Response to Comment on `Undamped electrostatic plasma waves' [Phys. Plasmas 19, 092103 (2012)]

Numerical and experimental evidence is given for the occurrence of the plateau states and concomitant corner modes proposed in \cite{valentini12}. It is argued that these states provide a better description of reality for small amplitude off-dispersion disturbances than the conventional Bernstein-Greene-Kruskal or cnoidal states such as those proposed in \cite{comment

The micrometeoroid complex and evolution of the lunar regolith

The interaction of the micrometeoroid complex with the lunar surface is evidenced by numerous glass-lined microcraters on virtually every lunar surface exposed to space. Such craters range in size from less than .1 micron to approximately 2 sq cm diameter. Using small scale laboratory cratering experiments for calibration, the observed crater-sized frequency distributions may be converted into micrometeoroid mass distributions. These lunar mass distributions are in essential agreement with satellite data. Some physical properties of micrometeoroids may be deduced by comparing lunar crater geometries with those obtained in laboratory experiments. The proponderance of circular outlines of lunar microcraters necessitates equidimensional, if not spherical, micrometeoroids

Undamped electrostatic plasma waves

Electrostatic waves in a collision-free unmagnetized plasma of electrons with fixed ions are investigated for electron equilibrium velocity distribution functions that deviate slightly from Maxwellian. Of interest are undamped waves that are the small amplitude limit of nonlinear excitations, such as electron acoustic waves (EAWs). A deviation consisting of a small plateau, a region with zero velocity derivative over a width that is a very small fraction of the electron thermal speed, is shown to give rise to new undamped modes, which here are named {\it corner modes}. The presence of the plateau turns off Landau damping and allows oscillations with phase speeds within the plateau. These undamped waves are obtained in a wide region of the $(k,\omega_{_R})$ plane ($\omega_{_R}$ being the real part of the wave frequency and $k$ the wavenumber), away from the well-known `thumb curve' for Langmuir waves and EAWs based on the Maxwellian. Results of nonlinear Vlasov-Poisson simulations that corroborate the existence of these modes are described. It is also shown that deviations caused by fattening the tail of the distribution shift roots off of the thumb curve toward lower $k$-values and chopping the tail shifts them toward higher $k$-values. In addition, a rule of thumb is obtained for assessing how the existence of a plateau shifts roots off of the thumb curve. Suggestions are made for interpreting experimental observations of electrostatic waves, such as recent ones in nonneutral plasmas.Comment: 11 pages, 10 figure

Relaminarisation of Re_τ=100 channel flow with globally stabilising linear feedback control

The problems of nonlinearity and high dimension have so far prevented a complete solution of the control of turbulent flow. Addressing the problem of nonlinearity, we propose a flow control strategy which ensures that the energy of any perturbation to the target profile decays monotonically. The controller’s estimate of the flow state is similarly guaranteed to converge to the true value. We present a one-time off-line synthesis procedure, which generalises to accommodate more restrictive actuation and sensing arrangements, with conditions for existence for the controller given in this case. The control is tested in turbulent channel flow (Re_τ = 100) using full-domain sensing and actuation on the wall-normal velocity. Concentrated at the point of maximum inflection in the mean profile, the control directly counters the supply of turbulence energy arising from the interaction of the wall-normal perturbations with the flow shear. It is found that the control is only required for the larger-scale motions, specifically those above the scale of the mean streak spacing. Minimal control effort is required once laminar flow is achieved. The response of the near-wall flow is examined in detail, with particular emphasis on the pressure and wall-normal velocity fields, in the context of Landahl’s theory of sheared turbulence

Vortex-to-Polarization Phase Transformation Path in Pb(ZrTi)O3_3 Nanoparticles

Phase transformation in finite-size ferroelectrics is of fundamental relevance for understanding collective behaviors and balance of competing interactions in low-dimensional systems. We report a first-principles effective Hamiltonian study of vortex-to-polarization transformation in Pb(Zr$_{0.5}$Ti$_{0.5}$)O$_3$ nanoparticles, caused by homogeneous electric fields normal to the vortex plane. The transformation is shown to (1) follow an unusual {\it macroscopic} path that is symmetry non-conforming and characterized by the occurrence of a previously unknown structure as the bridging phase; (2) lead to the discovery of a striking collective phenomenon, revealing how ferroelectric vortex is annihilated {\it microscopically}. Interactions underlying these behaviors are discussed

