Search Results (6)

Two systems of mathematical physics are defined by us, which are the first-order differential system (FODS) and the second-order differential system (SODS). Basing on the conventional Legendre transformation, we obtain a new kind of canonical equations of Hamilton (CEH) with some kind of symmetry. We show that the FODS can only be expressed by the new CEH, but do not by the conventional CEH, while the SODS can be done by both the new and the conventional CEHs, on basis of the same conventional Legendre transformation. As an example, we prove that the nonlinear Schrödinger equation can be expressed with the new CEH in a consistent way. Based on the new CEH, the approximate soliton solution of the nonlocal nonlinear Schrödinger equation is obtained, and the soliton stability is analysed analytically as well. Furthermore, because the symmetry of a system is closely connected with certain conservation theorem of the system, the new CEH may be useful in some complicated systems when the symmetry considerations are used. Full article

We present a novel finite element method to solve the thermal variables in welding problems. The mathematical model is based on the enthalpy formulation of the energy conservation law, which is simultaneously valid for the solid, liquid, and mushy regions. Both isothermal and non-isothermal melting models are considered to relate the enthalpy with the temperature. Quadratic triangular elements with local anisotropic mesh adaptation are employed for the space discretization of the governing equation, and a second-order backward differentiation formula is employed for the time discretization. The resulting non-linear discretized system is solved with a simple Newton algorithm with two versions: the $\theta$-Newton algorithm, which considers the temperature as the main unknown variable, as in most works in the literature, and the h-Newton algorithm, which considers the enthalpy, which is the main novelty of the present work. Then, we show via numerical experiments that the h-Newton method is robust and converges well to the solution, both for isothermal and non-isothermal melting. However, the $\theta$-method can only be applied to the case of non-isothermal melting and converges only for a sufficiently large melting temperature range or sufficiently small time step. Numerical experiments also confirm that the method is able to adequately capture the discontinuities or sharp variations in the solution without the need for any kind of numerical dissipation. Full article

The primary purpose of this article is to use the laws of thermodynamics, mainly the second and fourth laws, to evaluate three energy technologies of the future: fusion, solar, and fission. Among the criteria used to evaluate them, the most important are the amount of matter needed to sustain the technology itself and the environmental impact. Much emphasis is placed here on the fourth law of thermodynamics, which introduces the concept of material entropy. Zemansky–Georgescu-Roegen’s Law of Inevitable Dissipation of Useful Concentrated Matter states that, in the economic process, some matter is inevitably degraded and becomes unavailable matter. This has tremendous implications for humanity as a whole since the Earth is thermodynamically a closed system, meaning that it cannot exchange matter with space but is open to the flow of solar energy. This results in the need to conserve matter and natural resources. This law can be used as an important criterion for the selection of energy technology. Moreover, the flow–fund model, which was proposed by Georgescu-Roegen, was used to assess the viability of energy technologies. The final conclusion is that there is no Promethean technology of the third kind yet, but the closest to meeting this condition is solar technology. Technology based on nuclear fission has been rejected due to its adverse ecological effects, while fusion technology has proven to be less useful due to the matter criterion, the negative environmental impact, since radioactive waste only becomes safe for humans after 500 years, and the risks associated with nuclear proliferation. Solar technology can become Prometheus III only after all of humanity is involved with this project, which requires profound social changes, widespread demilitarization, and the development of organic agriculture. This implies the necessity of the emergence of a global solar society based on an economic system called solar communism. Full article

The counterpart for Euler’s buckling problem is Greenhill’s problem, which studies the forming of a loop in an elastic beam under torsion. In the context of twisted shafts, the optimal shape of the beam along its axis is searched. A priori form of the cross-section remains unknown. For the solution of the actual problem, the stability equations take into account all possible convex and simply connected shapes of the cross-section. The cross-sections are similar geometric figures related by a homothetic transformation with respect to a homothetic center on the axis of the beam and vary along its axis. The distribution of material along the length of a twisted shaft is optimized so that the beam is of the constant volume and will support the maximal moment without spatial buckling. The applications of the variational method for stability problems are illustrated in this manuscript. Full article

Based on the rigid finite element method and multibody dynamics, a discrete model of a flexible conveyor belt considering the material viscoelasticity is established. RFE (rigid finite element) and SDE (spring damping element) are used to describe the rigidity and flexibility of a conveyor belt. The dynamic differential equations of the RFE are derived by using Lagrange’s equation of the second kind of the non-conservative system. The generalized elastic potential capacity and generalized dissipation force of the SDE are considered. The forward recursive formula is used to construct the conveyor belt model. The validity of dynamic equations of conveyor belt is verified by field test. The starting mode of the conveyor is simulated by the model. Full article

A new 3D acquisition and processing procedure to map RGB, thermal IR and near infrared images (NIR) on a detailed 3D model of a building is presented. The combination and fusion of different data sources allows the generation of 3D thermal data useful for different purposes such as localization, visualization, and analysis of anomalies in contemporary architecture. The classic approach, which is currently used to map IR images on 3D models, is based on the direct registration of each single image by using space resection or homography. This approach is largely time consuming and in many cases suffers from poor object texture. To overcome these drawbacks, a “bi-camera” system coupling a thermal IR camera to a RGB camera has been setup. The second sensor is used to orient the “bi-camera” through a photogrammetric network also including free-handled camera stations to strengthen the block geometry. In many cases the bundle adjustment can be executed through a procedure for automatic extraction of tie points. Terrestrial laser scanning is adopted to retrieve the 3D model building. The integration of a low-cost NIR camera accumulates further radiometric information on the final 3D model. The use of such a sensor has not been exploited until now to assess the conservation state of buildings. Here some interesting findings from this kind of analysis are reported. The paper shows the methodology and its experimental application to a couple of buildings in the main Campus of Politecnico di Milano University, where IR thermography has previously been carried out for conservation and maintenance purposes. Full article