Combustion process of impinging hypergolic propellants

Combustor pressure poppings, stream mixing, and stream separation associated with combustion of impinging hypergolic propellant

Adiabatically coupled systems and fractional monodromy

We present a 1-parameter family of systems with fractional monodromy and adiabatic separation of motion. We relate the presence of monodromy to a redistribution of states both in the quantum and semi-quantum spectrum. We show how the fractional monodromy arises from the non diagonal action of the dynamical symmetry of the system and manifests itself as a generic property of an important subclass of adiabatically coupled systems

The Maslov index and nondegenerate singularities of integrable systems

We consider integrable Hamiltonian systems in R^{2n} with integrals of motion F = (F_1,...,F_n) in involution. Nondegenerate singularities are critical points of F where rank dF = n-1 and which have definite linear stability. The set of nondegenerate singularities is a codimension-two symplectic submanifold invariant under the flow. We show that the Maslov index of a closed curve is a sum of contributions +/- 2 from the nondegenerate singularities it is encloses, the sign depending on the local orientation and stability at the singularities. For one-freedom systems this corresponds to the well-known formula for the Poincar\'e index of a closed curve as the oriented difference between the number of elliptic and hyperbolic fixed points enclosed. We also obtain a formula for the Liapunov exponent of invariant (n-1)-dimensional tori in the nondegenerate singular set. Examples include rotationally symmetric n-freedom Hamiltonians, while an application to the periodic Toda chain is described in a companion paper.Comment: 27 pages, 1 figure; published versio

Foliations of Isonergy Surfaces and Singularities of Curves

It is well known that changes in the Liouville foliations of the isoenergy surfaces of an integrable system imply that the bifurcation set has singularities at the corresponding energy level. We formulate certain genericity assumptions for two degrees of freedom integrable systems and we prove the opposite statement: the essential critical points of the bifurcation set appear only if the Liouville foliations of the isoenergy surfaces change at the corresponding energy levels. Along the proof, we give full classification of the structure of the isoenergy surfaces near the critical set under our genericity assumptions and we give their complete list using Fomenko graphs. This may be viewed as a step towards completing the Smale program for relating the energy surfaces foliation structure to singularities of the momentum mappings for non-degenerate integrable two degrees of freedom systems.Comment: 30 pages, 19 figure

Singularities, Lax degeneracies and Maslov indices of the periodic Toda chain

The n-particle periodic Toda chain is a well known example of an integrable but nonseparable Hamiltonian system in R^{2n}. We show that Sigma_k, the k-fold singularities of the Toda chain, ie points where there exist k independent linear relations amongst the gradients of the integrals of motion, coincide with points where there are k (doubly) degenerate eigenvalues of representatives L and Lbar of the two inequivalent classes of Lax matrices (corresponding to degenerate periodic or antiperiodic solutions of the associated second-order difference equation). The singularities are shown to be nondegenerate, so that Sigma_k is a codimension-2k symplectic submanifold. Sigma_k is shown to be of elliptic type, and the frequencies of transverse oscillations under Hamiltonians which fix Sigma_k are computed in terms of spectral data of the Lax matrices. If mu(C) is the (even) Maslov index of a closed curve C in the regular component of R^{2n}, then (-1)^{\mu(C)/2} is given by the product of the holonomies (equal to +/- 1) of the even- (or odd-) indexed eigenvector bundles of L and Lmat.Comment: 25 pages; published versio

Hamiltonian dynamics and spectral theory for spin-oscillators

We study the Hamiltonian dynamics and spectral theory of spin-oscillators. Because of their rich structure, spin-oscillators display fairly general properties of integrable systems with two degrees of freedom. Spin-oscillators have infinitely many transversally elliptic singularities, exactly one elliptic-elliptic singularity and one focus-focus singularity. The most interesting dynamical features of integrable systems, and in particular of spin-oscillators, are encoded in their singularities. In the first part of the paper we study the symplectic dynamics around the focus-focus singularity. In the second part of the paper we quantize the coupled spin-oscillators systems and study their spectral theory. The paper combines techniques from semiclassical analysis with differential geometric methods.Comment: 32 page

