Transferring saturation, the finite cover property, and stability

Saturation is (mu,kappa)-transferable in T if and only if there is an expansion T_1 of T with |T_1| = |T| such that if M is a mu-saturated model of T_1 and |M| \geq kappa then the reduct M|L(T) is kappa-saturated. We characterize theories which are superstable without the finite cover property (f.c.p.), or without f.c.p. as, respectively those where saturation is (aleph_0,lambda)-transferable or (kappa(T),lambda)-transferable for all lambda. Further if for some mu \geq |T|, 2^mu > mu^+, stability is equivalent to: or all mu \geq |T|, saturation is (\mu,2^mu)-transferable.Comment: This version replaces the 1995 submission: Characterization of the finite cover property and stability. This version submitted by John T. Baldwin. The paper has been accepted for the Journal of Symbolic Logi

Une méthode mixte multi-échelles pour un simulateur de réservoir biphasé

A multiscale hybrid mixed finite element method is presented in this paper to solve two-phase flow equations on heterogeneous media under the effect of gravitational segregation. It is designed to cope with the complex geometry and inherent multiscale nature of the rocks, leading to stable and accurate multi-physics reservoir simulations. This multiscale approach makes use of coarse scale fluxes between subregions (macro domains) that allow to reduce substantially the dominant computational costs associated with the flux/pressure kernel embedded in the numerical model. As such, larger scale problems can be approximated in a reasonable computational time. Dividing the problems into macro domains leads to a hierarchy of meshes and approximation spaces, allowing the efficient use of static condensation and parallel computation strategies. The method documented in this work utilizes discretizations based on a general domain partition formed by poly-hedral subregions. The normal flux between these subregions is associated with a finite dimensional trace space. The global system to be solved for the fluxes and pressures is expressed only in terms of the trace variables and of a piecewise constant pressure associated with each subregion. The fine scale features are resolved by mixed finite element approximations using fine flux and pressure representations inside each subregion, and the trace variable (i.e. normal flux) as Neumann boundary conditions. This property implies that the flux approximation is globally H(div)-conforming, and, as in classical mixed formulations, local mass conservation is observed at the micro-scale elements inside the subregions, an essential property for flows in heterogeneous media

Model Theory for a Compact Cardinal

We would like to develop model theory for T, a complete theory in L_{theta,theta}(tau) when theta is a compact cardinal. We already have bare bones stability theory and it seemed we can go no further. Dealing with ultrapowers (and ultraproducts) naturally we restrict ourselves to "D a theta-complete ultrafilter on I, probably (I,theta)-regular". The basic theorems of model theory work and can be generalized (like Los theorem), but can we generalize deeper parts of model theory? The first section tries to sort out what occurs to the notion of stable T for complete L_{theta,theta}-theories T. We generalize several properties of complete first order T, equivalent to being stable (see [Sh:c]) and find out which implications hold and which fail. In particular, can we generalize stability enough to generalize [Sh:c, Ch. VI]? Let us concentrate on saturation in the local sense (types consisting of instances of one formula). We prove that at least we can characterize the T's (of cardinality < theta for simplicity) which are minimal for appropriate cardinal lambda > 2^kappa +|T| in each of the following two senses. One is generalizing Keisler order which measures how saturated are ultrapowers. Another asks: Is there an L_{theta,theta}-theory T_1 supseteq T of cardinality |T| + 2^theta such that for every model M_1 of T_1 of cardinality > lambda, the tau(T)-reduct M of M_1 is lambda^+-saturated. Moreover, the two versions of stable used in the characterization are different

Advanced composite aileron for L-1011 transport aircraft: Design and analysis

Detail design of the composite aileron has been completed. The aileron design is a multi-rib configuration with single piece upper and lower covers mechanically fastened to the substructure. Covers, front, spar and ribs are fabricated with graphite/epoxy tape or fabric composite material. The design has a weight savings of 23 percent compared to the aluminum aileron. The composite aileron has 50 percent fewer fasteners and parts than the metal aileron and is predicted to be cost competitive. Structural integrity of the composite aileron was verified by structural analysis and an extensive test program. Static, failsafe, and vibration analyses have been conducted on the composite aileron using finite element models and specialized computer programs for composite material laminates. The fundamental behavior of the composite materials used in the aileron was determined by coupon tests for a variety of environmental conditions. Critical details of the design were interrogated by static and fatigue tests on full-scale subcomponents and subassemblies of the aileron

