On the simplest (2+1) dimensional integrable spin systems and their equivalent nonlinear Schr\"odinger equations

Using a moving space curve formalism, geometrical as well as gauge equivalence between a (2+1) dimensional spin equation (M-I equation) and the (2+1) dimensional nonlinear Schr\"odinger equation (NLSE) originally discovered by Calogero, discussed then by Zakharov and recently rederived by Strachan, have been estabilished. A compatible set of three linear equations are obtained and integrals of motion are discussed. Through stereographic projection, the M-I equation has been bilinearized and different types of solutions such as line and curved solitons, breaking solitons, induced dromions, and domain wall type solutions are presented. Breaking soliton solutions of (2+1) dimensional NLSE have also been reported. Generalizations of the above spin equation are discussed.Comment: 32 pages, no figures, accepted for publication in J. Math. Phy

A Quantum Quasi-Harmonic Nonlinear Oscillator with an Isotonic Term

The properties of a nonlinear oscillator with an additional term $k_g/x^2$, characterizing the isotonic oscillator, are studied. The nonlinearity affects to both the kinetic term and the potential and combines two nonlinearities associated to two parameters, $\kappa$ and $k_g$, in such a way that for $\kappa=0$ all the characteristics of of the standard isotonic system are recovered. The first part is devoted to the classical system and the second part to the quantum system. This is a problem of quantization of a system with position-dependent mass of the form $m(x)=1/(1 - {\kappa} x^2)$, with a $\kappa$-dependent non-polynomial rational potential and with an additional isotonic term. The Schr\"odinger equation is exactly solved and the $(\kappa,k_g)$-dependent wave functions and bound state energies are explicitly obtained for both $\kappa0$.Comment: two figure

Motion of Curves and Surfaces and Nonlinear Evolution Equations in (2+1) Dimensions

It is shown that a class of important integrable nonlinear evolution equations in (2+1) dimensions can be associated with the motion of space curves endowed with an extra spatial variable or equivalently, moving surfaces. Geometrical invariants then define topological conserved quantities. Underlying evolution equations are shown to be associated with a triad of linear equations. Our examples include Ishimori equation and Myrzakulov equations which are shown to be geometrically equivalent to Davey-Stewartson and Zakharov -Strachan (2+1) dimensional nonlinear Schr\"odinger equations respectively.Comment: 13 pages, RevTeX, to appear in J. Math. Phy

Statistical Analysis of Peptide-Induced Graded and All-or-None Fluxes in Giant Vesicles

AbstractAntimicrobial, cytolytic, and cell-penetrating peptides induce pores or perturbations in phospholipid membranes that result in fluxes of dyes into or out of lipid vesicles. Here we examine the fluxes induced by four of these membrane-active peptides in giant unilamellar vesicles. The type of flux is determined from the modality of the distributions of vesicles as a function of their dye content using the statistical Hartigan dip test. Graded and all-or-none fluxes correspond to unimodal and bimodal distributions, respectively. To understand how these distributions arise, we perform Monte Carlo simulations of peptide-induced dye flux into vesicles using a very simple model. The modality of the distributions depends on the rate constants of pore opening and closing, and dye flux. If the rate constants of pore opening and closing are both much smaller than that of dye flux through the pore, all-or-none influx occurs. However, if one of them, especially the rate constant for pore opening, increases significantly relative to the flux rate constant, the process becomes graded. In the experiments, we find that the flux type is the same in giant and large vesicles, for all peptides except one. But this one exception indicates that the flux type cannot be used to unambiguously predict the mechanism of membrane permeabilization by the peptides

Comparison of sensory characteristics and biochemical parameters in commercial frozen prawns

Commercial samples of frozen shrimp of different styles of presentation and size grades were tested for sensory, physical (cooked yield and pH) and biochemical characteristics (moisture, total nitrogen, water extractable nitrogen, nonprotein nitrogen, alpha amino nitrogen, total volatile nitrogen and trimethylamine nitrogen). The test results are compared and correlated. The order of preference of the samples were HL>PUD>P & D. There was significant correlation between sensory score of cooked sample and WEN, NPN and ∞ – NHsub(2)-N values. TVN and TMA-N did not exhibit any correlation with sensory score. It is inferred that in quality measurement of frozen shrimps of commerce the quantity of water soluble components and the total dry matter can be used to support the sensory test results

A Group Theoretical Identification of Integrable Equations in the Li\'enard Type Equation x¨+f(x)x˙+g(x)=0\ddot{x}+f(x)\dot{x}+g(x) = 0 : Part II: Equations having Maximal Lie Point Symmetries

