The simple random walk and max-degree walk on a directed graph

We show bounds on total variation and $L^{\infty}$ mixing times, spectral gap and magnitudes of the complex valued eigenvalues of a general (non-reversible non-lazy) Markov chain with a minor expansion property. This leads to the first known bounds for the non-lazy simple and max-degree walks on a (directed) graph, and even in the lazy case they are the first bounds of the optimal order. In particular, it is found that within a factor of two or four, the worst case of each of these mixing time and eigenvalue quantities is a walk on a cycle with clockwise drift

Fearless Friday: Candice Montenegro

This Friday, we’re honoring Candice Montenegro ’20, for her incredible work in the Gettysburg College Community. Candice is a junior from Los Angeles, and a double major in Psychology and Spanish/Latin American Caribbean Studies. In her first year at Gettysburg College, she became a member of Latin American Students’ Association (LASA), and is now president of the group. Along with her involvement in LASA, she is an employee for the Center for Career Engagement, a psychology research assistant for Professor Sahana Mukherjee, a program coordinator of Sunday Swim with Casa de la Culture through the Center for Public Service, and the creator and house leader for the Latinx House. [excerpt

Influence of frustration on a d=3 diluted antiferromagnet: FexZn1−xF2Fe_{x}Zn_{1-x}F_{2}

The influence of a frustrated bond on the magnetic properties of a d=3 uniaxial (Ising) b.c.c. diluted antiferromagnet, with emphasis in the compound $Fe_{x}Zn_{1-x}F_{2}$, is investigated by a local mean-field numerical simulation. In particular we find that the initial drop of the saturation staggered magnetization ($M_{S}$) with concentration follows a percolation-like phenomenon characterized by an exponent $\beta_{p}$. For the frustrated samples, however, this regime is followed by a second one identified by a ``long tail" effect such that $M_{S}$ is zero only at the percolation threshold. Our numerical data also confirms a spin-glass phase near this threshold.Comment: 11 pages (Latex) with 3 uuencoded postscript figure

Microtransformers: controlled microscale navigation with flexible robots

Artificial microswimmers are a new technology with promising microfluidics and biomedical applications, such as directed cargo transport, microscale assembly, and targeted drug delivery. A fundamental barrier to realising this potential is the ability to control the trajectories of multiple individuals within a large group. A promising navigation mechanism for "fuel-based" microswimmers, for example autophoretic Janus particles, entails modulating the local environment to guide the swimmer, for instance by etching grooves in microchannels. However, such techniques are currently limited to bulk guidance. This paper will argue that by manufacturing microswimmers from phoretic filaments of flexible shape-memory polymer, elastic transformations can modulate swimming behaviour, allowing precision navigation of selected individuals within a group through complex environments