Study on Noncommutative Representations of Galilean Generators

The representations of Galilean generators are constructed on a space where both position and momentum coordinates are noncommutating operators. A dynamical model invariant under noncommutative phase space transformations is constructed. The Dirac brackets of this model reproduce the original noncommutative algebra. Also, the generators in terms of noncommutative phase space variables are abstracted from this model in a consistent manner. Finally, the role of Jacobi identities is emphasised to produce the noncommuting structure that occurs when an electron is subjected to a constant magnetic field and Berry curvature.Comment: Title changed, new references added, published in Int. J. Mod. Phys.

Deterministic and Stochastic Analysis of a Ratio-Dependent Predator-Prey System with Delay

Recently ratio-dependent predator-prey models have become the focus of considerable attention in theoretical ecology in their own right. In this paper, we have studied the deterministic and stochastic dynamical aspects of stability of a MichaelisMenten type ratio-dependent predator-prey system that includes discrete time-delay. Computer simulations are carried out to explain the analytical findings in deterministic environment. The biological implications of our analytical and numerical findings are discussed critically

Double-layer shocks in a magnetized quantum plasma

The formation of small but finite amplitude electrostatic shocks in the propagation of quantum ion-acoustic waves (QIAWs) obliquely to an external magnetic field is reported in a quantum electron-positron-ion (e-p-i) plasma. Such shocks are seen to have double-layer (DL) structures composed of the compressive and accompanying rarefactive slow-wave fronts. Existence of such DL shocks depends critically on the quantum coupling parameter $H$ associated with the Bohm potential and the positron to electron density ratio $\delta$. The profiles may, however, steepen initially and reach a steady state with a number of solitary waves in front of the shocks. Such novel DL shocks could be a good candidate for particle acceleration in intense laser-solid density plasma interaction experiments as well as in compact astrophysical objects, e.g., magnetized white dwarfs.Comment: 4 pages, 1 figure (to appear in Physical Review E

Electrical Conductance of Molecular Wires

Molecular wires (MW) are the fundamental building blocks for molecular electronic devices. They consist of a molecular unit connected to two continuum reservoirs of electrons (usually metallic leads). We rely on Landauer theory as the basis for studying the conductance properties of MW systems. This relates the lead to lead current to the transmission probability for an electron to scatter through the molecule. Two different methods have been developed for the study of this scattering. One is based on a solution of the Lippmann-Schwinger equation and the other solves for the {\bf t} matrix using Schroedinger's equation. We use our methodology to study two problems of current interest. The first MW system consists of 1,4 benzene-dithiolate (BDT) bonded to two gold nanocontacts. Our calculations show that the conductance is sensitive to the chemical bonding between the molecule and the leads. The second system we study highlights the interesting phenomenon of antiresonances in MW. We derive an analytic formula predicting at what energies antiresonances should occur in the transmission spectra of MW. A numerical calculation for a MW consisting of filter molecules attached to an active molecule shows the existence of an antiresonance at the energy predicted by our formula.Comment: 14 pages, 5 figure

Modelling of Shear Behaviour of Interfaces Involving Smooth Geomembrane and Nonwoven Geotextile Under Static and Dynamic Loading Conditions

© 2020, Springer Nature Switzerland AG. The constitutive modelling of geosynthetic–geosynthetic interfaces is essential to predict the performance of the engineering structures such as landfills, flood control dykes and geotextile encapsulated-sand systems for the protection of shore. This article presents a mathematical model to simulate the shear stress/force–displacement behaviour of the interfaces involving smooth geomembrane and nonwoven geotextile under static and dynamic loading conditions. The model is the extension of an existing technique developed for predicting the soil-structure interface shear behaviour under static loading conditions. The proposed model can predict the non-linear pre-peak and the post-peak strain softening/hardening behaviour of the interfaces observed during the laboratory testing. The shear stress/force–displacement response of the interfaces has been modelled by dividing it into three parts: pre-peak, peak and post-peak behaviour. Subsequently, the modelling parameters are obtained using the results from the laboratory direct shear tests and fixed–block type shake table tests conducted on these interfaces. Finally, the shear stress/force–displacement response of the interfaces is evaluated and compared with the experimental results. The predicted shear stress/force–displacement response of the interfaces is found to be in good agreement with the experimental data for both static and dynamic loading conditions

On Indexed Absolute Matrix Summability of an Infinite Series

Some results have been established on absolute index Riesz summability factor of an infinite series. Furthermore, these kind of results can be extended by taking other parameters and an absolute index matrix summability factor of an infinite series or some weaker conditions. In the present paper a new result on generalized absolute index matrix summability factor of an infinite series has been established

FEATURE SELECTION APPLIED TO THE TIME-FREQUENCY REPRESENTATION OF MUSCLE NEAR-INFRARED SPECTROSCOPY (NIRS) SIGNALS: CHARACTERIZATION OF DIABETIC OXYGENATION PATTERNS

Diabetic patients might present peripheral microcirculation impairment and might benefit from physical training. Thirty-nine diabetic patients underwent the monitoring of the tibialis anterior muscle oxygenation during a series of voluntary ankle flexo-extensions by near-infrared spectroscopy (NIRS). NIRS signals were acquired before and after training protocols. Sixteen control subjects were tested with the same protocol. Time-frequency distributions of the Cohen's class were used to process the NIRS signals relative to the concentration changes of oxygenated and reduced hemoglobin. A total of 24 variables were measured for each subject and the most discriminative were selected by using four feature selection algorithms: QuickReduct, Genetic Rough-Set Attribute Reduction, Ant Rough-Set Attribute Reduction, and traditional ANOVA. Artificial neural networks were used to validate the discriminative power of the selected features. Results showed that different algorithms extracted different sets of variables, but all the combinations were discriminative. The best classification accuracy was about 70%. The oxygenation variables were selected when comparing controls to diabetic patients or diabetic patients before and after training. This preliminary study showed the importance of feature selection techniques in NIRS assessment of diabetic peripheral vascular impairmen

Antiresonances in Molecular Wires

We present analytic and numerical studies based on Landauer theory of conductance antiresonances of molecular wires. Our analytic treatment is a solution of the Lippmann-Schwinger equation for the wire that includes the effects of the non-orthogonality of the atomic orbitals on different atoms exactly. The problem of non-orthogonality is treated by solving the transport problem in a new Hilbert space which is spanned by an orthogonal basis. An expression is derived for the energies at which antiresonances should occur for a molecular wire connected to a pair of single-channel 1D leads. From this expression we identify two distinct mechanisms that give rise to antiresonances under different circumstances. The exact treatment of non-orthogonality in the theory is found to be necessary to obtain reliable results. Our numerical simulations extend this work to multichannel leads and to molecular wires connected to 3D metallic nanocontacts. They demonstrate that our analytic results also provide a good description of these more complicated systems provided that certain well-defined conditions are met. These calculations suggest that antiresonances should be experimentally observable in the differential conductance of molecular wires of certain types.Comment: 22 pages, 5 figure