Symmetry Boundary Research Articles

O(1) loop model with different boundary conditions and symmetry classes of alternating-sign matrices

We analyze the interaction of a charged relativistic particle with the electromagnetic field given by a superposition of a stationary wave and a constant magnetic field. The refraction coefficient of the medium is taken different from one. We investigate the problem in the low-signal approximation. To test the results, we used computer simulation of the original system with two scales of the variation rate of the variables taken into account.

O(1) loop model with different boundary conditions and symmetry classes of alternating-sign matrices

This work as an extension of our recent paper where we have found a numerical evidence for the fact that the numbers of the states of the fully packed loop (FPL) model with fixed link-patterns coincide with the components of the ground state vector of the dense O(1) loop model for periodic boundary conditions and an even number of sites. Here we give two new conjectures related to different boundary conditions. Namely, we suggest that the numbers of the half-turn symmetric states of the FPL model with fixed link-patterns coincide with the components of the ground state vector of the dense O(1) loop model for periodic boundary conditions and an odd number of sites and that the corresponding numbers of the vertically symmetric states describe the case of the open boundary conditions and an even number of sites.

Moving least-square interpolants in the hybrid particle method

The hybrid particle method (HPM) is a particle-based method for the solution of high-speed dynamic structural problems. In the current formulation of the HPM, a moving least-squares (MLS) interpolant is used to compute the derivatives of stress and velocity components. Compared with the use of the MLS interpolant at interior particles, the boundary particles require two additional treatments in order to compute the derivatives accurately. These are the rotation of the local co-ordinate system and the imposition of boundary constraints, respectively. In this paper, it is first shown that the derivatives found by the MLS interpolant based on a complete polynomial are indifferent to the orientation of the co-ordinate system. Secondly, it is shown that imposing boundary constraints is equivalent to employing ghost particles with proper values assigned at these particles. The latter can further be viewed as placing the boundary particle in the centre of a neighbourhood that is formed jointly by the original neighbouring particles and the ghost particles. The benefit of providing a symmetric or a full circle of neighbouring points is revealed by examining the error terms generated in approximating the derivatives of a Taylor polynomial by using a linear-polynomial-based MLS interpolant. Symmetric boundaries have mostly been treated by using ghost particles in various versions of the available particle methods that are based on the strong form of the conservation equations. In light of the equivalence of the respective treatments of imposing boundary constraints and adding ghost particles, an alternative treatment for symmetry boundaries is proposed that involves imposing only the symmetry boundary constraints for the HPM. Numerical results are presented to demonstrate the validity of the proposed approach for symmetric boundaries in an axisymmetric impact problem. Copyright © 2005 John Wiley & Sons, Ltd.

Anisotropy in Grain Boundary Thermo-Kinetics: Atomic-Scale Computer Simulations

Anisotropy in grain boundary “thermo-kinetics” is central to our understanding of microstructural evolution during grain growth and recrystallization. This paper focusses on role of atomic-scale computer simulation techniques, in particular molecular dynamics (MD), in extracting fundamental grain boundary properties and elucidating the atomic-scale mechanisms that determine these properties. A brief overview of recent strides made in extraction of grain boundary mobility and energy is presented, with emphasis on plastic strain induced boundary motion (p-SIBM) during recrystallization and curvature driven boundary motion (CDBM) during grain growth. Simulations aimed at misorientation dependence of the grain boundary properties during p-SIBM and CDBM show that boundary mobility and energy exhibit extrema at high symmetry misorientations and boundary mobility is comparatively more anisotropic during CDBM. This suggests that boundary mobility is dependent on the driving force. Qualitative observations of the atomic-scale mechanisms in play during boundary motion corroborate the simulation data. p-SIBM is dominated by motion of dislocation-interaction induced stepped structure of the grain boundaries, while correlated shuffling of group of atoms preceded by rearrangement of grain boundary free volume due to single atomic-hops across the grain boundary is frequently observed during CDBM. Comparison of the simulation results with high-purity experimental data extracted in Al indicates that while there is excellent agreement in misorientation dependent anisotropic properties, there are significant differences in values of boundary mobility and migration activation enthalpy. This strongly suggests that minute concentration of impurities retard grain boundary kinetics via impurity drag. Finally, the paper briefly discusses current and future challenges facing the computer simulation community in studying grain boundary systems in real materials where extrinsic effects (vacancy, impurity, segregation and particle effects) significantly alter the microscopic structure-mechanism relations and play a decisive role in determining the boundary properties.

