Combustion dynamics in steady compressible flows

We study the evolution of a reactive field advected by a one-dimensional compressible velocity field and subject to an ignition-type nonlinearity. In the limit of small molecular diffusivity the problem can be described by a spatially discretized system, and this allows for an efficient numerical simulation. If the initial field profile is supported in a region of size l < lc one has quenching, i.e., flame extinction, where lc is a characteristic length-scale depending on the system parameters (reacting time, molecular diffusivity and velocity field). We derive an expression for lc in terms of these parameters and relate our results to those obtained by other authors for different flow settings.Comment: 6 pages, 5 figure

Nano-Scale Hydroxyapatite: Synthesis, Two-Dimensional Transport Experiments, and Application for Uranium Remediation

Synthetic nano-scale hydroxyapatite (NHA) was prepared and characterized using X-ray diffraction (XRD) and scanning electron microscopy (SEM) methods. The XRD data confirmed that the crystalline structure and chemical composition of NHA correspond to Ca5OH(PO4)3. The SEM data confirmed the size of NHA to be less than 50 nm. A two-dimensional physical model packed with saturated porous media was used to study the transport characteristics of NHA under constant flow conditions. The data show that the transport patterns of NHA were almost identical to tracer transport patterns. This result indicates that the NHA material can move with water like a tracer, and its movement was neither retarded nor influenced by any physicochemical interactions and/or density effects. We have also tested the reactivity of NHA with 1 mg/L hexavalent uranium (U(VI)) and found that complete removal of U(VI) is possible using 0.5 g/L NHA at pH 5 to 6. Our results demonstrate that NHA has the potential to be injected as a dilute slurry for in situ treatment of U(VI)-contaminated groundwater systems

New data on the kinetics and governing factors of the spall fracture of metals

This paper presents two examples of significant departures from usual trends of varying the resistance to spall fracture (spall strength) with changing loading history, load duration and peak shock stress. In experiments with vanadium single crystals we observed an important decrease of spall strength when increasing the shock stress. This was interpreted in terms of disruption of the matter homogeneity as a result of its twinning at shock compression. In experiments with 12Kh18N10T austenitic stainless steel we observed a sharp increase of recorded spall strength value when short load pulses of a triangular profile were replaced by shock pulses of long duration having a trapezoidal shape. This anomaly is associated with formation of the deformation-induced martensitic phase

Endomorphisms of quantized Weyl algebras

Belov-Kanel and Kontsevich conjectured that the group of automorphisms of the n'th Weyl algebra and the group of polynomial symplectomorphisms of C^2 are canonically isomorphic. We discuss how this conjecture can be approached by means of (second) quantized Weyl algebras at roots of unity

A PROSPECTIVE CONTROLLED STUDY OF LOW BACK SCHOOL IN THE GENERAL POPULATION

There are no data on the efficacy of a back school in primary prevention of back pain in the general population or on the characteristics of the population who volunteers. After announcement in the local press, 494 healthy adults volunteered and paid for a back school course in Switzerland. A total of 371 controls were matched for sex, age, profession, nationality and back pain. A statistically significant decrease in numbers of doctor's visits was found by the participants during the following 6 months compared with the controls. However, there were no significant between-group differences in the four remaining parameters (presence and intensity of back pain, drug intake and sick leave). Three-quarters of participants changed their attitudes after the back school. Volunteering for a back pain prevention programme was associated with the presence of back pain problems. Reasons for volunteering are further discussed. Overall, the results of this study showed that a back school for the general population may not solve the problem of low back pain, but improves self-help in a subgroup of the populatio

Response of Seven Crystallographic Orientations of Sapphire Crystals to Shock Stresses of 16 to 86 GPa

Shock-wave profiles of sapphire (single-crystal Al2O3) with seven crystallographic orientations were measured with time-resolved VISAR interferometry at shock stresses in the range 16 to 86 GPa. Shock propagation was normal to the surface of each cut. The angle between the c-axis of the hexagonal crystal structure and the direction of shock propagation varied from 0 for c-cut up to 90 degrees for m-cut in the basal plane. Based on published shock-induced transparencies, shock-induced optical transparency correlates with the smoothness of the shock-wave profile. The ultimate goal was to find the direction of shock propagation in sapphire that is most transparent as a window. Particle velocity histories were recorded at the interface between a sapphire crystal and a LiF window. In most cases measured wave profiles are noisy as a result of heterogeneity of deformation. Measured values of Hugoniot Elastic Limits (HELs) depend on direction of shock compression and peak shock stress. The largest HEL values were recorded for shock loading along the c-axis and perpendicular to c along the m-direction. Shock compression along the m- and s-directions is accompanied by the smallest heterogeneity of deformation and the smallest rise time of the plastic shock wave. m- and s-cut sapphire most closely approach ideal elastic-plastic flow, which suggests that m- and s-cut sapphire are probably the orientations that remains most transparent to highest shock pressures. Under purely elastic deformation sapphire has very high spall strength, which depends on load duration and peak stress. Plastic deformation of sapphire causes loss of its tensile strength.Comment: 18 pages, 18 figure

