First-order Perturbation Research Articles

Electromagnetic Properties in Samarium Isotopes Within the Framework of the IBM-2

Electromagnetic transitions between low-lying states in deformed even-even 148–154Sm nuclei were investigated within the framework of the SU(3) limit of the neutron-proton interacting boson model. To explain the M1 transitions between low-lying states and the E2 transition between interband states, we applied first-order perturbation theory by adding the proton-neutron quadrupole interaction Qπ· Qv that breaks F-spin symmetry in the dynamical symmetric SU(3) Hamiltonian as a perturbed term. We calculated the transition probabilities of the M1 and the E2 transition operators between low-lying interband states by using the 1/N expansion methods. The matrix elements of the proton-neutron quadrupole interaction Qπ· Qv were directly calculated, as shown in a previous study, by applying the F-spin operator Qπ· Qa instead of Qπ· Qv. The results of the present study for electromagnetic transitions were applied to some deformed even-even Samarium nuclei, and these theoretical results could effectively describe the experimental data.

Perturbation Solution for Four-Stream Infrared Radiative Transfer

Abstract A four-stream solution of the longwave radiative transfer is proposed. It is based on the exact perturbation method utilizing the absorption approximation equation as the zero-order solution. Scattering is handled by the first-order perturbation equation. The two- and four-stream approximations are compared both offline and using data from CALIPSO’s dual-wavelength lidar.

Linear perturbation model for simulating imaging through weak turbulence

A first-order linear perturbation model for simulating imaging through weak turbulence is introduced and developed. It is based on a first-order approximation of the Born expansion of paraxial propagation. The model generates a random scalar field that encodes information about the imaging parameters, such as wavelength, range, Cn2, and the aperture diameter. The gradients of the field are then multiplied to the corresponding gradients of the average turbulent image of a Lambertian target. The result is a model that can rapidly generate a sequence of turbulent images. Some limitations of the model are discussed, and possible improvements are suggested.

Perturbation analysis for the QX factorization for centrosymmetric matrices

The QX factorization of the centrosymmetric matrix is a structure-preserving QR factorization proposed by Konrad Burnik. In this paper, we first propose a sufficient condition for the uniqueness of this decomposition. Then, using the refined matrix equation approach, we derive the first-order normwise perturbation bounds convenient for computation for the QX factorization. Using the matrix-vector equation approach and the modified matrix-vector equation approach, we obtain the optimal first-order normwise perturbation bounds. Moreover, the normwise condition numbers for the QX factorization are also presented. Some numerical examples are given to illustrate our theoretical results.

Data Assimilation Using Subcritical Measurement of Prompt Neutron Decay Constant

The prompt neutron decay constant in a steady-state subcritical system can be directly measured using a reactor noise analysis method such as the Feynman- method. To reduce the nuclear data–induced uncertainty of for a target system, this study investigates the applicability of data assimilation techniques, i.e., the bias factor method and the cross-section adjustment method, based on a subcritical measurement of conducted at Kyoto University Critical Assembly (KUCA). The sensitivity coefficients of and with respect to the nuclear data were efficiently estimated using a deterministic SN transport code with first-order perturbation theory. As a result, the a priori relative uncertainty of due to the 56-group SCALE covariance data can be reduced if there is strong correlation between the measured and the target . The experimental value of contributes to improving the nuclear data of total fission spectrum and total fission neutron number via strong correlations between and prompt and between and prompt , by utilizing the sensitivity coefficients of with respect to prompt and .

Thermoelectric transport properties in 3D Dirac semimetal Cd3As2

Thermoelectric transport properties, namely, electrical conductivity, electronic thermal conductivity, and diffusion thermopower are theoretically investigated in 3D Dirac semimetal Cd3As2. We employ Boltzmann transport formalism and consider the electron scattering by charged impurities, short-range disorder, acoustic phonons, and optical phonons. The Boltzmann transport equation is solved using the Ritz iteration technique to obtain the first-order perturbation distribution function for the interaction of electrons with inelastic polar optical phonons scattering. The numerical results are presented in the temperature range 2–300 K with the electron concentration in the range (0.1–10) × 1018 cm−3. It is found that, at low temperature < ~70 K transport coefficients are dominated by charged impurity scattering and at higher temperature the phonon scattering is found to be dominant. The validity of Wiedemann–Franz law is examined. Recently observed experimental results are explained by our theory.