Homogeneity of isostatic pressure-assisted sintering of agglomerated powder

This article is dedicated to the modeling of the pressure-assisted sintering of agglomerated powders by the grain-boundary and the surface diffusion transport. Agglomerates are treated as volumes with dense particle packing. Kinetics of sintering during consolidation is estimated by a direct numerical analysis of the matter redistribution by diffusion around a single neck between identical spherical particles. Type of packing is introduced into the model through the definition of the packing angle and a special symmetry boundary condition for diffusion fluxes. The numerical analysis of sintering parameters for a single neck allows the evaluation of macroscopic viscosities of the material for different types of the particle packing and enables the estimation of the densification rate of agglomerates and non-agglomerated elements of powder compacts. Calculations show that, despite low initial density and low initial viscosity of a loose powder around agglomerates, isostatic pressing cannot provide a complete equalization of local densities in an agglomerated powder. In all considered cases, agglomerates have reached final density faster than elements with looser packing.

CONVERGENCE OF A NUMERICAL SCHEME FOR A NONLINEAR COUPLED SYSTEM OF RADIATIVE-CONDUCTIVE HEAT TRANSFER EQUATIONS

In this paper, we prove the convergence of a numerical scheme for one-dimensional coupled system of nonlinear partial and ordinary integro-differential equations. This system describes the steady-state coupled radiative-conductive heat transfer for a non-grey anisotropically absorbing, emitting and scattering medium, with axial symmetry and nonhomogeneous Dirichlet boundary conditions. The convergence proof follows from monotonicity arguments and the application of a discrete fixed-point problem, involving only to the temperature fields.

A numerical study of confined triple flames using a flamelet-generated manifold

Laminar triple flames are investigated numerically using detailed and reduced chemical reaction mechanisms. Triple flames are believed to play an essential role in flame propagation in partially premixed systems. In order to reduce the computational cost of the simulations, the flamelet-generated manifold (FGM) method is used to simplify the chemistry model. The FGM method is based on a library of premixed laminar flamelets. Mixture fraction variations in partially premixed flames are taken into account by using the mixture fraction as an extra degree of freedom. A comparison of the results computed with FGM and with detailed chemistry shows that FGM predicts the structure of triple flames very accurately. The gradient of the mixture fraction in the unburnt mixture is varied, and its influence on the structure and propagation of triple flames is studied. For decreasing gradients, the curvature of the premixed flame branch decreases and the propagation velocity increases. Due to the diffusive nature of the flow and the use of symmetry boundary conditions in the lateral direction, high mixture fraction gradients could not be realized at the position of the flame. As a result, the trailing diffusion flame branch is only weakly present. The heat release in the premixed flame branches is two orders of magnitude higher than in the diffusion flame branch. The premixed and diffusion flame branches are studied using a flamelet analysis. Flame stretch and curvature appear to be significant in the premixed flame branch of a triple flame. These effects cause a decrease in the local mass burning rate of almost 15%. The structure of the diffusion flame branch appears to be similar to the structure of a counterflow diffusion flame with the same scalar dissipation rate.

Study of three-dimensional plasmoid dynamics by the spontaneous fast reconnection model: effects of dawn–dusk magnetic field

The dawn–dusk magnetic field component ( B z ) in the plasmoid resulting of magnetic reconnections have been observed GEOTAIL satellite. We have studied the effects by B z component in the reconnection in geomagnetotail. This paper present the results of computer simulation about them. Our recent simulation apply the spontaneous fast reconnection model to the three-dimensional (3-D) plasmoid dynamics. Previous our original 3-D computational region (the first quadrant) is extended to the second quadrant and axis symmetry boundary conditions are used. Then, various initial values of dawn–dusk magnetic field component B z can be possibly assumed. As a result in all our simulation cases: (1) a large-scale plasmoid evolves, and (2) it propagates down to the geomagnetic tail, (3) slow shocks and finite amplitude intermediate waves simultaneously stand along the resulting plasmoid boundary layer. We also found that in the plasmoid where north–south magnetic field component ( B y ) changes its sign, B z also has a considerably big value, Which is consistent with the satellite observation result. We propose that the spontaneous fast reconnection mechanism could be most applicable to substorms.