Asymptotic Cohomology and Uniform Stability for Lattices in Semisimple Groups

It is, by now, classical that lattices in higher rank semisimple groups have various rigidity properties. In this work, we add another such rigidity property to the list: uniform stability with respect to the family of unitary operators on finite-dimensional Hilbert spaces equipped with submultiplicative norms. Namely, we show that for (most) high-rank lattices, every finite-dimensional unitary "almost-representation" of $\Gamma$ is a small deformation of a (true) unitary representation. This extends a result of Kazhdan (1983) for amenable groups and of Burger-Ozawa-Thom (2013) for SL(n,Z) (for n>2). Towards this goal, we first build an elaborate cohomological theory capturing the obstruction to such stability, and show that the vanishing of second cohomology implies uniform stability in this setting. This cohomology can be roughly thought of as an asymptotic version of bounded cohomology, and sheds light on a question raised in Monod (2006) about a possible connection between vanishing of second bounded cohomology and Ulam stability.Comment: 71 pages, 3 figures, Added clarifications in Section 4.2, Corrected typo

Nonlinear Optical Phenomena in Emerging Low-dimensional Materials

As digital information technologies continue to evolve at much faster rates than the growth of Si-based processors, the encroachment of light-based technologies into computing seems inevitable. With the advent of lasers, photonic crystals, and optical diodes, photonic computing has made significant strides in information technology over the past 30 years. This continuing integration of light into all-optical computing, optoelectronic components, and emerging optogenetic technologies demands the ability to control and manipulate light in a predictable fashion, or by design. Of particular interest, is the passive control and manipulation of light in all-optical switches, photonic diodes, and optical limiting which can be achieved by leveraging intrinsic non-linear optical properties of low dimensional materials. The reverse saturable absorption in fullerenes has been widely used to realize excellent passive optical limiters for the visible region up to 650 nm. However, there is still a need for passive optical switches and limiters with a low limiting threshold (\u3c0.5 J/cm2) and higher damage limits. The electronic structure of fullerenes can be modified either through doping or by the encapsulation of endohedral clusters to achieve exotic quantum states of matter such as superconductivity. Building on this ability, we discuss in Chapter 2 that the encapsulation of Sc3N, Lu3N or Y3N in C80 alters the HOMO-LUMO gap and leads to passive optical switches with a significantly low limiting threshold (0.3 J/cm2) and a wider operation window (average pulse energy \u3e0.3 mJ in the ns regime). In addition to extraordinary and strongly anisotropic electronic properties, two dimensional (2D) materials such as graphene and boron nitride, exhibit strong light-matter interactions despite their atomic thickness. The nonlinear light-matter interactions in 2D materials are well suited for several applications in photonics and optoelectronics, such as ultrafast optical switching and optical diodes. Unlike most 2D materials that display nonlinear saturable absorption or increased light transmission at higher fluences, hexagonal boron nitride nanoplatelets (BNNPs) exhibit enhanced opaqueness with increasing light fluence. A two-photon absorption (2PA) process was previously proposed to explain the intrinsic non-linear absorption in BNNPs at 1064 nm or 1.16 eV (Kumbhakar et al., Advanced Optical Materials, vol. 3, pp. 828, 2015); which is counter-intuitive because a 2PA process at 1.16 eV cannot excite electrons across the wide band gap of BNNPs (~5.75 eV). Here, through a systematic study of the non-linear properties of BNNPs we uncover a notoriously rare non-linear phenomenon, viz., five-photon absorption (5PA) at 1064 nm for low laser input fluences (below 0.6 J/cm2) that irreversibly transforms to a 2PA for higher laser input fluences (above 0.6 J/cm2). Our detailed experimental and theoretical findings delineated in Chapter 3 provide compelling evidence that the high laser fluence generates defects in BNNPs (e.g., oxygen/carbon doping), which support a 2PA process by inducing new electronic states within the wide band gap of BNNPs. MXenes comprise a new class of two-dimensional (2D) transition metal carbides, nitrides, and carbonitrides that exhibit unique light-matter interactions. Recently, 2D Ti3C2Tx (Tx represents functional groups such as –OH and –F) was found to exhibit nonlinear saturable absorption (SA) or increased transmittance at higher light fluences that is useful for mode locking in fiber-based femtosecond lasers. However, the fundamental origin and thickness-dependence of SA behavior in MXenes remains to be understood. We fabricated 2D Ti3C2Tx thin films of different thicknesses using an interfacial film formation technique to systematically study their nonlinear optical properties. Using the open aperture Z-scan method, we find that the SA behavior in Ti3C2Tx MXene arises from plasmon-induced increase in the ground state absorption at photon energies above the threshold for free carrier oscillations. The saturation fluence and modulation depth of Ti3C2TxMXene was observed to be dependent on the film thickness. Unlike other 2D materials, Ti3C2Tx was found to show higher threshold for light-induced damage with up to 50% increase in nonlinear transmittance. Lastly, building on the SA behavior of Ti3C2Tx MXenes, we demonstrate in Chapter 4 a Ti3C2Tx MXene-based photonic diode that breaks time-reversal symmetry to achieve non-reciprocal transmission of nanosecond laser pulses. Finally, in Chapter 5, we discuss the equilibrium and non-equilibrium free carrier dynamics in a 16 nm thick Ti3C2Tx film. High (~2 x 1021 cm-3) intrinsic charge carrier density and relatively high (~34 cm2/Vs) mobility of carriers within individual nanoplates (that comprise the Ti3C2Tx film) result in an exceptionally large (~ 46 000 cm-1) absorption in the THz range, implying the potential use of Ti3C2Tx for THz detection. We also demonstrate that Ti3C2Tx conductivity and THz transmission can be manipulated by photoexcitation, as absorption of near-infrared 800 nm pulses is found to cause transient suppression of the conductivity that recovers over hundreds of picoseconds. The possibility of controlling THz transmission and conductivity via photoexcitation makes 2D MXenes suggests a promising material for application in THz modulation devices and variable electromagnetic shielding

