Smoothening transition of a two-dimensional pressurized polymer ring

We revisit the problem of a two-dimensional polymer ring subject to an inflating pressure differential. The ring is modeled as a freely jointed closed chain of N monomers. Using a Flory argument, mean-field calculation and Monte Carlo simulations, we show that at a critical pressure, p_c ∼ N^-1, the ring undergoes a second-order phase transition from a crumpled, random-walk state, where its mean area scales as 〈A〉 ∼ N, to a smooth state with 〈A〉 ∼ N². The transition belongs to the mean-field universality class. At the critical point a new state of polymer statistics is found, in which 〈A〉 ∼ N^3/2. For p ≫ p_c we use a transfer-matrix calculation to derive exact expressions for the properties of the smooth state.     

Polymer translocation in a double-force arrangement

Using Langevin dynamics simulations, we investigate the translocation dynamics of an externally driven polymer chain through a nanopore, where a pulling force F is exerted on the first monomer whilst there is an opposing force F _E < F within the pore. Such a double-force arrangement has been proposed recently to allow better dynamical control of the translocation process in order to sequence biopolymers. We find that in the double-force arrangement translocation becomes slower as compared to the case under a single monomer pulling force of magnitude F - F _E , but scaling of the translocation time as a function of the chain length ∼ N ² does not change. The waiting time (m) for monomer m to exit the pore is found to be a monotonically increasing function of the bead number almost until m N , which indicates relatively well-defined slowing down and control of the chain velocity during translocation. We also study the waiting time distributions for the beads in the chain, and characterize in detail fluctuations in the bead positions and their transverse position coordinates during translocation. These data should be useful in estimating position-dependent sequencing errors in double-force experiments.     

Influence of hydrodynamics on the dynamics of a homopolymer

We present an analytical approach of the dynamics of a polymer when it is quenched from a solvent into a good or bad solvent. The dynamics is studied by means of a Langevin equation, first in the absence of hydrodynamic effect, then taking into account the hydrodynamic interactions with the solvent. The variation of the radius of gyration is studied as a function of time. In both cases, for the first stage of collapse or swelling, the evolution is described by a power law with a characteristic time proportional to N ^4/3 (N), where N is the number of monomers, without (with) hydrodynamic interactions. At larger times, scaling laws are derived for the diffusive relaxation time. Received: 10 March 1998 / Received in final form: 15 September 1998 / Accepted: 25 September 1998     

Reacting polymers with highly correlated initial conditions

We propose and theoretically study an experiment designed to measure short-time polymer reaction kinetics in melts or dilute solutions. The photolysis of groups centrally located along chain backbones, one group per chain, creates pairs of spatially highly correlated macroradicals. We calculate time-dependent rate coefficients κ(t) governing their first-order recombination kinetics, which are novel on account of the far-from-equilibrium initial conditions. In dilute solutions (good solvents) reaction kinetics are intrinsically weak, despite the highly reactive radical groups involved. This leads to a generalised mean-field kinetics in which the rate of radical density decay - ∼S(t), where S(t) ∼t ^{- (1 + g/3)} is the equilibrium return probability for 2 reactive groups, given initial contact. Here g≈ 0.27 is the correlation hole exponent for self-avoiding chain ends. For times beyond the longest coil relaxation time τ, - ∼S(t) remains true, but center of gravity coil diffusion takes over with rms displacement of reactive groups x(t) ∼t ^1/2 and S(t) ∼ 1/x ³(t). At the shortest times ( t 10^-6s), recombination is inhibited due to spin selection rules and we find ∼tS(t). In melts, kinetics are intrinsically diffusion-controlled, leading to entirely different rate laws. During the regime limited by spin selection rules, the density of radicals decays linearly, n(0) - n(t) ∼t. At longer times the standard result - ∼d ³(t)/d (for randomly distributed ends) is replaced by ∼d2x ³(t)/d ² for these correlated initial conditions. The long-time behavior, t > τ, has the same scaling form in time as for dilute solutions. Received 18 May 2000     

