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.

BRST invariant theory of a generalized 1+1 Dimensional nonlinear sigma model with topological term

We give a generalized Lagrangian density of 1 + 1 Dimensional O( 3) nonlinear sigma model with subsidiary constraints, different Lagrange multiplier fields and topological term, find a lost intrinsic constraint condition, convert the subsidiary constraints into inner constraints in the nonlinear sigma model, give the example of not introducing the lost constraint. N = 0, by comparing the example with the case of introducing the lost constraint, we obtain that when not introducing the lost constraint, one has to obtain a lot of various non-intrinsic constraints. We further deduce the gauge generator, give general BRST transformation of the model under the general conditions. It is discovered that there exists a gauge parameter beta originating from the freedom degree of BRST transformation in a general O( 3) nonlinear sigma model, and we gain the general commutation relations of ghost field.

Evolution induced catastrophe in a nonlinear dynamical model of material failure

In order to study the failure of disordered materials, the ensemble evolution of a nonlinear chain model was examined by using a stochastic slice sampling method. The following results were obtained. (1) Sample-specific behavior, i.e. evolutions are different from sample to sample in some cases under the same macroscopic conditions, is observed for various load-sharing rules except in the globally mean field theory. The evolution according to the cluster load-sharing rule, which reflects the interaction between broken clusters, cannot be predicted by a simple criterion from the initial damage pattern and even then is most complicated. (2) A binary failure probability, its transitional region, where globally stable (GS) modes and evolution-induced catastrophic (EIC) modes coexist, and the corresponding scaling laws are fundamental to the failure. There is a sensitive zone in the vicinity of the boundary between the GS and EIC regions in phase space, where a slight stochastic increment in damage can trigger a radical transition from GS to EIC. (3) The distribution of strength is obtained from the binary failure probability. This, like sample-specificity, originates from a trans-scale sensitivity linking meso-scopic and macroscopic phenomena. (4) Strong fluctuations in stress distribution different from that of GS modes may be assumed as a precursor of evolution-induced catastrophe (EIC).

A Nonlinear Threshold Model Applied to Spallation Analysis

Spallation in heterogeneous media is a complex, dynamic process. Generally speaking, the spallation process is relevant to multiple scales and the diversity and coupling of physics at different scales present two fundamental difficulties for spallation modeling and simulation. More importantly, these difficulties can be greatly enhanced by the disordered heterogeneity on multi-scales. In this paper, a driven nonlinear threshold model for damage evolution in heterogeneous materials is presented and a trans-scale formulation of damage evolution is obtained. The damage evolution in spallation is analyzed with the formulation. Scaling of the formulation reveals that some dimensionless numbers govern the whole process of deformation and damage evolution. The effects of heterogeneity in terms of Weibull modulus on damage evolution in spallation process are also investigated.

Threshold diversity and trans-scales sensitivity in a finite nonlinear evolution model of materials failure

We present a slice-sampling method and study the ensemble evolution of a large finite nonlinear system in order to model materials failure. There is a transitional region of failure probability. Its size effect is expressed by a slowly decaying scaling law. In a meso-macroscopic range (similar to 10(5)) in realistic failure, the diversity cannot be ignored. Sensitivity to mesoscopic details governs the phenomena. (C) 1997 Published by Elsevier Science B.V.

Failure process analysis of cement under explosive loading with a generalized driven nonlinear threshold model

The microstructural heterogeneity and stress fluctuation play important roles in the failure process of brittle materials. In this paper, a generalized driven nonlinear threshold model with stress fluctuation is presented to study the effects of microstructural heterogeneity on continuum damage evolution. As an illustration, the failure process of cement material under explosive loading is analyzed using the model. The result agrees well with the experimental one, which proves the efficiency of the model.

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.

General SU(2)(L) x SU(2)(R) x U(1)(EM) sigma model with external sources, dynamical breaking and spontaneous vacuum symmetry breaking

