Kramers Escape Rate in Nonlinear Diffusive Media

In this paper, we study nonlinear Kramers problem by investigating overdamped systems ruled by the one-dimensional nonlinear Fokker-Planck equation. We obtain an analytic expression for the Kramers escape rate under quasistationary conditions by employing

Stress Wave Propagation in a Gradient Elastic Medium

The gradient elastic constitutive equation incorporating the second gradient of the strains is used to determine the monochromatic elastic plane wave propagation in a gradient infinite medium and thin rod. The equation of motion, together with the internal material length, has been derived. Various dispersion relations have been determined. We present explicit expressions for the relationship between various wave speeds, wavenumber and internal material length.

Ice induced low temperature fatigue crack propagation in offshore structural steel A131

To investigate the low temperature fatigue crack propagation behavior of offshore structural steel A131 under random ice loading, three ice failure modes that are commonly present in the Bohai Gulf are simulated according to the vibration stress responses induced by real ice loading. The test data are processed by a universal software FCPUSL developed on the basis of the theory of fatigue crack propagation and statistics. The fundamental parameter controlling the fatigue crack propagation induced by random ice loading is determined to be the amplitude root mean square stress intensity factor K-arm. The test results are presented on the crack propagation diagram where the crack growth rate da/dN is described as the function of K-arm. It is evident that the ice failure modes have great influence on the fatigue crack propagation behavior of the steel in ice-induced vibration. However, some of the experimental phenomena and test results are hard to be physically explained at present. The work in this paper is an initial attempt to investigate the cause of collapse of offshore structures due to ice loading.

A probabilistic model for fatigue crack propagation analysis

A simple probabilistic model for predicting crack growth behavior under random loading is presented. In the model, the parameters c and m in the Paris-Erdogan Equation are taken as random variables, and their stochastic characteristic values are obtained through fatigue crack propagation tests on an offshore structural steel under constant amplitude loading. Furthermore, by using the Monte Carlo simulation technique, the fatigue crack propagation life to reach a given crack length is predicted. The tests are conducted to verify the applicability of the theoretical prediction of the fatigue crack propagation.

Dynamic analysis of arrest of buckle propagation on a beam on a nonlinear elastic foundation by FEM

Based on the dynamic governing equation of propagating buckle on a beam on a nonlinear elastic foundation, this paper deals with an important problem of buckle arrest by combining the FEM with a time integration technique. A new conclusion completely different from that by the quasi-static analysis about the buckle arrestor design is drawn. This shows that the inertia of the beam cannot be ignored in the analysis under consideration, especially when the buckle propagation is suddenly stopped by the arrestors.

Fatigue crack-growth rate in ferrite martensite dual-phase steel

An empirical study is made on the fatigue crack growth rate in ferrite-martensite dual-phase (FMDP) steel. Particular attention is given to the effect of ferrite content in the range of 24.2% to 41.5% where good fatigue resistance was found at 33.8%. Variations in ferrite content did not affect the crack growth rate when plotted against the effective stress intensity factor range  which was assumed to follow a linear relation with the crack tip stress intensity factor range ΔK. A high  corresponds to uniformly distributed small size ferrite and martensite. No other appreciable correlation could be ralated to the microstructure morphology of the FMDP steel. The closure stress intensity factor , however, is affected by the ferrite content with  reaching a maximum value of 0.7. In general, crack growth followed the interphase between the martensite and ferrite.

Dividing the fatigue crack growth process into Stage I and II where the former would be highly sensitive to changes in ΔK and the latter would increase with ΔK depending on the  ratio. The same data when correlated with the strain energy density factor range ΔS showed negligible dependence on mean stress or R ratio for Stage I crack growth. A parameter α involving the ratio of ultimate stress to yield stress, percent reduction of area and R is introduced for Stage II crack growth so that the  data for different R would collapse onto a single curve with a narrow scatter band when plotted against αΔS.

Effect of grain size on slow fatigue crack propagation and plastic deformation near crack tip

Fatigue crack growth and its threshold are investigated at a stress ratio of 0.5 for the three-point bend specimen made of Austenitic stainless steel. The effect of grain size on the crack tip plastic deformation is investigated. The results show that the threshold value Δkth increases linearly with the square root of grain size d and the growth rate is slower for materials with larger grain size. The plastic zone size and ratio for different grain sizes are different at the threshold. The maximum stress intensity factor is kmax and σys is the yield strength. At the same time, the characteristics of the plastic deformation development is discontinuous and anti-symmetric as the growth rate is increased from 2·10—8 to 10−7 mm/cycle.

Microscopic theory of chemical-reaction rate

In this paper we deduce the formulae for rate-constant of microreaction with high resolving power of energy from the time-dependent Schrdinger equation for the general case when there is a depression on the reaetional potential surface (when the depression is zero in depth, the case is reduced to that of Eyring). Based on the assumption that Bolzmann distribution is appropriate to the description of reactants, the formula for the constant of macrorate in a form similar to Eyring's is deduced and the expression for the coefficient of transmission is given. When there is no depression on the reactional potential surface and the coefficient of transmission does not seriously depend upon temperature, it is reduced to Eyring's. Thus Eyring's is a special case of the present work.