Systems of Hess-Appel'rot Type and Zhukovskii Property

We start with a review of a class of systems with invariant relations, so called {\it systems of Hess--Appel'rot type} that generalizes the classical Hess--Appel'rot rigid body case. The systems of Hess-Appel'rot type carry an interesting combination of both integrable and non-integrable properties. Further, following integrable line, we study partial reductions and systems having what we call the {\it Zhukovskii property}: these are Hamiltonian systems with invariant relations, such that partially reduced systems are completely integrable. We prove that the Zhukovskii property is a quite general characteristic of systems of Hess-Appel'rote type. The partial reduction neglects the most interesting and challenging part of the dynamics of the systems of Hess-Appel'rot type - the non-integrable part, some analysis of which may be seen as a reconstruction problem. We show that an integrable system, the magnetic pendulum on the oriented Grassmannian $Gr^+(4,2)$ has natural interpretation within Zhukovskii property and it is equivalent to a partial reduction of certain system of Hess-Appel'rot type. We perform a classical and an algebro-geometric integration of the system, as an example of an isoholomorphic system. The paper presents a lot of examples of systems of Hess-Appel'rot type, giving an additional argument in favor of further study of this class of systems.Comment: 42 page

Nonlinear AC resistivity in s-wave and d-wave disordered granular superconductors

We model s-wave and d-wave disordered granular superconductors with a three-dimensional lattice of randomly distributed Josephson junctions with finite self-inductance. The nonlinear ac resistivity of these systems was calculated using Langevin dynamical equations. The current amplitude dependence of the nonlinear resistivity at the peak position is found to be a power law characterized by exponent $\alpha$. The later is not universal but depends on the self-inductance and current regimes. In the weak current regime $\alpha$ is independent of the self-inductance and equal to 0.5 or both of s- and d-wave materials. In the strong current regime this exponent depends on the screening. We find $\alpha \approx 1$ for some interval of inductance which agrees with the experimental finding for d-wave ceramic superconductors.Comment: 4 pages, 5 figures, to appear in Phys. Rev. Let

Reliability, validity and psychometric properties of the Greek translation of the Major Depression Inventory

BACKGROUND: The Major Depression Inventory (MDI) is a brief self-rating scale for the assessment of depression. It is reported to be valid because it is based on the universe of symptoms of DSM-IV and ICD-10 depression. The aim of the current preliminary study was to assess the reliability, validity and psychometric properties of the Greek translation of the MDI. METHODS: 30 depressed patients of mean age 23.41 (± 5.77) years, and 68 controls patients of mean age 25.08 (± 11.42) years, entered the study. In 18 of them, the instrument was re-applied 1–2 days later and the Translation and Back Translation made. Clinical diagnosis was reached with the use of the SCAN v.2.0 and the International Personality Disorders Examination (IPDE). The Center for Epidemiological Studies-Depression (CES-D) and the Zung Depression Rating Scale (ZDRS) were applied for cross-validation purposes. Statistical analysis included ANOVA, the Spearman Product Moment Correlation Coefficient, Principal Components Analysis and the calculation of Cronbach's α. RESULTS: Sensitivity and specificity were 0.86 and 0.94, respectively, at 26/27. Cronbach's α for the total scale was equal to 0.89. The Spearman's rho between MDI and CES-D was 0.86 and between MDI and ZDRS was 0.76. The factor analysis revealed two factors but the first accounted for 54% of variance while the second only for 9%. The test-retest reliability was excellent (Spearman's rho between 0.53 and 0.96 for individual items and 0.89 for total score). CONCLUSION: The current study provided preliminary evidence concerning the reliability and validity of the Greek translation of the MDI. Its properties are similar to those reported in the international literature, but further research is necessary

Factor analysis of the Zung self-rating depression scale in a large sample of patients with major depressive disorder in primary care

<p>Abstract</p> <p>Background</p> <p>The aim of this study was to examine the symptomatic dimensions of depression in a large sample of patients with major depressive disorder (MDD) in the primary care (PC) setting by means of a factor analysis of the Zung self-rating depression scale (ZSDS).</p> <p>Methods</p> <p>A factor analysis was performed, based on the polychoric correlations matrix, between ZSDS items using promax oblique rotation in 1049 PC patients with a diagnosis of MDD (DSM-IV).</p> <p>Results</p> <p>A clinical interpretable four-factor solution consisting of a <it>core depressive </it>factor (I); a <it>cognitive </it>factor (II); an <it>anxiety </it>factor (III) and a <it>somatic </it>factor (IV) was extracted. These factors accounted for 36.9% of the variance on the ZSDS. The 4-factor structure was validated and high coefficients of congruence were obtained (0.98, 0.95, 0.92 and 0.87 for factors I, II, III and IV, respectively). The model seemed to fit the data well with fit indexes within recommended ranges (GFI = 0.9330, AGFI = 0.9112 and RMR = 0.0843).</p> <p>Conclusion</p> <p>Our findings suggest that depressive symptoms in patients with MDD in the PC setting cluster into four dimensions: <it>core depressive, cognitive, anxiety </it>and <it>somatic</it>, by means of a factor analysis of the ZSDS. Further research is needed to identify possible diagnostic, therapeutic or prognostic implications of the different depressive symptomatic profiles.</p