1,401,848 research outputs found
Six - Vertex Model with Domain wall boundary conditions. Variable inhomogeneities
We consider the six-vertex model with domain wall boundary conditions. We
choose the inhomogeneities as solutions of the Bethe Ansatz equations. The
Bethe Ansatz equations have many solutions, so we can consider a wide variety
of inhomogeneities. For certain choices of the inhomogeneities we study arrow
correlation functions on the horizontal line going through the centre. In
particular we obtain a multiple integral representation for the emptiness
formation probability that generalizes the known formul\ae for XXZ
antiferromagnets.Comment: 12 pages, 1 figur
On the Fundamental Limits of Random Non-orthogonal Multiple Access in Cellular Massive IoT
Machine-to-machine (M2M) constitutes the communication paradigm at the basis
of Internet of Things (IoT) vision. M2M solutions allow billions of multi-role
devices to communicate with each other or with the underlying data transport
infrastructure without, or with minimal, human intervention. Current solutions
for wireless transmissions originally designed for human-based applications
thus require a substantial shift to cope with the capacity issues in managing a
huge amount of M2M devices. In this paper, we consider the multiple access
techniques as promising solutions to support a large number of devices in
cellular systems with limited radio resources. We focus on non-orthogonal
multiple access (NOMA) where, with the aim to increase the channel efficiency,
the devices share the same radio resources for their data transmission. This
has been shown to provide optimal throughput from an information theoretic
point of view.We consider a realistic system model and characterise the system
performance in terms of throughput and energy efficiency in a NOMA scenario
with a random packet arrival model, where we also derive the stability
condition for the system to guarantee the performance.Comment: To appear in IEEE JSAC Special Issue on Non-Orthogonal Multiple
Access for 5G System
An Ensemble-Proper Orthogonal Decomposition Method for the Nonstationary Navier-Stokes Equations
The definition of partial differential equation (PDE) models usually involves
a set of parameters whose values may vary over a wide range. The solution of
even a single set of parameter values may be quite expensive. In many cases,
e.g., optimization, control, uncertainty quantification, and other settings,
solutions are needed for many sets of parameter values. We consider the case of
the time-dependent Navier-Stokes equations for which a recently developed
ensemble-based method allows for the efficient determination of the multiple
solutions corresponding to many parameter sets. The method uses the average of
the multiple solutions at any time step to define a linear set of equations
that determines the solutions at the next time step. To significantly further
reduce the costs of determining multiple solutions of the Navier-Stokes
equations, we incorporate a proper orthogonal decomposition (POD) reduced-order
model into the ensemble-based method. The stability and convergence results for
the ensemble-based method are extended to the ensemble-POD approach. Numerical
experiments are provided that illustrate the accuracy and efficiency of
computations determined using the new approach
Multiple boundary peak solutions for some singularly perturbed Neumann problems
We consider the problem \left \{
\begin{array}{rcl} \varepsilon^2 \Delta u - u + f(u) = 0 & \mbox{ in }& \ \Omega\\ u > 0 \ \mbox{ in} \ \Omega, \ \frac{\partial u}{\partial \nu} = 0 & \mbox{ on }& \ \partial\Omega,
\end{array} \right. where \Omega is a bounded smooth domain in R^N, \varepsilon>KK-peakH(P)K-peak$ solutions.
We first use the Liapunov-Schmidt method to reduce the problem to finite dimensions.
Then we use a maximizing procedure to obtain multiple boundary spikes
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