3,878,874 research outputs found
Earthquakes in the length-spectrum Teichm\"uller spaces
Let be a complete hyperbolic surface of infinite type that has a
geodesic pants decomposition with cuff lengths bounded above. The length
spectrum Teichm\"uller space consists of homotopy classes of
hyperbolic metrics on such that the ratios of the corresponding simple
closed geodesic for the hyperbolic metric on and for the other hyperbolic
metric are bounded from the below away from 0 and from the above away from
(cf. \cite{ALPS}). This paper studies earthquakes in the length
spectrum Teichm\"uller space . We find a necessary condition and
several sufficient conditions on earthquake measure such that the
corresponding earthquake describes the hyperbolic metric on
which is in the length spectrum Teichm\"uller space. Moreover, we give examples
of earthquake paths , for , such that for , and for .Comment: metadata correction, the same version as befor
Heat content and inradius for regions with a Brownian boundary
In this paper we consider , Brownian motion of time length , in -dimensional Euclidean space and on the -dimensional
torus . We compute the expectation of (i) the heat content at time
of for fixed and in the
limit , when is kept at temperature 1 for all and has initial temperature 0, and (ii)
the inradius of for in the
limit .Comment: 13 page
Invasion Percolation with Temperature and the Nature of SOC in Real Systems
We show that the introduction of thermal noise in Invasion Percolation (IP)
brings the system outside the critical point. This result suggests a possible
definition of SOC systems as ordinary critical systems where the critical point
correspond to set to 0 one of the parameters. We recover both IP and EDEN
model, for , and respectively. For small we find a
dynamical second order transition with correlation length diverging when .Comment: 4 pages, 2 figure
Efficiency of Energy Conversion in Thermoelectric Nanojunctions
Using first-principles approaches, this study investigated the efficiency of
energy conversion in nanojunctions, described by the thermoelectric figure of
merit . We obtained the qualitative and quantitative descriptions for the
dependence of on temperatures and lengths. A characteristic temperature:
was observed. When , . When , tends to a saturation value. The dependence of
on the wire length for the metallic atomic chains is opposite to that for
the insulating molecules: for aluminum atomic (conducting) wires, the
saturation value of increases as the length increases; while for
alkanethiol (insulating) chains, the saturation value of decreases as the
length increases. can also be enhanced by choosing low-elasticity bridging
materials or creating poor thermal contacts in nanojunctions. The results of
this study may be of interest to research attempting to increase the efficiency
of energy conversion in nano thermoelectric devices.Comment: 2 figure
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