrm {3/2}}\to ^{\mathrm {4}}{\kern -2.7pt}\mathrm {I}_{\mathrm {9/2}}\) shifted towards longer wavelength (red shift) and broadened, while the positions and linewidths of the \(^{\mathrm {4}}\mathrm {F}_{\mathrm {3/2}}\to ^{\mathrm {4}}{\kern -3.5pt}\mathrm {I}_{\mathrm {11/2}}\) transition lines remained constant by increasing the pumping energy. This is attributed to the thermal population as well as one-phonon and multiphonon emission processes in the ground state. This phenomenon degrades the output performance of the lasers.     

Induced-gravity GUT-scale Higgs inflation in supergravity

Models of induced-gravity inflation are formulated within Supergravity employing as inflaton the Higgs field which leads to a spontaneous breaking of a \(U(1)_{B-L}\) symmetry at \(M_\mathrm{GUT}=2\cdot 10^{16}~{\mathrm{GeV}}\). We use a renormalizable superpotential, fixed by a U(1) R symmetry, and Kähler potentials which exhibit a quadratic non-minimal coupling to gravity with or without an independent kinetic mixing in the inflaton sector. In both cases we find inflationary solutions of Starobinsky type whereas in the latter case, others (more marginal) which resemble those of linear inflation arise too. In all cases the inflaton mass is predicted to be of the order of \(10^{13}~{\mathrm{GeV}}\). Extending the superpotential of the model with suitable terms, we show how the MSSM \(\mu \) parameter can be generated. Also, non-thermal leptogenesis can be successfully realized, provided that the gravitino is heavier than about \(10~{\mathrm{TeV}}\).     

Reexploration of interacting holographic dark energy model: cases of interaction term excluding the Hubble parameter

In this paper, we make a deep analysis for the five typical interacting holographic dark energy models with the interaction terms \(Q=3\beta H_{0}\rho _\mathrm{{de}}\), \(Q=3\beta H_{0}\rho _\mathrm{{c}}\), \(Q=3\beta H_{0}(\rho _\mathrm{{de}}+\rho _\mathrm{c})\), \(Q=3\beta H_{0}\sqrt{\rho _\mathrm{{de}}\rho _\mathrm{c}}\), and \(Q=3\beta H_{0}\frac{\rho _\mathrm{{de}}\rho _{c}}{\rho _\mathrm{{de}}+\rho _\mathrm{c}}\), respectively. We obtain observational constraints on these models by using the type Ia supernova data (the Joint Light-Curve Analysis sample), the cosmic microwave background data (Planck 2015 distance priors), the baryon acoustic oscillations data, and the direct measurement of the Hubble constant. We find that the values of \(\chi _\mathrm{min}^2\) for all the five models are almost equal (around 699), indicating that the current observational data equally favor these IHDE models. In addition, a comparison with the cases of an interaction term involving the Hubble parameter H is also made.     

Kinetically modified non-minimal inflation with exponential frame function

We consider supersymmetric (SUSY) and non-SUSY models of chaotic inflation based on the \(\phi ^n\) potential with \(n=2\) or 4. We show that the coexistence of an exponential non-minimal coupling to gravity \(f_\mathcal{R}=\mathrm{e}^{c_\mathcal{R}\phi ^{p}}\) with a kinetic mixing of the form \(f_{\mathrm{K}}=c_{\mathrm{K}}f_\mathcal{R}^m\) can accommodate inflationary observables favored by the Planck and Bicep2/Keck Array results for \(p=1\) and 2, \(1\le m\le 15\) and \(2.6\times 10^{-3}\le r_{\mathcal {R}\mathrm{K}}=c_\mathcal{R}/c_{\mathrm{K}}^{p/2}\le 1,\) where the upper limit is not imposed for \(p=1\). Inflation is of hilltop type and it can be attained for subplanckian inflaton values with the corresponding effective theories retaining the perturbative unitarity up to the Planck scale. The supergravity embedding of these models is achieved employing two chiral gauge singlet supefields, a monomial superpotential and several (semi)logarithmic or semi-polynomial Kähler potentials.     

Dynamic Equations for a Free Particle Motion in a Discrete Space-Time Geometry

One considers the discrete space-time geometry \(\mathcal {G}_{\mathrm {d}}\), which is given on the set of points (events), where the geometry of Minkowski is given. This discrete geometry is not a geometry on lattice. Motion of a free particle is considered in \(\mathcal {G}_{\mathrm {d}}\). Free motion in \(\mathcal {G}_{\mathrm {d}}\) can be reduced to a motion in geometry of Minkowski \(\mathcal {G}_{\mathrm {M}}\) in some force field. Primordial free motion in \(\mathcal {G}_{\mathrm {d}}\) appears to be stochastic. In \(\mathcal {G }_{\mathrm {M}}\) it is difficult to describe the force field responsible for stochastic motion of a particle. The nature of this force field appears to be geometrical.     

