Flexible-to-semiflexible chain crossover on the pressure-area isotherm of a lipid bilayer

We find theoretically that competition between ∼K _f q ⁴ and ∼Qq ² terms in the Fourier-transformed conformational energy of a single-lipid chain, in combination with interchain entropic repulsion in the hydrophobic part of the lipid (bi)layer, may cause a crossover on the bilayer pressure-area isotherm P(A)∼(A−A ₀)^−α. The crossover manifests itself in the transition from α = 5/3 to α = 3. Our microscopic model represents a single-lipid molecule as a worm-like chain with a finite irreducible cross-section area A ₀, a flexural rigidity K _f , and a stretching modulus Q in a parabolic potential with the self-consistent curvature B(A) formed by entropic interactions between hydrocarbon chains in the lipid layer. The crossover area A* obeys the relation Q/√K _f B(A*) ≈ 2. We predict a peculiar possibility of deducing the effective elastic moduli K _f and Q of an individual hydrocarbon chain from the analysis of the isotherm with such a crossover. Also calculated is the crossover-related behavior of the area compressibility modulus K _A , the equilibrium area per lipid A _t , and the chain order parameter S(θ). The text was submitted by the authors in English.     

多量子位Heisenberg XX链中的杂质纠缠

通过分析系统的杂质位与其余部分间的纠缠N1-A以及单个正常位与其余部分间的纠缠NL-A研究了匀强磁场作用下含杂质Heisenberg XX链的纠缠特性.研究表明三量子位时纠缠存在的临界温度依赖于杂质参数J1和匀强磁场B.研究发现,当量子位L为奇数时,纠缠N1-A随量子位的增加而增大,而L为偶数时则相反,并且量子位L为偶数时的纠缠大于量子位L为奇数时的纠缠;对NL-A,量子位L为奇数时,纠缠随杂质参数J1的变化与L=3类似,而L为偶数时纠缠随杂质参数|J1|的增加而增加.     

多量子位Heisenberg XX链中的杂质纠缠

通过分析系统的杂质位与其余部分间的纠缠N_1-A以及单个正常位与其余部分间的纠缠N_L-A研究了匀强磁场作用下含杂质Heisenberg XX链的纠缠特性.研究表明三量子位时纠缠存在的临界温度依赖于杂质参数J₁和匀强磁场B.研究发现,当量子位L为奇数时,纠缠N_1-A随量子位的增加而增大,而L为偶数时则相反,并且量子位L为偶数时的纠缠大于量子位L为奇数时的纠缠;对N_L-A, 量子位L为奇数时,纠缠随杂质参数J₁的变化与L=3类似,而L为偶数时纠缠随杂质参数|J₁|的增加而增加.     

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 .     

Sum-of-Squares Results for Polynomials Related to the Bessis–Moussa–Villani Conjecture

We show that the polynomial S _m,k (A,B), that is the sum of all words in noncommuting variables A and B having length m and exactly k letters equal to B, is not equal to a sum of commutators and Hermitian squares in the algebra R〈X,Y〉, where X ²=A and Y ²=B, for all even values of m and k with 6≤k≤m−10, and also for (m,k)=(12,6). This leaves only the case (m,k)=(16,8) open. This topic is of interest in connection with the Lieb–Seiringer formulation of the Bessis–Moussa–Villani conjecture, which asks whether Tr (S _m,k (A,B))≥0 holds for all positive semidefinite matrices A and B. These results eliminate the possibility of using “descent + sum-of-squares” to prove the BMV conjecture.     

Comment: “On the computation of molecular auxiliary functions<Emphasis Type="Italic">A</Emphasis><Subscript>n</Subscript>and<Emphasis Type="Italic">B</Emphasis><Subscript>n</Subscript>”

Guseinov, Mamedov, Kara and Orbay (Pramana - J. Phys. 56, 691 (2001)) propose methods for evaluating the molecular auxiliary functionsA _n(p) andB _n(pt) for the range 17 ≤n ≤ 60 and 25 ≤pt ≤ 60. However, their procedure forA _n(p) is not new, and that forB _n(pt) is less efficient for their target range than another well-known method. Their approach does have merit for smaller non-zero values ofpt. Two minor errors in table 1 of their paper are also identified.     

