Extension the Noether's theorem to Lagrangian formulation with nonlocality

A Lagrangian formulation with nonlocality is investigated in this paper. The nonlocality of the Lagrangian is introduced by a new nonlocal argument that is defined as a nonlocal residual satisfying the zero mean condition. The nonlocal Euler-Lagrangian equation is derived from the Hamilton's principle. The Noether's theorem is extended to this Lagrangian formulation with nonlocality. With the help of the extended Noether's theorem, the conservation laws relevant to energy, linear momentum, angular momentum and the Eshelby tensor are determined in the nonlocal elasticity associated with the mechanically based constitutive model. The results show that the conservation laws exist only in the form of the integral over the whole domain occupied by body. The localization of the conservation laws is discussed in detail. We demonstrate that not every conservation law corresponds to a local equilibrium equation. Only when the nonlocal residual of conservation current exists, can a conservation law be transformed into a local equilibrium equation by localization.Comment: 13 page

The gauge theory of dislocations: static solutions of screw and edge dislocations

We investigate the T(3)-gauge theory of static dislocations in continuous solids. We use the most general linear constitutive relations bilinear in the elastic distortion tensor and dislocation density tensor for the force and pseudomoment stresses of an isotropic solid. The constitutive relations contain six material parameters. In this theory both the force and pseudomoment stresses are asymmetric. The theory possesses four characteristic lengths l1, l2, l3 and l4 which are given explicitely. We first derive the three-dimensional Green tensor of the master equation for the force stresses in the translational gauge theory of dislocations. We then investigate the situation of generalized plane strain (anti-plane strain and plane strain). Using the stress function method, we find modified stress functions for screw and edge dislocations. The solution of the screw dislocation is given in terms of one independent length l1=l4. For the problem of an edge dislocation, only two characteristic lengths l2 and l3 arise with one of them being the same l2=l1 as for the screw dislocation. Thus, this theory possesses only two independent lengths for generalized plane strain. If the two lengths l2 and l3 of an edge dislocation are equal, we obtain an edge dislocation which is the gauge theoretical version of a modified Volterra edge dislocation. In the case of symmetric stresses we recover well known results obtained earlier.Comment: 33 pages, 17 figure

New Mechanics of Traumatic Brain Injury

The prediction and prevention of traumatic brain injury is a very important aspect of preventive medical science. This paper proposes a new coupled loading-rate hypothesis for the traumatic brain injury (TBI), which states that the main cause of the TBI is an external Euclidean jolt, or SE(3)-jolt, an impulsive loading that strikes the head in several coupled degrees-of-freedom simultaneously. To show this, based on the previously defined covariant force law, we formulate the coupled Newton-Euler dynamics of brain's micro-motions within the cerebrospinal fluid and derive from it the coupled SE(3)-jolt dynamics. The SE(3)-jolt is a cause of the TBI in two forms of brain's rapid discontinuous deformations: translational dislocations and rotational disclinations. Brain's dislocations and disclinations, caused by the SE(3)-jolt, are described using the Cosserat multipolar viscoelastic continuum brain model. Keywords: Traumatic brain injuries, coupled loading-rate hypothesis, Euclidean jolt, coupled Newton-Euler dynamics, brain's dislocations and disclinationsComment: 18 pages, 1 figure, Late

Predispositional genome sequencing in healthy adults: design, participant characteristics, and early outcomes of the PeopleSeq Consortium

Background: Increasing numbers of healthy individuals are undergoing predispositional personal genome sequencing. Here we describe the design and early outcomes of the PeopleSeq Consortium, a multi-cohort collaboration of predispositional genome sequencing projects, which is examining the medical, behavioral, and economic outcomes of returning genomic sequencing information to healthy individuals. Methods: Apparently healthy adults who participated in four of the sequencing projects in the Consortium were included. Web-based surveys were administered before and after genomic results disclosure, or in some cases only after results disclosure. Surveys inquired about sociodemographic characteristics, motivations and concerns, behavioral and medical responses to sequencing results, and perceived utility. Results: Among 1395 eligible individuals, 658 enrolled in the Consortium when contacted and 543 have completed a survey after receiving their genomic results thus far (mean age 53.0 years, 61.4% male, 91.7% white, 95.5% college graduates). Most participants (98.1%) were motivated to undergo sequencing because of curiosity about their genetic make-up. The most commonly reported concerns prior to pursuing sequencing included how well the results would predict future risk (59.2%) and the complexity of genetic variant interpretation (56.8%), while 47.8% of participants were concerned about the privacy of their genetic information. Half of participants reported discussing their genomic results with a healthcare provider during a median of 8.0 months after receiving the results; 13.5% reported making an additional appointment with a healthcare provider specifically because of their results. Few participants (< 10%) reported making changes to their diet, exercise habits, or insurance coverage because of their results. Many participants (39.5%) reported learning something new to improve their health that they did not know before. Reporting regret or harm from the decision to undergo sequencing was rare (< 3.0%). Conclusions: Healthy individuals who underwent predispositional sequencing expressed some concern around privacy prior to pursuing sequencing, but were enthusiastic about their experience and not distressed by their results. While reporting value in their health-related results, few participants reported making medical or lifestyle changes

Gauge theory and defects in solids

This new series Mechanics and Physics of Discrete Systems aims to provide a coherent picture of the modern development of discrete physical systems. Each volume will offer an orderly perspective of disciplines such as molecular dynamics, crystal mechanics and/or physics, dislocation, etc. Emphasized in particular are the fundamentals of mechanics and physics that play an essential role in engineering applications.Volume 1, Gauge Theory and Defects in Solids, presents a detailed development of a rational theory of the dynamics of defects and damage in solids. Solutions to field

Umweltschutz und qualitatives Wachstum: Bekaempfung der Arbeitslosigkeit und Beschleunigung des qualitativen Wachstums durch mehr Umweltschutz

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