Application of Multi-Parameter Perturbation Method to Functionally-Graded, Thin, Circular Piezoelectric Plates

In this study, a multi-parameter perturbation method is used for the solution of a functionally-graded, thin, circular piezoelectric plate. First, by assuming that elastic, piezoelectric, and dielectric coefficients of the functionally-graded materials vary in the form of the same exponential function, the basic equation expressed in terms of two stress functions and one electrical potential function are established in cylindrical coordinate system. Three piezoelectric coefficients are selected as perturbation parameters, and the established equations are solved by the multi-parameter perturbation method, thus obtaining up to first-order perturbation solutions. The validity of the perturbation solution obtained is verified by numerical simulations, based on layer-wise theory. The perturbation process indicates that adopting three piezoelectric coefficients as perturbation parameters follows the basic idea of perturbation theory—i.e., if the piezoelectricity may be regarded as a kind of introduced disturbance, the zero-order solution of the disturbance system corresponds exactly to the solution of functionally-graded plates without piezoelectricity. The result also indicates that the deformation magnitude of piezoelectric plates is smaller than that of plates without piezoelectricity, due to the well-known piezoelectric stiffening effect.

Numerical benchmark study for flow in highly heterogeneous aquifers

This article presents numerical investigations on accuracy and convergence properties of several numerical approaches for simulating steady state flows in heterogeneous aquifers. Finite difference, finite element, discontinuous Galerkin, spectral, and random walk methods are tested on two-dimensional benchmark flow problems. Realizations of log-normal hydraulic conductivity fields are generated by Kraichnan algorithms in closed form as finite sums of random periodic modes, which allow direct code verification by comparisons with manufactured reference solutions. The quality of the methods is assessed for increasing number of random modes and for increasing variance of the log-hydraulic conductivity fields with Gaussian and exponential correlation. Experimental orders of convergence are calculated from successive refinements of the grid. The numerical methods are further validated by comparisons between statistical inferences obtained from Monte Carlo ensembles of numerical solutions and theoretical first-order perturbation results. It is found that while for Gaussian correlation of the log-conductivity field all the methods perform well, in the exponential case their accuracy deteriorates and, for large variance and number of modes, the benchmark problems are practically not solvable with reasonably large computing resources, for all the methods considered in this study.

Thermomechanically induced post-buckling analysis of functionally graded material plates with circular cut-outs resting on elastic foundations

Post-buckling analysis of functionally graded material (FGM) plates resting on Winkler and Pasternak elastic foundations subjected to thermomechanical loadings with circular cut-outs at centre and random material properties is presented. The material properties of each constituent’s materials, volume fraction index, thermal expansion coefficients, foundation stiffness parameters and thermal conductivities are taken as independent basic random input variables. The basic formulation is based on applying Reddy’s higher order shear deformation theory, which requires C1 continuous element approximation. A modified form C0 continuity is applied in the present investigation. A serum-free expansion medium with mean-centred first-order regular perturbation technique for composite plates is extended for FGM plates to solve the random eigenvalue problem. Typical numerical results are presented to examine the second-order statistics for effect of the volume fractions index, plate length-to-thickness ratios, plate aspect ratios, types of loadings, amplitude ratios, support conditions and various shape and size of holes with random thermomechanical properties. The results obtained by the present solution approach are validated with published papers and the robust method of simulation. It is found that the laminates with round cuts (FGM plates resting on Winkler and Pasternak elastic foundations) have a significant influence on the post-buckling response under Thermomechanical loading conditions. Present investigations are useful for the applications and further research.

A new study of associating inhomogeneous fluids with classical density functional theory

ABSTRACT A new density functional for the study of associating inhomogeneous fluids based on Wertheim's first-order thermodynamic perturbation theory is presented and compared to the most currently used associating density functionals. This functional is developed using the weighted density approximation in the range of association of hard spheres. We implement this functional within the framework of classical density functional theory together with modified fundamental measure theory to account for volume exclusion of hard spheres. This approach is tested against molecular simulations from literature of pure associating hard spheres and mixtures of non-associationg and associating hard spheres with different number of bonding sites close to a hard uniform wall. Furthermore, we compare and review our results with the performance of associating functionals from literature, one based on fundamental measure theory and the inhomogeneous version of Wertheim's perturbation theory. Results obtained with classical DFT and the three functionals show excellent agreement with molecular simulations in systems with one hard wall. For the cases of small pores where only one or two layers of fluid are allowed discrepancies between results with classical DFT and molecular simulations were found.

Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields

ABSTRACT In the present study, we consider planar piecewise linear vector fields with two zones separated by the straight line x = 0. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector fields. First, we provide a canonical form for these systems assuming that each linear system has centre, a real one for y<0 and a virtual one for y>0, and such that the real centre is a global centre. Then, working with a first-order piecewise linear perturbation we obtain piecewise linear differential systems with three crossing limit cycles. Second, we see that a sliding cycle can be detected after a second-order piecewise linear perturbation. Finally, imposing the existence of a sliding limit cycle we prove that only one adittional crossing limit cycle can appear. Furthermore, we also characterize the stability of the higher amplitude limit cycle and of the infinity. The main techniques used in our proofs are the Melnikov method, the Extended Chebyshev systems with positive accuracy, and the Bendixson transformation.

Watching a photon interfere with itself

We observe the self-interference of a photon at femtosecond timescales. The photon is one member of an entangled photon pair and, after passing through a Michelson interferometer, it is reunited with the second pair member in a nonlinear crystal. There the pair may recombine into a single photon; the probability of recombination as a function of the arrival time of the second photon reveals the self-interference of the Michelson photon, with bandwidth-limited temporal widths (≈20fsec) and with sub-femtosecond instrumental resolution. To support the observations, the pair recombination amplitude is determined from first-order perturbation theory in the interaction picture, which leads to good comparisons with the experimental results. It is demonstrated that our approach measures the arrival time of a photon with resolution orders of magnitude better than existing single-photon detectors.

Rotating Disc around a Schwarzschild Black Hole

A stationary and axisymmetric (in fact circular) metric is reviewed which describes the first-order perturbation of a Schwarzschild black-hole space-time due to a rotating finite thin disc encircling the hole symmetrically. The key Green functions of the problem (corresponding to an infinitesimally thin ring)—the one for the gravitational potential and the one for the dragging angular velocity—were already derived, in terms of infinite series, by Will in 1974, but we have now put them into closed forms using elliptic integrals. Such forms are more practical for numerical evaluation and for integration in problems involving extended sources. This last point mostly remains difficult, but we illustrate that it may be workable by using the simple case of a finite thin disc with constant Newtonian surface density.

Dispersion properties, nonlinear waves and birefringence in classical nonlinear electrodynamics

Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the electromagnetic vector potential is solved perturbatively about the known exact plane wave solution in both the case of a polarized vacuum without external field, as well as when a constant magnetic field is applied. A nonlinear wave equation with nonzero convective part for the (relatively) slowly varying amplitude of the first-order perturbation has been derived. This equation governs the propagation of electromagnetic waves with a reduced speed of light, where the reduction is roughly proportional to the intensity of the initial pumping plane wave. A system of coupled nonlinear wave equations for the two slowly varying amplitudes of the first-order perturbation, which describe the two polarization states, has been obtained for the case of constant magnetic field background. Further, the slowly varying wave amplitude behavior is shown to be similar to that of a cnoidal wave, known to describe surface gravity waves in shallow water. It has been demonstrated that the two wave modes describing the two polarization states are independent, and they propagate at different wave frequencies. This effect is usually called nonlinear birefringence.

Perturbation Theory in the Method of Characteristics

First-order perturbation theory for the multiplication coeffi cient based on the method of characteristics in the form used in the MCCG3D code is presented. Finite-difference analogs of the perturbation theory formulas are derived using the difference scheme of the MCCG3D code. Test calculations were performed. It is shown that the results obtained by perturbation theory and direct calculations converge.

Perturbation Analysis of Nonlinearity in Radio-Frequency Bulk Acoustic Wave Resonators Using the Mass-Spring Model.

This article describes derivation of an equivalent circuit for nonlinear responses in film bulk acoustic resonators from the first-order perturbation analysis using the piezoelectric constitutive equations with the h -form. For simplicity, electrodes and piezoelectric layers are considered as mass and spring, respectively, in the derivation. Then, it is demonstrated that the second- and third-order harmonic responses can be simulated well by the circuit. In addition, nonlinearity in the Si substrate is also taken into account and its impact is discussed. It is also discussed how the frequency dependences vary with the nonlinearity mechanisms as a finding from the derived equivalent circuit.

