Surface-induced dissociation and chemical reactions of C2D 4 + on stainless steel, carbon (HOPG), and two different diamond surfaces

Surface-induced interactions of the projectile ion C₂D₄⁺ with room-temperature (hydrocarbon covered) stainless steel, carbon highly oriented pyrolytic graphite (HOPG), and two different types of diamond surfaces (O-terminated and H-terminated) were investigated over the range of incident energies from a few eV up to 50 eV. The relative abundance of the product ions in dependence on the incident energy of the projectile ion [collision-energy resolved mass spectra, (CERMS) curves] was determined. The product ion mass spectra contained ions resulting from direct dissociation of the projectile ions, from chemical reactions with the hydrocarbons on the surface, and (to a small extent) from sputtering of the surface material. Sputtering of the surface layer by low-energy Ar⁺ ions (5–400 eV) indicated the presence of hydrocarbons on all studied surfaces. The CERMS curves of the product ions were analyzed to obtain both CERMS curves for the products of direct surface-induced dissociation of the projectile ion and CERMS curves of products of surface reactions. From the former, the fraction of energy converted in the surface collision into the internal excitation of the projectile ion was estimated as 10% of the incident energy. The internal energy of the surface-excited projectile ions was very similar for all studied surfaces. The H-terminated room-temperature diamond surface differed from the other surfaces only in the fraction of product ions formed in H-atom transfer surface reactions (45% of all product ions formed versus 70% on the other surfaces).     

Interpolation by $G^2$ Quintic Pythagorean-Hodograph Curves

In this paper, the $G^2$ interpolation by Pythagorean-hodograph (PH) quintic curves in $\mathbb{R}^d$, $d ≥2$, is considered. The obtained results turn out as a useful tool in practical applications. Independently of the dimension $d$, they supply a $G^2$ quintic PH spline that locally interpolates two points, two tangent directions and two curvature vectors at these points. The interpolation problem considered is reduced to a system of two polynomial equations involving only tangent lengths of the interpolating curve as unknowns. Although several solutions might exist, the way to obtain the most promising one is suggested based on a thorough asymptotic analysis of the smooth data case. The numerical algorithm traces this solution from a particular set of data to the general case by a homotopy continuation method. Numerical examples confirm the efficiency of the proposed method.     

Indirect optical crosstalk reduction by highly-doped backside layer in single-photon avalanche diode arrays

A method of reducing indirect optical crosstalk in single-photon avalanche diode arrays is investigated by TCAD simulations. The reduction is accomplished by taking advantage of an enhanced optical absorption in a highly-doped Si layer on the backside of the wafer. A simulation environment was developed to give information about optical crosstalk by incorporating the experimental optical constants of the materials constituting the crosstalk-reduction layer. It is shown that the indirect optical crosstalk is greatly reduced by increasing the thickness and doping of the layer. A crosstalk reduction of 5 orders of magnitude is gained with addition of 1-μm-thick \(\hbox {PureB}/\upalpha \hbox {-Si}\) stack for the array processed on a p-type substrate, while the same reduction is achieved with a 1-μm-thick highly-doped Si layer (As, \(1.1\times 10^{20}\, \hbox {cm}^{-3}\)) for an array processed on an n-type substrate.     

Thermodynamic and critical properties of an antiferromagnetically stacked triangular Ising antiferromagnet in a field

We study a stacked triangular lattice Ising model with both intra- and inter-plane antiferromagnetic interactions in a field, by Monte Carlo simulation. We find only one phase transition from a paramagnetic to a partially disordered phase, which is of second order and 3D XY universality class. At low temperatures we identify two highly degenerate phases: at smaller (larger) fields the system shows long-range ordering in the stacking direction (within planes) but not in the planes (stacking direction). Nevertheless, crossovers to these phases do not have a character of conventional phase transitions but rather linear-chain-like excitations.     