Development of Mountain Climate Generator and Snowpack Model for Erosion Predictions in the Western United States Using WEPP: Phase IV

Executive Summary: Introduction: This report summarizes work conducted during the funding period (December 1, 1991 through September 30, 1992) of a Research Joint Venture Agreement between the Intermountain Research Station, Forest Service, U. S. Department of Agriculture and the Utah Water Research Laboratory (UWRL), Utah State University (USU). The purpose of the agreement is to develop a Western Mountain Cilmate Generator (MCLIGEN) similar in function to the existing (non-orographic area) Climate Generator (CLIGEN), which is part of the Water Erosion Prediciton Project (WEPP) procedure. Aso, we are developing a Western U.S. Snowpack Simulation Model for includsion in WEPP. In the western U.S., topographic influences on climate make the climate too variable to be captured by one representatbie station per 100 km, as is done in CLIGEN. Also, few meteorological observations exist in high-elevation areas where Forest Service properties are located. Therefore, a procedure for estimating climatological variables in mountainous areas is needed to apply WEPP in these regions. A physically based approach, using an expanded and improved orographic precipitation model, is being utilized. It will use radiosonde lightning data to estimate historical weather sequences. Climatological sequences estimated at ungaged locations will be represented using stochastic models, similar to the approach used in the existing CLIGEN. By using these stochastic models, WEPP users will be able to synthesize climate sequences for input to WEPP. MCLIGEN will depend on historically based, physically interpolated weather sequences from a mesoscale-climate modeling system which is comprised of four nested layers: 1. an existing synoptic scale forecast model (200 x 300 km) 2. a regional scale slimate model (60 x60 km) 3. a local scale climate model (10 x 10 km); and 4. a specific point climate predictor, referred to as ZOOM. Two additional MCLIGEN components are: 5. a local scalses stochastic climate generator; and 6. a point energy balance snowmelt model Progress made during the reporting period in developing the physically based interpolation climate modeling system stochastic models, and snowpack models is summareized below

Stabilization and control of electrostatic accelerators.

The research carried out on the stabilization control and protection of two Van de Graaff electrostatic nuclear accelerators is described in this thesis. The system at Oxford consists of a single ended and a tandem accelerator with two different kinds of stabilizers; the results presented here are directly applicable to most electrostatic accelerators. As an end result of the mathematical analysis, the behaviour of the single ended injector with combined liner and spray control is formulated. The stabilizer designed for the injector, based on the analysis, incorporates automatic switch over to the auxiliary generating voltmeter stabilizer loop. The automatic gain control introduced into the slit amplifiers eliminates the necessity of manual gain adjustments for different operating conditions. The energy resolution of the injector was measured by using alpha capture resonance in [15]N. It was 0.65 keV at 4.46 MeV. The analysis presented here describes the behaviour of the corona stabilizer as used on the tandem. The predicted limitations due to the time delay and dispersion of the ions in high pressure gas are in good agreement with the measured performance figures. The two loop stabilizer with the auxiliary generating voltmeter loop provides facilities for semi-automatic operation. The resolution of the tandem was +/-1 keV by measuring the [28]Si(p,p)[28]Si resonance at 5.83 MeV. Multiple breakdowns on both the injector and the tandem were prevented by the introduction of the protection circuit. The circuit design was based on the analysis of the breakdown behaviour of the generators as described. The predicted performance of the circuit and its effect on the accelerators is well verified by the observed behaviour of the generators after total breakdown. The study of the computer controlled generator operation is described in Chapter 5. For the interfacing the internationally accepted Camac system is recommended