Non-commutative standard model: model building

A non-commutative version of the usual electro-weak theory is constructed. We discuss how to overcome the two major problems: (1) although we can have non-commutative U(n) (which we denote by _U* (n)) gauge theory we cannot have non-commutative SU(n) and (2) the charges in non-commutative QED are quantized to just . We show how the latter problem with charge quantization, as well as with the gauge group, can be resolved by taking the gauge group and reducing the extra U(1) factors in an appropriate way. Then we proceed with building the non-commutative version of the standard model by specifying the proper representations for the entire particle content of the theory, the gauge bosons, the fermions and Higgs. We also present the full action for the non-commutative standard model (NCSM). In addition, among several peculiar features of our model, we address the inherent CP violation and new neutrino interactions. Received: 23 January 2003, Published online: 18 June 2003     

Annealedn-vectorp-spin model

A disorderedn-vector model withp spin interactions is introduced and studied in mean field theory for the annealed case. We present complete solutions for the casesn=2 andn=3, and have obtained explicit order parameter equations for all the stable solutions for arbitraryn. For alln andp we find one stable high-temperature phase and one stable low-temperature phase. The phase transition is of first order. Forn=2, it is continuous in the order parameters for p4 and has a jump discontinuity in the order parameters ifp>4. Forn=3, it has a jump discontinuity in the order parameters for allp.     

Pairing-plus-quadrupole-plus-octupole model

The octupole-octupole interaction has been added to the old pairing-plus-quadrupole model. Symmetries of the HF mean field are discussed. It is shown that under the assumption of the S-symmetry of the HF mean field, only two quadrupole and two octupole parameters have non-zero expectation values in HFB ground state. A detailed analysis of two possible approaches to the HFB treatment of the model Hamiltonian is presented.We would like to thank Prof. J. de Boer for useful comments. This work was supported by DFG Bo 1109/1 and Volkswagen Foundation.     

Quenchedn-vectorp-spin model

A disorderedn-vector model withp spin interactions previously introduced is studied for the quenched case by means of the replica method and a generalized Parisi theory. We present formal solutions for generaln andp and then study the casep . The high-temperature solution is stable at all temperatures and there is only one phase transition at a temperatureT _g. Only longitudinal lowtemperature solutions are possible. There is one spin-glass solution, and it is stable for allT _g. The phase transition atT _g is of first order and displays a jump discontinuity in the order parametersq _j ^(L) andd. The spin-glass free energy is temperature dependent forn > 1 while it is constant whenn = 1.     

Quark-resonance model

We construct an effective Lagrangian for low energy hadronic interactions through an infinite expansion in inverse powers of the low energy cutoff Λ_χ of all possible chiral invariant non-renormalizable interactions between quarks and mesons degrees of freedom arising from the bosonization of a general Nambu-Jona Lasinio type Lagrangian including all multiquark effective interactions. We restrict our analysis to the leading terms in the 1N _c expansion and to the divergent part of the resonance effective Lagrangian resulting from the integration over the quark degrees of freedom. Indeed, the effective expansion is in (Q ²/Λ _χ ² ) ^P ln(Λ _χ ² /Q ²) ^M and we show that, while the finite terms cannot be traced back to a finite number of non renormalizable interactions, the divergent ones of order (Q ²/Λ _χ ² ) ln(Λ _χ ² /Q ²) receive contributions from a finite set of 1/Λ _χ ² terms of the original quark-meson Lagrangian. These terms modify the behaviour of physical quantities in the intermediateQ ² region. We explicitely discuss their relevance for the two point vector currents Green's function.     

Combustion kinetic model development using surrogate model similarity method

An ideal combustion kinetic model needs to be validated by different experimental targets over a wide range of temperatures and pressures that represent operating conditions in real engines. However, conditions of laboratory experiments for model validation are often limited by the constraint of experimental techniques. In order to improve model predictions under certain conditions (for example, at a relatively higher pressure), it is often needed to use the experimental data obtained under other conditions. In this work, the surrogate model similarity (SMS) method is proposed to find the experimental conditions or targets for model optimisation under certain conditions where the experiments are hard to be conducted. The similarity coefficient is calculated by the cosine similarity between the characteristic coefficients (vectors) of the High Dimensional Model Representation (HDMR) models for different model predictions. A larger similarity coefficient represents a closer relationship between two model predictions. The experimental data with larger similarity coefficients could be more effective to model uncertainty reduction under the concerned conditions. To demonstrate this method, simulations were conducted for two selected combustion systems with hydrogen or methanol as the fuel. In addition to its strength in available experimental data selection for model optimization, this method can be used to screen out experimental targets with strong constraint effect beforehand, thus providing an effective way to maximise utilisation of experimental resources.     

