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141.
The Shallow–Water Equations (SWEs), also referred to as the de Saint-Venant equations, constitute the current governing mathematical tool for free-surface water flows. These include, e.g., flood flows in rivers and in urban zones, flows across hydraulic structures as dams or wastewater facilities, flows in the environmental fields, glaciology, or meteorology. Despite this attractiveness, the system of two partial differential equations has an exact mathematical solution only for a limited number of problems of practical relevance.This historical work on the SWEs is based on a correspondence between two 19th-century scientists, de Saint-Venant and Boussinesq. Their well-known papers are thus commented from the point of development of their theory; the input of both scientists is evidenced by their writings, and comments of both to each other that led to what is commonly known as the SWEs. Given the age difference of the two of 45 years, the experienced engineer de Saint-Venant, and the mathematician Boussinesq, two eminent researchers, met to discuss not only problems in hydraulics, but in physics generally. In addition, their correspondence embraced also questions in ethics, religion, history of sciences, and personal news.The results of the SWEs cease to hold if streamline curvature effects dominate; this includes breaking waves, solitary and cnoidal waves, or non-linear waves in general. In most other cases, however, the SWEs perfectly apply to typical flows in engineering practice; they are considered the fundamental system of equations describing open channel flows. This work thus provides a background to its birth, including lots of comments as to its improvement, physical meanings, methods of solution, and a discussion of the results. This paper also deals with the steady flow equations, gives a short account on the main persons mentioned in the Correspondence, and provides a summary of further developments of the SWEs until 1920. 相似文献
142.
Juan F. Navarro M.C. Martínez–Belda 《Mathematical Methods in the Applied Sciences》2020,43(5):2289-2300
In the N-body ring problem, we investigate the motion of a massless body interacting with N bodies of equal masses at the vertices of a regular polygon that rotates around a central mass. In this paper, we analyze the use of different surfaces of section in the numerical exploration of the escape in the N-body ring problem in order to get some conclusions about the geometry of the basins of escape in the corresponding configuration spaces. 相似文献
143.
We revisit the derivation of the microscopic stress, linking the statistical mechanics of particle systems and continuum mechanics. The starting point in our geometric derivation is the Doyle–Ericksen formula, which states that the Cauchy stress tensor is the derivative of the free-energy with respect to the ambient metric tensor and which follows from a covariance argument. Thus, our approach to define the microscopic stress tensor does not rely on the statement of balance of linear momentum as in the classical Irving–Kirkwood–Noll approach. Nevertheless, the resulting stress tensor satisfies balance of linear and angular momentum. Furthermore, our approach removes the ambiguity in the definition of the microscopic stress in the presence of multibody interactions by naturally suggesting a canonical and physically motivated force decomposition into pairwise terms, a key ingredient in this theory. As a result, our approach provides objective expressions to compute a microscopic stress for a system in equilibrium and for force-fields expanded into multibody interactions of arbitrarily high order. We illustrate the proposed methodology with molecular dynamics simulations of a fibrous protein using a force-field involving up to 5-body interactions. 相似文献
144.
145.
Maryam S. Sadeghi Mohammad Reza Moghbeli William A. Goddard III 《Journal of polymer science. Part A, Polymer chemistry》2021,59(7):614-626
We followed the self-assembly of high-molecular weight MePEG- b -PCL (poly(methyl ethylene glycol)-block-poly(ε-caprolactone)) diblock and MePEG- b -PBO- b -PCL (poly(methyl ethylene glycol)-block-poly(1,2-butylene oxide)-block-poly(ε-caprolactone)) into micelles using molecular dynamics simulation with a coarse grain (CG) force field based on quantum mechanics (CGq FF). The triblock polymer included a short poly(1,2-butylene oxide) (PBO) at the hydrophilic-hydrophobic interface of these systems. Keeping the hydrophilic length fixed (MePEG45), we considered 250 chains in which the hydrophobic length changed from PCL44 or PBO6- b -PCL43 to PCL62 or PBO9- b -PCL61. The polymers were solvated in explicit water for 2 μs of simulations at 310.15 K. We found that the longer diblock system undergoes a morphological transition from an intermediate rod-like micelle to a prolate-sphere, while the micelle formed from the longer triblock system is a stable rod-like micelle. The two shorter diblock and triblock systems show similar self-assembly processes, both resulting in slightly prolate-spheres. The dynamics of the self-assembly is quantified in terms of chain radius of gyration, shape anisotropy, and hydration of the micelle cores. The final micelle structures are analyzed in terms of the local density components. We conclude that the CG model accurately describes the molecular mechanisms of self-assembly and the equilibrium micellar structures of hydrophilic and hydrophobic chains, including the quantity of solvent trapped inside the micellar core. 相似文献
146.
