13,239 research outputs found
Riemann-Hilbert method for N-soliton solution of the coupled Hirota system in nonlinear fiber
Under investigation in this work is the coupled Hirota system arising in
nonlinear fiber. The spectral analysis of the Lax pair is first carried out and
a Riemann-Hilbert problem is described. Then in the framework of the obtained
Riemann-Hilbert problem with the reflectionless case, N-soliton solution is
presented for the coupled Hirota system. Finally, via proper choices of the
involved parameters, a few plots are made to exhibit the localized structures
and dynamic characteristics of one-soliton solution.Comment: 10 page
Frobenius pull-back and stability of vector bundles in characteristic 2
Let X be a smooth projective curve of genus g>1 over an algebraically closed
field of characteristic 2. Pull-back by the (absolute) Frobenius on X only
defines a rational morphism on the moduli scheme of rank-2 vector bundles on X,
because the Frobenius pull-back may destory stability of a vector bundle. This
paper introduces and studies a Harder-Narasimhan type stratification on the
moduli scheme and proves that the family of semi-stable rank-2 vector bundles
(with a fixed degree) whose Frobenius pull-back are not semi-stable is
parameterized by an irreducible subscheme of dimension 3g-4.Comment: pdf, 9 page
Constructing Riemann-Hilbert problem and multi-soliton solutions for the N-coupled Hirota equations in an optical fiber
This paper focuses on investigation of the N-coupled Hirota equations arising
in an optical fiber. Starting from analyzing the spectral problem, a kind of
matrix Riemann-Hilbert problem is formulated strictly on the real axis. Then
based on the resulting matrix Riemann-Hilbert problem under the constraint of
no reflection, multi-soliton solutions to the N-coupled Hirota equations are
presented explicitly.Comment: 9 page
"Latent heat" of first-order varying pressure transitions
We consider the energy release associated with first-order transition by
Gibbs construction and present such energy release as an accumulation of a
series of tiny binding energy differences between over-compressed states and
stable ones. Universal formulae for the energy release from one homogeneous
phase to the other is given. We find the energy release per converted particle
varies with number density. As an example, the deconfinement phase transition
at supranuclear densities is discussed in detail. The mean energy release per
converted baryon is of order 0.1MeV in RMF theory and MIT bag descriptions for
hadronic matter and strange quark matter for a wider parameter region.Comment: 14pages, 6figure
Growth strategy of microbes on mixed carbon sources
A classic problem in microbiology is that bacteria display two types of
growth behavior when cultured on a mixture of two carbon sources: the two
sources are sequentially consumed one after another (diauxie) or they are
simultaneously consumed (co-utilization). The search for the molecular
mechanism of diauxie led to the discovery of the lac operon. However, questions
remain as why microbes would bother to have different strategies of taking up
nutrients. Here we show that diauxie versus co-utilization can be understood
from the topological features of the metabolic network. A model of optimal
allocation of protein resources quantitatively explains why and how the cell
makes the choice. In case of co-utilization, the model predicts the percentage
of each carbon source in supplying the amino acid pools, which is
quantitatively verified by experiments. Our work solves a long-standing puzzle
and provides a quantitative framework for the carbon source utilization of
microbes.Comment: Manuscript 25 pages 4 Figures, Supplemental Information 52 pages, 7
SI Tables, 7 SI Figure
Constraints on the Evolution of the Galaxy Stellar Mass Function I: Role of Star Formation, Mergers and Stellar Stripping
We study the connection between the observed star formation rate-stellar mass
(SFR-) relation and the evolution of the stellar mass function (SMF) by
means of a Subhalo Abundance Matching technique coupled to merger trees
extracted from a N-body simulation. Our approach, which considers both galaxy
mergers and stellar stripping, is to force the model to match the observed SMF
at redshift , and let it evolve down to the present time according to the
observed (SFR-) relation. In this study, we use two different sets of SMFs
and two SFR- relations: a simple power law and a relation with a
mass-dependent slope. Our analysis shows that the evolution of the SMF is more
consistent with a SFR- relation with a mass-dependent slope, in agreement
with predictions from other models of galaxy evolution and recent observations.
