Conformation of circular DNA in two dimensions

The conformation of circular DNA molecules of various lengths adsorbed in a 2D conformation on a mica surface is studied. The results confirm the conjecture that the critical exponent nu is topologically invariant and equal to the self-avoiding walk value (in the present case nu=3/4), and that the topology and dimensionality of the system strongly influence the crossover between the rigid regime and the self-avoiding regime at a scale L approximately 7l{p}. Additionally, the bond correlation function scales with the molecular length L as predicted. For molecular lengths L相似文献   

Modeling diffusion of adsorbed polymer with explicit solvent

Computer simulations of a polymer chain of length N strongly adsorbed at the solid-liquid interface in the presence of explicit solvent are used to delineate the factors affecting the N dependence of the polymer lateral diffusion coefficient, D(||). We find that surface roughness has a large influence, and D(||) scales as D(||) approximately N(-x), with x approximately 3/4 and x approximately 1 for ideal smooth and corrugated surfaces, respectively. The first result is consistent with the hydrodynamics of a "particle" of radius of gyration R(G) approximately N(nu) (nu=0.75) translating parallel to a planar interface, while the second implies that the friction of the adsorbed chains dominates. These results are discussed in the context of recent measurements.     

Observable N-N oscillation in high scale seesaw models

We discuss a realistic high scale (nu(B-L) approximately 10(12) GeV) supersymmetric seesaw model based on the gauge group SU(2)L x SU(2)R x SU(4)c where neutron-antineutron oscillation can be in the observable range. This is contrary to the naive dimensional arguments which say that tau(N-N) is proportional to nu(B-L)5 and should therefore be unobservable for seesaw scale nu(B-L) > or = 10(5) GeV. Two reasons for this enhancement are (i) accidental symmetries which keep some of the diquark Higgs masses at the weak scale and (ii) a new supersymmetric contribution from a lower dimensional operator. The net result is that tau(N-N) is proportional to nu(B-L)2 nu(wk)3 rather than nu(B-L)5. The model also can explain the origin of matter via the leptogenesis mechanism and predicts light diquark states which can be produced at LHC.     

Torus Knots and Links from Eikonal Equations and Knot Invariants for Classification of Atoms

The history of knot theory and physics has a deep roots. It started by Lord Kelvin, in 1867, when he conjectured that atoms were knotted vortex tubes of ether. In 1997, Faddeev and Niemi suggested that knots might exist as stable soliton solution in a simple three dimensional classical field theory. That opening up a wide range of possible applications in physics. In this work we consider the Eikonal equation, which is a partial differential equation describing the traveltime propagation, which is an important part of seismic imaging algorithms. We will follow the work of Wereszczynski of solving the Eikonal equation in cylindrical coordinates. We show that only torus knots and links do occur, so figure eight knot does not occur. We show that these solutions are not unique, which means the possible occurrence of the same knot type for different configurations. Using the idea of framed knots, it is shown that two Eikonal knots are equivalent if and only if they are ambient isotopic as a framed knots, i.e. if and only if they are of the same knot type and of the same twisting number.     

Predicting Optimal Lengths of Random Knots

In a thermally fluctuating long linear polymeric chain in a solution, the ends, from time to time, approach each other. At such an instance, the chain can be regarded as closed and thus will form a knot or rather a virtual knot. Several earlier studies of random knotting demonstrated that simpler knots show a higher occurrence for shorter random walks than do more complex knots. However, up to now there have been no rules that could be used to predict the optimal length of a random walk, i.e. the length for which a given knot reaches its highest occurrence. Using numerical simulations, we show here that a power law accurately describes the relation between the optimal lengths of random walks leading to the formation of different knots and the previously characterized lengths of ideal knots of a corresponding type.     

Adhesion-induced DNA naturation

DNA adsorption and naturation is modeled via two interacting flexible homopolymers coupled to a solid surface. DNA denatures if the entropy gain for unbinding the two strands overcomes the loss of binding energy. When adsorbed to a surface, the entropy gain is smaller than in the bulk, leading to a stronger binding and, upon neglecting self-avoidance, absence of a denatured phase. Now consider conditions where the binding potentials are too weak for naturation, and the surface potential too weak to adsorb single strands. In a variational approach it is shown that their combined action may lead to a naturated adsorbed phase. Conditions for the absence of naturation and adsorption are derived too. The phase diagram is constructed qualitatively.     

