A Conservative Front Tracking Algorithm

The discontinuities in the solutions of systems of conservation laws are widely considered as one of the difficulties in numerical simulation. A numerical method is proposed for solving these partial differential equations with discontinuities in the solution. The method is able to track these sharp discontinuities or interfaces while still fully maintain the conservation property. The motion of the front is obtained by solving a Riemann problem based on the state values at its both sides which are reconstructed by using weighted essentially non oscillatory (WENO) scheme. The propagation of the front is coupled with the evaluation of "dynamic" numerical fluxes. Some numerical tests in 1D and preliminary results in 2D are presented.

Front tracking with moving-least-squares surfaces

The representation of interfaces by means of the algebraic moving-least-squares (AMLS) technique is addressed. This technique, in which the interface is represented by an unconnected set of points, is interesting for evolving fluid interfaces since there is]to surface connectivity. The position of the surface points can thus be updated without concerns about the quality of any surface triangulation. We introduce a novel AMLS technique especially designed for evolving-interfaces applications that we denote RAMLS (for Robust AMLS). The main advantages with respect to previous AMLS techniques are: increased robustness, computational efficiency, and being free of user-tuned parameters. Further, we propose a new front-tracking method based on the Lagrangian advection of the unconnected point set that defines the RAMLS surface. We assume that a background Eulerian grid is defined with some grid spacing h. The advection of the point set makes the surface evolve in time. The point cloud can be regenerated at any time (in particular, we regenerate it each time step) by intersecting the gridlines with the evolved surface, which guarantees that the density of points on the surface is always well balanced. The intersection algorithm is essentially a ray-tracing algorithm, well-studied in computer graphics, in which a line (ray) is traced so as to detect all intersections with a surface. Also, the tracing of each gridline is independent and can thus be performed in parallel. Several tests are reported assessing first the accuracy of the proposed RAMLS technique, and then of the front-tracking method based on it. Comparison with previous Eulerian, Lagrangian and hybrid techniques encourage further development of the proposed method for fluid mechanics applications. (C) 2008 Elsevier Inc. All rights reserved.

Computational aspects of harmonic wavelet Galerkin methods and an application to a precipitation front propagation model

This article is dedicated to harmonic wavelet Galerkin methods for the solution of partial differential equations. Several variants of the method are proposed and analyzed, using the Burgers equation as a test model. The computational complexity can be reduced when the localization properties of the wavelets and restricted interactions between different scales are exploited. The resulting variants of the method have computational complexities ranging from O(N(3)) to O(N) (N being the space dimension) per time step. A pseudo-spectral wavelet scheme is also described and compared to the methods based on connection coefficients. The harmonic wavelet Galerkin scheme is applied to a nonlinear model for the propagation of precipitation fronts, with the front locations being exposed in the sizes of the localized wavelet coefficients. (C) 2011 Elsevier Ltd. All rights reserved.

A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation

We present a variable time step, fully adaptive in space, hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions. The method is based on the hybrid level set/front-tracking approach proposed in [H. D. Ceniceros and A. M. Roma, J. Comput. Phys., 205, 391400, 2005]. Geometric, interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance (level set) function, which is evaluated fast and to machine precision, is used as a fluid indicator. The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in [S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, J. Comput. Phys., 203, 493-516, 2005] whose success for greatly reducing parasitic currents has been demonstrated. The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude. To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic, adaptive mesh refinements. This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step, linearly implicit time integration scheme. We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications: the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability, an example of bubble ascending dynamics, and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.

Light Front Boson Model Propagation

The scope and aim of this work is to describe the two-body interaction mediated by a particle (either the scalar or the gauge boson) within the light-front formulation. To do this, first of all we point out the importance of propagators and Green functions in Quantum Mechanics. Then we project the covariant quantum propagator onto the light front time to get the propagator for scalar particles in these coordinates. This operator propagates the wave function from x(+) = 0 to x(+) > 0. It corresponds to the definition of the time ordering operation in the light front time x(+). We calculate the light-front Green's function for 2 interacting bosons propagating forward in x(+). We also show how to write down the light front Green's function from the Feynman propagator and finally make a generalization to N bosons.

Light front fermion model propagation

In this work we consider the propagation of two fermion fields interacting with each other by the exchange of intermediate scalar bosons in the light front. We obtain the corrections up to fourth order in the coupling constant using hierarchical equations in order to obtain the bound state equation (Bethe - Salpeter equation). © 2013 Chinese Physical Society and IOP Publishing Ltd.

