30,979 research outputs found
A modified particle method for semilinear hyperbolic systems with oscillatory solutions
We introduce a modified particle method for semi-linear hyperbolic systems with highly oscillatory solutions. The main feature of this modified particle method is that we do not require different families of characteristics to meet at one point. In the modified particle method, we update the ith component of the solution along its own characteristics, and interpolate the other components of the solution from their own characteristic points to the ith characteristic point. We prove the convergence of the modified particle method essentially independent of the small scale for the variable coefficient Carleman model. The same result also applies to the non-resonant Broadwell model. Numerical evidence suggests that the modified particle method also converges essentially independent of the small scale for the original Broadwell model if a cubic spline interpolation is used
Dynamically encircling exceptional points: in situ control of encircling loops and the role of the starting point
The most intriguing properties of non-Hermitian systems are found near the
exceptional points (EPs) at which the Hamiltonian matrix becomes defective. Due
to the complex topological structure of the energy Riemann surfaces close to an
EP and the breakdown of the adiabatic theorem due to non-Hermiticity, the state
evolution in non-Hermitian systems is much more complex than that in Hermitian
systems. For example, recent experimental work [Doppler et al. Nature 537, 76
(2016)] demonstrated that dynamically encircling an EP can lead to chiral
behaviors, i.e., encircling an EP in different directions results in different
output states. Here, we propose a coupled ferromagnetic waveguide system that
carries two EPs and design an experimental setup in which the trajectory of
state evolution can be controlled in situ using a tunable external field,
allowing us to dynamically encircle zero, one or even two EPs experimentally.
The tunability allows us to control the trajectory of encircling in the
parameter space, including the size of the encircling loop and the starting/end
point. We discovered that whether or not the dynamics is chiral actually
depends on the starting point of the loop. In particular, dynamically
encircling an EP with a starting point in the parity-time-broken phase results
in non-chiral behaviors such that the output state is the same no matter which
direction the encircling takes. The proposed system is a useful platform to
explore the topology of energy surfaces and the dynamics of state evolution in
non-Hermitian systems and will likely find applications in mode switching
controlled with external parameters.Comment: 15 pages, 11 figure
EFFECT OF EXHAUSTIVE UPHILL RUNNING ON KNEE JOINT MOTION DURING THE STANCE PHASE OF RUNNING
The purpose of this study was to imitate an exhaustive outdoor mountain road uphill running and investigate the effect on knee joint motion angles during the stance phase of running. Knee joint kinematical data collected from 8 male recreational runners running at 10 km/hr on a level treadmill prior to and following exhaustive uphill running revealed differences in flexion angles. These results demonstrated that exhaustive running can have an effect on knee joint running movement pattern. Due to these findings, the human natural movement control may be adjusted and the maintenance of preferred or optimal movement path costs more efforts which possibly play a role in many common lower extremity running injuries. This relevance may be applied to the future designing of assistive performance control shoes
Topology design and performance analysis of an integrated communication network
A research study on the topology design and performance analysis for the Space Station Information System (SSIS) network is conducted. It is begun with a survey of existing research efforts in network topology design. Then a new approach for topology design is presented. It uses an efficient algorithm to generate candidate network designs (consisting of subsets of the set of all network components) in increasing order of their total costs, and checks each design to see if it forms an acceptable network. This technique gives the true cost-optimal network, and is particularly useful when the network has many constraints and not too many components. The algorithm for generating subsets is described in detail, and various aspects of the overall design procedure are discussed. Two more efficient versions of this algorithm (applicable in specific situations) are also given. Next, two important aspects of network performance analysis: network reliability and message delays are discussed. A new model is introduced to study the reliability of a network with dependent failures. For message delays, a collection of formulas from existing research results is given to compute or estimate the delays of messages in a communication network without making the independence assumption. The design algorithm coded in PASCAL is included as an appendix
Necessary and sufficient conditions for local creation of quantum discord
We show that a local channel cannot create quantum discord (QD) for zero QD
states of size if and only if either it is a completely decohering
channel or it is a nontrivial isotropic channel. For the qubit case this
propertiy is additionally characteristic to the completely decohering channel
or the commutativity-preserving unital channel. In particular, the exact forms
of the completely decohering channel and the commutativity-preserving unital
qubit channel are proposed. Consequently, our results confirm and improve the
conjecture proposed by X. Hu et al. for the case of and improve the
result proposed by A. Streltsov et al. for the qubit case. Furthermore, it is
shown that a local channel nullifies QD in any state if and only if it is a
completely decohering channel. Based on our results, some protocols of quantum
information processing issues associated with QD, especially for the qubit
case, would be experimentally accessible.Comment: 8 page
A new multiscale finite element method for high-contrast elliptic interface problems
We introduce a new multiscale finite element method which is
able to accurately capture solutions of elliptic interface problems with high
contrast coefficients by using only coarse quasiuniform meshes, and without
resolving the interfaces. A typical application would be the modelling of flow
in a porous medium containing a number of inclusions of low (or high) permeability
embedded in a matrix of high (respectively low) permeability. Our
method is H^1- conforming, with degrees of freedom at the nodes of a triangular
mesh and requiring the solution of subgrid problems for the basis functions on
elements which straddle the coefficient interface but which use standard linear
approximation otherwise. A key point is the introduction of novel coefficientdependent
boundary conditions for the subgrid problems. Under moderate
assumptions, we prove that our methods have (optimal) convergence rate of
O(h) in the energy norm and O(h^2) in the L_2 norm where h is the (coarse)
mesh diameter and the hidden constants in these estimates are independent
of the “contrast” (i.e. ratio of largest to smallest value) of the PDE coefficient.
For standard elements the best estimate in the energy norm would be
O(h^(1/2−ε)) with a hidden constant which in general depends on the contrast.
The new interior boundary conditions depend not only on the contrast of the
coefficients, but also on the angles of intersection of the interface with the
element edges
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