Distances of qubit density matrices on Bloch sphere

We recall the Einstein velocity addition on the open unit ball \B of $\R^{3}$ and its algebraic structure, called the Einstein gyrogroup. We establish an isomorphism between the Einstein gyrogroup on \B and the set of all qubit density matrices representing mixed states endowed with an appropriate addition. Our main result establishes a relation between the trace metric for the qubit density matrices and the rapidity metric on the Einstein gyrogroup \B.Comment: I thank to my supervisor, Jimmie Lawson. This was accepted in Journal of Mathematical Physics at September 26, 201

Conservative, gravitational self-force for a particle in circular orbit around a Schwarzschild black hole in a Radiation Gauge

This is the second of two companion papers on computing the self-force in a radiation gauge; more precisely, the method uses a radiation gauge for the radiative part of the metric perturbation, together with an arbitrarily chosen gauge for the parts of the perturbation associated with changes in black-hole mass and spin and with a shift in the center of mass. We compute the conservative part of the self-force for a particle in circular orbit around a Schwarzschild black hole. The gauge vector relating our radiation gauge to a Lorenz gauge is helically symmetric, implying that the quantity h_{\alpha\beta} u^\alpha u^\beta (= h_{uu}) must have the same value for our radiation gauge as for a Lorenz gauge; and we confirm this numerically to one part in 10^{13}. As outlined in the first paper, the perturbed metric is constructed from a Hertz potential that is in term obtained algebraically from the the retarded perturbed spin-2 Weyl scalar, \psi_0 . We use a mode-sum renormalization and find the renormalization coefficients by matching a series in L = \ell + 1/2 to the large-L behavior of the expression for the self-force in terms of the retarded field h_{\alpha\beta}^{ret}; we similarly find the leading renormalization coefficients of h_{uu} and the related change in the angular velocity of the particle due to its self-force. We show numerically that the singular part of the self-force has the form f_{\alpha} \propto < \nabla_\alpha \rho^{-1}>, the part of \nabla_\alpha \rho^{-1} that is axisymmetric about a radial line through the particle. This differs only by a constant from its form for a Lorenz gauge. It is because we do not use a radiation gauge to describe the change in black-hole mass that the singular part of the self-force has no singularity along a radial line through the particle and, at least in this example, is spherically symmetric to subleading order in \rho.Comment: 21 pages, 2 figure

Necrotic tumor growth: an analytic approach

The present paper deals with a free boundary problem modeling the growth process of necrotic multi-layer tumors. We prove the existence of flat stationary solutions and determine the linearization of our model at such an equilibrium. Finally, we compute the solutions of the stationary linearized problem and comment on bifurcation.Comment: 14 pages, 3 figure

Free boundary problems for Tumor Growth: a Viscosity solutions approach

The mathematical modeling of tumor growth leads to singular stiff pressure law limits for porous medium equations with a source term. Such asymptotic problems give rise to free boundaries, which, in the absence of active motion, are generalized Hele-Shaw flows. In this note we use viscosity solutions methods to study limits for porous medium-type equations with active motion. We prove the uniform convergence of the density under fairly general assumptions on the initial data, thus improving existing results. We also obtain some additional information/regularity about the propagating interfaces, which, in view of the discontinuities, can nucleate and, thus, change topological type. The main tool is the construction of local, smooth, radial solutions which serve as barriers for the existence and uniqueness results as well as to quantify the speed of propagation of the free boundary propagation

Marine Protected Areas: Country Case Studies on Policy, Governance and Institutional Issues

This document presents case studies of the policy, governance and institutional issues of marine protected areas (MPAs) in South America (Northeastern)-Brazil; India, Palau and Senegal. It is the first of four in a global series of case studies on MPAs. An initial volume provides a synthesis and analysis of all the studies. The set of global MPA case studies was designed to close a deficit in information on the governance of MPAs and spatial management tools, within both fisheries management and biodiversity conservation contexts. The studies examine governance opportunities in and constraints on the use of spatial management measures at the national level. They were also designed to inform implementation of the FAO Technical Guidelines on marine protected areas (MPAs) and fisheries, which were developed to provide information and guidance on the use of MPAs in the context of fisheries

