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1.
We present a path independent (global) algorithm for phase unwrapping based on the minimisation of a robust cost function. The algorithm incorporates an outlier rejection mechanism making it robust to large inconsistencies and discontinuities. The proposal consists on an iterative incremental scheme that unwraps a sub-estimation of the residual phase at each iteration. The sub-estimation degree is controlled by an algorithm׳s parameter. We present an efficiently computational multigrid implementation based on a nested strategy: the process is iterated by using multiple resolutions. The proposal׳s performance is demonstrated by experiments with synthetic and real data, and successfully compared with algorithms of the state of the art.  相似文献   
2.
Stochastic systems with memory naturally appear in life science, economy, and finance. We take the modelling point of view of stochastic functional delay equations and we study these structures when the driving noises admit jumps. Our results concern existence and uniqueness of strong solutions, estimates for the moments and the fundamental tools of calculus, such as the Itô formula. We study the robustness of the solution to the change of noises. Specifically, we consider the noises with infinite activity jumps versus an adequately corrected Gaussian noise. The study is presented in two different frameworks: we work with random variables in infinite dimensions, where the values are considered either in an appropriate Lp-type space or in the space of càdlàg paths. The choice of the value space is crucial from the modelling point of view, as the different settings allow for the treatment of different models of memory or delay. Our techniques involve tools of infinite dimensional calculus and the stochastic calculus via regularisation.  相似文献   
3.
The article describes the study of cosmic rays above 10 19 eV. Following a brief introduction, the reasons for the current interest in this topic are discussed. The methods used to measure the properties of the very rare ultrahigh-energy cosmic rays are explained and the current data described. The data lead to an enigma and the many theories proposed to explain it are summarized. The properties and potential of new detectors are outlined.  相似文献   
4.
Andrew DeBenedictis 《Liquid crystals》2016,43(13-15):2352-2362
ABSTRACT

We consider a class of liquid crystal free-boundary problems for which both the equilibrium shape and internal configuration of a system must simultaneously be determined, for example in films with air–liquid or fluid–liquid crystal interfaces and elastomers. We develop a finite element algorithm to solve such problems with dynamic mesh control, achieved by supplementing the free energy with an auxiliary functional that promotes mesh quality and is minimised in the null space of the energy. We apply this algorithm to a flexible capacitor, as well as to determine the shape of liquid crystal tactoids as a function of the surface tension and elastic constants. These are compared with theoretical predictions and experimental observations of tactoids from the literature.  相似文献   
5.
We present a novel solution algorithm for 3D parameter identification based on low frequency electromagnetic data. With focus on large-scale applications such as monitoring of subsea oil production, CO2 sequestration, and geothermal systems, the proposed solution algorithm is designed to meet challenges related to low parameter sensitivity, nonuniqueness of the inverse solutions, nonlinearity in the mapping from the data to the parameter space, and costly numerical simulations. Motivated by earlier investigations on the relation between sensitivity, nonlinearity and scale, the proposed solution approach is based on a reduced, composite parameter representation. Though a reduced representation restricts the solution space, flexibility with respect to which parameter functions that can be represented is obtained by facilitating the estimation of the structure and smoothness of the representation itself. Moreover, the resolution of the parameter function is detached from the computational grid and determined as part of the estimation. The performance of the proposed solution algorithm is illustrated through numerical examples for identification of underground electric conductivity changes from time-lapse electromagnetic observations.  相似文献   
6.
We study the regularising properties of Tikhonov regularisation on the sequence space ?2 with weighted, non-quadratic penalty term acting separately on the coefficients of a given sequence. We derive sufficient conditions for the penalty term that guarantee the well-posedness of the method, and investigate to which extent the same conditions are also necessary. A particular interest of this paper is the application to the solution of operator equations with sparsity constraints. Assuming a linear growth of the penalty term at zero, we prove the sparsity of all regularised solutions. Moreover, we derive a linear convergence rate under the assumptions of even faster growth at zero and a certain injectivity of the operator to be inverted. These results in particular cover non-convex ?p regularisation with 0<p<1.  相似文献   
7.
