Shock and traveling wave phenomena on an externally damped, non-linear string

We examine the propagation of shocks and traveling wave phenomena on a one-dimensional string that is executing finite-amplitude, transverse vibrations in a resisting medium. As part of our study, we develop an approach that allows us to describe, albeit approximately, the evolution and propagation of a shock front using analytical methods. In addition, exact traveling wave solutions, one of which involves the Lambert W-function, of the string's equation of motion are determined and analyzed. Lastly, a possible new form of the solution to the linearized problem is presented and extensions and other applications of the present work are briefly discussed.     

Identification of stiffness, dissipation and input parameters of randomly excited non-linear systems: Capability of restricted potential models (RPM)

A dynamic identification technique in the time domain for time invariant systems under random external forces is presented. This technique is based on the use of the class of restricted potential models (RPM), which are characterized by a non-linear stiffness and a special form of damping, that is a product of the input power spectral density (PSD) matrix and the velocity gradient of a non-linear function of the total mechanical energy. By applying -s2.0-S0020746206000989-si21.gif"> stochastic differential calculus and by specific analytical manipulations, some algebraic equations, depending on the response statistics and on the mechanic parameters that characterize RPM, are obtained. These equations can be used for the dynamic identification of the above mechanic parameters once the response statistics of the system to be identified are evaluated. The proposed technique allows one to identify single-degree-of-freedom or multi-degrees-of-freedom systems in the case of unmeasurable input. Further, the probabilistic characteristics of the external forces can be completely estimated in terms of PSD matrix.     

Shocks and slip systems: Predictions from a mesoscale theory of continuum dislocation dynamics

Exploring a recently developed mesoscale continuum theory of dislocation dynamics, we derive three predictions about plasticity and grain boundary formation in crystals. (1) There is a residual stress jump across grain boundaries and plasticity-induced cell walls as they form, which self-consistently acts to attract neighboring dislocations; residual stress in this theory appears as a remnant of the driving force behind wall formation under both polygonization and plastic deformation. We derive the predicted asymptotic late-time dynamics of the grain-boundary formation process. (2) During grain boundary formation at high temperatures, there is a predicted cusp in the elastic energy density. (3) In early stages of plasticity, when only one type of dislocation is active (single-slip), cell walls do not form in the theory; instead we predict the formation of a hitherto unrecognized jump singularity in the dislocation density.     

Hydrodynamics of reactive systems: Chemical reactions near the critical points

The rate of a chemical reaction is expressed in terms of the correlation functions which are found from the full system of hydrodynamic equations in reactive systems. In the limiting cases one obtains all three types of behavior of reaction rates near the critical points found in experiments (slowing-down, speeding-up, insensitivity to criticality). This behavior depends on the number of reactive and inert components in a system, proximity and path of approach to the critical point.     

Local variation of the dielectric properties of poly(vinylidene fluoride) during the α- to β-phase transformation

The phase transformation from the non-polar α-phase to the polar electroactive β-phase of polyvinylidene fluoride (PVDF) has been investigated using the fluorescence from Nile red. Films of α-PVDF doped with Nile red were stretched at controlled rates at a temperature of 80 °C to produce the α- to β-phase transition. The thermo/mechanical dependent changes in the crystalline structure are related to the physical rotation of the polar (CH₂-CF₂) group, which can be monitored by steady state fluorescence techniques. The degree of phase transformation is related to variation in the fluorescence, which in turn is linked to local dielectric constant of the polymer. The variation of the refractive index is more associated to the alignment of the polymeric chains than to the phase transformation. Thus, fluorescence is a suitable technique to monitor phase transitions coupled to a variation in the polarity of the dielectric medium.     

A black hole with quantum core

A model black hole, holding a ‘quantum core’ characterized by the Planck order matter density, is revisited here. Based on the quantum improved Newton’s potential drawn out of the loop quantum cosmology we propose a Schwarzschild class, quantum improved black hole line-element that upholds the existence of Planck-dense quantum matter core. Causality is kept preserved in this proposal. Quite in a natural way the quantum core emerges closely homogeneous in its interior matter distribution. The radius of the quantum core turns out to be necessarily proportional to one-third power of the black hole mass. Hawking process of black hole evaporation leads to a shrinking quantum core, and as the mass of black hole approaches near about the Planck mass, the rate of evaporation diminishes rapidly and eventually leaves a cold remnant having a Planck order mass. Proposed model supports the standard quantum geometrical logarithmic correction to black hole entropy-area law.     

Hawking Radiation from Topological Kerr Anti-de-Sitter Black Hole with One Rotational Parameter via Covariant Anomalies

Using anomalous viewpoint, we study the Hawking radiation from a kind of topological Kerr Anti-de-Sitter （Kerr-AdS） black hole with one rotational parameter. We employ the covariant gauge and gravitational anomalies. The result supports the Robinson-Wilczek opinion and shows that the Hawking temperature can be correctly determined by cancelling covariant gauge and gravitational anomalies at the horizon.     

（Na0.52K0.44Li0.04）Nb0.9-xSbxTa0.1O3 Lead-Free Piezoelectric Ceramics with High Performance and High Curie Temperature

（Na0.52K0.44Li0.04）Nb0.9-x Sbx Ta0.1O3 lead-free piezoelectric ceramics are prepared by a solid-state reaction method. With increasing Sb content, the transition temperature from orthorhombic to tetragonal polymorphic phase decreased. A composition （Na0.52K0.44Li0.04）Nb0.863Sb0.037Ta0.1O3 is found to possess excellent piezo- electric and electromechanical performances （d33 = 306pC/N, kp =48%, and kt=50%）, and high Curie temperature （Tc = 320 ℃）. These results indicate that （Na0.52K0.44Li0.04）Nb0.863Sb0.037 Ta0.1O3 is a promising lead-free piezoceramics replacement for lead zirconate titanate.     

Effects of Li Substitution and Sintering Temperature on Properties of Bi0.5（Na,K）0.5TiO3 Lead-Free Piezoelectric Ceramics

Bi0.5 （Na0.72K0.28- x Lix ）0.5 TiO3 （BNKLT- 100x） lead-free piezoelectric ceramics are synthesized by conventional solid state sintering techniques. The dielectric and piezoelectric properties of the BNKLT-100x ceramics as a function of Li content are systematically investigated. It is found that not only Li content but also the sintering temperature has a strong effect on the piezoelectric properties of BNKLT. The piezoelectric constant d33 Of BNKLT varies from 120 to 252pC/N in the Li content range from 0.03 to 0.16. In the sintering temperature range from 1080 to 1130℃, the d33 value of BNKLT-6 changes from 200pC/N to 252pC/N. The BNKLT-6 sample sintered at 1100℃ has the highest piezoelectric constant d33 of 252pC/N, with the electromechanical coupling factors kp of 0.32 and kt of 0.44.     

Effect of Elongation on Critical Gradient for Toroidal Electron Temperature Gradient Modes

The electron temperature gradient mode is investigated in elongated toroidal plasmas with a gyrokinetic integral eigenmode equation code. Dependence of the critical electron temperature gradient on the elongation is calculated. It is found that when the elongation increases, the growth rate spectrum is greatly shifted towards shorter poloidal wavelength, and then the poloidal wavenumber at which the mode is destabilizing critically in elongated plasmas will be larger than that in circular plasmas.