Nonlinear experimental dye-doped nematic liquid crystal optical transmission spectra estimated by neural network empirical physical formulas

In this paper, two complementary objectives related to optical transmission spectra of nematic liquid crystals (NLCs) were achieved. First, at room temperature, for both pure and dye (DR9) doped E7 NLCs, the 10-250 W halogen lamp transmission spectra (wavelength 400-1200 nm) were measured at various bias voltages. Second, because the measured spectra were inherently highly nonlinear, it was difficult to construct explicit empirical physical formulas (EPFs) to employ as transmittance functions. To avoid this difficulty, layered feedforward neural networks (LFNNs) were used to construct explicit EPFs for these theoretically unknown nonlinear NLC transmittance functions. As we theoretically showed in a previous work, a LFNN, as an excellent nonlinear function approximator, is highly relevant to EPF construction. The LFNN-EPFs efficiently and consistently estimated both the measured and yet-to-be-measured nonlinear transmittance response values. The experimentally obtained doping ratio dependencies and applied bias voltage responses of transmittance were also confirmed by LFFN-EPFs. This clearly indicates that physical laws embedded in the physical data can be faithfully extracted by the suitable LFNNs. The extraordinary success achieved with LFNN here suggests two potential applications. First, although not attempted here, these LFNN-EPFs, by such mathematical operations as derivation, integration, minimization etc., can be used to obtain further transmittance related functions of NLCs. Second, for a given NLC response function, whose theoretical nonlinear functional form is yet unknown, a suitable experimental data based LFNN-EPF can be constructed to predict the yet-to-be-measured values.     

Applied electric field effect on light-scattering birefringence of dye-doped liquid crystal molecule and consistent neural network empirical physical formula construction for scattering intensities

In this paper, we realized two objectives. Firstly, birefringence of azo and anthraquinone dye-doped nematic liquid crystal (NLC) molecules was investigated by applied electric field dependent laser scattering intensities. The birefringence was essentially calculated from ordinary and extraordinary ray phase difference, which is determined from the measured intensities corresponding to parallel and perpendicular orientations of analyzer to polarizer. The birefringence was found to be dependent on both applied voltage and the kind of the doping dye. As the second objective, by nonlinear universal function approximator layered feedforward neural network (LFNN), we constructed explicit form of empirical physical formulas (EPFs) for experimentally measured dye-doped NLC nonlinear scattering intensities. Excellent LFNN test set predictions over yet-to-be measured experimental data proved that the constructed LFNN-EPFs estimated the measured intensities consistently. The correlation coefficients assessing the goodness of predictions were about r = 0.998for all cases. The LFNN-EPFs also extracted the intensity dependency on the kind of dye used. When theoretical and LFNN-EPFs intensities are compared, we conclude that given certain experimental conditions, theoretical and LFNN-EPFs predictions are in excellent agreement. In this sense, we can say that the physical laws embedded in the birefringence scattering data can be consistently extracted by LFNN. Therefore, judging from the consistent extraction of the molecular dependencies of pure and doped NLC intensities, we predict that the LFNN-EPFs can help to identify unknown molecular structural parameters in liquid crystal extracts. More concretely, by suitable mathematical operations such as differentiation, integration, minimization on these intensity LFNN-EPFs, some useful information into the charge distributions of the LC molecules can be gained.     

A modified K-matrix approach to many-channel processes

The definition of a K-matrix, that does not have the direct channel singularities of the scattering amplitude, is not unique. Different choices lead to different integral equations for K with different physical content. We discuss the choice where the intermediate states have a simple off-shell behaviour for each partial wave. Crossing leads to an identification of the singularities of the K-matrix elements and to an iterative method of finding the scattering amplitude starting from a “bare” world.     

Nonlinear refraction in photo-induced anisotropic states of azo-dye containing materials

The optical anisotropic states in the azo-dye Disperse Red 13 doped poly(methyl methacrylate) polymeric film are induced by polarized light and the nonlinear refractive index in these states are studied by the Z-scan technique. It is found that the n₂ of the sample can be controlled by changing both the polarization direction and the intensity of the 514 nm light. Photo-induced isomerization and reorientation of azo chromophores in polymer matrices are used to explain the results.     

Test of an analytic extrapolation to the hyperon poles of the forward kaon-proton scattering amplitude

An attempt is made to understand the nature of the statistical errors inherent in a method of analytic extrapolation of a discrepancy function which was recently used to estimate the effectiveK N Y coupling constant from experimental data onK ^± p forward scattering. The method is applied to simulated data generated from a model function which has the general features of the actual scattering amplitude and which incorporates a known value of the coupling constant. It is found that the output value of the coupling constant obtained from this method of extrapolation is subject to uncertainties which are not reflected by the standard error-matrix technique for estimating the statistical errors in fits to error-affected data. The implications of these results for such fits are discussed.     