First Hybrid Turbulence Modeling for Turbine Blade Cooling

Introduction G AS turbines require proper cooling mechanisms to protect the airfoils from thermal stresses generated by exposure to hot combustion gases. The problem becomes aggravated by the growing trend to use higher turbine inlet temperatures to generate more power. Thus, film cooling is used as a cooling mechanism, and it works in the form of row of holes located in the spanwise direction, through which cold jets are issued into the hot crossflow. The penetration of cold jets into the main flow creates a complex flowfield. Systematic investigation of such flowfield started in late 1950s. Figure 1 shows the schematic of a single round jet injected in the crossflow at an angle α = 35 deg. The figure also describes the boundary conditions applied at different faces. Even though use of symmetry boundary condition at the hole centerline would reduce the computational time by half, its use is avoided as it prevents the possibility of capturing the unsteady asymmetric vortical flow patterns. This geometry is well accepted by the gas-turbine community and has been extensively studied1 for cooling performance for a wide range of blowing ratios, M = ρ j Vj/ρfsVfs, where ρ and V are density and normal velocity, respectively, for jet j and freestream fs. Goldstein2 correlated film cooling effectiveness η = (Tfs − T )/ (Tfs − Tj ) with the parameter x/Mb, where x is the downstream distance; M is the blowing ratio; b is the slot width; and Tfs, T , and Tj are the temperatures of crossflow, blade, and jet, respectively. Sinha et al.1 carried out experimental work to study the relationship between the fluid-thermal parameters of jet and film cooling effectiveness using a row of inclined holes. The mixing of a jet in a cross stream is a fully three-dimensional phenomenon.3 Amer et al.4 pointed out that the flow predictions are greatly affected by the selection of the turbulence model. Roy5 documented the cooling performance of 12 different arrangements of holes with a combination of blowing ratio M , distance between the holes L , and jet angle α using a upwind-biased finite volume code and standard k–ω turbulence closure model. Garg and Rigby6 resolved the plenum and hole pipes for a three-row showerhead film cooling arrangement with Wilcox’s k–ω turbulence model. Heidmann et al.7 used Reynolds-averaged Navier–Stokes (RANS) to compute the heat transfer for a realistic turbine vane with 12 rows of film cooling holes with shaped holes and plena resolved. Though these studies provide good details of the flow, the anisotropic dynamic nature of the spanwise vortices that affect the film cooling process are more complex than that can be captured by the mixing models used in aforementioned papers. Acharya8 compared the re-

Explicit supersymmetry breaking on boundaries of warped extra dimensions

Explicit supersymmetry breaking is studied in higher-dimensional theories by having boundaries respect only a subgroup of the bulk symmetry. If the boundary symmetry is the maximal subgroup allowed by the boundary conditions imposed on the fields, then the symmetry can be consistently gauged; otherwise gauging leads to an inconsistent theory. In a warped fifth dimension, an explicit breaking of all bulk supersymmetries by the boundaries is found to be inconsistent with gauging; unlike the case of flat 5D, complete supersymmetry breaking by boundary conditions is not consistent with supergravity. Despite this result, the low energy effective theory resulting from boundary supersymmetry breaking becomes consistent in the limit where gravity decouples, and such models are explored in the hope that some way of successfully incorporating gravity can be found. A warped constrained standard model leads to a theory with one Higgs boson with mass expected close to the experimental limit. A unified theory in a warped fifth dimension is studied with boundary breaking of both SU(5) gauge symmetry and supersymmetry. The usual supersymmetric prediction for gauge coupling unification holds even though the TeV spectrum is quite unlike the MSSM. Such a theory may unify matter and Higgs in the same SU(5) hypermultiplet.

Numerical study on the influence of various physical parameters over the gas–solid two-phase flow in the 2D riser of a circulating fluidized bed

A numerical parametric study was performed on the influence of various physical aspects over the hydrodynamics of gas–solid two-phase flow in the riser of a circulating fluidized bed (CFB). The addressed features were the solid phase viscosity, the gas–solid interface momentum transfer correlations, and the coordinate system. An Eulerian continuum formulation was applied for both phases. The resulting two-fluid model and numerical procedure followed a version of the MICEFLOW code. The simulation results are compared to available experimental data. The effects of the concerning features on the flow behavior are shown, mainly regarding cluster evolution. The flow frequency fluctuations typical to CFB risers were observed. It was also observed that for high values of solid phase viscosity there is an accumulation of solids near the outlet forming large clusters. When those clusters fall down, the instantaneous cross-sectional average solid mass velocity becomes negative. For inviscid solid phase, no cluster formation is observed. The results show the incorrectness of assuming symmetry boundary condition at the axis of the riser when cylindrical coordinates are used. Quite different results were obtained for different correlations for gas–solid interface momentum transfer. Finally, a comparison is presented of predictions from the Illinois Institute of Technology (IIT) hydrodynamic models A and B.

