Order Gradient Research Articles

CORRECTION EFFECTS OF MACHINE DEPENDENCY ON THE TEXTURAL PARAMETERS OF ULTRASOUND IMAGES

In this paper we presented the effect of correction of machine dependency such as LookUpTable (LUT) correction , Time-Gain-Control(TGC) correction, Diffraction and Focusing correction on the textural parameters of ultrasound images. The group of texture parameters are: histogram parameters , coocurrance matrix parameters , first order gradient parameters , grey level run length matrix parameters ,texture feature Descriptors (TFD parameters),acoustical parameters. Mapping this parameters into color coded display improve the visual inspection to the sonographers. After correction an increase of some textural parameters and decrease of others improve the visual inspection from the ultrasonograohers point of view. These results can improve the segmentation quality of the ultrasound images that will facilitate the build of 3D ultrasound images and can have an accurate measurement from the images and from the 3D data.

New points of view on the nonlocal field theory and their applications to the fracture mechanics(II)—re-discuss nonlinear constitutive equations of nonlocal thermoelastic bodies

In this paper, nonlinear constitutive equations are deduced strictly according to the constitutive axioms of rational continuum mechanics. The existing judgments are modified and improved. The results show that the constitutive responses of nonlocal thermoelastic body are related to the curvature and higher order gradient of its material space, and there exists an antisymmetric stress whose average value in the domain occupied by thermoelastic body is equal to zero. The expressions of the antisymmetric stress and the nonlocal residuals are given. The conclusion that the directions of thermal conduction and temperature gradient are consistent is reached. In addition, the objectivity about the nonlocal residuals and the energy conservation law of nonlocal field is discussed briefly, and a formula for calculating the nonlocal residuals of energy changing with rigid motion of the spatial frame of reference is derived.

Second-order dc SQUID gradiometer from single layer of high temperature superconducting film

We developed a new design of the planar-type single-layer second-order SQUID gradiometer. The device consisted of 3 parallel-connected pickup loops, each of which is directly coupled to the step-edge junction dc SQUID. The device was made from a single layer of YBa/sub 2/Cu/sub 3/O/sub 7/ film patterned by photolithography with ion milling technique. Response of the device to various field distributions was tested, with 3 identical wire-wound coils coupled to each loop. Balancing was achieved by using a small piece of superconductor placed in the center loop. The gradiometer responded sensitively to the second-order field gradient, but did not respond to a uniform field or the first-order gradient. Measured off-balance was about 0.6% for the uniform field and 1.4% for the first order gradient.

Role of the coupling between strains and order parameter gradient in crystals

The manifestation and the role of coupling between order parameter gradient and strains, or equivalently between order parameter and gradient of strains, is reviewed. Dynamical phenomena occurring in perovskites, and in particular in quantum paraelectric phases, evidenced as a coupling between phonon branches at q≠0, and also in several other systems (quartz, Sn2P2Se6, Cs2HgBr4, and other systems satisfying the Lifshitz criterion) in relation with the formation of an incommensurate phase, are presented. Besides, the consequences in relation with domain walls, structure of incommensurate phases, and defects are also discussed.

Interfacial dynamics of viscoelastic fluid flows

The constitutive instability of the Johnson–Segalman (JS) model has been studied in order to understand the shear banding and the spurt effect of viscoelastic fluid flows. We have applied a new model, which incorporates a higher order gradient term of the deformation-rate tensor into the JS model, to investigate the dynamics of the mechanical interface induced by the constitutive instability. Computer modelling of two-dimensional Couette and Poiseuille flows has been carried out by a general Lagrangian–Eulerian scheme. It can track explicitly the evolution of the band structure under flow. Our results show that the new term plays an important role in selecting the steady state shear stress in the unstable region. The period of reaching the steady state can be 20 or more times longer than the intrinsic relaxation time of the JS fluid. We have verified experimental evidences on the existence of a mechanical metastable region, over which hysteresis in the flow curve might occur. The model reproduces many features of the experimental results.

Second gradient vs. surface energy in the Asaro-Grinfeld instability

This paper study an instability phenomenon that arise in epitaxial growth of single crystals with lattice mismatch. We compare a classical approach, based on the competition between the bulk and surface energies ith a non-staudard one when the surface tern is replaced by a term including the second gradient of the displacement, field. We evidence how second order gradients may stabilize lower modes of corrugated boundaries, via an intrisic length scale.

