Transient response of structures with uncertain properties to nonlinear shock loading

A method is presented to predict the transient response of a structure at the driving point following an impact or a shock loading. The displacement and the contact force are calculated solving the discrete convolution between the impulse response and the contact force itself, expressed in terms of a nonlinear Hertzian contact stiffness. Application of random point process theory allows the calculation of the impulse response function from knowledge of the modal density and the geometric characteristics of the structure only. The theory is applied to a wide range of structures and results are experimentally verified for the case of a rigid object hitting a beam, a plate, a thin and a thick cylinder and for the impact between two cylinders. The modal density of the flexural modes for a thick slender cylinder is derived analytically. Good agreement is found between experimental, simulated and published results, showing the reliability of the method for a wide range of situations including impacts and pyroshock applications. © 2013 Elsevier Ltd. All rights reserved.

Nonlinear Rashba model and spin relaxation in quantum wells

We find that the Rashba spin splitting is intrinsically a nonlinear function of the momentum, and the linear Rashba model may overestimate it significantly, especially in narrow-gap semiconductors. A nonlinear Rashba model is proposed, which is in good agreement with the numerical results from the eight-band k center dot p theory. Using this model, we find pronounced suppression of the D'yakonov-Perel' spin relaxation rate at large electron densities, and a nonmonotonic dependence of the resonance peak position of the electron spin lifetime on the electron density in [111]-oriented quantum wells, both in qualitative disagreement with the predictions of the linear Rashba model.

Linear and nonlinear intersubband optical properties in a step quantum well with an applied electric field

Within the framework of the effective-mass envelope-function theory, the field-dependent intersubband optical properties of a Al0.4Ga0.6As/Al0.2Ga0.8As/GaAs step quantum well are investigated theoretically based on the periodic boundary condition. A very large Stark shift occurs when the lowest subband electron remains confined to the small well while the higher subband electron confined to the big well. The optical nonlinearity in a step well due to resonant intersubband transition (ISBT) is analyzed using a density-matrix approach. The second-harmonic generation coefficient chi(2 omega)((2)) and nonlinear optical rectification chi(0)((2)) have also been investigated theoretically. The results show that the ISBT in a step well can generate very large second order optical nonlinearities, chi(0)((2)) and chi(2 omega)((2)) can be tuned by the electric field over a wide range.

Z-scan theory based on a diffraction model

Based on Fresnel-Mrchhoff diffraction theory, a diffraction model of nonlinear optical media interacting with a Gaussian beam has been set up that can interpret the Z-scan phenomenon in a new way. This theory not only is consistent with the conventional Z-scan theory for a small nonlinear phase shift but also can be used for larger nonlinear phase shifts. Numerical computations indicate that the shape of the Z-scan curve is greatly affected by the value of the nonlinear phase shift. The symmetric dispersionlike Z-scan curve is valid only for small nonlinear p base shifts (\Deltaphi(0)\ < pi), but, with increasingly larger nonlinear phase shifts, the valley of the transmittance is severely suppressed and the peak is greatly enhanced. The power output through the aperture will oscillate with increasing nonlinear phase shift caused by the input laser power. The aperture transmittance will attenuate and saturate with increasing Kerr constant. (C) 2003 Optical Society of America.

Superfluid nuclear matter in BCS theory and beyond

Medium polarization effects are studied for S-1(0) pairing in nuclear matter within BHF approach. The screening potential is calculated in the RPA limit, suitably renormalized to cure the low density mechanical instability of nuclear matter. The self-energy corrections are consistently included resulting in a strong depletion of the Fermi surface. The self-energy effects always lead to a quenching of the gap, whereas it is almost completely compensated by the anti-screening effect in nuclear matter.

Topological objects in the O(3) nonlinear sigma model

We study the topological defects in the nonlinear O(3) sigma model in terms of the decomposition of U(1) gauge potential. Time-dependent baby skyrmions are discussed in the (2 + 1)-dimensional spacetime with the CP1 field. Furthermore, we show that there are three kinds of topological defects-vortex lines, point defects and knot exist in the (3 + 1)-dimensional model, and their topological charges, locations and motions are determined by the phi-mapping topological current theory.

Improved BCS-type pairing for the relativistic mean-field theory

A density-dependent delta interaction (DDDI) is proposed in the formalism of BCS-type pairing correlations for exotic nuclei whose Fermi surfaces are close to the threshold of the unbound state. It provides the possibility to pick up those states whose wave functions are concentrated in the nuclear region by making the pairing matrix elements state dependent. On this basis, the energy level distributions, occupations, and ground-state properties are self-consistently studied in the RMF theory with deformation. Calculations are performed for the Sr isotopic chain. A good description of the total energy per nucleon, deformations, two-neutron separation energies and isotope shift from the proton drip line to the neutron drip line is found. Especially, by comparing the single-particle structure from the DDDI pairing interaction with that from the constant pairing interaction for a very neutron-rich nucleus it is demonstrated that the DDDI pairing method improves the treatment of the pairing in the continuum.

