Oblique Perforation of Thick Metallic Plates by Rigid Projectiles

Oblique perforation of thick metallic plates by rigid projectiles with various nose shapes is studied in this paper. Two perforation mechanisms, i.e., the hole enlargement for a sharp projectile nose and the plugging formation for a blunt projectile nose, are considered in the proposed analytical model. It is shown that the perforation of a thick plate is dominated by several non-dimensional numbers, i.e., the impact function, the geometry function of projectile, the non-dimensional thickness of target and the impact obliquity. Explicit formulae are obtained to predict the ballistic limit, residual velocity and directional change for the oblique perforation of thick metallic plates. The proposed model is able to predict the critical condition for the occurrence of ricochet. The proposed model is validated by comparing the predictions with other existing models and independent experimental data.The English text was polished by Keren Wang     

Photovoltaic effect in the single-junction DBP/PTCBI organic system under low intensity of monochromatic light

Photoelectric properties of the planar ITO/MoO3/DBP/PTCBI/BCP/Ag system were characterized on the basis of short-circuit current, open-circuit voltage and absorption spectra, and current-voltage measurements in the dark and under monochromatic illumination of low intensity. Photovoltaic performance of the system was compared with the performance of ideal semiconductor and excitonic cells of chosen bandgaps. Such analysis shows, that the fabricated cell exhibits quite high value of the open-circuit voltage, in comparison to the SQ limits calculated for semiconductor devices of bandgaps close to the LUMO_PTCBI-HOMO_DBP offset or crystalline silicon cells of the same absorptivity. This confirms that the DBP/PTCBI junction exhibits good properties for conversion of exciton energy to chemical energy of electron-hole pair. Moreover, open-circuit voltage and short-circuit current of the investigated cell practically do not change within the 520 nm–620 nm range, for which they reach the maximum values, making the junction of DBP/PTCBI attractive for use in indoor photovoltaics.     

Kinetic study of the oxidation reaction of 4-methylphenyl radical

A kinetic study of the reaction of the 4-methylphenyl radical (4-C₆H₄CH₃) with the oxygen molecule was conducted using experimental and theoretical approaches. The absorption spectrum for the λ = 266 nm photolysis of the 4-C₆H₄CH₃X (X = Cl, Br)/N₂/O₂ mixture was measured in the wavelength range of λ = 503-512 nm using N₂ as the buffer gas at a total pressure of 40 Torr using a cavity ring-down spectroscopy apparatus coupled with a pulsed laser photolysis system. Based on the absorbance of the product of the 4-C₆H₄CH₃ + O₂ reaction at λ = 504 nm, the reaction rate coefficient for the 4-C₆H₄CH₃ + O₂ reaction was determined to be k = (1.21 ± 0.10) × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹ and k = (1.18 ± 0.21) × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹ using 4-C₆H₄CH₃Cl and 4-C₆H₄CH₃Br, respectively, as the radical precursor. And there was no pressure dependence in the total pressure range of 10-90 Torr varying partial pressure of N₂ buffer gas at T = 296 ± 5 K. The geometries, vibration frequencies, and potential energy surfaces of the reactants, major products, and transition states in the 4-C₆H₄CH₃ + O₂ reaction were determined using the CBS-QB3 method. The k value at the high-pressure limit was calculated to be 1.26 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹ using the variational transition-state theory. The calculated value of k was consistent with the experimental value, which indicated that the 4-C₆H₄CH₃ + O₂ reaction reaches the high-pressure limit at 10 Torr. Therefore, the oxidation of the 4-C₆H₄CH₃ radical is almost 10 times faster than that of the benzyl radical, which has the same chemical formula, at the high-pressure limit.     

Hydrodynamic limit of the Robinson–Schensted–Knuth algorithm

We investigate the evolution in time of the position of a fixed number in the insertion tableau when the Robinson–Schensted–Knuth algorithm is applied to a sequence of random numbers. When the length of the sequence tends to infinity, a typical trajectory after scaling converges uniformly in probability to some deterministic curve.     

Homological approximations for profinite and pro-p limit groups

Abstract

We study homological approximations of the profinite completion of a limit group (see Thm. A) and obtain the analogous of Bridson and Howie’s Theorem for the profinite completion of a non-abelian limit group (see Thm. B).     

Reaction–Diffusion models: From particle systems to SDE’s

Let $V$ be any finite set and $p(?,?)$ a transition kernel on it. We present a construction of a family of Reaction–Diffusion models that converge after scaling to the solution to the $\left|V\right|$-dimensional SDE: $d{\zeta }_t=\left[{\Delta }_p{\zeta }_t?\beta ?{\zeta }_t^k\right]dt+\sqrt{\alpha ?{\zeta }_t^{?}}d{B}_t$with arbitrary initial condition ${\zeta }_0\in {\mathbb{R}}^V$. Here, ${\Delta }_p$ is the diffusion on $V$ corresponding to $p$, $\alpha$, $\beta$ are positive real numbers and $k$, $?$ are positive integers.     

Approximate fixed point sequences and convergence theorems for asymptotically pseudocontractive mappings

Let K be a nonempty closed convex and bounded subset of a real Banach space E and T:K→K be uniformly L-Lipschitzian, uniformly asymptotically regular with sequence {ε_n}, and asymptotically pseudocontractive with constant {k_n}, where {k_n} and {ε_n} satisfy certain mild conditions. Let a sequence {x_n} be generated from x₁∈K by x_n+1:=(1−λ_n)x_n+λ_nTⁿx_n−λ_nθ_n(x_n−x₁), for all integers n?1, where {λ_n} and {θ_n} are real sequences satisfying appropriate conditions, then ‖x_n−Tx_n‖→0 as n→∞. Moreover, if E is reflexive, and has uniform normal structure with coefficient N(E) and L<N(E)^1/2 and has a uniformly Gâteaux differentiable norm, and T satisfies an additional mild condition, then {x_n} also converges strongly to a fixed point of T.     

The inviscid limit for the complex Ginzburg-Landau equation

We study the inviscid limit of the complex Ginzburg-Landau equation. We observe that the solutions for the complex Ginzburg-Landau equation converge to the corresponding solutions for the nonlinear Schrödinger equation. We give its convergence rate. We estimate the integral forms of solutions for two equations.