Number Of Order Parameters Research Articles

SMART ELECTROMAGNETIC SIMULATIONS: GUIDELINES FOR DESIGN OF EXPERIMENTS TECHNIQUE

Electromagnetic design problems usually involve a large number of varying parameters. A designer can use difierent kinds of models in order to achieve optimum design. Some models, e.g., flnite-element model, can be very precise: however, it requires large computational costs (i.e., CPU time). Therefore, the designer should use a screening process to reduce the number of parameters in order to reduce the required computational time. In this paper, using the Design of Experiments (DOE) approach to reduce the number of parameters is explored. The beneflts of this technique are tremendous. For example, once researchers realize how much insight and information can be obtained in a relatively short amount of time from a well-designed experiment, DOE would become a regular part of the way they approach their simulation projects. The main objective of this paper is to apply the DOE technique to electromagnetic simulations of difierent systems and to explore its efiectiveness on a new fleld, namely the magnetic refrigeration systems. The methodology of the DOE is presented to assess the efiects of the difierent variables and their interaction involved in electromagnetic simulations design and optimization processes.

Majorana Fermions in Non-Abelian QCD Vortices

We study the internal structure of a non-Abelian vortex in color superconductivity with respect to quark degrees of freedom. Stable non-Abelian vortices appear in the Color-FlavorLocked phase whose symmetry SU(3)C+L+R is further broken to SU(2)C+L+R ⊗ U(1)C+L+R in the vortex cores. Fermionic description of vortices is made possible by the Bogoliubov-de Gennes (B-dG) equation. Quark spectra in the vortex are obtained from the B-dG equation by treating the diquark gap having the vortex configuration as a background field. We find that there are massless modes (zero modes) well-localized around a vortex, in the triplet and singlet states of the unbroken symmetry SU(2)C+L+R. §1. Vortices in superconductors have internal structure At various scales in nature, there appear vortices, for instance, Cosmic strings in space, typhoons on Earth, water flow in a sink, and quantized vortices in superconductors and liquid Helium. The vortices that we discuss here appear at the shortest scales, the scale of strong interaction, in particular in the color-flavor locked (CFL) phase of color superconductivity in high density quark matter. All the vortices are essentially two-dimensional objects and are characterized by non-zero winding numbers of order parameters or velocity fields. However, vortices in superconductors are unique because they have non-trivial internal structure originating from their microscopic degrees of freedom. Although theoretical framework of this problem was established long time ago in the context of inhomogeneous superconductors, 1) it has been attracting people’s attention with renewed interests. One of the recent developments is the possibilities of “unconventional” superconductors where the order parameters have non-trivial symmetries. 2) It is argued that one can determine the symmetry-breaking pattern of the order parameters by looking at the vortex internal structure. In some cases called “topological” superconductors, there exists a zero-energy fermionic mode (“Majorana fermions”). On the other hand, we know several examples where massless modes are present around defects or nontrivial configuration. For instance, domain-wall fermions used in lattice QCD, fermion zero modes of the Dirac operator in the presence of instantons, and the edge modes in quantum Hall effects. Hence, it is quite a natural interest to investigate the internal structure of vortices. We have a novel type of vortices with non-Abelian symmetry, which is realized in the CFL phase of high-density quark matter. Thus, we study the internal structure of such non-Abelian vortices. 3)

Nonequilibrium umbrella sampling in spaces of many order parameters

We recently introduced an umbrella sampling method for obtaining nonequilibrium steady-state probability distributions projected onto an arbitrary number of coordinates that characterize a system (order parameters) [A. Warmflash, P. Bhimalapuram, and A. R. Dinner, J. Chem. Phys. 127, 154112 (2007)]. Here, we show how our algorithm can be combined with the image update procedure from the finite-temperature string method for reversible processes [E. Vanden-Eijnden and M. Venturoli, "Revisiting the finite temperature string method for calculation of reaction tubes and free energies," J. Chem. Phys. (in press)] to enable restricted sampling of a nonequilibrium steady state in the vicinity of a path in a many-dimensional space of order parameters. For the study of transitions between stable states, the adapted algorithm results in improved scaling with the number of order parameters and the ability to progressively refine the regions of enforced sampling. We demonstrate the algorithm by applying it to a two-dimensional model of driven Brownian motion and a coarse-grained (Ising) model for nucleation under shear. It is found that the choice of order parameters can significantly affect the convergence of the simulation; local magnetization variables other than those used previously for sampling transition paths in Ising systems are needed to ensure that the reactive flux is primarily contained within a tube in the space of order parameters. The relation of this method to other algorithms that sample the statistics of path ensembles is discussed.