Multiple phase transitions in the XY model with nematic-like couplings

Critical behavior of the two-dimensional generalized XY model involving solely nematic-like terms of the second, third and fourth orders is studied by Monte Carlo method. We find that such a system can undergo three successive phase transitions. At higher temperatures there is a phase transition of the Berezinskii–Kosterlitz–Thouless type to the $q=4$ nematic-like phase, followed by two more transitions of the Ising type to the $q=2$ nematic-like and ferromagnetic phases, respectively. The q nematic-like phases are characterized by spin alignments with angles $2k\pi /q$, where $k\le q$ is an integer. The ferromagnetic phase appears at low temperatures even without the presence of magnetic interactions owing to a synergic effect of the nematic-like terms.     

Birefringence of SbSI and SbSeI crystals at the region of antiferroelectric phase transition

Anomalous behavior has been observed in the temperature range of T = 140–145 °C. The electric current I(T) of SbSI and SbSeI crystals along the c(z) axis changes significantly at the region of the antiferroelectric phase transition when DC voltage is applied. The peak positions are observed at 140 °C and 145 °C for SbSI and SbSeI, respectively. The birefringence spectra show temperature-dependent changes upon retardation m, confirming the antiferroelectric phase transition for both crystals. The peak positions observed from the optical measurements do not differ from the electrical measurements, showing the transition point at 140?°C and 145?°C for SbSI and SbSeI, respectively.     

Reactions of Doubly Ionized Benzene with Nitrogen and Water: A Nitrogen‐Mediated Entry into Superacid Chemistry

Even in the highly diluted gas phase, rather than electron transfer the benzene dication C₆H₆²⁺ undergoes association with dinitrogen to form a transient C₆H₆N₂²⁺ dication which is best described as a ring‐protonated phenyl diazonium ion. Isotopic labeling studies, photoionization experiments using synchrotron radiation, and quantum chemical computations fully support the formation of protonated diazonium, which is in turn a prototype species of superacidic chemistry in solution. Additionally, reactions of C₆H₆²⁺ with background water involve the transient formation of diprotonated phenol and, among other things, afford a long‐lived C₆H₆OH₂²⁺ dication, which is attributed to the hydration product of Hogeveen’s elusive pyramidal structure of C₆H₆²⁺, as the global minimum of doubly ionized benzene. Nitrogen is essential for the formation of the C₆H₆OH₂²⁺ dication in that it mediates the formation of the water adduct, while the bimolecular encounter of the C₆H₆²⁺ dication with water only leads to (dissociative) electron transfer.     

Generalized Cauchy type problems for nonlinear fractional differential equations with composite fractional derivative operator

This paper is devoted to proving the existence and uniqueness of solutions to Cauchy type problems for fractional differential equations with composite fractional derivative operator on a finite interval of the real axis in spaces of summable functions. An approach based on the equivalence of the nonlinear Cauchy type problem to a nonlinear Volterra integral equation of the second kind and applying a variant of the Banach’s fixed point theorem to prove uniqueness and existence of the solution is presented. The Cauchy type problems for integro-differential equations of Volterra type with composite fractional derivative operator, which contain the generalized Mittag-Leffler function in the kernel, are considered. Using the method of successive approximation, and the Laplace transform method, explicit solutions of the open problem proposed by Srivastava and Tomovski (2009) [11] are established in terms of the multinomial Mittag-Leffler function.     

Numerical simulations of water–gas flow in heterogeneous porous media with discontinuous capillary pressures by the concept of global pressure

We present an approach and numerical results for a new formulation modeling immiscible compressible two-phase flow in heterogeneous porous media with discontinuous capillary pressures. The main feature of this model is the introduction of a new global pressure, and it is fully equivalent to the original equations. The resulting equations are written in a fractional flow formulation and lead to a coupled degenerate system which consists of a nonlinear parabolic (the global pressure) equation and a nonlinear diffusion–convection one (the saturation equation) with nonlinear transmission conditions at the interfaces that separate different media. The resulting system is discretized using a vertex-centred finite volume method combined with pressure and flux interface conditions for the treatment of heterogeneities. An implicit Euler approach is used for time discretization. A Godunov-type method is used to treat the convection terms, and the diffusion terms are discretized by piecewise linear conforming finite elements. We present numerical simulations for three one-dimensional benchmark tests to demonstrate the ability of the method to approximate solutions of water–gas equations efficiently and accurately in nuclear underground waste disposal situations.