Calculation of Relativistic Nucleon-Nucleon Potentials in Three-Dimensions

In this paper, we have applied a three-dimensional approach for calculation of the relativistic nucleon-nucleon potential. The quadratic operator relation between the non-relativistic and the relativistic nucleon-nucleon interactions is formulated as a function of relative two-nucleon momentum vectors, which leads to a three-dimensional integral equation. The integral equation is solved by the iteration method, and the matrix elements of the relativistic potential are calculated from non-relativistic ones. Spin-independent Malfliet-Tjon potential is employed in the numerical calculations, and the numerical tests indicate that the two-nucleon observables calculated by the relativistic potential are preserved with high accuracy

Neuromuscular markers of non-contact anterior cruciate ligament injury during dynamic tasks

This thesis explores the added value of neuromuscular markers of non-contact ACL injury risk. First, a systematic review was conducted to establish the existing evidence from the literature. The outcome of this review served to select candidate neuromuscular observations to be included in a large-scale prospective study. The two main risk factors that were found to be supported with some evidence were the (i) hamstrings to quadriceps ratio (HQR) and (ii) a unique neuromuscular activation pattern during side cutting. These parameters were included in a prospective cohort study to establish injury risk factors. After two years of data collection we still had not seen any non-contact ACL injuries in our study sample. As a fall back plan, the collected database was explored in search of evidence that can help support previous findings. First, we showed that quadriceps strength meaningfully affects HQRs (as quadriceps gets stronger, HQR value gets lower), introducing bias when profiling individuals for injury risk. We demonstrated how through an allometric approach this bias can be removed for future investigation into HQR as a risk factor for injury. Second, we evaluated whether HQR explains neuromuscular activations of the knee musculature during the execution a dynamic task. We found that variations between individuals in muscle (co-)activations were not explained by differences in muscle strength or HQR. Overall, through this work we have obtained a clear overview on the limited evidence on neuromuscular risk factors of non-contact ACL injury, provided in-depth insights into HQR as a measure of muscular capacity, and demonstrated how one should be careful in linking observations of muscular capacity with observations of muscular activation and vice versa

Crystalline ground states for classical particles

Pair interactions whose Fourier transform is nonnegative and vanishes above a wave number K_0 are shown to give rise to periodic and aperiodic infinite volume ground state configurations (GSCs) in any dimension d. A typical three dimensional example is an interaction of asymptotic form cos(K_0 r)/r^4. The result is obtained for densities rho >= rho_d where rho_1=K_0/2pi, rho_2=(sqrt{3}/8)(K_0/pi)^2 and rho_3=(1/8sqrt{2})(K_0/pi)^3. At rho_d there is a unique periodic GSC which is the uniform chain, the triangular lattice and the bcc lattice for d=1,2,3, respectively. For rho>rho_d the GSC is nonunique and the degeneracy is continuous: Any periodic configuration of density rho with all reciprocal lattice vectors not smaller than K_0, and any union of such configurations, is a GSC. The fcc lattice is a GSC only for rho>=(1/6 sqrt{3})(K_0/pi)^3.Comment: final versio

Tiling Spaces are Inverse Limits

Let M be an arbitrary Riemannian homogeneous space, and let Omega be a space of tilings of M, with finite local complexity (relative to some symmetry group Gamma) and closed in the natural topology. Then Omega is the inverse limit of a sequence of compact finite-dimensional branched manifolds. The branched manifolds are (finite) unions of cells, constructed from the tiles themselves and the group Gamma. This result extends previous results of Anderson and Putnam, of Ormes, Radin and Sadun, of Bellissard, Benedetti and Gambaudo, and of G\"ahler. In particular, the construction in this paper is a natural generalization of G\"ahler's.Comment: Latex, 6 pages, including one embedded figur

Modelling quasicrystals at positive temperature

We consider a two-dimensional lattice model of equilibrium statistical mechanics, using nearest neighbor interactions based on the matching conditions for an aperiodic set of 16 Wang tiles. This model has uncountably many ground state configurations, all of which are nonperiodic. The question addressed in this paper is whether nonperiodicity persists at low but positive temperature. We present arguments, mostly numerical, that this is indeed the case. In particular, we define an appropriate order parameter, prove that it is identically zero at high temperatures, and show by Monte Carlo simulation that it is nonzero at low temperatures

Stimulation in vitro of galactocerebroside galactosidase by N‐decanoyl 2‐amino‐2‐methylpropanol

Amides resembling ceramide (fatty acyl sphingosine) were synthesized and tested in vitro for their effects on the rat brain β‐galactosidase which hydrolyzes galactosyl ceramide. The N‐decanoyl derivative of 2‐amino‐2‐methyl‐1‐propanol was most effective, giving a 34% stimulation at 0.15 mM concentration and a 60% stimulation at maximal levels. Addition of a hydroxyl group in the 3 position reduced the degree of stimulation, as did increasing or decreasing the length of the fatty acid portion. Omission of the branched methyl group resulted in inhibition instead of stimulation. Kinetic analysis indicates that the stimulator does not affect the binding of substrate to enzyme, but does speed the rate of hydrolytic action. Stimulation was also observed with the cerebrosidase in spleen and kidney. It is suggested that the stimulators act on an enzyme site other than the substrate‐active site.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141447/1/lipd0056.pd