The dependence of the conduction band edge of the alkali earth metal bismuthates on their composition

We present a comparative analysis of the conduction band edge of the alkali earth metal bismuthates containing Mg, Ca, Sr, and Ba. The conduction band edges were computed using the method suggested by Butler and Ginley. The calculations reveal that they depend on the bismuthate’s composition and vary over a wide range. We demonstrate that the energy of the conduction band increases in the series Ca?→?Sr?→?Ba. It also increases with an increase of the alkali earth metal content. The performed calculations help to determine the potential alkali earth metal bismuthate photocatalysts. The most promising compositions found in this study include strontium and barium bismuthates in which the number of the alkali earth metal atoms in the cationic sublattice exceeds the number of the bismuth atoms.     

A Law of Large Numbers for the Zeroes of Heine–Stieltjes Polynomials

We determine the limiting density of the zeroes of Heine–Stieltjes polynomials (or of any set of points satisfying the conclusion of Heine–Stieltjes Theorem) in the thermodynamic limit and use this to prove a strong law of large numbers for the zeroes.     

Macroscopic Dimension of 3-Manifolds

In this paper we give the answer to the Gromov's question about the macroscopic dimension of universal coverings of closed manifolds in dimension 3. We prove that the macroscopic dimension of a universal covering of a closed Riemannian 3-manifold cannot be equal to 2.     

Averaging of nonlinearity-managed pulses

We consider the nonlinear Schrodinger equation with the nonlinearity management which describes Bose-Einstein condensates under Feshbach resonance. By using an averaging theory, we derive the Hamiltonian averaged equation and compare it with other averaging methods developed for this problem. The averaged equation is used for analytical approximations of nonlinearity-managed solitons.     

In situ XPS study of Pd(1 1 1) oxidation. Part 1: 2D oxide formation in 10 mbar O2

The oxidation of the Pd(1 1 1) surface was studied by in situ XPS during heating and cooling in 3 × 10⁻³ mbar O₂. A number of adsorbed/dissolved oxygen species were identified by in situ XPS, such as the two dimensional surface oxide (Pd₅O₄), the supersaturated O_ads layer, dissolved oxygen and the R 12.2° surface structure.Exposure of the Pd(1 1 1) single crystal to 3 × 10⁻³ mbar O₂ at 425 K led to formation of the 2D oxide phase, which was in equilibrium with a supersaturated O_ads layer. The supersaturated O_ads layer was characterized by the O 1s core level peak at 530.37 eV. The 2D oxide, Pd₅O₄, was characterized by two O 1s components at 528.92 eV and 529.52 eV and by two oxygen-induced Pd 3d_5/2 components at 335.5 eV and 336.24 eV. During heating in 3 × 10⁻³ mbar O₂ the supersaturated O_ads layer disappeared whereas the fraction of the surface covered with the 2D oxide grew. The surface was completely covered with the 2D oxide between 600 K and 655 K. Depth profiling by photon energy variation confirmed the surface nature of the 2D oxide. The 2D oxide decomposed completely above 717 K. Diffusion of oxygen in the palladium bulk occurred at these temperatures. A substantial oxygen signal assigned to the dissolved species was detected even at 923 K. The dissolved oxygen was characterised by the O 1s core level peak at 528.98 eV. The “bulk” nature of the dissolved oxygen species was verified by depth profiling.During cooling in 3 × 10⁻³ mbar O₂, the oxidised Pd²⁺ species appeared at 788 K whereas the 2D oxide decomposed at 717 K during heating. The surface oxidised states exhibited an inverse hysteresis. The oxidised palladium state observed during cooling was assigned to a new oxide phase, probably the R 12.2° structure.     

Friction and diffusion of matter-wave bright solitons

We consider the motion of a matter-wave bright soliton under the influence of a cloud of thermal particles. In the ideal one-dimensional system, the scattering process of the quasiparticles with the soliton is reflectionless; however, the quasiparticles acquire a phase shift. In the realistic system of a Bose-Einstein condensate confined in a tight waveguide trap, the transverse degrees of freedom generate an extra nonlinearity in the system which gives rise to finite reflection and leads to dissipative motion of the soliton. We calculate the velocity and temperature-dependent frictional force and diffusion coefficient of a matter-wave bright soliton immersed in a thermal cloud.     

Time-dependent and outflow boundary conditions for Dissipative Particle Dynamics

We propose a simple method to impose both no-slip boundary conditions at fluid-wall interfaces and at outflow boundaries in fully developed regions for Dissipative Particle Dynamics (DPD) fluid systems. The procedure to enforce the no-slip condition is based on a velocity-dependent shear force, which is a generalized force to represent the presence of the solid-wall particles and to maintain locally thermodynamic consistency. We show that this method can be implemented in both steady and time-dependent fluid systems and compare the DPD results with the continuum limit (Navier-Stokes) results. We also develop a force-adaptive method to impose the outflow boundary conditions for fully developed flow with unspecified outflow velocity profile or pressure value. We study flows over the backward-facing step and in idealized arterial bifurcations using a combination of the two new boundary methods with different flow rates. Finally, we explore the applicability of the outflow method in time-dependent flow systems. The outflow boundary method works well for systems with Womersley number of O(1), i.e., when the pressure and flowrate at the outflow are approximately in-phase.     

An example of dynamically induced coherent states

We consider an example where coherent states appear naturally (dynamically). We study the interaction between an arbitrary quantized matter with a quantized electromagnetic field. Using an approximation that is similar to the Hartree–Fock one and a variational principle, we demonstrate that the electromagnetic field is created by the charged matter exactly in Glauber coherent states with parameters determined by mean currents of the matter.     

Full current statistics of incoherent "cold electrons"

We evaluate the full current statistics (FCS) in the low-dimensional (1D and 2D) diffusive conductors in the incoherent regime eV>E(Th)=D/L(2), E(Th) being the Thouless energy. It is shown that the Coulomb interaction substantially enhances the probability of big current fluctuations for short conductors with E(Th)>1/tau(E), tau(E) being the energy relaxation time, leading to the exponential tails in the current distribution. The current fluctuations are most strong for low temperatures, provided E(Th) approximately [(eV)(2)/Dnu(2)(1)](1/3) for 1D and E(Th) approximately (eV/g)ln(g for 2D, where g is a dimensionless conductance and nu(1) is a 1D density of states. The FCS in the "hot electron" regime is also discussed.     

Unbounded Energy Growth in Hamiltonian Systems with a Slowly Varying Parameter

We study Hamiltonian systems which depend slowly on time. We show that if the corresponding frozen system has a uniformly hyperbolic invariant set with chaotic behaviour, then the full system has orbits with unbounded energy growth (under very mild genericity assumptions). We also provide formulas for the calculation of the rate of the fastest energy growth. We apply our general theory to non-autonomous perturbations of geodesic flows and Hamiltonian systems with billiard-like and homogeneous potentials. In these examples, we show the existence of orbits with the rates of energy growth that range, depending on the type of perturbation, from linear to exponential in time. Our theory also applies to non-Hamiltonian systems with a first integral.