Crossover from attractive to repulsive Casimir forces and vice versa

Systems described by an O(n) symmetrical varphi;{4} Hamiltonian are considered in a d-dimensional film geometry at their bulk critical points. The critical Casimir forces between the film's boundary planes B_{j}, j=1,2, are investigated as functions of film thickness L for generic symmetry-preserving boundary conditions partial differential_{n}phi=c[over composite function]_{j}phi. The L-dependent part of the reduced excess free energy per cross-sectional area takes the scaling form f_{res} approximately D(c_{1}L;{Phi/nu},c_{2}L;{Phi/nu})/L;{d-1} when d<4, where c_{i} are scaling fields associated with the variables c[over composite function]_{i} and Phi is a surface crossover exponent. Explicit two-loop renormalization group results for the function D(c_{1},c_{2}) at d=4- dimensions are presented. These show that (i) the Casimir force can have either sign, depending on c_{1} and c_{2}, and (ii) for appropriate choices of the enhancements c[over composite function]_{j}, crossovers from attraction to repulsion and vice versa occur as L increases.     

Multiscale entanglement in ring polymers under spherical confinement

The interplay of geometrical and topological entanglement in semiflexible knotted polymer rings confined inside a spherical cavity is investigated by using advanced numerical methods. By using stringent and robust algorithms for locating knots, we characterize how the knot length l(k) depends on the ring contour length L(c) and the radius of the confining sphere R(c). In the no- and strong-confinement cases, we observe weak knot localization and complete knot delocalization, respectively. We show that the complex interplay of l(k), L(c), and R(c) that seamlessly bridges these two limits can be encompassed by a simple scaling argument based on deflection theory. The same argument is used to rationalize the multiscale character of the entanglement that emerges with increasing confinement.     

近红外光谱分析的实木板材节子形态反演

节子影响着实木板材力学性能,如何准确刻画出节子在实木板材内部的形态,进而计算出实木板材力学性能是一个具有应用价值的科学问题。目前,基于机器视觉的缺陷检测方法实现了实木板材表面缺陷检测与识别,超声波检测方法可以判断出实木板材中缺陷的存在,X-ray虽然可以全面的掌握实木信息,但其检测成本较高。近红外光谱分析具有结构丰富,测试方便、无损快速的特点,但是,光谱中存在的冗余与非线性信息影响建模精准度,提出一种基于Isomap和小波神经网络融合的节子倾角辨识方法,利用Isomap完成光谱信息非线性降维,运用小波神经网络建立节子边缘的物质成分与倾角间的非线性关联,通过边缘多点倾角反演出节子在实木板材内部的形态。首先,采用Pablo提出的节子斜圆锥模型,并结合图像处理提取实木板材表面的节子缺陷区域,计算出相应中心位置;提取节子边缘的多点位置,采集光谱信息并完成基线漂移和去噪处理;然后,利用K-S划分校正样本集,运用主成分与马氏距离结合剔除异常光谱;接着,运用Isomap方法设定降维数和邻近数,通过PLS完成不同光谱维度的快速建模,进而迭代出理想光谱特征;最后,应用具有局部信息优化能力的小波神经网络建立节子边缘光谱与该点倾角间的非线性关系,构建出1个12输入、1输出的网络模型,并运用梯度修正网络参数;将节子倾角预测结果输入Solidworks软件完成节子椎体形态的三维呈现。实验采用落叶松实木板材作为对象,选取并采集了40个节子的160组光谱数据,通过测量上、下表面节子的相对空间位置,计算出边缘点倾斜角数值并进行建模分析,实验结果表明：采用S-G平滑与一阶导数进行光谱预处理,得到的光谱轮廓更清晰、吸收峰更明显;采用Isomap特征降维方法,选取非线性降维数d=12、近邻数k=19时,SECV最小,可以消除光谱信息的冗余数据;采用小波神经网络建立的节子倾角非线性模型,其预测相关系数为0.88,预测标准差为7.65,相对分析误差为2.14;可以实现节子在实木板材内部的形态反演,可以为力学性能预测提供定量化分析手段。     

