Extreme objects with arbitrary large mass, or density, and arbitrary size

We consider a generalization of the interior Schwarzschild solution that we match to the exterior one to build global C^1 models that can have arbitrary large mass, or density, with arbitrary size. This is possible because of a new insight into the problem of localizing the center of symmetry of the models and the use of principal transformations to understand the structure of space.Comment: 20 pages, 6 figures. Fixed one reference. Added a new equatio

Bel-Robinson tensor and dominant energy property in the Bianchi type I Universe

Within the framework of Bianchi type-I space-time we study the Bel-Robinson tensor and its impact on the evolution of the Universe. We use different definitions of the Bel-Robinson tensor existing in the literature and compare the results. Finally we investigate the so called "dominant super-energy property" for the Bel-Robinson tensor as a generalization of the usual dominant energy condition for energy momentum tensors. Keywords: Bianchi type I model, super-energy tensors Pacs: 03.65.Pm and 04.20.HaComment: 15 pages, revised version, no figure

Simplicity of Completion Time Distributions for Common Complex Biochemical Processes

Biochemical processes typically involve huge numbers of individual reversible steps, each with its own dynamical rate constants. For example, kinetic proofreading processes rely upon numerous sequential reactions in order to guarantee the precise construction of specific macromolecules. In this work, we study the transient properties of such systems and fully characterize their first passage (completion) time distributions. In particular, we provide explicit expressions for the mean and the variance of the completion time for a kinetic proofreading process and computational analyses for more complicated biochemical systems. We find that, for a wide range of parameters, as the system size grows, the completion time behavior simplifies: it becomes either deterministic or exponentially distributed, with a very narrow transition between the two regimes. In both regimes, the dynamical complexity of the full system is trivial compared to its apparent structural complexity. Similar simplicity is likely to arise in the dynamics of many complex multi-step biochemical processes. In particular, these findings suggest not only that one may not be able to understand individual elementary reactions from macroscopic observations, but also that such understanding may be unnecessary

Ergodic and Nonergodic Anomalous Diffusion in Coupled Stochastic Processes

Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin process whose friction coefficient depends on the state of a similar, unobserved process. Integrating out the latter, we derive the long time behaviour of the mean square displacement. Anomalous diffusion is found. Since the diffusion exponent can not be predicted using a simple scaling argument, anomalous scaling appears as well. We also find that the coupling can lead to ergodic or non-ergodic behaviour of the studied process. We compare our theoretical predictions with numerical simulations and find an excellent agreement. The findings caution against treating biochemical systems coupled with unobserved dynamical degrees of freedom by means of standard, diffusive Langevin descriptions

Electromagnetic radiation produces frame dragging

It is shown that for a generic electrovacuum spacetime, electromagnetic radiation produces vorticity of worldlines of observers in a Bondi--Sachs frame. Such an effect (and the ensuing gyroscope precession with respect to the lattice) which is a reminiscence of generation of vorticity by gravitational radiation, may be linked to the nonvanishing of components of the Poynting and the super--Poynting vectors on the planes othogonal to the vorticity vector. The possible observational relevance of such an effect is commented.Comment: 8 pages RevTex 4-1; updated version to appear in Physical Review

Graviton-Graviton Scattering, Bel-Robinson and Energy (Pseudo)-Tensors

Motivated by recent work involving the graviton-graviton tree scattering amplitude, and its twin descriptions as the square of the Bel-Robinson tensor, B_{\m\n\a\b}, and as the "current-current interaction" square of gravitational energy pseudo-tensors t_{\a\b},we find an exact tensor-square root equality B_{\mn\a\b} = \pa^2_\mn t_{\a\b}, for a combination of Einstein and Landau-Lifschitz t_\ab, in Riemann normal coordinates. In the process, we relate, on-shell, the usual superpotential basis for classifying pseudo-tensors with one spanned by polynomials in the curvature.Comment: 7 page

Energy and Momentum Distributions of a (2+1)-dimensional black hole background

Using Einstein, Landau-Lifshitz, Papapetrou and Weinberg energy-momentum complexes we explicitly evaluate the energy and momentum distributions associated with a non-static and circularly symmetric three-dimensional spacetime. The gravitational background under study is an exact solution of the Einstein's equations in the presence of a cosmological constant and a null fluid. It can be regarded as the three-dimensional analogue of the Vaidya metric and represents a non-static spinless (2+1)-dimensional black hole with an outflux of null radiation. All four above-mentioned prescriptions give exactly the same energy and momentum distributions for the specific black hole background. Therefore, the results obtained here provide evidence in support of the claim that for a given gravitational background, different energy-momentum complexes can give identical results in three dimensions. Furthermore, in the limit of zero cosmological constant the results presented here reproduce the results obtained by Virbhadra who utilized the Landau-Lifshitz energy-momentum complex for the same (2+1)-dimensional black hole background in the absence of a cosmological constant.Comment: 19 pages, LaTeX, v3: references added, to appear in Int.J.Mod.Phys.

Derivation of Source-Free Maxwell and Gravitational Radiation Equations by Group Theoretical Methods

We derive source-free Maxwell-like equations in flat spacetime for any helicity "j" by comparing the transformation properties of the 2(2j+1) states that carry the manifestly covariant representations of the inhomogeneous Lorentz group with the transformation properties of the two helicity "j" states that carry the irreducible representations of this group. The set of constraints so derived involves a pair of curl equations and a pair of divergence equations. These reduce to the free-field Maxwell equations for j=1 and the analogous equations coupling the gravito-electric and the gravito-magnetic fields for j=2.Comment: 15 pages, no figures, to appear in Int. J. Mod. Phys.

Policy stringency under the European Union Emission trading system and its impact on technological change in the energy sector

In this study, we use patent count data for overall Climate Change Mitigation Technologies, and for those related to energy production and distribution to evaluate the relationship between the sizable oversupply of European Union emissions Allowances and a policy shift marked by the transition from Phase I to Phase II under the European Union Emission Trading System, on the one hand, and on “green” patenting, on the other. According to our results, the expected negative impact of this oversupply on technological change seems to be confirmed. Thus, stakeholders take the actual supply of certificates into account when determining their innovative activity. In the same vein, they do so with respect to policy changes related to greater stringency, which generated a sizeable increase in patenting activity when controlling for other economic factors. Our results suggest that a critical evaluation of emission caps and allowances distribution must be undertaken

A local potential for the Weyl tensor in all dimensions

In all dimensions and arbitrary signature, we demonstrate the existence of a new local potential -- a double (2,3)-form -- for the Weyl curvature tensor, and more generally for all tensors with the symmetry properties of the Weyl curvature tensor. The classical four-dimensional Lanczos potential for a Weyl tensor -- a double (2,1)-form -- is proven to be a particular case of the new potential: its double dual.Comment: 7 pages; Late