Singularities and the distribution of density in the Burgers/adhesion model

We are interested in the tail behavior of the pdf of mass density within the one and $d$-dimensional Burgers/adhesion model used, e.g., to model the formation of large-scale structures in the Universe after baryon-photon decoupling. We show that large densities are localized near ``kurtoparabolic'' singularities residing on space-time manifolds of codimension two ($d \le 2$) or higher ($d \ge 3$). For smooth initial conditions, such singularities are obtained from the convex hull of the Lagrangian potential (the initial velocity potential minus a parabolic term). The singularities contribute {\em \hbox{universal} power-law tails} to the density pdf when the initial conditions are random. In one dimension the singularities are preshocks (nascent shocks), whereas in two and three dimensions they persist in time and correspond to boundaries of shocks; in all cases the corresponding density pdf has the exponent -7/2, originally proposed by E, Khanin, Mazel and Sinai (1997 Phys. Rev. Lett. 78, 1904) for the pdf of velocity gradients in one-dimensional forced Burgers turbulence. We also briefly consider models permitting particle crossings and thus multi-stream solutions, such as the Zel'dovich approximation and the (Jeans)--Vlasov--Poisson equation with single-stream initial data: they have singularities of codimension one, yielding power-law tails with exponent -3.Comment: LATEX 11 pages, 6 figures, revised; Physica D, in pres

Dispersive stabilization of the inverse cascade for the Kolmogorov flow

It is shown by perturbation techniques and numerical simulations that the inverse cascade of kink-antikink annihilations, characteristic of the Kolmogorov flow in the slightly supercritical Reynolds number regime, is halted by the dispersive action of Rossby waves in the beta-plane approximation. For beta tending to zero, the largest excited scale is proportional to the logarithm of one over beta and differs strongly from what is predicted by standard dimensional phenomenology which ignores depletion of nonlinearity.Comment: 4 pages, LATEX, 3 figures. v3: revised version with minor correction

High current and low q95 scenario studies for FAST in the view of ITER and DEMO

The Fusion Advanced Study Torus (FAST) has been proposed as a possible European satellite, in view of ITER and DEMO, in order to: a) explore plasma wall interaction in reactor relevant conditions b) test tools and scenarios for safe and reliable tokamak operation up to the border of stability c) address fusion plasmas with a significant population of fast particles. A new FAST scenario has been designed focusing on low-q operation, at plasma current IP=10 MA, toroidal field BT=8.5T, with a q95=2.3 that would correspond to IP=20 MA in ITER. The flat-top of the discharge can last a couple of seconds (i.e. half the diffusive resistive time and twice the energy confinement time), and is limited by the heating of the toroidal field coils. A preliminary evaluation of the end-of-pulse temperatures and of the electromagnetic forces acting on the central solenoid pack and poloidal field coils has been performed. Moreover, a VDE plasma disruption has been simulated and the maximum total vertical force applied on the vacuum vessel has been estimated

Optimal transport by omni-potential flow and cosmological reconstruction

One of the simplest models used in studying the dynamics of large-scale structure in cosmology, known as the Zeldovich approximation, is equivalent to the three-dimensional inviscid Burgers equation for potential flow. For smooth initial data and sufficiently short times it has the property that the mapping of the positions of fluid particles at any time $t_1$ to their positions at any time $t_2\ge t_1$ is the gradient of a convex potential, a property we call omni-potentiality. Are there other flows with this property, that are not straightforward generalizations of Zeldovich flows? This is answered in the affirmative in both two and three dimensions. How general are such flows? Using a WKB technique we show that in two dimensions, for sufficiently short times, there are omni-potential flows with arbitrary smooth initial velocity. Mappings with a convex potential are known to be associated with the quadratic-cost optimal transport problem. This has important implications for the problem of reconstructing the dynamical history of the Universe from the knowledge of the present mass distribution.Comment: Dedicated to the memory of Roman Juszkiewicz. 17 pages, 2 figures, 27 references. Accepted in Journal of Mathematical Physics. Bibliography correcte

Near term perspectives for fusion research and new contributions by the Ignitor program

