Infinitely Many Strings in De Sitter Spacetime: Expanding and Oscillating Elliptic Function Solutions

The exact general evolution of circular strings in $2+1$ dimensional de Sitter spacetime is described closely and completely in terms of elliptic functions. The evolution depends on a constant parameter $b$, related to the string energy, and falls into three classes depending on whether $b<1/4$ (oscillatory motion), $b=1/4$ (degenerated, hyperbolic motion) or $b>1/4$ (unbounded motion). The novel feature here is that one single world-sheet generically describes {\it infinitely many} (different and independent) strings. The world-sheet time $\tau$ is an infinite-valued function of the string physical time, each branch yields a different string. This has no analogue in flat spacetime. We compute the string energy $E$ as a function of the string proper size $S$, and analyze it for the expanding and oscillating strings. For expanding strings $(\dot{S}>0)$: $E\neq 0$ even at $S=0$, $E$ decreases for small $S$ and increases $\propto\hspace*{-1mm}S$ for large $S$. For an oscillating string $(0\leq S\leq S_{max})$, the average energy $$ over one oscillation period is expressed as a function of $S_{max}$ as a complete elliptic integral of the third kind.Comment: 32 pages, Latex file, figures available from the authors under request. LPTHE-PAR 93-5

Controlling a leaky tap

We apply the Ott, Grebogy and Yorke mechanism for the control of chaos to the analytical oscillator model of a leaky tap obtaining good results. We exhibit the robustness of the control against both dynamical noise and measurement noise.A possible way of controlling experimentally a leaky tap using magnetic-field-produced variations in the viscosity of a magnetorheological fluid is suggested.Comment: 14 pages, 12 figures. Submitted to Physics Letters

Enhancing Biodiversity and Multifunctionality of an Organic Farmscape in California’s Central Valley

Organic farmers in the USA increasingly manage the margins of previously monocultured farmed landscapes to increase biodiversity, e.g. they restore and protect riparian corridors, plant hedgerows and construct vegetated tailwater ponds. This study attempts to link habitat enhancements, biodiversity and changes in ecosystem functions by: 1. inventorying the existing biodiversity and the associated belowground community structure and composition in the various habitats of an organic farm in California’s Central Valley; and 2. monitoring key ecosystem functions of these habitats. Two years of inventories show greater native plant diversity in non-cropped areas. While nematode diversity did not differ between habitats, functional groups were clearly associated with particular habitats as were soil microbial communities (phospholipid fatty acid analysis). Earthworm diversity did not differ between habitats, but biomass was higher in non-cropped areas. Habitats with woody vegetation stored 20% of the farmscape’s total carbon (C), despite their relatively small size (only 5% of the total farm). Two years of monitoring data of farmscape C and nitrogen (N) through emissions, run-off and leaching showed distinct tradeoffs in function associated with each habitat. Clearly habitat restoration in field margins will increase both landscape biodiversity and the multifunctionality of the farmscape as a whole

Effect of zinc intake on growth in infants: A meta-analysis

A systematic review and meta-analysis of available randomized controlled trials (RCTs) was conducted to evaluate the effect of zinc (Zn) intake on growth in infants. Out of 5500 studies identified through electronic searches and reference lists, 19 RCTs were selected after applying the exclusion/inclusion criteria. The influence of Zn intake on growth was considered in the overall meta-analysis. Other variables were also taken into account as possible effect modifiers: doses of Zn intake, intervention duration, nutritional status, and risk of bias. From each select growth study, final measures of weight, length, mid upper arm circumference (MUAC), head circumference, weight for age z-score (WAZ), length for age z-score (LAZ), and weight for length z-score (WLZ) were assessed. Pooled β and 95% confidence interval (CI) were calculated. Additionally, we carried out a sensitivity analysis. Zn intake was not associated with weight, length, MUAC, head circumference, and LAZ in the pooled analyses. However, Zn intake had a positive and statistically effect on WAZ (β = 0.06; 95%CI 0.02 to 0.10) and WLZ (β = 0.05; 95%CI 0.01 to 0.08). The dose–response relationship between Zn intake and these parameters indicated that a doubling of Zn intake increased WAZ and WLZ by approximately 4%. Substantial heterogeneity was present only in length analyses (I2 = 45%; p = 0.03). Zn intake was positively associated with length values at short time (four to 20 weeks) (β = 0.01; CI 95% 0 to 0.02) and at medium doses of Zn (4.1 to 8 mg/day) (β = 0.003; CI 95% 0 to 0.01). Nevertheless, the effect magnitude was small. Our results indicate that Zn intake increases growth parameters of infants. Nonetheless, interpretation of these results should be carefully considered

