Spread of a catalytic branching random walk on a multidimensional lattice

For a supercritical catalytic branching random walk on ${\mathbb{Z}}^d$, $d\in \mathbb{N}$, with an arbitrary finite catalysts set we study the spread of particles population as time grows to infinity. It is shown that in the result of the proper normalization of the particles positions in the limit there are a.s. no particles outside the closed convex surface in ${\mathbb{R}}^d$ which we call the propagation front and, under condition of infinite number of visits of the catalysts set, a.s. there exist particles on the propagation front. We also demonstrate that the propagation front is asymptotically densely populated and derive its alternative representation.     

Synthesis, structural characterization, photophysical properties and theoretical analysis of gold(I) thiolate-phosphine complexes

A series of luminescent dinuclear neutral complexes of stoichiometry [(AuSPh)(2)(PPh(2)-(C(6)H(4))(n)-PPh(2))] (n = 1, 2, 3) as well as their tetranuclear cationic derivatives [(Au(2)SPh)(2)(PPh(2)-(C(6)H(4))(n)-PPh(2))(2)](PF(6))(2) are reported. Their crystal structures have been elucidated by X-ray studies. These studies indicate that, for the dinuclear species, only when n = 1 the molecules exhibit intermolecular aurophilic interactions. None of the tetranuclear species crystallizes in their molecular form, due to the formation of aggregates through Au···Au interactions. The origin of the luminescence has been analyzed by computational studies indicating that the presence or absence of aurophilic interactions does not affect the luminescent behavior and that intraligand charge transfer processes which involve the thiolate and the diphosphine are responsible for the emissions. The result is in contrast with the thiolate-gold charge transfer processes which dominate the photophysics of gold-thiolate compounds and reveals the influence of the phenylene spacers in the emissive behavior of these compounds.     

Micro-bore titanium housed polymer monoliths for reversed-phase liquid chromatography of small molecules

A new method for the fixation of polymethacrylate monoliths within titanium tubing of up to 0.8 mm I.D. for use as a chromatographic column under elevated temperatures and pressures is described. The preparation of butyl methacrylate–ethylene dimethacrylate-based monolithic stationary phases with desired porous structures was achieved within titanium tubing with pre-oxidised internal walls. The oxidised titanium surface was subsequently silanised with 3-trimethoxysilylpropyl methacrylate resulting in tight bonding of butyl methacrylate porous monolith to the internal walls, providing stationary phase stability at column temperatures up to 110 °C and at operating column pressure drops of >28 MPa. The titanium housed monoliths exhibited a uniform and dense porous structure, which provided peak efficiencies of up to 59,000 theoretical plates per meter when evaluated for the separation of small molecules in reversed-phase mode, under optimal conditions (achieved at 15 μL/min and temperature of 110 °C for naphthalene with a retention factor, k = 0.58). The developed column was applied to the reversed-phase isocratic separation of a text mixture of pesticides.     

Scattering of kinks of the sinh-deformed $$\varphi ^4$$ model

We consider the scattering of kinks of the sinh-deformed \(\varphi ^4\) model, which is obtained from the well-known \(\varphi ^4\) model by means of the deformation procedure. Depending on the initial velocity \(v_\mathrm {in}\) of the colliding kinks, different collision scenarios are realized. There is a critical value \(v_\mathrm {cr}\) of the initial velocity, which separates the regime of reflection (at \(v_\mathrm {in}>v_\mathrm {cr}\)) and that of a complicated interaction (at \(v_\mathrm {in}<v_\mathrm {cr}\)) with kinks’ capture and escape windows. Besides that, at \(v_\mathrm {in}\) below \(v_\mathrm {cr}\) we observe the formation of a bound state of two oscillons, as well as their escape at some values of \(v_\mathrm {in}\).     

Experimentally-based recommendations of density functionals for predicting properties in mechanically interlocked molecules

Mechanically interlocked molecules (rotaxanes and catenanes) have already revolutionized molecular electronics and have the promise of a similar impact in other areas of nanotechnology, ranging from nanoactuators to in vivo drug nanocarriers. However, it would be most useful to have quantitative criteria for predicting structures, binding, and excitation energies for use in designing molecules with mechanical bonds. We assess here the use of density functional theory (DFT) to a noncovalently bound complex and find that no density functional is fully satisfactory. However, we find that the new M06-suite of density functionals, which include attractive medium-range interactions, leads to dramatic improvements in the structures (error of 0.04 A in the interplanar distances for M06-L compared to 0.42 A for B3LYP) and excitation energies (within 0.08 eV for TD-M06-HF without empirical correction compared to 2.2 eV error for TD-B3LYP). However, M06 predicts the complex to be too strongly bound by 22.6 kcal mol(-1) (B3LYP leads to too weak a bond by 29 kcal mol(-1)), while current empirical FF DREIDING is too weakly bound by only 15 kcal mol(-1).     

Probabilistic time-dependent vehicle routing problem

Central European Journal of Operations Research - The probabilistic time-dependent vehicle routing problem is presented in this paper. It is a novel variant of the vehicle routing problem. The...