Sergio Conti Matteo Focardi Flaviana Iurlano 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(2):455-474
We consider the Griffith fracture model in two spatial dimensions, and prove existence of strong minimizers, with closed jump set and continuously differentiable deformation fields. One key ingredient, which is the object of the present paper, is a generalization to the vectorial situation of the decay estimate by De Giorgi, Carriero, and Leaci. This is based on replacing the coarea formula by a method to approximate functions with small jump set by Sobolev functions, and is restricted to two dimensions. The other two ingredients will appear in companion papers and consist respectively in regularity results for vectorial elliptic problems of the elasticity type and in a method to approximate in energy functions by ones. 相似文献
147.
《Journal of Coordination Chemistry》2012,65(2):305-317
Abstract The conformational behaviour of a series of ring substituted (ortho-Cl, F and meta or para OH) Pt(II) complexes of general formula [(1,2-hydroxyphenyl)ethylenediamine]PtL2 [L ? Cl, 1] has been studied by molecular mechanics (MM) methods. Preferred orientations of the phenyl rings, which are important for the complexes′ biological activity, were obtained by calculations of rotational energies about Csp3?Car bonds for all theoretically possible isomers and conformers, meso-λ (R,S/S,R-λ), meso-δ (R,S/S,R-δ), d,l-δ (S,S/R,R-λ) and d,l-λ (S,S/R, R-δ). The influence of the ring substituents and the conformation type on the positions of the energy minima and barriers to rotations about Csp3?Car and Car-O(H) bonds were investigated in detail. Theoretical predictions were compared with the experimental results where appropriate. 相似文献
148.
In this work, the sliding contact of viscoelastic layers of finite thickness on rigid sinusoidal substrates is investigated within the framework of Green's functions approach. The periodic Green's functions are determined by means of a novel formalism, which can be applied, in general, to either 2D and 3D viscoelastic periodic contacts, regardless of the contact geometry and boundary conditions.Specifically, two different configurations are considered here: a free layer with a uniform pressure applied on the top, and a layer rigidly confined on the upper boundary. It is shown that the thickness affects the contact behavior differently, depending on the boundary conditions. In particular, the confined layer exhibits increasing contact stiffness when the thickness is reduced, leading to higher loads for complete contact to occur. The free layer, instead, becomes more and more compliant as thickness is reduced.We find that, in partial contact, the layer thickness and the boundary conditions significantly affect the frictional behavior. In fact, at low contact penetrations, the confined layer shows higher friction coefficients compared to the free layer case; whereas, the scenario is reversed at large contact penetrations. Furthermore, for confined layers, the sliding speed related to the friction coefficient peak is shifted as the contact penetration increases. However, once full contact is established, the friction coefficient shows a unique behavior regardless of the layer thickness and boundary conditions. 相似文献
149.
This paper investigates the novel development of a mass sensitive nanosensor based on the use of individual spherical fullerenes. The main advantage of the mass sensing ability of spherical fullerenes in comparison with other nanomaterials such as carbon nanotubes (CNTs) or graphene nanoribbons (GNRs) is the fact that they present almost perfect geometric symmetry and thus a unique vibrational behavior which is independent from the location of the externally added nanoparticle. The study is conducted by the use of a computationally effective numerical scheme based on the adoption of appropriate three dimensional line spring elements as well as point mass elements to simulate the atomistic structure of fullerenes and interatomic interactions appearing between carbon atoms. The free vibration of C20, C60, C80 and C180 molecules is analyzed without and with an external nanoparticle of specific mass attached on their structure to calculate the arisen change in their natural frequencies and corresponding shape modes. A parametric study concerning the magnitude and location of the added mass is performed in order to evaluate the mass sensing ability of the fullerenes under consideration. 相似文献
150.
Alexander Gluhovsky Christopher Tong 《Communications in Nonlinear Science & Numerical Simulation》2012,17(7):3112-3113
Extensive prior literature (not referenced in the paper) on links between mechanical gyrostats and nonlinear dynamical systems with strange attractors is called to the readers’ attention. 相似文献