Mechanical Blocking Mechanism for the Columnar to Equiaxed Transition

Mechanical blocking of the columnar front during the columnar to equiaxed transition (CET) is studied by quantitatively comparing the CET positions obtained with one stochastic model and two deterministic models for the unidirectional solidification of an Al-7 (wt pct) Si alloy. One of the deterministic models is based on the solutal blocking of the columnar front, whereas the other model is based on the mechanical blocking. The solutal-blocking model and the mechanical-blocking model with the traditional blocking fraction of 0.49 give columnar zones larger than those predicted with the stochastic model. When a blocking fraction of 0.2 is adopted, however, the agreement is very good for a range of nucleation undercoolings and number density of equiaxed grains. Therefore, changing the mechanical-blocking fraction in deterministic models from 0.49 to 0.2 seems to model more accurately the mechanical-blocking process that can lead to the CET.

An unstructured CVFEM and moving interface algorithm for non-Newtonian Hele-Shaw flows in injection molding

Purpose - The purpose of this paper is to develop a novel unstructured simulation approach for injection molding processes described by the Hele-Shaw model. Design/methodology/approach - The scheme involves dual dynamic meshes with active and inactive cells determined from an initial background pointset. The quasi-static pressure solution in each timestep for this evolving unstructured mesh system is approximated using a control volume finite element method formulation coupled to a corresponding modified volume of fluid method. The flow is considered to be isothermal and non-Newtonian. Findings - Supporting numerical tests and performance studies for polystyrene described by Carreau, Cross, Ellis and Power-law fluid models are conducted. Results for the present method are shown to be comparable to those from other methods for both Newtonian fluid and polystyrene fluid injected in different mold geometries. Research limitations/implications - With respect to the methodology, the background pointset infers a mesh that is dynamically reconstructed here, and there are a number of efficiency issues and improvements that would be relevant to industrial applications. For instance, one can use the pointset to construct special bases and invoke a so-called ""meshless"" scheme using the basis. This would require some interesting strategies to deal with the dynamic point enrichment of the moving front that could benefit from the present front treatment strategy. There are also issues related to mass conservation and fill-time errors that might be addressed by introducing suitable projections. The general question of ""rate of convergence"" of these schemes requires analysis. Numerical results here suggest first-order accuracy and are consistent with the approximations made, but theoretical results are not available yet for these methods. Originality/value - This novel unstructured simulation approach involves dual meshes with active and inactive cells determined from an initial background pointset: local active dual patches are constructed ""on-the-fly"" for each ""active point"" to form a dynamic virtual mesh of active elements that evolves with the moving interface.

Pion form factor in the light-front

The pion electromagnetic form factor is calculated with a light-front quark model. The plus and minus components of the electromagnetic current are used to calculate the electromagnetic form factor in the the Breit frame with two models for the q (q) over bar vertex. The light-front constituent quark model describes very well the hadronic wave functions for pseudo-scalar and vector particles. Symmetry problems arising in the light-front approcah are solved by the pole dislocation method. The results are compared with new experimental data and with other quark models.

Electromagnetic form factor of the pion in the space- and time-like regions within the front-form dynamics

The pion electromagnetic form factor is calculated in the space- and time-like regions from -10 (GeV/c)2 up to 10 (GeV/c)2, within a front-form model. The dressed photon vertex where a photon decays in a quark-antiquark pair is depicted generalizing the vector meson dominance ansatz, by means of the vector meson vertex functions. An important feature of our model is the description of the on-mass-shell vertex functions in the valence sector, for the pion and the vector mesons, through the front-form wave functions obtained within a realistic quark model. The theoretical results show an excellent agreement with the data in the space-like region, while in the time-like region the description is quite encouraging. © 2003 Elsevier B.V. All rights reserved.

Deeply virtual Compton scattering in a relativistic quark model

This thesis is mainly concerned with a model calculation for generalized parton distributions (GPDs). We calculate vectorial- and axial GPDs for the N N and N Delta transition in the framework of a light front quark model. This requires the elaboration of a connection between transition amplitudes and GPDs. We provide the first quark model calculations for N Delta GPDs. The examination of transition amplitudes leads to various model independent consistency relations. These relations are not exactly obeyed by our model calculation since the use of the impulse approximation in the light front quark model leads to a violation of Poincare covariance. We explore the impact of this covariance breaking on the GPDs and form factors which we determine in our model calculation and find large effects. The reference frame dependence of our results which originates from the breaking of Poincare covariance can be eliminated by introducing spurious covariants. We extend this formalism in order to obtain frame independent results from our transition amplitudes.