We give a general SU(2)(L) x SU(2)(R) x U(1)(EM) sigma model with external sources, dynamical breaking and spontaneous vacuum symmetry breaking, and present the general formulation of the model. It is found that sigma and pi(0) without electric charges have electromagnetic interaction effects coming front the internal structures. A general Lorentz transformation relative to external sources J(gauge) - (J(A mu) J(A mu)(kappa)) derived, using the general Lorentz transformation and the four-dimensional current of nuclear matter of the ground si ate with J(gauge) = 0, we give the four-dimensional general relations between the different currents of nuclear matter systems with J(gauge) not equal 0 and those with J(gauge) = 0. The relation of the density's coupling with external magnetic field is derived, which conforms well to dense nuclear matter in a strong magnetic field. We show different condensed effects in strong interaction about fermions and antifermions, and give the concrete scalar and pseudoscalar condensed expressions of sigma(0) and pi(0) bosons. About different dynamical breaking and spontaneous vacuum symmetry breaking, the concrete expressions of different mass spectra are obtained in field theory. This paper acquires the running spontaneous vacuum breaking value sigma'(0), and obtains the spontaneous vacuum breaking in tenus of the running sigma'(0), which make nucleon, sigma, and pi particles gain effective masses. We achieve both the effect of external sources and nonvanishing value of the condensed scalar and pseudoscalar paticles. It is deduced that the masses of nucleons, sigma and pi generally depend on different external sources.

Topological solitons in the CPN model

We investigate the solitons in the CPN supercript stop model in terms of the decomposition of gauge potential. Based on the phi-mapping topological current theory, the charge and position of solitons is determined by the properties of the typical component. Furthermore, the motion and the bifurcation of multi-soliton is discussed. And the knotted solitons in high dimension is explored also.

Pull-In Instability Of Micro-Switch Actuators: Model Review

The existing three widely used pull-in theoretical models (i.e., one-dimensional lumped model, linear supposition model and planar model) are compared with the nonlinear beam mode in this paper by considering both cantilever and fixed-fixed type micro and nano-switches. It is found that the error of the pull-in parameters between one-dimensional lumped model and the nonlinear beam model is large because the denominator of the electrostatic force is minimal when the electrostatic force is computed at the maximum deflection along the beam. Since both the linear superposition model and the slender planar model consider the variation of electrostatic force with the beam's deflection, these two models not only are of the same type but also own little error of the pull-in parameters with the nonlinear beam model, the error brought by these two models attributes to that the boundary conditions are not completely satisfied when computing the numerical integration of the deflection.

Nonlinear Mechanical Modeling Of Cell Adhesion

Cell adhesion, which is mediated by the receptor-ligand bonds, plays an essential role in various biological processes. Previous studies often described the force-extension relationship of receptor-ligand bond with linear assumption. However, the force-extension relationship of the bond is intrinsically nonlinear, which should have significant influence on the mechanical behavior of cell adhesion. In this work, a nonlinear mechanical model for cell adhesion is developed, and the adhesive strength was studied at various bond distributions. We find that the nonlinear mechanical behavior of the receptor-ligand bonds is crucial to the adhesive strength and stability. This nonlinear behavior allows more bonds to achieve large bond force simultaneously, and therefore the adhesive strength becomes less sensitive to the change of bond density at the outmost periphery of the adhesive area. In this way, the strength and stability of cell adhesion are soundly enhanced. The nonlinear model describes the cell detachment behavior better than the linear model. (C) 2007 Elsevier Ltd. All rights reserved.

Nonlinear Dynamic Responses of the Tensioned Tether under Parametric Excitations

The nonlinear dynamic responses of the tensioned tether subjected to combined surge and heave motions of floating platform are investigated using 2-D nonlinear beam model. It is shown that if the transverse-axial coupling of nonlinear beam model and the combined surge-heave motions of platform are considered, the governing equation is not Mathieu equation any more, it becomes nonlinear Hill equation. The Hill stability chart is obtained by using the Hill's infinite determinant and harmonic balance method. A parameter M, which is the function of tether length, the surge and heave amplitude of platform, is defined. The Hill stability chart is obviously different from Mathieu stability chart which is the specific case as M=0. Some case studies are performed by employing linear and nonlinear beam model respectively. It can be found that the results differences between nonlinear and linear model are apparent.

Antikaon condensation and deconfinement phase transition in neutron stars

Antikaon condensation and deconfinement phase transition in neutron stars are investigated in a chiral hadronic model (also referred as to the FST model) for the hadronic phase and in the MIT bag model for the deconfined quark matter phase. It is shown that the existence of quark matter phase makes antikaon condensation impossible in neutron stars. The properties of neutron stars are sensitive to the bag constant. For the small values of the bag constant, the pure quark matter core appears and hyperons are strongly suppressed in neutron stars, whereas for the large bag constant, the hadron-quark mixed phase exists in the center of neutron stars. The maximum masses of neutron stars with the quark matter phase are lower than those without the quark matter phase; meanwhile, the maximum masses of neutron stars with the quark matter phase increase with the bag constant.

The nonlinear evolution equation on the shallow water wave

Based on the variation principle, the nonlinear evolution model for the shallow water waves is established. The research shows the Duffing equation can be introduced to the evolution model of water wave with time.