In this second of the set of two papers on Lie symmetry analysis of a class of Li\'enard type equation of the form $\ddot {x} + f(x)\dot {x} + g(x)= 0$, where over dot denotes differentiation with respect to time and $f(x)$ and $g(x)$ are smooth functions of their variables, we isolate the equations which possess maximal Lie point symmetries. It is well known that any second order nonlinear ordinary differential equation which admits eight parameter Lie point symmetries is linearizable to free particle equation through point transformation. As a consequence all the identified equations turn out to be linearizable. We also show that one can get maximal Lie point symmetries for the above Li\'enard equation only when $f_{xx} =0$ (subscript denotes differentiation). In addition, we discuss the linearising transformations and solutions for all the nonlinear equations identified in this paper.Comment: Accepted for publication in Journal of Mathematical Physic

A fault diagnosis methodology for an external gear pump with the use of Machine Learning classification algorithms: Support Vector Machine and Multilayer Perceptron

This paper presents a fault diagnosis Machine Learning (ML) computational strategy for an external gear pump. The method uses supervised learning of descriptive features. The focus is on two types of ML nonlinear multi-class classification algorithms: Support Vector Machine (SVM) and Multilayer Perceptron (MLP) algorithms. Although significant work has been reported by previous authors, it is still difficult to optimise ab initio the choice of the hyper parameters (ML method dependent) for each specific application. For instance, the type of SVM kernel function or the selection of the MLP activation function and the optimum number of hidden layers (and neurons). As it is well known, reliability of ML algorithms is strongly dependent upon the existence of a sufficiently large quantity of high-quality training data. In our case, and in the absence of experimental data, high-fidelity in-silico data (generated via the software PumpLinx) have been used for the training of the underlying ML metamodel. A variety of working conditions are recreated, ranging from healthy to various kinds of faulty scenarios (i.e., clogging, radial gap variations, viscosity variations). In addition, noise perturbation has been considered in order to increase the sample data available for ML training. This paper explores and compares the use of SVM and MLP algorithms for predictive maintenance. To reduce the high computational cost during the training stage in the MLP algorithm, some predefined network architectures, like 2n neurons per hidden layer, are used to speed up the identification of the precise number of neurons (shown to be useful when the sample data set is sufficiently large). A series of benchmark tests are presented, enabling to conclude that the use of wavelet features and SVM or MLP algorithms can provide the best accuracy for classification

Quantal Two-Centre Coulomb Problem treated by means of the Phase-Integral Method II. Quantization Conditions in the Symmetric Case Expressed in Terms of Complete Elliptic Integrals. Numerical Illustration

The contour integrals, occurring in the arbitrary-order phase-integral quantization conditions given in a previous paper, are in the first- and third-order approximations expressed in terms of complete elliptic integrals in the case that the charges of the Coulomb centres are equal. The evaluation of the integrals is facilitated by the knowledge of quasiclassical dynamics. The resulting quantization conditions involving complete elliptic integrals are solved numerically to obtain the energy eigenvalues and the separation constants of the $1s\sigma$ and $2p\sigma$ states of the hydrogen molecule ion for various values of the internuclear distance. The accuracy of the formulas obtained is illustrated by comparison with available numerically exact results.Comment: 19 pages, RevTeX 4, 4 EPS figures, submitted to J. Math. Phy

A nonlocal connection between certain linear and nonlinear ordinary differential equations/oscillators

We explore a nonlocal connection between certain linear and nonlinear ordinary differential equations (ODEs), representing physically important oscillator systems, and identify a class of integrable nonlinear ODEs of any order. We also devise a method to derive explicit general solutions of the nonlinear ODEs. Interestingly, many well known integrable models can be accommodated into our scheme and our procedure thereby provides further understanding of these models.Comment: 12 pages. J. Phys. A: Math. Gen. 39 (2006) in pres

A non-linear Oscillator with quasi-Harmonic behaviour: two- and nn-dimensional Oscillators

A nonlinear two-dimensional system is studied by making use of both the Lagrangian and the Hamiltonian formalisms. The present model is obtained as a two-dimensional version of a one-dimensional oscillator previously studied at the classical and also at the quantum level. First, it is proved that it is a super-integrable system, and then the nonlinear equations are solved and the solutions are explicitly obtained. All the bounded motions are quasiperiodic oscillations and the unbounded (scattering) motions are represented by hyperbolic functions. In the second part the system is generalized to the case of $n$ degrees of freedom. Finally, the relation of this nonlinear system with the harmonic oscillator on spaces of constant curvature, two-dimensional sphere $S^2$ and hyperbolic plane $H^2$, is discussed.Comment: 30 pages, 4 figures, submitted to Nonlinearit