Studying the influence of supply pulse duration on the phase composition of iron oxides obtained by the plasma-dynamic method

Magnetic materials and in particular iron oxides are of a great practical interest. The magnetite phase and the unique epsilon phase of iron oxide can be especially pointed out. The main difficulty in the synthesis of the epsilon phase is connected with the fact that it can exist only in a nanoscale state and is extremely difficult to obtain. We used the method of direct plasma dynamic synthesis, which allows to obtain multiphase powders of iron oxides containing both the epsilon phase and magnetite. It was found that by varying the initial parameters of the power system, namely the pulse duration by increasing the capacitance of the capacitive energy storage, it is possible to influence the phase composition of the obtained products and to achieve the preferential output of the epsilon phase. In addition, in the mode with the maximum pulse duration, when the best product is obtained from the point of the epsilon phase output, the system efficiency of converting the stored energy into released energy significantly increases. In general, it has been established that such a regime is most favorable for the system operation for the purpose of the iron oxides synthesis

Super-A-polynomials for Twist Knots

We conjecture formulae of the colored superpolynomials for a class of twist knots $K_p$ where p denotes the number of full twists. The validity of the formulae is checked by applying differentials and taking special limits. Using the formulae, we compute both the classical and quantum super-A-polynomial for the twist knots with small values of p. The results support the categorified versions of the generalized volume conjecture and the quantum volume conjecture. Furthermore, we obtain the evidence that the Q-deformed A-polynomials can be identified with the augmentation polynomials of knot contact homology in the case of the twist knots.Comment: 22+16 pages, 16 tables and 5 figures; with a Maple program by Xinyu Sun and a Mathematica notebook in the ancillary files linked on the right; v2 change in appendix B, typos corrected and references added; v3 change in section 3.3; v4 corrections in Ooguri-Vafa polynomials and quantum super-A-polynomials for 7_2 and 8_1 are adde

HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations

Explicit answer is given for the HOMFLY polynomial of the figure eight knot $4_1$ in arbitrary symmetric representation R=[p]. It generalizes the old answers for p=1 and 2 and the recently derived results for p=3,4, which are fully consistent with the Ooguri-Vafa conjecture. The answer can be considered as a quantization of the \sigma_R = \sigma_{[1]}^{|R|} identity for the "special" polynomials (they define the leading asymptotics of HOMFLY at q=1), and arises in a form, convenient for comparison with the representation of the Jones polynomials as sums of dilogarithm ratios. In particular, we construct a difference equation ("non-commutative A-polynomial") in the representation variable p. Simple symmetry transformation provides also a formula for arbitrary antisymmetric (fundamental) representation R=[1^p], which also passes some obvious checks. Also straightforward is a deformation from HOMFLY to superpolynomials. Further generalizations seem possible to arbitrary Young diagrams R, but these expressions are harder to test because of the lack of alternative results, even partial.Comment: 14 page

In the Realm of the Geometric Transitions

We complete the duality cycle by constructing the geometric transition duals in the type IIB, type I and heterotic theories. We show that in the type IIB theory the background on the closed string side is a Kahler deformed conifold, as expected, even though the mirror type IIA backgrounds are non-Kahler (both before and after the transition). On the other hand, the Type I and heterotic backgrounds are non-Kahler. Therefore, on the heterotic side these backgrounds give rise to new torsional manifolds that have not been studied before. We show the consistency of these backgrounds by verifying the torsional equation.Comment: 60 pages, 2 .eps figures, Harvmac; v2: Minor typos corrected and references added; v3: Some more typos corrected. Final version to appear in Nucl. Phys.

Dipole-Deformed Bound States and Heterotic Kodaira Surfaces

We study a particular N = 1 confining gauge theory with fundamental flavors realised as seven branes in the background of wrapped five branes on a rigid two-cycle of a non-trivial global geometry. In parts of the moduli space, the five branes form bound states with the seven branes. We show that in this regime the local supergravity solution is surprisingly tractable, even though the background topology is non-trivial. New effects such as dipole deformations may be studied in detail, including the full backreactions. Performing the dipole deformations in other ways leads to different warped local geometries. In the dual heterotic picture, which is locally given by a C* fibration over a Kodaira surface, we study details of the geometry and the construction of bundles. We also point out the existence of certain exotic bundles in our framework.Comment: 40 pages, 3 .eps figures, Harvma

