Theoretically palatable flavor combinations of astrophysical neutrinos

The flavor composition of high-energy astrophysical neutrinos can reveal the physics governing their production, propagation, and interaction. The IceCube Collaboration has published the first experimental determination of the ratio of the flux in each flavor to the total. We present, as a theoretical counterpart, new results for the allowed ranges of flavor ratios at Earth for arbitrary flavor ratios in the sources. Our results will allow IceCube to more quickly identify when their data imply standard physics, a general class of new physics with arbitrary (incoherent) combinations of mass eigenstates, or new physics that goes beyond that, e.g., with terms that dominate the Hamiltonian at high energy.Comment: 13 pages, 12 figures. Matches published versio

A two-state kinetic model for the unfolding of single molecules by mechanical force

We investigate the work dissipated during the irreversible unfolding of single molecules by mechanical force, using the simplest model necessary to represent experimental data. The model consists of two levels (folded and unfolded states) separated by an intermediate barrier. We compute the probability distribution for the dissipated work and give analytical expressions for the average and variance of the distribution. To first order, the amount of dissipated work is directly proportional to the rate of application of force (the loading rate), and to the relaxation time of the molecule. The model yields estimates for parameters that characterize the unfolding kinetics under force in agreement with those obtained in recent experimental results (Liphardt, J., et al. (2002) {\em Science}, {\bf 296} 1832-1835). We obtain a general equation for the minimum number of repeated experiments needed to obtain an equilibrium free energy, to within $k_BT$, from non-equilibrium experiments using the Jarzynski formula. The number of irreversible experiments grows exponentially with the ratio of the average dissipated work, \bar{\Wdis}, to $k_BT$.}Comment: PDF file, 5 page

The Nonequilibrium Thermodynamics of Small Systems

The interactions of tiny objects with their environment are dominated by thermal fluctuations. Guided by theory and assisted by micromanipulation tools, scientists have begun to study such interactions in detail.Comment: PDF file, 13 pages. Long version of the paper published in Physics Toda

Epidemic model on a network: analysis and applications to COVID-19

We analyze an epidemic model on a network consisting of susceptible-infected-recovered equations at the nodes coupled by diffusion using a graph Laplacian. We introduce an epidemic criterion and examine different vaccination/containment strategies: we prove that it is most effective to vaccinate a node of highest degree. The model is also useful to evaluate deconfinement scenarios and prevent a so-called second wave. The model has few parameters enabling fitting to the data and the essential ingredient of importation of infected; these features are particularly important for the current COVID-19 epidemic

A one-dimensional model for theoretical analysis of single molecule experiments

In this paper we compare two polymer stretching experiments. The outcome of both experiments is a force-extension relation. We use a one-dimensional model to show that in general the two quantities are not equal. In certain limits, however, both force-extension relations coincide.Comment: 11 pages, 5 figure

The closed-edge structure of graphite and the effect of electrostatic charging

The properties of graphite, and of few-layer graphene, can be strongly influenced by the edge structure of the graphene planes, but there is still much that we do not understand about the geometry and stability of these edges. We present an experimental and theoretical study of the closed edges of graphite crystals, and of the effect of an electric field on their structure. High-resolution transmission electron microscopy is used to image the edge structure of fresh graphite and of graphite that has been exposed to an electric field, which experiences a separation of the graphene layers. Computer simulations based on density functional theory are used to rationalise and quantify the preference for the formation of multiple concentric loops at the edges. A model is also presented to explain how the application of an electric field leads to the separation of the folded edges

Condensation transition in DNA-polyaminoamide dendrimer fibers studied using optical tweezers

When mixed together, DNA and polyaminoamide (PAMAM) dendrimers form fibers that condense into a compact structure. We use optical tweezers to pull condensed fibers and investigate the decondensation transition by measuring force-extension curves (FECs). A characteristic plateau force (around 10 pN) and hysteresis between the pulling and relaxation cycles are observed for different dendrimer sizes, indicating the existence of a first-order transition between two phases (condensed and extended) of the fiber. The fact that we can reproduce the same FECs in the absence of additional dendrimers in the buffer medium indicates that dendrimers remain irreversibly bound to the DNA backbone. Upon salt variation FECs change noticeably confirming that electrostatic forces drive the condensation transition. Finally, we propose a simple model for the decondensing transition that qualitatively reproduces the FECs and which is confirmed by AFM images.Comment: Latex version, 4 pages+3 color figure