We present experiments on the dynamic buckling and fragmentation of slender rods axially impacted by a projectile. By combining the results of Saint-Venant and elastic beam theory, we derive a preferred wavelength λ for the buckling instability, and experimentally verify the resulting scaling law for a range of materials including teflon, dry pasta, glass, and steel. For brittle materials, buckling leads to the fragmentation of the rod. Measured fragment length distributions show two clear peaks near λ/2 and λ/4. The non-monotonic nature of the distributions reflect the influence of the deterministic buckling process on the more random fragmentation processes.Long, thin supports are ubiquitous in natural and engineered load bearing structures, from spider legs to the steel struts of a skyscraper [1,2]. A single rod will buckle if too much force is applied along its axis, which can lead to the catastrophic failure of the structure. The buckling instability is seen at all sizes, from pole vaulting [3] to protein microtubules confined in vesicles [4] and carbon nanotube atomic force microscope probes [5]. While the classic Euler buckling of a rod is due to a static axial load [6], a different physical process occurs when the stress is applied suddenly, as during impact [7,8,9]. In this Letter, we show that this "dynamic buckling" [10] obeys a simple scaling law, which we derive by combining the approach of Saint-Venant with the classical theory of elastic rods [6,7]. For brittle rods, buckling often leads to breaking, for which we find the distribution of fragment lengths displays a unique non-monotonic shape reflecting the primary buckling instability.The process of dynamic buckling and subsequent fragmentation is illustrated in Fig. 1, in which a falling weight strikes an upright brittle rod (dry pasta). Within a fraction of a millisecond after impact, a sinusoidal perturbation appears (Fig. 1b), much different than the halfwavelength seen in Euler buckling. A few tenths of a millisecond later, the pasta has buckled appreciably and begins to shatter (Fig. 1c). This imparts angular momentum of alternating signs to the fragments, which rotate and scatter (Fig. 1d-f).Our experimental setup consists of a simple metal holder for the rod, and a pneumatic cannon in which a pressure reservoir at 60 psi delivers an impulse to a steel cylindrical projectile (1.46 cm diameter, 24.9 or 10.0 g) held at the end of a 1.5 m acrylic tube with two magnets. The holder rests on a steel plate in a sandbox which serves as a shock absorber to stop the projectile. The buckling and fragmentation dynamics were imaged by a high speed digital video camera (Phantom v5.0), capable of capturing up to 62,000 frames per second. The speed of the projectile was also measured just before impact using the video system. The materials used included dry pasta (ρ = 1.5 g/cm 3 , d = 1.1 mm and 1.9 mm) [11], borosilicate glass (ρ = 2.4 g/cm 3 , d = 2.0 mm), type 303 stainless steel (ρ = 7.9 g/cm 3 , d = 1.6 mm), and teflon (PTFE) (ρ = 2.2 g/cm 3 , d = 2.0...

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We present an experimental study of the motion of a viscoelastic micellar fluid around a moving cylinder, which ranges from fluidlike flow to solidlike tearing and fracture, depending on the cylinder radius and velocity. The observation of crack propagation driven by the cylinder indicates an extremely low tear strength, approximately equal to the steady state surface tension of the fluid. At the highest speeds a driven crack is observed in front of the cylinder, propagating with a fluctuating speed equal on average to the cylinder speed, here as low as 5% of the elastic wave speed.

Highly concentrated micelles in CTAB/NaSal solutions with a fixed salt/surfactant ratio of 0.6 have been studied using Small Angle Neutron Scattering (SANS) as a function of temperature and concentration. A worm-like chain model analysis of the SANS data using a combination of a cylindrical form factors for the polydisperse micellar length, circular cross-sectional radius with Gaussian polydispersity, and the structure factor based on a random phase approximation (RPA) suggests that these micelle solutions have a worm-like micellar structure that is independent of the concentration and temperature. The size of the micelle decreases monotonically with increasing temperature and increases with concentration. These observations indicate that large micelles are formed at low temperature and begin to break up to form smaller micelles with increasing temperature.

Abstract-Modifications in the measurement of the complex permittivity are described, based on the transmission and reflection coefficients of a dielectric slab. The measurement uses TRL twoport calibration to bring the reference planes accurately to the sample surface. The complex permittivity as a function of frequency is computed by minimizing the difference between the measured and the ideal scattering parameters. An alternative procedure for determining the complex permittivity uses the fractional linear data fitting to a Qcircle of the virtual short-circuit and/or virtual open circuit data. In that case, the sample must be a multiple of one-quarter wavelength long within the measured range of frequencies. Comparison with results obtained by other traditional procedures is provided.

Lattice dynamics and elasticity of silver thiogallate ( AgGaS 2 ) from ab initio calculations Ab initio calculations of the basic properties of solids have advanced significantly, and it is now possible to simply access a crystal structure database, and from the given constituent atoms and their positions, calculate reasonably accurate values for elastic constants and thermomechanical properties that may be derived from them. However, progress has been impeded by a unique discrepancy involving the sign of one of the elastic constants of an important material: Al 2 O 3 . In this letter, this longstanding discrepancy is resolved with experimental measurements.

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