Optimizing the process of plasma dynamic synthesis for increasing the yield and purity of e-Fe2O3 phase

Various crystalline modifications of iron oxide are widely used in different fields of science and technology, however, a special attention has recently been paid to the synthesis of the epsilon phase e-Fe2O3. The existing problems connected with the synthesis and production of this phase in the form of a dispersed powdered product significantly limit the possibilities of its application and studying the properties. In this regard, the search and development of high-performance method for the synthesis of the e-Fe2O3 phase is an urgent task. In this paper, the possibility of optimizing the well-known method of plasma dynamic synthesis for obtaining products with a high content of the e-Fe2O3 phase was studied. The influence of the power supply pulse duration on the energy parameters of the synthesis process and the characteristics of the powdered products were studied in detail. It was established that an increase in the pulse duration due to the introduction of an additional inductance into the discharge circuit while simultaneously maintaining the magnitude of the arc discharge current at a level of 120 kA allows obtaining a product with the epsilon phase content of ~ 65 wt.%

Superpolynomials for toric knots from evolution induced by cut-and-join operators

The colored HOMFLY polynomials, which describe Wilson loop averages in Chern-Simons theory, possess an especially simple representation for torus knots, which begins from quantum R-matrix and ends up with a trivially-looking split W representation familiar from character calculus applications to matrix models and Hurwitz theory. Substitution of MacDonald polynomials for characters in these formulas provides a very simple description of "superpolynomials", much simpler than the recently studied alternative which deforms relation to the WZNW theory and explicitly involves the Littlewood-Richardson coefficients. A lot of explicit expressions are presented for different representations (Young diagrams), many of them new. In particular, we provide the superpolynomial P_[1]^[m,km\pm 1] for arbitrary m and k. The procedure is not restricted to the fundamental (all antisymmetric) representations and the torus knots, still in these cases some subtleties persist.Comment: 23 pages + Tables (51 pages

Studying the influence of supply pulse duration on the phase composition of iron oxides obtained by the plasma-dynamic method

Magnetic materials and in particular iron oxides are of a great practical interest. The magnetite phase and the unique epsilon phase of iron oxide can be especially pointed out. The main difficulty in the synthesis of the epsilon phase is connected with the fact that it can exist only in a nanoscale state and is extremely difficult to obtain. We used the method of direct plasma dynamic synthesis, which allows obtaining multiphase powders of iron oxides containing both the epsilon phase and magnetite. It was found that by varying the initial parameters of the power system, namely the pulse duration by increasing the capacitance of the capacitive energy storage, it is possible to influence the phase composition of the obtained products and to achieve the preferential output of the epsilon phase. In addition, in the mode with the maximum pulse duration, when the best product is obtained from the point of the epsilon phase output, the system efficiency of converting the stored energy into released energy significantly increases. In general, it has been established that such a regime is most favorable for the system operation for the purpose of the iron oxides synthesis

Faces of matrix models

Partition functions of eigenvalue matrix models possess a number of very different descriptions: as matrix integrals, as solutions to linear and non-linear equations, as tau-functions of integrable hierarchies and as special-geometry prepotentials, as result of the action of W-operators and of various recursions on elementary input data, as gluing of certain elementary building blocks. All this explains the central role of such matrix models in modern mathematical physics: they provide the basic "special functions" to express the answers and relations between them, and they serve as a dream model of what one should try to achieve in any other field.Comment: 10 page

Chern-Simons Modified General Relativity

Chern-Simons modified gravity is an effective extension of general relativity that captures leading-order, gravitational parity violation. Such an effective theory is motivated by anomaly cancelation in particle physics and string theory. In this review, we begin by providing a pedagogical derivation of the three distinct ways such an extension arises: (1) in particle physics, (2) from string theory and (3) geometrically. We then review many exact and approximate, vacuum solutions of the modified theory, and discuss possible matter couplings. Following this, we review the myriad astrophysical, solar system, gravitational wave and cosmological probes that bound Chern-Simons modified gravity, including discussions of cosmic baryon asymmetry and inflation. The review closes with a discussion of possible future directions in which to test and study gravitational parity violation.Comment: 104 pages, 2 figures, 186 references, Invited Review accepted for publication in Phys. Repts. This version corrects a minor typo in Eq. (174) of the published versio