In order to fully and realistically describe the evolution of the SMF, both
mergers and stellar stripping must be considered, and we find that both have
almost equal effects on the evolution of SMF at the massive end. Taking into
account the systematic uncertainties in the observed data, the high-mass end of
the SMF obtained by considering stellar stripping results in good agreement
with recent observational data from the Sloan Digital Sky Survey (SDSS). At
, our prediction at z=0.1 is close to \citet{li-white09} data,
but the high-mass end () is in better agreement with
\citet{dsouza15} data which account for more massive galaxies.Comment: 16 pages, 9 figures. Accepted by Ap
In-medium effect on the thermodynamics and transport coefficients in van der Waals hadron resonance gas
An extension of the van der Waals hadron resonance gas (VDWHRG) model which
includes in-medium thermal modification of hadron masses, the TVDWHRG model, is
considered in this paper. Based on the 2+1 flavor Polyakov Linear Sigma
Model(PLSM) and the scaling mass rule for hadrons we obtain the temperature
behavior of all hadron masses for different fixed baryon chemical potentials
. We calculate various thermodynamic observables at GeV in
TVDWHRG model. An improved agreement with the lattice data by TVDWHRG model in
the crossover region ( GeV) is observed as compared to those
by VDWHRG and Ideal HRG (IHRG) models. We further discuss the effects of
in-medium modification of hadron masses and VDW interactions on the transport
coefficients such as shear viscosity (), scaled thermal ()
and electrical ( conductivities in IHRG model at different
, by utilizing quasi-particle kinetic theory with relaxation time
approximation.Comment: 17 pages, 13 figure
Sparse-View CT Reconstruction via Convolutional Sparse Coding
Traditional dictionary learning based CT reconstruction methods are
patch-based and the features learned with these methods often contain shifted
versions of the same features. To deal with these problems, the convolutional
sparse coding (CSC) has been proposed and introduced into various applications.
In this paper, inspired by the successful applications of CSC in the field of
signal processing, we propose a novel sparse-view CT reconstruction method
based on CSC with gradient regularization on feature maps. By directly working
on whole image, which need not to divide the image into overlapped patches like
dictionary learning based methods, the proposed method can maintain more
details and avoid the artifacts caused by patch aggregation. Experimental
results demonstrate that the proposed method has better performance than
several existing algorithms in both qualitative and quantitative aspects
High temperature superconducting phase of HBr under pressure predicted by first-principles calculations
The high pressure phases of HBr are explored with an ab initio crystal
structure search. By taking into account the contribution of zero-point energy
(ZPE), we find that the P4/nmm phase of HBr is thermodynamically stable in the
pressure range from 150 to 200 GPa. The superconducting critical temperature
(Tc) of P4/nmm HBr is evaluated to be around 73 K at 170 GPa, which is the
highest record so far among binary halogen hydrides. Its Tc can be further
raised to around 95K under 170 GPa if half of the bromine atoms in the P4/nmm
HBr are substituted by the lighter chlorine atoms. Our study shows that, in
addition to lower mass, higher coordination number, shorter bonds, and more
highly symmetric environment for the hydrogen atoms are important factors to
enhance the superconductivity in hydrides.Comment: 8 pages, 7 figures. Accepted by PRB. (Email: [email protected]
On vector bundles destabilized by Frobenius pull-back
Let X be an irreducible smooth projective curve of genus at least two over an
algebraically closed field k of characteristic p>0. In this paper we study the
natural stratification, defined using the absolute Frobenius of X, on the
moduli space of vector bundles on X of suitable rank. In characteristic two we
provide a complete classification of rank two semi-stable vector bundles whose
Frobenius pull-back is not semi-stable. We also obtain fairly good information
about the strata of the Frobenius stratification, including the irreducibility
and the dimension of each non-empty Frobenius stratum. In particular we show
that the locus of Frobenius destabilized bundles has dimension 3g-4 in the
moduli space of semi-stable bundles of rank two. We also construct stable
bundles that are destabilized by Frobenius in the following situations:
characteristic p=2 and rank four, (2) characteristic p=rank=3, (3)
characteristic p=rank=5 and g at least three.
We also explore (in any characteristic) the connection between Frobenius
destabilized bundles and (pre)-opers, this approach allows us to reinterpret
some of our results in terms of pre-opers and also allows us to construct
Frobenius destablised bundles from certain pre-opers (or opers).
The other result we obtain is (for characteristic two): we show that the
Gunning bundle descends under Frobenius when genus g is even. If g is odd, then
the Gunning bundle twisted by any odd degree line bundle also descends.Comment: 16 page
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