An Efficient Multiple Object Detection and Tracking Framework for Automatic Counting and Video Surveillance Applications

Automatic visual object counting and video surveillance have important applications for home and business environments, such as security and management of access points. However, in order to obtain a satisfactory performance these technologies need professional and expensive hardware, complex installations and setups, and the supervision of qualified workers. In this paper, an efficient visual detection and tracking framework is proposed for the tasks of object counting and surveillance, which meets the requirements of the consumer electronics: off-the-shelf equipment, easy installation and configuration, and unsupervised working conditions. This is accomplished by a novel Bayesian tracking model that can manage multimodal distributions without explicitly computing the association between tracked objects and detections. In addition, it is robust to erroneous, distorted and missing detections. The proposed algorithm is compared with a recent work, also focused on consumer electronics, proving its superior performance.

Registration of temporal sequences of coronal and sagittal MR images through respiratory patterns

This work discusses the determination of the breathing patterns in time sequence of images obtained from magnetic resonance (MR) and their use in the temporal registration of coronal and sagittal images. The registration is made without the use of any triggering information and any special gas to enhance the contrast. The temporal sequences of images are acquired in free breathing. The real movement of the lung has never been seen directly, as it is totally dependent on its surrounding muscles and collapses without them. The visualization of the lung in motion is an actual topic of research in medicine. The lung movement is not periodic and it is susceptible to variations in the degree of respiration. Compared to computerized tomography (CT), MR imaging involves longer acquisition times and it is preferable because it does not involve radiation. As coronal and sagittal sequences of images are orthogonal to each other, their intersection corresponds to a segment in the three-dimensional space. The registration is based on the analysis of this intersection segment. A time sequence of this intersection segment can be stacked, defining a two-dimension spatio-temporal (2DST) image. The algorithm proposed in this work can detect asynchronous movements of the internal lung structures and lung surrounding organs. It is assumed that the diaphragmatic movement is the principal movement and all the lung structures move almost synchronously. The synchronization is performed through a pattern named respiratory function. This pattern is obtained by processing a 2DST image. An interval Hough transform algorithm searches for synchronized movements with the respiratory function. A greedy active contour algorithm adjusts small discrepancies originated by asynchronous movements in the respiratory patterns. The output is a set of respiratory patterns. Finally, the composition of coronal and sagittal image pairs that are in the same breathing phase is realized by comparing of respiratory patterns originated from diaphragmatic and upper boundary surfaces. When available, the respiratory patterns associated to lung internal structures are also used. The results of the proposed method are compared with the pixel-by-pixel comparison method. The proposed method increases the number of registered pairs representing composed images and allows an easy check of the breathing phase. (C) 2010 Elsevier Ltd. All rights reserved.

Arterial wall dosimetry for non-Hodgkin lymphoma patients treated with radioimmunotherapy.

Tumors in non-Hodgkin lymphoma (NHL) patients are often proximal to the major blood vessels in the abdomen or neck. In external-beam radiotherapy, these tumors present a challenge because imaging resolution prevents the beam from being targeted to the tumor lesion without also irradiating the artery wall. This problem has led to potentially life-threatening delayed toxicity. Because radioimmunotherapy has resulted in long-term survival of NHL patients, we investigated whether the absorbed dose (AD) to the artery wall in radioimmunotherapy of NHL is of potential concern for delayed toxicity. SPECT resolution is not sufficient to enable dosimetric analysis of anatomic features of the thickness of the aortic wall. Therefore, we present a model of aortic wall toxicity based on data from 4 patients treated with (131)I-tositumomab. METHODS: Four NHL patients with periaortic tumors were administered pretherapeutic (131)I-tositumomab. Abdominal SPECT and whole-body planar images were obtained at 48, 72, and 144 h after tracer administration. Blood-pool activity concentrations were obtained from regions of interest drawn on the heart on the planar images. Tumor and blood activity concentrations, scaled to therapeutic administered activities-both standard and myeloablative-were input into a geometry and tracking model (GEANT, version 4) of the aorta. The simulated energy deposited in the arterial walls was collected and fitted, and the AD and biologic effective dose values to the aortic wall and tumors were obtained for standard therapeutic and hypothetical myeloablative administered activities. RESULTS: Arterial wall ADs from standard therapy were lower (0.6-3.7 Gy) than those typical from external-beam therapy, as were the tumor ADs (1.4-10.5 Gy). The ratios of tumor AD to arterial wall AD were greater for radioimmunotherapy by a factor of 1.9-4.0. For myeloablative therapy, artery wall ADs were in general less than those typical for external-beam therapy (9.4-11.4 Gy for 3 of 4 patients) but comparable for 1 patient (32.6 Gy). CONCLUSION: Blood vessel radiation dose can be estimated using the software package 3D-RD combined with GEANT modeling. The dosimetry analysis suggested that arterial wall toxicity is highly unlikely in standard dose radioimmunotherapy but should be considered a potential concern and limiting factor in myeloablative therapy.