Saving on a Rainy Day, Borrowing for a Rainy Day

The aim of this paper is to understand what a recession means for individual consumers, and to model in a life-cycle framework how individuals respond to recessions. Our focus is on the sharp increase in savings rates that have been observed in the current and recent recessions. We show empirically that these saving spikes were short-lived and common to all working age groups. We then study life-cycle models in which recessions involve one or more of: (i) an aggregate permanent negative shock to individual income; (ii) an increase in the variance of idiosyncratic permanent shocks; (iii) a tightening of credit constraints; (iv) asset market crashes. In simulations and in the data we aggregate explicitly from individual behavior. We model credit tightening as a constraint on new borrowing and this generates an option value of borrowing in good times. We show that the rise in the aggregate savings ratio is driven by increases in uncertainty, rather than tightening of credit; temporary shocks to the supply of credit generate increases in saving only among younger agents

Age Dating of a High-Redshift QSO B1422+231 at Z=3.62 and its Cosmological Implications

The observed Fe II(UV+optical)/Mg II lambda lambda 2796,2804 flux ratio from a gravitationally lensed quasar B1422+231 at z=3.62 is interpreted in terms of detailed modeling of photoionization and chemical enrichment in the broad-line region (BLR) of the host galaxy. The delayed iron enrichment by Type Ia supernovae is used as a cosmic clock. Our standard model, which matches the Fe II/Mg II ratio, requires the age of 1.5 Gyr for B1422+231 with a lower bound of 1.3 Gyr, which exceeds the expansion age of the Einstein-de Sitter Omega_0=1 universe at a redshift of 3.62 for any value of the Hubble constant in the currently accepted range, H_0=60-80 km,s^{-1},Mpc^{-1}. This problem of an age discrepancy at z=3.62 can be unraveled in a low-density Omega_0<0.2 universe, either with or without a cosmological constant, depending on the allowable redshift range of galaxy formation. However, whether the cosmological constant is a required option in modern cosmology awaits a thorough understanding of line transfer processes in the BLRs.Comment: 7 pages including 3 figures, to appear in ApJ Letter

Light Sheets and the Covariant Entropy Conjecture

We examine the holography bound suggested by Bousso in his covariant entropy conjecture, and argue that it is violated because his notion of light sheet is too generous. We suggest its replacement by a weaker bound.Comment: 5 pages, to appear in Classical and Quantum Gravit

Multifluid magnetohydrodynamic turbulent decay

It is generally believed that turbulence has a significant impact on the dynamics and evolution of molecular clouds and the star formation which occurs within them. Non-ideal magnetohydrodynamic effects are known to influence the nature of this turbulence. We present the results of a suite of 512-cubed resolution simulations of the decay of initially super-Alfvenic and supersonic fully multifluid MHD turbulence. We find that ambipolar diffusion increases the rate of decay of the turbulence while the Hall effect has virtually no impact. The decay of the kinetic energy can be fitted as a power-law in time and the exponent is found to be -1.34 for fully multifluid MHD turbulence. The power spectra of density, velocity and magnetic field are all steepened significantly by the inclusion of non-ideal terms. The dominant reason for this steepening is ambipolar diffusion with the Hall effect again playing a minimal role except at short length scales where it creates extra structure in the magnetic field. Interestingly we find that, at least at these resolutions, the majority of the physics of multifluid turbulence can be captured by simply introducing fixed (in time and space) resistive terms into the induction equation without the need for a full multifluid MHD treatment. The velocity dispersion is also examined and, in common with previously published results, it is found not to be power-law in nature.Comment: 16 pages, 15 figures, Accepted for publication in Ap

Error Voltage Components in Quantitative Voltage Contrast Measurement Systems

This paper presents the results of computer simulation studies into the respective contributions of the potential barrier, the off-normal incidence injection of secondary electrons (SEs) into the retarding field and analyser geometry on Types I and II local field error voltages for a practical 20 mm wide planar retarding field energy analyser. Results show that the error voltage component due to the off-normal incidence injection effect of SEs into the retarding field dominates the Type I local field error. For type II LFE, the error voltage component due to analyser geometry effect is the higher contributing factor. The presence of a neighbouring electrode voltage tends to draw SEs away from the central axis of the energy analyser, thus causing the electron trajectories to be more sensitive to the influence of the analyser geometry