The propagation and deposition of fast muons in dense DT mixture

The propagation of the fast muon population mainly due to collisional effect in a dense deuterium-tritium (DT for short) mixture is investigated and analysed within the framework of the relativistic Fokker-Planck equation. Without the approximation that the muons propagate straightly in the DT mixture, the muon penetration length, the straggling length, and the mean transverse dispersion radius are calculated for different initial energies, and especially for different densities of the densely compressed DT mixture in our suggested muon-driven fast ignition (FI). Unlike laser-driven FI requiring super-high temperature, muons can catalyze DT fusion at lower temperatures and may generate an ignition sparkle before the self-heating fusion follows. Our calculation is important for the feasibility and the experimental study of muon-driven FI.

Self-focusing, Raman, and modulation instability of shaped relativistic laser pulse in plasmas

The interaction of shaped laser pulses with plasmas is studied in a strict theoretical framework without adopting the slow-varying envelope approximation (SVEA). Any physical quantities involved in the interaction are denoted as a summation of different real quantities of respective phases. The relationships among the phases of those real quantities and their moduli are strictly analyzed. Such strict analyses lead to a more exact equation set for the three-dimensional envelope of the laser pulse, which is not based on SVEA. Based on this equation set, self-focusing, Raman, and modulation instabilities could be discussed in a unified framework. The solutions of this equation set for the laser envelope reveal many possible multicolor laser modes in plasmas. The energy and the shape of a pulse determine its propagation through plasmas in a multicolor mode or in a monochromic mode. A global growth rate is introduced to measure the speed of the transition from the monochromic mode in vacuum to a possible mode in plasmas. (c) 2006 American Institute of Physics.

Nonlinear propagation of ultraslow pulses in media with electromagnetically induced transparency

The nonlinear behavior of a probe pulse propagating in a medium with electromagnetically induced transparency is studied both numerically and analytically. A new type of nonlinear wave equation is proposed in which the noninstantaneous response of nonlinear polarization is treated properly. The resulting nonlinear behavior of the propagating probe pulse is shown to be fundamentally different from that predicted by the simple nonlinear Schrodinger-like wave equation that considers only instantaneous Kerr nonlinearity. (c) 2005 Optical Society of America.

Influence of temperature and salinity fluctuations on propagation behaviour of partially coherent beams in oceanic turbulence

A theoretical study of the behaviour of partially coherent beams propagating through oceanic turbulence has been performed. Based on the previously developed knowledge of beam spreading of a partially coherent beam in the atmosphere and the spatial power spectrum of the refractive index of ocean water, we study the normalized root-mean-square width of a partially coherent beam on propagation through oceanic turbulence and its turbulence distance which may be a measure of turbulence resistance. Our analysis indicates that the behaviour of partially coherent beams on propagation may be described by the rate of dissipation of the mean-squared temperature chi(T) and that of salinity chi(S). In terms of a quantity w that defines the contributions of the temperature and salinity distributions to the distribution of the refractive index, chi(S) could be written as a function of chi(T) and w. Therefore, the behaviour of partially coherent beams on propagation can be characterized only by chi(T) for a given w. The results are shown for curved surfaces, from which one can see that partially coherent beams exhibit robust turbulence resistance when the water volume has a smaller chi(T).

Corrections to the paraxial approximation of an arbitrary free-propagation beam

A relatively simple transform from an arbitrary solution of the paraxial wave equation to the corresponding exact solution of the Helmholtz wave equation is derived in the condition that the evanescent waves are ignored and is used to study the corrections to the paraxial approximation of an arbitrary free-propagation beam. Specifically, the general lowest-order correction field is given in a very simple form and is proved to be exactly consistent with the perturbation method developed by Lax et nl. [Phys. Rev. A 11, 1365 (1975)]. Some special examples, such as the lowest-order correction to the paraxial approximation of a fundamental Gaussian beam whose waist plane has a parallel shin from the z = 0 plane, are presented. (C) 1998 Optical Society of America.

Calculation of propagation loss in photonic crystal waveguides by FDTD technique and Pade approximation

The propagation losses in single-line defect waveguides in a two-dimensional (2D) square-lattice photonic crystal (PC) consisted of infinite dielectric rods and a triangular-lattice photonic crystal slab with air holes are studied by finite-difference time-domain (FDTD) technique and a Pade approximation. The decaying constant beta of the fundamental guided mode is calculated from the mode frequency, the quality factor (Q-factor) and the group velocity v(g) as beta = omega/(2Qv(g)). In the 2D square-lattice photonic crystal waveguide (PCW), the decaying rate ranged from 10(3) to 10(-4) cm(-1) can be reliably obtained from 8 x 10(3)-item FDTD output with the FDTD computing time of 0.386 ps. And at most 1 ps is required for the mode with the Q-factor of 4 x 10(11) and the decaying rate of 10(-7) cm(-1). In the triangular-lattice photonic crystal slab, a 10(4)-item FDTD output is required to obtain a reliable spectrum with the Q-factor of 2.5 x 10(8) and the decaying rate of 0.05 cm(-1). (c) 2004 Elsevier B.V. All rights reserved.

Calculation of the current noise spectrum in mesoscopic transport: A quantum master equation approach

Based on our recent work on quantum transport [X. Q. Li , Phys. Rev. B 71, 205304 (2005)], we show how an efficient calculation can be performed for the current noise spectrum. Compared to the classical rate equation or the quantum trajectory method, the proposed approach is capable of tackling both the many-body Coulomb interaction and quantum coherence on an equal footing. The practical applications are illustrated by transport through quantum dots. We find that this alternative approach is in a certain sense simpler and more straightforward than the well-known Landauer-Buttiker scattering matrix theory.