188 research outputs found
The n-dimensional analogue of the catenary: Prescribed area
We study âheavyâ nâdimensional surfaces which are suspended from some given boundary data Ï 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 Ï
The -dimensional analogue of the catenary: existence and nonexistence
We study "heavy" A?-dimensional surfaces suspended from some prescribed (n â 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: EinfluĂfaktoren der Technisierung jenseits traditioneller Technikfolgenforschung
Ausgehend davon, daĂ das VerhĂ€ltnis von Technikgeneseforschung zu Technikfolgenforschung komplementĂ€r sein muĂ, werden in dem Beitrag die strukturellen, institutionellen und organisatorischen, die kognitiven wie perzeptiven Voraussetzungen dafĂŒr untersucht, welche Technikfolgen wie systematisch und rational in frĂŒhen Phasen der Technikentstehung wahrgenommen, berĂŒcksichtigt und technisch umgesetzt werden und welche nicht, um in der sozialwissenschaftlichen Rekonstruktion der Bedingungen technischer Innovationen die gesellschaftlichen und organisatorischen EinfluĂparameter, die Selektionsprozesse bei der NeueinfĂŒhrung von Techniken prĂ€gen, 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 ErklĂ€rungskategorien zu erfassen. Der zentrale Beitrag des organisationskulturellen Forschungsansatzes der Technikgenese liegt in der Möglichkeit, diejenigen Faktoren herauszukristallisieren, die eine Organisation dazu befĂ€higen, innovative Impulse selbst zu generieren oder entsprechende Stimuli aus ihrer Umwelt aufzunehmen und umzusetzen. AbschlieĂend 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: âpay-to-stayâ PS, ârisk avoidanceâ 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, âpunishmentâ 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
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