Spectral analysis of a nonlinear oscillator driven by random and periodic forces. I. Linearized theory

We have combined the techniques of statistical and harmonic linearization to develop a linearized approximation theory for the calculation of the second-order statistics (i.e., autocorrelation functions and spectral densities) of nonlinear systems driven by both random and periodic forces. For the special case of a Duffing oscillator (a damped anharmonic oscillator with a cubic nonlinearity) driven by Gaussian white noise and by a sinusoidal force, explicit expressions for the renormalized (linearized) frequency, the autocorrelation function, and the spectral density of the oscillator displacement in terms of all the system parameters have been derived. We have determined the region of the parameter space in which the applied periodic force has a significant influence on the second-order statistics of the oscillator.This research was supported by the Office of Naval Research, by the National Science Foundation under grant No. CHE78-21460 and by a grant from Charles and Reneé Taubman.     

Single-pulse stimulated Raman scattering spectroscopy

We demonstrate the acquisition of stimulated Raman scattering spectra with the use of a single femtosecond pulse. High-resolution vibrational spectra are obtained by shifting the phase of a narrow band of frequencies within the input pulse spectrum, using spectral shaping. The vibrational lines are resolved via amplitude features formed in the spectrum after interaction with the sample. Using this technique, low-frequency Raman lines (<100 cm?1) are observed on both the Stokes and anti-Stokes sides.     

Chiral enhancement in the confined space of zeolites for the asymmetric synthesis of β-hydroxy nitroalkanes

(1S,2S)-N¹,N²-Bis(3-chlorobenzyl)cyclohexane-1,2-diamine 1a′ and (1S,2S)-N¹,N²-bis(4-chlorobenzyl)cyclohexane-1,2-diamine 1b′ were used to prepare chiral Cu(II) complexes Cu-Y-1a, Cu-Y-1b, Cu-mZSM5-1a, and Cu-mZSM5-1b by a flexible ligand method using copper exchanged zeolite Y and mesoporous ZSM-5. The characterization of zeolite supported complexes was performed by microanalysis, IR-, diffuse reflectance spectroscopy (DRS), EPR spectroscopy, specific rotation and thermogravimetric analysis (TGA). The catalytic activity of these supported complexes was explored for the asymmetric nitroaldol reaction of various aldehydes with nitromethane at 0 °C. Excellent yields (up to 99%) of β-hydroxy nitroalkane with an ee of up to 94% were achieved in the case of benzaldehyde as substrate. Significantly, the performance of the supported catalyst was better in terms of enantioselectivity than the complex under homogenous conditions. The supported catalysts were recycled four times with no observable loss in performance and no leaching of the catalytically active complex during the nitroaldol reaction.     

Frequency lock-in phenomenon for oscillating airfoils in buffeting flows

Navier-Stokes based computer simulations are conducted to determine the aerodynamic flow field response that is observed for a NACA0012 airfoil that undergoes prescribed harmonic oscillation in transonic buffeting flows, and also in pre-buffet flow conditions. Shock buffet is the term for the self-sustained shock oscillations that are observed for certain combinations of Mach number and steady mean flow angle of attack even in the absence of structural motion. The shock buffet frequencies are typically on the order of the elastic structural frequencies, and therefore may be a contributor to transonic aeroelastic response phenomena, including limit-cycle oscillations. Numerical simulations indicate that the pre-shock-buffet flow natural frequency increases with mean angle of attack, while the flow damping decreases and approaches zero at the onset of buffet. Airfoil harmonic heave motions are prescribed to study the interaction between the flow fields induced by the shock buffet and airfoil motion, respectively. At pre-shock-buffet conditions the flow response is predominantly at the airfoil motion frequency, with some smaller response at multiplies of this frequency. At shock buffet conditions, a key effect of prescribed airfoil motions on the buffeting flow is to create the possibility of a lock-in phenomenon, in which the shock buffet frequency is synchronized to the prescribed airfoil motion frequency for certain combinations of airfoil motion frequencies and amplitudes. Aerodynamic gain-phase models for the lock-in region, as well as for the pre-shock-buffet conditions are suggested, and also a possible relationship between the lock-in mechanism and limit-cycle oscillation is discussed.     

A modified newton-raphson method for the solution of systems of equations

An implicit function theorem and a resulting modified Newton-Raphson method for roots of functions between finite dimensional spaces, without assuming non-singularity of the Jacobian at the initial approximation. Research supported by the Swope Foundation.     

A generalized Weiszfeld method for the multi-facility location problem

An iterative method is proposed for the K facilities location problem. The problem is relaxed using probabilistic assignments, depending on the distances to the facilities. The probabilities, that decompose the problem into K single-facility location problems, are updated at each iteration together with the facility locations. The proposed method is a natural generalization of the Weiszfeld method to several facilities.     

Leadership Hijacking in Docker Swarm and Its Consequences

With the advent of microservice-based software architectures, an increasing number of modern cloud environments and enterprises use operating system level virtualization, which is often referred to as container infrastructures. Docker Swarm is one of the most popular container orchestration infrastructures, providing high availability and fault tolerance. Occasionally, discovered container escape vulnerabilities allow adversaries to execute code on the host operating system and operate within the cloud infrastructure. We show that Docker Swarm is currently not secured against misbehaving manager nodes. This allows a high impact, high probability privilege escalation attack, which we refer to as leadership hijacking, the possibility of which is neglected by the current cloud security literature. Cloud lateral movement and defense evasion payloads allow an adversary to leverage the Docker Swarm functionality to control each and every host in the underlying cluster. We demonstrate an end-to-end attack, in which an adversary with access to an application running on the cluster achieves full control of the cluster. To reduce the probability of a successful high impact attack, container orchestration infrastructures must reduce the trust level of participating nodes and, in particular, incorporate adversary immune leader election algorithms.