Modelling of the strain softening and localization in dynamical problems

The strain localization problems in softening solids under dynamic loading are considered. Two different models are accepted. One is elastoviscoplastic model with a strain softening diagram and another is the second order gradient elastoplastic model. By the asymptotic method of matching rapidly and slowly changing solutions for the partially differential equations with a small parameter, developed by the author [1], the close form solution for a one-dimensional dynamic localization problem was obtained for the both models. A bar loaded instantaneously by forcing both ends to move with a constant opposite velocity of the magnitude v 0 is considered. After the collision of generated elastic waves at the middle point of a bar the plastic strain is appeared. The plastic strains e e * concentrate at the middle point of the bar, e * is the strain related to the maximum stress. The zone of these large strains forms a band of strain localization with the width slowly growing in time. The solution describing the structure of the bands is obtained in an analytical form for both models. The profile of the elastoviscoplastic solution is monotone, while for the second gradient theory it is oscillating, but the effective width of the band for the both models is similar and is growing in time as t 1/2 . Note, that the linear analysis predicts constant width of a localization band and the solution [2] obtained for strain rate-insensitive elastoplastic material shows that localization takes place only at one point.

First order gradient optimization in LISP

In this paper we develop algorithms in programming language SCHEME for implementation of the main first order gradient techniques for unconstrained optimization. Implementation of the descent techniques which use non-optimal descent steps as well as implementation of the optimal descent techniques are described. Also, we investigate implementation of the global problem, called optimization along a line. Developed programs are effective and simpler with respect to the corresponding in the procedural programming languages. Several numerical examples are reported.

Remote determination of magnetic properties and improved drill targeting of magnetic anomaly sources by Differential Vector Magnetometry (DVM)

The induced magnetisation of a magnetic source is proportional to the ambient magnetic field and varies in response to natural geomagnetic variations, such as diurnal changes, storm fields and pulsations. In contrast, the remanent magnetisation is independent of changes in the ambient field. The local perturbation of the geomagnetic variations arising from a subsurface magnetic body can be determined by simultaneous monitoring of geomagnetic variations at two sites: one within the static magnetic anomaly associated with the body and another at a remote base station. Total field measurements can only provide a qualitative indication of the relative contributions of remanent and induced magnetisation to the anomaly. Monitoring of all three field components at the on-anomaly and base stations, however, allows the components of the second order gradient tensor of the anomalous pseudogravitational potential to be determined. This tensor depends only on the source geometry and the measurement location and is independent of the nature (remanent or induced), magnitude or direction of the source magnetisation.Without making any assumptions about source geometry or location, the Koenigsberger ratio (Q), the direction of remanence and the direction of total magnetisation can be obtained from the components of this tensor. This information can constrain magnetic modelling prior to drilling and remove a major source of ambiguity in magnetic interpretation. The direction to the centre of a compact source can be determined directly from diagonalisation of the tensor. Values of Q constrain the magnetic mineralogy of the source and the remanence direction can discriminate sources of different ages or geological histories. Thus the method can also alleviate the geological ambiguity that afflicts magnetic interpretation.Field trials of differential vector magnetometry (DVM) at several sites, including the Tallawang magnetite deposit, New South Wales, have demonstrated the validity of the proposed in situ method. However, a number of technical difficulties must be resolved before this method can be used routinely. Accurate characterisation of departures from mutual orthogonality of the components measured by each vector sensor, and the relative orientation of the anomaly and base station sensors, are crucial to the successful implementation of the method.

Scale Effects in Media With Periodic and Nearly Periodic Microstructures, Part I: Macroscopic Properties

Traditional averaging and homogenization techniques, developed to predict the macroscopic properties of heterogeneous media, typically ignore microstructure related scale effects—that is, the influence of the size of the representative volume, relative to the size of the unit cell. This issue is presently investigated by exploring the behavior of a nonlinearly elastic, planar, lattice model, which is subjected to general macroscopic deformations. For these materials, scale effects may be due to nonuniformities in the macroscopic strain field throughout the specimen, or alternatively, to the presence of microstructural imperfections that may be either geometric or constitutive in nature. For the case of macroscopic strain nonuniformities, it is shown that the microstructure related scale effects can be accounted for by the presence of higher order gradient terms in the macroscopic strain energy density of the model. For the case of microstructural imperfections, the difference between the respective macroscopic properties of the perfect and imperfect models are shown to depend on the relative size of the specimen, and on the imperfection amplitude and wavelength, while being nearly insensitive to the imposed macroscopic strain. For all of the cases considered, several analytical approximations are proposed to predict the influence of scale on the macroscopic properties, and the accuracy of each method is examined.