Theoretical study of the X-ray Kβ emission spectrum of an argon atom

The influence of many-particle effects on absolute values and the shape of the doubly differential cross section of resonant inelastic scattering of a linearly polarized X-ray photon by a free Ar atom close to the K- and KM ₂₃-ionization thresholds is studied theoretically. The evolution of the spatially extended profile of the scattering cross section to the principal Kβ_1,3 and satellite Kβ₅ structures of the Ar X-ray Kβ emission spectrum is demonstrated. The calculations are performed in the nonrelativistic Hartree-Fock approximation for the wave functions of one-electron states and in the dipole approximation for the anomalous-dispersion amplitude of the scattering probability. The effects of the radial relaxation of electron shells, the correlation loosening, vacuum correlations, the spin-orbit and multiplet splitting, as well as the Auger and radiative decays of the vacancies produced are taken into account. The calculation results have a predictive character and, for the case of the incident photon energies of 3199.2 and 3245.9 eV, they are in good agreement with the results of the synchrotron experiment on measuring the X-ray Kβ emission spectrum of a free Ar atom.     

Direct determination of the elastic constant K2 of nematics

A twisted nematic liquid crystal (NLC) is placed between two horizontal glass discs, the upper disc being suspended by a quartz thread. The torque of the NLC is statically balanced by the torque of the twisted thread. From the measured torque the elastic constant K₂ is directly determined.     

Soft modes below the incommensurate transition in K2SeO4

A coordinated series of Raman and Brillouin scattering measurements were carried out in K₂SeO₄ with emphasis on temperatures near and below the incommensurate structural phase transition (T_i=129 K). Below the lock-in phase transition (T_c=99 K) Raman scattering from both the amplitude mode and the phase mode analog was observed. However, only the amplitude mode could be followed into the incommensurate phase. Details of the amplitude mode frequency and damping are reported for temperatures considerably closer to T_i than previously possible. Our results do not confirm the diverging linewidth extrapolated from earlier Raman work. We also report here the first Brillouin scattering results in K₂SeO₄. Although substancial interaction effects between the acoustic phonons and the soft amplitude mode are evident near T_i, the coupled mode lineshapes can be well described without the introduction of a relaxing self energy for the soft mode. Finally, limits on the characteristics of the phason are drawn from our failure to observe it directly in the incommensurate phase.     

Pion-nucleon scattering: The P11 channel

A simple model is presented for the πN scattering in the P₁₁ channel from the threshold to the Roper resonance N(1470). The model starts with the πBB′ coupling of the Yukawa type where B (and B') stands for N, R or Δ. A unitarized scattering amplitude is constructed from the K-matrix which is obtained perturbatively. With appropriate coupling constants and form factors for the πBB′ interactions, which conform to the quark model, the P₁₁ scattering can be well reproduced. It is emphasized that the process πN → ππΔ → πN, which has been ignored hitherto, plays a crucial role in the energy region considered.     

An approximation to the cross sections of Z l boson production at CLIC by using neural networks

In this work, the possible dynamics associated with leptophilic Z _l boson at CLIC (Compact Linear Collider) have been investigated by using artificial neural networks (ANNs). These hypotetic massive boson Z _l have been shown through the process e ⁺ e ^?→µ⁺µ^?. Furthermore, the invariant mass distributions for final muons have been consistently predicted by using ANN. For these highly non-linear data, we have constructed consistent empirical physical formulas (EPFs) by appropriate feed-forward ANN. These ANNEPFs can be used to derive further physical functions which could be relevant to studying Z _l .     

Tensor exchange in meson-baryon scattering

Amplitudes for A₂ quantum number exchange in K^±N scattering are determined at p_L = 3, 4 and 6 GeV using new K^±N CEX differential cross-section data supplemented by sum rule estimates of polarizations. Amplitudes for ? quantum number exchange are calculated from πN scattering by SU(3) octet symmetry. This is justified by K^±N FESR, which furthermore are used to resolve ambiguities in the analysis. Comparison with other reactions involving charge and hyperchange exchange shows reasonable overall consistency between data, SU(3), and the tensor amplitudes. The phase of the A₂s-channel helicity flip amplitude is well described by a Regge pole term with trajectory displaced downwards relative to that appropriate for the ? flip amplitude. This is shown to be the main mechanism contributing to the difference between differential cross sections for the K^±N CEX processes, connected by line reversal. It is suggested that this mechanism may persist at higher energies. The A₂ non-flip amplitude does not have the standard peripheral form.     

Nuclear-matter incompressibility from fits of generalized Skyrme force to breathing-mode energies

In an attempt to extend the range of values of K_v, the incompressibility of symmetric nuclear matter, for which fits to the measured breathing-mode energies are possible, we investigate generalized Skyrme-type forces with a term that is both density- and momentum-dependent. Acceptable fits are found to be possible only for values of K_v in the range 215±15 MeV. For higher values fits are impossible, while for lower values fits are achieved only by introducing an unphysical collapse of nuclear matter. Thus our generalization of the Skyrme force does not permit a significantly wider range of values of K_v than that already given by force SkM¹. However, with a view to having a more reliable estimate of the compressional properties of the highly neutron-rich nuclear matter that comprises the core of collapsed stars, we present a new version of this latter force giving a much better fit to the masses of neutron-rich nuclei. Comparison with force SkM¹ also shows that the value of K_v extracted from the breathing-mode energies is essentially independent of the choice of effective mass. By providing a counter-example, we show that K_v cannot be extracted from masses and charge distributions alone. As for the third-order coefficient K′, we cannot be more precise than to say that it lies in the interval 700 ± 500 MeV.     