Flamelet structures in spray ignition

In typical liquid-fueled burners the fuel is injected as a high-velocity liquid jet that breaks up to form the spray. The initial heating and vaporization of the liquid fuel rely on the relatively large temperatures of the sourrounding gas, which may include hot combustion products and preheated air. The heat exchange between the liquid and the gas phases is enhanced by droplet dispersion arising from the turbulent motion. Chemical reaction takes place once molecular mixing between the fuel vapor and the oxidizer has occurred in mixing layers separating the spray flow from the hot air stream. Since in most applications the injection velocities are much larger than the premixed-flame propagation velocity, combustion stabilization relies on autoignition of the fuel-oxygen mixture, with the combustion stand-off distance being controlled by the interaction of turbulent transport, droplet heating and vaporization, and gas-phase chemical reactions. In this study, conditions are identified under which analyses of laminar flamelets canshed light on aspects of turbulent spray ignition. This study extends earlier fundamental work by Liñan & Crespo (1976) on ignition in gaseous mixing layers to ignition of sprays. Studies of laminar mixing layers have been found to be instrumental in developing un-derstanding of turbulent combustion (Peters 2000), including the ignition of turbulent gaseous diffusion flames (Mastorakos 2009). For the spray problem at hand, the configuration selected, shown in Figure 1, involves a coflow mixing layer formed between a stream of hot air moving at velocity UA and a monodisperse spray moving at velocity USUA. The boundary-layer approximation will be used below to describe the resulting sl ender flow, which exhibits different igniting behaviors depending on the characteristics of t he fuel. In this approximation, consideration of the case U A = U S enables laminar ignition distances to be related to ignition times of unstrained spray flamelets, thereby pro viding quantitative information of direct applicability in regions of low scala r dissipation-rate in turbulent reactive flows (see the discussion in pp. 181–186 of Peters (2000)) . This report is organized as follows. Effects of droplet dispersion dynamics on ignition of sprays in turbulent mixing layers are discussed in Section 2. The formulation f or ignition in laminar mixing layers is outlined in Sections 3 and 4. The results are presented in Section 5. In Section 6, the mixture-fraction field and associated scalar dissipat ion rates for spray ignition are discussed. Finally, some brief conclusions are drawn in Section 7

Mass Spectrum of Strings in Anti de Sitter Spacetime

We perform string quantization in anti de Sitter (AdS) spacetime. The string motion is stable, oscillatory in time with real frequencies $\omega_n= \sqrt{n^2+m^2\alpha'^2H^2}$ and the string size and energy are bounded. The string fluctuations around the center of mass are well behaved. We find the mass formula which is also well behaved in all regimes. There is an {\it infinite} number of states with arbitrarily high mass in AdS (in de Sitter (dS) there is a {\it finite} number of states only). The critical dimension at which the graviton appears is $D=25,$ as in de Sitter space. A cosmological constant $\Lambda\neq 0$ (whatever its sign) introduces a {\it fine structure} effect (splitting of levels) in the mass spectrum at all states beyond the graviton. The high mass spectrum changes drastically with respect to flat Minkowski spacetime. For $\Lambda\sim \mid\Lambda\mid N^2,$ {\it independent} of $\alpha',$ and the level spacing {\it grows} with the eigenvalue of the number operator, $N.$ The density of states $\rho(m)$ grows like \mbox{Exp}[(m/\sqrt{\mid\Lambda\mid}\;)^{1/2}] (instead of \rho(m)\sim\mbox{Exp}[m\sqrt{\alpha'}] as in Minkowski space), thus {\it discarding} the existence of a critical string temperature. For the sake of completeness, we also study the quantum strings in the black string background, where strings behave, in many respects, as in the ordinary black hole backgrounds. The mass spectrum is equal to the mass spectrum in flat Minkowski space.Comment: 31 pages, Latex, DEMIRM-Paris-9404

An in vitro experimental investigation of oscillatory flow in the cerebral aqueduct

This in vitro study aims at clarifying the relation between the oscillatory flow of cerebrospinal fluid (CSF) in the cerebral aqueduct, a narrow conduit connecting the third and fourth ventricles, and the corresponding interventricular pressure difference. Dimensional analysis is used in designing an anatomically correct scaled model of the aqueduct flow, with physical similarity maintained by adjusting the flow frequency and the properties of the working fluid. The time-varying pressure difference across the aqueduct corresponding to a given oscillatory flow rate is measured in parametric ranges covering the range of flow conditions commonly encountered in healthy subjects. Parametric dependences are delineated for the time-averaged pressure fluctuations and for the phase lag between the transaqueductal pressure difference and the flow rate, both having clinical relevance. The results are validated through comparisons with predictions obtained with a previously derived computational model. The parametric quantification in this study enables the derivation of a simple formula for the relation between the transaqueductal pressure and the stroke volume. This relationship can be useful in the quantification of transmantle pressure differences based on non-invasive magnetic-resonance-velocimetry measurements of aqueduct flow for investigation of CSF-related disorders.National Institutes of Health/ National Institute of Neurological Diseases and Stroke through contract # 1R01NS120343-0