Holographic screening length in a hot plasma of two sphere

We study the screening length \(L_{\mathrm{max}}\) of a moving quark–antiquark pair in a hot plasma, which lives in a two sphere, \(S^2\), using the AdS/CFT correspondence in which the corresponding background metric is the four-dimensional Schwarzschild–AdS black hole. The geodesic of both ends of the string at the boundary, interpreted as the quark–antiquark pair, is given by a stationary motion in the equatorial plane by which the separation length L of both ends of the string is parallel to the angular velocity \(\omega \). The screening length and total energy H of the quark–antiquark pair are computed numerically and show that the plots are bounded from below by some functions related to the momentum transfer \(P_c\) of the drag force configuration. We compare the result by computing the screening length in the reference frame of the moving quark–antiquark pair, in which the background metrics are “Boost-AdS” and Kerr–AdS black holes. Comparing both black holes, we argue that the mass parameters \(M_{\mathrm{Sch}}\) of the Schwarzschild–AdS black hole and \(M_{\mathrm{Kerr}}\) of the Kerr–AdS black hole are related at high temperature by \(M_{\mathrm{Kerr}}=M_{\mathrm{Sch}}(1-a^2l^2)^{3/2}\), where a is the angular momentum parameter and l is the AdS curvature.     

Rapid communication: $$K_{S}^{0}$$ Production from beryllium target using 120 $$\hbox {GeV}/\hbox {c}$$GeV/c protons beam interactions at the MIPP experiment

We have measured the cross-section for the \(K_{S}^{0}\) production from beryllium target using 120 \(\hbox {GeV}/\hbox {c}\) protons beam interactions at the main injector particle production (MIPP) experiment at Fermilab. The data were collected with target having a thickness of 0.94% of the nuclear interaction length. The \(K_{S}^{0}\) inclusive differential cross-section in bins of momenta is presented covering momentum range from \(0.4\,\hbox {GeV}/\hbox {c}\) to \(30\,\hbox {GeV}/\hbox {c}\). The measured inclusive \(K_{S}^{0}\) production cross-section amounts to \(39.54\pm 1.46\delta _{\mathrm {stat}}\pm 6.97\delta _{\mathrm {syst}}\) mb and the value is compared with the prediction of FLUKA hadron production model.     

Likelihood analysis of the minimal AMSB model

We perform a likelihood analysis of the minimal anomaly-mediated supersymmetry-breaking (mAMSB) model using constraints from cosmology and accelerator experiments. We find that either a wino-like or a Higgsino-like neutralino LSP, \(\tilde{\chi }^0_{1}\), may provide the cold dark matter (DM), both with similar likelihoods. The upper limit on the DM density from Planck and other experiments enforces \(m_{\tilde{\chi }^0_{1}} \lesssim 3 \,\, \mathrm {TeV}\) after the inclusion of Sommerfeld enhancement in its annihilations. If most of the cold DM density is provided by the \(\tilde{\chi }^0_{1}\), the measured value of the Higgs mass favours a limited range of \(\tan \beta \sim 5\) (and also for \(\tan \beta \sim 45\) if \(\mu > 0\)) but the scalar mass \(m_0\) is poorly constrained. In the wino-LSP case, \(m_{3/2}\) is constrained to about \(900\,\, \mathrm {TeV}\) and \(m_{\tilde{\chi }^0_{1}}\) to \(2.9\pm 0.1\,\, \mathrm {TeV}\), whereas in the Higgsino-LSP case \(m_{3/2}\) has just a lower limit \(\gtrsim 650\,\, \mathrm {TeV}\) (\(\gtrsim 480\,\, \mathrm {TeV}\)) and \(m_{\tilde{\chi }^0_{1}}\) is constrained to \(1.12 ~(1.13) \pm 0.02\,\, \mathrm {TeV}\) in the \(\mu >0\) (\(\mu <0\)) scenario. In neither case can the anomalous magnetic moment of the muon, \((g-2)_\mu \), be improved significantly relative to its Standard Model (SM) value, nor do flavour measurements constrain the model significantly, and there are poor prospects for discovering supersymmetric particles at the LHC, though there are some prospects for direct DM detection. On the other hand, if the \(\tilde{\chi }^0_{1}\) contributes only a fraction of the cold DM density, future LHC Open image in new window -based searches for gluinos, squarks and heavier chargino and neutralino states as well as disappearing track searches in the wino-like LSP region will be relevant, and interference effects enable \(\mathrm{BR}(B_{s, d} \rightarrow \mu ^+\mu ^-)\) to agree with the data better than in the SM in the case of wino-like DM with \(\mu > 0\).     

