Dressing method and quadratic bundles related to symmetric spaces. Vanishing boundary conditions

We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m)x U(n)). The simplest representative of the corresponding integrable hierarchy is given by a multi-component Kaup-Newell derivative nonlinear Schroedinger equation which serves as a motivational example for our general considerations. We extensively discuss how one can apply Zakharov-Shabat's dressing procedure to derive reflectionless potentials obeying zero boundary conditions. Those could be used for one to construct fast decaying solutions to any nonlinear equation belonging to the same hierarchy. One can distinguish between generic soliton type solutions and rational solutions.Comment: 18 page

Fluctuation-Induced Interactions Between Ellipsoidal Particle and Planar Substrate Immersed in Critical Medium

In our study we investigate the behaviour of the net force (NF) emerging between an ellipsoidal particle and a thick plate (slab), when the interaction takes place in a near critical fluid medium with account for the omnipresent van der Waals forces (vdWF). Here we consider the case of complete wetting of the objects surfaces by the medium, due to strong adsorbing local surface potentials, exerted by thin solid coating films. The influence of the bulk inner regions of the particle and the slab on the constituents of the fluid results in long-ranged competing dispersion potentials. As a consequence from the critical fluctuations of the medium, the system experiences an additional effective interaction, traditionally termed critical Casimir force (CCF). The forces of interest are evaluated numerically from integral expressions obtained utilizing general scaling arguments and mean-field type calculations in combination with the so-called "surface integration approach" (SIA). Within the scenario considered here, this technique is applicable if one has knowledge of the forces between two parallel semi-infinite plates, confining in between some fluctuating fluid medium characterized by its temperature $T$ and chemical potential $\mu$. It is demonstrated that for a suitable set of particle-fluid, slab-fluid, and fluid-fluid coupling parameters the competition between the effects due to the coatings and the core regions of the objects result, when one changes $T$ or $\mu$, in {\it sign change} of the NF acting between the ellipsoid and the slab.Comment: 8 pages, 2 figues. arXiv admin note: text overlap with arXiv:1702.0491

Terahertz time-domain spectroscopy of edible oils.

Chemical degradation of edible oils has been studied using conventional spectroscopic methods spanning the spectrum from ultraviolet to mid-IR. However, the possibility of morphological changes of oil molecules that can be detected at terahertz frequencies is beginning to receive some attention. Furthermore, the rapidly decreasing cost of this technology and its capability for convenient, in situ measurement of material properties, raises the possibility of monitoring oil during cooking and processing at production facilities, and more generally within the food industry. In this paper, we test the hypothesis that oil undergoes chemical and physical changes when heated above the smoke point, which can be detected in the 0.05-2 THz spectral range, measured using the conventional terahertz time-domain spectroscopy technique. The measurements demonstrate a null result in that there is no significant change in the spectra of terahertz optical parameters after heating above the smoke point for 5 min

Nonlocal Reductions of a Generalized Heisenberg Ferromagnet Equation

We study nonlocal reductions of coupled equations in $1+1$ dimensions of the Heisenberg ferromagnet type. The equations under consideration are completely integrable and have a Lax pair related to a linear bundle in pole gauge. We describe the integrable hierarchy of nonlinear equations related to our system in terms of generating operators. We present some special solutions associated with four distinct discrete eigenvalues of scattering operator. Using the Lax pair diagonalization method, we derive recurrence formulas for the conserved densities and find the first two simplest conserved densities.Comment: 14 pages. arXiv admin note: substantial text overlap with arXiv:1711.0635

Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice

We present two new families of stationary solutions for equations of Bose-Fermi mixtures with an elliptic function potential with modulus $k$. We also discuss particular cases when the quasiperiodic solutions become periodic ones. In the limit of a sinusoidal potential ($k\to 0$) our solutions model a quasi-one dimensional quantum degenerate Bose-Fermi mixture trapped in optical lattice. In the limit $k\to 1$ the solutions are expressed by hyperbolic function solutions (vector solitons). Thus we are able to obtain in an unified way quasi-periodic and periodic waves, and solitons. The precise conditions for existence of every class of solutions are derived. There are indications that such waves and localized objects may be observed in experiments with cold quantum degenerate gases.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Reducing switching losses through MOSFET-IGBT combination

This paper introduces a configuration aimed at switching losses reduction trough a power leg constructed by combining a MOSFET and an IGBT. The combined use of these different switches leads to the turn-on losses reduction trough the use of the faster freewheeling diode of the IGBT, and the turn-off losses reduction trough use of the MOSFET’s lower losses because of the lack of tailing current, typical for IGBT’s. The introduced leg structure can be used to build single phase – full bridge invertors or three phase inverters. The proposed leg is realized, experimented and validated

Remarks on Quadratic Bundles Related to Hermitian Symmetric Spaces

We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m)\times U(n)). We discuss the spectral properties of scattering operator, develop the direct scattering problem associated with it and stress on the effect of reduction on these. By applying a modification of Zakharov-Shabat\u27s dressing procedure we demonstrate how one can obtain reflectionless potentials. That way one is able to generate soliton solutions to the nonlinear evolution equations belonging to the integrable hierarchy associated with quadratic bundles under study

On Multicomponent Derivative Nonlinear Schrodinger Equation Related to Symmetric Spaces

We study derivative nonlinear Schrodinger equations related to symmetric spaces of the type A.III. We discuss the spectral properties of the corresponding Lax operator and develop the direct scattering problem connected to it. By applying an appropriately chosen dressing factor we derive soliton solutions to the nonlinear equation. We find the integrals of motion by using the method of diagonalization of Lax pair