Actinide collisions for QED and superheavy elements with the time-dependent Hartree-Fock theory and the Balian-V\'en\'eroni variational principle

Collisions of actinide nuclei form, during very short times of few zs ($10^{-21}$ s), the heaviest ensembles of interacting nucleons available on Earth. Such collisions are used to produce super-strong electric fields by the huge number of interacting protons to test spontaneous positron-electron pair emission (vacuum decay) predicted by the quantum electrodynamics (QED) theory. Multi-nucleon transfer in actinide collisions could also be used as an alternative way to fusion in order to produce neutron-rich heavy and superheavy elements thanks to inverse quasifission mechanisms. Actinide collisions are studied in a dynamical quantum microscopic approach. The three-dimensional time-dependent Hartree-Fock (TDHF) code {\textsc{tdhf3d}} is used with a full Skyrme energy density functional to investigate the time evolution of expectation values of one-body operators, such as fragment position and particle number. This code is also used to compute the dispersion of the particle numbers (e.g., widths of fragment mass and charge distributions) from TDHF transfer probabilities, on the one hand, and using the Balian-Veneroni variational principle, on the other hand. A first application to test QED is discussed. Collision times in $^{238}$U+$^{238}$U are computed to determine the optimum energy for the observation of the vacuum decay. It is shown that the initial orientation strongly affects the collision times and reaction mechanism. The highest collision times predicted by TDHF in this reaction are of the order of $\sim4$ zs at a center of mass energy of 1200 MeV. According to modern calculations based on the Dirac equation, the collision times at $E_{cm}>1$ GeV are sufficient to allow spontaneous electron-positron pair emission from QED vacuum decay, in case of bare uranium ion collision. A second application of actinide collisions to produce neutron-rich transfermiums is discussed. A new inverse quasifission mechanism associated to a specific orientation of the nuclei is proposed to produce transfermium nuclei ($Z>100$) in the collision of prolate deformed actinides such as $^{232}$Th+$^{250}$Cf. The collision of the tip of one nucleus with the side of the other results in a nucleon flux toward the latter. The probability distributions for transfermium production in such a collision are computed. The produced nuclei are more neutron-rich than those formed in fusion reactions, thus, leading to more stable isotopes closer to the predicted superheavy island of stability. In addition to mass and charge dispersion, the Balian-Veneroni variational principle is used to compute correlations between $Z$ and $N$ distributions, which are zero in standard TDHF calculations.Comment: Proceeding of the FUSION11 conferenc

A surplus and welfare analysis of asymmetric regulation

Some European regulators have decided to force competition in their nationalmarkets. They have decided to go beyond the second directive and apply asymmetric regulation. Gas release programs and market shares constraints are the two asymmetric decisions imposed to incumbents. When a regulator imposes a gas release program to an incumbent, this operator is compelled to release quantities of its long term contracts to its competitor. In this paper, we will focus on gas release and its impact on welfare, consumer surplus and on the level of released quantities set by regulators. The aim of a gas release program is to give access to natural gas to competitors. They become actives on the market and are in competition with the incumbent. These programs are time limited. They only help competitors in expecting the development of hubs or new investments in importation infrastructures. If competitors want to stay active after the program, they may find others supply sources to increase security of supply. The gas release can induce Raising Rival's Costs or "Self-Sabotage" strategies. We use a Cournot model with capacity constraints to answer two questions. First, we will study the impact of these strategies on consumer surplus and welfare. We will show that there are no impact on consumer surplus but the welfare decreases. The gas release program introduces a transfer of profit between competitor and incumbent, reduces welfare because of the increase in costs of supply, but has no impact on total consumed quantities. Then, we will suppose that the regulator is setting released quantities maximising welfare. Gas release price is often based on costs plus a bid or a fixed premium. Quantities are set with a less obvious process. We will demonstrate that the regulator must set released quantities :- that would not be so high if incumbent's supplies are small to avoid Self- Sabotage or RRC strategies ;- as a function of incumbent's supplies if they are in intermediate values to avoid strategies seen above and to optimise quantities sold on the market ;- at a sufficient level to let the two operators playing their Cournot best reply function. Finally, we will conclude that the regulator can avoid RRC or Self-Sabotage strategies in maximising the welfare when it decides gas released quantities. Gathering from empirical studies, these quantities should not be so high in order to let a significant difference between the capacities of both competitor and incumbent to avoid collusive behaviours.Energy market ; Gas release ; Regulation ; Optimal released quantities ; Efficiency ; Welfare