Swelling of two-dimensional polymer rings by trapped particles

The mean area of a two-dimensional Gaussian ring of N monomers is known to diverge when the ring is subject to a critical pressure differential, p _c ∼ N ^-1. In a recent publication (Eur. Phys. J. E 19, 461 (2006)) we have shown that for an inextensible freely jointed ring this divergence turns into a second-order transition from a crumpled state, where the mean area scales as 〈A〉 ∼ N, to a smooth state with 〈A〉 ∼ N ². In the current work we extend these two models to the case where the swelling of the ring is caused by trapped ideal-gas particles. The Gaussian model is solved exactly, and the freely jointed one is treated using a Flory argument, mean-field theory, and Monte Carlo simulations. For a fixed number Q of trapped particles the criticality disappears in both models through an unusual mechanism, arising from the absence of an area constraint. In the Gaussian case the ring swells to such a mean area, 〈A〉 ∼ NQ, that the pressure exerted by the particles is at p _c for any Q. In the freely jointed model the mean area is such that the particle pressure is always higher than p _c, and 〈A〉 consequently follows a single scaling law, 〈A〉 ∼ N ² f (Q/N), for any Q. By contrast, when the particles are in contact with a reservoir of fixed chemical potential, the criticality is retained. Thus, the two ensembles are manifestly inequivalent in these systems. An erratum to this article is available at .     

Interaction force between incompatible star-polymers in dilute solution

We consider a low-density assembly of spherical colloids, such that each is clothed by L end-grafted chemically incompatible polymer chains either of types A or B. These are assumed to be dissolved in a good common solvent. We assume that colloids are of small size to be considered as star-polymers. Two adjacent star-polymers A and B interact through a force F originating from both excluded-volume effects and chemical mismatch between unlike monomers. Using a method developed by Witten and Pincus (Macromolecules 19, 2509 (1986)) in the context of star-polymers of the same chemical nature, we determine exactly the force F as a function of the center-to-center distance h. We find that this force is the sum of two contributions F _e and F _s. The former, that results from the excluded volume, decays as F _e∼A _L h ^-1, with the L -dependent universal amplitude A _L∼L ^3/2. While the second, which comes from the chemical mismatch, decays more slowly as F _s∼χB _L h ^{-1 - τ}, where τ is a critical exponent whose value is found to be τ 0.40, and χ is the standard Flory interaction parameter. We find that the corresponding L-dependent universal amplitude is B _L∼L ^{3 + τ /2}. Theses forces are comparable near the cores of two adjacent star-polymers, i.e. for h∼h _c∼a (a is the monomer size). Finally, for two star-polymers of the same chemical nature (A or B), the force F that simply results from excluded-volume effects coincides exactly with F _e, and then the known result is recovered. Received 2 October 2000 and Received in final form 24 January 2001     

打结高分子链穿孔行为的研究

以三叶草型结(即3₁结)为例,采用分子动力学(MD)方法,研究打结高分子链在外场力作用下穿越微孔的动力学过程.模拟发现,在拉动打结高分子链的过程中,结的大小呈涨落变化,直至最后散结.定性讨论了结的存在对高分子链穿孔速率的影响.在外场力作用下,打结高分子链平均穿孔时间(τ)与链长(N)满足标度关系τ～N ^α,其中标度系数α随外场力f增大而增大.对于短链,外场力越大,平均穿孔时间越短     

Scaling of Linking and Writhing Numbers for Spherically Confined and Topologically Equilibrated Flexible Polymers

Scaling laws for Gauss linking number Ca and writhing number Wr for spherically confined flexible polymers with thermally fluctuating topology are analyzed. For ideal (phantom) polymers each of N segments of length unity confined to a spherical pore of radius R there are two scaling regimes: for sufficiently weak confinement (R≫N ^1/3) each chain has |Wr|≈N ^1/2, and each pair of chains has average |Ca|≈N/R ^3/2; alternately for sufficiently tight confinement (N ^1/3≫R), |Wr|≈|Ca|≈N/R ^3/2. Adding segment-segment avoidance modifies this result: for n chains with excluded volume interactions |Ca|≈(N/n)^1/2 f(φ) where f is a scaling function that depends approximately linearly on the segment concentration φ=nN/R ³. Scaling results for writhe are used to estimate the maximum writhe of a polymer; this is demonstrated to be realizable through a writhing instability that occurs for a polymer which is able to change knotting topology and which is subject to an applied torque. Finally, scaling results for linking are used to estimate bounds on the entanglement complexity of long chromosomal DNA molecules inside cells, and to show how “lengthwise” chromosome condensation can suppress DNA entanglement.     

