Are Energy Efficiency Standards Justified?

This paper develops and parameterizes an overarching analytical framework to estimate the welfare effects of energy efficiency standards applied to automobiles and electricity-using durables. We also compare standards with sectoral and economywide pricing policies. The model captures a wide range of externalities and preexisting energy policies, and it allows for possible “misperceptions”—market failures that cause underinvestment in energy efficiency.Automobile fuel economy standards are not part of the first-best policy to reduce gasoline: fuel taxes are always superior because they reduce the externalities related to vehicle miles traveled. For the power sector, potential welfare gains from supplementing pricing instruments with efficiency standards are small at best. If pricing instruments are not feasible, a large misperceptions failure is required to justify efficiency standards, and even in this case the optimal reductions in fuel and electricity use are relatively modest. Reducing economywide carbon dioxide emissions through regulatory packages (combining efficiency and emissions standards) involves much higher costs than pricing instruments.standards, energy taxes, market failure, climate, power sector, gasoline

Critical Exponents and Stability at the Black Hole Threshold for a Complex Scalar Field

This paper continues a study on Choptuik scaling in gravitational collapse of a complex scalar field at the threshold for black hole formation. We perform a linear perturbation analysis of the previously derived complex critical solution, and calculate the critical exponent for black hole mass, $\gamma \approx 0.387106$. We also show that this critical solution is unstable via a growing oscillatory mode.Comment: 15 pages of latex/revtex; added details of numerics, in press in Phys Rev D; 1 figure included, or available by anonymous ftp to ftp://ftp.itp.ucsb.edu/figures/nsf-itp-95-58.ep

On the fluctuations of jamming coverage upon random sequential adsorption on homogeneous and heterogeneous media

The fluctuations of the jamming coverage upon Random Sequential Adsorption (RSA) are studied using both analytical and numerical techniques. Our main result shows that these fluctuations (characterized by $\sigma_{\theta_J}$) decay with the lattice size according to the power-law $\sigma_{\theta_J} \propto L^{-1/ \nu}$. The exponent $\nu$ depends on the dimensionality $D$ of the substrate and the fractal dimension of the set where the RSA process actually takes place ($d_f$) according to $\nu = 2 / (2D - d_f)$.This theoretical result is confirmed by means of extensive numerical simulations applied to the RSA of dimers on homogeneous and stochastic fractal substrates. Furthermore, our predictions are in excellent agreement with different previous numerical results. It is also shown that, studying correlated stochastic processes, one can define various fluctuating quantities designed to capture either the underlying physics of individual processes or that of the whole system. So, subtle differences in the definitions may lead to dramatically different physical interpretations of the results. Here, this statement is demonstrated for the case of RSA of dimers on binary alloys.Comment: 20 pages, 8 figure

Criticality and Bifurcation in the Gravitational Collapse of a Self-Coupled Scalar Field

We examine the gravitational collapse of a non-linear sigma model in spherical symmetry. There exists a family of continuously self-similar solutions parameterized by the coupling constant of the theory. These solutions are calculated together with the critical exponents for black hole formation of these collapse models. We also find that the sequence of solutions exhibits a Hopf-type bifurcation as the continuously self-similar solutions become unstable to perturbations away from self-similarity.Comment: 18 pages; one figure, uuencoded postscript; figure is also available at http://www.physics.ucsb.edu/people/eric_hirschman

Symmetry Algebras of Large-N Matrix Models for Open Strings

We have discovered that the gauge invariant observables of matrix models invariant under U($N$) form a Lie algebra, in the planar large-N limit. These models include Quantum Chromodynamics and the M(atrix)-Theory of strings. We study here the gauge invariant states corresponding to open strings (`mesons'). We find that the algebra is an extension of a remarkable new Lie algebra ${\cal V}_{\Lambda}$ by a product of more well-known algebras such as $gl_{\infty}$ and the Cuntz algebra. ${\cal V}_{\Lambda}$ appears to be a generalization of the Lie algebra of vector fields on the circle to non-commutative geometry. We also use a representation of our Lie algebra to establish an isomorphism between certain matrix models (those that preserve `gluon number') and open quantum spin chains. Using known results on quantum spin chains, we are able to identify some exactly solvable matrix models. Finally, the Hamiltonian of a dimensionally reduced QCD model is expressed explicitly as an element of our Lie algebra.Comment: 44 pages, 8 eps figures, 3 tables, LaTeX2.09; this is the published versio

Some flows in shape optimization

Geometric flows related to shape optimization problems of Bernoulli type are investigated. The evolution law is the sum of a curvature term and a nonlocal term of Hele-Shaw type. We introduce generalized set solutions, the definition of which is widely inspired by viscosity solutions. The main result is an inclusion preservation principle for generalized solutions. As a consequence, we obtain existence, uniqueness and stability of solutions. Asymptotic behavior for the flow is discussed: we prove that the solutions converge to a generalized Bernoulli exterior free boundary problem

Heat release by controlled continuous-time Markov jump processes

We derive the equations governing the protocols minimizing the heat released by a continuous-time Markov jump process on a one-dimensional countable state space during a transition between assigned initial and final probability distributions in a finite time horizon. In particular, we identify the hypotheses on the transition rates under which the optimal control strategy and the probability distribution of the Markov jump problem obey a system of differential equations of Hamilton-Bellman-Jacobi-type. As the state-space mesh tends to zero, these equations converge to those satisfied by the diffusion process minimizing the heat released in the Langevin formulation of the same problem. We also show that in full analogy with the continuum case, heat minimization is equivalent to entropy production minimization. Thus, our results may be interpreted as a refined version of the second law of thermodynamics.Comment: final version, section 2.1 revised, 26 pages, 3 figure

The Spectrum of Electromagnetic Jets from Kerr Black Holes and Naked Singularities in the Teukolsky Perturbation Theory

We give a new theoretical basis for examination of the presence of the Kerr black hole (KBH) or the Kerr naked singularity (KNS) in the central engine of different astrophysical objects around which astrophysical jets are typically formed: X-ray binary systems, gamma ray bursts (GRBs), active galactic nuclei (AGN), etc. Our method is based on the study of the exact solutions of the Teukolsky master equation for electromagnetic perturbations of the Kerr metric. By imposing original boundary conditions on the solutions so that they describe a collimated electromagnetic outflow, we obtain the spectra of possible {\em primary jets} of radiation, introduced here for the first time. The theoretical spectra of primary electromagnetic jets are calculated numerically. Our main result is a detailed description of the qualitative change of the behavior of primary electromagnetic jet frequencies under the transition from the KBH to the KNS, considered here as a bifurcation of the Kerr metric. We show that quite surprisingly the novel spectra describe linearly stable primary electromagnetic jets from both the KBH and the KNS. Numerical investigation of the dependence of these primary jet spectra on the rotation of the Kerr metric is presented and discussed.Comment: 18 pages, 35 figures, LaTeX file. Final version. Accepted for publication in Astrophysics and Space Science. Amendments. Typos corrected. Novel notion -"primary jet" is introduced. New references and comments adde