Order of the phase transition in models of DNA thermal denaturation

We examine the behavior of a model which describes the melting of double-stranded DNA chains. The model, with displacement-dependent stiffness constants and a Morse on-site potential, is analyzed numerically; depending on the stiffness parameter, it is shown to have either (i) a second-order transition with nu( perpendicular) = -beta = 1,nu(||) = gamma/2 = 2 (characteristic of short-range attractive part of the Morse potential) or (ii) a first-order transition with finite melting entropy, discontinuous fraction of bound pairs, divergent correlation lengths, and critical exponents nu( perpendicular) = -beta = 1/2,nu(||) = gamma/2 = 1.     

Normal forms of twisted wire knots

This article is a continuation of the study of new types of knot energy undertaken in [1, 2] (but is formally independent of those articles); it describes some experiments with mechanical models of knots (that we call twisted wire knots), contains rigorous definitions of their mathematical counterparts, formulations of a series of problems and conjectures. Different energy functionals for various classes of knot types and the corresponding normal forms are discussed and compared.     

The X-ray emission from the knots in 3C 120

3C 120 is a Seyfert galaxy with a well detected X-ray jet. We investigate the X-ray emission of its five jet knots and fit their spectral energy distributions (SEDs) from the radio to the X-ray bands with a single-zone lepton model. We find that the SEDs of knots k7, s2, and s3 can be explained by synchrotron radiation, and the X-rays are the simple extension of the radio-optical emission component, but that of the inner knot k4 requires the IC/CMB model, in which the X-rays are due to the inverse Compton scattering of the cosmic microwave background photons by relativistic electrons in the jet with a beaming factor δ∼14. The outer knot k25 is resolved into a three-part sub-structure. It is shown that the fitting of the X-rays from this knot with the IC/CMB model needs an extraordinary beaming factor δ∼15–25 for a jet at the kpc scale. If the X-rays of knot k25 are produced by synchrotron radiation similar to k7, s2, and s3, they may be contributed by a relativistic electron population whose radiations in other wavelengths are not detected.

     

Evolving dark energy with w not = -1

Theories of evolving quintessence are constructed that generically lead to deviations from the w = -1 prediction of nonevolving dark energy. The small mass scale that governs evolution, m(phi) approximately = 10(-33) eV, is radiatively stable, and the "Why now?" problem is solved. These results rest on seesaw cosmology: Fundamental physics and cosmology can be broadly understood from only two mass scales, the weak scale nu and the Planck scale M. Requiring a scale of dark energy rho(DE)(1/4) governed by nu2/M and a radiatively stable evolution rate m(phi) given by nu4/M3 leads to a distinctive form for the equation of state w(z). Dark energy resides in the potential of a hidden axion field that is generated by a new QCD-like force that gets strong at the scale lambda approximately = nu2/M approximately = rho(DE)(1/4). The evolution rate is given by a second seesaw that leads to the axion mass m(phi) approximately = lambda2/f, with f approximately = M.     

Critical exponents for random knots

The size of a zero-thickness (no excluded volume) nonphantom polymer ring is shown to scale with chain length N in the same way as the size of the excluded-volume (self-avoiding) linear polymer, that is, as Nnu, where nu approximately 0.588. The consequences of this fact are examined, including the sizes of trivial and nontrivial knots.     

Upper bound on the scale of Majorana-neutrino mass generation

We derive a model-independent upper bound on the scale of Majorana-neutrino mass generation. The upper bound is 4pi (nu2)/square root3 m(nu), where nu approximately 246 GeV is the weak scale and m(nu) is the Majorana-neutrino mass. For neutrino masses implied by neutrino oscillation experiments, all but one of these bounds are less than the Planck scale, and they are all within a few orders of magnitude of the grand-unification scale.     

