No Arabic abstract
In medicolegal situations, the consequences of a stabbing incident are described in terms that are qualitative without being quantitative. Here, the mechanical variables involved in knife-tissue penetration events are used to determine the parameters needed to be controlled in a measurement device. They include knife geometry, in-plane mechanical stress state of skin, angle and speed of knife penetration, and underlying fascia. Four household knives with different geometries were used. Synthetic materials were used to simulate the response of skin, fat and cartilage: polyurethane, foam, and ballistic soap, respectively. The force and energy applied by the blade and the skin displacement were used to identify skin penetration. The skin tension is shown to have a direct effect on the force and energy for knife penetration and on the depth of displacement of the simulant prior to penetration: larger levels of in-plane tension in the skin are associated with lower penetration forces, energies and displacements. Less force and energy are required for puncture when the blade is parallel to a direction of greater skin tension than when perpendicular. Surprisingly, evidence suggests that the quality control processes used to manufacture knives fail to produce consistently uniform blade points in nominally identical knives, leading to penetration forces which can vary widely.
We introduce and study the mechanical system which describes the dynamics and statics of rigid bodies of constant density floating in a calm incompressible fluid. Since much of the standard equilibrium theory, starting with Archimedes, allows bodies with vertices and edges, we assume the bodies to be convex and take care not to assume more regularity than that implied by convexity. One main result is the (Liapunoff) stability of equilibria satisfying a condition equivalent to the standard metacentric criterion.
Collagen is a key structural protein in the human body, which undergoes mineralization during the formation of hard tissues. Earlier studies have described the mechanical behavior of bone at different scales highlighting material features across hierarchical structures. Here we present a study that aims to understand the mechanical properties of mineralized collagen fibrils upon tensile/compressive transient loads, investigating how the kinetic energy propagates and it is dissipated at the molecular scale, thus filling a gap of knowledge in this area. These specific features are the mechanisms that Nature has developed to passively dissipate stress and prevent structural failures. In addition to the mechanical properties of the mineralized fibrils, we observe distinct nanomechanical behaviors for the two regions (i.e., overlap and gap) of the D-period to highlight the effect of the mineralization. We notice decreasing trends for both wave speeds and Young s moduli over input velocity with a marked strengthening effect in the gap region due to the accumulation of the hydroxyapatite. In contrast, the dissipative behavior is not affected by either loading conditions or the mineral percentage, showing a stronger dampening effect upon faster inputs compatible to the bone behavior at the macroscale. Our results improve the understanding of mineralized collagen composites unveiling the energy dissipative behavior of such materials. This impacts, besides the physiology, the design and characterization of new bioinspired composites for replacement devices (e.g., prostheses for sound transmission or conduction) and for optimized structures able to bear transient loads, e.g., impact, fatigue, in structural applications.
Newtonian physics is describes macro-objects sufficiently well, however it does not describe microobjects. A model of Extended Mechanics for Quantum Theory is based on an axiomatic generalization of Newtonian classical laws to arbitrary reference frames postulating the description of body dynamics by differential equations with higher derivatives of coordinates with respect to time but not only of second order ones and follows from Mach principle. In that case the Lagrangian $L(t,q,dot{q},ddot{q},...,dot {q}^{(n)},...)$ depends on higher derivatives of coordinates with respect to time. The kinematic state of a body is considered to be defined if n-th derivative of the body coordinate with respect to time is a constant (i.e. finite). First, kinematic state of a free body is postulated to invariable in an arbitrary reference frame. Second, if the kinematic invariant of the reference frame is the n-th order derivative of coordinate with respect to time, then the body dynamics is describes by a 2n-th order differential equation. For example, in a uniformly accelerated reference frame all free particles have the same acceleration equal to the reference frame invariant, i.e. reference frame acceleration. These bodies are described by third-order differential equation in a uniformly accelerated reference frame.
We put forth the idea that Hamiltons equations coincide with deterministic and reversible evolution. We explore the idea from five different perspectives (mathematics, measurements, thermodynamics, information theory and state mapping) and we show how they in the end coincide. We concentrate on a single degree of freedom at first, then generalize. We also discuss possible philosophical reasons why the laws of physics can only describe such processes, even if others must exist.
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture) that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamilton-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical picture and establish a correspondence which provides a basis for understanding how the instability in the geometrical picture is manifested in the instability of the original Hamiltonian motion.