Study of opto-mechanical characteristics of interaction of ultrashort laser pulses with polymer materials

The opto-mechanical characteristics, such as the specific mechanical recoil momentum, the specific impulse, and the energy efficiency, of the laser ablation of flat polymer targets ((C₂F₄) _n , (CH₂O) _n ) have been determined experimentally for the first time for the case of excitation with femtosecond pulses (τ ∼ 45–70 fs) of UV-IR (λ ∼ 266, 400, 800 nm) laser radiation (I ₀ up to 10¹⁵ W/cm²) under normal atmospheric and vacuum (p ∼ 10⁻⁴ mbar) conditions. The efficiency of mechanical recoil momentum generation is analyzed for various regimes of the laser irradiation.     

Signature of chaos in power spectrum

We investigate the nature of the numerically computed power spectral densityP(f, N, τ) of a discrete (sampling time interval,τ) and finite (length,N) scalar time series extracted from a continuous time chaotic dynamical system. We highlight howP(f, N, τ) differs from the true power spectrum and from the power spectrum of a general stochastic process. Non-zeroτ leads to aliasing;P(f, N, τ) decays at high frequencies as [πτ/sinπτf]², which is an aliased form of the 1/f ² decay. This power law tail seems to be a characteristic feature of all continuous time dynamical systems, chaotic or otherwise. Also the tail vanishes in the limit ofN → ∞, implying that the true power spectral density must be band width limited. In striking contrast the power spectrum of a stochastic process is dominated by a term independent of the length of the time series at all frequencies.     

Plasma parameters in the upgraded Trimyx-M Galathea

Results are presented from measurements of the plasma parameters in the upgraded Trimyx-M Galathea. After the barrier magnetic field and the energy of the injected hydrogen plasma bunch were increased to B _bar ∼ 0.1 T and W ₀ ≈ 200 J, respectively, the following plasma parameters were achieved: the density n ∼ 5 × 10¹³ cm⁻³, the plasma confinement time τ* = 800–900 μs, the elergy of the confined plasma W ₁ ∼ 100 J, the ratio of the plasma pressure to the barrier magnetic pressure β ₀ ∼ 0.2, the electron temperature T _e ∼ 20 eV, and the ion temperature T _i ∼ 2T _e . The maximum time during which the plasma density decreased e-fold, τ _p , was found to be 300 μs at B _bar = 0.1 T, which agrees with the classical transport model.     

Level statistics inside the core of a superconductive vortex

A microscopic theory of the Efetov supermatrix sigma-model type is constructed for the low-lying electron states in a mixed superconductive-normal system with disorder. This technique is used for the study of the localized states in the core of a vortex in a moderately clean superconductor with τ ⁻¹≫ω ₀∼Δ²/E _F . At low energies ε≪ω _Th∼ (ω ₀/τ)^1/2, the energy level statistics is described by the “zero-dimensional” limit of this supermatrix theory, and the result for the density of states is equivalent to that obtained within Altland-Zirnbauer random matrix model. Nonzero modes of the sigma model increase the mean interlevel distance by the relative amount [2 ln (1/ω ₀ τ)]⁻¹. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 78–83 (10 July 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Giant negative magnetoresistance in a nonmagnetic semiconductor

