Numerical methods for construction reachability sets of dynamical systems

The research is devoted to the problem of reachability sets construction and representation in a control problem of a dynamical system. The paper discusses two numerical methods for construction reachability sets of dynamical systems. These methods differ in the way of representations of the reachability sets. The first method is oriented on solution of the control problem on the plane and connected with a representation of sets in the form of polygons. The second one is connected with a pixel representation of sets in the m-dimensional Euclidian space and simplicial complexes. © 2012 American Institute of Physics

Orbital structure and magnetic ordering in stoichiometric and doped crednerite CuMnO2

The exchange interactions and magnetic structure in layered system CuMnO2 (mineral crednerite) and in nonstoichiometric system Cu1.04Mn0.96O2, with triangular layers distorted due to orbital ordering of the Mn3+ ions, are studied by ab-initio band-structure calculations, which were performed within the GGA+U approximation. The exchange interaction parameters for the Heisenberg model within the Mn-planes and between the Mn-planes were estimated. We explain the observed in-plane magnetic structure by the dominant mechanism of the direct d-d exchange between neighboring Mn ions. The superexchange via O ions, with 90 degree Mn-O-Mn bonds, plays less important role for the in-plane exchange. The interlayer coupling is largely dominated by one exchange path between the half-filled 3z^2-r^2 orbitals of Mn3+. The change of interlayer coupling from antiferromagnetic in pure CuMnO2 to ferromagnetic in doped material is also explained by our calculations

Electronic structure of V4_4O7_7: charge ordering, metal-insulator transition and magnetism

The low and high-temperature phases of V$_4$O$_7$ have been studied by \textit{ab initio} calculations. At high temperature, all V atoms are electronically equivalent and the material is metallic. Charge and orbital ordering, associated with the distortions in the V pseudo-rutile chains, occur below the metal-insulator transition. Orbital ordering in the low-temperature phase, different in V$^{3+}$ and V$^{4+}$ chains, allows to explain the distortion pattern in the insulating phase of V$_4$O$_7$. The in-chain magnetic couplings in the low-temperature phase turn out to be antiferromagnetic, but very different in the various V$^{4+}$ and V$^{3+}$ bonds. The V$^{4+}$ dimers formed below the transition temperature form spin singlets, but V$^{3+}$ ions, despite dimerization, apparently participate in magnetic ordering.Comment: 10 pages, 6 figures, 2 table

Carrier transport and screening in n-i-p-i crystals

The variation of the energy spectrum of n-i-p-i crystals under excitation was examined and the influence of the reduction of the screening length on the ratio between the coefficient of diffusion and the mobility of the current carriers was established. It is shown that the filling of subband states by carriers results in an anomalous behaviour of the diffusivity-mobility ratio. The effect occurs in the electric quantum limit and at room temperature as well

Calculation of energy characteristics for Si1-xGex-Si strucrures with single quantum wells

Energy characteristics of Si1–xGex–Si quantum-size structures with single quantum wells were calculated numerically based on a four-band k⋅p method. Analytical expressions for the Luttinger parameters are obtained as functions of the component composition of Si1–xGex compounds. Analytical expressions for the energy h−ω of optical band-to-band transitions are obtained in an effective mass approximation and agree well with numerical calculations by the k⋅p method. This allows one to determine accurately a range of changes while varying the component compositions and thickness of the active and barrier layers

Abnormal Character of the Diffusivity-mobility Ratio in Doping Superlattices

The influence of high level of doping in type n-i-p-i crystal structures on electron and hole state distributions is examined. Abnormal behaviour in the diffusivity- mobility ratio due to shortening of the density state tails under excitation of doping Superlattices is described

Production of broadband modal gain spectra in asymmetric multiple quantum-well Ga0.47In0.53As/Ga0.18In0.82As0.4P0.6 heterostructures

The modal gain spectra of asymmetric multiple quantum-well Ga0.47In0.53As/Ga0.18In0.82As0.4P0.6 hetero- structures are theoretically analysed within the framework of the four-band kp method. An efficient procedure for obtaining the broadband and almost êat gain spectrum is proposed. The designs of semiconductor radiation sources with different sets of nonuniformly excited quantum wells producing broadband amplification in spectral ranges from 1.28 to 1.525 \mu m and from 1.36 to 1.6 \mu m are calculated

Structural transition in AuAgTe4 under pressure

Gold is inert and forms very few compounds. One of the most interesting of those is calaverite AuTe2, which has incommensurate structure and which becomes superconducting when doped or under pressure. There exist a "sibling" of AuTe2 the mineral sylvanite AuAgTe4, which properties are almost unknown. In sylvanite Au and Ag ions are ordered in stripes, and Te6 octahedra around metals are distorted in such a way that Ag becomes linearly coordinated, what is typical for Ag^{1+}, whereas Au is square coordinated - it is typical for d^8 configurations, i.e. one can assign to Au the valence 3+. Our theoretical study shows that at pressure P_C ~ 5 GPa there should occur in it a structural transition such that above this critical pressure Te6 octahedra around Au and Ag become regular and practically identical. Simultaneously Te-Te dimers, existing at P = 0 GPa, disappear, and material from a bad metal becomes a usual metal with predominantly Te 5p states at the Fermi energy. We expect that, similar to AuTe2, AuAgTe4 should become superconducting above P_C.Comment: 8 pages, 4 figure