Magnetic flux distribution in the bulk of the pure type-II superconductor niobium measured with positive muons

The spin precession of positive muons in ultra-pure Nb single crystals of high perfection, cooled down in transverse magnetic fields 0.68B _c2≤B _appl≤0.84B _c2 (B _c2=upper critical field) from temperatures well above the superconducting transition temperatureT _c=9.25 K, has been investigated in the temperature range 2.6 K≤T≤8.0 K. The experiments confirm the periodic fieldB(r) of triangular flux-line lattices as calculated from numerical solutions of the microscopic BCS-Gor'kov theory. The observed broadening of the van Hove singularities in the field distribution is discussed in terms of the combined effects of muon diffusion and random perturbations of the flux-line lattice.     

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.     

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     

Integrability ofSU(N) spin chains with elliptic exchange

For some one-parameter setH _N of linear combinations ofN(N−1)/2 elementary transpositions {P _jk} (1≤j<k≤N) at arbitrary naturalN≥3 one can construct a variety {I _m} (3≤m≤N) of operators which commute withH _N. Being applied toSU(n) spin representations of the permutation group, this proves the integrability of 1D periodic spin chains with elliptic short-range interaction. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

On the computation of molecular auxiliary functions A n and B n

Molecular auxiliary functions A _n (p) and B _n (pt), arising in the Hartree-Fock-Roothaan (HFR) approximation for molecules, Ewald’s crystal lattice theory, electromagnetic stopping theory, and other approximate methods, are evaluated and analysed in the range of 17≤n≤60 and 25≤pt≤60.     

Drift of a polymer chain in a porous medium --A Monte Carlo study

We investigate the drift of an end-labeled telehelic polymer chain in a frozen disordered medium under the action of a constant force applied to the one end of the macromolecule by means of an off-lattice bead spring Monte Carlo model. The length of the polymers N is varied in the range 8 < N < 128, and the obstacle concentration in the medium C is varied from zero up to the percolation threshold C≈ 0.75. For field intensities below a C-dependent critical field strength B _c, where jamming effects become dominant, we find that the conformational properties of the drifting chains can be interpreted as described by a scaling theory based on Pincus blobs. The variation of drag velocity with C in this interval of field intensities is qualitatively described by the law of Mackie-Meares. The threshold field intensity B _c itself is found to decrease linearly with C. Received 20 August 2001 and Received in final form 19 November 2001     

Influence of magnetic field on the superconducting transition in a Nd1.82Ce0.18CuO4−δ film

The temperature and magnetic-field dependences of the resistivity ρ and Hall effect R(j‖ab, B‖c) in a Nd_1.82Ce_0.18CuO_4−δ single crystal film (T _c =6 K) is investigated at temperatures 1.4≤T≤20 K and magnetic fields 0≤B≤5.5 T. At the lowest temperature T=1.4 K the resistive state (exhibiting resistivity and the Hall effect) arises in a magnetic field B=0.5 T. A transition to the normal state is completed at B _c 2≃3 T, where the Hall coefficient becomes nearly constant. The negative magnetoresistance due to the weak-localization effect in the normal state is observed for B>3 T. The nonmonotonic behavior and the inversion of the sign of R(B) in the mixed state are explained in a reasonable way by the flux-flow model with the effect of pinning taken into account. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 6, 407–411 (25 September 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

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).     

Muon spin relaxation study on magnetism in high quality single crystal of a high transition temperature superconductor La2−xSrxCuO4−σ (0.11≤x≤0.14)

The positive muon spin relaxation method is applied to probe magnetic ordering in the superconducting phase of a high quality single crystal of La_2−xSr_xCuO_4−σ (0.11≤x≤0.14). The well characterized crystal ofx=0.11 (T _c=34.5 K) with nearly complete flux exclusion exhibits spin freezing at 8K(T _f) with significant spin fluctuation up to 20 K. The onset of spin fluctuation andT _f decrease against increasingx towardsx=0.15, suggesting an existence of a magnetic phase boundary aroundx whereT _c becomes maximum.     

