Crack nucleation in a peridynamic solid

A condition for the emergence of a discontinuity in an elastic peridynamic body is proposed, resulting in a material stability condition for crack nucleation. The condition is derived by determining whether a small discontinuity in displacement, superposed on a possibly large deformation, grows over time. Stability is shown to be determined by the sign of the eigenvalues of a tensor field that depends only on the linearized material properties. This condition for nucleation of a discontinuity in displacement can be interpreted in terms of the dynamic stability of plane waves with very short wavelength. A numerical example illustrates that cracks in a peridynamic body form spontaneously as the body is loaded

Positive approximations of the inverse of fractional powers of SPD M-matrices

This study is motivated by the recent development in the fractional calculus and its applications. During last few years, several different techniques are proposed to localize the nonlocal fractional diffusion operator. They are based on transformation of the original problem to a local elliptic or pseudoparabolic problem, or to an integral representation of the solution, thus increasing the dimension of the computational domain. More recently, an alternative approach aimed at reducing the computational complexity was developed. The linear algebraic system $\cal A^\alpha \bf u=\bf f$, $0< \alpha <1$ is considered, where $\cal A$ is a properly normalized (scalded) symmetric and positive definite matrix obtained from finite element or finite difference approximation of second order elliptic problems in $\Omega\subset\mathbb{R}^d$, $d=1,2,3$. The method is based on best uniform rational approximations (BURA) of the function $t^{\beta-\alpha}$ for $0 < t \le 1$ and natural $\beta$. The maximum principles are among the major qualitative properties of linear elliptic operators/PDEs. In many studies and applications, it is important that such properties are preserved by the selected numerical solution method. In this paper we present and analyze the properties of positive approximations of $\cal A^{-\alpha}$ obtained by the BURA technique. Sufficient conditions for positiveness are proven, complemented by sharp error estimates. The theoretical results are supported by representative numerical tests

Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains

We explore the connection between fractional order partial differential equations in two or more spatial dimensions with boundary integral operators to develop techniques that enable one to efficiently tackle the integral fractional Laplacian. In particular, we develop techniques for the treatment of the dense stiffness matrix including the computation of the entries, the efficient assembly and storage of a sparse approximation and the efficient solution of the resulting equations. The main idea consists of generalising proven techniques for the treatment of boundary integral equations to general fractional orders. Importantly, the approximation does not make any strong assumptions on the shape of the underlying domain and does not rely on any special structure of the matrix that could be exploited by fast transforms. We demonstrate the flexibility and performance of this approach in a couple of two-dimensional numerical examples

A peridynamic based machine learning model for one-dimensional and two-dimensional structures

With the rapid growth of available data and computing resources, using data-driven models is a potential approach in many scientific disciplines and engineering. However, for complex physical phenomena that have limited data, the data-driven models are lacking robustness and fail to provide good predictions. Theory-guided data science is the recent technology that can take advantage of both physics-driven and data-driven models. This study presents a novel peridynamics based machine learning model for one and two-dimensional structures. The linear relationships between the displacement of a material point and displacements of its family members and applied forces are obtained for the machine learning model by using linear regression. The numerical procedure for coupling the peridynamic model and the machine learning model is also provided. The numerical procedure for coupling the peridynamic model and the machine learning model is also provided. The accuracy of the coupled model is verified by considering various examples of a one-dimensional bar and two-dimensional plate. To further demonstrate the capabilities of the coupled model, damage prediction for a plate with a pre-existing crack, a two-dimensional representation of a three-point bending test, and a plate subjected to dynamic load are simulated

Derivation of dual horizon state-based peridynamics formulation based on euler-lagrange equation

The numerical solution of peridynamics equations is usually done by using uniform spatial discretisation. Although implementation of uniform discretisation is straightforward, it can increase computational time significantly for certain problems. Instead, non-uniform discretisation can be utilised and different discretisation sizes can be used at different parts of the solution domain. Moreover, the peridynamic length scale parameter, horizon, can also vary throughout the solution domain. Such a scenario requires extra attention since conservation laws must be satisfied. To deal with these issues, dual-horizon peridynamics was introduced so that both non-uniform discretisation and variable horizon sizes can be utilised. In this study, dual-horizon peridynamics formulation is derived by using Euler–Lagrange equation for state-based peridynamics. Moreover, application of boundary conditions and determination of surface correction factors are also explained. Finally, the current formulation is verified by considering two benchmark problems including plate under tension and vibration of a plate

The Relationship between Oral Squamous Cell Carcinoma and Human Papillomavirus: A Meta-Analysis of a Chinese Population (1994–2011)

Background: Previous studies indicated that oral squamous cell carcinomas (OSCC) might be related to human papilloma virus (HPV) infection. However, up to now, there still lacks a large sample study to analyze the relationship between OSCC in a Chinese population and oral HPV infection. In the present study, we used a meta-analysis to evaluate the relationship of OSCC with HPV infection in a Chinese population. Methods: The reports on HPV and OSCC in a Chinese population published between January, 1994, and September, 2011 were retrieved via CNKI/WANFANG/OVID/MEDLINE databases. According to the inclusion criteria, we selected 18 eligible case-control studies. After testing the heterogeneity of the studies by the Cochran Q test, the meta-analyses for HPV and HPV16 were performed using the fixed effects model. Results: The overall positive rates of HPV and HPV16 in OSCC were 58.0 % (354/610; 95 % confidence interval [CI], 54.1–61.9) and 47.47 % (169/356; 95 % CI: 42.3–52.7), respectively; which were significantly higher than those in normal controls 10.44% (26/249; 95 % CI: 7.2–14.7) and 7.1 % (13/182; 95 % CI: 4.2–11.8). Quantitative meta-analysis revealed that, compared with normal controls, the combined odds ratios of OSCC with HPV or HPV16 infection were 12.7 (95 % CI: 8.0–20.0) and 9.0 (95% CI: 5.1–15.6), respectively. Both Begg’s test and funnel plots revealed that no publication bias was found in this present study (P.0.05)

Fluconazole for empiric antifungal therapy in cancer patients with fever and neutropenia

BACKGROUND: Several clinical trials have demonstrated the efficacy of fluconazole as empiric antifungal therapy in cancer patients with fever and neutropenia. Our objective was to assess the frequency and resource utilization associated with treatment failure in cancer patients given empiric fluconazole antifungal therapy in routine inpatient care. METHODS: We performed a retrospective cohort study of cancer patients treated with oral or intravenous fluconazole between 7/97 and 6/01 in a tertiary care hospital. The final study cohort included cancer patients with neutropenia (an absolute neutrophil count below 500 cells/mm(3)) and fever (a temperature above 38°C or 100.4°F), who were receiving at least 96 hours of parenteral antibacterial therapy prior to initiating fluconazole. Patients' responses to empiric therapy were assessed by reviewing patient charts. RESULTS: Among 103 cancer admissions with fever and neutropenia, treatment failure after initiating empiric fluconazole antifungal therapy occurred in 41% (95% confidence interval (CI) 31% – 50%) of admissions. Patients with a diagnosis of hematological malignancy had increased risk of treatment failure (OR = 4.6, 95% CI 1.5 – 14.8). When treatment failure occurred the mean adjusted increases in length of stay and total costs were 7.4 days (95% CI 3.3 – 11.5) and $18,925 (95% CI 3,289 – 34,563), respectively. CONCLUSION: Treatment failure occurred in more than one-third of neutropenic cancer patients on fluconazole as empiric antifungal treatment for fever in routine clinical treatment. The increase in costs when treatment failure occurs is substantial