Processing the capillary viscometry data of fluids with yield stress   总被引:1,自引:0,他引:1  
The capillary viscometer is used to measure the shear stress-shear rate relationship of a wide range of purely viscous fluids. It is however not considered as an appropriate instrument for obtaining the yield stress and the post-yield behaviour of fluids that have a yield stress. This is partly because conventional methods of processing the capillary viscometry data of purely viscous fluids cannot be applied to similar data of fluids with yield stress. The unavoidable experimental noise in the capillary data, particularly at low shear rates, also makes it difficult to obtain a reliable estimate of the yield stress from capillary data. In this investigation the problem of converting the capillary viscometry data of yield stress fluids into a shear stress-shear rate curve and a yield stress is formulated as a Volterra integral equation of the first kind. This is an ill-posed problem i.e. noise in the data will be amplified by inappropriate methods of data processing. A method, based on Tikhonov regularisation that takes into account the ill-posed nature of the problem, is then developed to solve this problem for fluids with yield stress. The performance of this method is assessed by applying it to a set of “synthetic” capillary viscometry data with added random noise and to a set of experimental data for a concentrated suspension of TiO2 taken from the literature. In both cases Tikhonov regularisation was able to extract the complete shear properties of these fluids from capillary viscometry data alone. Received: 22 November 1999/Accepted: 17 December 1999  相似文献   
8.
Conditional Source-term Estimation (CSE) obtains the conditional species mass fractions by inverting a Fredholm integral equation of the first kind. In the present work, a Bayesian framework is used to compare two different regularisation methods: zeroth-order temporal Tikhonov regulatisation and first-order spatial Tikhonov regularisation. The objectives of the current study are: (i) to elucidate the ill-posedness of the inverse problem; (ii) to understand the origin of the perturbations in the data and quantify their magnitude; (iii) to quantify the uncertainty in the solution using different priors; and (iv) to determine the regularisation method best suited to this problem. A singular value decomposition shows that the current inverse problem is ill-posed. Perturbations to the data may be caused by the use of a discrete mixture fraction grid for calculating the mixture fraction PDF. The magnitude of the perturbations is estimated using a box filter and the uncertainty in the solution is determined based on the width of the credible intervals. The width of the credible intervals is significantly reduced with the inclusion of a smoothing prior and the recovered solution is in better agreement with the exact solution. The credible intervals for temporal and spatial smoothing are shown to be similar. Credible intervals for temporal smoothing depend on the solution from the previous time step and a smooth solution is not guaranteed. For spatial smoothing, the credible intervals are not dependent upon a previous solution and better predict characteristics for higher mixture fraction values. These characteristics make spatial smoothing a promising alternative method for recovering a solution from the CSE inversion process.  相似文献   
9.
Digital image restoration has drawn much attention in the recent years and a lot of research has been done on effective variational partial differential equation models and their theoretical studies. However there remains an urgent need to develop fast and robust iterative solvers, as the underlying problem sizes are large. This paper proposes a fast multigrid method using primal relaxations. The basic primal relaxation is known to get stuck at a ‘local’ non-stationary minimum of the solution, which is usually believed to be ‘non-smooth’. Our idea is to utilize coarse level corrections, overcoming the deadlock of a basic primal relaxation scheme. A further refinement is to allow non-regular coarse levels to correct the solution, which helps to improve the multilevel method. Numerical experiments on both 1D and 2D images are presented.  相似文献   
10.
Most simulation methods for compressible flow attain numerical stability at the cost of swamping the fine turbulent flow structures by artificial dissipation. This article demonstrates that numerical stability can also be attained by preserving conservation laws at the discrete level. A new mathematical explanation of conservation in compressible flow reveals that many conservation properties of convection are due to the skew-symmetry of the convection operator. By preserving this skew-symmetry at the discrete level, a fourth-order accurate collocated symmetry-preserving discretisation with excellent conservation properties is obtained. Also a new symmetry-preserving regularisation subgrid-scale model is proposed. The proposed techniques are assessed in simulations of compressible turbulent channel flow. The symmetry-preserving discretisation for compressible flow has good stability without artificial dissipation and yields acceptable results already on coarse grids. Regularisation does not consistently improve upon no-model results, but often compares favourably with eddy-viscosity models.  相似文献   
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