Simplified simulation methods for polyphase brushless DC motors

This paper presents a simulation method for brushless DC motors. The purpose of this method is to provide a solution to the initial design process, where the simulation speed is important due to the numerous variables that have to be considered. The method requires a reduced number of parameters in order to simplify it and to facilitate the design process. It is applicable to polyphase motors regardless of its connection or phase number. The simulation method can simulate the phase current control system or a DC bus current feedback system. The later control system is widely used in low-cost brushless DC motors. The simulation method is based upon the average value modelling of the inverter leg, at the PWM scale, in different modulation conditions, modelling almost all the inverter structures with transistors as active elements. The experimental results from a seven-phase brushless DC motor with one uncontrolled phase validate the modelling method. The comparison of the average torque, the current, voltage and torque waveforms in several operating conditions shows that the simulation method can predict the comportment of a brushless DC motor without an excessive computational burden, so it can be readily used as a design tool for this kind of motor.

Tuning Range Image Segmentation by Genetic Algorithm

Several range image segmentation algorithms have been proposed, each one to be tuned by a number of parameters in order to provide accurate results on a given class of images. Segmentation parameters are generally affected by the type of surfaces (e.g., planar versus curved) and the nature of the acquisition system (e.g., laser range finders or structured light scanners). It is impossible to answer the question, which is the best set of parameters given a range image within a class and a range segmentation algorithm? Systems proposing such a parameter optimization are often based either on careful selection or on solution space-partitioning methods. Their main drawback is that they have to limit their search to a subset of the solution space to provide an answer in acceptable time. In order to provide a different automated method to search a larger solution space, and possibly to answer more effectively the above question, we propose a tuning system based on genetic algorithms. A complete set of tests was performed over a range of different images and with different segmentation algorithms. Our system provided a particularly high degree of effectiveness in terms of segmentation quality and search time.

Flexoelectric effect and statistical properties in polar liquid crystals

The structural properties and flexoelectric coefficients e 1 and e 3 of polar liquid crystals (LCs) such as 4-n-pentyl-4′-cyanobiphenyl (5CB) are studied in the nematic phase by the molecular-dynamics and statistical-mechanics methods. A number of order parameters, $$\bar P_{2L} (L = 1,2,3)$$ and $$\bar P_2 (r)$$ , and orientational correlations ξλ for the nearest and next-nearest neighbors were investigated. The calculations show the absence of spontaneous polarization $$(\bar P_1 \simeq 0)$$ in the nondeformed polar 5CB liquid crystal over the entire range of temperatures corresponding to the nematic phase. The origination of spontaneous polarization (characterized by two independent flexoelectric coefficients e 1 and e 3) in response to an external deformation of a 5CB sample is studied. The calculated e 1 and e 3 coefficients agree well with the experimental data for 5CB obtained by the pyroelectric method.

Simplified modellization of gear micropitting

This document gives a simplified method of calculating gear micropitting. The method has been developed by EUROCOPTER. The objective was to provide a model that took into consideration the maximum number of parameters in order to model the different physical phenomena, particularly: an oil-film thickness calculation taking the influence of pressure into consideration a simplified modellization of roughness an estimation of the plastification effect on the roughness overpressure at the contact surface taking into account the combined effects of roughness and oil-film thickness. The elaborated model is presented in an Excel file form. The application program is called APICS (approche du pitting par calculs simplifiés). In order to validate this model, this program has been applied to: An epicyclic gear train of a helicopter. Tests on discs as part of the ASETT European program. Discs are in hardened M50NiL Duplex (surface treatment: carburized and nitrided). Different kinds of surface finishing were proposed. The reference case of discs in 16NCD13 without thermochemical treatment has been also treated. FZG gear benchtests, also as part of the ASETT program. Gears have been manufactured in hardened M50NiL Duplex, with different kinds of surface finishing proposed. The results of the calculations express quite exactly the experimental facts observed on discs and gears for a wide range of studied cases, covering different materials, different kinds of case hardening and different kinds of surface finishing.

A theoretical study of atom ordering in copper–gold nanoalloy clusters

Energy calculations have been carried out on high symmetry icosahedral and cuboctahedral Cu–Au nanoalloy clusters of various compositions, with the interatomic interactions modelled by the Gupta many-body potential. For each composition, the lowest energy isomers (“homotops”) tend to have predominantly Au atoms on the surface and Cu atoms in the core, and this phenomenon is explained in terms of surface energy, atomic size and trends in cohesive energies. A number of order parameters and mixing energies have been introduced and it is shown that there is good correlation between the cluster binding energy and the average distance of the Au atoms from the centre of the cluster. Comparisons are made with previous theoretical calculations on Cu–Au clusters, as well as with experimental studies of the structures and atom ordering of deposited Cu–Au particles.