Knotted configurations with arbitrary Hopf index from the eikonal equation

The complex eikonal equation in (3 + 1) dimensions is investigated. It is shown that this equation generates many multi-knot configurations with an arbitrary value of the Hopf index. In general, these eikonal knots do not have the toroidal symmetry. For example, a solution with the topology of the trefoil knot is found. Moreover, we show that the eikonal knots provide an analytical framework in which qualitative (shape, topology) as well as quantitative (energy) features of the Faddeev-Niemi hopfions can be captured. This might suggest that the eikonal knots can be helpful in the construction of approximated (but analytical) knotted solutions of the Faddeev-Skyrme-Niemi model.Received: 5 April 2005, Revised: 16 May 2005, Published online: 19 July 2005     

Ground-state phase diagram of 2D electrons in a high Landau level: a density-matrix renormalization group study.

The ground-state phase diagram of 2D electrons in a high Landau level (index N = 2) is studied by the density-matrix renormalization group method. Pair correlation functions are systematically calculated for various filling factors from nu = 1/8 to 1/2. It is shown that the ground-state phase diagram consists of three different charge density wave states called stripe phase, bubble phase, and Wigner crystal. The boundary between the stripe and the bubble phases is determined to be nu(s-b)c approximately 0.38, and that for the bubble phase and Wigner crystal is nu(b-W)c approximately 0.24. Each transition is of first order.     

High-Resolution Infrared Spectrum of CD(3)CN: Analysis of the Interacting nu(3) and nu(6) Bands and Evaluation of the A(0) Constant

The infrared spectrum in the range 900-1230 cm(-1) including the fundamental bands nu(3) and nu(6) of CD(3)CN has been studied. The resolution attained was 0.0025 cm(-1) in the measurement on the Bruker 120 HR Fourier spectrometer in Oulu. About 4000 lines were assigned in the nu(6) band. For the weak nu(3) band, which has not been observed earlier directly, we were able to assign 206 lines in three subbands K=8-10. These lines become detectable due to the strong nu(3)/nu(6) Coriolis resonance. There is also an l(1,-2) resonance between nu(3) and nu(6), which made it possible to obtain a value 2.647721(50) cm(-1) for the axial rotational constant A(0), when D(0)(K) from force field calculations was applied. Different types of resonances with the overtone 3nu(8) and the combinations nu(4)+nu(8) and nu(7)+nu(8) were observed. A fit with a standard deviation of 0.0019 cm(-1) was attained by using a model of 10 different resonances. Copyright 2001 Academic Press.     

Scaling laws of single polymer dynamics near attractive surfaces

We present a molecular dynamics study of a generic model for single polymer diffusion on surfaces, which have variable atomic-scale corrugation but no artificial, impenetrable obstacles. The diffusion coefficient D scales as D is proportional to (-3/2) with the degree of polymerization N for strongly adsorbed, linear polymers on solid substrates in good solvents. Weaker scaling, i.e., D is proportional to (-1), is found if (i) the substrate is a fluid, e.g., a membrane, (ii) the polymer is a ring polymer, and (iii) the polymer is commensurate with the substrate. In poor solvents, diffusion on solids slows exponentially fast with N. Reptation is not observed in any of the simulations presented here.     

Zero-bias tunneling anomaly in a clean 2D electron gas caused by smooth density variations

We show that smooth variations, delta n(r), of the local electron concentration in a clean 2D electron gas give rise to a zero-bias anomaly in the tunnel density of states, nu(omega), even in the absence of scatterers, and thus, without the Friedel oscillations. The energy width, omega 0, of the anomaly scales with the magnitude, delta n, and characteristic spatial extent, D, of the fluctuations as (delta n/D)2/3, while the relative magnitude delta nu/nu scales as (delta n/D). With increasing omega, the averaged delta nu oscillates with omega. We demonstrate that the origin of the anomaly is a weak curving of the classical electron trajectories due to the smooth inhomogeneity of the gas. This curving suppresses the corrections to the electron self-energy which come from the virtual processes involving two electron-hole pairs.