Spall fracture and twinning in laser shock-loaded single-crystal magnesium

As a major failure process in materials subjected to dynamic loading, spall fracture is one of the most widely studied issues in shock physics. To investigate its dependence on the microstructure, including both initial and shock-induced features, laser shock experiments were performed on single crystal magnesium. Shock loading was applied in directions parallel and perpendicular to the c-axis of the crystals. Both the spall strength and the fracture surface morphology are found to depend on the direction of the shock application with respect to crystal orientations. The results complement data obtained previously over ranges of lower strain rates. A detailed analysis of the residual microstructure and crack patterns in the recovered samples shows strong correlations between damage localization and twins, both pre-existing and shock-induced. Thus, cracks match specific twinning directions, which is discussed on the basis of deformation mechanisms reported under quasi-static loading conditions, either prismatic slip or twinning depending on local orientations

Peculiarities of evolutions of elastic-plastic shock compression waves in different materials

In the paper, we discuss such unexpected features in the wave evolution in solids as strongly nonlinear uniaxial elastic compression in a picosecond time range, a departure from self-similar development of the wave process which is accompanied with apparent sub-sonic wave propagation, changes of shape of elastic precursor wave as a result of variations in the material structure and the temperature, unexpected peculiarities of reflection of elastic-plastic waves from free surface

Metallic liquid hydrogen and likely Al2O3 metallic glass

Dynamic compression has been used to synthesize liquid metallic hydrogen at 140 GPa (1.4 million bar) and experimental data and theory predict Al2O3 might be a metallic glass at ~300 GPa. The mechanism of metallization in both cases is probably a Mott-like transition. The strength of sapphire causes shock dissipation to be split differently in the strong solid and soft fluid. Once the 4.5-eV H-H and Al-O bonds are broken at sufficiently high pressures in liquid H2 and in sapphire (single-crystal Al2O3), electrons are delocalized, which leads to formation of energy bands in fluid H and probably in amorphous Al2O3. The high strength of sapphire causes shock dissipation to be absorbed primarily in entropy up to ~400 GPa, which also causes the 300-K isotherm and Hugoniot to be virtually coincident in this pressure range. Above ~400 GPa shock dissipation must go primarily into temperature, which is observed experimentally as a rapid increase in shock pressure above ~400 GPa. The metallization of glassy Al2O3, if verified, is expected to be general in strong oxide insulators. Implications for Super Earths are discussed.Comment: 8 pages, 5 figures, 14th Liquid and Amorphous Metals Conference, Rome 201

Flame Enhancement and Quenching in Fluid Flows

We perform direct numerical simulations (DNS) of an advected scalar field which diffuses and reacts according to a nonlinear reaction law. The objective is to study how the bulk burning rate of the reaction is affected by an imposed flow. In particular, we are interested in comparing the numerical results with recently predicted analytical upper and lower bounds. We focus on reaction enhancement and quenching phenomena for two classes of imposed model flows with different geometries: periodic shear flow and cellular flow. We are primarily interested in the fast advection regime. We find that the bulk burning rate v in a shear flow satisfies v ~ a*U+b where U is the typical flow velocity and a is a constant depending on the relationship between the oscillation length scale of the flow and laminar front thickness. For cellular flow, we obtain v ~ U^{1/4}. We also study flame extinction (quenching) for an ignition-type reaction law and compactly supported initial data for the scalar field. We find that in a shear flow the flame of the size W can be typically quenched by a flow with amplitude U ~ alpha*W. The constant alpha depends on the geometry of the flow and tends to infinity if the flow profile has a plateau larger than a critical size. In a cellular flow, we find that the advection strength required for quenching is U ~ W^4 if the cell size is smaller than a critical value.Comment: 14 pages, 20 figures, revtex4, submitted to Combustion Theory and Modellin