Search results for "Mathematical physics"
showing 10 items of 2687 documents
Neutrino oscillations and Non-Standard Interactions
2017
Current neutrino experiments measure the neutrino mixing parameters with an unprecedented accuracy. The upcoming generation of experiments will be sensitive to subdominant effects that can give information on the unknown neutrino parameters: the Dirac CP-violating phase, the mass ordering and the $\theta_{23}$ octant. Determining the exact values of neutrino mass and mixing parameters is crucial to test neutrino models and flavor symmetries. In the first part of this review, we summarize the current status of neutrino oscillation parameters. We consider the most recent data from solar experiments and the atmospheric data from Super-Kamiokande, IceCube and ANTARES. We implement the data from…
International Scoping Study (ISS) for a future neutrino factory and Super-Beam facility. Detectors and flux instrumentation for future neutrino facil…
2009
Technical report by The ISS Detector Working Group; This report summarises the conclusions from the detector group of the International Scoping Study of a future Neutrino Factory and Super-Beam neutrino facility. The baseline detector options for each possible neutrino beam are defined as follows: 1. A very massive (Megaton) water Cherenkov detector is the baseline option for a sub-GeV Beta Beam and Super Beam facility. 2. There are a number of possibilities for either a Beta Beam or Super Beam (SB) medium energy facility between 1-5 GeV. These include a totally active scintillating detector (TASD), a liquid argon TPC or a water Cherenkov detector. 3. A 100 kton magnetized iron neutrino det…
The kinetics of defect accumulation under irradiation: many-particle effects
1993
The kinetics of Frenkel defect accumulation under permanent particle source (irradiation) is discussed with special emphasis on many-particle effects. Defect accumulation is restricted by their diffusion and annihilation, A + B → 0, if the relative distance is less than the critical distance r0. A novel formalism of many-point particle densities based on Kirkwood's superposition approximation is developed to take into account aggregation of similar defects (A−A, B−B). The dependence of the saturation concentration after a prolonged irradiation upon spatial dimension ( = 1, 2, 3), defect mobility and the initial correlation within geminate pairs is analyzed. It is shown that the defect conce…
Thermalization of Levy flights: Path-wise picture in 2D
2013
We analyze two-dimensional (2D) random systems driven by a symmetric L\'{e}vy stable noise which, under the sole influence of external (force) potentials $\Phi (x) $, asymptotically set down at Boltzmann-type thermal equilibria. Such behavior is excluded within standard ramifications of the Langevin approach to L\'{e}vy flights. In the present paper we address the response of L\'{e}vy noise not to an external conservative force field, but directly to its potential $\Phi (x)$. We prescribe a priori the target pdf $\rho_*$ in the Boltzmann form $\sim \exp[- \Phi (x)]$ and next select the L\'evy noise of interest. Given suitable initial data, this allows to infer a reliable path-wise approxima…
Pattern formation driven by cross–diffusion in a 2D domain
2012
Abstract In this work we investigate the process of pattern formation in a two dimensional domain for a reaction–diffusion system with nonlinear diffusion terms and the competitive Lotka–Volterra kinetics. The linear stability analysis shows that cross-diffusion, through Turing bifurcation, is the key mechanism for the formation of spatial patterns. We show that the bifurcation can be regular, degenerate non-resonant and resonant. We use multiple scales expansions to derive the amplitude equations appropriate for each case and show that the system supports patterns like rolls, squares, mixed-mode patterns, supersquares, and hexagonal patterns.
Stretching semiflexible polymer chains: Evidence for the importance of excluded volume effects from Monte Carlo simulation
2011
Semiflexible macromolecules in dilute solution under very good solvent conditions are modeled by self-avoiding walks on the simple cubic lattice ($d=3$ dimensions) and square lattice ($d=2$ dimensions), varying chain stiffness by an energy penalty $\epsilon_b$ for chain bending. In the absence of excluded volume interactions, the persistence length $\ell_p$ of the polymers would then simply be $\ell_p=\ell_b(2d-2)^{-1}q_b^{-1}$ with $q_b= \exp(-\epsilon_b/k_BT)$, the bond length $\ell_b$ being the lattice spacing, and $k_BT$ is the thermal energy. Using Monte Carlo simulations applying the pruned-enriched Rosenbluth method (PERM), both $q_b$ and the chain length $N$ are varied over a wide r…
Scaling property of variational perturbation expansion for a general anharmonic oscillator with xp-potential
1995
We prove a powerful scaling property for the extremality condition in the recently developed variational perturbation theory which converts divergent perturbation expansions into exponentially fast convergent ones. The proof is given for the energy eigenvalues of an anharmonic oscillator with an arbitrary $x^p$-potential. The scaling property greatly increases the accuracy of the results.
Statistical and systematic errors in Monte Carlo sampling
1991
We have studied the statistical and systematic errors which arise in Monte Carlo simulations and how the magnitude of these errors depends on the size of the system being examined when a fixed amount of computer time is used. We find that, depending on the degree of self-averaging exhibited by the quantities measured, the statistical errors can increase, decrease, or stay the same as the system size is increased. The systematic underestimation of response functions due to the finite number of measurements made is also studied. We develop a scaling formalism to describe the size dependence of these errors, as well as their dependence on the “bin length” (size of the statistical sample), both…
Optimized analysis of the critical behavior in polymer mixtures from Monte Carlo simulations
1992
A complete outline is given for how to determine the critical properties of polymer mixtures with extrapolation methods similar to the Ferrenberg-Swendsen techniques recently devised for spin systems. By measuring not only averages but the whole distribution of the quantities of interest, it is possible to extrapolate the data obtained in only a few simulations nearT c over the entire critical region, thereby saving at least 90% of the computer time normally needed to locate susceptibility peaks or cumulant intersections and still getting more precise results. A complete picture of the critical properties of polymer mixtures in the thermodynamic limit is then obtained with finite-size scali…
Monte Carlo study of the ising model phase transition in terms of the percolation transition of “physical clusters”
1990
Finite squareL×L Ising lattices with ferromagnetic nearest neighbor interaction are simulated using the Swendsen-Wang cluster algorithm. Both thermal properties (internal energyU, specific heatC, magnetization 〈|M|〉, susceptibilityχ) and percolation cluster properties relating to the “physical clusters,” namely the Fortuin-Kasteleyn clusters (percolation probability 〈P∞〉, percolation susceptibilityχp, cluster size distributionnl) are evaluated, paying particular attention to finite-size effects. It is shown that thermal properties can be expressed entirely in terms of cluster properties, 〈P∞〉 being identical to 〈|M|〉 in the thermodynamic limit, while finite-size corrections differ. In contr…