Phenomenology of the CAH+ measure

The CAH+ measure regulates the infinite spacetime volume of the multiverse by constructing a surface of constant comoving apparent horizon (CAH) and then removing the future lightcones of all points on that surface (the latter prescription is referred to by the "+" in the name of the measure). This measure was motivated by the conjectured duality between the bulk of the multiverse and its future infinity and by the causality condition, requiring that the cutoff surfaces of the measure should be spacelike or null. Here we investigate the phenomenology of the CAH+ measure and find that it does not suffer from any known pathologies. The distribution for the cosmological constant Lambda derived from this measure is in a good agreement with the observed value, and the distribution for the number of inflationary e-foldings satisfies the observational constraint. The CAH+ measure does not exhibit any "runaway" behaviors at zero or negative values of Lambda, which have been recently shown to afflict a number of other measures.Comment: 35 pages, including 6 figures and 2 appendices; v2 corrections in Section 2.4, conclusions unchange

Statistical Understanding of Quark and Lepton Masses in Gaussian Landscapes

The fundamental theory of nature may allow a large landscape of vacua. Even if the theory contains a unified gauge symmetry, the 22 flavor parameters of the Standard Model, including neutrino masses, may be largely determined by the statistics of this landscape, and not by any symmetry. Then the measured values of the flavor parameters do not lead to any fundamental symmetries, but are statistical accidents; their precise values do not provide any insights into the fundamental theory, rather the overall pattern of flavor reflects the underlying landscape. We investigate whether random selection from the statistics of a simple landscape can explain the broad patterns of quark, charged lepton, and neutrino masses and mixings. We propose Gaussian landscapes as simplified models of landscapes where Yukawa couplings result from overlap integrals of zero-mode wavefunctions in higher-dimensional supersymmetric gauge theories. In terms of just five free parameters, such landscapes can account for all gross features of flavor, including: the hierarchy of quark and charged lepton masses; small quark mixing angles, with 13 mixing less than 12 and 23 mixing; very light Majorana neutrino masses, with the solar to atmospheric neutrino mass ratio consistent with data; distributions for leptonic 12 and 23 mixings that are peaked at large values, while the distribution for 13 mixing is peaked at low values; and order unity CP violating phases in both the quark and lepton sectors. While the statistical distributions for flavor parameters are broad, the distributions are robust to changes in the geometry of the extra dimensions. Constraining the distributions by loose cuts about observed values leads to narrower distributions for neutrino measurements of 13 mixing, CP violation, and neutrinoless double beta decay.Comment: 86 pages, 26 figures, 2 tables, and table of content

Quark and Lepton Masses from Gaussian Landscapes

The flavor structure of the standard model (SM) might arise from random selection on a landscape. We propose a class of simple models, “Gaussian landscapes,” where Yukawa couplings derive from overlap integrals of Gaussian wave functions on extra-dimensions. Statistics of vacua are generated by scanning the peak positions of these zero-modes, giving probability distributions for all flavor observables. Gaussian landscapes can account for all observed flavor patterns with few free parameters. Although they give broad probability distributions, the predictions are correlated and accounting for measured parameters sharpens the distributions of future neutrino measurements

Neutrino mixing and mass hierarchy in Gaussian landscapes

The flavor structure of the Standard Model may arise from random selection on a landscape. In a class of simple models, called "Gaussian landscapes," Yukawa couplings derive from overlap integrals of Gaussian zero-mode wavefunctions on an extra-dimensional space. Statistics of vacua are generated by scanning the peak positions of these wavefunctions, giving probability distributions for all flavor observables. Gaussian landscapes can account for all of the major features of flavor, including both the small electroweak mixing in the quark sector and the large mixing observed in the lepton sector. We find that large lepton mixing stems directly from lepton doublets having broad wavefunctions on the internal manifold. Assuming the seesaw mechanism, we find the mass hierarchy among neutrinos is sensitive to the number of right-handed neutrinos, and can provide a good fit to neutrino oscillation measurements.Comment: 11 pages, 2 figure

A signature of anisotropic bubble collisions

Our universe may have formed via bubble nucleation in an eternally-inflating background. Furthermore, the background may have a compact dimension---the modulus of which tunnels out of a metastable minimum during bubble nucleation---which subsequently grows to become one of our three large spatial dimensions. When in this scenario our bubble universe collides with other ones like it, the collision geometry is constrained by the reduced symmetry of the tunneling instanton. While the regions affected by such bubble collisions still appear (to leading order) as disks in an observer's sky, the centers of these disks all lie on a single great circle, providing a distinct signature of anisotropic bubble nucleation.Comment: 10 pages, 5 figures; v2: crucial error corrected, conclusions revise

Landau and Ott scaling for the kinetic energy density and the low TcT_c conventional superconductors, Li2Pd3BLi_{2}Pd_{3}B and Nb

