arXiv subjects

Matthew F. Lapa

Publications and source records attributed to Matthew F. Lapa.

20 records · Page 2Linked to original sources

arXiv2013

Swimming at Low Reynolds Number in Fluids with Odd (Hall) Viscosity

We apply the geometric theory of swimming at low Reynolds number to the study of nearly circular swimmers in two-dimensional fluids with non-vanishing Hall, or "odd", viscosity. The Hall viscosity gives an off-diagonal contribution to the fluid stress-tensor, which results in a number of striking effects. In particular, we find that a swimmer whose area is changing will experience a torque proportional to the rate of change of the area, with the constant of proportionality given by the coefficient $η^o$ of odd viscosity. After working out the general theory of swimming in fluids with Hall viscosity for a class of simple swimmers, we give a number of example swimming strokes which clearly demonstrate the differences between swimming in a fluid with conventional viscosity and a fluid which also has a Hall viscosity. A number of more technical results, including a proof of the torque-area relation for swimmers of more general shape, are explained in a set of appendices.

cond-mat.soft↗

arXiv2012

Ground States of the Classical Antiferromagnet on the Pyrochlore Lattice

We study the classical ground states of the exchange-coupled Heisenberg antiferromagnet on the Pyrochlore lattice, a non-Bravais lattice made of corner-sharing tetrahedra. In particular, we map out the entire phase diagram for the case of first and second nearest neighbor interactions. In this phase diagram we find {\it four} complex non-coplanar ground states based on different ordering modes. These are the Cuboctahedral Stack state, a $<111>$ stacking of Cuboctahedral states, and three families of commensurate spiral: the Kawamura states, constructed from three different combinations of $\{\tfrac{3}{4}\tfrac{3}{4}0\}$ modes, the Double-Twist state, also constructed from $\{\tfrac{3}{4}\tfrac{3}{4}0\}$ modes, and the Multiply-Modulated Commensurate Spiral state, constructed from $\{\tfrac{3}{4}\tfrac{1}{4}\tfrac{1}{2}\}$ modes. We also briefly look at states involving the two kinds of third nearest neighbor interactions on the Pyrochlore lattice. In this region of parameter space we again find the Cuboctahedral Stack state, and we also find another non-coplanar state in the form of a new kind of Alternating Conic Spiral.

cond-mat.str-el↗