Nonlinear Internal Model Control using Local Model Networks

Local Model Networks represent a nonlinear dynamical system by a set of locally valid submodels across the operating range. Training such feedforward structures involves the combined estimation of the submodel parameters and those of the interpolation functions. The paper describes a new hybrid learning approach for local model networks that uses a combination of singular value decomposition and second order gradient optimization. A new nonlinear Internal Model Control scheme is proposed which has the important property that the controller can be derived analytically. Simulation studies of a pH neutralization process confirm the excellent modelling and control performance using the local model approach.

Computation of magnetic gradients due to three-dimensional bodies

Thc expressions of magnetic gradients due to 3-D homogeneous magnetized polyhedra are systematically derived and presented, fronr which the forward problem of magnetic gradients of an arbitrary shaped geological body is solved. It is shown that in the rotation of coordinate systems there is an essential difference between the transformation of magnetic fields and that of their gradients. In a 2-D coordinate system a unified transformation formula of any order gradients can he derived, hut cannot in the 3-D case. The calculations of synthetic models show the correctness of the expressioils or magnetic gradients.

Dynamic hydro-thermal economic dispatch with water availability constraints and variable water head

Operation of a system having both hydro and thermal plants is quite complex as hydro plants have negligible operating cost, but are required to operate under constraints of water available for hydro generation in a given period of time. The problem thus belongs to the realm of dynamic optimization. The earliest work on optimal load flow for hydro-thermal systems was probably due to Ramamoorthy [1]. Head variation was neglected and nonlinear programming techniques were employed. In this paper, the problem of minimizing the operating cost of a hydro-thermal system can be viewed as one of minimizing the fuel cost of thermal plants under the constraint of water availability (storage and inflow) and variable water head for hydro generation over a given period of operation. Optimization will be carried out with thermal power generation and water discharge rate as control variables, with transmission losses accounted for by the exact network model, namely the load flow equations. The problem is solved here using nonlinear programming technique in conjunction with successive approximation method. The method of solution has been accelerated to reduce the computational time burden using the first order gradient method. Because of the large-scale nature of the problem, special attention is paid to finding convergence characteristics and realistic initial guess estimates for the algorithm.

Layer thickness optimisation in a laminated composite

Abstract The paper describes a method to optimise the thickness balance within a composite laminate with layers oriented according to a limited set of angles. The laminate must be symmetric, balanced and loaded in-plane. The optimisation process is particularly suited to be used in conjunction with a finite element program. It provides the designer with the optimal overall engineering characteristics anda list of all the possible orientation combinations ranked with respect to their safety factor. The optimisation method is based on the first order gradient optimum search method and operates iteratively in the engineering elastic characteristics field. The cost function implemented up to now is the structure stiffness but no conceptual limitations exist for different functions. Some simple applications are listed at the end of the paper in order to verify the capabilities of the method.

A GENERALIZED VARIABLE FORMULATION FOR GRADIENT DEPENDENT SOFTENING PLASTICITY

A mesh-independent finite element method for elastoplastic problems with softening is proposed. The regularization of the boundary value problem is achieved introducing in the yield function the second order gradient of the plastic multiplier. The backward-difference integrated finite-step problem enriched with the gradient term is given a variational formulation where the consitutive equations are treated in weak form as well as the other field equations. A predictor–corrector scheme is proposed for the solution of the non-linear algebraic problem resulting from the finite element discretization of the functional. The expression of the consistent tangent matrix is provided and the corrector phase is formulated as a Linear Complementarity Problem. The effectiveness of the proposed methodology is verified by one- and two-dimensional tests.