CGC/saturation approach: re-visiting the problem of odd harmonics in angular correlations

In this paper we demonstrate that the selection of events with different multiplicities of produced particles, leads to the violation of the azimuthal angular symmetry, \(\phi \rightarrow \pi - \phi \). We find for LHC and lower energies, that this violation can be so large for the events with multiplicities \(n \ge 2 \bar{n}\), where \(\bar{n}\) is the mean multiplicity, that it leads to almost no suppression of \(v_n\), with odd n. However, this can only occur if the typical size of the dipole in DIS with a nuclear target is small, or \(Q^2 \,>\,Q^2_s\left( A; Y_{\mathrm{min}},b\right) \), where \(Q_s\) is the saturation momentum of the nucleus at \(Y = Y_{\mathrm{min}}\). In the case of large sizes of dipoles, when \(Q^2 \,<\,Q^2_s\left( A; Y_{\mathrm{min}},b\right) \), we show that \(v_n =0\) for odd n. Hadron-nucleus scattering is discussed.     

Consequences of R-parity violating interactions for anomalies in $${\bar{B}}\rightarrow D^{(*)} \tau {\bar{\nu }}$$ and $$b\rightarrow s \mu ^+\mu ^-$$b→sμ+μ-

We investigate the possibility of explaining the enhancement in semileptonic decays of \({\bar{B}} \rightarrow D^{(*)} \tau {\bar{\nu }}\), the anomalies induced by \(b\rightarrow s\mu ^+\mu ^-\) in \({\bar{B}}\rightarrow (K, K^*, \phi )\mu ^+\mu ^-\) and violation of lepton universality in \(R_K = \mathrm{Br}({\bar{B}}\rightarrow K \mu ^+\mu ^-)/\mathrm{Br}({\bar{B}}\rightarrow K e^+e^-)\) within the framework of R-parity violating MSSM. The exchange of down type right-handed squark coupled to quarks and leptons yields interactions which are similar to leptoquark induced interactions that have been proposed to explain the \({\bar{B}} \rightarrow D^{(*)} \tau {\bar{\nu }}\) by tree level interactions and \(b\rightarrow s \mu ^+\mu ^-\) anomalies by loop induced interactions, simultaneously. However, the Yukawa couplings in such theories have severe constraints from other rare processes in B and D decays. Although this interaction can provide a viable solution to the \(R(D^{(*)})\) anomaly, we show that with the severe constraint from \({\bar{B}} \rightarrow K \nu {\bar{\nu }}\), it is impossible to solve the anomalies in the \(b\rightarrow s \mu ^+\mu ^-\) process simultaneously.     

Spin-label Order Parameter Calibrations for Slow Motion

Calibrations are given to extract orientation order parameters from pseudo-powder electron paramagnetic resonance line shapes of ¹⁴N-nitroxide spin labels undergoing slow rotational diffusion. The nitroxide z-axis is assumed parallel to the long molecular axis. Stochastic-Liouville simulations of slow-motion 9.4-GHz spectra for molecular ordering with a Maier–Saupe orientation potential reveal a linear dependence of the splittings, \(2A_{\hbox{max} }\) and \(2A_{\hbox{min} }\), of the outer and inner peaks on order parameter \(S_{zz}\) that depends on the diffusion coefficient \(D_{{{\text{R}} \bot }}\) which characterizes fluctuations of the long molecular axis. This results in empirical expressions for order parameter and isotropic hyperfine coupling: \(S_{zz} = s_{1} \times \left( {A_{\hbox{max} } - A_{\hbox{min} } } \right) - s_{o}\) and \(a_{o}^{{}} = \tfrac{1}{3}\left( {f_{\hbox{max} } A_{\hbox{max} } + f_{\hbox{min} } A_{\hbox{min} } } \right) + \delta a_{o}\), respectively. Values of the calibration constants \(s_{1}\), \(s_{\text{o}}\), \(f_{\hbox{max} }\), \(f_{\hbox{min} }\) and \(\delta a_{o}\) are given for different values of \(D_{{{\text{R}} \bot }}\) in fast and slow motional regimes. The calibrations are relatively insensitive to anisotropy of rotational diffusion \((D_{{{\text{R}}//}} \ge D_{{{\text{R}} \bot }} )\), and corrections are less significant for the isotropic hyperfine coupling than for the order parameter.     