On the numerical characteristics of an inverse solution for three-term radiative transfer

Certain numerical characteristics of an inverse formulation for three-term scattering radiative transfer are investigated. Specifically, approximate solutions to the direct problem are constructed by the F_N and Monte Carlo methods, allowing approximation of the various surface angular moments and related quantities needed for the inverse calculation. Several numerical schemes are employed in order of demonstrate the computational characteristics for some specific phase functions. The numerical results indicate that the single-scatter albedo can be calculated fairly consistently and accurately, but higher order coefficients of the scattering law are more difficult to obtain by this method.     

Evidence for two back-to-back high-p T jets inK + p interactions at 70 GeV/c

Nucleon structure functions obtained from neutrino and anti-neutrino scattering on iron nuclei at high energies (E _v =30 to 250 GeV) are presented. These results are compared with the results of other lepton-nucleon scattering experiments. The structure functions are used to test the validity of the Gross-Llewellyn-smith sum rule, which measures the number of valence quarks in the nucleons, and to obtain leading and second order QCD fits.     

Comment on the real part of the K±p forward scattering amplitude

It is observed that the K_L⁰n→K_S⁰n regeneration measurements require positivity of the real part of the K^?p forward scattering amplitude above p ～ 1.3 GeV/c. This invalidates some of the earlier dispersion relation predictions and the preliminary experimental results from Batavia.     

A determination of the forward K±p B amplitude and the hyperon coupling constants

From the K^±p forward B amplitude a new amplitude is constructed in such a way that its imaginary part can be calculated from the K^±p polarization data. A prediction of the B amplitude is obtained and the hyperon coupling constants are determined with the result (G_NΛK²+0.8G_NΣK²)/4π = 12.2 ± 2.5.     

A new “parametrization” of the differential cross section for elastic scattering

A new parametrization of the differential cross section for elastic scattering is proposed. The parametrization incorporates correct analytic properties of the differential cross section and is based on optimized polynomial expansions of an analytic function. It is, in principle, valid for all energies and all angles. The parametrization has been tested for pp, $\text{p}\text{p}$, pd, π^± and K^±p elastic scattering at high energies and small angles. The results of the new fits are compared with those of the old ones. It has been found that with the same number of parameters one obtains practically the same values of χ². However, the new values of physical quantities, such as slope, α and (dσ/dt)₀, in most cases differ considerably from those obtained by the old parametrization. In particular, it has been found that the slope of the differential cross section for pp, $\text{p}\text{p}$, pd and K^±p elastic scattering increases continuously as the forward direction is approached.     

Inhomogeneous threshold director reorientation in a planar nematic flexoelectric cell with finite anchoring energy

The dependence of the threshold parameters and the period of the electric-field-induced spatially periodic reorientation of the director in a flexoelectric nematic liquid crystal (NLC) on the anchoring conditions at the surface of a planar NLC cell has been studied. The threshold electric field and the corresponding wave-number of the periodic structure of the director field have been numerically calculated for arbitrary values of the anchoring energy. In the case of strong anchoring, the corresponding analytical expressions are obtained in a single-constant approximation. A decrease in the azimuthal anchoring energy leads to an increase in the intervals of possible values of the flexoelectric parameter ν and the ratio K₂/K₁ of the Frank elastic constants. A decrease in the polar anchoring energy leads to narrowing of these intervals as compared to the case of infinitely strong anchoring at the NLC cell surface.     

High-mass diffraction and Regge behavior of total cross sections

We consider a modified two-component model of particle production in which diffractive excitation into high mass states gives a contribution to K^±p, π^±p and pp total cross sections of sufficient magnitude and with the proper associated threshold to be a possible explanation of deviations of σ_tot from Regge pole model fits at Serpukhov energies. We present tests of the model. for K⁺p scattering by extrapolating σ_tot to National Accelerator Laboratory energies and by calculating the high mass diffraction contribution to the forward peak in inclusive reactions. The consistency of this scheme is discussed in relation to the pomeron intercept and the form of the triple-pomeron coupling.     

Second-order contributions to the structure functions in deep inelastic scattering: (II) Comparison with experiment for the non-singlet contributions to e, μ-nucleon scattering

Quantum chromodynamics predictions for the non-singlet structure functions of ep and μp inclusive scattering are tested against experiment. Target mass corrections and leading and next-to-leading terms α_c are taken into account. The fits to experimental data are very good; they improve systematically when including second-order corrections. The preferred value for the invariant parameter Λ entering α_c is Λ=0.20 ± 0.06 GeV, when second-order and target mass corrections are taken into account.