The influence of scale size on the stability of periodic solids and the role of associated higher order gradient continuum models

Of interest here is the scale size effect on the stability of finitely strained, rate-independent solids with periodic microstructures. Using a multiple scales asymptotic technique, we express the critical load at the onset of the first instability and the corresponding eigenmode in terms of the scale size parameter ε. The zeroth order ε terms in these expansions depend on the standard (first order gradient) macroscopic moduli tensor, while all the higher order ε terms require the determination of higher order gradient macroscopic moduli. These macroscopic moduli, which are calculated by solving appropriate boundary value problems on the unit cell, relate the macroscopic (unit cell average) stress rate increment to the macroscopic displacement rate gradients. The proposed general theory is subsequently applied to the investigation of the failure surfaces in periodic solids of infinite extent. For these solids one can define in macroscopic strain space a microscopic (local) failure surface, which corresponds to the onset of the first bulking-type instability in the solid, and a macroscopic (global) failure surface, which corresponds to the onset of the first long wavelength instability in the solid. The determination of the macrofailure surface is considerably easier than the determination of the microfailure surface, for it requires the calculation of the standard macroscopic moduli tensor. In addition, the regions where the two surfaces coincide is of significant practical interest, for a macroscopic localized mode of deformation (e.g. in the form of a shear band or a kink band) appears in the post-bifurcation regime. The prediction of these coincidence zones is based on a necessary criterion that depends on the higher order gradient macroscopic moduli. A detailed example is given for the case of layered composites, in view of the possibility of obtaining closed form expressions for all the required macroscopic moduli and in view of the existence of an analytical solution to the microscopic failure problem. Two applications are presented, one for a foam rubber composite and another for a graphite-epoxy composite whose properties have been determined experimentally. Following the verification of the above mentioned necessary criterion for the coincidence of the micro- and macrofailure surfaces in the two examples, the presentation is concluded by a discussion and suggestions for further work.

Stochastic growth equations and reparametrization invariance

It is shown that, by imposing reparametrization invariance, one may derive a variety of stochastic equations describing the dynamics of surface growth and identify the physical processes responsible for the various terms. This approach provides a particularly transparent way to obtain continuum growth equations for interfaces. It is straightforward to derive equations which describe the coarse grained evolution of discrete lattice models and analyze their small gradient expansion. In this way, the authors identify the basic mechanisms which lead to the most commonly used growth equations. The advantages of this formulation of growth processes is that it allows one to go beyond the frequently used no-overhang approximation. The reparametrization invariant form also displays explicitly the conservation laws for the specific process and all the symmetries with respect to space-time transformations which are usually lost in the small gradient expansion. Finally, it is observed, that the knowledge of the full equation of motion, beyond the lowest order gradient expansion, might be relevant in problems where the usual perturbative renormalization methods fail.

A Reduced Memory Marquardt Algorlthm for Training Feedforward Neural Networks

Efficient techniques (measured by convergence properties, computation/memory complexity, training accuracy, etc.) for training large-scale networks with thousands of weights and training samples are not fully developed. The Marquardt algorithm has been used effectively to solve nonlinear least squares problems. It has been proven to be more efficient than first order gradient methods and their variants for off-line batch training of feedforward neural networks with a few hundred weights. However for large networks, the memory requirements of the algorithm make it impractical for most current machines. For training a network containing n weights and N training samples, it normally requires operations (including inversion) of matrices of sizes N × n. In the present paper, we give alternatives to implementing the Ma.rqua.rdt algorithm with reduced memory requirement.

Accuracy versus cost for three efficient finite-element solvers

Three efficient finite-element schemes are compared for Poisson problems on triangular meshes: (1) uniform subdivision of first order triangles and the incomplete Choleski conjugate gradient method; (2) uniform subdivision of first-order triangles and a multilevel preconditioned conjugate gradient method; and (3) uniform increase of polynomial order and diagonally-preconditioned conjugate gradients. Errors in the computed energy, and computational costs, are obtained for a square, air-filled coaxial cable; a linear, current-driven magnetostatic problem; and a microstrip transmission line. Increasing the polynomial order is by far the best approach, i.e. gives the best accuracy for a given cost.

Cracks in gradient elastic bodies with surface energy

In the present paper the effect of higher order gradients on the structure of line-crack tips is determined. In particular we introduce in the constitutive equations of the linear deformation of an elastic solid a volumetric energy term, which includes the contribution of the strain gradient, and a surface energy gradient dependent term and then determine the effect of these terms on the structure of the mode-III crack tip and the associated stress and strain fields. By making use of the solution in terms of Fourier transform of the equation of elastic equilibrium we solve the half-plane boundary value problems of: (a) specified tractions, and (b) prescribed displacements, along the crack surface, respectively.