Mixed Bruhat operators and Yang-Baxter equations for Weyl groups

We introduce and study a family of operators which act in the span of a Weyl group $W$ and provide a multi-parameter solution to the quantum Yang-Baxter equations of the corresponding type. Our operators generalize the "quantum Bruhat operators" that appear in the explicit description of the multiplicative structure of the (small) quantum cohomology ring of $G/B$. The main combinatorial applications concern the "tilted Bruhat order," a graded poset whose unique minimal element is an arbitrarily chosen element $w\in W$. (The ordinary Bruhat order corresponds to the case $w=1$.) Using the mixed Bruhat operators, we prove that these posets are lexicographically shellable, and every interval in a tilted Bruhat order is Eulerian. This generalizes well known results of Verma, Bjorner, Wachs, and Dyer.Comment: 19 page

Kinetic Theory of Creep and Long-Term Strength of Metals

This chapter deals with the simulation of the creep process and the effect of long-term strength of metals, notably, in both uniaxial and complex stress states. A description of a creep experiment and the simplest creep models are presented, that is, the theory of steady creep, the theory of ageing, the theory of flow and the theory of hardening. In creep process simulation, a kinetic theory based on the introduction of structural parameters characterising the state of the metal at a given time is widely used. Among such parameters, metal damage in the creep process, work of stresses on creep deformations (energy version) and concentration of an aggressive medium in the metal were studied. The coupled problem of creep and long tensile strength is also considered taking into account the mutual influence of damage accumulation and one-dimensional diffusion of the aggressive medium. The times to fracture are determined both in the presence of an aggressive medium and in the absence of one. A significant contribution of Soviet (Russian), European, American and Japanese scientists to the development of continuum damage mechanics is highlighted

Parameterized Complexity of Secluded Connectivity Problems

The Secluded Path problem models a situation where a sensitive information has to be transmitted between a pair of nodes along a path in a network. The measure of the quality of a selected path is its exposure, which is the total weight of vertices in its closed neighborhood. In order to minimize the risk of intercepting the information, we are interested in selecting a secluded path, i.e. a path with a small exposure. Similarly, the Secluded Steiner Tree problem is to find a tree in a graph connecting a given set of terminals such that the exposure of the tree is minimized. The problems were introduced by Chechik et al. in [ESA 2013]. Among other results, Chechik et al. have shown that Secluded Path is fixed-parameter tractable (FPT) on unweighted graphs being parameterized by the maximum vertex degree of the graph and that Secluded Steiner Tree is FPT parameterized by the treewidth of the graph. In this work, we obtain the following results about parameterized complexity of secluded connectivity problems. We give FPT-algorithms deciding if a graph G with a given cost function contains a secluded path and a secluded Steiner tree of exposure at most k with the cost at most C. We initiate the study of "above guarantee" parameterizations for secluded problems, where the lower bound is given by the size of a Steiner tree. We investigate Secluded Steiner Tree from kernelization perspective and provide several lower and upper bounds when parameters are the treewidth, the size of a vertex cover, maximum vertex degree and the solution size. Finally, we refine the algorithmic result of Chechik et al. by improving the exponential dependence from the treewidth of the input graph.Comment: Minor corrections are don

Magnetic ionization-thermal instability

Linear analysis of the stability of diffuse clouds in the cold neutral medium with uniform magnetic field is performed. We consider that gas in equilibrium state is heated by cosmic rays, X-rays and electronic photoeffect on the surface of dust grains, and it is cooled by the collisional excitation of fine levels of the CII. Ionization by cosmic rays and radiative recombinations is taken into account. A dispersion equation is solved analytically in the limiting cases of small and large wave numbers, as well as numerically in the general case. In particular cases the dispersion equation describes thermal instability of Field (1965) and ionization-coupled acoustic instability of Flannery and Press (1979). We pay our attention to magnetosonic waves arising in presence of magnetic field, in thermally stable region, $35 \leq T \leq 95$ K and density n\lessapprox 10^3\,\mbox{cm}^{-3}. We have shown that these modes can be unstable in the isobarically stable medium. The instability mechanism is similar to the mechanism of ionization-coupled acoustic instability. We determine maximum growth rates and critical wavelengths of the instability of magnetosonic waves depending on gas temperature, magnetic field strength and the direction of wave vector with respect to the magnetic field lines. The minimum growth time of the unstable slow magnetosonic waves in diffuse clouds is of $4-60$ Myr, minimum and the most unstable wavelengths lie in ranges $0.05-0.5$ and $0.5-5$ pc, respectively. We discuss the application of considered instability to the formation of small-scale structures and the generation of MHD turbulence in the cold neutral medium.Comment: 11 pages, 9 figures, 2 tables, accepted for publication in MNRA

Phonon spectrum engineering in rolled-up micro- and nano-architectures

We report on a possibility of efficient engineering of the acoustic phonon energy spectrum in multishell tubular structures produced by a novel high-tech method of self-organization of micro- and nano-architectures. The strain-driven roll-up procedure paved the way for novel classes of metamaterials such as single semiconductor radial micro- and nano-crystals and multi-layer spiral micro- and nano-superlattices. The acoustic phonon dispersion is determined by solving the equations of elastodynamics for InAs and GaAs material systems. It is shown that the number of shells is an important control parameter of the phonon dispersion together with the structure dimensions and acoustic impedance mismatch between the superlattice layers. The obtained results suggest that rolled up nano-architectures are promising for thermoelectric applications owing to a possibility of significant reduction of the thermal conductivity without degradation of the electronic transport

Phonon Spectrum Engineering in Rolled-up Nano- and Micro-Architectures

We report on a possibility of efficient engineering of the acoustic phonon energy spectrum in multishell tubular structures produced by a novel high-tech method of self-organization of nano- and micro-architectures. The strain-driven roll-up procedure paved the way for novel classes of metamaterials such as single semiconductor radial micro- and nano-crystals and multi-layer spiral micro- and nano-superlattices. The acoustic phonon dispersion is determined by solving the equations of elastodynamics for InAs and GaAs material systems. It is shown that the number of shells is an important control parameter of the phonon dispersion together with the structure dimensions and acoustic impedance mismatch between the superlattice layers. The obtained results suggest that rolled up nano-architectures have potential for thermoelectric applications owing to a possibility of significant reduction of the thermal conductivity without degradation of the electronic transport.Comment: 17 pages; 8 figure

Urban food security in Gaborone, Botswana

This research examines factors that shape food insecurity among urban dwellers in Gaborone, Botswana, by assessing household food access and choice/consumption patterns. With low subsistence agricultural production, Botswana depends largely on South Africa for food imports. The paper questions the notion that African foodscapes are simply transitioning towards a homogenously ‘modern’ state. Food consumption practice in Gaborone can be read and explored through a hybridity paradigm. Depending on access to and availability of new foodstuffs, participant households’ experiment with (re)producing familiar traditional food cultures and creating hybrid meals based on new life style arrangements in the city.Doctor of Philosoph