Detection of oscillatory solutions in a vacuum diode with total electron reflection

Stability features of steady-state solutions for a vacuum diode with complete deceleration of electron beam is studied. A boundary line on the (inter-electrode gap, external voltage)-plane separating stable solutions from unstable ones is built up. An instability development is shown to end in a state with non-linear oscillations of the electric field but with no virtual cathode in a plasma. Existence of non-linear oscillations of the electric field in a vacuum diode with total reflection of an electron beam points out that such a diode can be a basis to create microwave generator.

The Influence of WENO Schemes on Large-Eddy Simulations of a Neutral Atmospheric Boundary Layer

This work explores the influence of Weighted Essentially Non-Oscillatory (WENO) schemes on Cloud Model 1 (CM1) large-eddy simulations (LES) of a quasi-steady, horizontally homogeneous, fully developed, neutral atmospheric boundary layer (ABL). An advantage of applying WENO schemes to scalar advection in compressible models is the elimination of acoustic waves and associated oscillations of domain-total vertical velocity. Applying WENO schemes to momentum advection in addition to scalar advection yields no further advantage, but has an adverse effect on resolved turbulence within LES. As a tool designed to reduce numerically generated spurious oscillations, WENO schemes also suppress physically realistic instability development in turbulence-resolving simulations. Thus, applying WENO schemes to momentum advection reduces vortex stretching, suppresses the energy cascade, reduces shear-production of resolved Reynolds stress, and eventually amplifies the differences between the surface-layer mean wind profiles in the LES and the mean wind profiles expected in accordance with the filtered law of the wall (LOTW). The role of WENO schemes in adversely influencing surface-layer turbulence has inspired a concept of anti-WENO (AWENO) schemes to enhance instability development in regions where energy-containing turbulent motions are inadequately resolved by LES grids. The success in reproducing the filtered LOTW via AWENO schemes suggests that improving advection schemes is a critical component toward faithfully simulating near-surface turbulence and dealing with other "Terra Incognita" problems.

Theoretical and numerical investigation of the mode I delamination of composite laminate with uneven thickness

In this paper, a theoretical analysis model and two simulation methods are applied to characterize the quasi-static and fatigue delamination of composite laminate with uneven thicknesses. The test data of partially reinforced double-cantilever beam (DCB) were used as benchmark to verify the analysis model and simulation, and cohesive zone models (CZMs) and virtual crack closure technique (VCCT) are used in simulation. It’s shown that the partially reinforced DCB has a unique double-peak load-displacement relationship, and produces instability development during the delamination. By comparing the results of simulation and experiment, it is found that the simulation based on the exponential CZM can simulate the delamination process of partially reinforced DCB under both quasi-static and fatigue loading; while VCCT method will generate a straight delamination front edge in the area of reinforcement, and lost the micro-damage of the previous loading step between load steps, and result in an incorrect delamination behavior.

State evolution laws and earthquake nucleation

<p>In models of faults as elastic continua with a frictional interface, earthquake nucleation is the initiation of a propagating dynamic fault rupture nucleated by a localized slip instability. A mechanism capturing both the weakening process leading to nucleation as well as fault healing between events, is a slip rate- and state-dependent friction, with so-called direct effect and evolution effects [Dieterich, JGR 1979; Ruina, JGR 1983]. While the constitutive representation of the direct effect is theoretically supported [e.g., Nakatani, JGR 2001; Rice et al., JMPS 2001], that of the evolution effect remains empirical and a number of state-evolution laws have been proposed to fit lab rock friction data [Ruina, JGR 1983; Kato and Tullis, GRL 2001; Bar-Sinai et al., GRL 2012; Nagata et al., JGR 2012]. These laws may share a common linearization about steady-state, such that a linear stability analysis of steady, uniform sliding yields a single critical wavelength for unstable growth of perturbations [Rice and Ruina, JAM 1983]. However, the laws’ differences are apparent at later, non-linear stages of instability development.</p><div>Previously, we showed that instability development under aging-law state evolution could be understood in terms of dynamical systems [Viesca, PR-E 2016, PRS-A 2016]: the non-linear acceleration of slip occurs as the attraction of a fault’s slip rate to a fixed point, corresponding to slip rate diverging with a fixed spatial distribution and rate of acceleration. Here we show that this framework can also be applied to understand slip instability development under all commonly used evolution laws, including the so-called slip and Nagata laws. To do so, we develop an intermediate state evolution law that transitions between the slip and aging laws with the adjustment of a single parameter. We show that, to within a variable transformation, the intermediate law is equivalent to the Nagata law and that fixed-point blow-up solutions exist for any value of the transition parameter. We assess these fixed-points’ stability via a linear stability analysis and provide an explanation for previously observed behavior in numerical solutions for slip rate and state evolution under various evolution laws [Ampuero and Rubin, JGR 2008; Kame et al., 2013; Bar-Sinai et al., PR-E 2013; Bhattacharya and Rubin, JGR 2014].</div>