The scaling approach recently proposed by Landau and Ott for isothermal magnetization curves is extended to the average kinetic energy density of the condensate. Two low $T_c$ superconductors, Nb and $Li_{2}Pd_{3}B$ are studied and their isothermal reversible magnetization shown to display Landau and Ott scaling. Good agreement is obtained for the upper critical field $H_{c2}(T)$, determined from the Abrikosov approximation for the reversible region (standard linear extrapolation of the magnetization curve), and from the maximum of the kinetic energy curves. For the full range of data, which includes the irreversible region, the isothermal $d.M.B/H^2$ curves for $Li_2Pd_3B$ show an impressive collapse into a single curve over the entire range of field measurements. The Nb isothermal $d.M.B/H^2$ curves exhibit the interesting feature of a constant and temperature independent minimum value

A Robust Solution Procedure for Hyperelastic Solids with Large Boundary Deformation

Compressible Mooney-Rivlin theory has been used to model hyperelastic solids, such as rubber and porous polymers, and more recently for the modeling of soft tissues for biomedical tissues, undergoing large elastic deformations. We propose a solution procedure for Lagrangian finite element discretization of a static nonlinear compressible Mooney-Rivlin hyperelastic solid. We consider the case in which the boundary condition is a large prescribed deformation, so that mesh tangling becomes an obstacle for straightforward algorithms. Our solution procedure involves a largely geometric procedure to untangle the mesh: solution of a sequence of linear systems to obtain initial guesses for interior nodal positions for which no element is inverted. After the mesh is untangled, we take Newton iterations to converge to a mechanical equilibrium. The Newton iterations are safeguarded by a line search similar to one used in optimization. Our computational results indicate that the algorithm is up to 70 times faster than a straightforward Newton continuation procedure and is also more robust (i.e., able to tolerate much larger deformations). For a few extremely large deformations, the deformed mesh could only be computed through the use of an expensive Newton continuation method while using a tight convergence tolerance and taking very small steps.Comment: Revision of earlier version of paper. Submitted for publication in Engineering with Computers on 9 September 2010. Accepted for publication on 20 May 2011. Published online 11 June 2011. The final publication is available at http://www.springerlink.co

Onset of phase correlations in YBa2Cu3O{7-x} as determined from reversible magnetization measurements

Isofield magnetization curves are obtained and analyzed for three single crystals of YBa2Cu3O{7-x}, ranging from optimally doped to very underdoped, as well as the BCS superconductor Nb, in the presence of magnetic fields applied both parallel and perpendicular to the $ab$ planes. Near Tc, the magnetization exhibits a temperature dependence \sqrt{M} [Ta(H)-T]^m. In accordance with recent theories, we associated Ta(H) with the onset of coherent phase fluctuations of the superconducting order parameter. For Nb and optimally doped YBaCuO, Ta(H) is essentially identical to the mean-field transition line Tc(H). The fitting exponent m=0.5 takes its mean-field value for Nb, and varies just slightly from 0.5 for optimally doped YBaCuO. However, underdoped YBCO samples exhibit anomalous behavior, with Ta(H)>Tc for H applied parallel to the c axis, suggesting that the magnetization is probing a region of temperatures above Tc where phase correlations persist. In this region, the fitting exponent falls in the range 0.5 < m < 0.8 for H\parallel c, compared with m~0. for $H\parallel ab planes. The results are interpreted in terms of an anisotropic pairing symmetry of the order parameter: d-wave along the ab planes and s-wave along the c axis.Comment: 5 pages, 4 figure

Non-centro-symmetric superconductors Li2Pd3B and Li2(Pd0.8Pt0.2)3B: amplitude and phase fluctuations analysis of the experimental magnetization data

We report on magnetization data obtained as a function of temperature and magnetic field in Li2 (Pd0.8Pt0.2)3B and Li2Pd3B non-centro-symmetric superconductors. Reversible magnetization curves were plotted as M1/2 vs. T. This allows study of the asymptotic behavior of the averaged order parameter amplitude (gap) near the superconducting transition. Results of the analysis show, as expected, a mean field superconducting transition for Li2Pd3B. On contrary, a large deviation from the mean field behavior is revealed for Li2(Pd0.8Pt0.2)3B. This is interpreted as due to the strength of the non s-wave spin-triplet pairing in this Pt-containing compound which produces nodes in the order parameter and consequently, phase fluctuations. The diamagnetic signal above Tc(H) in Li2Pd3B is well explained by superconducting Gaussian fluctuations, which agrees with the observed mean field transition. For Li2(Pd0.8Pt0.2)3B the diamagnetic signal above Tc(H) is much higher than the expected Gaussian values and appears to be well explained by three dimensional critical fluctuations of the lowest-Landau-level type, which somehow agrees with the scenario of a phase mediated transition.Comment: 7 pages (1 column) 3 figure