Performance of ring oscillators composed of gate-all-around FETs with varying numbers of nanowire channels using TCAD simulation

In this paper, we investigate the performance of ring oscillators composed of gate-all-around (GAA) silicon nanowire (NW) field-effect transistors (FETs) with four different numbers of NW channels, for sub-10-nm logic applications. Our simulations reveal that ring oscillators with double, triple, and quadruple NW channels exhibit improvements of up to 50%, 85%, and 97%, respectively, in the oscillation frequencies (f_osc), compared to a ring oscillator with a single NW channel, due to the large drive current, in spite of the increased intrinsic capacitance of a given device. Moreover, our work shows that the f_osc improvement ratio of the ring oscillators becomes saturated with triple NW channels with additional load capacitances of 0.1 fF and 0.01 fF, which are similar to, or less than the intrinsic device capacitance (∼0.1 fF). Thus, our study provides an insight for determining the capacitive load and optimal number of NW channels, for device development and circuit design of GAA NW FETs.     

Interbasis expansions for isotropic harmonic oscillator

The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n.     

变形谐振子势的能谱方程

讨论了3种变形谐振子势:左右两边不同参数的谐振子势、左边方形势加右边谐振子势和谐振子势中间加δ势中的能量本征态函数.这些函数都可以由厄米函数表示.由波函数及其一次导数在原点的衔接条件,得到了能谱方程.     

A perturbed martingale approach to global optimization

A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting to the directional update term additional layers of random perturbations referred to as ‘coalescence’ and ‘scrambling’. A selection step, constituting yet another avenue for random perturbation, completes the global search. The direction-driven nature of the search is manifest in the local extremization and coalescence components, which are posed as martingale problems that yield gain-like update terms upon discretization. As anticipated and numerically demonstrated, to a limited extent, against the problem of parameter recovery given the chaotic response histories of a couple of nonlinear oscillators, the proposed method appears to offer a more rational, more accurate and faster alternative to most available evolutionary schemes, prominently the particle swarm optimization.     

Poisson discretizations of Wiener functionals and Malliavin operators with Wasserstein estimates

This article proposes a global, chaos-based procedure for the discretization of functionals of Brownian motion into functionals of a Poisson process with intensity $\lambda >0$. Under this discretization we study the weak convergence, as the intensity of the underlying Poisson process goes to infinity, of Poisson functionals and their corresponding Malliavin-type derivatives to their Wiener counterparts. In addition, we derive a convergence rate of $O\left({\lambda }^{?1∕4}\right)$ for the Poisson discretization of Wiener functionals by combining the multivariate Chen–Stein method with the Malliavin calculus. Our proposed sufficient condition for establishing the mentioned convergence rate involves the kernel functions in the Wiener chaos, yet we provide examples, especially the discretization of some common path dependent Wiener functionals, to which our results apply without committing the explicit computations of such kernels. To the best our knowledge, these are the first results in the literature on the universal convergence rate of a global discretization of general Wiener functionals.     

Interaction of modulated pulses in nonlinear oscillator chains

We formally derive and rigorously justify the modulation equations of lowest order for the interaction of two modulated pulses on a one-dimensional nonlinear oscillator chain. We show that solutions with the initial form of the assumed ansatz preserve this form over time intervals with positive macroscopic length, and we show a bound on the possible shift of the envelope caused by the interaction. Thus, we rigorously justify and quantify the statement that under the given conditions there is almost no interaction of the modulated pulses.     

Peculiarities of wave dynamics in media with oscillating inclusions

The article is concerned with mathematical models for media with oscillating inclusions. These models consist of mutually connected equations, one of which is the wave equation for carrying medium and others are equations of motion for partial oscillators. To close these models, we use cubic and nonlocal equations of state for the carrying medium. Travelling wave solutions to these models are studied in detail. Using qualitative analysis methods, the phase space is shown to contain periodic, homo- and heteroclinic trajectories. Moreover, in the case of nonlocal models we observe the creation of quasiperiodic and chaotic regimes. Bifurcations of localized regimes are studied via the Poincaré section technique.     

UV spectral characterization of a smectic-C liquid crystal: Theoretical support to the experiment

In the present article, UV spectral characterization of a smectic-C liquid crystal 4,4′-bis(n-alkoxy)azoxybenzene (n = 14) (C₄₀H₆₆N₂O₃) has been carried out. Structure of the molecule has been optimized using the Density functional B3LYP with 6-31+G (d) basis set using crystallographic geometry as input. The absorption spectra have been estimated in the UV region by employing the DFT method, semiempirical CNDO/S and INDO/S parameterizations. The oscillator strength (f) and vertical transition energy (E_V) have been reported corresponding to absorption wavelength (λ_max). These values have been compared with the experimental value reported in the literature to offer theoretical support to the experimental value. Further, some electrochemical properties have been reported for the molecule.     

Absolute configuration assignment made easier by the VCD of coupled oscillating carbonyls: the case of (−)-propanedioic acids, 2-(2,3)-dihydro-3-oxo-1H-isoindol-1-yl)-1,3-dimethyl ester

Depending on their relative orientation, coupled oscillating carbonyl groups provide a VCD spectrum with a characteristic CO bond stretching region showing a strong bisignate VCD feature, which can be readily predicted adopting long available semiempirical methods. The extended coupled oscillator (ECO) formalism has been used to assign the absolute configuration of a recently synthesized chiral 3-substituted isoindolinone. The prediction of (S) configuration for the (−) enantiomer has been confirmed by quantum mechanical calculations.