Scattering of light by a periodic structure in the presence of randomness VII: Application of statistical detection test

Detection of periodic structures, hidden in random surfaces has been addressed by us for some time and the ‘extended matched filter’ method, developed by us, has been shown to be effective in detecting the hidden periodic part from the light scattering data in circumstances where conventional data analysis methods cannot reveal the successive peaks due to scattering by the periodic part of the surface. It has been shown that if r ₀ is the coherence length of light on scattering from the rough part and Λ is the wavelength of the periodic part of the surface, the extended matched filter method can detect hidden periodic structures for (r ₀/Λ) ≥ 0.11, while conventional methods are limited to much higher values ((r ₀/Λ) ≥ 0.33). In the method developed till now, the detection of periodic structures involves the detection of the central peak, first peak and second peak in the scattered intensity of light, located at scattering wave vectors v _x = 0, Q, 2Q, respectively, where Q = 2Gp/Λ, their distinct identities being obfuscated by the fact that the peaks have width Δv _x = 2Gp/r ₀ ≫ Q. The relative magnitudes of these peaks and the consequent problems associated in identifying them is discussed. The Kolmogorov-Smirnov statistical goodness test is used to justify the identification of the peaks. This test is used to ‘reject’ or ‘not reject’ the null hypothesis which states that the successive peaks do exist. This test is repeated for various values of r ₀/Λ, which leads to the conclusion that there is really a periodic structure hidden behind the random surface.      

Existence of Noncompact Static Spherically Symmetric Solutions of Einstein SU(2)-Yang–Mills Equations

We consider static spherically symmetric solutions of the Einstein equations with cosmological constant Λ coupled to the SU(2)-Yang–Mills equations that are smooth at the origin r=0. We prove that all such solutions have a radius r _c at which the solution in Schwarzschild coordinates becomes singular. However, for any positive integer N, there exists a small positive Λ _N such that whenever 0<Λ<Λ _N , there exist at least N distinct solutions for which the singularity is only a coordinate singularity and the solution can be extended to r≥r _c . Received: 5 June 2000 / Accepted: 13 March 2001     

Quark Confinement Mechanism and the Scale Λ QCD

The confinement mechanism proposed earlier by the author is applied to problem of arising the so-called scale Λ _QCD within the framework of QCD. The natural physical assumption consists of that 1/Λ _QCD  ∼ 〈r〉 where 〈r〉 is a characteristic size of hadron (radius of confinement). The above confinement mechanism allows us to calculate 〈r〉 for mesons in terms of quark and gluonic degrees of freedom and this permits to conclude that Λ _QCD should slightly change from hadron to hadron.     

Time-reversal symmetry breaking by ac field: Effect of commensurability in the frequency domain

It is shown that the variance of the linear dc conductance fluctuations in an open quantum dot under high-frequency ac pumping depends significantly on the spectral content of the ac field. For a sufficiently strong ac field the dc conductance fluctuations are much stronger for the periodic pumping than in the case of the noise ac field of the same intensity. The reduction factor r in a static magnetic field takes the universal value of 2 only for the white-noise pumping. In general r may deviate from 2 thus signalling on the time-reversal breaking by the ac field. For the bi-harmonic ac field of the form A(t) = A ₀[cos(ω ₁ t) − cos(ω ₂ t)] we predict the enchancement of effects of T-symmetry breaking at commensurate frequencies ω ₂/ω ₁ = P/Q. In the high-temperature limit there is also the parity effect; the enchancement is only present if either P or Q is even.     

Effect of tangential interface motion on the viscous instability in fluid flow past flexible surfaces

The stability of linear shear flow of a Newtonian fluid past a flexible membrane is analysed in the limit of low Reynolds number as well as in the intermediate Reynolds number regime for two different membrane models. The objective of this paper is to demonstrate the importance of tangential motion in the membrane on the stability characteristics of the shear flow. The first model assumes the wall to be a “spring-backed” plate membrane, and the displacement of the wall is phenomenologically related in a linear manner to the change in the fluid stresses at the wall. In the second model, the membrane is assumed to be a two-dimensional compressible viscoelastic sheet of infinitesimal thickness, in which the constitutive relation for the shear stress contains an elastic part that depends on the local displacement field and a viscous component that depends on the local velocity in the membrane. The stability characteristics of the laminar flow in the limit of low are crucially dependent on the tangential motion in the membrane wall. In both cases, the flow is stable in the low Reynolds number limit in the absence of tangential motion in the membrane. However, the presence of tangential motion in the membrane destabilises the shear flow even in the absence of fluid inertia. In this case, the non-dimensional velocity (Λ_t) required for unstable fluctuations is proportional to the wavenumber k ( Λ _t∼k) in the plate membrane type of wall while it scales as k² in the viscoelastic membrane type of wall ( Λ _t∼k ²) in the limit k→ 0. The results of the low Reynolds number analysis are extended numerically to the intermediate Reynolds number regime for the case of a viscoelastic membrane. The numerical results show that for a given set of wall parameters, the flow is unstable only in a finite range of Reynolds number, and it is stable in the limit of large Reynolds number. Received 8 November 2000 and Received in final form 20 March 2001     

