Theory of electron transport in normal metal/superconductor junctions

On the basis of the Keldysh method of non-equilibrium systems, we develop a theory of electron tunneling in normal-metal/superconductor junctions. By using the tunneling Hamiltonian model (being appropriate for the tight-binding systems), the tunneling current can be exactly obtained in terms of the equilibrium Green functions of the normal metal and the superconductor. We calculate the conductance of various junctions. The discrepancy between the present treatment and the well-known scheme by Blonder, Tinkham, and Klapwijk is found for some junctions of low interfacial potential barrier.Comment: 5 pages, 4 figure

octonionic Dirac operators in bounded lattices: convergence and Plemlj projections

This article explores octonionic analysis on the lattice $\mathbb Z^8$, emphasizing the octonionic discrete Cauchy integral within a bounded domain, the Sokhotski-Plemelj jump formulas, and the convergence of discrete regular functions. We address the challenge of articulating the discrete Cauchy-Pompeiu integral formula, particularly the complexities tied to the associator of octonions. Adopting an innovative approach, we assimilate complicating terms into integral kernels, leading to distinct surface and volume kernels. A new'star product' arises in handling octonionic function multiplications. Our study connects closely with the Teodorescu operator and singular kernel management, utilizing a Fourier variant with 24 unique singular points. Drawing from the foundational work of Shivakumar and Wong about the asymptotic expansion of the Fourier transform, we bridge the relationship between the Cauchy and Teodorescu integrals. This allows us to provide quantitative estimates for these kernels, which prove to be pivotal in the theory of discrete regular extensions. The research culminates in the revelation that a continuous octonionic function is regular precisely when it is a scale limit of discrete regular functions

The twisted group algebra structure of the Cayley-Dickson algebra

The Cayley-Dickson algebra has long been a challenge due to the lack of an explicit multiplication table. Despite being constructible through inductive construction, its explicit structure has remained elusive until now. In this article, we propose a solution to this long-standing problem by revealing the Cayley-Dickson algebra as a twisted group algebra with an explicit twist function $\sigma(A,B)$. We show that this function satisfies the equation $$e_Ae_B=(-1)^{\sigma(A,B)}e_{A\oplus B}$$ and provide a formula for the relationship between the Cayley-Dickson algebra and split Cayley-Dickson algebra, thereby giving an explicit expression for the twist function of the split Cayley-Dickson algebra. Our approach not only resolves the lack of explicit structure for the Cayley-Dickson algebra and split Cayley-Dickson algebra but also sheds light on the algebraic structure underlying this fundamental mathematical object

User-Friendly Covariance Estimation for Heavy-Tailed Distributions

We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we introduce element-wise and spectrum-wise truncation operators, as well as their $M$-estimator counterparts, to robustify the sample covariance matrix. Different from the classical notion of robustness that is characterized by the breakdown property, we focus on the tail robustness which is evidenced by the connection between nonasymptotic deviation and confidence level. The key observation is that the estimators needs to adapt to the sample size, dimensionality of the data and the noise level to achieve optimal tradeoff between bias and robustness. Furthermore, to facilitate their practical use, we propose data-driven procedures that automatically calibrate the tuning parameters. We demonstrate their applications to a series of structured models in high dimensions, including the bandable and low-rank covariance matrices and sparse precision matrices. Numerical studies lend strong support to the proposed methods.Comment: 56 pages, 2 figure

Numerical Simulation of Compressible Reactive Flows

Numerical simulation has been widely employed to investigate the compressible flows since it is difficult to carry out the experimental measurements, especially in the reactive flows. The shock-wave capturing scheme will be necessary for resolving the compressible flows, and moreover the careful treatments of chemical reaction should be considered for proceeding numerical simulation stable and fast. Recently, the present authors have tried to establish a high-resolution numerical solver for computing the compressible reactive flows. This chapter presents the numerical procedures acquired in this solver for computing the fluxes using weighted essentially non-oscillatory (WENO) scheme, dealing with chemical stiffness problems, and tracing droplets and their interaction with the compressible fluids. As examples, the Taylor-Green vortex (TGV) problem considering the passive scalar mixing, the spatially developing reactive mixing layer flows taken gas-phase hydrogen, and liquid n-decane as fuel are simulated, respectively. Many important characteristics of flow, flame, and ignition are analyzed under the supersonic condition

Investigation of the effects of temperature and ions on the interaction between ECG and BSA by the fluorescence quenching method

The effects of temperature and common ions on binding (-)-epicatechin gallate (ECG) to bovine serum albumin (BSA) are investigated. The binding constants (Ka) between ECG and BSA are 1.20 Ч 106 (17°C), 1.38 Ч 106 (27°C), and 5.69 x 106 L mol-1 (37°C), and the number of binding sites (n) were 1.14, 1.15, and 1.26, respectively. These results showed that the increasing temperature improves the stability of the ECG-BSA system, which results in a higher binding constant and the number of binding sites of the ECG-BSA system. The presence of Co2+ and Zn2+ ions decreased the binding constants (Ka) and the number of binding sites (n) of ECG-BSA complex. However, the presence of Cu2+ and Ni2+ increased the affinity of ECG for BSA largely. The positive ΔH and positive ΔS indicated that hydrophobic forces might play a major role in the binding between ECG and BSA

A LES Study on Passive Mixing in Supersonic Shear Layer Flows Considering Effects of Baffle Configuration

Under the background of dual combustor ramjet (DCR), a numerical investigation of supersonic mixing layer was launched, focused on the mixing enhancement method of applying baffles with different geometric configurations. Large eddy simulation with high order schemes, containing a fifth-order hybrid WENO compact scheme for the convective flux and sixth-order compact one for the viscous flux, was utilized to numerically study the development of the supersonic mixing layer. The supersonic cavity flow was simulated and the cavity configuration could influence the mixing characteristics, since the impingement process of large scale structures formed inside the cavity could raise the vorticity and promote the mixing. The effect of baffle's configurations on the mixing process was analyzed by comparing the flow properties, mixing efficiency, and total pressure loss. The baffle could induce large scale vortexes, promote the mixing layer to lose its stability easily, and then lead to the mixing efficiency enhancement. However, the baffle could increase the total pressure loss. The present investigation could provide guidance for applying new passive mixing enhancement methods for the supersonic mixing

A close phylogenetic relationship between Sipuncula and Annelida evidenced from the complete mitochondrial genome sequence of Phascolosoma esculenta

<p>Abstract</p> <p>Background</p> <p>There are many advantages to the application of complete mitochondrial (mt) genomes in the accurate reconstruction of phylogenetic relationships in Metazoa. Although over one thousand metazoan genomes have been sequenced, the taxonomic sampling is highly biased, left with many phyla without a single representative of complete mitochondrial genome. Sipuncula (peanut worms or star worms) is a small taxon of worm-like marine organisms with an uncertain phylogenetic position. In this report, we present the mitochondrial genome sequence of <it>Phascolosoma esculenta</it>, the first complete mitochondrial genome of the phylum.</p> <p>Results</p> <p>The mitochondrial genome of <it>P</it>.<it>esculenta </it>is 15,494 bp in length. The coding strand consists of 32.1% A, 21.5% C, 13.0% G, and 33.4% T bases (AT = 65.5%; AT skew = -0.019; GC skew = -0.248). It contains thirteen protein-coding genes (PCGs) with 3,709 codons in total, twenty-two transfer RNA genes, two ribosomal RNA genes and a non-coding AT-rich region (AT = 74.2%). All of the 37 identified genes are transcribed from the same DNA strand. Compared with the typical set of metazoan mt genomes, sipunculid lacks <it>trnR </it>but has an additional <it>trnM</it>. Maximum Likelihood and Bayesian analyses of the protein sequences show that Myzostomida, Sipuncula and Annelida (including echiurans and pogonophorans) form a monophyletic group, which supports a closer relationship between Sipuncula and Annelida than with Mollusca, Brachiopoda, and some other lophotrochozoan groups.</p> <p>Conclusion</p> <p>This is the first report of a complete mitochondrial genome as a representative within the phylum Sipuncula. It shares many more similar features with the four known annelid and one echiuran mtDNAs. Firstly, sipunculans and annelids share quite similar gene order in the mitochondrial genome, with all 37 genes located on the same strand; secondly, phylogenetic analyses based on the concatenated protein sequences also strongly support the sipunculan + annelid clade (including echiurans and pogonophorans). Hence annelid "key-characters" including segmentation may be more labile than previously assumed.</p

Exact solutions of embedding the four-dimensional perfect fluid in a five- or higher-dimensional Einstein spacetime and the cosmological interpretations

We investigate an exact solution that describes the embedding of the four-dimensional (4D) perfect fluid in a five-dimensional (5D) Einstein spacetime. The effective metric of the 4D perfect fluid as a hypersurface with induced matter is equivalent to the Robertson-Walker metric of cosmology. This general solution shows interconnections among many 5D solutions, such as the solution in the braneworld scenario and the topological black hole with cosmological constant. If the 5D cosmological constant is positive, the metric periodically depends on the extra dimension. Thus we can compactify the extra dimension on $S^1$ and study the phenomenological issues. We also generalize the metric ansatz to the higher-dimensional case, in which the 4D part of the Einstein equations can be reduced to a linear equation.Comment: 8 pages, 1 figures; v2: minor errors corrected; v3: references added; v4: matches the version to appear in PL