Realistic image synthesis of plant structures for genetic analysis

Abstract The objective of this study was to develop a systematic method to restore images of plants using a small number of parameters in order to facilitate investigation of genetic behaviour of branching patterns by computer models. Based on biological data, a generic methodology for image synthesis of plant structures was proposed. The corresponding algorithms for feature extracting and tuning were designed. Images of plant structures were synthesised with a higher accuracy by a model that was constructed using parametric L-systems. The algorithms were validated by comparing the synthetic images with the real plants. The approach makes it possible to assess the virtual architectures of plants by computer models, instead of real experiments, and to investigate the relationship between plant morphology and their genetic behaviours. This may aid the understanding of complex branching patterns that result from a plant's genetic behaviour.

Rotational viscosity in a nematic liquid crystal: a theoretical treatment and molecular dynamics simulation.

The rotational viscosity coefficient gamma(1) of 4-n-pentyl-4(')-cyanobiphenyl in the nematic phase is investigated by combination of existing statistical-mechanical approaches (SMAs), based on a rotational diffusion model and computer simulation technique. The SMAs rest on a model in which it is assumed that the reorientation of an individual molecule is a stochastic Brownian motion in a certain potential of mean torque. According to the SMAs, gamma(1) is found to be a function of temperature, density, rotational diffusion coefficient, and a number of order parameters (OPs). The diffusion coefficient and the OPs were obtained from an analysis of a trajectory generated in a molecular dynamics simulation using realistic atom-atom interactions. In addition, a set of experimentally determined diffusion coefficients and OPs was used for evaluation of gamma(1). Reasonable agreement between calculated and experimental values of gamma(1) is obtained. It is shown that near the clearing point gamma(1) is proportional to (-)P22, where (-)P2 is the second-rank OP. This limiting value of gamma(1) is in agreement with mean-field theory.

Conduction in perylene - , - and - complexes

Perylene (Per) was reacted with , and in solid-solution reactions to produce solvent-free , and . X-ray diffraction identified the unit cells of the compounds as being orthorhombic in the first two cases and tetragonal in the last case. All of the compounds exhibited an increase in resistance with decreasing temperature indicative of a semiconducting type of behaviour and had room temperature resistivities of , , and , respectively. The conduction process has been analysed by fitting the data with a number of parameters in order to account for a nonlinearity in the versus 1/T curves. The polaronic hopping model employed includes contributions of multiphonon processes, and intragrain and intergrain effects, and provides a good fit to the resistivity data as well as consistency with the results of Hall effect measurements.

Transitions to Simultaneously Incommensurateand Ferroelectric Phases When the Numberof (Proper) Order Parameters Is One

Transitions from prototypic phases to simultaneously incommensurate and ferroelectric phases are possible even when the number of (proper) order parameters is one. A case is investigated where the prototype point group is mmm and the (proper) order parameter belongs to the zero-wavenumber irreducible representation, B 2 u . A subsidiary order parameter, which is not soft like the proper one but moderately hard, is taken into account; it belongs to B 1 u . The B 2 u and B 1 u order parameters can be identified with polarization components P y and P z respectively. The free energy function contains term P y ( P z ∂ z P y - P y ∂ z P z ). This term can generate a phase incommensurate in the z direction and ferroelectric in the y direction. Sufficient conditions are found out for this ferroelectric incommensurate phase to outrival other ferroic phases in succeeding the prototypic phase.

Possibility of Semicommensurate Phases When the Corresponding Purely Incommensurate Phases Are Forbidden: A Second Type

The number of order parameters is assumed to be two, denoted by Q and Q * . The degree of anisotropy of the free energy function, Φ, in its gradientless part is assumed to be 2α with α as an integer ≥2. The preceding paper [J. Phys. Soc. Jpn. 58 (1989) 2817] clarified that, when all Lifshitz terms are forbidden, a term expressed as ( Q α + Q *α ) or ( Q α - Q *α )×( Q * ∂ z Q - Q ∂ z Q * ) can exist in Φ and can generate semicommensurateness. Following this paper, the present paper clarifies, on the assumption of α=2, that, when all Lifshitz terms and all terms of the type described above are forbidden, a term expressed as ( Q - Q * )( Q * ∂ x Q - Q ∂ x Q * )-i ( Q + Q * )( Q * ∂ y Q - Q ∂ y Q * ) can exist in Φ and can generate semicommensurateness. This clarification is performed by studying the 4/ mmm - E u case. A case of three order parameters is also studied.

