8,344 research outputs found
Riemann-Liouville Fractional Cosine Functions
In this paper, a new notion, named Riemann-Liouville fractional cosine
function is presented. It is proved that a Riemann-Liouville -order
fractional cosine function is equivalent to Riemann-Liouville -order
fractional resolvents introduced in [Z.D. Mei, J.G. Peng, Y. Zhang, Math.
Nachr. 288, No. 7, 784-797 (2015)]
Early and late stage profiles for a new chemotaxis model with density-dependent jump probability and quorum-sensing mechanisms
In this paper, we derive a new chemotaxis model with degenerate diffusion and
density-dependent chemotactic sensitivity, and we provide a more realistic
description of cell migration process for its early and late stages. Different
from the existing studies focusing on the case of non-degenerate diffusion, the
new model with degenerate diffusion causes us some essential difficulty on the
boundedness estimates and the propagation behavior of its compact support. In
the presence of logistic damping, for the early stage before tumour cells
spread to the whole body, we first estimate the expanding speed of tumour
region as for . Then, for the late stage of
cell migration, we further prove that the asymptotic profile of the original
system is just its corresponding steady state. The global convergence of the
original weak solution to the steady state with exponential rate
for some is also obtained
Gapped spin liquid with -topological order for kagome Heisenberg model
We apply symmetric tensor network state (TNS) to study the nearest neighbor
spin-1/2 antiferromagnetic Heisenberg model on Kagome lattice. Our method keeps
track of the global and gauge symmetries in TNS update procedure and in tensor
renormalization group (TRG) calculation. We also introduce a very sensitive
probe for the gap of the ground state -- the modular matrices, which can also
determine the topological order if the ground state is gapped. We find that the
ground state of Heisenberg model on Kagome lattice is a gapped spin liquid with
the -topological order (or toric code type), which has a long
correlation length unit cell length. We justify that the TRG
method can handle very large systems with over thousands of spins. Such a long
explains the gapless behaviors observed in simulations on smaller systems
with less than 300 spins or shorter than 10 unit cell length. We also discuss
experimental implications of the topological excitations encoded in our
symmetric tensors.Comment: 10 pages, 7 figure
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