Holonomic constraints : an analytical result

Systems subjected to holonomic constraints follow quite complicated dynamics that could not be described easily with Hamiltonian or Lagrangian dynamics. The influence of holonomic constraints in equations of motions is taken into account by using Lagrange multipliers. Finding the value of the Lagrange multipliers allows to compute the forces induced by the constraints and therefore, to integrate the equations of motions of the system. Computing analytically the Lagrange multipliers for a constrained system may be a difficult task that is depending on the complexity of systems. For complex systems, it is most of the time impossible to achieve. In computer simulations, some algorithms using iterative procedures estimate numerically Lagrange multipliers or constraint forces by correcting the unconstrained trajectory. In this work, we provide an analytical computation of the Lagrange multipliers for a set of linear holonomic constraints with an arbitrary number of bonds of constant length. In the appendix of the paper, one would find explicit formulas for Lagrange multipliers for systems having 1, 2, 3, 4 and 5 bonds of constant length, linearly connected.Comment: 13 pages, no figures. To appear in J. Phys. A : Math. The

BBN For Pedestrians

The simplest, `standard' model of Big Bang Nucleosynthesis (SBBN) assumes three light neutrinos (N_nu = 3) and no significant electron neutrino asymmetry, leaving only one adjustable parameter: the baryon to photon ratio eta. The primordial abundance of any one nuclide can, therefore, be used to measure the baryon abundance and the value derived from the observationally inferred primordial abundance of deuterium closely matches that from current, non-BBN data, primarily from the WMAP survey. However, using this same estimate there is a tension between the SBBN-predicted 4He and 7Li abundances and their current, observationally inferred primordial abundances, suggesting that N_nu may differ from the standard model value of three and/or that there may be a non-zero neutral lepton asymmetry (or, that systematic errors in the abundance determinations have been underestimated or overlooked). The differences are not large and the allowed ranges of the BBN parameters permitted by the data are quite small. Within these ranges, the BBN-predicted abundances of D, 3He, 4He, and 7Li are very smooth, monotonic functions of eta, N_nu, and the lepton asymmetry. It is possible to describe the dependencies of these abundances (or powers of them) upon the three parameters by simple, linear fits which, over their ranges of applicability, are accurate to a few percent or better. The fits presented here have not been maximized for their accuracy but, for their simplicity. To identify the ranges of applicability and relative accuracies, they are compared to detailed BBN calculations; their utility is illustrated with several examples. Given the tension within BBN, these fits should prove useful in facilitating studies of the viability of proposals for non-standard physics and cosmology, prior to undertaking detailed BBN calculations.Comment: Submitted to a Focus Issue on Neutrino Physics in New Journal of Physics (www.njp.org

Invalidation of the Kelvin Force in Ferrofluids

Direct and unambiguous experimental evidence for the magnetic force density being of the form $M\nabla B$ in a certain geometry - rather than being the Kelvin force $M\nabla H$ - is provided for the first time. (M is the magnetization, H the field, and B the flux density.)Comment: 4 pages, 4 figure

Testing two nuclear physics approximations used in the standard leaky box model for the spallogenic production of LiBeB

The spallative production rates of Lithium, Beryllium and Boron (LiBeB) are a necessary component in any calculation of the evolution of these nuclei in the Galaxy. Previous calculations of these rates relied on two assumptions relating to the nuclear physics aspects: the straight-ahead approximation that describes the distribution of fragment energies and the assumption that the major contributor to the production rate arises from single-step reactions between primary cosmic ray projectiles and interstellar medium targets. We examine both assumptions by using a semi-empirical description for the spall's energy distribution and by including the reactions that proceed via intermediary fragments. After relaxing the straight-ahead approximation we find the changes in the production rates and emerging fluxes are small and do not warrant rejection of this approximation. In contrast we discover that two-step reactions can alter the production rate considerably leading to noticeable increases in the efficiency of producing the LiBeB nuclei. Motivated by this result we introduce a cascade technique to compute the production rates exactly and find that the results differ only slightly from those of our two-step calculations. We thus conclude that terminating the reaction network at the two-step order is sufficiently accurate for current studies of spallation.Comment: accepted in Ap

Collective neutrino flavor transitions in supernovae and the role of trajectory averaging

