Application of Laplace transform technique to the solution of certain third-order non-linear systems

A number of papers have appeared on the application of operational methods and in particular the Laplace transform to problems concerning non-linear systems of one kind or other. This, however, has met with only partial success in solving a class of non-linear problems as each approach has some limitations and drawbacks. In this study the approach of Baycura has been extended to certain third-order non-linear systems subjected to non-periodic excitations, as this approximate method combines the advantages of engineering accuracy with ease of application to such problems. Under non-periodic excitations the method provides a procedure for estimating quickly the maximum response amplitude, which is important from the point of view of a designer. Limitations of such a procedure are brought out and the method is illustrated by an example taken from a physical situation.

The pulse response of non-linear third order systems

The response of a third order non-linear system subjected to a pulse excitation is analysed. A transformation of the displacement variable is effected. The transformation function chosen is the solution of the linear problem subjected to the same pulse. With this transformation the equation of motion is brought into a form in which the method of variation of parameters is applicable for the solution of the problem. The method is applied to a single axis gyrostabilized platform subjected to an exponentially decaying pulse. The analytical results are compared with digital and analog computer solutions.

Suppression of the zero-order term in off-axis digital holography through nonlinear filtering

We present experimental validation of a new reconstruction method for off-axis digital holographic microscopy (DHM). This method effectively suppresses the object autocorrelation,namely, the zero-order term,from holographic data,thereby improving the reconstruction bandwidth of complex wavefronts. The algorithm is based on nonlinear filtering and can be applied to standard DHM setups with realistic recording conditions.We study the robustness of the technique under different experimental configurations,and quantitatively demonstrate its enhancement capabilities on phase signals.

Induced higher-order aberrations after laser in situ keratomileusis (LASIK) performed with wavefront-guided IntraLase femtosecond laser in moderate to high astigmatism

Background Wavefront-guided Laser-assisted in situ keratomileusis (LASIK) is a widespread and effective surgical treatment for myopia and astigmatic correction but whether it induces higher-order aberrations remains controversial. The study was designed to evaluate the changes in higher-order aberrations after wavefront-guided ablation with IntraLase femtosecond laser in moderate to high astigmatism. Methods Twenty-three eyes of 15 patients with moderate to high astigmatism (mean cylinder, −3.22 ± 0.59 dioptres) aged between 19 and 35 years (mean age, 25.6 ± 4.9 years) were included in this prospective study. Subjects with cylinder ≥ 1.5 and ≤2.75 D were classified as moderate astigmatism while high astigmatism was ≥3.00 D. All patients underwent a femtosecond laser–enabled (150-kHz IntraLase iFS; Abbott Medical Optics Inc) wavefront-guided ablation. Uncorrected (UDVA), corrected (CDVA) distance visual acuity in logMAR, keratometry, central corneal thickness (CCT) and higher-order aberrations (HOAs) over a 6 mm pupil, were assessed before and 6 months, postoperatively. The relationship between postoperative change in HOA and preoperative mean spherical equivalent refraction, mean astigmatism, and postoperative CCT were tested. Results At the last follow-up, the mean UDVA was increased (P < 0.0001) but CDVA remained unchanged (P = 0.48) and no eyes lost ≥2 lines of CDVA. Mean spherical equivalent refraction was reduced (P < 0.0001) and was within ±0.50 D range in 61 % of eyes. The average corneal curvature was flatter by 4 D and CCT was reduced by 83 μm (P < 0.0001, for all), postoperatively. Coma aberrations remained unchanged (P = 0.07) while the change in trefoil (P = 0.047) postoperatively, was not clinically significant. The 4th order HOAs (spherical aberration and secondary astigmatism) and the HOA root mean square (RMS) increased from −0.18 ± 0.07 μm, 0.04 ± 0.03 μm and 0.47 ± 0.11 μm, preoperatively, to 0.33 ± 0.19 μm (P = 0.004), 0.21 ± 0.09 μm (P < 0.0001) and 0.77 ± 0.27 μm (P < 0.0001), six months postoperatively. The change in spherical aberration after the procedure increased with an increase in the degree of preoperative myopia. Conclusions Wavefront-guided IntraLASIK offers a safe and effective option for vision and visual function improvement in astigmatism. Although, reduction of HOA is possible in a few eyes, spherical-like aberrations are increased in majority of the treated eyes.

An investigation of first-order transition across charge ordered and ferromagnetic phases in Gd0.5Sr0.5MnO3 single crystals by magnetic and magnetotransport studies

Gadolinium strontium manganite single crystals of the composition Gd0.5Sr0.5MnO3 were grown using the optical float zone method. We report here the magnetic and magnetotransport properties of these crystals. A large magnetoresistance similar to 10(9)% was observed at 45 K under the application of a 110 kOe field. We have observed notable thermomagnetic anomalies such as open hysteresis loops across the broadened first-order transition between the charge order insulator and the ferromagnetic metallic phase while traversing the magnetic field-temperature (H-T) plane isothermally or isomagnetically. In order to discern the cause of these observed anomalies, the H-T phase diagram for Gd0.5Sr0.5MnO3 is formulated using the magnetization-field (M-H), magnetization-temperature (M-T) and resistance-temperature (R-T) measurements. The temperature dependence of the critical field (i.e. H-up, the field required for transformation to the ferromagnetic metallic phase) is non-monotonic. We note that the non-monotonic variation of the supercooling limit is anomalous according to the classical concepts of the first-order phase transition. Accordingly, H-up values below similar to 20 K are unsuitable to represent the supercooling limit. It is possible that the nature of the metastable states responsible for the observed open hysteresis loops is different from that of the supercooled ones.