New Coherent String States and Minimal Uncertainty in WZWN Models

We study the properties of {\bf exact} (all level $k$) quantum coherent states in the context of string theory on a group manifold (WZWN models). Coherent states of WZWN models may help to solve the unitarity problem: Having positive norm, they consistently describe the very massive string states (otherwise excluded by the spin-level condition). These states can be constructed by (at least) two alternative procedures: (i) as the exponential of the creation operator on the ground state, and (ii) as eigenstates of the annhilation operator. In the $k\to\infty$ limit, all the known properties of ordinary coherent states are recovered. States (i) and (ii) (which are equivalent in the context of ordinary quantum mechanics and string theory in flat spacetime) are not equivalent in the context of WZWN models. The set (i) was constructed by these authors in a previous article. In this paper we provide the construction of states (ii), we compare the two sets and discuss their properties. We analyze the uncertainty relation, and show that states (ii) satisfy automatically the {\it minimal uncertainty} condition for any $k$; they are thus {\it quasiclassical}, in some sense more classical than states (i) which only satisfy it in the $k\to\infty$ limit. Modification to the Heisenberg relation is given by $2 {\cal H}/k$, where ${\cal H}$ is connected to the string energy.Comment: More discussion on relation to previous work. More references added. 14 pages, Latex, no figure

Semi-Classical Quantization of Circular Strings in De Sitter and Anti De Sitter Spacetimes

We compute the {\it exact} equation of state of circular strings in the (2+1) dimensional de Sitter (dS) and anti de Sitter (AdS) spacetimes, and analyze its properties for the different (oscillating, contracting and expanding) strings. The string equation of state has the perfect fluid form $P=(\gamma-1)E,$ with the pressure and energy expressed closely and completely in terms of elliptic functions, the instantaneous coefficient $\gamma$ depending on the elliptic modulus. We semi-classically quantize the oscillating circular strings. The string mass is $m=\sqrt{C}/(\pi H\alpha'),\;C$ being the Casimir operator, $C=-L_{\mu\nu}L^{\mu\nu},$ of the $O(3,1)$-dS [$O(2,2)$-AdS] group, and $H$ is the Hubble constant. We find \alpha'm^2_{\mbox{dS}}\approx 5.9n,\;(n\in N_0), and a {\it finite} number of states N_{\mbox{dS}}\approx 0.17/(H^2\alpha') in de Sitter spacetime; m^2_{\mbox{AdS}}\approx 4H^2n^2 (large $n\in N_0$) and N_{\mbox{AdS}}=\infty in anti de Sitter spacetime. The level spacing grows with $n$ in AdS spacetime, while is approximately constant (although larger than in Minkowski spacetime) in dS spacetime. The massive states in dS spacetime decay through tunnel effect and the semi-classical decay probability is computed. The semi-classical quantization of {\it exact} (circular) strings and the canonical quantization of generic string perturbations around the string center of mass strongly agree.Comment: Latex, 26 pages + 2 tables and 5 figures that can be obtained from the authors on request. DEMIRM-Obs de Paris-9404

Sinh-Gordon, Cosh-Gordon and Liouville Equations for Strings and Multi-Strings in Constant Curvature Spacetimes

We find that the fundamental quadratic form of classical string propagation in $2+1$ dimensional constant curvature spacetimes solves the Sinh-Gordon equation, the Cosh-Gordon equation or the Liouville equation. We show that in both de Sitter and anti de Sitter spacetimes (as well as in the $2+1$ black hole anti de Sitter spacetime), {\it all} three equations must be included to cover the generic string dynamics. The generic properties of the string dynamics are directly extracted from the properties of these three equations and their associated potentials (irrespective of any solution). These results complete and generalize earlier discussions on this topic (until now, only the Sinh-Gordon sector in de Sitter spacetime was known). We also construct new classes of multi-string solutions, in terms of elliptic functions, to all three equations in both de Sitter and anti de Sitter spacetimes. Our results can be straightforwardly generalized to constant curvature spacetimes of arbitrary dimension, by replacing the Sinh-Gordon equation, the Cosh-Gordon equation and the Liouville equation by higher dimensional generalizations.Comment: Latex, 19 pages + 1 figure (not included