33,153 research outputs found
A Diabatic Surface Hopping Algorithm based on Time Dependent Perturbation Theory and Semiclassical Analysis
Surface hopping algorithms are popular tools to study dynamics of the
quantum-classical mixed systems. In this paper, we propose a surface hopping
algorithm in diabatic representations, based on time dependent perturbation
theory and semiclassical analysis. The algorithm can be viewed as a Monte Carlo
sampling algorithm on the semiclassical path space for piecewise deterministic
path with stochastic jumps between the energy surfaces. The algorithm is
validated numerically and it shows good performance in both weak coupling and
avoided crossing regimes
Stochastic Geometry Modeling of Cellular Networks: Analysis, Simulation and Experimental Validation
Due to the increasing heterogeneity and deployment density of emerging
cellular networks, new flexible and scalable approaches for their modeling,
simulation, analysis and optimization are needed. Recently, a new approach has
been proposed: it is based on the theory of point processes and it leverages
tools from stochastic geometry for tractable system-level modeling, performance
evaluation and optimization. In this paper, we investigate the accuracy of this
emerging abstraction for modeling cellular networks, by explicitly taking
realistic base station locations, building footprints, spatial blockages and
antenna radiation patterns into account. More specifically, the base station
locations and the building footprints are taken from two publicly available
databases from the United Kingdom. Our study confirms that the abstraction
model based on stochastic geometry is capable of accurately modeling the
communication performance of cellular networks in dense urban environments.Comment: submitted for publicatio
Complex Monge-Amp\`ere equations on quasi-projective varieties
We introduce generalized Monge-Amp\`ere capacities and use these to study
complex Monge-Amp\`ere equations whose right-hand side is smooth outside a
divisor. We prove, in many cases, that there exists a unique normalized
solution which is smooth outside the divisor
The Intensity Matching Approach: A Tractable Stochastic Geometry Approximation to System-Level Analysis of Cellular Networks
The intensity matching approach for tractable performance evaluation and
optimization of cellular networks is introduced. It assumes that the base
stations are modeled as points of a Poisson point process and leverages
stochastic geometry for system-level analysis. Its rationale relies on
observing that system-level performance is determined by the intensity measure
of transformations of the underlaying spatial Poisson point process. By
approximating the original system model with a simplified one, whose
performance is determined by a mathematically convenient intensity measure,
tractable yet accurate integral expressions for computing area spectral
efficiency and potential throughput are provided. The considered system model
accounts for many practical aspects that, for tractability, are typically
neglected, e.g., line-of-sight and non-line-of-sight propagation, antenna
radiation patterns, traffic load, practical cell associations, general fading
channels. The proposed approach, more importantly, is conveniently formulated
for unveiling the impact of several system parameters, e.g., the density of
base stations and blockages. The effectiveness of this novel and general
methodology is validated with the aid of empirical data for the locations of
base stations and for the footprints of buildings in dense urban environments.Comment: Submitted for Journal Publicatio
On the singularity type of full mass currents in big cohomology classes
Let be a compact K\"ahler manifold and be a big cohomology
class. We prove several results about the singularity type of full mass
currents, answering a number of open questions in the field. First, we show
that the Lelong numbers and multiplier ideal sheaves of
-plurisubharmonic functions with full mass are the same as those of the
current with minimal singularities. Second, given another big and nef class
, we show the inclusion Third, we characterize big classes whose full
mass currents are "additive". Our techniques make use of a characterization of
full mass currents in terms of the envelope of their singularity type. As an
essential ingredient we also develop the theory of weak geodesics in big
cohomology classes. Numerous applications of our results to complex geometry
are also given.Comment: v2. Theorem 1.1 updated to include statement about multiplier ideal
sheaves. Several typos fixed. v3. we make our arguments independent of the
regularity results of Berman-Demaill
L^1 metric geometry of big cohomology classes
Suppose is a compact K\"ahler manifold of dimension , and
is closed -form representing a big cohomology class. We
introduce a metric on the finite energy space ,
making it a complete geodesic metric space. This construction is potentially
more rigid compared to its analog from the K\"ahler case, as it only relies on
pluripotential theory, with no reference to infinite dimensional Finsler
geometry. Lastly, by adapting the results of Ross and Witt Nystr\"om to the big
case, we show that one can construct geodesic rays in this space in a flexible
manner
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