8,384 research outputs found
Magnetostatics of Magnetic Skyrmion Crystals
Magnetic skyrmion crystals are topological magnetic textures arising in the
chiral ferromagnetic materials with Dzyaloshinskii-Moriya interaction. The
magnetostatic fields generated by magnetic skyrmion crystals are first studied
by micromagnetic simulations. For N\'eel-type skyrmion crystals, the fields
will vanish on one side of the crystal plane, which depend on the helicity;
while for Bloch-type skyrmion crystals, the fields will distribute over both
sides, and are identical for the two helicities. These features and the
symmetry relations of the magetostatic fields are understood from the magnetic
scalar potential and magnetic vector potential of the hybridized triple-Q
state. The possibility to construct magnetostatic field at nanoscale by
stacking chiral ferromagnetic layers with magnetic skyrmion crystals is also
discussed, which may have potential applications to trap and manipulate neutral
atoms with magnetic moments.Comment: 5 pages, 2 figure
Mean-field backward stochastic differential equations on Markov chains
In this paper, we deal with a class of mean-field backward stochastic
differential equations (BSDEs) related to finite state, continuous time Markov
chains. We obtain the existence and uniqueness theorem and a comparison theorem
for solutions of one-dimensional mean-field BSDEs under Lipschitz condition
Stochastic viscosity solution for stochastic PDIEs with nonlinear Neumann boundary condition
This paper is an attempt to extend the notion of viscosity solution to
nonlinear stochastic partial differential integral equations with nonlinear
Neumann boundary condition. Using the recently developed theory on generalized
backward doubly stochastic differential equations driven by a L\'evy process,
we prove the existence of the stochastic viscosity solution, and further extend
the nonlinear Feynman-Kac formula.Comment: 16 pag
Control of Ultracold Atoms with a Chiral Ferromagnetic Film
We show that the magnetic field produced by a chiral ferromagnetic film can
be applied to control ultracold atoms. The film will act as a magnetic mirror
or a reflection grating for ultracold atoms when it is in the helical phase or
the skyrmion crystal phase respectively. By applying a bias magnetic field and
a time-dependent magnetic field, one-dimensional or two-dimensional magnetic
lattices including honeycomb, Kagome, triangular types can be created to trap
the ultracold atoms. We have also discussed the trapping height, potential
barrier, trapping frequency, and Majorana loss rate for each lattice. Our
results suggest that the chiral ferromagnetic film can be a platform to develop
artificial quantum systems with ultracold atoms based on modern spintronics
technologies.Comment: 9 pages, 6 figure
Non-smooth analysis method in optimal investment- a BSDE approach
In this paper, our aim is to investigate necessary conditions for optimal
investment. We model the wealth process by Backward differential stochastic
equations (shortly for BSDE) with or without constraints on wealth and
portfolio process. The constraints can be very general thanks the non-smooth
analysis method we adopted
Deep Competitive Pathway Networks
In the design of deep neural architectures, recent studies have demonstrated
the benefits of grouping subnetworks into a larger network. For examples, the
Inception architecture integrates multi-scale subnetworks and the residual
network can be regarded that a residual unit combines a residual subnetwork
with an identity shortcut. In this work, we embrace this observation and
propose the Competitive Pathway Network (CoPaNet). The CoPaNet comprises a
stack of competitive pathway units and each unit contains multiple parallel
residual-type subnetworks followed by a max operation for feature competition.
This mechanism enhances the model capability by learning a variety of features
in subnetworks. The proposed strategy explicitly shows that the features
propagate through pathways in various routing patterns, which is referred to as
pathway encoding of category information. Moreover, the cross-block shortcut
can be added to the CoPaNet to encourage feature reuse. We evaluated the
proposed CoPaNet on four object recognition benchmarks: CIFAR-10, CIFAR-100,
SVHN, and ImageNet. CoPaNet obtained the state-of-the-art or comparable results
using similar amounts of parameters. The code of CoPaNet is available at:
https://github.com/JiaRenChang/CoPaNet.Comment: To appear in ACML1
Reflected backward stochastic differential equations with jumps in time-dependent random convex domains
In this paper, we study a class of multi-dimensional reflected backward
stochastic differential equations when the noise is driven by a Brownian motion
and an independent Poisson point process, and when the solution is forced to
stay in a time-dependent adapted and continuous convex domain . We prove the existence an uniqueness of the solution, and we also
show that the solution of such equations may be approximated by backward
stochastic differential equations with jumps reflected in appropriately defined
discretizations of , via a penalization method.Comment: 43 pages. arXiv admin note: text overlap with arXiv:1307.2124 by
other author
Continuous dependence property of BSDE with constraints
In this paper, we study continuous properties of adapted solutions for
backward stochastic differential equations with constraints (CBSDEs in short).
Comparing with many existing literatures about this topic, our case is very
general in the sense that constraints are formulated by general non-negative
real functions. In general case, we proved a continuous property from below and
a lower semi-continuous property of the minimal super-solution of CBSDE in its
effective domain. Furthermore, in the special convex case, we obtained a
continuous property with the help of convex analysis
Mean-field backward stochastic differential equations with subdifferrential operator and its applications
In this paper, we deal with a class of mean-field backward stochastic
differential equations with subdifferrential operator corresponding to a lower
semi-continuous convex function. By means of Yosida approximation, the
existence and uniqueness of the solution is established. As an application, we
give a probability interpretation for the viscosity solutions of a class of
nonlocal parabolic variational inequalities
Multivalued backward doubly stochastic differential equations with time delayed coefficients
In this paper, we deal with a class of multivalued backward doubly stochastic
differential equations with time delayed coefficients. Based on a slight
extension of the existence and uniqueness of solutions for backward doubly
stochastic differential equations with time delayed coefficients, we establish
the existence and uniqueness of solutions for these equations by means of
Yosida approximation.Comment: 12 page
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