Drowsy Cheetah Hunting Antelopes: A Diffusing Predator Seeking Fleeing Prey

We consider a system of three random walkers (a `cheetah' surrounded by two `antelopes') diffusing in one dimension. The cheetah and the antelopes diffuse, but the antelopes experience in addition a deterministic relative drift velocity, away from the cheetah, proportional to their distance from the cheetah, such that they tend to move away from the cheetah with increasing time. Using the backward Fokker-Planck equation we calculate, as a function of their initial separations, the probability that the cheetah has caught neither antelope after infinite time.Comment: 5 page

Phase Ordering Dynamics of the O(n) Model - Exact Predictions and Numerical Results

We consider the pair correlation functions of both the order parameter field and its square for phase ordering in the $O(n)$ model with nonconserved order parameter, in spatial dimension $2\le d\le 3$ and spin dimension $1\le n\le d$. We calculate, in the scaling limit, the exact short-distance singularities of these correlation functions and compare these predictions to numerical simulations. Our results suggest that the scaling hypothesis does not hold for the $d=2$ $O(2)$ model. Figures (23) are available on request - email [email protected]: 23 pages, Plain LaTeX, M/C.TH.93/2

Dynamical properties of the hypercell spin glass model

The spreading of damage technique is used to study the sensibility to initial conditions in a heath bath Monte Carlo simulation of the spin glass hypercubic cell model. Since the hypercubic cell in dimension 2D and the hypercubic lattice in dimension D resemble each other closely at finite dimensions and both converge to mean field when dimension goes to infinity, it allows us to study the effect of dimensionality on the dynamical behavior of spin glasses.Comment: 13 pages, RevTex, 8 ps figure

Status of Platanthera praeclara Sheviak & Bowles (Western Prairie Fringed Orchid) in the Platte River Valley in Nebraska from Hamilton to Garden Counties

During June and July, 1991, a search for western prairie fringed orchid was conducted in the Platte River Valley in central and west-central Nebraska. No orchids were found in the 370 sites surveyed. Factors which may contribute to the scarcity of this orchid in the area surveyed include drought conditions in the previous three years; habitat alteration by draining, ditching, herbicide application, mowing for hay, crop cultivation and planting of non-native species for hay fields; invasion of the area by trees; and the presence of alkaline soils in some area

Blowup of Jang's equation at outermost marginally trapped surfaces

The aim of this paper is to collect some facts about the blowup of Jang's equation. First, we discuss how to construct solutions that blow up at an outermost MOTS. Second, we exclude the possibility that there are extra blowup surfaces in data sets with non-positive mean curvature. Then we investigate the rate of convergence of the blowup to a cylinder near a strictly stable MOTS and show exponential convergence near a strictly stable MOTS.Comment: 15 pages. This revision corrects some typo

Evidence for the droplet/scaling picture of spin glasses

We have studied the Parisi overlap distribution for the three dimensional Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T around 0.7Tc and system sizes upto L=32, we found a P(q) as expected for the full Parisi replica symmetry breaking, just as was also observed in recent Monte Carlo simulations on a cubic lattice. However, for lower temperatures our data agree with predictions from the droplet or scaling picture. The failure to see droplet model behaviour in Monte Carlo simulations is due to the fact that all existing simulations have been done at temperatures too close to the transition temperature so that sytem sizes larger than the correlation length have not been achieved.Comment: 4 pages, 6 figure

Identification of the critical temperature from non-equilibrium time-dependent quantities

We present a new procedure able to identify and measure the critical temperature. This method is based on the divergence of the relaxation time approaching the critical point in quenches from infinite temperature. We introduce a dimensionless quantity that turns out to be time-independent at the critical temperature. The procedure does not need equilibration and allows for a relatively fast identification of the critical temperature. The method is first tested in the ferromagnetic Ising model and then applied to the one-dimensional Ising spin glass with power-law interactions. Here we always find a finite critical temperature also in presence of a uniform external field, in agreement with the mean-field picture for the low temperature phase of spin glasses.Comment: 6 pages, 10 figure

Is the droplet theory for the Ising spin glass inconsistent with replica field theory?

