Phonons, Instabilities and Origin of Polarization in KDP Crystals

The -phonons of KH2PO4 (KDP) and its deuterated analog DKDP are studied via first-principles linear response calculations. The paraelectric phase shows two instabilities. One for a z-polarized mode, which leads to the spontaneous polarization Ps of the ferroelectric phase. The other corresponds to a two-fold degenerate xy-polarized mode. Other phonons are analyzed, which couple to the ferroelectric one at large amplitudes and are relevant for the ferroelectric transition. We show that Ps is mainly of electronic nature, since it arises mostly from an off-diagonal component of the Born effective charge tensor of H, with minor contribution from P atoms displacements.

Current-induced atomic dynamics, instabilities, and Raman signals: Quasiclassical Langevin equation approach

We derive and employ a semiclassical Langevin equation obtained from path integrals to describe the ionic dynamics of a molecular junction in the presence of electrical current. The electronic environment serves as an effective nonequilibrium bath. The bath results in random forces describing Joule heating, current-induced forces including the nonconservative wind force, dissipative frictional forces, and an effective Lorentz-type force due to the Berry phase of the nonequilibrium electrons. Using a generic two-level molecular model, we highlight the importance of both current-induced forces and Joule heating for the stability of the system. We compare the impact of the different forces, and the wide-band approximation for the electronic structure on our result. We examine the current-induced instabilities (excitation of runaway "waterwheel" modes) and investigate the signature of these in the Raman signals.

The use of a GA to improve the postbuckling strength of stiffened composite panels susceptible to secondary instabilities

The use of genetic algorithms (GAs) for structural optimisation is well established but little work has been reported on the inclusion of damage variables within an optimisation framework. This approach is particularly useful in the optimisation of composite structures which are prone to delamination damage. In this paper a challenging design problem is presented where the objective was to delay the catastrophic failure of a postbuckling secondary-bonded stiffened composite panel susceptible to secondary instabilities. It has been conjectured for some time that the sudden energy release associated with secondary instabilities may initiate structural failure, but this has proved difficult to observe experimentally. The optimisation methodology confirmed this indirectly by evolving a panel displaying a delayed secondary instability whilst meeting all other design requirements. This has important implication in the design of thin-skinned lightweight aerostructures which may exhibit this phenomenon.

Optimization of Composite Structures to Delay Mode Jump Instabilities

Numerous studies have shown that postbuckling stiffened panels may undergo abrupt changes in buckled mode
shape when loaded in uniaxial compression. This phenomenon is often referred to as a mode jump or secondary
instability. The resulting sudden release of stored energy may initiate damage in vulnerable regions within a
structure, for example, at the skin-stiffener interface of a stiffened composite panel. Current design practice is to
remove a mode jump by increasing the skin thickness of the postbuckling region. A layup optimization methodology,
based on a genetic algorithm, is presented, which delays the onset of secondary instabilities in a composite structure
while maintaining a constant weight and subject to a number of design constraints. A finite element model was
developed of a stiffened panel’s skin bay, which exhibited secondary instabilities. An automated numerical routine
extracted information directly from the finite element displacement results to detect the onset of initial buckling and
secondary instabilities. This routine was linked to the genetic algorithm to find a revised layup for the skin bay, within
appropriate design constraints, to delay the onset of secondary instabilities. The layup optimization methodology,
resulted in a panel that had a higher buckling load, prebuckling stiffness, and secondary instability load than the
baseline design.

A study of secondary instabilities in postbuckling composite aerostructures

A number of experimental studies have shown that postbuckling stiffened composite panels, loaded in uniaxial compression, may undergo secondary instabilities, characterised by an abrupt change in the buckled mode-shape of the skin between the supporting stiffeners. In this study high-speed digital speckle photogrammetry is used to gain further insight into an I-stiffened panel's response during this transient phase. This energy-dissipating phenomenon will be shown to be able to cause catastrophic structural failure in vulnerable structures. It is therefore imperative that an accurate and reliable methodology is available to predict this phenomenon. The shortcomings of current non-linear implicit solution schemes, found in most commercially-available finite element codes, are discussed. A robust and efficient strategy, which utilises an automated quasi-, static/pseudo-transient hybrid scheme, is presented in this paper and validated using a number of experimental tests. This approach is shown to be able to predict mode-jumping with good accuracy.

