Darboux-integration of id\rho/dt=[H,f(\rho)]

A Darboux-type method of solving the nonlinear von Neumann equation $i\dot \rho=[H,f(\rho)]$, with functions $f(\rho)$ commuting with $\rho$, is developed. The technique is based on a representation of the nonlinear equation by a compatibility condition for an overdetermined linear system. von Neumann equations with various nonlinearities $f(\rho)$ are found to possess the so-called self-scattering solutions. To illustrate the result we consider the Hamiltonian $H$ of a one-dimensional harmonic oscillator and $f(\rho)=\rho^q-2\rho^{q-1}$ with arbitary real $q$. It is shown that self-scattering solutions possess the same asymptotics for all $q$ and that different nonlinearities may lead to effectively indistinguishable evolutions. The result may have implications for nonextensive statistics and experimental tests of linearity of quantum mechanics.Comment: revtex, 5 pages, 2 eps figures, submitted to Phys.Lett.A infinite-dimensional example is adde

Wake characteristics of large-scale wind turbines

The next generation of large-scale wind turbines will exceed 10 MW of rated power and will reach rotor diameters of about 200 m. Their rotor aerodynamics are also extreme with Reynolds numbers that reach 40 million. The wakes generated by these wind turbines cover a very large area downstream of their installation positions which increases the possibility that the wake vortices generated by these large wind turbines may affect passing-by flying vehicles. In this paper a CFD study of a large wind turbine was carried out to predict the power curves and aerodynamic loads on the rotor blades. Flow control devices of active leading and trailing edge flaps were also considered in the CFD study and the effects of flaps were investigated. The near wake flow was captured in the CFD study and the flaps add more complexity to the wake flow. To study the potential wind turbine wake encounters by aircraft, engineering wake models were developed to predict the wind turbine far wakes. The wake induced velocity fields were integrated into an aircraft flight dynamics model to simulate wind turbine wake encounter scenarios, designed for a light aircraft approaching an airport, where a wind turbine is installed. The severity of the wind turbine wake encounter was analysed using off-line flight simulations. The off-line simulation results indicated that the wake encounter severity was highly dependent on the ways that the wake vortex circulation and the core size were calculated, which suggested that field measurements of large wind turbines wake flow are needed to verify the modelling and CFD results

Calibration of the 7—equation transition model for high Reynolds flows at low mach

The numerical simulation of flows over large-scale wind turbine blades without considering the transition from laminar to fully turbulent flow may result in incorrect estimates of the blade loads and performance. Thanks to its relative simplicity and promising results, the Local-Correlation based Transition Modelling concept represents a valid way to include transitional effects into practical CFD simulations. However, the model involves coefficients that need tuning. In this paper, the γ—equation transition model is assessed and calibrated, for a wide range of Reynolds numbers at low Mach, as needed for wind turbine applications. An aerofoil is used to evaluate the original model and calibrate it; while a large scale wind turbine blade is employed to show that the calibrated model can lead to reliable solutions for complex three-dimensional flows. The calibrated model shows promising results for both two-dimensional and three-dimensional flows, even if cross-flow instabilities are neglected

Quantum corrections to static solutions of Nahm equation and Sin-Gordon models via generalized zeta-function

One-dimensional Yang-Mills Equations are considered from a point of view of a class of nonlinear Klein-Gordon-Fock models. The case of self-dual Nahm equations and non-self-dual models are discussed. A quasiclassical quantization of the models is performed by means of generalized zeta-function and its representation in terms of a Green function diagonal for a heat equation with the correspondent potential. It is used to evaluate the functional integral and quantum corrections to mass in the quasiclassical approximation. Quantum corrections to a few periodic (and kink) solutions of the Nahm as a particular case of the Ginzburg-Landau (phi-in-quadro) and and Sin-Gordon models are evaluated in arbitrary dimensions. The Green function diagonal for heat equation with a finite-gap potential is constructed by universal description via solutions of Hermit equation. An alternative approach based on Baker-Akhiezer functions for KP equation is proposed . The generalized zeta-function and its derivative at zero point as the quantum corrections to mass is expressed in terms of elliptic integrals.Comment: Workshop Nonlinear Physics and Experiment; Gallipoli, 200

