13,972 research outputs found
Discrete concavity and the half-plane property
Murota et al. have recently developed a theory of discrete convex analysis
which concerns M-convex functions on jump systems. We introduce here a family
of M-concave functions arising naturally from polynomials (over a field of
generalized Puiseux series) with prescribed non-vanishing properties. This
family contains several of the most studied M-concave functions in the
literature. In the language of tropical geometry we study the tropicalization
of the space of polynomials with the half-plane property, and show that it is
strictly contained in the space of M-concave functions. We also provide a short
proof of Speyer's hive theorem which he used to give a new proof of Horn's
conjecture on eigenvalues of sums of Hermitian matrices.Comment: 14 pages. The proof of Theorem 4 is corrected
Testing Lorentz Invariance by Comparing Light Propagation in Vacuum and Matter
We present a Michelson-Morley type experiment for testing the isotropy of the
speed of light in vacuum and matter. The experiment compares the resonance
frequency of a monolithic optical sapphire resonator with the resonance
frequency of an orthogonal evacuated optical cavity made of fused silica while
the whole setup is rotated on an air bearing turntable once every 45 s.
Preliminary results yield an upper limit for the anisotropy of the speed of
light in matter (sapphire) of \Delta c/c < 4x10^(-15), limited by the frequency
stability of the sapphire resonator operated at room temperature. Work to
increase the measurement sensitivity by more than one order of magnitude by
cooling down the sapphire resonator to liquid helium temperatures (LHe) is
currently under way.Comment: Presented at the Fifth Meeting on CPT and Lorentz Symmetry,
Bloomington, Indiana, June 28-July 2, 201
Modeling river delta formation
A new model to simulate the time evolution of river delta formation process
is presented. It is based on the continuity equation for water and sediment
flow and a phenomenological sedimentation/ erosion law. Different delta types
are reproduced using different parameters and erosion rules. The structures of
the calculated patterns are analyzed in space and time and compared with real
data patterns. Furthermore our model is capable to simulate the rich dynamics
related to the switching of the mouth of the river delta. The simulation
results are then compared with geological records for the Mississippi river
Injection Locking of a Trapped-Ion Phonon Laser
We report on injection locking of optically excited mechanical oscillations of a single, trapped ion. The injection locking dynamics are studied by analyzing the oscillator spectrum with a spatially selective Fourier transform technique and the oscillator phase with stroboscopic imaging. In both cases we find excellent agreement with theory inside and outside the locking range. We attain injection locking with forces as low as 5(1)×10^(-24)  N so this system appears promising for the detection of ultraweak oscillating forces
Behavior of confined granular beds under cyclic thermal loading
We investigate the mechanical behavior of a confined granular packing of
irregular polyhedral particles under repeated heating and cooling cycles by
means of numerical simulations with the Non-Smooth Contact Dynamics method.
Assuming a homogeneous temperature distribution as well as constant temperature
rate, we study the effect of the container shape, and coefficients of thermal
expansions on the pressure buildup at the confining walls and the density
evolution. We observe that small changes in the opening angle of the
confinement can lead to a drastic peak pressure reduction. Furthermore, the
displacement fields over several thermal cycles are obtained and we discover
the formation of convection cells inside the granular material having the shape
of a torus. The root mean square of the vorticity is then calculated from the
displacement fields and a quadratic dependency on the ratio of thermal
expansion coefficients is established
Building an integrated modeling framework for assessing land-use change and its consequences for areal water balance in mountainous Southwest China
The opening up of China's industry towards market orientation has a distinct impact on natural resources as well as on social structures. The example of rubber introduction in Yunnan province (SW China) shows the mutual interdependencies between economy, natural resources, and social structures. We assess the impacts of rubber introduction and possible development paths in the study area. An integrated modeling framework (NabanFrame) is developed for the catchment of the Naban River (size 270 km2), a tributary to the Mekong River. NabanFrame comprises an agro-economic, ecological, and social model. Altogether they interact with a land-use change model via defined interfaces. Effects on the water cycle are considered by additionally integrating the spatially distributed rainfall-runoff and water balance model AKWA-M® in the model framework. Therefore, a reasonable parameterization is needed to assess the land-use changes on areal water fluxes. The authors conclude that the chosen hydrological model is able to assess the impacts of land conversion (from forest to rubber plantations) on catchment hydrology and address further adaptations to be implemented in the hydrological model.BMBF/LILA
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