Search results for "equation"

Angular Pseudomomentum Theory for the Generalized Nonlinear Schr\"{o}dinger Equation in Discrete Rotational Symmetry Media

2009

We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schr\"odinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear Schr\"odinger equation with a nonlinearity depending on the modulus of the field. We provide a rigorous proof of a set of mathematical results justifying that these solitons can be classified according to the irreducible representations of a discrete group. Then we extend this theory to non-stationary solutions and study the relationship between angular momentum and pseudomomentum. We illustrate these theoretical results with numerical examples. Finally, we…

A second strain gradient elasticity theory with second velocity gradient inertia – Part II: Dynamic behavior

2013

Abstract This paper is the sequel of a companion Part I paper devoted to the constitutive equations and to the quasi-static behavior of a second strain gradient material model with second velocity gradient inertia. In the present Part II paper, a multi-cell homogenization procedure (developed in the Part I paper) is applied to a nonhomogeneous body modelled as a simple material cell system, in conjunction with the principle of virtual work (PVW) for inertial actions (i.e. momenta and inertia forces), which at the macro-scale level takes on the typical format as for a second velocity gradient inertia material model. The latter (macro-scale) PVW is used to determine the equilibrium equations …

A gradient elasticity theory for second-grade materials and higher order inertia

2012

Abstract Second-grade elastic materials featured by a free energy depending on the strain and the strain gradient, and a kinetic energy depending on the velocity and the velocity gradient, are addressed. An inertial energy balance principle and a virtual work principle for inertial actions are envisioned to enrich the set of traditional theoretical tools of thermodynamics and continuum mechanics. The state variables include the body momentum and the surface momentum, related to the velocity in a nonstandard way, as well as the concomitant mass-accelerations and inertial forces, which do intervene into the motion equations and into the force boundary conditions. The boundary traction is the …

Predicting maximum annual values of event soil loss by USLE-type models

2017

Abstract Previous experimental investigations showed that a large proportion of total plot soil erosion over a long time period is generally due to relatively few, large storms. Consequently, erosion models able to accurately predict the highest plot soil loss values have practical importance since they could allow to improve the design of soil conservation practices in an area of interest. At present USLE-based models are attractive from a practical point of view, since the input data are generally easy to obtain. The USLE was developed with specific reference to the mean annual temporal scale but it was also applied at the event scale. Other models, such as the USLE-M and the USLE-MM, app…

FRACTIONAL-ORDER GENERALIZATION OF TRANSPORT EQUATIONS IN FRACTAL POROUS MEDIA

2014

Quality parameters, bioactive compounds and their correlation with antioxidant capacity of commercial fruit-based baby foods

2013

Comprehensive research is required to achieve the optimization of the antioxidant protection through baby foods, in particular, the commercially available fruit-based baby foods. This study investigated the physicochemical properties, ascorbic acid (AA), total carotenoids (TC), total phenolic content (TPC), trolox equivalent antioxidant capacity (TEAC) and oxygen radical absorbance capacity (ORAC) of 23 different commercially available fruit-based baby foods. The main contribution to the total antioxidant capacity (trolox equivalent antioxidant capacity and oxygen radical absorbance capacity) was provided by ascorbic acid, followed by phenolic compounds, in accordance with a mathematical e…

New indefinite integrals from a method using Riccati equations

2018

ABSTRACTAn earlier method for obtaining indefinite integrals of special function from the second-order linear equations which define them has been reformulated in terms of Riccati equations, which ...

Closure properties for integral problems driven by regulated functions via convergence results

2018

Abstract In this paper we give necessary and sufficient conditions for the convergence of Kurzweil–Stieltjes integrals with respect to regulated functions, using the notion of asymptotical equiintegrability. One thus generalizes several well-known convergence theorems. As applications, we provide existence and closure results for integral problems driven by regulated functions, both in single- and set-valued cases. In the particular setting of bounded variation functions driving the equations, we get features of the solution set of measure integrals problems.

Local regularity for quasi-linear parabolic equations in non-divergence form

2018

Abstract We consider viscosity solutions to non-homogeneous degenerate and singular parabolic equations of the p -Laplacian type and in non-divergence form. We provide local Holder and Lipschitz estimates for the solutions. In the degenerate case, we prove the Holder regularity of the gradient. Our study is based on a combination of the method of alternatives and the improvement of flatness estimates.

Oscillation criteria for even-order neutral differential equations

2016

Abstract We study oscillatory behavior of solutions to a class of even-order neutral differential equations relating oscillation of higher-order equations to that of a pair of associated first-order delay differential equations. As illustrated with two examples in the final part of the paper, our criteria improve a number of related results reported in the literature.