On Pressure Gradients and Rapid Migration of Solids in an Inhomogeneous Solar Nebula

We study the motions of small solids, ranging from micron-sized dust grains to 100-m objects, in the vicinity of a local density enhancement of an isothermal gaseous solar nebula. Being interested in possible application of the results to the formation of clumps and spiral arms in a circumstellar disk, we numerically integrate the equations of motion of such solids and study their migration for different values of their sizes and masses and also for different physical properties of the gas, such as its density and temperature. We show that, considering the drag force of the gas and also the gravitational attraction of the nebula, it is possible for solids, within a certain range of size and mass, to migrate rapidly (i.e. within ~1000 years) toward the location of a local maximum density where collisions and coagulation may result in an accelerated rate of planetesimal formation.Comment: 20 pages, 7 figures, submitted for publicatio

Eminence Grise Coalitions: On the Shaping of Public Opinion

We consider a network of evolving opinions. It includes multiple individuals with first-order opinion dynamics defined in continuous time and evolving based on a general exogenously defined time-varying underlying graph. In such a network, for an arbitrary fixed initial time, a subset of individuals forms an eminence grise coalition, abbreviated as EGC, if the individuals in that subset are capable of leading the entire network to agreeing on any desired opinion, through a cooperative choice of their own initial opinions. In this endeavor, the coalition members are assumed to have access to full profile of the underlying graph of the network as well as the initial opinions of all other individuals. While the complete coalition of individuals always qualifies as an EGC, we establish the existence of a minimum size EGC for an arbitrary time-varying network; also, we develop a non-trivial set of upper and lower bounds on that size. As a result, we show that, even when the underlying graph does not guarantee convergence to a global or multiple consensus, a generally restricted coalition of agents can steer public opinion towards a desired global consensus without affecting any of the predefined graph interactions, provided they can cooperatively adjust their own initial opinions. Geometric insights into the structure of EGC's are given. The results are also extended to the discrete time case where the relation with Decomposition-Separation Theorem is also made explicit.Comment: 35 page

Limits to ion energy control in high density glow discharges: Measurement of absolute metastable ion concentrations

Unprecedented demands for uniformity, throughput, anisotropy, and damage control in submicron pattern transfer are spurring development of new, low pressure, high charge density plasma reactors. Wafer biasing, independent of plasma production in these new systems is intended to provide improved ion flux and energy control so that selectivity can be optimized and damage can be minimized. However, as we show here, an inherent property of such discharges is the generation of significant densities of excited, metastable ionic states that can bombard workpiece surfaces with higher translational and internal energy. Absolute metastable ion densities are measured using the technique of self-absorption, while the corresponding velocity distributions and density scaling with pressure and electron density are measured using laser-induced fluorescence. For a low pressure, helicon-wave excited plasma, the metastable ion flux is at least 24% of the total ion flux to device surfaces. Because the metastable ion density scales roughly as the reciprocal of the pressure and as the square of the electron density, the metastable flux is largest in low pressure, high charge density plasmas. This metastable ion energy flux effectively limits ion energy and flux control in these plasma reactors, but the consequences for etching and deposition of thin films depend on the material system and remain an open question

Generating and Adding Flows on Locally Complete Metric Spaces

As a generalization of a vector field on a manifold, the notion of an arc field on a locally complete metric space was introduced in \cite{BC}. In that paper, the authors proved an analogue of the Cauchy-Lipschitz Theorem i.e they showed the existence and uniqueness of solution curves for a time independent arc field. In this paper, we extend the result to the time dependent case, namely we show the existence and uniqueness of solution curves for a time dependent arc field. We also introduce the notion of the sum of two time dependent arc fields and show existence and uniqueness of solution curves for this sum.Comment: 29 pages,6 figure

