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-$M_*$) 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 $z>2$, and let it evolve down to the present time according to the observed (SFR-$M_*$) relation. In this study, we use two different sets of SMFs and two SFR-$M_*$ 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-$M_*$ 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 $\log M_* < 11.2$, our prediction at z=0.1 is close to \citet{li-white09} data, but the high-mass end ($\log M_* > 11.2$) 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 $\mu_{B}$. We calculate various thermodynamic observables at $\mu_{B}=0$ GeV in TVDWHRG model. An improved agreement with the lattice data by TVDWHRG model in the crossover region ($T\sim 0.16-0.19$ 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 ($\eta$), scaled thermal ($\lambda/T^{2}$) and electrical ($\sigma_{el}/T$ conductivities in IHRG model at different $\mu_{B}$, 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