Lax matrix solution of c=1 Conformal Field Theory

To a correlation function in a two-dimensional conformal field theory with the central charge $c=1$, we associate a matrix differential equation $\Psi' = L \Psi$, where the Lax matrix $L$ is a matrix square root of the energy-momentum tensor. Then local conformal symmetry implies that the differential equation is isomonodromic. This provides a justification for the recently observed relation between four-point conformal blocks and solutions of the Painlev\'e VI equation. This also provides a direct way to compute the three-point function of Runkel-Watts theory -- the common $c\rightarrow 1$ limit of Minimal Models and Liouville theory.Comment: 20 pages, v3: Corrected sign mistakes in eqs. (4.35), (4.37), (4.42), (4.45) and (4.52). Conclusions unchange

Seiberg-Witten equations and non-commutative spectral curves in Liouville theory

We propose that there exist generalized Seiberg-Witten equations in the Liouville conformal field theory, which allow the computation of correlation functions from the resolution of certain Ward identities. These identities involve a multivalued spin one chiral field, which is built from the stress-energy tensor. We solve the Ward identities perturbatively in an expansion around the heavy asymptotic limit, and check that the first two terms of the Liouville three-point function agree with the known result of Dorn, Otto, Zamolodchikov and Zamolodchikov. We argue that such calculations can be interpreted in terms of the geometry of non-commutative spectral curves.Comment: 25 pages, v2: minor changes in Appendices A.3 and B.

Reply to the correspondence: "On the fracture toughness of bioinspired ceramic materials"

This is a reply to the correspondence of Prof. Robert Ritchie: "On the fracture toughness of bioinspired ceramic materials", submitted to Nature Materials, which discusses the fracture toughness values of the following papers: Bouville, F., Maire, E., Meille, S., Van de Moort\`ele, B., Stevenson, A. J., & Deville, S. (2014). Strong, tough and stiff bioinspired ceramics from brittle constituents. Nature Materials, 13(5), 508-514 and Le Ferrand, H., Bouville, F., Niebel, T. P., & Studart, A. R. (2015). Magnetically assisted slip casting of bioinspired heterogeneous composites. Nature Materials, 14(11), 1172-1172.Comment: 5 pages, 2 figure

BiocharFX: Production with carbonFX technology, characterization and applications in potting soil related to plant production

Airex Energy started its R&D activities on torrefaction technology in 2010 and has been operating the first and only commercial-scale biocoal plant in Canada since 2015. The company has developed the patented CarbonFXTM process for biomass torrefaction. The biochar produced from this technology can be used for different applications, one of them being as a soil amendment. The biochar produced by Airex Energy is called BiocharFXTM. In Canada, the use of biochar as a soil amendment for agriculture, horticulture or mixed with other porous media, requires a certification from the Canadian Food Inspection Agency. Please click on the file below for full content of the abstract

Walking Stabilization Using Step Timing and Location Adjustment on the Humanoid Robot, Atlas

While humans are highly capable of recovering from external disturbances and uncertainties that result in large tracking errors, humanoid robots have yet to reliably mimic this level of robustness. Essential to this is the ability to combine traditional "ankle strategy" balancing with step timing and location adjustment techniques. In doing so, the robot is able to step quickly to the necessary location to continue walking. In this work, we present both a new swing speed up algorithm to adjust the step timing, allowing the robot to set the foot down more quickly to recover from errors in the direction of the current capture point dynamics, and a new algorithm to adjust the desired footstep, expanding the base of support to utilize the center of pressure (CoP)-based ankle strategy for balance. We then utilize the desired centroidal moment pivot (CMP) to calculate the momentum rate of change for our inverse-dynamics based whole-body controller. We present simulation and experimental results using this work, and discuss performance limitations and potential improvements

Straight-Leg Walking Through Underconstrained Whole-Body Control

We present an approach for achieving a natural, efficient gait on bipedal robots using straightened legs and toe-off. Our algorithm avoids complex height planning by allowing a whole-body controller to determine the straightest possible leg configuration at run-time. The controller solutions are biased towards a straight leg configuration by projecting leg joint angle objectives into the null-space of the other quadratic program motion objectives. To allow the legs to remain straight throughout the gait, toe-off was utilized to increase the kinematic reachability of the legs. The toe-off motion is achieved through underconstraining the foot position, allowing it to emerge naturally. We applied this approach of under-specifying the motion objectives to the Atlas humanoid, allowing it to walk over a variety of terrain. We present both experimental and simulation results and discuss performance limitations and potential improvements.Comment: Submitted to 2018 IEEE International Conference on Robotics and Automatio