Shock and traveling wave phenomena on an externally damped, non-linear string

We examine the propagation of shocks and traveling wave phenomena on a one-dimensional string that is executing finite-amplitude, transverse vibrations in a resisting medium. As part of our study, we develop an approach that allows us to describe, albeit approximately, the evolution and propagation of a shock front using analytical methods. In addition, exact traveling wave solutions, one of which involves the Lambert W-function, of the string's equation of motion are determined and analyzed. Lastly, a possible new form of the solution to the linearized problem is presented and extensions and other applications of the present work are briefly discussed.     

Noether-Type Symmetries and Conservation Laws Via Partial Lagrangians

We show how one can construct conservation laws of Euler-Lagrange-type equations via Noether-type symmetry operators associated with what we term partial Lagrangians. This is even in the case when a system does not directly have a usual Lagrangian, e.g. scalar evolution equations. These Noether-type symmetry operators do not form a Lie algebra in general. We specify the conditions under which they do form an algebra. Furthermore, the conditions under which they are symmetries of the Euler-Lagrange-type equations are derived. Examples are given including those that admit a standard Lagrangian such as the Maxwellian tail equation, and equations that do not such as the heat and nonlinear heat equations. We also obtain new conservation laws from Noether-type symmetry operators for a class of nonlinear heat equations in more than two independent variables.     

Shocks and slip systems: Predictions from a mesoscale theory of continuum dislocation dynamics

Exploring a recently developed mesoscale continuum theory of dislocation dynamics, we derive three predictions about plasticity and grain boundary formation in crystals. (1) There is a residual stress jump across grain boundaries and plasticity-induced cell walls as they form, which self-consistently acts to attract neighboring dislocations; residual stress in this theory appears as a remnant of the driving force behind wall formation under both polygonization and plastic deformation. We derive the predicted asymptotic late-time dynamics of the grain-boundary formation process. (2) During grain boundary formation at high temperatures, there is a predicted cusp in the elastic energy density. (3) In early stages of plasticity, when only one type of dislocation is active (single-slip), cell walls do not form in the theory; instead we predict the formation of a hitherto unrecognized jump singularity in the dislocation density.     

Some characterizations of magnetic Sobolev spaces

ABSTRACT

The aim of this note is to survey recent results contained in Nguyen H-M, Squassina M. [On anisotropic Sobolev spaces. Commun Contemp Math, to appear. DOI:10.1142/S0219199718500177]; Nguyen H-M, Pinamonti A, Squassina M, et al. [New characterizations of magnetic Sobolev spaces. Adv Nonlinear Anal. 2018;7(2):227–245]; Pinamonti A, Squassina M, Vecchi E. [Magnetic BV functions and the Bourgain-Brezis-Mironescu formula. Adv Calc Var, to appear. DOI:10.1515/acv-2017-0019]; Pinamonti A, Squassina M, Vecchi E. [The Maz'ya-Shaposhnikova limit in the magnetic setting. J Math Anal Appl. 2017;449:1152–1159] and Squassina M, Volzone B. [Bourgain-Brezis-Mironescu formula for magnetic operators. C R Math Acad Sci Paris. 2016;354:825–831], where the authors extended to the magnetic setting several characterizations of Sobolev and BV functions.     

Thermodynamic description of the viscosity of liquid solder alloys with minor Co impurities

Because of the increasing complexity and cost of experiments carried out, the data for the multi-component alloy systems have frequently been obtained by numerical modelling. It is clear that the related calculations require reliable data dealing with the pure components and binary alloy systems. Selecting the reliable data concerning the pure components from the literature, the viscosities for the SAC and (SAC)_1?x Co_x solder alloys have been calculated using different viscosity models (geometric and physical). The viscosity decreases as the amount of tin content increases in the SAC387 alloy while the addition of the cobalt to SAC387 solder results in the increasing of the viscosity. Moreover, by computing the root mean square values between theoretical and experimental viscosities, it can be concluded that the lowest value among all models is that of obtained by Kaptay equation.     

A novel synthetic strategy for preparing semi‐aromatic components modified polyamide 6 polymer

In this work, a novel synthetic path for preparing semi‐armotic components modified polyamide 6 was developed by caprolactam as solvent of purified terephthalic acid and 1,6‐hexanediamine. First, the ring opening reaction and poly‐addition of caprolactam were initiated by 1,6‐hexanediamine to generate a prepolymer containing amino groups in both ends, then followed by the poly‐condensation reaction with purified terephthalic acid, a long chain copolymer was produced, which the reaction time was reduced by 4 h compared with conventional hydrolytic ring‐opening polymerization of pure caprolactam. By varying the ratio of terephthalic acid and 1,6‐hexanediamine, a series of copolymers with different number average molecular weight and physical properties were prepared. Analytical results showed that the conversion percentage of caprolactam is significantly increased by the proposed method. Furthermore, this new copolymers exhibited excellent transparence and high decomposition temperature. Besides, the copolymers with average molecular weight ≥15,000 present good mechanical properties, making it a potentially useful application in plastics, textile yarn, and membranes. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 959–967     

A UPLC‐TOF/MS‐based metabolomics study of rattan stems of Schisandra chinensis effects on Alzheimer's disease rats model

A UPLC‐TOF/MS‐based metabolomics method was established to explore the therapeutic mechanisms of rattan stems of S. chinensis (SCS) in Alzheimer's disease (AD). Experimental AD model was induced by intra‐hippocampal Aβ_1–42 injection in rats. Cognitive function and oxidative stress condition in brain of AD rats were assessed using Morris water maze tests and antioxidant assays [malondialdehyde (MDA), superoxide dismutase (SOD) and glutathione peroxidase (GSH‐Px)], respectively. UPLC‐TOF/MS combined with multivariate statistical analysis were conducted to study the changes in metabolic networks in serum of rats. The results indicated that the AD model was established successfully and the inducement of Aβ_1–42 caused a decline in spatial learning and memory of rats. The injection of Aβ_1–42 in rat brains significantly elevated the level of MDA, and reduced SOD and GSH‐Px activities. In addition, SCS showed significant anti‐AD effects on model rats. A total of 30 metabolites were finally identified as potential biomarkers of AD and 14 of them had a significant recovery compared with the AD model after SCS administration. Changes in AD metabolite profiling were restored to different levels through the regulation of 13 pathways. This is first report on the use of the UPLC‐TOF/MS‐based serum metabolomics method to investigate therapeutic effects of SCS on AD, and enrich potential biomarkers and metabolic networks of AD.