The reaction pp→pΛK + near threshold

We analyze the recent total cross section data for pp→pΛK ⁺ near threshold measured at COSY. Using an effective range approximation for the on-shell pΛ S-wave final state interaction we extract from these data the combination ?= (2|K _s|²+|K _t|²)^−1/2= 0.38 fm⁴ of the singlet (K _s) and triplet (K _t) threshold transition amplitudes. We present an exploratory calculation of various (tree-level) vector and pseudoscalar meson exchange diagrams. Pointlike ω-exchange alone and the combined (ρ⁰,ω,K^*+)-exchange can explain the experimental value of ?. The pseudoscalar meson exchanges based on a SU(3) chiral Lagrangian turn out to be too large. However, when adding π⁰-exchange in combination with the resonant πN→S ₁₁(1650) →KΛ transition and introducing monopole form factors with a cut-off Λ_c= 1.5 GeV one is again able to reproduce the experimental value of ?. More exclusive measurements are necessary to reveal the details of the pp→pΛK ⁺ production mechanism. Received: 28 October 1998 / Revised version: 12 January 1999     

Two body non-leptonic Λ b decays in the largeN c limit

The two body non-leptonic Λ _b decays are analysed in the HQET with factorization approximation and largeN _c limit. In this limit, Λ _b and Λ _c baryons can be treated as the bound states of chiral soliton and heavy meson, and consequently the Isgur-Wise function comes out in a straight forward manner. The results obtained remain well below their previously predicted upper limit.     

Measurements of mode field diameter and effective area of photonic crystal fibers by far-field scanning technique

We have demonstrated that the correction factor k _n = A _eff/(πw ²), where ω = MFD/2 (MFD: mode field diameter), is above 1.20 for photonic crystal fibers (PCFs) with structural parameters in the range of d/Λ ≅ 0.40 to 0.90 (d/Λ ratio of hole diameter d and pitch Λ). By using the far-field scanning (FFS) technique and the finite difference method, the results of experimental measurements and numerical simulations differed by only 0.9 to 3.0% for two types of PCFs. The finding that k _n ≠ 1.0 for PCFs indicates that their electrical field distribution is non-Gaussian and cannot be determined by assuming a conventional step-index distribution for PCFs. It was also found that the ITU-T Petermann II definition is the most suitable for MFD measurements of PCFs with non-Gaussian distribution.     

Fourier transform of supermeasures

In the note, a Smolyanov-Shavgulidze model of infinite-dimensional superspace H _Λ = Λ₀ H ₀ ⊕ Λ₁ H ₁ corresponding to a Hilbert space H = H ₀ ⊕ H ₁ over a Hilbert superalgebra Λ = Λ₀ ⊕ Λ₁ is considered. Its relation to the Khrennikov superspace is discussed. Moreover, H _Λ is equipped with the structure of Hilbert superspace with an inner superproduct (·, ·)_Λ. The supermeasures are defined as Λ^ℂ (∧H ₁)-valued measures on H ₀ (Λ^ℂ stands for the complexification of Λ). The definition of the Fourier supertransform is similar to the ordinary one, (y) = μ(dz). It turns out that the values of the Fourier supertransform of a supermeasure on the subspace = H ₀ ⊕ Λ₁ H ₁ can be obtained by applying a certain operator to the values of the classical Fourier transform. The main result is the theorem claiming that the Fourier supertransform of supermeasures is isometric on superspaces with zero even part (H ₀ = {0}). As a corollary, we note that the operator of Fourier supertransform is injective. We also give necessary and sufficient conditions for the countable additivity of cylindrical supermeasures in terms of continuity of their Fourier supertransforms (an analog of the Minlos-Sazonov theorem).     

Dark Energy with Generalized Equation of State in Bianchi Type-I Cosmological Model

Dark energy with the usually used equation of state p=γρ, where γ=const<0 is hydrodynamically unstable. To overcome this drawback we consider the cosmology of a perfect fluid with a linear equation of state of a more general form p=α(ρ−ρ ₀), where the constants α and ρ ₀ are free parameters. The anisotropic Bianchi type-I cosmological model filled with dark energy has been considered. A generalized equation of state for the dark energy component of the universe has been used. The exact solutions to the corresponding Einstein field equations and the statefinder diagnostic pair i.e. {r,s} parameters have been obtained in three interesting cases (i) when ρ _Λ>0 and A>0 (ii) when ρ _Λ>0 and A<0 and (iii) when ρ _Λ<0 and A>0 at the singularities i.e. t→0 and t→±∞.     