Quantum Lattice Fluctuations and Luminescence in C_60

We consider luminescence in photo-excited neutral C_60 using the Su-Schrieffer-Heeger model applied to a single C_60 molecule. To calculate the luminescence we use a collective coordinate method where our collective coordinate resembles the displacement of the carbon atoms of the Hg(8) phonon mode and extrapolates between the ground state "dimerisation" and the exciton polaron. There is good agreement for the existing luminescence peak spacing and fair agreement for the relative intensity. We predict the existence of further peaks not yet resolved in experiment. PACS Numbers : 78.65.Hc, 74.70.Kn, 36.90+

Update on pion weak decay constants in nuclear matter

The QCD sum rule calculation of the in-medium pion decay constants using pseudoscalar-axial vector correlation function, $i \int d^4x e^{ip\cdot x} < \rho| T[{\bar d}(x) i \gamma_5 u (x) {\bar u}(0) \gamma_\mu \gamma_5 d (0)] | \rho>$ is revisited. In particular, we argue that the dimension 5 condensate, $_N + {1\over 8} < {\bar q} g_s \sigma \cdot {\cal G} q >_N$, which is crucial for splitting the time ($f_t$) and space ($f_s$) components of the decay constant, is not necessarily restricted to be positive. Its positive value is found to yield a tachyonic pion mass. Using the in-medium pion mass as an input, we fix the dimension 5 condensate to be around $-0.025 {\rm GeV}^2 \sim -0.019$ GeV$^2$. The role of the $N$ and $\Delta$ intermediate states in the correlation function is also investigated. The $N$ intermediate state is found not to contribute to the sum rules. For the $\Delta$ intermediate state, we either treat it as a part of the continuum or propose a way to subtract explicitly from the sum rules. With (and without) explicit $\Delta$ subtraction while allowing the in-medium pion mass to vary within 139 MeV $\le m_\pi^* \le$ 159 MeV, we obtain $f_s/f_\pi = 0.37 \sim 0.78$ and $f_t / f_\pi = 0.63 \sim 0.79$.Comment: 18 pages including 5 postscript figure

The Gap Between What We Know and What We Do About Childhood Obesity: A Multi-factor Model for Assessment, Intervention, and Prevention

Childhood obesity in the United States has increased alarmingly and much is becoming known about multiple factors that contribute to this epidemic. These include environmental (e.g., prevalent junk foods), behavioral (e.g., inactivity), intrapsychic (e.g., depression), interpersonal (e.g., parenting style), as well as biological, socioeconomic, and cultural factors, to name just a few. A comprehensive multi-factor model of childhood obesity is presented based on extant research and its implications for assessment, intervention, and prevention are explored. Emphasis is placed on the importance of developing sound assessment approaches, on the potential value of treatment matching using interventions focused on assessment results on each child’s unique combination of causal factors, and more broadly on public health implications for prevention

Developmental Differences in the Ability to Provide Temporal Information about Repeated Events

Children (n = 372) aged 4 - 8 years participated in 1 or 4 occurrences of a similar event and were interviewed 1 week later. Compared to 85% of children who participated once, less than 25% with repeated experience gave the exact number of times they participated, although all knew they participated more than once. Children with repeated experience were asked additional temporal questions and there were clear developmental differences. Older children were more able than younger children to judge relative order and temporal position of the four occurrences. They also demonstrated improved temporal memory for the first and last relative to the middle occurrences, while younger children did so only for the first. This is the first systematic demonstration of children’s memory for temporal information after a repeated event. We discuss implications for theories of temporal memory development and the practical implications of asking children to provide temporal information