Charge-order-driven multiferroic properties of Y1-xCaxMnO3

Dielectric measurements on the charge-ordered insulators, Y1-xCaxMnO3 (x = 0.4. 0.45 and 0.5), show maxima in the dielectric constant around the charge ordering transition temperature while magnetic measurements show the presence of weak ferromagnetic interactions at low temperatures. Besides the magnetic field dependence of the dielectric constant, these manganites also exhibit second harmonic generation. Thus, the charge-ordered Y1-xCaxMnO3 compositions are multiferroic and magnetoelectric, in accordance with theoretical predictions. Magnetoelectric properties are retained in small particles of Y0.5Ca0.5MnO3. (C) 2008 Elsevier Ltd. All rights reserved.

A Combinatorial Optimization Problem for High Order PODs with Few Sensors

Experimental characterization of high dimensional dynamic systems sometimes uses the proper orthogonal decomposition (POD). If there are many measurement locations and relatively fewer sensors, then steady-state behavior can still be studied by sequentially taking several sets of simultaneous measurements. The number required of such sets of measurements can be minimized if we solve a combinatorial optimization problem. We aim to bring this problem to the attention of engineering audiences, summarize some known mathematical results about this problem, and present a heuristic (suboptimal) calculation that gives reasonable, if not stellar, results.

Energy identities in water wave theory for free-surface boundary condition with higher-order derivatives

A modified form of Green's integral theorem is employed to derive the energy identity in any water wave diffraction problem in a single-layer fluid for free-surface boundary condition with higher-order derivatives. For a two-layer fluid with free-surface boundary condition involving higher-order derivatives, two forms of energy identities involving transmission and reflection coefficients for any wave diffraction problem are also derived here by the same method. Based on this modified Green's theorem, hydrodynamic relations such as the energy-conservation principle and modified Haskind–Hanaoka relation are derived for radiation and diffraction problems in a single as well as two-layer fluid.

Constructing commutative semifields of square order

The projection construction has been used to construct semifields of odd characteristic using a field and a twisted semifield [Commutative semi-fields from projection mappings, Designs, Codes and Cryptography, 61 (2011), 187{196]. We generalize this idea to a projection construction using two twisted semifields to construct semifields of odd characteristic. Planar functions and semifields have a strong connection so this also constructs new planar functions.

Bond-order wave phase, spin solitons, and thermodynamics of a frustrated linear spin-1/2 Heisenberg antiferromagnet

The linear spin-1/2 Heisenberg antiferromagnet with exchanges J(1) and J(2) between first and second neighbors has a bond-order wave (BOW) phase that starts at the fluid-dimer transition at J(2)/J(1)=0.2411 and is particularly simple at J(2)/J(1)=1/2. The BOW phase has a doubly degenerate singlet ground state, broken inversion symmetry, and a finite-energy gap E-m to the lowest-triplet state. The interval 0.4 < J(2)/J(1) < 1.0 has large E-m and small finite-size corrections. Exact solutions are presented up to N = 28 spins with either periodic or open boundary conditions and for thermodynamics up to N = 18. The elementary excitations of the BOW phase with large E-m are topological spin-1/2 solitons that separate BOWs with opposite phase in a regular array of spins. The molar spin susceptibility chi(M)(T) is exponentially small for T << E-m and increases nearly linearly with T to a broad maximum. J(1) and J(2) spin chains approximate the magnetic properties of the BOW phase of Hubbard-type models and provide a starting point for modeling alkali-tetracyanoquinodimethane salts.

Hidden order in crackling noise during peeling of an adhesive tape

We address the longstanding problem of recovering dynamical information from noisy acoustic emission signals arising from peeling of an adhesive tape subject to constant traction velocity. Using the phase space reconstruction procedure we demonstrate the deterministic chaotic dynamics by establishing the existence of correlation dimension as also a positive Lyapunov exponent in a midrange of traction velocities. The results are explained on the basis of the model that also emphasizes the deterministic origin of acoustic emission by clarifying its connection to stick-slip dynamics.

Dynamo onset as a first-order transition: Lessons from a shell model for magnetohydrodynamics

We carry out systematic and high-resolution studies of dynamo action in a shell model for magnetohydro-dynamic (MHD) turbulence over wide ranges of the magnetic Prandtl number Pr-M and the magnetic Reynolds number Re-M. Our study suggests that it is natural to think of dynamo onset as a nonequilibrium first-order phase transition between two different turbulent, but statistically steady, states. The ratio of the magnetic and kinetic energies is a convenient order parameter for this transition. By using this order parameter, we obtain the stability diagram (or nonequilibrium phase diagram) for dynamo formation in our MHD shell model in the (Pr-M(-1), Re-M) plane. The dynamo boundary, which separates dynamo and no-dynamo regions, appears to have a fractal character. We obtain a hysteretic behavior of the order parameter across this boundary and suggestions of nucleation-type phenomena.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Existence and approximations of solutions to some fractional order functional integral equations

In this paper we shall study a fractional order functional integral equation. In the first part of the paper, we proved the existence and uniqueness of mile and global solutions in a Banach space. In the second part of the paper, we used the analytic semigroups theory oflinear operators and the fixed point method to establish the existence, uniqueness and convergence of approximate solutions of the given problem in a separable Hilbert space. We also proved the existence and convergence of Faedo-Galerkin approximate solution to the given problem. Finally, we give an example.