Symmetry arguments are used to derive a set of exact identities between irreducible vertex functions for the replica symmetric field theory of the Ising spin glass in zero magnetic field. Their range of applicability spans from mean field to short ranged systems in physical dimensions. The replica symmetric theory is unstable for d>8, just like in mean field theory. For 6<d<8 and d<6 the resummation of an infinite number of terms is necessary to settle the problem. When d<8, these Ward-like identities must be used to distinguish an Almeida-Thouless line from the replica symmetric droplet phase.Comment: 4 pages. Accepted for publication in J.Phys.A. This is the accepted version with the following minor changes: one extra sentence in the abstract; footnote 2 slightly extended; last paragraph somewhat reformulate

Evaluation of antigens for the serodiagnosis of kala-azar and oriental sores by means of the indirect immunofluorescence antibody test (IFAT)

Antigens and corresponding sera were collected from travellers with leishmaniasis returning to Germany from different endemic areas of the old world. The antigenicity of these Leishmania strains, which were maintained in Syrian hamsters, was compared by indirect immunofluorescence (IFAT). Antigenicity was demonstrated by antibody titres in 18 sera from 11 patients. The amastigotic stages of nine strains of Leishmania donovani and four strains of Leishmania tropica were compared with each other and with the culture forms of insect flagellates (Strigomonas oncopelti and Leptomonas ctenocephali). Eighteen sera from 11 patients were available for antibody determination with these antigens. The maximal antibody titres in a single serum varied considerably depending on which antigen was used for the test. High antibody levels could only be maintained when Leishmania donovani was employed as the antigen, but considerable differences also occurred between the different strains of this species. The other antigens were weaker. No differences in antigenicity between amastigotes and promastigotes of the same strain were observed. It is important to select suitable antigens. Low titres may be of doubtful specificity and are a poor baseline for the fall in titre which is an essential index of effective treatment.Wir sammelten Parasiten und Seren von Reisenden, die aus verschiedenen endemischen Gebieten der Alten Welt mit einer Leishmaniasis nach Deutschland zurückkehrten. Die Antigenaktivitäten der isolierten und fortlaufend in Goldhamstern gehaltenenLeishmania-Stämme wurden im indirekten Immunofluoreszenztest (IFAT) verglichen. Die Antigenität wurde an Hand von Antikörpertitern in 18 Serumproben von 11 Patienten bewiesen. Neun Stämme desLeishmania donovani-Komplexes und vierLeishmania tropica-Isolate wurden in ihrem amastigoten Stadium miteinander verglichen. Hinzu kamen zwei Insekten-Flagellaten als Kulturformen:Strigomonas oncopelti undLeptomonas ctenocephali. 18 Serumproben von 11 Patienten standen für die Antikörperbestimmung mit diesen Antigenen zur Verfügung. Die maximalen Titerhöhen variierten in ein- und derselben antiserumprobe zum Teil erheblich, je nachdem, welches Antigen für den Test benutzt wurde. Hohe Antikörpertiter konnten nur erhalten werden, wennLeishmania donovani als Antigen vorlag, es ergaben sich aber auch zwischen den einzelnen Stämmen dieser Leishmaniaart erhebliche Unterschiede in der Antigenaktivität. Antigene anderer Art erwiesen sich als wenig wirksam. Zwischen amastigoten und promastigoten Entwicklungsformen einesLeishmania donovani-Stammes konnten keine Unterschiede in der Antigenaktivität erkannt werden. Für den Nachweis möglichst hoher Antikörpertiter im IFAT ist die Auswahl geeigneter Antigene von ausschlaggebender Bedeutung. Niedrige Titer erschweren deren Beurteilung als spezifisch und sind eine schlechte Ausgangsposition für die Beobachtung des obligatorischen Titerabfalles nach erfolgreicher Therapie

Asymptotically hyperbolic manifolds with small mass

For asymptotically hyperbolic manifolds of dimension $n$ with scalar curvature at least equal to $-n(n-1)$ the conjectured positive mass theorem states that the mass is non-negative, and vanishes only if the manifold is isometric to hyperbolic space. In this paper we study asymptotically hyperbolic manifolds which are also conformally hyperbolic outside a ball of fixed radius, and for which the positive mass theorem holds. For such manifolds we show that the conformal factor tends to one as the mass tends to zero