A fully-discrete scheme for systems of nonlinear Fokker-Planck-Kolmogorov equations

We consider a system of Fokker-Planck-Kolmogorov (FPK) equations, where the dependence of the coefficients is nonlinear and nonlocal in time with respect to the unknowns. We extend the numerical scheme proposed and studied recently by the authors for a single FPK equation of this type. We analyse the convergence of the scheme and we study its applicability in two examples. The first one concerns a population model involving two interacting species and the second one concerns two populations Mean Field Games

Time machines: the Principle of Self-Consistency as a consequence of the Principle of Minimal Action

We consider the action principle to derive the classical, non-relativistic motion of a self-interacting particle in a 4-D Lorentzian spacetime containing a wormhole and which allows the existence of closed time-like curves. For the case of a `hard-sphere' self-interaction potential we show that the only possible trajectories (for a particle with fixed initial and final positions and which traverses the wormhole once) minimizing the classical action are those which are globally self-consistent, and that the `Principle of self-consistency' (originally introduced by Novikov) is thus a natural consequence of the `Principle of minimal action.'Comment: 26 pages, plain latex; modified version includes extra constraint for collinear collision case and other minor misprints correction

Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain

We give analytical solutions for the time-optimal synthesis of entangling gates between indirectly coupled qubits 1 and 3 in a linear spin chain of three qubits subject to an Ising Hamiltonian interaction with equal coupling $J$ plus a local magnetic field acting on the intermediate qubit. The energy available is fixed, but we relax the standard assumption of instantaneous unitary operations acting on single qubits. The time required for performing an entangling gate which is equivalent, modulo local unitary operations, to the $\mathrm{CNOT}(1, 3)$ between the indirectly coupled qubits 1 and 3 is $T=\sqrt{3/2} J^{-1}$, i.e. faster than a previous estimate based on a similar Hamiltonian and the assumption of local unitaries with zero time cost. Furthermore, performing a simple Walsh-Hadamard rotation in the Hlibert space of qubit 3 shows that the time-optimal synthesis of the $\mathrm{CNOT}^{\pm}(1, 3)$ (which acts as the identity when the control qubit 1 is in the state $\ket{0}$, while if the control qubit is in the state $\ket{1}$ the target qubit 3 is flipped as $\ket{\pm}\rightarrow \ket{\mp}$) also requires the same time $T$.Comment: 9 pages; minor modification

Time Optimal Unitary Operations

Extending our previous work on time optimal quantum state evolution, we formulate a variational principle for the time optimal unitary operation, which has direct relevance to quantum computation. We demonstrate our method with three examples, i.e. the swap of qubits, the quantum Fourier transform and the entangler gate, by choosing a two-qubit anisotropic Heisenberg model.Comment: 4 pages, 1 figure. References adde

Cosmology as Relativistic Particle Mechanics: From Big Crunch to Big Bang

Cosmology can be viewed as geodesic motion in an appropriate metric on an `augmented' target space; here we obtain these geodesics from an effective relativistic particle action. As an application, we find some exact (flat and curved) cosmologies for models with N scalar fields taking values in a hyperbolic target space for which the augmented target space is a Milne universe. The singularities of these cosmologies correspond to points at which the particle trajectory crosses the Milne horizon, suggesting a novel resolution of them, which we explore via the Wheeler-deWitt equation.Comment: 17 pages, 3 figures, references and comments adde

Dynamical Generation of Spacetime Signature by Massive Quantum Fields on a Topologically Non-Trivial Background

The effective potential for a dynamical Wick field (dynamical signature) induced by the quantum effects of massive fields on a topologically non-trivial $D$ dimensional background is considered. It is shown that when the radius of the compactified dimension is very small compared with $\Lambda^{1/2}$ (where $\Lambda$ is a proper-time cutoff), a flat metric with Lorentzian signature is preferred on ${\bf R}^4 \times {\bf S}^1$. When the compactification radius becomes larger a careful analysis of the 1-loop effective potential indicates that a Lorentzian signature is preferred in both $D=6$ and $D=4$ and that these results are relatively stable under metrical perturbations

A Decentralized and Proactive Architecture based on the Cyber Physical System Paradigm for Smart Transmission Grids Modelling, Monitoring and Control

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Does the Presence of an Iliac Aneurysm Affect Outcome of Endoluminal AAA Repair? An Analysis of 336 Cases

AbstractObjective: to determine whether the presence of an iliac aneurysm compromises outcome of endovascular exclusion of AAA and to ascertain the fate of the iliac aneurysmal sac.Patients and methods: between April 1997 and March 2001, data on 336 consecutive patients undergoing endovascular repair for AAA were entered in a prospective database. Suitability for endovascular repair was assessed by preoperative contrast-enhanced computed tomography. A maximum common iliac artery (CIA) diameter ≥20mm was defined as iliac aneurysm. Patients with and without iliac aneurysms were compared to early (immediate conversion or perioperative death) and late failure (increase in aneurysm diameter or persisting graft-related endoleak, or late AAA rupture or conversion).Results: fifty-nine patients (18%) had iliac aneurysms, 19 were bilateral, for a total of 78 aneurysmal iliac arteries (median diameter 23mm; range 20–50mm). A distal seal was achieved by landing in 33 external iliac arteries, in 20 ectatic CIAs, and in 25 normal CIAs. Operating time differed significantly between patients with and without CIA aneurysms (153±71 vs 123±55min,p =0.0001), whereas no statistically significant differences were found with respect to early and late failure (2% vs 3%, p=0.5 and 14% vs 8%, p=0.11, respectively). There were no cases of buttock or colon necrosis. At a median follow-up of 14 months (range 0–46; i.q.r. 7–27 months) common iliac diameter decreased ≥2mm in 49 cases, remained stable in 25, and increased ≥2mm in 3.Conclusion: the presence of iliac aneurysm rendered endoluminal AAA repair more complex but did not affect feasibility and long-term outcome of the procedure. In our experience internal iliac exclusion was never associated with significant morbidity. These data may be useful when considering endovascular repair in high-risk patients with challenging anatomy

Structural properties and thermoelectric performance of the double-filled skutterudite (Sm,Gd)y(FexNi1-x)4Sb12

The structural and thermoelectric properties of the filled skutterudite (Sm,Gd)y(FexNi1-x)4 Sb12 were investigated and critically compared to the ones in the Sm-containing system with the aim of unravelling the effect of double filling on filling fraction and thermal conductivity. Several samples (x = 0.50-0.90 and y = 0.15-0.48) were prepared by melting-sintering, and two of them were densified by spark plasma sintering in order to study their thermoelectric features. The crystallographic study enables the recognition of the role of the filler size in ruling the filling fraction and the compositional location of the p/n crossover: It has been found that the former lowers and the latter moves toward lower x values with the reduction of the filler ionic size, as a consequence of the progressively weaker interaction of the filler with the Sb12 cavity. The analysis of thermoelectric properties indicates that, despite the Sm3+/Gd3+ small mass difference, the contemporary presence of these ions in the 2a site significantly affects the thermal conductivity of both p- and n-compositions. This occurs by reducing its value with respect to the Sm-filled compound at each temperature considered, and making the overall thermoelectric performance of the system comparable to several multi-filled (Fe, Ni)-based skutterudites described in the literature