Analytical expressions for the polarizability of the honeycomb lattice

We present analytical expressions for the polarizability $P_\mu(q_x,\omega)$ of graphene modeled by the hexagonal tight-binding model for small wave number $q_x$, but arbitrary chemical potential $\mu$. Generally, we find $P_\mu(q_x,\omega)=P_\mu^(\omega)$ with $\omega_q=v_Fq_x$ the Dirac energy, where the first term is due to intra-band and the second due to inter-band transitions. Explicitly, we derive the analytical expression for the imaginary part of the polarizability including intra-band contributions and recover the result obtained from the Dirac cone approximation for $\mu\rightarrow0$. For $\mu<\sqrt{3}t$, there is a square-root singularity at $\omega_q=v_Fq_x$ independent of $\mu$. For doping levels close to the van Hove singularity, $\mu=t\pm\delta\mu$, $ImP_\mu(q_x,\omega)$ is constant for $\delta\mu/t<\omega/\omega_q\ll1$.Comment: 5 pages, 3 figures, 1 tabl

A unique problem of muscle adaptation from weightlessness: The deceleration deficiency

Decelerator problems of the knee are emphasized since the lower leg musculature is known to atrophy in response to weightlessness. However, other important decelerator functions are served by the shoulder muscles, in particular the rotator cuff muscles. Problems in these muscles often result in tears and dislocations as seen in baseball pitchers. It is noteworthy that at least one device currently exists that can measure concentric and eccentric muscle loading including a submaximal simulated free weight exercise (i.e., force-controlled) and simultaneously record integrated EMG analysis appropriate for assessment of all muscle functional activities. Studies should be undertaken to provide information as to the performance of maximal and submaximal exercise in space travelers to define potential problems and provide rationale for prevention