Existence and Uniqueness of a Steady State Solution of a Coupled Radiative–Conductive Heat Transfer Problem for a Non-grey Anisotropically and Participating Medium

In this paper, we prove the existence, uniqueness and regularity results for a one-dimensional coupled system of nonlinear partial and ordinary integro-differential equations. This system describes the steady-state coupled radiative–conductive heat transfer for a non-grey anisotropically absorbing, emitting and scattering medium, with axial symmetry and nonhomogeneous Dirichlet boundary conditions. We reformulate the full coupled system of equations as a compact fixed-point problem. This formulation is applied to prov existence and uniqueness results for the radiation intensity and the temperature fields. The Banach and Schauder fixed point theorems are the principal tools used to solve this problem.

Four-dimensional wavelet compression of arbitrarily sized echocardiographic data.

Wavelet-based methods have become most popular for the compression of two-dimensional medical images and sequences. The standard implementations consider data sizes that are powers of two. There is also a large body of literature treating issues such as the choice of the "optimal" wavelets and the performance comparison of competing algorithms. With the advent of telemedicine, there is a strong incentive to extend these techniques to higher dimensional data such as dynamic three-dimensional (3-D) echocardiography [four-dimensional (4-D) datasets]. One of the practical difficulties is that the size of this data is often not a multiple of a power of two, which can lead to increased computational complexity and impaired compression power. Our contribution in this paper is to present a genuine 4-D extension of the well-known zerotree algorithm for arbitrarily sized data. The key component of our method is a one-dimensional wavelet algorithm that can handle arbitrarily sized input signals. The method uses a pair of symmetric/antisymmetric wavelets (10/6) together with some appropriate midpoint symmetry boundary conditions that reduce border artifacts. The zerotree structure is also adapted so that it can accommodate noneven data splitting. We have applied our method to the compression of real 3-D dynamic sequences from clinical cardiac ultrasound examinations. Our new algorithm compares very favorably with other more ad hoc adaptations (image extension and tiling) of the standard powers-of-two methods, in terms of both compression performance and computational cost. It is vastly superior to slice-by-slice wavelet encoding. This was seen not only in numerical image quality parameters but also in expert ratings, where significant improvement using the new approach could be documented. Our validation experiments show that one can safely compress 4-D data sets at ratios of 128:1 without compromising the diagnostic value of the images. We also display some more extreme compression results at ratios of 2000:1 where some key diagnostically relevant key features are preserved.

Observation of splintered Josephson vortices at grain boundaries in YBa(2)Cu(3)O(7-delta).

We have directly observed well-separated Josephson vortex splinters with unquantized magnetic flux at asymmetric 45 degrees grain boundaries in YBa(2)Cu(3)O(7-delta) films by imaging magnetic flux with scanning SQUID microscopy. The existence of these splinter vortices has been predicted and is well described by a model based on dx(2)(-y(2)) pairing symmetry and facetting of the grain boundary on a length scale shorter than the Josephson penetration depth.

Motion of an antiviral compound in a rhinovirus capsid under rotational symmetry boundary conditions

A molecular dynamics (MD) simulation of a complex of a rhinovirus protein shell referred to as a “capsid” and an anti-rhinovirus drug, WIN52084s, was performed under the rotational symmetry boundary conditions. For the simulation, the energy parameters of WIN52084s in all-atom approximations were determined by ab initio calculations using a 6-31G ∗ basis set and the two-conformational two-stage restricted electrostatic potential fit method. The motion of WIN52084s and the capsid was focused on in the analysis of the trajectory of the simulation. The root mean square deviations of WIN52084s from the X-ray structure were decomposed to conformational, translational, and rotational components. The translation was further decomposed to radial, longitudinal, and lateral components. The conformation of WIN52084s was rigid, but moving in the pocket. The easiest path of motion for WIN52084s was on the longitudinal line, providing a track for the binding process required of the anti-rhinovirus drug to enter the pocket. The conformation of the pocket was also preserved in the simulation, although the position of the pocket in the capsid fluctuated in the lateral and radial directions.