The impact of asymmetric regulation on surplus and welfare : the case of gas release programmes

Some European regulators have decided to force competition in their nationalmarkets. They have decided to go beyond the second directive and apply asymmetric regulation. Gas release programs and market shares constraints are the two asymmetric decisions imposed to incumbents. When a regulator imposes a gas release program to an incumbent, this operator is compelled to release quantities of its long term contracts to its competitor. In this paper, we will focus on gas release and its impact on welfare, consumer surplus and on the level of released quantities set by regulators. The aim of a gas release program is to give access to natural gas to competitors. They become actives on the market and are in competition with the incumbent. These programs are time limited. They only help competitors in expecting the development of hubs or new investments in importation infrastructures. If competitors want to stay active after the program, they may find others supply sources to increase security of supply. The gas release can induce Raising Rival's Costs or “Self-Sabotage” strategies. We use a Cournot model with capacity constraints to answer two questions. First, we will study the impact of these strategies on consumer surplus and welfare. We will show that there are no impact on consumer surplus but the welfare decreases. The gas release program introduces a transfer of profit between competitor and incumbent, reduces welfare because of the increase in costs of supply, but has no impact on total consumed quantities. Then, we will suppose that the regulator is setting released quantities maximising welfare. Gas release price is often based on costs plus a bid or a fixed premium. Quantities are set with a less obvious process. We will demonstrate that the regulator must set released quantities : - that would not be so high if incumbent's supplies are small to avoid Self- Sabotage or RRC strategies; - as a function of incumbent's supplies if they are in intermediate values to avoid strategies seen above and to optimise quantities sold on the market; - at a sufficient level to let the two operators playing their Cournot best reply function. Finally, we will conclude that the regulator can avoid RRC or Self-Sabotage strategies in maximising the welfare when it decides gas released quantities. Gathering from empirical studies, these quantities should not be so high in order to let a significant difference between the capacities of both competitor and incumbent to avoid collusive behaviours.REGULATION ; MARCHE INTERIEUR ; GAZ NATUREL ; MARCHE CONCURRENTIEL ; GAS RELEASE

Asymptotically locally flat spacetimes and dynamical black flowers in three dimensions

The theory of massive gravity proposed by Bergshoeff, Hohm and Townsend is considered in the special case of the pure irreducibly fourth order quadratic Lagrangian. It is shown that the asymptotically locally flat black holes of this theory can be consistently deformed to "black flowers" that are no longer spherically symmetric. Moreover, we construct radiating spacetimes settling down to these black flowers in the far future. The generic case can be shown to fit within a relaxed set of asymptotic conditions as compared to the ones of general relativity at null infinity, while the asymptotic symmetries remain the same. Conserved charges as surface integrals at null infinity are constructed following a covariant approach, and their algebra represents BMS$_{3}$, but without central extensions. For solutions possessing an event horizon, we derive the first law of thermodynamics from these surface integrals.Comment: 14 pages, no figure

Distributed image reconstruction for very large arrays in radio astronomy

Current and future radio interferometric arrays such as LOFAR and SKA are characterized by a paradox. Their large number of receptors (up to millions) allow theoretically unprecedented high imaging resolution. In the same time, the ultra massive amounts of samples makes the data transfer and computational loads (correlation and calibration) order of magnitudes too high to allow any currently existing image reconstruction algorithm to achieve, or even approach, the theoretical resolution. We investigate here decentralized and distributed image reconstruction strategies which select, transfer and process only a fraction of the total data. The loss in MSE incurred by the proposed approach is evaluated theoretically and numerically on simple test cases.Comment: Sensor Array and Multichannel Signal Processing Workshop (SAM), 2014 IEEE 8th, Jun 2014, Coruna, Spain. 201

A new inverse quasifission mechanism to produce neutron-rich transfermium nuclei

Based on time-dependent Hartree-Fock theory, a new inverse quasifission mechanism is proposed to produce neutron-rich transfermium nuclei, in collision of prolate deformed actinides. Calculations show that collision of the tip of one nucleus with the side of the other results in a nucleon flux toward the latter. The role of nucleon evaporation and impact parameter, as well as the collision time are discussed.Comment: 8 pages, 7 figure

Constrained Variational Calculus for Higher Order Classical Field Theories

We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of application are studied, in particular, applications to the geometrical description of optimal control theory for partial differential equations.Comment: 25 pages; 4 diagram