Conservation laws, classical symmetries and exact solutions of the generalized KdV-Burgers-Kuramoto equation

For a generalized KdV-Burgers-Kuramoto equation we have studied conservation laws by using the multiplier method, and investigated its first-level and second level potential systems. Furthermore, the Lie point symmetries of the equation and the Lie point symmetries associated with the conserved vectors are determined. We obtain travellingwave reductions depending on the form of an arbitrary function. We present some explicit solutions: soliton solutions, kinks and antikinks

Orthopedic surgery increases atherosclerotic lesions and necrotic core area in ApoE-/- mice

Background and aims Observational studies show a peak incidence of cardiovascular events after major surgery. For example, the risk of myocardial infarction increases 25-fold early after hip replacement. The acuteness of this increased risk suggests abrupt enhancement in plaque vulnerability, which may be related to intra-plaque inflammation, thinner fibrous cap and/or necrotic core expansion. We hypothesized that acute systemic inflammation following major orthopedic surgery induces such changes. Methods ApoE−/− mice were fed a western diet for 10 weeks. Thereafter, half the mice underwent mid-shaft femur osteotomy followed by realignment with an intramedullary K-wire, to mimic major orthopedic surgery. Mice were sacrificed 5 or 15 days post-surgery (n = 22) or post-saline injection (n = 13). Serum amyloid A (SAA) was measured as a marker of systemic inflammation. Paraffin embedded slides of the aortic root were stained to measure total plaque area and to quantify fibrosis, calcification, necrotic core, and inflammatory cells. Results Surgery mice showed a pronounced elevation of serum amyloid A (SAA) and developed increased plaque and necrotic core area already at 5 days, which reached significance at 15 days (p = 0.019; p = 0.004 for plaque and necrotic core, respectively). Macrophage and lymphocyte density significantly decreased in the surgery group compared to the control group at 15 days (p = 0.037; p = 0.024, respectively). The density of neutrophils and mast cells remained unchanged. Conclusions Major orthopedic surgery in ApoE−/− mice triggers a systemic inflammatory response. Atherosclerotic plaque area is enlarged after surgery mainly due to an increase of the necrotic core. The role of intra-plaque inflammation in this response to surgical injury remains to be fully elucidated. © 2016 Elsevier Ireland Lt

Optimal polygonal L1 linearization and fast interpolation of nonlinear systems

The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using polygonal (continuous piecewise linear) models under the L1 norm. A thorough error analysis is developed to guide an optimal design of two kinds of polygonal approximations in the asymptotic case of a large budget of evaluation subintervals N. The method allows the user to obtain the level of linearization (N) for a target approximation error and vice versa. It is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), allowing real-time performance of computationally demanding applications. The quality and efficiency of the technique has been measured in detail on two nonlinear functions that are widely used in many areas of scientific computing and are expensive to evaluate

DYNAMIC MODELLING OF HIGH SPEED BALLASTED RAILWAY TRACKS: ANALYSIS OF THE BEHAVIOUR

[EN] The aim of the paper is to present a numerical model for a ballasted railway track that includes the dynamic effect of a moving train load and predicts the values of the vertical stiffness of the infrastructure. This model is therefore deemed to be a tool for the evaluation of the state of the track during service situations as well as a predictive model of the behaviour of the system. Consequently, it will be very useful when sizing the cross section of a new railway line is required. The main modelling tool is the finite element method. In regard to this, the application of damping elements to avoid the elastic wave reflection on the boundaries of the numerical domain will be studied. The proposed dynamic analysis consider the change in time of the value of the train load, but not the change in position along the tracks. In the end, a set of suggestions for the numerical model with moving loads will be summarize aiming for the mitigation of the unusual behaviour of the contact surface between the ballast and the sleepers.Gallego, I.; Rivas, A.; Sánchez-Cambronero, S.; Lajara, J. (2016). DYNAMIC MODELLING OF HIGH SPEED BALLASTED RAILWAY TRACKS: ANALYSIS OF THE BEHAVIOUR. En XII Congreso de ingeniería del transporte. 7, 8 y 9 de Junio, Valencia (España). Editorial Universitat Politècnica de València. 615-623. https://doi.org/10.4995/CIT2016.2015.4218OCS61562

Symmetry reductions for thin film type equations

The lubrication equation ut = (u nuxxx)x plays an important role in the study of the interface movements. In this work we analyze the generalizations of the above equation given by ut = (u nuxxx)x − kumux. By using Lie classical method the corresponding reductions are performed and some solutions are characterized

Generalized Camassa-Holm Equations: Symmetry, Conservation Laws and Regular Pulse and Front Solutions

In this paper, we consider a member of an integrable family of generalized Camassa-Holm (GCH) equations. We make an analysis of the point Lie symmetries of these equations by using the Lie method of infinitesimals. We derive nonclassical symmetries and we find new symmetries via the nonclassical method, which cannot be obtained by Lie symmetry method. We employ the multiplier method to construct conservation laws for this family of GCH equations. Using the conservation laws of the underlying equation, double reduction is also constructed. Finally, we investigate traveling waves of the GCH equations. We derive convergent series solutions both for the homoclinic and heteroclinic orbits of the traveling-wave equations, which correspond to pulse and front solutions of the original GCH equations, respectively

Experimentación, simulación y análisis de artefactos improvisados-proyectiles formados por explosión

Dentro de los artefactos explosivos improvisados se encuentran aquellos que generan proyectiles formados por explosión, penetradores de blindajes y sistemas acorazados, como los utilizados por grupos insurgentes contra las fuerzas aliadas en zona de operaciones. El objeto de este estudio es reproducir y entender el comportamiento de dichos artefactos explosivos improvisados capaces de generar proyectiles de alta velocidad y gran capacidad de penetración. La comprensión de su comportamiento permitirá mejorar el conocimiento sobre ellos, y por ende, combatirlos de forma más eficaz. Para ello se han realizado los ensayos correspondientes, obteniéndose las primeras caracterizaciones de proyectiles formados por explosión construidos de manera artesanal, tal y como haría un terrorista. Además, se han creado los modelos numéricos correspondientes a cada ensayo, que simulan todo el evento desde su inicio hasta el impacto en el objetivo, recorriendo todos los pasos intermedios. Se han ensayado 3 configuraciones y posteriormente se han simulado, usando el software de análisis por elementos finitos, LS-DYNA, con una configuración 2D axisimétrica, con mallados lagrangianos. Los resultados obtenidos por el modelo han alcanzado un alto grado de precisión con relación a los datos experimentales. A partir de aquí se puede concluir que los artefactos explosivos improvisados-proyectiles formados por explosión son una seria amenaza, y que los modelos generados permitirán conocer y ahorrar costes en la lucha contra esta amenaza, y por ende contra el terrorismo, al disponer de un enfoque holístico de la amenaza, y finalmente reducir los costes de la experimentación

Lie Point Symmetries, Traveling Wave Solutions and Conservation Laws of a Non-linear Viscoelastic Wave Equation

This paper studies a non-linear viscoelastic wave equation, with non-linear damping and source terms, from the point of view of the Lie groups theory. Firstly, we apply Lie's symmetries method to the partial differential equation to classify the Lie point symmetries. Afterwards, we reduce the partial differential equation to some ordinary differential equations, by using the symmetries. Therefore, new analytical solutions are found from the ordinary differential equations. Finally, we derive low-order conservation laws, depending on the form of the damping and source terms, and discuss their physical meaning.The support of the Plan Propio de Investigacion de la Universidad de Cadiz is gratefully acknowledged. The authors also thank the referees for their suggestions to improve the quality of the paper