We show a result on propagation of the anisotropic Gabor wave front set for linear operators with a tempered distribution Schwartz kernel. The anisotropic Gabor wave front set is parametrized by a positive parameter relating the space and frequency variables. The anisotropic Gabor wave front set of the Schwartz kernel is assumed to satisfy a graph type criterion. The result is applied to a class of evolution equations that generalizes the Schrödinger equation for the free particle. The Laplacian is replaced by any partial differential operator with constant coefficients, real symbol and order at least two.

The assumption that exoplanets are ‘in equilibrium’ with their surroundings has not given way to life's transmissivity on large spatial scales. The spread of human diseases and the life recovery rate after mass extinctions on our planet, on the other hand, may exhibit spatial and temporal scaling as well as distribution correlations that influence the mappable range of their characteristics. We model hypothetical bio-dispersal within a single Galactic region using the stochastic infection dynamics process, which is inspired by these local properties of life dispersal on Earth. We split the population of stellar systems into different categories regarding habitability and evolved them through time using probabilistic cellular automata rules analogous to the model. As a dynamic effect, we include the existence of natural dispersal vectors (e.g. dust, asteroids) in a way that avoids assumptions about their agency (i.e. questions of existence). Moreover, by assuming that dispersal vectors have a finite velocity and range, the model includes the parameter of ‘optical depth of life spreading’. The effect of the oscillatory infection rate ($b( t,\; \, d)$) on the long-term behaviour of the dispersal flux, which adds a diffusive component to its progression, is also taken into account. The life recovery rate ($g( t,\; \, d)$) was only included in the model as a link to macrofaunal diversity data, which shows that all mass extinctions have a 10 Myr ‘speed rate’ in diversity recovery. This parameter accounts for the repopulation of empty viable niches as well as the formation of new ones, without ruling out the possibility of genuine life reemergence on other habitable worlds in the Galaxy that colossal extinctions have sterilized. All life-transmission events within the Galactic patch have thus been mapped into phase space characterized by parameters $b$ and $g$. We found that phase space is separated into subregions of long-lasting transmission, rapidly terminated transmission, and a transition region between the two. We observed that depending on the amplitude of the oscillatory life-spreading rate, life-transmission in the Galactic patch might take on different geometrical shapes (i.e. ‘waves’). Even if some host systems are uninhabited, life transmission has a certain threshold, allowing a patch to be saturated with viable material over a long period. Although stochastic fluctuations in the local density of habitable systems allow for clusters that can continuously infect one another, the spatial pattern disappears when life transmission is below the observed threshold, so that transmission process is not permanent in time. Both findings suggest that a habitable planet in a densely populated region may remain uninfected.

We consider beams that are described by a four-dimensional (4D) transverse distribution f (x, y, x′, y′), where x′ ≡ px /pz and z is the axial coordinate. A two-slit scanner is commonly employed to measure, over a sequence of shots, a two-dimensional (2D) projection of such a beam's phase space, for example, f (x, x′). Another scanner might yield f (y, y′) or, using crossed slits, f (x, y). A small set of such 2D scans does not uniquely specify f (x, y, x′, y′). We have developed “tomographic” techniques to synthesize a “reasonable” set of particles in a 4D phase space having 2D densities consistent with the experimental data. We briefly summarize one method and describe progress in validating it, using simulations of the High Current Experiment at Lawrence Berkeley National Laboratory.

The High Current Experiment (HCX) is being assembled at Lawrence Berkeley National Laboratory as part of the U.S. program to explore heavy ion beam transport at a scale representative of the low-energy end of an induction linac driver for fusion energy production. The primary mission of this experiment is to investigate aperture fill factors acceptable for the transport of space-charge dominated heavy ion beams at high space-charge intensity (line-charge density ∼ 0.2 μC/m) over long pulse durations (>4 μs). This machine will test transport issues at a driver-relevant scale resulting from nonlinear space-charge effects and collective modes, beam centroid alignment and beam steering, matching, image charges, halo, lost-particle induced electron effects, and longitudinal bunch control. We present the first experimental results carried out with the coasting K+ ion beam transported through the first 10 electrostatic transport quadrupoles and associated diagnostics. Later phases of the experiment will include more electrostatic lattice periods to allow more sensitive tests of emittance growth, and also magnetic quadrupoles to explore similar issues in magnetic channels with a full driver scale beam.

The gravitational n—body problem is chaotic. Phase trajectories that start very near each other separate rapidly. The rate looks exponential over long times. At any instant, trajectories separated in certain directions move apart rapidly (unstable directions), while those separated in other directions stay about the same (stable directions). Unstable directions lie along eigenvectors that correspond to positive eigenvalues of the matrix of force gradients. The number of positive eigenvalues of that matrix gives the dimensionality of stable regions. This number has been studied numerically in a series of 100—body integrations. It continues to change as long as the integration continues because the matrix changes extremely rapidly. On average, there are about 1.2n unstable directions out of 3n. Issues of dimensionality arise when the tools of ergodic studies are brought to bear on the problem of trajectory separation. A method of estimating the rate of trajectory separation based on matrix descriptions is presented in this note. Severe approximations are required.