Study of FCNC mediated Z boson effectin the semileptonic rare baryonic decays Λ b → Λl + l -

We study the effect of the FCNC mediated Z boson in the rare semileptonic baryonic decays Λ_b → Λl⁺l^-. We consider the model where the standard model fermion sector is extended by an extra vector-like down quark, as a consequence of which it allows for CP-violating Z mediated flavor changing neutral current at the tree level. We find that due to this non-universal Zbs coupling, the branching ratios of the rare semileptonic Λ_b decays are enhanced reasonably from their corresponding standard model values and the zero point of the forward-backward asymmetry for Λ_b → Λ_μ⁺_μ^- is shifted to the left. Received: 2 June 2005, Published online: 26 October 2005 PACS: 13.30.Ce, 12.60.-i, 11.30.Hv     

Neighborhood preferences in random matching problems

We consider a class of random matching problems where the distance between two points has a probability law which, for a small distance l, goes like l^r. In the framework of the cavity method, in the limit of an infinite number of points, we derive equations for p_k, the probability for some given point to be matched to its kth nearest neighbor in the optimal configuration. These equations are solved in two limiting cases: r = 0 -- where we recover p _k = 1/2^k, as numerically conjectured by Houdayer et al. and recently rigorously proved by Aldous -- and r→ + ∞. For 0 < r < + ∞, we are not able to solve the equations analytically, but we compute the leading behavior of p_k for large k. Received 14 February 2001     

A search for colour van der Waals interaction

It is suggested that the strength of nuclear colour van der Waals interaction, if present, can be determined by measuring deviations from Rutherford scattering of charged hadrons from nuclei, at energies well below the Coulomb barrier. Experimental limit on the strength of such a potential is obtained asλ<50, when the colour van der Waals potential is given byV(r)=λ(hc/r ₀)(r ₀/r)⁷, withr ₀, the scaling length, taken as 1 fm. This limit is obtained from an analysis of existing experiments and by performing scattering experiments of 3–4.6 MeV protons from a²⁰⁸Pb target.     

The search for and study of the strange multibaryon states in systems with Λ-hyperon and Ks0 -meson in pA collision at momentum of 10 GeV/c

Exotic strange multibaryon states have been observed in the effective mass spectra of: Λπ^±, Λπ⁺π⁻, Λp, Λpp, Λπp, ΛΛ and ΛK _s ⁰, K _s ⁰ p, K _s ⁰π^± subsystems. The measured Λ/π⁺ ratio for average multiplicities from the pC reaction is equal to (5.3 ± 0.8) × 10⁻², and it is approximately two times larger than the Λ/π⁺ ratio simulated by the FRITIOF model and than that of experimental pp reactions at the same energy. The observed wellknown resonances Σ*⁺ (1385) and K*^± (892) from PDG are good tests of this method. The mean value of the mass for the Σ*⁻(1385) resonance is shifted to 1370 MeV/c ² and the width is two times larger than the same value from PDG. Such kind of behavior for the width and invariant mass of Σ*⁻ (1385) resonance is interpreted as an extensive contribution from stopped Ξ⁻ → Λπ⁻ and medium effect. There is enhancement of the production contribution for all observed hyperons. A few events were registered by hypothesis of light H ⁰ and heavy H ^{0, +} dihyperons. Dihyperons were observed by weak decay channels: (Σ⁻ p), (Λpπ⁻), (Λpπ⁰), and (K ⁻ pp). The text was submitted by the author in English.     

Cluster model of s- and p-shell ΛΛ hypernuclei

The ΛΛ binding energy (B _ΛΛ) of the s- and p-shell hypernuclei are calculated variationally in the cluster model and multidimensional integrations are performed using Monte Carlo. A variety of phenomenological Λ-core potentials consistent with the Λ-core energies and a wide range of simulated s-state ΛΛ potentials are taken as input. The B _ΛΛ of _ΛΛ⁶He is explained and _ΛΛ⁵He and _ΛΛ⁵H are predicted to be particle stable in the ΛΛ-core model. The results for s-shell hypernuclei are in excellent agreement with those of non-VMC calculations. The _ΛΛ¹⁰Be in ΛΛαα model is overbound for combinations of ΛΛ and Λα potentials. A phenomenological dispersive three-body force, V _Λαα, consistent with the B _Λ of _Λ⁹Be in the Λαα model underbinds _ΛΛ¹⁰Be. The incremental ΔB _ΛΛ values for the s- and p-shell cannot be reconciled, consistent with the finding of earlier analyses.      