The response of hot wires in high Reynolds-number turbulent pipe flow

Issues concerning the accuracy of hot-wire measurements in turbulent pipe flow are addressed for pipe Reynolds numbers up to 6 × 106 and hot-wire Reynolds numbers up to Rew ap 250. These include the optimization of spatial and temporal resolution and the associated feature of signal-to-noise ratio. Very high wire Reynolds numbers enable the use of wires with reduced length-to-diameter ratios compared to those typical of atmospheric conditions owing to increased wire Nusselt numbers. Simulation of the steady-state heat balance for the wire and the unetched portion of wire are used to assess static end-conduction effects: they are used to calculate wire Biot numbers, \sqrt{c_0}l , and fractional end-conduction losses, σ, which confirm the 'conduction-only' theory described by Corrsin. They show that, at Rew ap 250, the wire length-to-diameter ratio can be reduced to about 50, while keeping \sqrt{c_0}l\gt3 and σ < 7% in common with accepted limits at Rew ap 3. It is shown that these limits depend additionally on the choice of wire material and the length of unetched wire. The dynamic effects of end-cooling are also assessed using the conduction-only theory

Expanded Very Large Arrays Observations of a Proto-Cluster of Molecular Gas-Rich Galaxies at z = 4.05

We present observations of the molecular gas in the GN20 proto-cluster of galaxies at z = 4.05 using the Expanded Very Large Array (EVLA). This group of galaxies is the ideal laboratory for studying the formation of massive galaxies via luminous, gas-rich starbursts within 1.6 Gyr of the big bang. We detect three galaxies in the proto-cluster in CO 2-1 emission, with gas masses (H_2) between 10^(10) and 10^(11) × (α/0.8) M_⊙. The emission from the brightest source, GN20, is resolved with a size ~2'' and has a clear north-south velocity gradient, possibly indicating ordered rotation. The gas mass in GN20 is comparable to the stellar mass (1.3 × 10^(11) × (α/0.8) M_⊙ and 2.3 × 10^(11) M_⊙, respectively), and the sum of gas plus stellar mass is comparable to the dynamical mass of the system (~3.4 × 10^(11)[sin (i)/sin (45°)]^(–2) M_⊙), within a 5 kpc radius. There is also evidence for a tidal tail extending another 2'' north of the galaxy with a narrow velocity dispersion. GN20 may be a massive, gas-rich disk that is gravitationally disturbed, but not completely disrupted. There is one Lyman-break galaxy (BD29079) in the GN20 proto-cluster with an optical spectroscopic redshift within our search volume, and we set a 3σ limit to the molecular gas mass of this galaxy of 1.1 × 10^(10) × (α/0.8) M_⊙

Imaging the molecular gas in a submm galaxy at z = 4.05: cold mode accretion or a major merger?

We present a high resolution (down to 0.18"), multi-transition imaging study of the molecular gas in the z = 4.05 submillimeter galaxy GN20. GN20 is one of the most luminous starburst galaxy known at z > 4, and is a member of a rich proto-cluster of galaxies at z = 4.05 in GOODS-North. We have observed the CO 1-0 and 2-1 emission with the VLA, the CO 6-5 emission with the PdBI Interferometer, and the 5-4 emission with CARMA. The H_2 mass derived from the CO 1-0 emission is 1.3 \times 10^{11} (\alpha/0.8) Mo. High resolution imaging of CO 2-1 shows emission distributed over a large area, appearing as partial ring, or disk, of ~ 10kpc diameter. The integrated CO excitation is higher than found in the inner disk of the Milky Way, but lower than that seen in high redshift quasar host galaxies and low redshift starburst nuclei. The VLA CO 2-1 image at 0.2" resolution shows resolved, clumpy structure, with a few brighter clumps with intrinsic sizes ~ 2 kpc. The velocity field determined from the CO 6-5 emission is consistent with a rotating disk with a rotation velocity of ~ 570 km s^{-1} (using an inclination angle of 45^o), from which we derive a dynamical mass of 3 \times 10^{11} \msun within about 4 kpc radius. The star formation distribution, as derived from imaging of the radio synchrotron and dust continuum, is on a similar scale as the molecular gas distribution. The molecular gas and star formation are offset by ~ 1" from the HST I-band emission, implying that the regions of most intense star formation are highly dust-obscured on a scale of ~ 10 kpc. The large spatial extent and ordered rotation of this object suggests that this is not a major merger, but rather a clumpy disk accreting gas rapidly in minor mergers or smoothly from the proto-intracluster medium. ABSTRACT TRUNCATEDComment: 33 pages, 8 figures, submitted to the ApJ, aas latex forma

Geometric invariant theory of syzygies, with applications to moduli spaces

We define syzygy points of projective schemes, and introduce a program of studying their GIT stability. Then we describe two cases where we have managed to make some progress in this program, that of polarized K3 surfaces of odd genus, and of genus six canonical curves. Applications of our results include effectivity statements for divisor classes on the moduli space of odd genus K3 surfaces, and a new construction in the Hassett-Keel program for the moduli space of genus six curves.Comment: v1: 23 pages, submitted to the Proceedings of the Abel Symposium 2017, v2: final version, corrects a sign error and resulting divisor class calculations on the moduli space of K3 surfaces in Section 5, other minor changes, In: Christophersen J., Ranestad K. (eds) Geometry of Moduli. Abelsymposium 2017. Abel Symposia, vol 14. Springer, Cha