Directed Percolation and Generalized Friendly Walkers

We show that the problem of directed percolation on an arbitrary lattice is equivalent to the problem of m directed random walkers with rather general attractive interactions, when suitably continued to m=0. In 1+1 dimensions, this is dual to a model of interacting steps on a vicinal surface. A similar correspondence with interacting self-avoiding walks is constructed for isotropic percolation.Comment: 4 pages, 3 figures, to be published in Phys. Rev. Let

The Metamodern Man

Abstract The first time I heard the term, “Metamodern Age,” I was actively involved in a discussion about the various themes in Mary Shelley’s Frankenstein. The setting was a Master of Liberal Studies class (Rollins College, MLS 604), entitled “Modernity” taught by Dr. Tom Cook. It was October of 2015. Frankenstein, also known as The Modern Prometheus, is a masterpiece and a solid sample from the Modern Era. Following approximately fifty years of Postmodern Era sludge, we are now in what could be identified as the Metamodern Era. Our Modernity class speculated confidently that the current Age of Metamodernism is a positive societal rebuild in the terrifying wake of 9/11. I strong identify with metamodernism, as opposed to postmodernism, and believe that the Metamodern Age began to mature as the internet became culturally dominant in the 1990s, prior to 9/11. I am intrigued by the concept of metamodernism – an age born, unofficially, the same year as I was, 1975. In June, 2016; I took a trip to Amsterdam with fellow Rollins’ Master of Liberal Studies students, past and present. My curiosity erupted into fascination with metamodern thought as I connected it to my personal masculine identity struggle in our zeitgeist. It is a Post-postmodern Era wherein masculinity is too often seen as toxic. For the first time in my life, I traveled abroad and talked about culture, politics, and gender expectations with anybody and everybody who had experiences and opinions to share. Amsterdam humbly lent itself to my curiosity in defining metamodern masculinity, and thus The Metamodern Man. On June 18, 2017 (Father’s Day), I began to organize my massive pile of MLS notes and mentally filter my Amsterdam experience, in order to concentrate on my MLS thesis. With the consistent support of my wife and children, I decided to focus on my midlife masculine place in our current zeitgeist, and commit to writing about the metamodern man. I put pen to paper on Labor Day, 2017, after talking to my boys (ages 6 and 14) about what it means to be a man in metamodern society, specifically in America. We discussed what the future holds for masculinity. The potential is positively great. This thesis paper is my attempt at comprehending midlife masculinity and defining the reality of what being a successful metamodern man means

Cosmo-dynamics and dark energy with a quadratic EoS: anisotropic models, large-scale perturbations and cosmological singularities

In general relativity, for fluids with a linear equation of state (EoS) or scalar fields, the high isotropy of the universe requires special initial conditions, and singularities are anisotropic in general. In the brane world scenario anisotropy at the singularity is suppressed by an effective quadratic equation of state. There is no reason why the effective EoS of matter should be linear at the highest energies, and a non-linear EoS may describe dark energy or unified dark matter (Paper I, astro-ph/0512224). In view of this, here we study the effects of a quadratic EoS in homogenous and inhomogeneous cosmological models in general relativity, in order to understand if in this context the quadratic EoS can isotropize the universe at early times. With respect to Paper I, here we use the simplified EoS P=alpha rho + rho^2/rho_c, which still allows for an effective cosmological constant and phantom behavior, and is general enough to analyze the dynamics at high energies. We first study anisotropic Bianchi I and V models, focusing on singularities. Using dynamical systems methods, we find the fixed points of the system and study their stability. We find that models with standard non-phantom behavior are in general asymptotic in the past to an isotropic fixed point IS, i.e. in these models even an arbitrarily large anisotropy is suppressed in the past: the singularity is matter dominated. Using covariant and gauge invariant variables, we then study linear perturbations about the homogenous and isotropic spatially flat models with a quadratic EoS. We find that, in the large scale limit, all perturbations decay asymptotically in the past, indicating that the isotropic fixed point IS is the general asymptotic past attractor for non phantom inhomogeneous models with a quadratic EoS. (Abridged)Comment: 16 pages, 6 figure

Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences.Comment: 25 page

Devil's Staircase in Magnetoresistance of a Periodic Array of Scatterers

The nonlinear response to an external electric field is studied for classical non-interacting charged particles under the influence of a uniform magnetic field, a periodic potential, and an effective friction force. We find numerical and analytical evidence that the ratio of transversal to longitudinal resistance forms a Devil's staircase. The staircase is attributed to the dynamical phenomenon of mode-locking.Comment: two-column 4 pages, 5 figure

Perturbation Energy Production in Pipe Flow over a Range of Reynolds Numbers using Resolvent Analysis

The response of pipe flow to physically realistic, temporally and spatially continuous(periodic) forcing is investigated by decomposing the resolvent into orthogonal forcing and response pairs ranked according to their contribution to the resolvent 2-norm. Modelling the non-linear terms normally neglected by linearisation as unstructured forcing permits qualitative extrapolation of the resolvent norm results beyond infinitesimally small perturbations to the turbulent case. The concepts arising have a close relationship to input output transfer function analysis methods known in the control systems literature. The body forcings that yield highest disturbance energy gain are identified and ranked by the decomposition and a worst-case bound put on the energy gain integrated across the pipe cross-section. Analysis of the spectral variation of the corresponding response modes reveals interesting comparisons with recent observations of the behavior of the streamwise velocity in high Reynolds number (turbulent) pipe flow, including the importance of very long scales of the order of ten pipe radii, in the extraction of turbulent energy from the mean flow by the action of turbulent shear stress against the velocity gradient

The AGeS2 (Awards for Geochronology Student research 2) Program: Supporting Community Geochronology Needs and Interdisciplinary Science

Geochronology is essential in the geosciences. It is used to resolve the durations and rates of earth processes, as well as test causative relationships among events. Such data are increasingly required to conduct cutting-edge, transformative, earth-science research. The growing need for geochronology is accompanied by strong demand to enhance the ability of labs to meet this pressure and to increase community awareness of how these data are produced and interpreted. For example, a 2015 National Science Foundation (NSF) report on opportunities and challenges for U.S. geochronology research noted: While there has never been a time when users have had greater access to geo-chronologic data, they remain, by and large, dissatisfied with the available style/ quantity/cost/efficiency (Harrison et al., 2015, p. 1). And the 2012 National Research Council NROES (New Research Opportunities in the Earth Sciences) report (Lay et al., 2012, p. 82) recommended: [NSF] EAR should explore new mechanisms for geochronology laboratories that will service the geochronology requirements of the broad suite of research opportunities while sustaining technical advances in methodologies. The AGeS (Awards for Geochronology Student research) program is one way that these calls are being answered