Studies of a classical III–V semiconductor (InSb) doped with 3d magnetic ions (Mn²⁺, having a localized spin S=55/2) reveal some unexpected transport properties. It is found that the transition from the metallic to the low-temperature insulator phase occurs at an impurity concentration N _Mn∼N _cr=2× 10¹⁷ cm⁻³ and a temperature T<T _cr∼1 K. Under these conditions a giant negative magnetoresistance arises. The experimental results can be explained in terms of the onset of a hard Mott-Hubbard gap Δ in the impurity band formed by the shallow manganese acceptor in InSb at N _Mn∼N _cr. A model describing the gap formation is proposed. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 5, 358–362 (10 March 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

A travelling cluster approximation for lattice fermions strongly coupled to classical degrees of freedom

We suggest and implement a new Monte Carlo strategy for correlated models involving fermions strongly coupled to classical degrees of freedom, with accurate handling of quenched disorder as well. Current methods iteratively diagonalise the full Hamiltonian for a system of N sites with computation time τ_N ∼N⁴. This limits achievable sizes to N ∼100. In our method the energy cost of a Monte Carlo update is computed from the Hamiltonian of a cluster, of size N_c, constructed around the reference site, and embedded in the larger system. As MC steps sweep over the system, the cluster Hamiltonian also moves, being reconstructed at each site where an update is attempted. In this method τ_N,Nc ∼NN_c³. Our results are obviously exact when N_c=N, and converge quickly to this asymptote with increasing N_c, particularly in the presence of disorder. We provide detailed benchmarks on the Holstein model and the double exchange model. The `locality' of the energy cost, as evidenced by our results, suggests that several important but inaccessible problems can now be handled with control. This method forms the basis of our studies in Europhys. Lett. 68, 564 (2004), Phys. Rev. Lett. 94, 136601 (2005), and Phys. Rev. Lett. 96, 016602 (2006).     

Investigation of scaling laws as applied to the gas discharge in the case of a barrier-discharge-excited Kr/CCl<Subscript>4</Subscript> mixture

The electrical and luminescent characteristics of a barrier-discharge lamp filled with a Kr/CCl₄ (150: 1) mixture are experimentally studied versus the value of pd, which varies in the range (7.6–14) × 10³ Pa cm. When simulating the gas discharge using similarity parameters, the following relationships are fulfilled: for pd = const (p is the pressure, d is the interelectrode distance), the pulse duration and the mean current density are τ _j ∼ 1/p and 〈j〉 ∼ p; the surface charge density on the electrodes, σ ∼ const; the duration of the UV radiation pulse and the efficiency of UV radiation due to a KrCl* (222 nm) exciplex, τ_rad ∼ 1/p and η ∼ p ². The maximal radiation efficiency achieved in the experiments is about 13%. Deviations from the similarity laws for the gas discharge are related to the filamentary form of the observed discharge. Qualitative analysis indicates that similarity laws may be fulfilled for such a form of discharge as well but locally, within a single filament.     

Perturbative and non-perturbative Kolmogorov turbulence in a gluon plasma

In numerical simulations of nonabelian plasma instabilities in the hard-loop approximation, a turbulent spectrum has been observed that is characterized by a phase-space density of particles n(p)∼p ^−ν with exponent ν≃2, which is larger than expected from relativistic 2↔2 scatterings. Using the approach of Zakharov, L’vov and Falkovich, we analyze possible Kolmogorov coefficients for relativistic (m≥4)-particle processes, which give at most ν=5/3 perturbatively for an energy cascade. We discuss non-perturbative scenarios which lead to larger values. As an extreme limit we find the result ν=5 generically in an inherently non-perturbative effective field theory situation, which coincides with results obtained by Berges et al. in large-N scalar field theory. If we instead assume that scaling behavior is determined by Schwinger–Dyson resummations such that the different scaling of bare and dressed vertices matters, we find that intermediate values are possible. We present one simple scenario, which would single out ν=2.     

Scalar field dynamics on a brane

The dynamics of a flat isotropic brane Universe with two-component matter source —perfect fluid with the equation of statep = (γ − 1)ρ and a scalar field with a power-law potentialV ∼ φ^α is investigated. We describe solutions for which the scalar field energy density scales as a power-law of the scale factor. We also describe solutions existing in regions of the parameter space where these scaling solutions are unstable or do not exist.     