A New Perspective on Path Integral Quantum Mechanics in Curved Space-Time

A fundamentally different approach to path integral quantum mechanics in curved space-time is presented, as compared to the standard approaches currently available in the literature. Within the context of scalar particle propagation in a locally curved background, such as described by Fermi or Riemann normal co-ordinates, this approach requires use of a constructed operator to rotate the initial, intermediate, and final position ket vectors onto their respective local tangent spaces, defined at each local time step along some arbitrary classical reference worldline. Local time translation is described using a quantum mechanical representation of Lie transport, that while strictly non-unitary in operator form, nevertheless correctly recovers the free-particle Lagrangian in curved space-time, along with new contributions. This propagator yields the prediction that all probability violating terms due to curvature contribute to a quantum violation of the weak equivalence principle, while the remaining terms that conserve probability also correspondingly satisfy the weak equivalence principle, at least to leading-order in the particle's Compton wavelength. Furthermore, this propagator possesses an overall curvature-dependent and gauge-invariant phase factor that can be interpreted as the gravitational Aharonov-Bohm effect and Berry's phase.Comment: 14 pages, 1 figure; major additions and revisions introduced; main conclusions are unchanged; new affiliation adde

Versatile silicon-waveguide supercontinuum for coherent mid-infrared spectroscopy

Infrared spectroscopy is a powerful tool for basic and applied science. The molecular spectral fingerprints in the 3 um to 20 um region provide a means to uniquely identify molecular structure for fundamental spectroscopy, atmospheric chemistry, trace and hazardous gas detection, and biological microscopy. Driven by such applications, the development of low-noise, coherent laser sources with broad, tunable coverage is a topic of great interest. Laser frequency combs possess a unique combination of precisely defined spectral lines and broad bandwidth that can enable the above-mentioned applications. Here, we leverage robust fabrication and geometrical dispersion engineering of silicon nanophotonic waveguides for coherent frequency comb generation spanning 70 THz in the mid-infrared (2.5 um to 6.2 um). Precise waveguide fabrication provides significant spectral broadening and engineered spectra targeted at specific mid-infrared bands. We use this coherent light source for dual-comb spectroscopy at 5 um.Comment: 26 pages, 5 figure

Development of NASH in Obese Mice is Confounded by Adipose Tissue Increase in Inflammatory NOV and Oxidative Stress

Aim. Nonalcoholic steatohepatitis (NASH) is the consequence of insulin resistance, fatty acid accumulation, oxidative stress, and lipotoxicity.We hypothesize that an increase in the inflammatory adipokine NOV decreases antioxidant Heme Oxygenase 1 (HO- 1) levels in adipose and hepatic tissue, resulting in the development of NASH in obese mice. Methods. Mice were fed a high fat diet (HFD) and obese animals were administered an HO-1 inducer with or without an inhibitor of HO activity to examine levels of adipose-derived NOV and possible links between increased synthesis of inflammatory adipokines and hepatic pathology. Results. NASH mice displayed decreased HO-1 levels and HO activity, increased levels of hepatic heme, NOV, MMP2, hepcidin, and increased NAS scores and hepatic fibrosis. IncreasedHO-1 levels are associated with a decrease in NOV, improved hepatic NAS score, ameliorated fibrosis, and increases in mitochondrial integrity and insulin receptor phosphorylation. Adipose tissue function is disrupted in obesity as evidenced by an increase in proinflammatory molecules such as NOV and a decrease in adiponectin. Importantly, increased HO-1 levels are associated with a decrease of NOV, increased adiponectin levels, and increased levels of thermogenic and mitochondrial signaling associated genes in adipose tissue. Conclusions.These results suggest that the metabolic abnormalities in NASH are driven by decreased levels of hepatic HO-1 that is associated with an increase in the adipose-derived proinflammatory adipokine NOV in our obese mouse model of NASH. Concurrently, induction of HO-1 provides protection against insulin resistance as seen by increased insulin receptor phosphorylation. Pharmacological increases in HO-1 associated with decreases in NOV may offer a potential therapeutic approach in preventing fibrosis, mitochondrial dysfunction, and the development of NASH

A Metamaterial-Inspired Model for Electron Waves in Bulk Semiconductors

Based on an analogy with electromagnetic metamaterials, we develop an effective medium description for the propagation of electron matter waves in bulk semiconductors with a zincblende structure. It is formally demonstrated that even though departing from a different starting point, our theory gives results for the energy stationary states consistent with Bastard's envelope function approximation in the long-wavelength limit. Using the proposed approach, we discuss the time evolution of a wave packet in a bulk semiconductor with a zero-gap and linear energy-momentum dispersion.Comment: 43 pages, 4 figure