Monte Carlo simulation of electron avalanches and avalanche size distributions in methane

The simulation of electron avalanches and avalanche size distributions in methane is presented in this paper. A model for electron transport under the influence of a constant electric field based on the Monte Carlo method is described in detail. The model is verified and then used to simulate the avalanche development, to calculate the number of electrons in the avalanche (avalanche size), and to determine the avalanche size distribution. The simulated avalanche size distributions in methane are compared with the experimental results, and a good agreement is observed. The influence of inter‐electrode distance, pressure, and reduced electric field on the shape of the avalanche size distribution is discussed. The assumption from the literature that for a constant reduced electric field the shape of the reduced avalanche size distribution is independent of the mean size of the avalanche is confirmed for a wide range of experimental conditions. The simulations have shown that avalanche size distributions depend only on the reduced electric field, confirming the similarity principle.     

Influence of small harmonic terms on eigenvalues of monodromy matrix of piecewise-linear oscillators

In this paper we consider the problem which can appear at the determination of the dynamical stability of the responses of oscillators with discontinuous or steep derivative of the restoring characteristic obtained in the frequency domain. For that purpose, a simple one degree-of-freedom system with piecewise-linear force-displacement relationship subjected to a harmonic excitation is analysed. Stability of the periodic response obtained in the frequency domain by the incremental harmonic balance method is determined by using the Floquet-Liapounov theorem. Confirmation of the results obtained in the frequency domain is done by comparing with the results obtained in the time domain by the method of piecing the exact solutions. Determination of the dynamical stability can be made more reliable by using the proposed plot of maximum modulus of the eigenvalues of the monodromy matrix in dependence of non-dimensional frequency and the number of harmonics included in the supposed approximate solution.     

The dynamics of two-dimensional cantilevered plates with an additional spring support in axial flow

In this paper, the dynamics of two-dimensional cantilevered flexible plates in axial flow is investigated using a fluid–structure interaction model. An additional spring support of either linear or cubic type is installed at various locations on the plate; its presence qualitatively affects the dynamics of the fluid–structure system. Without the spring, the cantilevered plate loses stability by flutter when the flow velocity exceeds a critical value; as the flow velocity increases further, the system dynamics is qualitatively the same: the plate undergoes symmetric limit cycle oscillations with increasing amplitude. With a linear spring, a state of static buckling is added to the dynamics. Rich nonlinear dynamics can be observed when a cubic spring is considered; the plate may be stable and buckled, and it may undergo either symmetric or asymmetric limit cycle oscillations. Moreover, when the flow velocity is sufficiently high, the plate may exhibit chaotic motions via a period-doubling route.     

Efficient Direct Nitrosylation of α-Diimine Rhenium Tricarbonyl Complexes to Structurally Nearly Identical Higher Charge Congeners Activable towards Photo-CO Release

The reaction of rhenium α-diimine (N-N) tricarbonyl complexes with nitrosonium tetrafluoroborate yields the corresponding dicarbonyl-nitrosyl [Re(CO)₂(NO)(N-N)X]⁺ species (where X = halide). The complexes, accessible in a single step in good yield, are structurally nearly identical higher charge congeners of the tricarbonyl molecules. Substitution chemistry aimed at the realization of equivalent dicationic species (intended for applications as potential antimicrobial agents), revealed that the reactivity of metal ion in [Re(CO)₂(NO)(N-N)X]⁺ is that of a hard Re acid, probably due to the stronger π-acceptor properties of NO⁺ as compared to those of CO. The metal ion thus shows great affinity for π-basic ligands, which are consequently difficult to replace by, e.g., σ-donor or weak π-acids like pyridine. Attempts of direct nitrosylation of α-diimine fac-[Re(CO)₃]⁺ complexes bearing π-basic OR-type ligands gave the [Re(CO)₂(NO)(N-N)(BF₄)][BF₄] salt as the only product in good yield, featuring a stable Re-FBF₃ bond. The solid state crystal structure of nearly all molecules presented could be elucidated. A fundamental consequence of the chemistry of [Re(CO)₂(NO)(N-N)X]⁺ complexes, it that the same can be photo-activated towards CO release and represent an entirely new class of photoCORMs.     

The brachistochronic motion of a wheeled vehicle

The paper considers the brachistochronic motion of a wheeled vehicle on a horizontal plane surface. The objective is to transfer the vehicle from the specified initial position with given initial kinetic energy to the specified terminal position in minimum time with conserved total mechanical energy of the vehicle. The problem is solved by applying Pontryagin’s maximum principle and singular optimal control theory. The projection of the reaction force of the horizontal plane applied on the front vehicle wheels onto the axis of the front vehicle axle is taken for a control variable. The cases of unbounded and bounded value of this projection are considered. The shooting method is used to solve the two-point boundary value problem arising from Pontryagin’s maximum principle and singular optimal control theory.     

EPR and optical-absorption studies of Cu2+-doped Zn(NH2(CH2)3NHOH)2Ni(CN)4 single crystals

Electron paramagnetic resonance of Cu²⁺-doped catena-trans-bis(N-(2-hydroxyethyl)-ethylenediamine) zinc(II)-tetra-μ-cyanonicelate(II) [Zn(NH₂(CH₂)₃NHOH)₂Ni(CN)₄] single crystals and powder are examined at room temperature. The spectra show the substitution of the Zn²⁺ ion with the Cu²⁺ ion. The crystal field around the Cu²⁺ ion is nearly axial. There is a single paramagnetic site withg _xx=2.073,g _yy=2.060,g _zz=2.248,A _xx=40.5 G,A _yy=50.8 G,A _zz=172.0 G. The ground-state wave function is an admixture of d _x ²−y ² and d _z ² states. The optical-absorption studies show two bands at 320 nm (31250 cm⁻¹) and 614 nm (16286 cm⁻¹) which confirm the axial symmetry. The crystal field parameters and the wave function are determined.     

Elastic scattering of electrons by deuterons in the framework of the source theory by J. Schwinger

Cross sections of the elastic scattering of electrons from the deuterons are calculated with the concept of primitive interaction, disregarding the form factors of the deuteron. Formulas are derived for the various possibilities of the electron and deuteron polarization. Numerical results are given for 175 MeV scattering in the rest frame.     

Some new classes of Banach-Mackey spaces

Some weakenings of property (K) of Antosik for locally convex spaces are introduced: local property (K) and, for spaces with Schauder-type decompositions, two variants of property (K) defined in terms of block- and tail-sequences. It is shown that if a space enjoys any of these new properties, then it is Banach-Mackey. An application to the barrelledness of the spaces of Pettis integrable functions is given, and examples are provided to distinguish between the various K-type properties.