The generalized ladder series of Feynman diagrams for scattering of two particles by scalar-meson exchange is expanded, using functional methods, to obtain the relativistic eikonal approximation and the next two terms of an expansion about the eikonal limit. The established similarity between nonrelativistic and relativistic eikonal approximations is shown to persist, in part, to the higher-order terms in the relativistic eikonal expansion. The leading-order correction to the eikonal limit differs only kinematically from its nonrelativistic counterpart. In second order, there is again much similarity with nonrelativistic results; however, a part of the second-order eikonal correction explicitly depends on the relative time coordinate of the scattering particles. An approximate relativistic Schrodinger equation is found to reproduce the leading corrections to the eikonal limit by means of a simple kinematic generalization of the nonrelativistic potential theory results; however, the relativistic time effect cannot be readily incorporated , into a three-dimensional wave equation.
Jump features in winter terrain parks frequently pose a hazard to patrons and may represent a significant liability risk to winter resorts. By performing a simple dynamic analysis of terrain park jumps, the relative risk to impact injuries for any proposed jump design can be quantified thereby allowing terrain park designers to minimize the risk from this class of injury.
Ski jump landing surface shapes can be created to cushion jumper landing by specifying a value of equivalent fall height (EFH) but, because the shape is calculated by integrating a differential equation, an infinite number of solutions results from the arbitrary boundary conditions. This paper provides a natural rationale for selection of the least expensive (minimum snow budget) one of these that nevertheless satisfies other design constraints, mainly limited normal acceleration and jerk during approach and landing transitions. Choosing the maximum allowable normal acceleration during the approach transition brings the entire infinite family of landing surfaces as close as possible to the parent slope. Limiting the rate of change of normal acceleration (jerk) decreases the likelihood of loss of balance at takeoff and consequent catastrophic spinal cord injuries on landing. An analogous choice, satisfying limited normal acceleration during the landing transition, selects the single member of the infinite family (providing the desired EFH) that lies closest to the parent slope and is therefore least costly to build. Software in the form of a graphical user interface is described that implements these algorithms and is appropriate for inexperienced users to calculate design details before actual fabrication of landing surfaces at a specific jump site.
In an attempt to address issues accompanying the unnecessary change of wound dressings of patients in traditional wound care management, we are developing smart wound dressing material, based on magnetic nanosensors, for wireless monitoring of the wound healing process. The technology is based on magnetizing the cellulose component of the dressing and tuning the resulting magnetic cellulose to respond to temperature changes of the wound. Here, we report the development of the magnetic cellulose through grafting of magnetic CoFe 2 O 4 nanoparticles (CoFe 2 O 4 NPs) onto cellulose fibers using a layer-by-layer method. Three different methods were used for the synthesis, but the CoFe 2 O 4 NPs with superior properties were obtained through hydrothermal autoclaving followed by annealing. They had 98% match to the XRD reference pattern and rod-like shape (agglomerating into nanowires), with diameter between 30 and 50 nm and length ranging from 582 nm to 5.42 μm and magnetization and demagnetization values of 84.5 emu g −1 and −84.5 emu g −1 , respectively. Upon grafting the CoFe 2 O 4 NP onto fibers, the cellulose became magnetic, with magnetization values dependent on the initial concentration of the CoFe 2 O 4 NP in the grafting media. Computational investigation revealed that the CoFe 2 O 4 NPs are covalently bonded onto the cellulose fiber through the formation of −Co−O−C− bonding. In brief, the current findings advanced the development of a wireless wound-healing monitoring technology based on integration of sensory ferrimagnet CoFe 2 O 4 NPs into cellulose fibers of wound dressings.
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