Study of ΛΛ dynamics and ground state structure of low and medium mass double Λ hypernuclei

We critically review the ΛΛ dynamics by examining Λ - Λ and Λ-nucleon phenomenological potentials in the study of the bound state properties of double-Λ hypernuclei _ΛΛ ⁶ He, _ΛΛ ¹⁰ Be, _ΛΛ ¹⁴ C, _ΛΛ ¹⁸ O, _ΛΛ ²² Ne, _ΛΛ ²⁶ Mg, _ΛΛ ³⁰ Si, _ΛΛ ³⁴ S, _ΛΛ ³⁸ Ar, _ΛΛ ⁴² Ca, _ΛΛ ⁴⁶ Ti, _ΛΛ ⁵⁰ Cr, _ΛΛ ⁵⁴ Fe, _ΛΛ ⁵⁸ Ni, _ΛΛ ⁶² Zn, _ΛΛ ⁶⁶ Ge, _ΛΛ ⁷⁰ Se, _ΛΛ ⁷⁴ Kr, _ΛΛ ⁷⁸ Sr, _ΛΛ ⁸² Zr, _ΛΛ ⁸⁶ Mo, _ΛΛ ⁹⁰ Ru, _ΛΛ ⁹⁴ Pd, _ΛΛ ⁹⁸ Cd, _ΛΛ ¹⁰² Sn in the frame work of (core+Λ+Λ) three body model. An effective ΛN potential is obtained by folding the phenomenological ΛN potential into the density distribution of the core nuclei. The former two cases (i.e. _ΛΛ ⁶ He and _ΛΛ ¹⁰ Be) are revisited to justify the correctness of the present potential model. Assuming the same potential model we predicted some of the structural properties of heavier doubly Λ-hypernuclei. The hyperspherical harmonics expansion method, which is an essentially exact method has been employed for the three body system. A convergence in binding energy up to 0.15% for K _max=20 has been achieved. In our calculation we have made no approximation in restricting the allowed l-values of the interacting pairs.     

The challenge of polarizations in hadronic hyperon production

The large amount of data on hyperon polarizations in inclusive production by hadrons at high energies has recently been extended to Λ and Ξ ⁻ production by Σ ⁻ beams. The sign of the Ξ ⁻ polarization is negative and the same as in Λ and Ξ ⁻ production by protons. The sign of the Λ polarization, however, is positive, in contrast to the negative sign expected by analogy to the proton beam data for Λ and Ξ ⁻ polarization. Theoretical expectations, for instance from a recombination model, also favoured negative polarization of Λ produced by Σ ⁻. Moreover, while the Λ polarization increases with p _t at values below ≈1 GeV/c as observed for other hyperon polarizations, it vanishes above p _t ≈ 1.2 GeV/c. Such a breakdown at large pt has not been observed in any other beam/hyperon combination.     

On the investigation of magnetic critical phenomena in ferromagnets by μSR and PAC

On the basis of current theoretical views on the critical phenomena in isotropic Heisenberg ferromagnets the power temperature behavior Λ=c(τ)λ₀τ^-w has been derived for the muon spin relaxation rate Λ as π-T _c ⁻¹ (T-T _c ) → 0⁺. It is shown that the crossover from an exchange critical regime to a dipolar one is accompanied not only with the change in the critical exponentw in the above law, but also with the reduction of the coefficientc(π). A comparison with the temperature behaviour of the inverse nuclear relaxation timet _R ⁻¹ measured in the PAC experiment is carried out.     

Λ and K s 0 production in pC collisions at 10 GeV/c

The experimental data from the 2-m propane bubble chamber have been analyzed for pC → Λ(K _s ⁰ )X reactions at 10 GeV/c. The estimation of experimental inclusive cross sections for Λ and K _s ⁰ production in the p ¹²C collision is equal to σ_Λ = (13.3 ± 1.7) mb and σ _{K s} ⁰ = (4.6 ± 0.6) mb, respectively. The measured 〈Λ〉/〈π⁺〉 ratio from pC reaction is equal to (5.3 ± 0.8) × 10⁻², and it is approximately two times larger than the 〈Λ〉/〈π⁺〉 ratio simulated by the FRITIOF model and than that of experimental pp reactions at the same energy. The text was submitted by the authors in English.     

Production of V0 pairs in the hyperon experiment WA89

We present a comprehensive study of the inclusive production of V⁰V⁰ pairs (V⁰=Λ, Λ̄ or K_S ) by Σ^- and π^- of 340 GeV/c momentum and neutrons of 260 GeV/c mean momentum in copper and carbon targets. In particular, the dependence of the x_F spectra on the combination of beam-particle and produced V⁰V⁰ pair is investigated and compared to predictions obtained from PYTHIA and QSGM calculations. The data and these predictions differ in many details, the agreement can at best be termed as qualitative. A signal from decays of the tensor meson f’₂(1525) was observed in the K_S K_S mass distribution and inclusive production cross sections were measured. No signal was found from the double-strange H-dibaryon decaying to ΛΛ.