Numerical renormalization group calculation of impurity internal energy and specific heat of quantum impurity models

We introduce a method to obtain the specific heat of quantum impurity models via a direct calculation of the impurity internal energy requiring only the evaluation of local quantities within a single numerical renormalization group (NRG) calculation for the total system. For the Anderson impurity model, we show that the impurity internal energy can be expressed as a sum of purely local static correlation functions and a term that involves also the impurity Green function. The temperature dependence of the latter can be neglected in many cases, thereby allowing the impurity specific heat, $C_{\rm imp}$, to be calculated accurately from local static correlation functions; specifically via $C_{\rm imp}=\frac{\partial E_{\rm ionic}}{\partial T} + 1/2\frac{\partial E_{\rm hyb}}{\partial T}$, where $E_{\rm ionic}$ and $E_{\rm hyb}$ are the energies of the (embedded) impurity and the hybridization energy, respectively. The term involving the Green function can also be evaluated in cases where its temperature dependence is non-negligible, adding an extra term to $C_{\rm imp}$. For the non-degenerate Anderson impurity model, we show by comparison with exact Bethe ansatz calculations that the results recover accurately both the Kondo induced peak in the specific heat at low temperatures as well as the high temperature peak due to the resonant level. The approach applies to multiorbital and multichannel Anderson impurity models with arbitrary local Coulomb interactions. An application to the Ohmic two state system and the anisotropic Kondo model is also given, with comparisons to Bethe ansatz calculations. The new approach could also be of interest within other impurity solvers, e.g., within quantum Monte Carlo techniques.Comment: 16 pages, 15 figures, published versio

Signals from the Yolk Cell Induce Mesoderm, Neuroectoderm, the Trunk Organizer, and the Notochord in Zebrafish

AbstractWe have analyzed the role of the zebrafish yolk cell in the processes of mesoderm induction and establishment of the organizer. By recombining blastomere-free yolk cells and animal cap tissue we have shown that the yolk cell itself can induce mesoderm in neighboring blastomeres. We further demonstrate the competence of all blastomeres to form mesoderm, suggesting the endogenous mesoderm inducing signal to be locally restricted. Ablation of the vegetal third of the yolk cell during the first 20 min of development does not interfere with mesoderm formation in general, but results in completely ventralized embryos. These embryos lack the notochord, neuroectoderm, and the anterior-most 14–15 somites, demonstrating that the ablation affects the formation of the trunk-, but not the tail region of the embryo. This suggests the presence of a trunk organizer in fish. The dorsalized mutant swirl (zbmp-2b) shows expanded dorsal structures and missing ventral structures. In contrast to the phenotypes obtained upon the ablation treatment in wild-type embryos, removal of the vegetal-most yolk in swirl mutants results in embryos which do form neuroectoderm and anterior trunk somites. However, both wild-type and swirl mutants lack a notochord upon vegetal yolk removal. These ablation experiments in wild-type and swirl mutant embryos demonstrate that in zebrafish dorsal determining factors originate from the vegetal part of the yolk cell. These factors set up two independent activities: one induces the notochord and the other is involved in the formation of the neuroectoderm and the trunk region by counteracting the function of swirl. In addition, these experiments show that the establishment of the anteroposterior axis is independent of the dorsoventral axis

Atmospheric neutrons

Contributions to fast neutron measurements in the atmosphere are outlined. The results of a calculation to determine the production, distribution and final disappearance of atmospheric neutrons over the entire spectrum are presented. An attempt is made to answer questions that relate to processes such as neutron escape from the atmosphere and C-14 production. In addition, since variations of secondary neutrons can be related to variations in the primary radiation, comment on the modulation of both radiation components is made

Living IoT: A Flying Wireless Platform on Live Insects

Sensor networks with devices capable of moving could enable applications ranging from precision irrigation to environmental sensing. Using mechanical drones to move sensors, however, severely limits operation time since flight time is limited by the energy density of current battery technology. We explore an alternative, biology-based solution: integrate sensing, computing and communication functionalities onto live flying insects to create a mobile IoT platform. Such an approach takes advantage of these tiny, highly efficient biological insects which are ubiquitous in many outdoor ecosystems, to essentially provide mobility for free. Doing so however requires addressing key technical challenges of power, size, weight and self-localization in order for the insects to perform location-dependent sensing operations as they carry our IoT payload through the environment. We develop and deploy our platform on bumblebees which includes backscatter communication, low-power self-localization hardware, sensors, and a power source. We show that our platform is capable of sensing, backscattering data at 1 kbps when the insects are back at the hive, and localizing itself up to distances of 80 m from the access points, all within a total weight budget of 102 mg.Comment: Co-primary authors: Vikram Iyer, Rajalakshmi Nandakumar, Anran Wang, In Proceedings of Mobicom. ACM, New York, NY, USA, 15 pages, 201

Effective algebraic degeneracy

We prove that any nonconstant entire holomorphic curve from the complex line C into a projective algebraic hypersurface X = X^n in P^{n+1}(C) of arbitrary dimension n (at least 2) must be algebraically degenerate provided X is generic if its degree d = deg(X) satisfies the effective lower bound: d larger than or equal to n^{{(n+1)}^{n+5}}

Intracellular uptake of macromolecules by brain lymphatic endothelial cells during zebrafish embryonic development

The lymphatic system controls fluid homeostasis and the clearance of macromolecules from interstitial compartments. In mammals brain lymphatics were only recently discovered, with significant implications for physiology and disease. We examined zebrafish for the presence of brain lymphatics and found loosely connected endothelial cells with lymphatic molecular signature covering parts of the brain without forming endothelial tubular structures. These brain lymphatic endothelial cells (BLECs) derive from venous endothelium, are distinct from macrophages, and are sensitive to loss of Vegfc. BLECs endocytose macromolecules in a selective manner, which can be blocked by injection of mannose receptor ligands. This first report on brain lymphatic endothelial cells in a vertebrate embryo identifies cells with unique features, including the uptake of macromolecules at a single cell level. Future studies will address whether this represents an uptake mechanism that is conserved in mammals and how these cells affect functions of the embryonic and adult brain