Kinetic six-vertex model as model of bcc crystal growth

The growth of bcc crystals is studied using van Beijeren's mapping onto the six-vertex model. The growth-evaporation processes are described in terms of vertices. The time evolution is given by a master equation for the probability of the six-vertex configurations. The model, studied in the finite-size case by both Monte Carlo and analytic methods, applies to the (001) surface and its vicinal surfaces. Different growth modes (including nucleation) are found, depending on the strength of disequilibrium and on temperature, and the transition between them is investigated.On leave of absence from the Institute of Physics, Czechoslovak Academy of Science, Prague, Czechoslovakia.     

\sigma-\omega model and compressible bag model

Compressible bag model is formulated on the basis of lagrangian field theory. A specific application is done in conjunction with - model. The results are similar to Chin-Walecka model and almost reproduce our previous results. The effective nucleon mass does not become so small owing to the compressibility, in contrast to Chin-Walecka model. Received: 12 May 1998 / Revised version: 9 July 1998 / Published online: 8 September 1998     

Discrete-time Glauber model as a generalized Ehrenfest urn model

Glauber's continuous-time stochastic model for relaxation of spin systems is “imbedded” in discrete time as a Markov chain. The chain is a generalization of the Ehrenfest urn model as formulated by Hess. Some properties of the chain are discussed.     

Two-site model and its relation to the polaron-crystal model

A symmetric two-site, one-electron model is treated within perturbation theory in electron wavefunction overlap from different sites. The significant role of the double degeneracy of levels in the unperturbed Hamiltonian is pointed out. It is shown that as a result of this the terms of the perturbative expansion for the correction to the energy of an unperturbed level produce different results depending on the parity of the order. Namely, even terms give rise to a level shift (an analog of the polaron shift in the polaron-crystal model), while odd terms result in splitting (an analog of the polaron band width). Also, the shift of the levels decreases with increasing vibronic coupling constant by a power law, and their splitting, exponentially. This is in full accord with the well-known results of small-radius polaron theory. Fiz. Tverd. Tela (St. Petersburg) 39, 2159–2167 (December 1997)     

Adhesive contact: from atomistic model to continuum model

Two types of Lennard-Jones potential are widely used in modeling adhesive contacts. However, the relationships between the parameters of the two types of Lennard-Jones potential are not well defined. This paper employs a self-consistent method to derive the Lennard-Jones surface force law from the interatomic Lennard-Jones potential with emphasis on the relationships between the parameters. The effect of using correct parameters in the adhesion models is demonstrated in single sphere-flat contact via continuum models and an atomistic model. Furthermore, the adhesion hysteresis behaviour is investigated, and the S-shaped force-distance relation is revealed by the atomistic model. It shows that the adhesion hysteresis loop is generated by the jump-to-contact and jump-off-contact, which are illustrated by the S-shaped force-distance curve.     

Three-dimensional vertex model in statistical mechanics from Baxter-Bazhanov model

We find that the Boltzmann weight of the three-dimensional Baxter-Bazhanov model is dependent on four spin variables which are the linear combinations of the spins on the corner sites of the cube, and the Wu-Kadanoff-Wegner duality between the cube- and vertex-type tetrahedron equations is obtained explicitly for the Baxter-Bazhanov model. Then a three-dimensional vertex model is obtained by considering the symmetry property of the weight function, which corresponds to the three-dimensional Baxter-Bazhanov model. The vertex-type weight function is parametrized as the dihedral angles between the rapidity planes connected with the cube. We write down the symmetry relations of the weight functions under the actions of the symmetry groupG of the cube. The six angles with a constraint condition appearing in the tetrahedron equation can be regarded as the six spectra connected, with the six spaces in which the vertextype tetrahedron equation is defined.