A meshless approach, collocation discrete least square (CDLS) method, is extended in this paper, for solving elasticity problems. In the present CDLS method, the problem domain is discretized by distributed field nodes. The field nodes are used to construct the trial functions. The moving least-squares interpolant is employed to construct the trial functions. Some collocation points that are independent of the field nodes are used to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of the residuals for the collocation points. The final stiffness matrix is symmetric and therefore can be solved via efficient solvers. The boundary conditions are easily enforced by the penalty method. The present method does not require any mesh so it is a truly meshless method. Numerical examples are studied in detail, which show that the present method is stable and possesses good accuracy, high convergence rate and high efficiency.

Least squares is a robust and simple method in function approximation. Collocated Discrete Least Squares (CDLS) is a meshless method based on least squares technique. In this paper CDLS is used with a non-incremental projection method for the solution of incompressible generalized Newtonian fluid flow equations in the simulation of laminar flow of power-law fluids. The scheme is used to solve two benchmark problems named lid-driven cavity flow and flow past a circular cylinder for the power-law fluids.

Cornelia de Lange syndrome (CDLS) is a rare syndrome characterized by multiple congenital anomalies, mental retardation, characteristic facial appearance, developmental delay, skeletal malformation, hirsutism, and various cardiac and ophthalmological problems. The diagnosis of this syndrome is clinical. The patient of the present case report was the second case of CDLS from Iran; only a few cases of CDLS have thus far been reported from countries outside Europe and North America. Reporting CDLS cases of different ethnic backgrounds can add nuances to the phenotypic description of the syndrome and be helpful in diagnosis. Furthermore, an increased awareness of this syndrome may result in an early diagnosis and a decrease in morbidity.

Introduction: Cornelia de Lange syndrome (CDLS) is a rare non-hereditary syndrome. The key diagnosis is unique facial features, limb anomalies, and growth retardation. Cardiac defects with gastrointestinal and genitourinary anomalies may be associated. Case Presentation: This is a case of neonatal CDLS that we think is interesting due to its association with a novel congenital heart complex. Conclusions: Patients with CDLS have a high incidence of congenital heart disease (CHD), so a cardiologic study of all of these patients is suggested.

Introduction: Literature regarding the different degrees of hearing loss in patients with Cornelia de Lange syndrome (CDLS) reports that half of the affected patients exhibit severe to profound sensorineural hearing loss. We present the first pre-school child with CDLS who underwent cochlear implantation for congenital profound sensorineural hearing loss. Case Report: A 3-year-old boy with CDLS underwent unilateral cochlear implantation for bilateral profound sensorineural hearing loss. He had characteristic facial features, bushy eyebrows and synophrys, limb anomalies, growth and mental retardation. Based on the results of postoperative speech perception and production tests, his gain in language skills and expressive vocabulary was modest. However, a cochlear implantation had a significant effect on auditory development, in terms of making him aware of sound localization and the different types of environmental sound. Conclusion: Criteria for cochlear implantation are expanding and now include children with disabilities in addition to deafness, such as those with CDLS. Profoundly hearing-impaired children affected by borderline mental retardation should be considered as potential candidates for cochlear implantation.

Background: Dose modulation is a key factor in practical proton therapy. This study investigates the dose modulation methodology of irregular radiation field (IRF)-based proton therapy using forward radiation treatment planning and conformal dose layer stacking (CDLS) methods. Materials and Methods: The geometric configuration of a virtual multi-leaf system was constructed to generate IRFs during Monte Carlo simulations. Two patient geometries— lymphatic metastasis and brain tumors— were configured to investigate the dosimetric feasibility and applications of IRF-based proton therapy in ideal patient anatomies. The investigated tumors were divided into slices perpendicular to proton beam axis. Segments were designed to be conformal to the profiles of these tumor slices. Conformal dose layers were produced by modulating the proton intensities and energies of the predesigned segments. Then, these dose layers were stacked throughout the tumors to obtain sufficient and conformal tumor doses. Results: From the proposed IRF-based proton therapy, tumors with 4-7 cm extents along the depth direction could be treated with fewer than 10 segments. The lymphatic metastasis and brain tumors were sufficiently covered by 95% dose lines, while appropriate distal and proximal dose conformities were achieved. The maximum tumor doses did not exceed 110%. Conclusions: Theoretically, the proposed IRF-based proton therapy using forward planning and CDLS methods is feasible from the viewpoint of dosimetry. This study can serve as a foundation for future investigations of potential proton therapy methods based on fast conformal dose layer stacking using radiation fields with irregular shapes.

A simple node enrichment strategy using a gradient based error estimator is presented for the Collocated Discrete Least Squares (CDLS) meshless method. Also, a procedure is defined to distribute collocation points according to the field nodes position. Here, shape functions are constructed using Radial Point Interpolation Method (RPIM). As temporal discretization a first-order accurate scheme, named semi-incremental fractional step method is used. One of the advantages of this scheme is its capability to use large time step sizes for the solution of the governing equations on steady state problems. The capability of the presented strategy is shown by investigating Carreau-Yasuda fluid flow model in solving lid-driven cavity flow problem with different curve fitting indices values.

Collocated Discrete Least Squares (CDLS) meshfree method, is used for the numerical simulation of the Sain-Venant torsion problem and obtaining the shear stresses in the sections with irregular and complex boundaries. In this paper a matrix formulation is applied in discretizing the governing equations, which make the procedure easy to code and efficient in calculation. In the applied method, a limited number of neighbor nodes are considered in the producing radial basis shape functions, which make the matrices sparse and prepare a suitable condition for sparse matrices algebra and applying available subroutine in this case. In order to validate the proposed method in the analyzing stresses due to torsion, firstly an elliptic section is considered, which in this case, there is an analytical solution. In the second problem, a thin walled section is considered and solved by the theory of Saint-Venant in torsion and results are compared with the closed solution obtaining from the theory of the torsion of thin walled sections. In the third problem, torsion in a hollow elliptical section is solved. Finally, the torsion stresses in sections with more complex geometry is considered.