The n-dimensional analogue of the catenary: Prescribed area

We study ”heavy” n–dimensional surfaces which are suspended from some given boundary data ϕ and have prescribed surface area A. Using a fixed point argument we show existence of a solution provided A is close to the area of the corresponding minimal surface spanned by ϕ

The nn-dimensional analogue of the catenary: existence and nonexistence

We study "heavy" A?-dimensional surfaces suspended from some prescribed (n — 1) -dimensional boundary data. This leads to a mean curvature type equation with a non-monotone right hand side. We show that the equation has no solution if the boundary data are too small, and, using a fixed point argument, that the problem always has a smooth solution for sufficiently large boundary data

Wetting and Minimal Surfaces

We study minimal surfaces which arise in wetting and capillarity phenomena. Using conformal coordinates, we reduce the problem to a set of coupled boundary equations for the contact line of the fluid surface, and then derive simple diagrammatic rules to calculate the non-linear corrections to the Joanny-de Gennes energy. We argue that perturbation theory is quasi-local, i.e. that all geometric length scales of the fluid container decouple from the short-wavelength deformations of the contact line. This is illustrated by a calculation of the linearized interaction between contact lines on two opposite parallel walls. We present a simple algorithm to compute the minimal surface and its energy based on these ideas. We also point out the intriguing singularities that arise in the Legendre transformation from the pure Dirichlet to the mixed Dirichlet-Neumann problem.Comment: 22 page

Doubly connected minimal surfaces and extremal harmonic mappings

The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected domains are where one first observes nontrivial conformal invariants. Herbert Groetzsch and Johannes C. C. Nitsche addressed this issue for quasiconformal and harmonic mappings, respectively. Combining these concepts we obtain sharp estimates for quasiconformal harmonic mappings between doubly connected domains. We then apply our results to the Cauchy problem for minimal surfaces, also known as the Bjorling problem. Specifically, we obtain a sharp estimate of the modulus of a doubly connected minimal surface that evolves from its inner boundary with a given initial slope.Comment: 35 pages, 2 figures. Minor edits, references adde

Reggeon exchange from gauge/gravity duality

We perform the analysis of quark-antiquark Reggeon exchange in meson-meson scattering, in the framework of the gauge/gravity correspondence in a confining background. On the gauge theory side, Reggeon exchange is described as quark-antiquark exchange in the t channel between fast projectiles. The corresponding amplitude is represented in terms of Wilson loops running along the trajectories of the constituent quarks and antiquarks. The paths of the exchanged fermions are integrated over, while the "spectator" fermions are dealt with in an eikonal approximation. On the gravity side, we follow a previously proposed approach, and we evaluate the Wilson-loop expectation value by making use of gauge/gravity duality for a generic confining gauge theory. The amplitude is obtained in a saddle-point approximation through the determination near the confining horizon of a Euclidean "minimal surface with floating boundaries", i.e., by fixing the trajectories of the exchanged quark and antiquark by means of a minimisation procedure, which involves both area and length terms. After discussing, as a warm-up exercise, a simpler problem on a plane involving a soap film with floating boundaries, we solve the variational problem relevant to Reggeon exchange, in which the basic geometry is that of a helicoid. A compact expression for the Reggeon-exchange amplitude, including the effects of a small fermion mass, is then obtained through analytic continuation from Euclidean to Minkowski space-time. We find in particular a linear Regge trajectory, corresponding to a Regge-pole singularity supplemented by a logarithmic cut induced by the non-zero quark mass. The analytic continuation leads also to companion contributions, corresponding to the convolution of the same Reggeon-exchange amplitude with multiple elastic rescattering interactions between the colliding mesons.Comment: 60+1 pages, 14 figure

Technikgenese: Einflußfaktoren der Technisierung jenseits traditioneller Technikfolgenforschung

Ausgehend davon, daß das Verhältnis von Technikgeneseforschung zu Technikfolgenforschung komplementär sein muß, werden in dem Beitrag die strukturellen, institutionellen und organisatorischen, die kognitiven wie perzeptiven Voraussetzungen dafür untersucht, welche Technikfolgen wie systematisch und rational in frühen Phasen der Technikentstehung wahrgenommen, berücksichtigt und technisch umgesetzt werden und welche nicht, um in der sozialwissenschaftlichen Rekonstruktion der Bedingungen technischer Innovationen die gesellschaftlichen und organisatorischen Einflußparameter, die Selektionsprozesse bei der Neueinführung von Techniken prägen, manifest werden zu lassen. Ziele und Grundlagen der sozialwissenschaftlichen Technikgeneseforschung werden dargestellt. Indem Technikgenese in organisationskulturellen Kontexten analysiert wird, wird ein neuer Forschungsansatz konzipiert, der im Kern beansprucht, das Selektions- und Entscheidungsverhalten von Organisationen mit Hilfe von Erklärungskategorien zu erfassen. Der zentrale Beitrag des organisationskulturellen Forschungsansatzes der Technikgenese liegt in der Möglichkeit, diejenigen Faktoren herauszukristallisieren, die eine Organisation dazu befähigen, innovative Impulse selbst zu generieren oder entsprechende Stimuli aus ihrer Umwelt aufzunehmen und umzusetzen. Abschließend wird das weitere Vorgehen sozialwissenschaftlicher Forschung zur Technikgenese skizziert. (ICA

Helper Response to Experimentally Manipulated Predation Risk in the Cooperatively Breeding Cichlid Neolamprologus pulcher

Background We manipulated predation risk in a field experiment with the cooperatively breeding cichlid Neolamprologus pulcher by releasing no predator, a medium- or a large-sized fish predator inside underwater cages enclosing two to three natural groups. We assessed whether helpers changed their helping behaviour, and whether within-group conflict changed, depending on these treatments, testing three hypotheses: ‘pay-to-stay’ PS, ‘risk avoidance’ RA, or (future) reproductive benefits RB. We also assessed whether helper food intake was reduced under risk, because this might reduce investments in other behaviours to save energy. Methodology/Principal Findings Medium and large helpers fed less under predation risk. Despite this effect helpers invested more in territory defence, but not territory maintenance, under the risk of predation (supporting PS). Experimentally covering only the breeding shelter with sand induced more helper digging under predation risk compared to the control treatment (supporting PS). Aggression towards the introduced predator did not differ between the two predator treatments and increased with group member size and group size (supporting PS and RA). Large helpers increased their help ratio (helping effort/breeder aggression received, ‘punishment’ by the dominant pair in the group) in the predation treatments compared to the control treatment, suggesting they were more willing to PS. Medium helpers did not show such effects. Large helpers also showed a higher submission ratio (submission/ breeder aggression received) in all treatments, compared to the medium helpers (supporting PS). Conclusions/Significance We conclude that predation risk reduces helper food intake, but despite this effect, helpers were more willing to support the breeders, supporting PS. Effects of breeder punishment suggests that PS might be more important for large compared to the medium helpers. Evidence for RA was also detected. Finally, the results were inconsistent with RB

Singulaere Variationsprobleme und Hindernisprobleme

34 refs.Copy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman