3,875 research outputs found
Optimal Control Computation via Evolution Partial Differential Equation with Arbitrary Definite Conditions
The compact Variation Evolving Method (VEM) that originates from the
continuous-time dynamics stability theory seeks the optimal solutions with
variation evolution principle. It is further developed to be more flexible in
solving the Optimal Control Problems (OCPs), by relaxing the definite
conditions from a feasible solution to an arbitrary one for the derived
Evolution Partial Differential Equation (EPDE). To guarantee the validity, an
unconstrained Lyapunov functional that has the same minimum as the original OCP
is constructed, and it ensures the evolution towards the optimal solution from
infeasible solutions. With the semi-discrete method, the EPDE is transformed to
the finite-dimensional Initial-value Problem (IVP), and then solved with common
Ordinary Differential Equation (ODE) numerical integration methods.
Illustrative examples are presented to show the effectiveness of the proposed
method.Comment: arXiv admin note: substantial text overlap with arXiv:1709.02242,
arXiv:1711.0299
Convolutional neural networks with fractional order gradient method
This paper proposes a fractional order gradient method for the backward
propagation of convolutional neural networks. To overcome the problem that
fractional order gradient method cannot converge to real extreme point, a
simplified fractional order gradient method is designed based on Caputo's
definition. The parameters within layers are updated by the designed gradient
method, but the propagations between layers still use integer order gradients,
and thus the complicated derivatives of composite functions are avoided and the
chain rule will be kept. By connecting every layers in series and adding loss
functions, the proposed convolutional neural networks can be trained smoothly
according to various tasks. Some practical experiments are carried out in order
to demonstrate fast convergence, high accuracy and ability to escape local
optimal point at last
Bragg solitons in an electromagnetically induced transparency medium
In this Letter we discuss the possibility of producing Bragg solitons in an
electromagnetically induced transparency medium. We show that this coherent
medium can be engineered to be a Bragg grating with a large Kerr nonlinearity
through proper arrangements of light fields. Unlike in previous studies, the
parameters of the medium can be easily controlled through adjusting the
intensities and detunings of lasers. Thus this scheme may provide an
opportunity to study the dynamics of Bragg solitons. And doing experiments with
low power lights is possible.Comment: 4 pages, 3 figure
Energy band of graphene ribbons under the tensile force
According to the tight-binding approximation, we investigate the electronic
structures of graphene ribbons with zigzag shaped edges (ZGRs) and armchair
shaped edges (AGRs) drawn by the tensile force, and obtain the analytic
relations between the energy bands of pi-electrons in ZGR, AGR and the tensile
force based on only considering the nearest-neighbor interaction and the
hydrogen-like atomic wave function is considered as pi-electron wave function.
Importantly, we find the tensile force can open an energy gap at the K point
for ZGR and AGR, and the force perpendicular to the zigzag edges can open
energy gap more easily besides the gap values of ZGR and AGR at the K point
both increase as the tensile force increases
Two-dimensional quantum walk with non-Hermitian skin effects
We construct a two-dimensional, discrete-time quantum walk exhibiting
non-Hermitian skin effects under open-boundary conditions. As a confirmation of
the non-Hermitian bulk-boundary correspondence, we show that the emergence of
topological edge states are consistent with Floquet winding numbers calculated
using a non-Bloch band theory invoking time-dependent generalized Billouin
zones. Further, the non-Bloch topological invariants associated with
quasienergy bands are captured by a non-Hermitian local Chern marker in real
space, defined through local biorthogonal eigen wave functions of the
non-unitary Floquet operator. Our work would stimulate further studies of
non-Hermitian Floquet topological phases where skin effects play a key role.Comment: 8 pages, 4 figure
Matching the Quasi Meson Distribution Amplitude in RI/MOM scheme
The -dependence of light-cone distribution amplitude (LCDA) can be
directly calculated from a quasi distribution amplitude (DA) in lattice QCD
within the framework of large-momentum effective theory (LaMET). In this paper,
we study the one-loop renormalization of the quasi-DA in the
regularization-independent momentum subtraction (RI/MOM) scheme. The
renormalization factor for the quasi parton distribution function can be used
to renormalize the quasi-DA provided that they are implemented on lattice and
in perturbation theory in the same manner. We derive the one-loop matching
coefficient that matches quasi-DA in the RI/MOM scheme onto LCDA in the
scheme. Our result provides the crucial step to extract the
LCDAs from lattice matrix elements of quasi-DAs.Comment: 7 pages, 0 figure
Effects of temperature gradient on the interface microstructure and diffusion of diffusion couples: phase-field simulation
The temporal interface microstructure and diffusion in the diffusion couples
with the mutual interactions of temperature gradient, concentration difference
and initial aging time of the alloys were studied by phase-field simulation,
the diffusion couples are produced by the initial aged spinodal alloys with
different compositions. Temporal composition evolution and volume fraction of
the separated phase indicates the element diffusion direction through the
interface under the temperature gradient. The increased temperature gradient
induces a wide single-phase region at two sides of the interface. The uphill
diffusion proceeds through the interface, no matter the diffusion directions
are up or down to the temperature gradient. For an alloy with short initial
aging time, phase transformation accompanying the interdiffusion results in the
straight interface with the single-phase regions at both sides. Comparing with
the temperature gradient, composition difference of diffusion couple and
initial aging time of the alloy show greater effect on the diffusion and
interface microstructure.Comment: 18 pages,11 figure
Adaptive backstepping control for FOS with nonsmooth nonlinearities
This paper proposes an original solution to input saturation and dead zone of
fractional order system. To overcome these nonsmooth nonlinearities, the
control input is decomposed into two independent parts by introducing an
intermediate variable, and thus the problem of dead zone and saturation
transforms into the problem of disturbance and saturation afterwards. With the
procedure of fractional order adaptive backstepping controller design, the
bound of disturbance is estimated, and saturation is compensated by the virtual
signal of an auxiliary system as well. In spite of the existence of nonsmooth
nonlinearities, the output is guaranteed to track the reference signal
asymptotically on the basis of our proposed method. Some simulation studies are
carried out in order to demonstrate the effectiveness of method at last
Manipulating quantum states with aspheric lenses
We present an experimental demonstration to manipulate the width and position
of the down-converted beam waist. Our results can be used to engineer the
two-photon orbital angular momentum (OAM) entangled states (such as
concentrating OAM entangled states) and generate Hermite-Gaussian (HG) modes
entangled states.Comment: Revised edition, to appear in PL
Three-observer classical dimension witness violation with weak measurement
Based on weak measurement technology, we propose the first three-observer
dimension witness protocol in a prepare-and-measure setup. By applying the
dimension witness inequality based on the quantum random access code and the
nonlinear determinant value, we demonstrate that double classical dimension
witness violation is achievable if we choose appropriate weak measurement
parameters. Analysis of the results will shed new light on the interplay
between the multi-observer quantum dimension witness and the weak measurement
technology, which can also be applied in the generation of
semi-device-independent quantum random numbers and quantum key distribution
protocols
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