Spin-orientation phase transitions in itinerant multiple spin-density-wave systems

Using a simple Landau model the authors have found six different magnetic phases: one cubic (TSDW), three tetragonal (SSDW, DSDW, ASDW) and two orthorhombic (OSDW and GSDW) phases. The above phases may be categorised by the number of order parameters and the number of non-zero magnetic moments. It is found that second-order transitions between states with different numbers of magnetic components have discontinuities in the elastic constants, whereas those maintaining the number of components have vanishing shear components. For a specific parametrisation of the authors' model they find a sequence of ground states that have identical symmetries to those found in the Mn-Ni system. The authors predict the vanishing of a shear elastic constant at one of the tetragonal-to-orthorhombic phase transitions but not the other. They also discuss an alternative microscopic model for determining the onset of the various phases. This involves the calculation of the n-point static Green functions in the long-wavelength limit for a simple one-band model.

Generalized Phase Rule and Possible Singular Point Sets in Physical Systems

There have been phase rules of coexistence point sets (Gibbs phase rule) and of critical point sets (Griffiths phase rule) in one order parameter systems. Other than these singular point sets, we have complex singular point sets like the critical end point and the critical double point which are attracting attentions recently. The generalized phase rule has been proved for all of these singluar point sets in a system with an arbitrary number of order parameters. It includes the Gibbs phase rule and the Griffiths phase rule as special cases. All possible singular point sets and their variance in relatively simple physical systems are also tabulated from the point of view of the catastrophe theory.

Second-Order Transitions from Prototypic Phases to Simultaneously Incommensurate and Ferroelectric Phases of a Newly Proposed Type

Three possible types of simultaneously incommensurate and ferroelectric phases have been proposed hitherto. In this paper a fourth type is proposed. Ferroelectric incommensurate phases of this type are due to relation P = J ( Q α Q α * - Q β Q β * ) or, more generally, P = f (| Q α | 2 ,| Q β | 2 ,| Q γ | 2 ,…), where P denotes a polarization component; J is a mere coefficient; Q α , Q α * , Q β etc. compose a degenerate set of order parameters; f is a function of any number of order parameters depending only on their absolute values and not on their arguments. These ferroelectric incommensurate phases, unlike those of the former three types, can succeed prototypic phases by second-order transition. Two imaginary examples of ferroelectric incommensurate phases of the fourth type are presented and investigated. In one of them the ferroelectric direction is perpendicular to the incommensurate direction, while in the other the two directions are parallel.

Density functional theory of freezing of the hard sphere liquid into FCC against HCP structures

The density functional theory is applied to study the freezing of the hard sphere liquid into the close packed structures. To describe the short-range correlations in the solid phases a reference liquid is introduced, whose density is fixed by a stationary condition. The thermodynamic properties of the two solid structures are calculated for increasing numbers of order parameters until convergence is achieved. According to the calculation the FCC structure is slightly more stable than the HCP one, but the difference in the grand potentials is comparable with the error of the calculation.

Recent theoretical estimates of the critical exponents

It is shown that the latest estimates of the critical exponents obtained by different methods can be represented as fractions: η=1/32 and v=17/27. New formulas are given which reproduce the values of the critical exponents for systems with various dimensionalities and numbers of order parameters.

Josephson arrays in an incommensurate magnetic field.

We study the irrationally frustrated two-dimensional XY model, which is a model for Josephson-junction arrays in an incommensurate magnetic field, and provide evidence that there is no phase transition at finite temperatures. We use the Hubbard-Stratanovich transform to construct the Landau-Ginzburg-Wilson Hamiltonian, characterized by an infinite number of order parameters, which may be expressed in the form of a continuous function of z (0\ensuremath{\le}1), the ${q}_{2}$ component of the critical mode. It is suggested that the fluctuations may be expressed in terms of an infinite number of coupled XY models. The renormalization-group idea then allows us to obtain the effective Hamiltonian in the form of a bond-diluted XY model, which in turn leads to the conclusion that there is no phase transition at finite temperatures. Also indicated is the existence of an upper bound for the transition temperature of a system with a sufficiently small rational frustration.

Real space refinement

Publisher Summary The real space refinement method (RSR) emphasis placed on ensuring the beneficial adjustments and that the canons of stereochemistry is observed in most respects even if the process stopped short of the ultimate minimum residual. The lack of atomic resolution, which makes free refinement of atomic coordinates impossible, is combated by reducing the number of positional parameters from three per atom to less than one per atom by using dihedral angles as independent variables and by incorporating filtering techniques to combat ill-conditioning. The RSR method treats the protein or other polymer as a flexible chain using only internal rotations as independent variables, the atomic coordinates being dependent on these. The objectives in so doing are the reduction of the number of parameters in order that the ratio of the number of observations to the number of parameters should be sufficiently high, and making the provision of a routine refinement procedure for proteins possible on a 32K machine (IBM 360/ 44).