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.

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.

Beyond fractional derivatives: local approximation of other convolution integrals

Dynamic systems involving convolution integrals with decaying kernels, of which fractionally damped systems form a special case, are non-local in time and hence infinite dimensional. Straightforward numerical solution of such systems up to time t needs O(t(2)) computations owing to the repeated evaluation of integrals over intervals that grow like t. Finite-dimensional and local approximations are thus desirable. We present here an approximation method which first rewrites the evolution equation as a coupled in finite-dimensional system with no convolution, and then uses Galerkin approximation with finite elements to obtain linear, finite-dimensional, constant coefficient approximations for the convolution. This paper is a broad generalization, based on a new insight, of our prior work with fractional order derivatives (Singh & Chatterjee 2006 Nonlinear Dyn. 45, 183-206). In particular, the decaying kernels we can address are now generalized to the Laplace transforms of known functions; of these, the power law kernel of fractional order differentiation is a special case. The approximation can be refined easily. The local nature of the approximation allows numerical solution up to time t with O(t) computations. Examples with several different kernels show excellent performance. A key feature of our approach is that the dynamic system in which the convolution integral appears is itself approximated using another system, as distinct from numerically approximating just the solution for the given initial values; this allows non-standard uses of the approximation, e. g. in stability analyses.

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.

Off-axis field approximations for ion traps with apertures

In recent work (Int. J. Mass Spec., vol. 282, pp. 112–122) we have considered the effect of apertures on the fields inside rf traps at points on the trap axis. We now complement and complete that work by considering off-axis fields in axially symmetric (referred to as “3D”) and in two dimensional (“2D”) ion traps whose electrodes have apertures, i.e., holes in 3D and slits in 2D. Our approximation has two parts. The first, EnoAperture, is the field obtained numerically for the trap under study with apertures artificially closed. We have used the boundary element method (BEM) for obtaining this field. The second part, EdueToAperture, is an analytical expression for the field contribution of the aperture. In EdueToAperture, aperture size is a free parameter. A key element in our approximation is the electrostatic field near an infinite thin plate with an aperture, and with different constant-valued far field intensities on either side. Compact expressions for this field can be found using separation of variables, wherein the choice of coordinate system is crucial. This field is, in turn, used four times within our trap-specific approximation. The off-axis field expressions for the 3D geometries were tested on the quadrupole ion trap (QIT) and the cylindrical ion trap (CIT), and the corresponding expressions for the 2D geometries were tested on the linear ion trap (LIT) and the rectilinear ion trap (RIT). For each geometry, we have considered apertures which are 10%, 30%, and 50% of the trap dimension. We have found that our analytical correction term EdueToAperture, though based on a classical small-aperture approximation, gives good results even for relatively large apertures.

Kernel-based spatial-color modeling for fast moving object tracking

Visual tracking has been a challenging problem in computer vision over the decades. The applications of Visual Tracking are far-reaching, ranging from surveillance and monitoring to smart rooms. Mean-shift (MS) tracker, which gained more attention recently, is known for tracking objects in a cluttered environment and its low computational complexity. The major problem encountered in histogram-based MS is its inability to track rapidly moving objects. In order to track fast moving objects, we propose a new robust mean-shift tracker that uses both spatial similarity measure and color histogram-based similarity measure. The inability of MS tracker to handle large displacements is circumvented by the spatial similarity-based tracking module, which lacks robustness to object's appearance change. The performance of the proposed tracker is better than the individual trackers for tracking fast-moving objects with better accuracy.

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.

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.

Modified density matrix renormalization group algorithm for the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange: Comparison with field theory at large J(2)/J(1)

A modified density matrix renormalization group (DMRG) algorithm is applied to the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange J(1) and J(2) between first and second neighbors. The modified algorithm yields accurate results up to J(2)/J(1) approximate to 4 for the magnetic gap Delta to the lowest triplet state, the amplitude B of the bond order wave phase, the wavelength lambda of the spiral phase, and the spin correlation length xi. The J(2)/J(1) dependences of Delta, B, lambda, and xi provide multiple comparisons to field theories of the zigzag chain. The twist angle of the spiral phase and the spin structure factor yield additional comparisons between DMRG and field theory. Attention is given to the numerical accuracy required to obtain exponentially small gaps or exponentially long correlations near a quantum phase transition.

An asymptotic analysis of a simple model for the structure and dynamics of the Ramdas layer

This paper presents a complete asymptotic analysis of a simple model for the evolution of the nocturnal temperature distribution on bare soil in calm clear conditions. The model is based on a simplified flux emissivity scheme that provides a nondiffusive local approximation for estimating longwave radiative cooling near ground. An examination of the various parameters involved shows that the ratio of the characteristic radiative to the diffusive timescale in the problem is of order 10(-3), and can therefore be treated as a small parameter (mu). Certain other plausible approximations and linearization lead to a new equation whose asymptotic solution as mu --> 0 can be written in closed form. Four regimes, consishttp://eprints.iisc.ernet.in/cgi/users/home?screen=EPrint::Edit&eprintid=27192&stage=core#tting of a transient at nominal sunset, a radiative-diffusive boundary ('Ramdas') layer on ground, a boundary layer transient and a radiative outer solution, are identified. The asymptotic solution reproduces all the qualitative features of more exact numerical simulations, including the occurrence of a lifted temperature minimum and its evolution during night, ranging from continuing growth to relatively sudden collapse of the Ramdas layer.

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.