Matrix-fluid-fracture decoupled-based elastic impedance variation with angle and azimuth inversion for fluid modulus and fracture weaknesses

The ratio of normal-to-shear fracture compliances, approximate to the product of two ratios of shear-to-compressional (S-to-P) wave velocity and normal-to-tangential fracture weakness, has been treated as an indicator of fluid content for an oil-bearing reservoir with aligned fractures. However, this indicator depends on both fluid saturation and fracturing strength of rocks, while the effective fluid bulk modulus as a sensitive indicator decouples the double effects of rock porosity and pore fluid. Moreover, an incorrect value of S- and P-wave velocity ratio may have a significant effect on the estimation of normal-to-shear fracture compliances. Based on the anisotropic poroelasticity amplitude variation with offset and azimuth (AVOAz) theory, we use the Born formalism and a first-order perturbation assumption to derive a matrix-fluid-fracture decoupled-based linearized PP-wave reflection coefficient in an oil-bearing fractured porous medium. Our derived formula reveals that the combined effects of background matrix, pore fluids and fracture strength on seismic amplitudes are separated, more applicable to implement the fluid identification and fracture detection in a liquid-filled porous reservoir with aligned fractures. Following a Bayesian framework, we develop a Bayesian inversion method to reasonably obtain the fluid modulus and saturated fracture weaknesses. The implementation methodology includes two steps: a model-based least-squares inversion for azimuthal elastic impedances and an iterative Bayesian seismic inversion for model parameters. Tests on synthetic data corrupted with moderate random noise indicate that these model parameters can be estimated reasonably and accurately when the oil-saturated rock is permeated with a single fracture system. Test on a real data set validates that the reliable estimates of fluid and fracture parameters can be used to realize the fluid identification and fracture detection in an oil-bearing fractured porous reservoir in a more direct manner than previous approach.

Weibel instability oscillation in a dusty plasma with counter-streaming electrons

AbstractWe investigate the Weibel instability (WI) in a dusty plasma which is driven to oscillation by the addition of dust grains in the plasma. Our analysis predicts the existence of three modes in a dusty plasma. There is a high-frequency electromagnetic mode, whose frequency increases with an increase in the relative number density of dust grains and which approaches instability due to the presence of dust grains. The second mode is a damping mode which exists due to dust charge fluctuations in plasma. The third mode is the oscillating WI mode. The dispersion relation and the growth rate of various modes in the dusty plasma are derived using the first-order perturbation theory. The effect of dust grain parameters on frequency and growth rate is also studied and reported.

The Generalized Droop Formula for Low Signal to Noise Ratio Optical Links

We present a theoretical model that fully supports the recently disclosed generalized droop formula (GDF) for calculating the signal-to-noise ratio (SNR) of constant-output power (COP) amplified coherent links operated at a very low SNR. For single-mode nonlinear COP links we compare the GDF-SNR to the better known generalized SNR (GSNR) that uses the Gaussian noise (GN) model for constant-gain (CG) amplifiers. We find that at all medium to large SNRs the GSNR well matches with the GDF, while at GSNR below 6 dB the GSNR over-estimates the correct GDF-SNR by more than 0.5 dB. Fortunately, the GDF-SNR turns out to be approximately a simple function of the GSNR, which allows adaptation of the widespread GSNR also to very low SNR links. A key finding of this article is that the end-to-end model underlying the GDF is a concatenation of per-span first-order regular perturbation (RP1) models with end-span power renormalization. This fact allows the GDF to well reproduce the SNR of highly nonlinear systems, well beyond the RP1 limit underlying the GN model. The GDF is successfully extended to the case where the bandwidth/modes of the COP amplifiers are not entirely filled by the transmitted multiplex. Finally, the GDF is extended to CG amplified links and is shown to improve on known GN models of highly nonlinear propagation with CG amplifiers.

Stochastic nonlinear multiscale computational scheme for short fiber reinforced composites to study the influence of microstructural variability on damage propagation

In this paper, a stochastic nonlinear multiscale computational scheme is proposed to study the influence of the variability in both physical parameters of constituent materials and geometrical parameters such as fiber orientation, fiber arrangement of short fiber reinforced composites on the damage propagation. The aim is to predict many probable damage patterns in a huge number of scenarios under complex strain conditions and to discuss the influential level of variability in the physical and geometrical parameters for short fiber reinforced composites. The parameterization and numerical modelling for short fiber reinforced plastics made by injection molding are conducted. The random physical parameters are considered theoretically by the first-order perturbation based stochastic homogenization method, while sampling is used for the random geometrical parameters. When the scenario becomes huge in the stochastic nonlinear analysis, a computational scheme using sub-sampling is proposed. Moreover, the stochastic prediction of the homogenized properties of the composite material and their probable degradation are discussed. The stochastic computation of microscopic strains is analyzed though the damage propagation simulation. When the geometrical variability is considered, a definition of an average strain distribution among many samples is also presented. The efficiency of the accelerated element-by-element scaled conjugate gradient iterative solver is shown by solving many three-dimension random short fiber reinforced models with hundreds of thousands of degrees of freedom. The stochastic computational scheme provides a suitable reference to predict failure under specific reliability requirements of short fiber reinforced composites or other composite materials.