Effect of the Dzyaloshinskii-Moriya interaction on heat conductivity in one-dimensional quantum Ising chains

The effect of the Dzyaloshinskii-Moriya (DM) interaction on the heat conduction in the quantum Ising chain has been studied by solving the Lindblad master equation. The chain is subject to a uniform transverse field h, while the exchange couplings {J _m } between the nearest-neighbor spins are either uniform, random or quasi-periodic. The average energy-density profile and the average energy current in the non-equilibrium steady state have been numerically calculated. The ballistic transport is observed in the uniform Ising chain with DM interaction. For the random Ising chain with DM interaction, the energy gradient is observed in the bulk of the spin chain whose energy current appears to scale as the system size ⟨Q⟩ ∼ exp(βN) with β < 0. For the quasi-periodic Ising chain with DM interaction, the J _m takes the two values J _A and J _B arranged in the Fibonacci sequence. The energy gradient also exists in the spin chain and the energy current behaves as ⟨Q⟩ ∼ N ^α with α < 0. By increasing the strength of the DM interaction D, a non-trivial transition from the thermal insulator heat transport to anomalous heat conduction is found in the Fibonacci Ising chain with large ratio of couplings λ = J _A /J _B . A rough phase diagram of λ vs. D is given in this paper as well.     

Single-particle levels of nuclei in the vicinity of the doubly magic nuclei 2048 Ca28 and 2856 Ni28

Isotonic and isotopic dependences of single-particle energies of neutron and proton states in 20 ≤ Z ≤ 28 and 24 ≤ N ≤ 32 nuclei are investigated, these energies being determined by matching data on nucleon-stripping and nucleon-pickup reactions on the same nucleus. Regularities of the formation of the spectra of single-particle levels in Z, N = 20, 28 magic nuclei are demonstrated. A distinctive feature is found in the isotonic dependence of the energy of the 1 f _5/2 neutron level, this feature being consistent with the assumption that j _>-j _< interaction is operative in nuclei. The single-particle energies calculated by using the potential of the dispersive optical model are found to be consistent with experimental data within their errors. Original Russian Text ? O.V. Bespalova, I.N. Boboshin, V.V. Varlamov, T.A. Ermakova, B.S. Ishkhanov, E.A. Romanovsky, T.I. Spasskaya, T.P. Timokhina, 2008, published in Yadernaya Fizika, 2008, Vol. 71, No. 1, pp. 37–49.     

Extensions of Lieb’s Concavity Theorem

The operator function (A,B)→ Trf(A,B)(K ^*)K, defined in pairs of bounded self-adjoint operators in the domain of a function f of two real variables, is convex for every Hilbert Schmidt operator K, if and only if f is operator convex. We obtain, as a special case, a new proof of Lieb’s concavity theorem for the function (A,B)→ TrA ^p K ^* B ^q K, where p and q are non-negative numbers with sum p+q ≤ 1. In addition, we prove concavity of the operator function

Calculation of spectroscopic constants and radiative parameters for A1Σ u+ -X1Σ g+ and B1Πu-X1Σ g+ electronic transitions of sodium dimer

Vibrational, rotational, and centrifugal spectroscopic constants and radiative parameters, i.e., the Einstein coefficients, oscillator strengths, and wave numbers for vibrational transitions in electronic systems of bands A ¹Σ _u ⁺-X ¹Σ _g ⁺ (0 ≤ v′ ≤ 25; 0 ≤ v″ ≤ 44), B ¹Π _u -X ¹Σ _g ⁺ (0 ≤ v′ ≤ 29; 0 ≤ v″ ≤ 47), and the radiative lifetimes for the vibrational levels of excited states of the sodium dimer, are calculated. The calculations are carried out based on semiempirical potential curves constructed in this study. The calculated spectroscopic constants and radiative lifetimes are compared to the experimental values.