Self-assembly of star block copolymers by dynamic density functional theory

The dynamic mean-field density functional method, driven from the generalized time-dependent Ginzburg-Landau equation, was applied to the mesoscopic dynamics of the multi-arms star block copolymer melts in two-dimensional lattice model. The implicit Gaussian density functional expression of a multi-arms star block copolymer chain for the intrinsic chemical potentials was constructed for the first time. Extension of this calculation strategy to more complex systems, such as hyperbranched copolymer or dendrimer, should be straightforward. The original application of this method to 3-arms block copolymer melts in our present works led to some novel ordered microphase patterns, such as hexagonal (HEX) honeycomb lattice, core-shell HEX lattice, knitting pattern, etc. The observed core-shell HEX lattice ordered structure is qualitatively in agreement with the experiment of Thomas [Macromolecules 31, 5272 (1998)].

Chemical bond analysis of the correlation between crystal structure and nonlinear optical properties of complex crystals

Second order nonlinear optical (NLO) properties of single crystals with complex structures are studied, from the chemical bond viewpoint. Contributions of each type of constituent chemical bond to the total linearity and nonlinearity are calculated from the actual crystal structure, using the chemical bond theory of complex crystals and the modified bond charge model. We have quantitatively proposed certain relationships between the crystal structure and its NLO properties. Several relations have been established from the calculation. Our method makes it possible for us to identify, predict and modify new NLO materials according to our needs. (C) 1999 Elsevier Science B.V. All rights reserved.

Calculation of nonlinear optical coefficients of orthorhombic Re-2(MoO4)(3) crystals

From the chemical bond viewpoint, the second-order nonlinear optical (NLO) tensor coefficients of some Re-2(MoO4)(3) (ReMO)-type tare earth molybdates, with Re = Pr, Nd, Sm, Eu, Gd, Tb and Dy, have been calculated by using the chemical bond theory of complex crystals and the modified bond charge model. All kinds of constituent chemical bonds are considered in the calculation. The major part of the NLO properties of these ReMO crystals is found from the ReO7 groups. The NLO coefficients of these ReMO crystals decrease with Re from Pr to Dy. (C) 1998 Elsevier Science Ltd. All rights reserved.

The role of Li-O bonds in calculations of nonlinear optical coefficients of LiXO3-type complex crystals

The second-order nonlinear optical (NLO) tenser coefficients of LiXO3 (X = I; Nb or Ta) type complex crystals have been calculated using the chemical bond theory of complex crystals. Contributions of each type of bond to the total second-order NLO coefficient d(ij) and the linear susceptibility X are quantitatively determined. All tensor values thus calculated are in good agreement with experimental data. The Li-O bonds are found to be an important group in the contributions to the total NLO tenser coefficient, especially for those in LiNbO3 and LiTaO3. The importance of Li-O bonds depends on the environment of Li atom in these crystals.

Calculation of nonlinear optical properties of KNdP4O12

The second-order nonlinear optical (NLO) tensor coefficients of KNdP4O12 (KNP) are theoretically predicted from its crystal structural data, by using the chemical bond theory of complex crystals and the modified bond charge model. Linear and nonlinear optical contributions of each type of bond to the total linearity (chi) and nonlinearity (d(ij)) of KNP are quantitatively determined. The structure-property relationship of KNP is systematically investigated, from the chemical bond viewpoint. Based on the discussion of its structural modifications, we point out that NLO properties of I(NP can be improved effectively using the doping method. Theoretical predictions show KNP to be a promising: self-frequency-doubling laser material.

Bond-charge calculation of nonlinear optical susceptibilities of LiXO3 type complex crystals

Second order nonlinear optical (NLO) tensor coefficients of LiXO3 (X = I, Nb, Ta) type crystals have been evaluated on the basis of the dielectric theory of complex crystals and the modified bond charge model. The current method is capable of calculating single bond contributions to the total second order NLO susceptibility. The tenser values thus calculated agree well with experimental data. By introducing the subformula equation and the concept of the effective charge of one valence electron, we are able to successfully treat such complex crystals as LiXO3 type compounds. In addition, the bond charge expression is modified to a more reasonable form for complex crystals. (C) 1998 Elsevier Science B.V.

Nonlinear optical properties of (B3O7)(5-) and (B3O6)(3-) groups

From the chemical bond viewpoint, LiB3O5 (LBO) crystal has been studied by using the bond valence theory of complex crystals. Chemical bond parameters and linear and nonlinear optical (NLO) properties of each type of constituent chemical bonds are quantitatively determined. Because of the different crystal structure characteristics of LBO from those of beta-BaB2O4 (BBO), the two anionic groups, (B3O7)(5-) in LBO and (B3O6)(3-) in BBO, play different roles in contributions to their own total NLO tensor coefficients of LBO and BBO, respectively. By comparison, we find that planar (B3O6)(3-) groups are the ideal structure model, leading to little cancellation of contributions of each kind of bond in these groups, and this gives us a useful guide to design new NLO materials in the future.