18,768 research outputs found
Continuous-time Diffusion Monte Carlo and the Quantum Dimer Model
A continuous-time formulation of the Diffusion Monte Carlo method for lattice
models is presented. In its simplest version, without the explicit use of trial
wavefunctions for importance sampling, the method is an excellent tool for
investigating quantum lattice models in parameter regions close to generalized
Rokhsar-Kivelson points. This is illustrated by showing results for the quantum
dimer model on both triangular and square lattices. The potential energy of two
test monomers as a function of their separation is computed at zero
temperature. The existence of deconfined monomers in the triangular lattice is
confirmed. The method allows also the study of dynamic monomers. A finite
fraction of dynamic monomers is found to destroy the confined phase on the
square lattice when the hopping parameter increases beyond a finite critical
value. The phase boundary between the monomer confined and deconfined phases is
obtained.Comment: 4 pages, 4 figures, revtex; Added a figure showing the
confinement/deconfinement phase boundary for the doped quantum dimer mode
A comparison of two magnetic ultra-cold neutron trapping concepts using a Halbach-octupole array
This paper describes a new magnetic trap for ultra-cold neutrons (UCNs) made
from a 1.2 m long Halbach-octupole array of permanent magnets with an inner
bore radius of 47 mm combined with an assembly of superconducting end coils and
bias field solenoid. The use of the trap in a vertical, magneto-gravitational
and a horizontal setup are compared in terms of the effective volume and
ability to control key systematic effects that need to be addressed in high
precision neutron lifetime measurements
Asymptotic entanglement capacity of the Ising and anisotropic Heisenberg interactions
We compute the asymptotic entanglement capacity of the Ising interaction ZZ,
the anisotropic Heisenberg interaction XX + YY, and more generally, any
two-qubit Hamiltonian with canonical form K = a XX + b YY. We also describe an
entanglement assisted classical communication protocol using the Hamiltonian K
with rate equal to the asymptotic entanglement capacity.Comment: 5 pages, 1 figure; minor corrections, conjecture adde
Guarantees of Riemannian Optimization for Low Rank Matrix Completion
We study the Riemannian optimization methods on the embedded manifold of low
rank matrices for the problem of matrix completion, which is about recovering a
low rank matrix from its partial entries. Assume entries of an
rank matrix are sampled independently and uniformly with replacement. We
first prove that with high probability the Riemannian gradient descent and
conjugate gradient descent algorithms initialized by one step hard thresholding
are guaranteed to converge linearly to the measured matrix provided
\begin{align*} m\geq C_\kappa n^{1.5}r\log^{1.5}(n), \end{align*} where
is a numerical constant depending on the condition number of the
underlying matrix. The sampling complexity has been further improved to
\begin{align*} m\geq C_\kappa nr^2\log^{2}(n) \end{align*} via the resampled
Riemannian gradient descent initialization. The analysis of the new
initialization procedure relies on an asymmetric restricted isometry property
of the sampling operator and the curvature of the low rank matrix manifold.
Numerical simulation shows that the algorithms are able to recover a low rank
matrix from nearly the minimum number of measurements
Nonlinear nonlocal multicontinua upscaling framework and its applications
In this paper, we discuss multiscale methods for nonlinear problems. The main
idea of these approaches is to use local constraints and solve problems in
oversampled regions for constructing macroscopic equations. These techniques
are intended for problems without scale separation and high contrast, which
often occur in applications. For linear problems, the local solutions with
constraints are used as basis functions. This technique is called Constraint
Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM).
GMsFEM identifies macroscopic quantities based on rigorous analysis. In
corresponding upscaling methods, the multiscale basis functions are selected
such that the degrees of freedom have physical meanings, such as averages of
the solution on each continuum.
This paper extends the linear concepts to nonlinear problems, where the local
problems are nonlinear. The main concept consists of: (1) identifying
macroscopic quantities; (2) constructing appropriate oversampled local problems
with coarse-grid constraints; (3) formulating macroscopic equations. We
consider two types of approaches. In the first approach, the solutions of local
problems are used as basis functions (in a linear fashion) to solve nonlinear
problems. This approach is simple to implement; however, it lacks the nonlinear
interpolation, which we present in our second approach. In this approach, the
local solutions are used as a nonlinear forward map from local averages
(constraints) of the solution in oversampling region. This local fine-grid
solution is further used to formulate the coarse-grid problem. Both approaches
are discussed on several examples and applied to single-phase and two-phase
flow problems, which are challenging because of convection-dominated nature of
the concentration equation
An experimental study on a motion sensing system for sports training
In sports science, motion data collected from athletes is
used to derive key performance characteristics, such as stride length
and stride frequency, that are vital coaching support information. The
sensors for use must be more accurate, must capture more vigorous
events, and have strict weight and size requirements, since they must
not themselves affect performance. These requirements mean each
wireless sensor device is necessarily resource poor and yet must be
capable of communicating a considerable amount of data, contending
for the bandwidth with other sensors on the body. This paper analyses
the results of a set of network traffic experiments that were designed
to investigate the suitability of conventional wireless motion sensing
system design � which generally assumes in-network processing - as
an efficient and scalable design for use in sports training
Quality-of-service routing with two concave constraints
Routing is a process of finding a network path from a source node to a destination node. A good routing protocol should find the "best path" from a source to a destination. When there are independent constraints to be considered, the "best path" is not well-defined. In our previous work, we developed a line segment representation for Quality-of-Service routing with bandwidth and delay requirements. In this paper, we propose how to adopt the line segment when a request has two concave constraints. We have developed a series of operations for constructing routing tables under the distance-vector protocol. We evaluate the performance through extensive simulations. ©2008 IEEE.published_or_final_versio
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