Single flexible and semiflexible polymers at high shear: Non-monotonic and non-universal stretching response

Using Brownian hydrodynamic simulation techniques, we study single polymers in shear. We investigate the effects of hydrodynamic interactions, excluded volume, chain extensibility, chain length and semiflexibility. The well-known stretching behavior with increasing shear rate [(g)\dot] \dot{{\gamma}} is only observed for low shear [(g)\dot] \dot{{\gamma}} < [(g)\dot]^max \dot{{\gamma}}^{{\max}}_{} , where [(g)\dot]^max \dot{{\gamma}}^{{\max}}_{} is the shear rate at maximum polymer extension. For intermediate shear rates [(g)\dot]^max \dot{{\gamma}}^{{\max}}_{} < [(g)\dot] \dot{{\gamma}} < [(g)\dot]^min \dot{{\gamma}}^{{\min}}_{} the radius of gyration decreases with increasing shear with minimum chain extension at [(g)\dot]^min \dot{{\gamma}}^{{\min}}_{} . For even higher shear [(g)\dot]^min \dot{{\gamma}}^{{\min}}_{} < [(g)\dot] \dot{{\gamma}} the chain exhibits again shear stretching. This non-monotonic stretching behavior is obtained in the presence of excluded-volume and hydrodynamic interactions for sufficiently long and inextensible flexible polymers, while it is completely absent for Gaussian extensible chains. We establish the heuristic scaling laws [(g)\dot]^max \dot{{\gamma}}^{{\max}}_{} ∼ N ^-1.4 and [(g)\dot]^min \dot{{\gamma}}^{{\min}}_{} ∼ N ^0.7 as a function of chain length N , which implies that the regime of shear-induced chain compression widens with increasing chain length. These scaling laws also imply that the chain response at high shear rates is not a universal function of the Weissenberg number Wi = [(g)\dot] \dot{{\gamma}} t \tau anymore, where t \tau is the equilibrium relaxation time. For semiflexible polymers a similar non-monotonic stretching response is obtained. By extrapolating the simulation results to lengths corresponding to experimentally studied DNA molecules, we find that the shear rate [(g)\dot]^max \dot{{\gamma}}^{{\max}}_{} to reach the compression regime is experimentally realizable.     

The Precise Measurement of the μ+ Lifetime

The lifetime of the positive muon (τ_μ ⁺) can be directly associated with the Fermi Coupling Constant (G _F ), which is one of the most basic parameters of the Standard Model. However, the current experimental accuracy of the τ_μ ⁺ is ∼30 ppm and it has not been improved for more than 15 years. We propose a new experiment for a pulsed muon facility such as RIKEN-RAL to measure the muon lifetime with multi-decay per one time window method. The advantage of our setup, no time window limitation, enables us to test the exponential decay law (EDL) in the long decay time region at the same time. The preliminary analysis set a new upperlimit for the EDL deviation in the muon decay. We accumulated ∼10¹⁰ muon decays and analysis is in progress. This revised version was published online in August 2006 with corrections to the Cover Date.     

Scaling of the energy of ion beams in the low-altitude plasma sheet boundary layer

The scaling of the energy of ion beams (beamlets) in resonance regions of the low-altitude plasma sheet boundary layer has been analyzed using the measurements made on the Interball-2 and Cluster satellites at distances of 3.0 to 6.0 Earth’s radii and numerical simulations of the acceleration of ions in the current sheet of the Earth’s magnetotail. The experimental test of the previously theoretically predicted scaling W _N ∼ N ^A (where W _N is the energy at the Nth resonance and A ∼ 1.33) shows that the real scaling of resonance energies varies in a wide range A ∈ [0.61, 1.75] and is independent of the geomagnetic indices K _p and AE. Model calculations with allowance for an electric field E _z perpendicular to the current sheet are in good agreement with the experimental data. They indicate that the scaling increases in the case of the dominance of the ion current and decreases in the case of the dominance of the electron current (A > 1.33 and A < 1.33, respectively).