Von Neumann equations with time-dependent Hamiltonians and supersymmetric quantum mechanics

Starting with a time-independent Hamiltonian $h$ and an appropriately chosen solution of the von Neumann equation $i\dot\rho(t)=[ h,\rho(t)]$ we construct its binary-Darboux partner $h_1(t)$ and an exact scattering solution of $i\dot\rho_1(t)=[h_1(t),\rho_1(t)]$ where $h_1(t)$ is time-dependent and not isospectral to $h$. The method is analogous to supersymmetric quantum mechanics but is based on a different version of a Darboux transformation. We illustrate the technique by the example where $h$ corresponds to a 1-D harmonic oscillator. The resulting $h_1(t)$ represents a scattering of a soliton-like pulse on a three-level system.Comment: revtex, 3 eps file

Discrete symmetry's chains and links between integrable equations

The discrete symmetry's dressing chains of the nonlinear Schrodinger equation (NLS) and Davey-Stewartson equations (DS) are consider. The modified NLS (mNLS) equation and the modified DS (mDS) equations are obtained. The explicitly reversible Backlund auto-transformations for the mNLS and mDS equations are constructed. We demonstrate discrete symmetry's conjugate chains of the KP and DS models. The two-dimensional generalization of the P4 equation are obtained.Comment: 20 page

Visualization and measurement of the cell-free layer (CFL) in a microchannel network

In the past years, in vitro blood studies have revealed several significant hemodynamic phenomena that have played a key role in recent developments of biomedical microdevices for cells separation, sorting and analysis. However, the blood flow phenomena happening in complex geometries, such as microchannel networks, have not been fully understood. Thus, it is important to investigate in detail the blood flow behavior occurring at microchannel networks. In the present study, by using a high-speed video microscopy system, we have used two working fluids with different haematocrit (1% Hct and 15% Hct) and we have investigated the cell-free layer (CFL) in a microchannel network composed by asymmetric bifurcations. By using the Z Project method from the image analysis software ImageJ, it was possible to conclude that the successive bifurcations and confluences influence the formation of the CFL not only along the upper and lower wall of the microchannel but also at the region immediately downstream of the confluence apex.The authors acknowledge the financial support provided by the project POCI-01-0145 FEDER-016861 (with associated reference PTDC/QEQ-FTT/4287/2014), UID/EMS/00532/2013 and UID/CEC/00319/2013 funded by FCT (Foundation for Science and Technology), through national funds (PIDDAC), and FEDER through COMPETE2020 - Programa Operacional Competitividade e Internacionalização (POCI). D. Bento acknowledges the PhD scholarship SFRH/BD/91192/2012 granted by FCT. The authors also acknowledge the financial support provided by the project Nos. UID/EMS/00532/2013 and UID/EMS/04077/2013 and the project Nos. UID/EMS/00532/2013, UID/EMS/04077/2013, POCI-01-0145-FEDER-007043, UID/CEC/00319/2013info:eu-repo/semantics/publishedVersio

Infinitesimal symmetries and conservation laws of the DNLSE hierarchy and the Noether's theorem

The hierarchy of the integrable nonlinear equations associated with the quadratic bundle is considered. The expressions for the solution of the linearization of these equations and their conservation law in the terms of the solutions of the corresponding Lax pairs are found. It is shown for the first member of the hierarchy that the conservation law is connected with the solution of the linearized equation due to the Noether's theorem. The local hierarchy and three nonlocal ones of the infinitesimal symmetries and the conservation laws that are explicitly expressed through the variables of the nonlinear equations are derived.Comment: 12 pages, LaTe