The main advances made within the Ignitor program, that is aimed at investigating the physics of fusion burning plasmas near ignition, are described. In particular, the operation of the machine in the H and I regimes at the 10 MA plasma current levels has been considered and analyzed. The unique properties of the plasmas that can be generated by operating the machine with reduced parameters (lower magnetic fields and plasma currents) relative to those needed to achieve ignition are identified. A key feature of this operation is the relatively fast duty cycle that can be maintained. The Ideal Ignition Conditions, under which the density barrier due to bremsstrahlung emission in high density plasmas is removed, can be attained in this case. The plasma heating cycles are identified for which the contribution of ICRH is used both to enter the H-regime and to optimize the time needed for ignition. The on going effort to set up a test ICRH facility is described. The initial results (2 km/sec) of the high speed pellet injection system developed for Ignitor and operated at Oak Ridge are reported. The combined structural analysis and integration of the entire machine core (Load Assembly) is discussed. The adopted control system for both the machine and the plasma column has been designed and is described. The design solutions of the vertical field coils made of MgB2 and operating at 10 K have been identified and the relevant R&D program is underway. The analysis of the Caorso site and of its facility for the operation of the Ignitor with approved safety standards is completed. The relevant results are being made available for the operation of Ignitor at the Triniti site within the framework of the Italy-Russia agreement on the joint construction and operation of the Ignitor facility. A development effort concerning the advanced diagnostic systems that is being carried out for fusion burning plasma regimes is described. An initial analysis of the characteristics of a neutron source based on a system of Ignitor-like machines is reported

Inertio-elastic focusing of bioparticles in microchannels at high throughput

Controlled manipulation of particles from very large volumes of fluid at high throughput is critical for many biomedical, environmental and industrial applications. One promising approach is to use microfluidic technologies that rely on fluid inertia or elasticity to drive lateral migration of particles to stable equilibrium positions in a microchannel. Here, we report on a hydrodynamic approach that enables deterministic focusing of beads, mammalian cells and anisotropic hydrogel particles in a microchannel at extremely high flow rates. We show that on addition of micromolar concentrations of hyaluronic acid, the resulting fluid viscoelasticity can be used to control the focal position of particles at Reynolds numbers up to Re≈10,000 with corresponding flow rates and particle velocities up to 50 ml min[superscript −1] and 130 m s[superscript −1]. This study explores a previously unattained regime of inertio-elastic fluid flow and demonstrates bioparticle focusing at flow rates that are the highest yet achieved.National Institute for Biomedical Imaging and Bioengineering (U.S.) (P41 BioMicroElectroMechanical Systems Resource Center)National Institute for Biomedical Imaging and Bioengineering (U.S.) (P41 EB002503)National Science Foundation (U.S.). Graduate Research FellowshipUnited States. Army Research Office (Institute for Collaborative Biotechnologies Grant W911NF-09-0001

Divertor of the European DEMO: Engineering and technologies for power exhaust

In a power plant scale fusion reactor, a huge amount of thermal power produced by the fusion reaction and external heating must be exhausted through the narrow area of the divertor targets. The targets must withstand the intense bombardment of the diverted particles where high heat fluxes are generated and erosion takes place on the surface. A considerable amount of volumetric nuclear heating power must also be exhausted. To cope with such an unprecedented power exhaust challenge, a highly efficient cooling capacity is required. Furthermore, the divertor must fulfill other critical functions such as nuclear shielding and channeling (and compression) of exhaust gas for pumping. Assuring the structural integrity of the neutron-irradiated (thus embrittled) components is a crucial prerequisite for a reliable operation over the lifetime. Safety, maintainability, availability, waste and costs are another points of consideration. In late 2020, the Pre-Conceptual Design activities to develop the divertor of the European demonstration fusion reactor were officially concluded. On this occasion, the baseline design and the key technology options were identified and verified by the project team (EUROfusion Work Package Divertor) based on seven years of R&D efforts and endorsed by Gate Review Panel. In this paper, an overview of the load specifications, brief descriptions of the design and the highlights of the technology R&D work are presented together with the further work still needed