Gravitational Collapse in Turbulent Molecular Clouds. II. Magnetohydrodynamical Turbulence

Hydrodynamic supersonic turbulence can only prevent local gravitational collapse if the turbulence is driven on scales smaller than the local Jeans lengths in the densest regions, a very severe requirement (Paper I). Magnetic fields have been suggested to support molecular clouds either magnetostatically or via magnetohydrodynamic (MHD) waves. Whereas the first mechanism would form sheet-like clouds, the second mechanism not only could exert a pressure onto the gas counteracting the gravitational forces, but could lead to a transfer of turbulent kinetic energy down to smaller spatial scales via MHD wave interactions. This turbulent magnetic cascade might provide sufficient energy at small scales to halt local collapse. We test this hypothesis with MHD simulations at resolutions up to 256^3 zones, done with ZEUS-3D. We first derive a resolution criterion for self-gravitating, magnetized gas: in order to prevent collapse of magnetostatically supported regions due to numerical diffusion, the minimum Jeans length must be resolved by four zones. Resolution of MHD waves increases this requirement to roughly six zones. We then find that magnetic fields cannot prevent local collapse unless they provide magnetostatic support. Weaker magnetic fields do somewhat delay collapse and cause it to occur more uniformly across the supported region in comparison to the hydrodynamical case. However, they still cannot prevent local collapse for much longer than a global free-fall time.Comment: 32 pages, 14 figures, accepted by Ap

Linking and causality in globally hyperbolic spacetimes

The linking number $lk$ is defined if link components are zero homologous. Our affine linking invariant $alk$ generalizes $lk$ to the case of linked submanifolds with arbitrary homology classes. We apply $alk$ to the study of causality in Lorentz manifolds. Let $M^m$ be a spacelike Cauchy surface in a globally hyperbolic spacetime $(X^{m+1}, g)$. The spherical cotangent bundle $ST^*M$ is identified with the space $N$ of all null geodesics in $(X,g).$ Hence the set of null geodesics passing through a point $x\in X$ gives an embedded $(m-1)$-sphere $S_x$ in $N=ST^*M$ called the sky of $x.$ Low observed that if the link $(S_x, S_y)$ is nontrivial, then $x,y\in X$ are causally related. This motivated the problem (communicated by Penrose) on the Arnold's 1998 problem list to apply link theory to the study of causality. The spheres $S_x$ are isotopic to fibers of $(ST^*M)^{2m-1}\to M^m.$ They are nonzero homologous and $lk(S_x,S_y)$ is undefined when $M$ is closed, while $alk(S_x, S_y)$ is well defined. Moreover, $alk(S_x, S_y)\in Z$ if $M$ is not an odd-dimensional rational homology sphere. We give a formula for the increment of \alk under passages through Arnold dangerous tangencies. If $(X,g)$ is such that $alk$ takes values in $\Z$ and $g$ is conformal to $g'$ having all the timelike sectional curvatures nonnegative, then $x, y\in X$ are causally related if and only if $alk(S_x,S_y)\neq 0$. We show that $x,y$ in nonrefocussing $(X, g)$ are causally unrelated iff $(S_x, S_y)$ can be deformed to a pair of $S^{m-1}$-fibers of $ST^*M\to M$ by an isotopy through skies. Low showed that if (\ss, g) is refocussing, then $M$ is compact. We show that the universal cover of $M$ is also compact.Comment: We added: Theorem 11.5 saying that a Cauchy surface in a refocussing space time has finite pi_1; changed Theorem 7.5 to be in terms of conformal classes of Lorentz metrics and did a few more changes. 45 pages, 3 figures. A part of the paper (several results of sections 4,5,6,9,10) is an extension and development of our work math.GT/0207219 in the context of Lorentzian geometry. The results of sections 7,8,11,12 and Appendix B are ne

Low-energy interaction of composite spin-half systems with scalar and vector fields

We consider a composite spin-half particle moving in spatially-varying scalar and vector fields. The vector field is assumed to couple to a conserved charge, but no assumption is made about either the structure of the composite or its coupling to the scalar field. A general form for the piece of the spin-orbit interaction of the composite with the scalar and vector fields which is first-order in momentum transfer ${\bf Q}$ and second-order in the fields is derived.Comment: 10 pages, RevTe