Non-linear effects on supernova neutrino oscillations, associated with neutrino self-interactions, are known to induce collective flavor transitions near the supernova core for theta_13 \neq 0. In scenarios with very shallow electron density profiles, these transformations have been shown to couple with ordinary matter effects, jointly producing spectral distortions both in normal and inverted hierarchy. In this work we consider a complementary scenario, characterized by higher electron density, as indicated by post-bounce shock-wave simulations. In this case, early collective flavor transitions are decoupled from later, ordinary matter effects. Moreover, such transitions become more amenable to both numerical computations and analytical interpretations in inverted hierarchy, while they basically vanish in normal hierarchy. We numerically evolve the neutrino density matrix in the region relevant for self-interaction effects. In the approximation of averaged intersection angle between neutrino trajectories, our simulations neatly show the collective phenomena of synchronization, bipolar oscillations, and spectral split, recently discussed in the literature. In the more realistic (but computationally demanding) case of non-averaged neutrino trajectories, our simulations do not show new significant features, apart from the smearing of ``fine structures'' such as bipolar nutations. Our results seem to suggest that, at least for non-shallow matter density profiles, averaging over neutrino trajectories plays a minor role in the final outcome. In this case, the swap of nu_e and nu_{\mu,\tau} spectra above a critical energy may represent an unmistakable signature of the inverted hierarchy, especially for theta_{13} small enough to render further matter effects irrelevant.Comment: v2 (27 pages, including 9 eps figures). Typos removed, references updated. Minor comments added. Corrected numerical errors in Eq.(6). Matches the published versio

The Effect of Bound Dineutrons upon BBN

We have examined the effects of a bound dineutron, n2, upon big bang nucleosynthesis (BBN) as a function of its binding energy B_n2. We find a weakly bound dineutron has little impact but as B_n2 increases its presence begins to alter the flow of free nucleons to helium-4. Due to this disruption, and in the absence of changes to other binding energies or fundamental constants, BBN sets a reliable upper limit of B_n2 <~ 2.5 MeV in order to maintain the agreement with the observations of the primordial helium-4 mass fraction and D/H abundance

Residence Time Statistics for Normal and Fractional Diffusion in a Force Field

We investigate statistics of occupation times for an over-damped Brownian particle in an external force field. A backward Fokker-Planck equation introduced by Majumdar and Comtet describing the distribution of occupation times is solved. The solution gives a general relation between occupation time statistics and probability currents which are found from solutions of the corresponding problem of first passage time. This general relationship between occupation times and first passage times, is valid for normal Markovian diffusion and for non-Markovian sub-diffusion, the latter modeled using the fractional Fokker-Planck equation. For binding potential fields we find in the long time limit ergodic behavior for normal diffusion, while for the fractional framework weak ergodicity breaking is found, in agreement with previous results of Bel and Barkai on the continuous time random walk on a lattice. For non-binding potential rich physical behaviors are obtained, and classification of occupation time statistics is made possible according to whether or not the underlying random walk is recurrent and the averaged first return time to the origin is finite. Our work establishes a link between fractional calculus and ergodicity breaking.Comment: 12 page

Neutrino Scattering, Absorption and Annihilation above the accretion disks of Gamma Ray Bursts

The central engine that drives gamma ray burst (GRB) explosions may derive from the ability of electrons/positrons and nucleons to tap into the momentum and energy from the large neutrino luminosity emitted by an accretion disk surrounding a black hole. This transfer of momentum and energy occurs due to neutrino absorption, scattering, and annihilation and the non-spherical geometry of the source both increases the annihilation efficiency and, close to the black hole, directs the momentum transfer towards the disk axis. We present annihilation efficiencies and the momentum/energy transfers for a number of accretion disk models and compute the critical densities of infalling material below which the transfer of neutrino momentum/energy will lead to an explosion. Models in which the neutrinos and antineutrinos become trapped within the disk have noticeably different momentum and energy deposition structure compared to thin disk models that may lead to significant differences in the explosion dynamics

Neutrino Spectra from Accretion Disks: Neutrino General Relativistic Effects and the Consequences for Nucleosynthesis

Black hole accretion disks have been proposed as good candidates for a range of interesting nucleosynthesis, including the r-process. The presence of the black hole influences the neutrino fluxes and affects the nucleosynthesis resulting from the interaction of the emitted neutrinos and hot outflowing material ejected from the disk. We study the impact of general relativistic effects on the neutrinos emitted from black hole accretion disks. We present abundances obtained by considering null geodesics and energy shifts for two different disk models. We find that both the bending of the neutrino trajectories and the energy shifts have important consequences for the nucleosynthetic outcomeComment: 18 pages, 17 figures, submitted to Ap

Cosmological limit on the neutrino mass

We have performed a careful analysis of constraints on the neutrino mass from current cosmological data. Combining data from the cosmic microwave background and the 2dF galaxy survey yields an upper limit on the sum of the three neutrino mass eigenstates of \sum m_nu < 3 eV (95% conf.), without including additional priors. Including data from SNIa observations, Big Bang nucleosynthesis, and HST Hubble key project data on H_0 tightens the limit to \sum m_nu < 2.5 eV (95% conf.). We also perform a Fisher matrix analysis which illustrates the cosmological parameter degeneracies affecting the determination of \sum m_nu.Comment: 6 pages, 2 figures, uses Revtex