GLOBAL SOLUTIONS TO THE NAVIER-STOKES EQUATIONS FOR COMPRESSIBLE HEAT-CONDUCTING FLOW WITH SYMMETRY AND FREE BOUNDARY

ABSTRACT Global solutions of the multidimensional Navier-Stokes equations for compressible heat-conducting flow are constructed, with spherically symmetric initial data of large oscillation between a static solid core and a free boundary connected to a surrounding vacuum state. The free boundary connects the compressible heat-conducting fluids to the vacuum state with free normal stress and zero normal heat flux. The fluids are initially assumed to fill with a finite volume and zero density at the free boundary, and with bounded positive density and temperature between the solid core and the initial position of the free boundary. One of the main features of this problem is the singularity of solutions near the free boundary. Our approach is to combine an effective difference scheme to construct approximate solutions with the energy methods and the pointwise estimate techniques to deal with the singularity of solutions near the free boundary and to obtain the bounded estimates of the solutions and the free boundary as time evolves. The convergence of the difference scheme is established. It is also proved that no vacuum develops between the solid core and the free boundary, and the free boundary expands with finite speed.

A numerical treatment of the symmetry boundary condition via the finite gradient in the coordinate-free form

A survey of literature reveals that available textbooks discuss the symmetry boundary conditions mainly with the orthogonal control volumes, probably because detailed discussion calls for a complicated coordinate transformation. In the present work, the symmetry boundary conditions are treated via the finite gradient recently developed. The compactness and clarity acquired by employing the finite gradient are noteworthy in handling the non-orthogonal control volumes.

The Structure and Stability of Twist Boundaries in SrTiO3 First Principles

AbstractA first principles density funtional computational method has been used to investigate the atomic stucture and energy of various distinct forms of the σ = 5(001) twist grain boundary in SrTiO3. The study focuses on four non-stoichiometric geometries which are all found to be stable to be the most stable. The grain boundary energies are computed as a function of TiO2 chemical potential and these define the limits of stability. The computed volume expansions are consistent with experimental observation and the in plane relaxations lower the boundary symmetry.

Microstructural evolution and rheological behaviour of marbles deformed at different crustal levels

Microstructures from naturally deformed marbles were investigated from a nappe pile with inverted Barrovian metamorphic zones. Detailed microstructural and textural work combined with existing PT data allows us to correlate microstructural types with tectonic events. Type 1 microstructure related to D1 continental underthrusting shows highly asymmetrical grain boundaries, increasing grain size and increasing intensity of lattice-preferred orientation with increasing metamorphic grade. These characteristics suggest that dislocation creep with concommitant grain boundary migration operated during the simple shear dominated underthrusting regime. Paleopiezometric and strain rate estimates show a decrease of flow stress with increasing metamorphic temperature and a strain rate of around 10 −14 s −1. Thrust related microstructure Type 2 is developed in Upper and Lower Nappes and is characterised by grain size reduction, increase of grain boundary symmetry and weaker textures. Microstructural and textural studies indicate dislocation creep with possible contribution of grain boundary sliding. Sub-grain rotation paleopiezometry and strain rate estimates show a decrease in flow stress with respect to the Type 1 microstructure and strain rate increase to around 10 −12 to 10 −13 s −1. Type 3 microstructure is developed in thrust related shear zones in the Parautochthon and syn-convergent extensional zones in the top of the nappe pile. This microstructure shows a high contribution of diffusion creep indicating low values of flow stress and significant weakening of marble layers. The general feature of studied area is the localisation of deformation into marbles during thrusting in low metamorphic grades while in higher grades marbles are not exploited as lubricating layers.

Spontaneous symmetry breaking in thegl(N)-NLS hierarchy on the half line

We describe an algebraic framework for studying the symmetry properties of integrable quantum systems on the half line. The approach is based on the introduction of boundary operators. It turns out that these operators both encode the boundary conditions and generate integrals of motion. We use this direct relationship between boundary conditions and symmetry content to establish the spontaneous breakdown of some internal symmetries, due to the boundary.