Buoyant MHD flows in a vertical channel: the levitation regime

Buoyant magnetohydrodynamic (MHD) flows with Joulean and viscous heating effects are considered in a vertical parallel plate channel. The applied magnetic field is uniform and perpendicular to the plates which are subject to adiabatic and isothermal boundary conditions, respectively. The main issue of the paper is the levitation regime, i.e., the fully developed flow regime for large values of the Hartmann number M, when the hydrodynamic pressure gradient evaluated at the temperature of the adiabatic wall is vanishing. The problem is solved analytically by Taylor series method and the solution is validated numerically. It is found that the fluid velocity points everywhere and for all values of M downward. For small M's, the velocity field extends nearly symmetrically (with respect to the mid-plane) over the whole section of the channel between the adiabatic and the isothermal walls. For large values of M, by contrast, the fluid levitates over a broad transversal range of the channel, while the motion becomes concentrated in a narrow boundary layer in the neighborhood of the isothermal wall. Accordingly, the fluid temperature is nearly uniform in the levitation range and decreases rapidly within the boundary layer in front of the isothermal wall. It also turns out that not only the volumetric heat generation by the Joule effect, but also that by viscous friction increases rapidly with increasing values of M, the latter effect being even larger than the former one for all

Eye movements and mental imagery during reading of literary texts with different narrative styles

Based on Kuzmicova's (2014) phenomenological typology of narrative styles, we studied the specific contributions of mental imagery to literary reading experience and to reading behavior by combining questionnaires with eye-tracking methodology. Specifically, we focused on the two main categories in Kuzmicova's (2014) typology, i.e., texts dominated by an "enactive" style, and texts dominated by a "descriptive" style. "Enactive" style texts render characters interacting with their environment, and "descriptive" style texts render environments dissociated from human action. The quantitative analyses of word category distributions of two dominantly enactive and two dominantly descriptive texts indicated significant differences especially in the number of verbs, with more verbs in enactment compared to descriptive texts. In a second study, participants read two texts (one theoretically cueing descriptive imagery, the other cueing enactment imagery) while their eye movements were recorded. After reading, participants completed questionnaires assessing aspects of the reading experience generally, as well as their text-elicited mental imagery specifically. Results show that readers experienced more difficulties conjuring up mental images during reading descriptive style texts and that longer fixation duration on words were associated with enactive style text. We propose that enactive style involves more imagery processes which can be reflected in eye movement behavior

Integrability and level crossing manifolds in a quantum Hamiltonian system

We consider a two-spin model, represented classically by a nonlinear autonomous Hamiltonian system with two degrees of freedom and a nontrivial integrability condition, and quantum mechanically by a real symmetric Hamiltonian matrix with blocks of dimensionalities K=l(l+1)/2, l=1,2,... In the six-dimensional (6D) parameter space of this model, classical integrability is satisfied on a 5D hypersurface, and level crossings occur on 4D manifolds that are completely embedded in the integrability hypersurface except for some lower-D sub-manifolds. Under mild assumptions, the classical integrability condition can be reconstructed from a purely quantum mechanical study of level degeneracies in finite-dimensional invariant blocks of the Hamiltonian matrix. Our conclusions are based on rigorous results for K=3 and on numerical results for K=6,10.Comment: 8 pages, 3 figure

Creative Techniques in the Framework of Market and Evolution

This paper tries to reframe the man-machine problem, which has frequently changed throughout history. Originally, a machine was a helper of man, but later became its competitor and substitute. As a consequence of this, man has been pushed out of production and possibly, out of life itself. For today, nearly all the man’s functions – except for consumption and creativity – can be furnished by machines. Creativity should have a special place because it is the last “shelter” of man in the conflict with machine. Almost every other faculty of man has more or less been simulated by technology. There are some key questions to be answered: Whom do the creative techniques serve? Is the target group the men or machines

Integrability and action operators in quantum Hamiltonian systems

For a (classically) integrable quantum mechanical system with two degrees of freedom, the functional dependence $\hat{H}=H_Q(\hat{J}_1,\hat{J}_2)$ of the Hamiltonian operator on the action operators is analyzed and compared with the corresponding functional relationship $H(p_1,q_1;p_2,q_2) = H_C(J_1,J_2)$ in the classical limit of that system. The former is shown to converge toward the latter in some asymptotic regime associated with the classical limit, but the convergence is, in general, non-uniform. The existence of the function $\hat{H}=H_Q(\hat{J}_1,\hat{J}_2)$ in the integrable regime of a parametric quantum system explains empirical results for the dimensionality of manifolds in parameter space on which at least two levels are degenerate. The comparative analysis is carried out for an integrable one-parameter two-spin model. Additional results presented for the (integrable) circular billiard model illuminate the same conclusions from a different angle.Comment: 9 page

Chiral Solitons in a Current Coupled Schr\"odinger Equation With Self Interaction

Recently non-topological chiral soliton solutions were obtained in a derivatively coupled non-linear Schr\"odinger model in 1+1 dimensions. We extend the analysis to include a more general self-coupling potential (which includes the previous cases) and find chiral soliton solutions. Interestingly even the magnitude of the velocity is found to be fixed. Energy and U(1) charge associated with this non-topological chiral solitons are also obtained.Comment: 8 pages, no figure, to appear in Phys. Rev.

Signatures of quantum integrability and nonintegrability in the spectral properties of finite Hamiltonian matrices

For a two-spin model which is (classically) integrable on a five-dimensional hypersurface in six-dimensional parameter space and for which level degeneracies occur exclusively (with one known exception) on four-dimensional manifolds embedded in the integrability hypersurface, we investigate the relations between symmetry, integrability, and the assignment of quantum numbers to eigenstates. We calculate quantum invariants in the form of expectation values for selected operators and monitor their dependence on the Hamiltonian parameters along loops within, without, and across the integrability hypersurface in parameter space. We find clear-cut signatures of integrability and nonintegrability in the observed traces of quantum invariants evaluated in finite-dimensional invariant Hilbert subspaces, The results support the notion that quantum integrability depends on the existence of action operators as constituent elements of the Hamiltonian.Comment: 11 page

Integrable quadratic Hamiltonians on so(4) and so(3,1)

We investigate a special class of quadratic Hamiltonians on so(4) and so(3,1) and describe Hamiltonians that have additional polynomial integrals. One of the main results is a new integrable case with an integral of sixth degree.Comment: 16 page