$$\varvec{B^0\rightarrow K^{*0}\mu ^+\mu ^-}$$ decay in the aligned two-Higgs-doublet model

In the aligned two-Higgs-doublet model, we perform a complete one-loop computation of the short-distance Wilson coefficients \(C_{7,9,10}^{(\prime )}\), which are the most relevant ones for \(b\rightarrow s\ell ^+\ell ^-\) transitions. It is found that, when the model parameter \(\left| \varsigma _{u}\right| \) is much smaller than \(\left| \varsigma _{d}\right| \), the charged scalar contributes mainly to chirality-flipped \(C_{9,10}^\prime \), with the corresponding effects being proportional to \(\left| \varsigma _{d}\right| ^2\). Numerically, the charged-scalar effects fit into two categories: (A) \(C_{7,9,10}^\mathrm {H^\pm }\) are sizable, but \(C_{9,10}^{\prime \mathrm {H^\pm }}\simeq 0\), corresponding to the (large \(\left| \varsigma _{u}\right| \), small \(\left| \varsigma _{d}\right| \)) region; (B) \(C_7^\mathrm {H^\pm }\) and \(C_{9,10}^{\prime \mathrm {H^\pm }}\) are sizable, but \(C_{9,10}^\mathrm {H^\pm }\simeq 0\), corresponding to the (small \(\left| \varsigma _{u}\right| \), large \(\left| \varsigma _{d}\right| \)) region. Taking into account phenomenological constraints from the inclusive radiative decay \(B\rightarrow X_{s}{\gamma }\), as well as the latest model-independent global analysis of \(b\rightarrow s\ell ^+\ell ^-\) data, we obtain the much restricted parameter space of the model. We then study the impact of the allowed model parameters on the angular observables \(P_2\) and \(P_5'\) of \(B^0\rightarrow K^{*0}\mu ^+\mu ^-\) decay, and we find that \(P_5'\) could be increased significantly to be consistent with the experimental data in case B.     

Cosmological tests with strong gravitational lenses using Gaussian processes

Strong gravitational lenses provide source/lens distance ratios \({\mathcal {D}}_{\mathrm{obs}}\) useful in cosmological tests. Previously, a catalog of 69 such systems was used in a one-on-one comparison between the standard model, \(\varLambda \)CDM, and the \(R_{\mathrm{h}}=ct\) universe, which has thus far been favored by the application of model selection tools to many other kinds of data. But in that work, the use of model parametric fits to the observations could not easily distinguish between these two cosmologies, in part due to the limited measurement precision. Here, we instead use recently developed methods based on Gaussian Processes (GP), in which \({\mathcal {D}}_{\mathrm{obs}}\) may be reconstructed directly from the data without assuming any parametric form. This approach not only smooths out the reconstructed function representing the data, but also reduces the size of the \(1\sigma \) confidence regions, thereby providing greater power to discern between different models. With the current sample size, we show that analyzing strong lenses with a GP approach can definitely improve the model comparisons, producing probability differences in the range \(\sim \) 10–30%. These results are still marginal, however, given the relatively small sample. Nonetheless, we conclude that the probability of \(R_{\mathrm{h}}=ct\) being the correct cosmology is somewhat higher than that of \(\varLambda \)CDM, with a degree of significance that grows with the number of sources in the subsamples we consider. Future surveys will significantly grow the catalog of strong lenses and will therefore benefit considerably from the GP method we describe here. In addition, we point out that if the \(R_{\mathrm{h}}=ct\) universe is eventually shown to be the correct cosmology, the lack of free parameters in the study of strong lenses should provide a remarkably powerful tool for uncovering the mass structure in lensing galaxies.     