Lay-up optimization of composite plates to delay mode-jump instabilities

Experimental and numerical studies have shown that the occurrence of abrupt secondary instabilities, or mode-jumps, in a postbuckling stiffened composite panel may initiate structural failure. This study presents an optimisation methodology, using a genetic algorithm and finite element analysis for the lay-up optimisation of postbuckling composite plates to delay the onset of mode-jump instabilities. A simple and novel approach for detecting modejumps is proposed, based on the RMS value of out-of-plane pseudo-velocities at a number of locations distributed over the postbuckling structure

Evidence of locally enhanced target heating due to instabilities of counter-streaming fast electron beams

The high-current fast electron beams generated in high-intensity laser-solid interactions require the onset of a balancing return current in order to propagate in the target material. Such a system of counter-streaming electron currents is unstable to a variety of instabilities such as the current-filamentation instability and the two-stream instability. An experimental study aimed at investigating the role of instabilities in a system of symmetrical counter-propagating fast electron beams is presented here for the first time. The fast electron beams are generated by double-sided laser-irradiation of a layered target foil at laser intensities above 10(19) W/cm(2). High-resolution X-ray spectroscopy of the emission from the central Ti layer shows that locally enhanced energy deposition is indeed achieved in the case of counter-propagating fast electron beams

Inheritance of ductile and brittle structures in the development of large rock slope instabilities: Examples from western Norway

The high density of slope failures in western Norway is due to the steep relief and to the concentration of various structures that followed protracted ductile and brittle tectonics. On the 72 investigated rock slope instabilities, 13 were developed in soft weathered mafic and phyllitic allochthons. Only the intrinsic weakness of such rocks increases the susceptibility to gravitational deformation. In contrast, the gravitational structures in the hard gneisses reactivate prominent ductile or/and brittle fabrics. At 30 rockslides along cataclinal slopes, weak mafic layers of foliation are reactivated as basal planes. Slope-parallel steep foliation forms back-cracks of unstable columns. Folds are specifically present in the Storfjord area, together with a clustering of potential slope failures. Folding increases the probability of having favourably orientated planes with respect to the gravitational forces and the slope. High water pressure is believed to seasonally build up along the shallow-dipping Caledonian detachments and may contribute to destabilization of the rock slope upwards. Regional cataclastic faults localized the gravitational structures at 45 sites. The volume of the slope instabilities tends to increase with the amount of reactivated prominent structures and the spacing of the latter controls the size of instabilities.

Ferromagnetic instabilities in neutron matter at finite temperature with the Skyrme interaction

The properties of spin-polarized neutron matter are studied at both zero and finite temperature using Skyrme-type interactions. It is shown that the critical density at which ferromagnetism takes place decreases with temperature. This unexpected behavior is associated to an anomalous behavior of the entropy that becomes larger for the polarized phase than for the unpolarized one above a certain critical density. This fact is a consequence of the dependence of the entropy on the effective mass of the neutrons with different third spin component. A new constraint on the parameters of the effective Skyrme force is derived if this behavior is to be avoided.

On instabilities in data assimilation algorithms

Data assimilation algorithms are a crucial part of operational systems in numerical weather prediction, hydrology and climate science, but are also important for dynamical reconstruction in medical applications and quality control for manufacturing processes. Usually, a variety of diverse measurement data are employed to determine the state of the atmosphere or to a wider system including land and oceans. Modern data assimilation systems use more and more remote sensing data, in particular radiances measured by satellites, radar data and integrated water vapor measurements via GPS/GNSS signals. The inversion of some of these measurements are ill-posed in the classical sense, i.e. the inverse of the operator H which maps the state onto the data is unbounded. In this case, the use of such data can lead to significant instabilities of data assimilation algorithms. The goal of this work is to provide a rigorous mathematical analysis of the instability of well-known data assimilation methods. Here, we will restrict our attention to particular linear systems, in which the instability can be explicitly analyzed. We investigate the three-dimensional variational assimilation and four-dimensional variational assimilation. A theory for the instability is developed using the classical theory of ill-posed problems in a Banach space framework. Further, we demonstrate by numerical examples that instabilities can and will occur, including an example from dynamic magnetic tomography.

Coupled Kelvin-wave and mirage-wave instabilities in semigeostrophic dynamics

A weak instability mode, associated with phase-locked counterpropagating coastal Kelvin waves in horizontal anticyclonic shear, is found in the semigeostrophic (SG) equations for stratified flow in a channel. This SG instability mode approximates a similar mode found in the Euler equations in the limit in which particle-trajectory slopes are much smaller than f/N, where f is the Coriolis frequency and N > f the buoyancy frequency. Though weak under normal parameter conditions, this instability mode is of theoretical interest because its existence accounts for the failure of an Arnol’d-type stability theorem for the SG equations. In the opposite limit, in which the particle motion is purely vertical, the Euler equations allow only buoyancy oscillations with no horizontal coupling. The SG equations, on the other hand, allow a physically spurious coastal “mirage wave,” so called because its velocity field vanishes despite a nonvanishing disturbance pressure field. Counterpropagating pairs of these waves can phase-lock to form a spurious “mirage-wave instability.” Closer examination shows that the mirage wave arises from failure of the SG approximations to be self-consistent for trajectory slopes f/N.