Non-linear elastic effects in phase field crystal and amplitude equations: Comparison to ab initio simulations of bcc metals and graphene

We investigate non-linear elastic deformations in the phase field crystal model and derived amplitude equations formulations. Two sources of non-linearity are found, one of them based on geometric non-linearity expressed through a finite strain tensor. It reflects the Eulerian structure of the continuum models and correctly describes the strain dependence of the stiffness. In general, the relevant strain tensor is related to the left Cauchy-Green deformation tensor. In isotropic one- and two-dimensional situations the elastic energy can be expressed equivalently through the right deformation tensor. The predicted isotropic low temperature non-linear elastic effects are directly related to the Birch-Murnaghan equation of state with bulk modulus derivative $K'=4$ for bcc. A two-dimensional generalization suggests $K'_{2D}=5$. These predictions are in agreement with ab initio results for large strain bulk deformations of various bcc elements and graphene. Physical non-linearity arises if the strain dependence of the density wave amplitudes is taken into account and leads to elastic weakening. For anisotropic deformations the magnitudes of the amplitudes depend on their relative orientation to the applied strain.Comment: 16 page

Detecting fasciculations in cranial nerve innervated muscles with ultrasound in amyotrophic lateral sclerosis

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A visual brain-computer interface as communication aid for patients with amyotrophic lateral sclerosis

Objective: Brain-Computer Interface (BCI) spellers that make use of code-modulated Visual Evoked Potentials (cVEP) may provide a fast and more accurate alternative to existing visual BCI spellers for patients with Amyotrophic Lateral Sclerosis (ALS). However, so far the cVEP speller has only been tested on healthy participants. Methods: We assess the brain responses, BCI performance and user experience of the cVEP speller in 20 healthy participants and 10 ALS patients. All participants performed a cued and free spelling task, and a free selection of Yes/No answers. Results: 27 out of 30 participants could perform the cued spelling task with an average accuracy of 79% for ALS patients, 88% for healthy older participants and 94% for healthy young participants. All 30 participants could answer Yes/No questions freely, with an average accuracy of around 90%. Conclusions: With ALS patients typing on average 10 characters per minute, the cVEP speller presented in this paper outperforms other visual BCI spellers. Significance These results support a general usability of cVEP signals for ALS patients, which may extend far beyond the tested speller to control e.g. an alarm, automatic door, or TV within a smart home