Method of uniform effective field in structure-dynamic approach of nanoionics

In the structure-dynamic approach of nanoionics, the method of a uniform effective field \( {F}_{\mathrm{eff}}^{j,k} \) of a crystallographic planeX ^j has been substantiated for solid electrolyte nanostructures. The \( {F}_{\mathrm{eff}}^{j,k} \)is defined as an approximation of a non-uniform field \( {F}_{\mathrm{dis}}^j \)of X ^j with a discrete- random distribution of excess point charges. The parameters of \( {F}_{\mathrm{eff}}^{j,k} \)are calculated by correction of the uniform Gauss field \( {F}_{\mathrm{G}}^j \) of X ^j . The change in an average frequency of ionic jumps X ^k ?→?X ^k?+?1 between adjacent planes of nanostructure is determined by the sum of field additives to the barrier heights η _k , _k?+?1, and for \( {F}_{\mathrm{G}}^j \) and \( {F}_{\mathrm{dis}}^j \), these sums are the same decimal order of magnitude. For nanostructures with length ~4 nm, the application of \( {F}_{\mathrm{G}}^j \) (as \( {F}_{\mathrm{eff}}^{j,k} \)) gives the accuracy ~20 % in calculations of ion transport characteristics. The computer explorations of the “universal” dynamic response (Reσ ^??∝?ω ⁿ ) show an approximately the same power n < ≈1 for\( {F}_{\mathrm{G}}^j \) and \( {F}_{\mathrm{eff}}^{j,k} \).     

Aharonov and Bohm versus Welsh eigenvalues

We consider a class of two-dimensional Schrödinger operator with a singular interaction of the \(\delta \) type and a fixed strength \(\beta \) supported by an infinite family of concentric, equidistantly spaced circles, and discuss what happens below the essential spectrum when the system is amended by an Aharonov–Bohm flux \(\alpha \in [0,\frac{1}{2}]\) in the center. It is shown that if \(\beta \ne 0\), there is a critical value \(\alpha _{\mathrm {crit}}\in (0,\frac{1}{2})\) such that the discrete spectrum has an accumulation point when \(\alpha <\alpha _{\mathrm {crit}}\), while for \(\alpha \ge \alpha _{\mathrm {crit}}\) the number of eigenvalues is at most finite, in particular, the discrete spectrum is empty for any fixed \(\alpha \in (0,\frac{1}{2})\) and \(|\beta |\) small enough.     

Test the mergers of the primordial black holes by high frequency gravitational-wave detector

The black hole could have a primordial origin if its mass is less than \(1M_\odot \). The mergers of these black hole binaries generate stochastic gravitational-wave background (SGWB). We investigate the SGWB in high frequency band \(10^{8}\)–\(10^{10}\,\mathrm {Hz}\). It can be detected by high frequency gravitational-wave detector. Energy density spectrum and amplitude of the SGWB are derived. The upper limit of the energy density spectrum is around \(10^{-7}\). Also, the upper limit of the amplitude ranges from \(10^{-31.5}\) to \(10^{-29.5}\). The fluctuation of spacetime origin from gravitational wave could give a fluctuation of the background electromagnetic field in a high frequency gravitational-wave detector. The signal photon flux generated by the SGWB in the high frequency band \(10^{8}\)–\(10^{10}\,\mathrm {Hz}\) is derived, which ranges from 1 to \(10^2\,\mathrm {s^{-1}}\). The comparison between the signal photon flux generated by relic gravitational waves (RGWs) and the SGWB is also discussed in this paper. It is shown that the signal photon flux generated by the RGW, which is predicted by the canonical single-field slow-roll inflation models, is sufficiently lower than the one generated by the SGWB in the high frequency band \(10^{8}\)–\(10^{10}\,\mathrm {Hz}\). Our results indicate that the SGWB in the high frequency band \(10^{8}\)–\(10^{10}\,\mathrm {Hz}\) is more likely to be detected by the high frequency gravitational-wave detector.     

Feasibility study to investigate diffusion of Fe in Si using a Mössbauer spectroscopic microscope

A prototype Mössbauer Spectroscopic Microscope is applied for the feasibility study of ⁵⁷Fe impurity diffusion in Si wafers. A 2nm- ⁵⁷Fe deposited Si wafer is annealed at 430 °C for 1 hour, and subsequently the 1/3 area of the wafer is further grinded with an angle of 6 degrees to the original surface to get a higher depth resolution for the mapping. Subsequently, the mapping images for Fe\(_{\text {sub}}^{\mathrm {0}}\), Fe\(_{\text {int}}^{\mathrm {0}}\), and Fe\(_{\text {int}}^{\mathrm {+}}\) states are measured separately for the two different areas: one area (A) along the grinded surface, and the other (B) along the original wafer surface crossing through the ⁵⁷Fe-deposition boundary. By integrating the mapping intensity the diffusivity of each Fe component along the two different directions can be evaluated and compared with an average Fe diffusivity in Si, which is measured by EDS mapping data obtained for the same area.