A high-order FEM formulation for free and forced vibration analysis of a nonlocal nonlinear graded Timoshenko nanobeam based on the weak form quadrature element method

The purpose of this paper is to provide a high-order finite element method (FEM) formulation of nonlocal nonlinear nonlocal graded Timoshenko based on the weak form quadrature element method (WQEM). This formulation offers the advantages and flexibility of the FEM without its limiting low-order accuracy. The nanobeam theory accounts for the von Kármán geometric nonlinearity in addition to Eringen’s nonlocal constitutive models. For the sake of generality, a nonlinear foundation is included in the formulation. The proposed formulation generates high-order derivative terms that cannot be accounted for using regular first- or second-order interpolation functions. Hamilton’s principle is used to derive the variational statement which is discretized using WQEM. The results of a WQEM free vibration study are assessed using data obtained from a similar problem solved by the differential quadrature method (DQM). The study shows that WQEM can offer the same accuracy as DQM with a reduced computational cost. Currently the literature describes a small number of high-order numerical forced vibration problems, the majority of which are limited to DQM. To obtain forced vibration solutions using WQEM, the authors propose two different methods to obtain frequency response curves. The obtained results indicate that the frequency response curves generated by either method closely match their DQM counterparts obtained from the literature, and this is despite the low mesh density used for the WQEM systems

The role of COX-2 in rectal cancer treated with preoperative radiotherapy

Radiotherapy is one of the principal modalities of rectal cancer treatment, and the ability to predict radio resistance could potentially improve survival through a targeted treatment approach. Cyclooxygenase-2 (COX-2) may protect against damage by irradiation that would justify the use of COX-2 inhibitors. The purpose of this study was to investigate the potential role of COX-2 in tumor response and outcome of patients with rectal cancer treated preoperatively with radiotherapy. Using immunohistochemistry, we examined COX-2 expression in 88 surgical specimens of rectal cancer treated preoperatively and in 26 pretherapeutic biopsies. We tested whether COX-2 expression was correlated with clinico-pathologic parameters and with survival and local recurrence. COX-2 was expressed in 50% of the pretherapeutic tumor biopsies and in 88.6% of post-irradiated surgical samples. COX-2 expression was correlated only with enhanced tumor inflammation (p=0.03) and with tumor volume exceeding 30 cc (p=0.05). COX-2 was not significantly correlated with patient survival, but none of the patients with COX-2 negative tumors did recur locally, whereas 80% of patients with local recurrences have COX-2 positive tumors. We conclude that COX-2 expression is overexpressed in the majority of rectal cancers treated with radiotherapy and likely plays a role in local relapse

A Markov analysis of social learning and adaptation

Adaptive learning, Markov chain, Cobweb model, C62, D83,