Superposition of finite deformations in Mooney-Rivlin materials

Six controllable states are known to exist for all homogeneous, isotropic, incompressible, elastic bodies. It is shown that certain pairs of these controllable states may be superposed in Mooney-Rivlin materials thereby constructing new controllable states for these materials.

---

Zusammenfassung Es gibt sechs kontrollierbare Zustände für alle homogenen, isotropischen, inkompressiblen, elastischen Körper. Es ist gezeigt dass gewisse Paare dieser kontrollierbaren Zustände geschichtet werden können in Mooney-Rivlin Materialen und dadurch neue kontrollierbare Zustände für diese Materialen geschaffen werden.

---

---

This work was carried out while both authors were associated with the Department of Aerospace Engineering and Engineering Mechanics at The University of Texas at Austin and was supported by U.S. National Science Foundation Grant GK-37367 to that institution.     

Averaging of Noisy Nonlinear Systems with Rapidly Oscillating and Decaying Components

We consider a noisy n-dimensional nonlinear dynamical system containing rapidly oscillating and decaying components. We extend the results of Papanicolaou and Kohler and Namachchivaya and Lin; these results state that as the noise becomes smaller, a lower dimensional Markov process characterizes the limiting behavior. Our approach springs from a direct consideration of the martingale problem and considers both quadratic and cubic nonlinearities.     

Electron irradiation-enhanced core/shell organization of Al(Cr,Fe, Mn)Si dispersoids in Al–Mg–Si alloys

The age hardening 6061-T6 aluminium alloy has been chosen as structural material for the core vessel of the material testing Jules Horowitz nuclear reactor. The alloy contains incoherent Al(Cr, Fe, Mn)Si dispersoids whose characterization by energy-filtered transmission electron microscopy (EFTEM) analysis shows a core/shell organization tendency where the core is (Mn, Fe) rich, and the shell is Cr rich. The present work studies the stability of this organization under irradiation. TEM characterization on the same particles, before and after 1 MeV electron irradiation, reveals that the core/shell organization is enhanced after irradiation. It is proposed that the high level of point defects, created by irradiation, ensures a radiation-enhanced diffusion process favourable to the unmixing forces between (Fe, Mn) and Cr. Shell formation may result in the low-energy interface segregation of Cr atoms within the (Fe, Mn) system combined with the unmixing of Cr, Fe and Mn components.     

Serial Femtosecond Crystallography

X-ray free-electron lasers produce brief flashes of X-rays that are of about a billion times higher peak brightness than achievable from storage ring sources. Such a tremendous jump in X-ray source capabilities, which came in 2009 when the Linac Coherent Light Source began operations, was unprecedented in the history of X-ray science. Protein structure determination through the method of macromolecular crystallography has consistently benefited from the many increases in source performance from rotating anodes to all generations of synchrotron facilities. But when confronted with the prospects of such bright beams for structural biology, enthusiastic proposals were tempered by trepidation of the effects of such beams on samples and challenges to record data [1 M. Wilmanns, J. Synchr. Rad. 7, 41 (2000).[Crossref], [PubMed] , [Google Scholar]]. A decade after these discussions (and others in the USA) on the applications of X-ray FELs for biology, the first experiments took place at LCLS, giving results that fulfilled many of the dreams of the early visionaries. In particular, the concept that diffraction representing the pristine object could be recorded before the X-ray pulse completely vaporizes the object was validated [2 H.N. Chapman, Nature 470, 73 (2011).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]], confirming predictions [3 R. Neutze, Nature 406, 753 (2000).[Crossref], [Web of Science ®] , [Google Scholar]] that established dose limits could be vastly exceeded using femtosecond-duration pulses. The first experiments illuminated a path to achieve room-temperature structures free of radiation damage, from samples too small to provide useful data at synchrotron facilities, as well as providing the means to carry out time-resolved crystallography at femtoseconds to milliseconds. In the five years since, progress has been substantial and rapid, invigorating the field of macromolecular crystallography [4 J.C.H. Spence and H.N. Chapman, Phi. Trans. Roy. Soc. B 369, 20130309 (2014).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar], 5 I. Schlichting, IUCrJ 2, 246 (2015).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]. This phase of development is far from over, but with both the LCLS and the SPring-8 Ångström Compact Free-electron Laser (SACLA) providing facilities for measurements, the benefits of X-ray FELs are already being translated into new biological insights.     

Fractal-Generated Turbulence in Opposed Jet Flows

The opposed jet configuration presents a canonical geometry suitable for the evaluation of calculation methods seeking to reproduce the impact of strain and re-distribution on turbulent transport in reacting and non-reacting flows. The geometry has the advantage of good optical access and, in principle, an absence of complex boundary conditions. Disadvantages include low frequency flow motion at high nozzle separations and comparatively low turbulence levels causing bulk strain to exceed the turbulent contribution at small nozzle separations. In the current work, fractal generated turbulence has been used to increase the turbulent strain and velocity measurements for isothermal flows are reported with an emphasis on the axis, stagnation plane and the distribution of mean and instantaneous strain rates. Energy spectra were also determined. The instrumentation comprised hot-wire anemometry and particle image velocimetry with the flows to both nozzles seeded with 1  $\upmu$ m silicon oil droplets providing a relaxation time of ? 3 $\upmu$ s. It is shown that fractal grids increase the turbulent Reynolds number range from 48–125 to 109–220 for bulk velocities from 4 to 8 m/s as compared to conventional perforated plate turbulence generators. Low frequency motion of the order 10 Hz could not be completely eliminated and probability density functions were determined for the location of the stagnation plane. Results show that the fluctuation in the position of the stagnation plane is of the order of the integral length scale, which was determined to be 3.1±0.1 mm at the nozzle exits through the use of hot-wire anemometry. Flow statistics close to the fractal plate located upstream of the nozzle exit were also determined using a transparent glass nozzle.     

Spontaneous symmetry-breaking in the 3-D wake of a long cylinder simulated by the lattice gas method and drag coefficient measurements

We present a direct numerical simulation by the lattice gas method of the three-dimensional non-stationary incompressible flow at a Reynolds number of 74, past a circular cylinder, with a uniform incident flow. We describe the three-dimensional structure and the time-evolution of the wake, which leads to an oblique vortex shedding situation.We also present early results on measurements of drag coefficients for spheres and cylinders at a Reynolds number of 20.